EPA-600/2-77-131
July 1977
Environmental Protection Technology Series
SIGNIFICANCE OF SIZE REDUCTION
IN SOLID WASTE MANAGEMENT
Municipal Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-77-131
July 1977
SIGNIFICANCE OF SIZE REDUCTION
IN SOLID WASTE MANAGEMENT
by
George J. Trezek
The Regents of the University of California
Berkeley, California 94720
Grant No. R804034
Project Officer
Carlton C. Wiles
Solid and Hazardous Waste Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
-------
DISCLAIMER
This report has been reviewed by the Municipal Environmental
Research laboratory, U.S. Environmental Protection Agency, and
approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the U.S.
Environmental Protection Agency, nor does mention of trade names
or commercial products constitute endorsement or recommendation
for use.
11
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FOREWORD
The Environmental Protection Agency was created because of
increasing public and government concern about the dangers of
pollution to the health and welfare of the American people.
Noxious air, foul water, and spoiled land are tragic testimony to
the deterioration of our natural environment. The complexity of
that environment and the interplay among its components require
a concentrated and integrated attack on the problem.
Research and development is that necessary first step in
problem solution, and it involves defining the problem, measuring
its impact, and searching for solutions. The Municipal Environ-
mental Research Laboratory develops new and improved technology
and systems for the prevention, treatment, and management of
wastewater and solid and hazardous waste pollutant discharges
from municipal and community sources, for the preservation and
treatment of public drinking water supplies, and for minimizing
the adverse economic, social, health, and aesthetic effects of
pollution. This publication is one of the products of that
research and is a most vital communications link between the
researcher and the user community.
This report presents information resulting from research
conducted on the size reduction of municipal solid waste. Shred-
ding is an important processing step in preparing solid waste
for additional processing, including resource recovery. It is
hoped that the information provided in this report will help to
clarify this important size reduction step and improve overall
solid waste processing systems.
Francis T. Mayo
Director
Municipal Environmental
Research Laboratory
111
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PREFACE
The preparation of municipal solid waste (MSW) for the
purpose of recovering material and energy resources usually requires
primary and often secondary size reduction. Size reduction can
be considered a preprocessing step used to prepare the solid
waste for many subsequent processing operations ranging from
volume reduction before landfilling to fine grinding for pyrolysis
to recover oils, gas, char, etc.
As important as MSW shredding has been and continues to be,
insufficient data and theory are available to fully understand
it. Initially, many assumed that any crusher, grinder, or machine
that could size-reduce stone effectively could surely size-
reduce MSW. This assumption proved false in most cases. MSW is
heterogeneous and contains only about 25% brittle materials.
Since the standard stone crusher, grinders, hammermills and
similar equipment are designed basically for brittle materials
that tend to shatter on impact, their adaptability to a more
nonbrittle, heterogeneous material such as MSW proved unsatis-
factory. Operating, maintenance, and other costs associated with
grinding MSW have therefore been relatively high.
As it became more evident that shredding was to be an
important unit operation in solid waste management, the U.S.
Environmental Protection Agency (EPA) started some early studies
at Johnson City, Tennessee, and New York City to attempt field
measurements for evaluating and characterizing the hammermills
available at these sites. Most of the currently available data
on shredders relate to these projects and others at Madison,
Wisconsin, Gainesville, Florida, and St. Louis, Missouri.
In addition to these projects, EPA decided that a more basic
approach would be helpful to better define MSW size reduction.
The Solid and Hazardous Waste Research Division therefore imple-
mented research aimed at studying and developing data and basic
relationships involved in size-reducing MSW. The objectives
included accumulation of data for improving the design and opera-
tion of MSW size-reduction equipment.
The work was done under controlled laboratory conditions,
since field conditions are not conducive to isolation of inde-
pendent variables. In general, findings have characterized the
iv
-------
relationships between refuse size distribution, particle size,
grinding speed, moisture content, energy consumption, and feed-
rate. Scientific publications arising from this research have
made significant contributions to the available knowledge about
solid waste size reduction.
The research was conducted by Professor George J. Trezek
and his staff at the solid waste laboratory, Richmond Field
Station, University of California, Berkeley. This report
presents the bulk of the findings to date. The theoretical
relationships presented have been developed from actual laboratory
measurements. Therefore, though the report provides supporting
information of wide interest, it is also valuable to researchers,
design engineers, and other personnel involved in the design and
operation of selected shredders for MSW processing.
The next logical step in the research and development cycle
would be to match the theoretical relationships developed here
under controlled laboratory conditions with large-scale equipment
in actual operating plants.
Carlton C. Wiles
Project Officer
Solid and Hazardous Waste
Research Division
Municipal Environmental Research
Laboratory
v
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ABSTRACT
This report presents information resulting from investiga-
tions conducted on the size reduction of municipal solid waste.
The research was conducted by Professor George Trezek under
controlled laboratory conditions. The results discussed here
characterize relationships between refuse, size distribution,
particle size, grinding speed, moisture content, energy
consumption and feed rates. Information is presented to provide
some basic considerations for refuse shredder design.
This report was submitted in fulfillment of Grant No. R804034
by The Regents of the University of California under sponsor-
ship of the U.S. Environmental Protection Agency. This report
covers the period May 15, 1971 to June 29, 1976, and work was
completed as of December 1976.
vx
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CONTENTS
Foreword iii
Preface iv
Abstract vi
Figures viii
Tables xiii
Metric Conversion Table xiv
1. Introduction 1
2. Size Distribution 34
3. Behavior of the Comminution Parameters 73
4. Wear, Maintenance, and Shredder Selection
Aspects of Refuse Comminution 89
5. Analytical Aspects of Comminution Ill
References 130
Appendices 137
A. Mill Matrix Circuit Analysis 137
B. Some Size Distribution Relations Prepared by
D.M. Obeng 142
Vll
-------
FIGURES
Number Pa?e
1 Stress-strain characteristics of some refuse
components 8
Energy required for volume reduction of common
3
4
5
6
7
8
9
10
11
Energy requirements for steady compression rate
Compressibility of modified raw solid waste • • •
Compressibility of solid waste after primary
Compressibility of solid waste after secondary
Compressibility of solid waste passed through a
rasp
Overall view of the V—belt ...........
Input conveyor and grinder (size reduction unit) .
Basic dry plant
Grinder discharge into air classifier and heavies
recovery
11
15
16
17
18
23
26
27
28
12 Light fraction processing facility - air
classifier, light fraction discharge, and
13 Components of the light fraction processin
15 Svstem flow diacrram
g
. . . . 30
. . . . 31
• • . . 32
Vlll
-------
Number Page
16 Anerobic digestion 33
17 Cumulative weight (% raw refuse total) of objects
with longest dimension greater than given
lengths 37
18 Cumulative weight (% raw refuse total) of objects
that will pass through a square mesh, plotted
vs. mesh size 37
19 Number of objects per ton of raw refuse vs.
length (longest dimension of object) for
principal categories of refuse 38
20 Total weight per ton of raw refuse of objects in
given length ranges for principal categories of
refuse 39
21 Cumulative distributions of raw waste 40
22 Moisture content analysis. Percent moisture
loss vs. drying time 46
23 Product size distribution for the primary
grinding of municipal refuse with 22.0%
moisture content 48
24 Product size distribution for the primary
grinding of municipal refuse with 40.4%
moisture content 49
25 Product size distribution for the primary
grinding of municipal refuse with 55.3%
moisture content 50
26 Product size distribution for the secondary
grinding of municipal refuse with 21.0%
moisture content 51
27 Product size distribution for the secondary
grinding of municipal refuse with 19.6%
moisture content 52
28 Product size distribution for the tertiary
grinding of municipal refuse with 19.2%
moisture content 53
IX
-------
Number Page
29 Plot of £n 1 vs. sieve size for primary,
:FY
secondary, and tertiary grinding of municipal
refuse 54
30 Typical particle size distributions for milled
refuse from both mills in 1972 56
31 Cumulative distributions of primary waste 58
32 Cumulative distributions of secondary waste .... 59
33 Cumulative distributions of rasped waste 60
34 Component size distribution of shredded municipal
solid waste - 1,814 kg/hr (2 tons/hr), 1,200 rpm
swing hammermill 62
35 Component size distribution of air-classified
heavy fraction 64
36 Component size distribution of air-classified
light fraction 65
37 Composition of air-classified shredded solid
waste - 70%/30% split 67
38 Component size distribution of oversize from
9.5 x 10~3 m (3/8 in.) Trommel screen 69
39 Component size distribution of undersize from
9.5 x 10~3 m (3/8 in.) Trommel screen 70
40 Composition of screen air-classified light
fraction 72
41 Size distribution comparison for raw municipal
refuse and residential refuse shredded at 1,200,
790, and 555 rpm. Effect of moisture content
(MC), and secondary and tertiary grinding .... 74
42 Effect of moisture content (MC) on particle size
distribution 77
43 Effect of grate size on particle size distribution
at Madison 77
44 Characteristic particle size vs. grate spacing . . 78
x
-------
Number Page
45 Effect of hammer wear on particle size
distribution - Tollemache Mill 79
46 Changes in Particle Size Distribution as a
result of cumulative hammer wear 79
47 Specific energy consumption to achieve a given
characteristic particle size 80
48 Specific energy consumption at different grinder
rpm (dry weight basis) 82
49 Influence of grinder rotor speed on energy
consumption vs. size distribution of residential
refuse 83
50 Effect of moisture content on specific energy
consumption for grinder rotor speeds of 1,200
and 790 rpm 84
51 Comparison of Characteristic Particle Size (Xo)
and specific energy for commercial and
residential solid waste 86
52 Size distribution of refuse from various shredders. 87
53 Characteristic particle size vs. specific energy
consumption 88
54 Manganese steel hammer with hard facing weld
material applied about the crushing face .... 90
55 Hammer configuration 91
56 Non-hard-faced hammers after grinding 70 tons
of refuse at 1,200 rpm 94
57 Summary of worn hammer profiles . 95
58 Effect of grinder speed on hammer wear 96
59 Horsepower required for size reduction of MSW
as a function of feedrate and desired product
size . .107
60 Grate spacing required to produce a desired
product size 110
XI
-------
Number Page
61 Comparison between computed and experimental
product size distributions for primary,
secondary, and tertiary grinding using the
ir-breakage process model 126
62 Comparison between computed and experimental
product size distributions for primary
grinding using the ir, K-breakage process model . .127
63 Comparison, between computed and experimental
product size distributions for primary grinding
using the repeated breakage cycle model 129
A-l Hammermill analysis 138
Xll
-------
TABLES
Number Page
1 Composition of Municipal Solid Waste, as
Discarded, United States, 1973 4
2 Average Composition for Residential, Commercial,
and Industrial Solid Waste for Some San
Francisco Bay Area Counties 5
3 Stress vs. Strain Data.
4 Municipal-Scale Shredding Operations by State or
Country and Date of First Installation 21
5 Bulk Composition (Weight Percent) of Refuse
Samples 35
6 Analysis of Experimental Error: Feedrate
(Ton/hr) 44
7 Composition of Madison's Solid Waste
(November 1968) 55
8 Summary of Refuse Composition at Gainesville,
Florida 57
9 Composition of Air-Classified, Shredded Solid
Waste, 70/30 Split 68
10 Composition of Screened, Air-Classified Light
Fraction 71
11 Hammer Wear 92
12 Grate Bar Wear 93
13 Average Wear for Hammers and Grate Bars at
Different Grinder Operating Speeds 99
14 Suitability of Hard Facing Coating for Various
Base Materials 102
15 Breakage Function Elements of the First
Column b-Q 124
xiii
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METRIC CONVERSION TABLE
English system
Metric system
Inch
Foot
Yard
Square
Square
Square
inch
foot
yard
2.54 cm
30.48 cm
0.914 m
6.452 cm2
0.092 m2
0.836 m2
Cubic inch
Cubic foot
(1,728 in3)
Cubic yard
(27 ft3)
OF
Pound
avdp. (16 dr)
troy (12 oz)
Ton
long (2,240 Ib)
short (2,000 Ib)
16.387 cm3
0.028 m3
0.7646 m3
-17°C
453.592 g
373.24 g
1.016 t
0.907 t
xiv
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SECTION 1
INTRODUCTION
The range of applications of size reduction (comminution)
in solid waste management is becoming progressively broader.
The history of shredding, along with a summary of reasons cited
for shredding, has been reviewed recently by Ham (1). In the
1950's, European countries such as England and France initiated
the practice of shredding wastes as a preparative step for land-
fill disposal. Although there was some concern for salvage,
(i.e., resource recovery), the predominant early use of shredding
in solid waste management was for landfilling. Eventually,
shredding procedures began to be used in the United States.
One of the earliest uses was as an initial step in composting.
Later, in light of the European experience, the possibilities of
improving the overall quality of landfills and increasing land-
fill life through increased compaction and elimination of a daily
cover motivated the establishment of the Madison Wisconsin demon-
stration project by the U.S. Environmental Protection Agency (EPA)
(formerly the Public Health Service) in 1966. In general, the
Madison experience affirmatively demonstrated that a shredded
solid waste landfill could omit a daily cover without causing the
rodent, insect, odor, fire, blowing debris, and aesthetic problems
that are commonly considered as indicators of the quality of land-
filling operations (2).
The physical characteristics of refuse are changed after it
undergoes a comminution process. For example, the basic refuse
odor may be replaced by a more earthy smell. For the most part,
the shredded material becomes unattractive to such scavengers as
sea gulls, flies, and rodents. The characteristic particle size
is reduced by at least one order of magnitude over that of raw
refuse. Size distributions of shredded refuse typically span
three to four orders of magnitude. This evidence contradicts
the visual claims that state that after refuse is shredded, the
size of the product tends to be uniform. Actually, from the
resource recovery point of view, it is fortunate that uniformity
in size does not occur; as will be discussed, certain materials
tend to fall into various size range bands, and as such, they
can be separated.
The number of waste processing shredding installations in
-------
our country has steadily grown during the past decade. It has
been estimated that there are currently some 70 to 100 waste
processing shredding installations in operation. The activities
conducted at these facilities cover a wide variety of applications
dealing with landfilling, reducing bulky wastes, industrial
processing, and various material and energy recovery projects.
Because of recent energy and certain material shortages, the use
of shredding in solid waste management over the last few years
has shifted toward recovery operations. It is important to note
that although the number of waste processing facilities using
shredders has increased, the paucity of data regarding both equip-
ment and facilities design as well as data describing the refuse
size reduction process in terms of the quantitative behavior of
comminution parameters is only recently being alleviated.
Front end systems, the majority of which employ shredding
as the first processing step, are common to most modern material
and energy resource recovery processing operations. The modular
concept in resource recovery provides for the fact that there is
a hierarchy of material values in the waste stream so that the
entire stream need not be committed to one type of process. In
effect, known technology can be implemented on a scale compatible
with existing markets for materials and energy. The spectrum
covers options ranging from simple shredding followed by ferrous
materials separation, advanced forms of fiber recovery involving
shredding and front end processing followed by wet pulping size
reduction, and processes for creating refuse-derived fuels that
may require secondary shredding.
Ability to control the shredding process is important for
the successful operation of subsequent processing stages in
resource recovery operations. When the waste stream is to be
used for energy, the increased surface area of size-reduced refuse
can also serve as an aid in various combustion processes by cre-
ating more sites for rapid oxidation. Even though refuse is a
heterogeneous mixture, size reduction tends to homogenize the
mixture so that a combustion process is presented with a fuel of
relatively constant heating value. Various trade-offs between
coarse and fine size distributions must be considered in terms of
producing a fuel with good combustion characteristics and yet not
creating an energy-intensive fuel preparation process such as
might be the case if fine grinding were required as a secondary
size reduction stage. Densified, pellet-type, refuse-derived
fuels usually require primary and secondary size reduction as
part of their preparation.
In general, with the exception of explosives and materials
yielding potential shock loads, the shredding of industrial,
commercial, and residential solid wastes is now accomplished in a
relatively reliable and controlled manner. Refuse is a difficult
material to size reduce and offers considerable wear and strain
-------
on the comminution machinery that still operates under the
premise of brute force. Nonetheless, refuse comminution is an
emerging technology that will reach higher levels of sophistica-
tion as increased operating and design data are generated and
advanced predictive methods are developed.
NATURE OF THE WASTE STREAM
The refuse waste stream is a heterogeneous material whose
characteristics and properties can have geographical and seasonal
variations. Estimates for the rate of municipal refuse generation
reported in the literature vary according to the time of their
publication; those published before the early 1970's tend to be
higher than those made from about 1972 and thereafter (3) . The
latter are more realistic because they are based to a considerable
degree on measured rather than estimated outputs. Estimates based
on measured outputs are about 3 Ib/capita-day, whereas those
geared to estimates are about 5.16 Ib/capita-day.
Typical types of materials normally found in municipal solid
waste (MSW) are such forms of cellulose or fiber as newsprint,
cardboard, mixed paper waste (including high grade stationery),
computer printout, tissue, printing rejects, general office wastes,
and food packaging containers such as milk cartons, cereal boxes,
prepared food containers, etc.; plastics; ferrous, aluminum and
other metals; glass, ceramics, stone, etc.; organic components
such as putrescible grass and tree cuttings, etc.; and a range of
miscellaneous objects encompassing occasional tires, leather and
rubber goods, wood wastes, and the like. Different percentages
of each category have been reported as being representative of the
waste stream. As indicated by the nature of the waste stream,
there exists a hierarchy of material values in the total array
of objects. When the waste stream is to be processed for material
and/or energy recovery, the processing steps will involve some
phase of comminution that should be controlled according to the
precise waste stream content and processing purpose.
EPA has published a type of national average waste stream
composition (4) shown in Table 1.
The waste stream characterization for San Francisco Bay
Area Region yields an analysis that differs significantly from
the EPA's analysis in certain categories. The average composition
for residential, commercial, and industrial solid waste for four
large Bay Area counties (Table 2) indicates that the fiber content
of the waste stream is on the order of 40% to 50%. In general,
these data compare favorably with the composition data presented
by National Center for Resource Recovery (NCRR) as a national
average for various materials derived from municipal solid wastes
(5). Fiber predominates as the major constituent of the waste
stream. It is important to note that the local generation of
-------
TABLE 1. COMPOSITION OF MUNICIPAL SOLID WASTE,
AS DISCARDED, UNITED STATES, 1973a>b
Component (millions of tons) % of total
Paper
Newspaper
Corrugated
Office paper
Other
Glass
Ferrous metals
Nonferrous metals
Food waste
Yard waste
Other
44.2
8.0
11.8
5.4
19.0
13.2
11.0
1.4
22.4
25.0
17.2
33.1
6.0
9.0
4.0
14.1
9.9
8.2
1.0
16.6
18.5
12.8
Total 134.4 100.0
aSmith, F.A., U.S. Environmental Protection Agency.
Unpublished data.
l~»
Includes wastes generated in households, commercial and
business establishments, and institutions (schools,
hospitals, etc.); excluded are industrial process wastes,
agricultural and animal wastes, construction and demo-
lition wastes, mining wastes, abandoned automobiles,
ashes, street sweepings, and sewage sludge. Wastes now
being recycled are also excluded.
fiber in certain areas can far exceed the 40% to 50% value. For
example, if a concentration of commercial routes were lumped in
some area in the region, the percentage of fiber might be as high
as 70% to 85%. Data taken at the Richmond Field Station laboratory
support this generalization. Their average fiber content is
reported to be about 43%, whereas results obtained from selected
areas reach the higher percentages. If processing plants are
constructed on the 500 to 1,000 tons/day modular size range, then
it is important to adequately sample the waste stream in the
particular region and not rely on overall averages. This will
undoubtedly have an effect on the combination of processing
technology that can be most advantageously implemented to insure
optimum materials and energy recovery.
The solid waste generation rate in the Bay Area ranges from
3.5 to 13.7 Ib/capita-day. Of interest here is the fact that
the national generation rate of 3 to 5 Ib/capita-day is often taken
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TABLE 2. AVERAGE COMPOSITION FOR RESIDENTIAL, COMMERCIAL, AND INDUSTRIAL SOLID
WASTE FOR SOME SAN FRANCISCO BAY AREA COUNTIES
Waste
constituent
Newsprint
Corrugated
Other paper
Total fiber
Ferrous
Aluminum
Other nonferrous
Total metals
Glass , ceramics , rocks
Plastic, rubber, rags,
etc.
Garbage , yard wastes
Alameda
9.0
22.0
12.0
43.0
8.0
0.7
0.3
9.0
10.0
5.0
33.0
Contra
Costa
9
6
35
50
7
1
-
8
10
6
20
.0
.0
.0
.0
.0
.0
—
.0
.0
.0
.0
San
Francisco
8
2
38
48
8
1
-
' 9
13
5
5
.0
.0
.0
.0
.0
.0
--
.0
.0
.0
.0
Santa
Clara
8.
6.
31.
45.
6.
0.
—
6.
6.
6.
26.
0
0
0
0
0
5
-
5
0
0
0
MSW
Richmond
Calif. (6)
_
-
43
7
0
-
8
10
4
23
—
—
.2
.3
.7
—
.0
.8
.5
.5
Avg.
NCRR
—
—
43.
8.
0.
0.
9.
10.
5.
26.
MSW
(5)
—
-
0
0
7
3
0
0
0
0
Other, miscellaneous,
unclassified fines 6.0 20.0 10.5 10.0 7.0
-------
as valid for regions whose waste is generated by a multitude of
various manufacturing, residential, or agricultural activities.
Thus one generation rate is taken as valid for all locations but
for different reasons.
PHYSICAL CHARACTERISTICS OF REFUSE
The heterogeneous nature of the waste stream gives rise to
a material whose components contain a variety of mechanical
properties. Measurements have been made of the ultimate strengths
and strain and rupture energy for some major refuse components
such as magnetic and aluminum cans, kraft paper (from brown paper
bags) , light cardboard box material (typical of food packaging) ,
and polyvinyl chloride (PVC) and polyethylene (PE) plastics (7).
All of the above specimens were actual objects, or parts thereof,
found in municipal refuse. The stress-strain data allowed modulus
of elasticity values to be computed. A comparison of the stress-
strain characteristics of the waste stream components listed in
Table 3 is shown in Figure 1.
The steel specimens have the greatest values of ultimate
strength (about 82,000 lb/in. ) and the least value of ultimate
strain (0.004 in./in-)- This value of ultimate strength is in
general agreement with those obtained for plane carbon, cold
worked steels, which range from 70,000 to 100,000 lb/in.2, depend-
ing on the carbon content and degree of cold work of the material.
The modulus of elasticity (E) computed from the stress-strain
data has a value of 28.5 x 10° lb/in.2, which compares favorably
with the usual values of E of 29 to 30 x 106 lb/in. for carbon
and low alloy steels. Values for the ultimate strength of the
aluminum specimens were approximately 30,500 lb/in.2, and they
compare with known values, which range between 13,000 and 82,000
lb/in.2 depending on the alloy content and heat or cold working
treatments. A value of E of 10.0 x 106 lb/in.2 was computed from
the aluminum stress-strain data.
The characteristics of the fiber materials are summarized as
follows: Cardboard and paper have ultimate strengths of 6,400 lb/
in.2 and 4,000 lb/in.2, respectively, and both have an ultimate
strain of 0.025 in./in. Modulus of elasticity (E) for cardboard
was computed as being 0.5 x 106 lb/in.2, and 0.32 x 106 lb/in-.2
for paper. In the paper industry it is common to consider
strength in terms of the maximum length (meters) that a strip of
paper can hang free before rupture or tearing occurs. If the paper
density is known, (p) values of the stress (S) at the top of the
strip can be computed; that is, S = w/A = Lp where w is the weight
of the strip, L the length, A the cross sectional area, p the weight
density, and S the stress. Typical values of strength range from
2,000 to 5,000 meters at maximum stress of 2,100 to 5,200 lb/in.2
The behavior of the plastic samples differs considerably from
-------
TABLE 3. STRESS VS. STRAIN DATA
Material
Steel
Aluminum
Type of
container
12-oz
beverage
can
12-oz
beverage
can
Container shape
and specimen
locations
Cylinder;
specimen cut
from side,
axially and
circumferen-
tially
Same as
above
Specimen
thickness
(in.)
0.007
0.006
Ultimate
strength
(psi)
82,000
31,000
Ultimate
strain
(in. /in.)
0.005
0.012
Rupture
energy .,
(ft.-lb/in. )
9.4
26.5
Card-
board
Paper
Laundry
detergent
box
Rectangular box;
specimen cut
from front and
back panels
0.025
Brown paper "Grocery" type
bag bag specimen
cut at various
locations
0.009
Plastic, Liquid
poly- soap
vinyl- bottle
chloride
Plastic, Shampoo
poly- bottle
ethylene
Sculpted molding; 0.19
specimen cut to
from front and 0.026
back panels
Cylinder; 0.028
specimen cut as to
in cans above 0.036
6,400
4,000
4,000
to
5,000
0.025
8.3
0.025
5.1
0.360-4=0.la lll-e=0.1
0.130-e=1.0 44-e=1.0
0.060-e=10 19-6=10
0.80 for e=0.1 56-e=0.1
1,000 0.84 for e=1.0 60-e=1.0
0.90 for e=10 66-e=10
e = elongation rate, all materials were tested at e = 0.1, 1.0 and 10 in./min.,
with the plastics showing the effects of elongation rate as given above. Materials
other than the plastics showed no elongation rate effects.
-------
10'
10
(/I
4->
OO
10"
10'
T I I
1 i i i i i r
Dimensions (Inches)of
Test Specimens
"Aluminum Can
Cardboard ^
(Detergent
Box)
Specimens taken from
actual containers.
x-point of rupture
Brown paper bag
x
'Polyvinyl Chloride
^Polyethylene
AB6]
Rupture Occurring at
Elongation Rates of
i i i
a)
b)
c)
0.1 in/min
1.0 in/min
10.0 in/min
i i i
10
-3
Figure 1
10"2 10"1
Strain (in/in)
Stress-Strain Characteristics
of Some Refuse Components
1.0
that of metal and cardboard samples. For PVC the modulus of
elasticity was computed as being 0.2 x 10 lb/in.2, and the ranges
of ultimate strength and of strain were 4,000 to 5,000 lb/in. and
0.060 to 0.360 in./in., respectively. The corresponding range of
normally accepted values for PVC without plasticizers is a modu-
lus of 0.2 x 10° to 0.6 x 10°; and ultimate strength and strain
values of 5,000 to 9,000 lb/in.2 and 0.02 to 0.40 in./in.,
respectively. On the other hand, the PE sample has a lower modu-
lus of elasticity (0.014 x 10 lb/in.2), a lower ultimate strength
(1,000 lb/in.2), and higher values for ultimate strain (0.8 to
0.9 in./in.). Depending on the polymer density, molecular weight,
and manufacturing processes, the corresponding values of modulus,
and ultimate strength and strain for PE are within the range of
0 - 01 x 106 to 0.04 x 106 lb/in.2, 1,000 to 1,400 lb/in.2 and
-------
0.5 to 7.0 in./in., respectively.
Energy requirements needed to effect various degress of
volume reduction by both pure compression and impact for several
types of containers normally found in municipal refuse are avail-
able. These data also consider object orientation, because
geometrical asymmetries and certain types of supportive elements
such as rims on the ends of cans can have an effect on the amount
of energy required for a particular amount of volume reduction.
Specifically, the orientation of the objects in these tests was
as follows: a) The steel and aluminum cans were subjected to
separate radial and axial tests; b) cardboard boxes and cartons
were tested in the upright and horizontal positions; and c) glass
bottles were tested in steady compression until they fractured.
In effect, determination of the area under the curve for load vs.
volume reduction yields a relation between energy expenditure
and volume reduction. The impact tests were performed in a manner
in which the energy required to effect a given volume reduction
could be obtained directly by impacting an object with a known
weight falling through a known distance.
The energy required to effect a certain volume reduction on
glass, metal, and cardboard containers normally found in refuse
is indicated by the curves in Figure 2. Here the results of both
volume reduction techniques are compared, that is, the steady
compression method (solid curves) and the impact method (dashed
curves) . In each case there appear to be two distinct slopes for
the energy-volume curves. Except for glass, the first slope
occurs at volume reductions up to 60% to 70%. This slope is
essentially linear and is representative of the initial buckling
and folding of the container wall. In the case of glass, this
slope prevailed up to a volume of about 35% and is representative
of the initial fracture.
During this linear portion, the forces required to effect a
volume reduction are generally constant. It is reasonable to
assume that during this phase of volume reduction, the greatest
part of the energy or input work is directed toward the elimina-
tion of the large interior voids of the containers, and essen-
tially no plastic deformation occurs. As would be expected,
after the first phase of volume reduction has occurred, the amount
of subsequent work or energy required for continued volume reduc-
tion increases rapidly. It is then necessary to begin deformation
of the container wall materials and the slope of the force-
compression curves approach the elastic moduli of the respective
materials. The volume reduction can occur, and this is noted in
Figure 2 for the types of specimens considered. The energy data
regimes are summarized in Figure 3.
Each of the objects exhibits different behavior. For example,
the steel and aluminum specimens, when tested in tension, are not
-------
160
140
120
_ 100
1 I I I ' I
VOLUME OF MATERIAL IN CONTAINERS
STEEL CAN 1.4 %
ALUMINUM CAN 1.2 %
CORREGATED
CARDBOARD BOX 14%
AND WITH COMPRESSED
CORREGATIONS 3.5%
CARDBOARD
CARTON
PLASTIC (PVC)
BOTTLE
2.8 7c
3
CD
CC
UJ
80
60
40
20
0
20 40 60
VOLUME REDUCTION (%)
80
STEADY COMPRESSION:
STEEL CAN- RADIAL LOADING
STEEL CAN-AXIAL LOADING
ALUMINUM CAN - RADIAL
ALUMINUM CAN - AXIAL
CORREGATED CARDBOARD BOX
CARDBOARD CARTON
100
IMPACT:
STEEL CAN - RADIAL
STEEL CAN - AXIAL
ALUMINUM CAN - RADIAL
ALUMINUM CAN - AXIAL
GLASS BOTTLE- AXIAL a RADIAL
Figure 2 Energy Required for Volume Reduction of
Common Containers Found in Refuse
10
-------
140
120
100
*-r
JQ
i
£ 80
60
UJ
40
20
ENERGY REQUIREMENTS FOR
STEADY COMPRESSION RATE
TESTS. RESULTS SHOWN
INCLUDE RADIAL AND AXIAL
LOADING TESTS AND DATA
SCATTER.
20 40 60 80
VOLUME REDUCTION .(%)
100
Figure 3 Energy Requirements for Steady
Compression Rate Tests
strain-rate-dependent in the range considered and broke abruptly
in a manner characteristic of a brittle material. On the other
hand, the strain rate had a significant effect on the ultimate
strain of the plastic specimens. PVC was more sensitive to this
parameter than was PE. Extensive local deformation or "necking"
characterized these specimens. In general, the mechanisms
involved in straining polymers are complex and not completely
understood. Changes in experimental conditions, such as strain
rates, are known to affect the probability of fracture under given
circumstances. As the strain rate is increased, the typical
behavior of such specimens is a localized heating that leads to a
decrease in stability and to breaking strains.
During compression, glass bottles have a tendency to break in
areas of stress concentration, such as the vicinity of the bottle
neck and near the bottom. Bottles with more complex shapes
generally fracture at lower levels of stress. As glass pieces
become smaller, the stress requirements for further crushing
11
-------
increase. The stress requirements for small glass pieces loaded
in pure compression are much greater than for pieces where tensile
stresses are also present, such as in bending.
The amount of force required to crush metal cans is affected
by the method of load application. The amount depends on both the
direction of the application of the force, such as axial or radial
compression, and on the shape of the crushing member. With respect
to the values reported here, specimens were compressed between
large flat plates.
DENSITY AND COMPRESSIBILITY OF REFUSE
Design of various solid waste management schemes requires
knowledge of the density and potential compressibility of raw and
processed solid waste. This is especially germane to certain
aspects of material handling such as conveying and processed
material transport in either loose or baled form. Planning for
disposal by landfill also requires knowledge of density and
compressibility. Ruf (8) has reviewed the available data on the
subject, defined terminology in terms of models, and conducted
controlled laboratory experiments that produced density and
compressibility data for both raw and shredded refuse. In addi-
tion, the feasibility of baling refuse has been considered in a
report prepared by the Department of Public Works in the City of
San Diego, California. Other work dealing with compaction and
baling has been prepared by the American Public Works Association
(APWA) for the EPA (9, 10).
In his considerations, Ruf defines the particle structure of
refuse as being an assemblage of particles interspaced with open
air spaces called voids or pores. Unlike soil, the moisture is
generally not contained in the voids as free moisture but rather
absorbed in the material itself. Certain terminology then follows
from the fact that the total volume of material is composed of the
volume of the solids plus the volume of the voids or
V = V + v
m solid void
The void ratio is given as e = V /V and the porosity is n = V /V .
The density is the ratio of weight to total volume. A wet weight"1
density is defined as the ratio of total weight, including water,
to the volume; the dry density, sometimes referred to as the
apparent or bulk density, is given as the ratio of the weight of
solids alone to the total volume. The true or absolute density is
given as the ratio of the weight of solids to the volume of solids.
In his work, Ruf elaborates on the fact that since solid waste
is not rigid, depending on the pressures applied to reduce the void
spaces, various values of bulk density can be achieved. Further,
12
-------
the bulk density can vary because of different waste compactions,
irrespective of its porosity. Comparison of the density of various
materials shows that the components in the waste stream contribute
to a wide range of densities. For example, the average density of
steel scrap is on the order of 13,000 Ib/yd3, whereas that of
highly densified paper bales is only 1,500 lb/yd3. An average
density of refuse computed from the material composition indicates
that the theoretically highest density possible for dry refuse
compacted in a high density baler is on the order of 1,400 lb/yd3.
According to Ruf, density is not affected by differences in the
size of particles, but is instead influenced by the particle
arrangement. For wastes high in paper content, the contribution
of moisture to the density could be greater than 50%, since in the
absence of swelling, the moisture is absorbed, thus contributing
to the weight but not the volume. Also, higher densities can be
achieved with greater pressure and smaller particle size.
Since refuse contains little free moisture and relatively
large particles, the time lag for compression is small compared
to a material such as soil, where the water must be squeezed out
during compression. Ruf's experiments show that as pressure is
applied to solid waste, the volume is reduced and the density
increased because of the crushing, deforming, and relocating of
individual particles. Such hollow objects as containers begin to
collapse at various pressures. For example, cans and bottles
begin collapsing at pressures of 10 to 30 psi and 5 to 35 psi,
respectively. Thus, some phases of the compaction process are
reversible, and others are not. The data obtained by the APWA
indicate that the volume reduction of loose residential refuse of
similar density was about 9:1 and 13:1 for applied pressures of
900 psi and 3,000 to 3,500 psi, respectively. For different
types of refuse subjected to the same pressure, the volume reduc-
tion varied between 7:1 and 23:1. The former value was for a
high-dirt-content waste. Normal variations were between 8:1 and
18:1. In the APWA experiment, the consolidation theory was
observed; namely, larger densities were obtained when the applied
pressures were retained.
For the case of shredded refuse, the APWA has concluded that
shredding does not aid the compression process or contribute to
the stability of the bale as compared to direct baling of
unprocessed waste. Data concerning the relationship between ap-
plied pressure to the density of shredded refuse has been assembled
by the American Baler Company (9).
The effects of springback after the release of pressure and
stability in compressed refuse have been considered in several
studies. The APWA results show that an approximate 20% expansion
occurs a few seconds after pressure release and can continue to
50% to 60% of the original compressed volume after several minutes.
In general, this study indicates that the stability of bales
13
-------
improves with increased pressure and application time for proper
moisture contents. Pressures in the range of 500 to 1,000 psi
produce fragile bales, but 1,000 to 1,500 psi pressures show
improved stability. The greatest improvement in stability occurs
in the pressure range between 2,000 to 3,500 psi.
The experimental data obtained by Ruf for density (0 pressure)
compressibility, and springback are given in Figures 4,5,6, and 7
for raw, primary, secondary, and rasp-shredded wastes, respectively
His apparatus consisted of of a 10-ton capacity laboratory model
hydraulic press fitted with a compression cylinder test chamber.
Approximately 20 3-lb samples of each category (except the rasp
samples, which were 9 6-lb samples) were dried for 2 to 4 days at
70 to 75°C and then tested. Ruf found that the compression curves
were smoother for the small particle waste. The greatest variation
occurred with raw refuse.
SIZE REDUCTION EQUIPMENT
The type of equipment available for the size reduction or
comminution of brittle materials along with their subsequent.
performance characteristics is well documented in the mineral
dressing and processing industry (11). Raw material characteriza-
tion and the type of product specified (e.g., graded, granular,
fine, abraded, flake, rounded, sharp, etc.) are the predominant
factors considered in the selection of a particular type of mill.
Another consideration used in specifying brittle material comminu-
tion is the so-called grindability of the material. Basically,
this refers to the response of a material to the grinding effort.
Materials are generally classed as a) hard, friable, abrasive,
b) hard and tough, c) medium hard friable, d) soft, friable,
e) soupy, and f) sticky.
Comminution devices generally used for the dry size reduction
of brittle materials have been grouped accordingly: 1) Fixed path
mills, containing relatively few comminution elements that follow
a definite path, and 2) tumbling mills, where the elements are
multifarious and not constrained to individual paths. Examples
of fixed path mills are attrition mills, impact mills of the
hammermill or jet pulverizer type, pan mills, roller mills, and
other types and variations of these. Tumbling mills include ball
and pebble mills, rod mills, compartment mills, and other modifica-
tions of the rotating-drum principle.
Refuse, a heterogeneous material, contains only about 25%
brittle materials. As a result, the machine selection criterion
used for a purely brittle material is not directly applicable.
When the size reduction of refuse is considered, the term
"shredding" as opposed to grinding, pulverizing, crushing, etc.
has emerged as the terminology depicting refuse comminution. The
following types of machines have been designated as shredders by
14
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I200I ' I ' I ' I I I ' I I I I I I I
1000
95% CONFIDENCE
LIMITS
I
J_
0 20 40 60 80 100 I2O 140 160 180
APPLIED PRESSURE (psi)
Figure 4 Compressibility of Modified Raw
Solid Waste
15
-------
1200
iiiiiiII^nT i ^ i
1000-
•o
>»
3
U
Q)
Q.
-------
1200
1000 —
3 800
in
.O
95% CONFIDENCE
LIMITS
600 -
z
Ul
o
40°
200
0 I 1
1 I 1
0 20 40 60 80 100 120 140 160 180
APPLIED PRESSURE (psi)
Figure 6 Compressibility of Solid Waste After
Secondary Shredding
17
-------
1200
95% CONFIDENCE
LIMITS
200
1 1 I I I I I I I I
I
20 40 60 80 100 120 140
APPLIED PRESSURE (psi)
160 180
Figure 7 Compressibility of Solid Waste
Passed Through a Rasp
18
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the Waste Management Equipment Manufactures Institute: crushers,
cage disintegrators, shears, shredders, cutters and clippers, rasp
mills, drum pulverizers, disk mills, wet pulpers, hammermills, and
grinders.
Hammermills are the most commonly used type of machine in
refuse processing. This fact stems from the nature of the waste
stream components (particularly the high non-brittle fibrous
fraction) and the manner in which the size reduction is effected.
As previously mentioned, hammermills are a class of impact crusher
in which the load, a combination of tensile, compressive, or shear
forces, is applied to the material by striking particles in sus-
pension or by hurling them at high speed against stationary
surfaces. This action differs from a typical crushing machine,
such as a rock crusher, which takes in a coarse feed and applies
pressure gradually to the particles which take the load as
simple beams or short columns.
In some sense, the greater part of size reduction of refuse
with the hammermill is accomplished by brute force. There are
horizontal and vertical shaft machines of either the swing or
rigid hammer type. The horizontal swing hammer machine, whose
principle parts are the rotor, hammers, grates, frame, and fly
wheel, is the type most frequently used. The machine construction
is relatively simple. Here the rotor and fly wheel are mounted
through the bearings to the frame, the bottom portion of which
also holds the grates. The hammers, which can assume a number of
configurations, depending on the particular manufacturer, are
attached to the rotor by means of the hammer pins. These are long
rods, which in effect lace the hammers to the rotor by running them
through the holes in the rotor and hammers. Actual hammer configu-
rations vary from simple rectangular blocks having typical
dimensions of 12 x 4 x 1 in. to the more elaborate type of chopper,
which may have a protruding wearing surface with sharpened edges.
When the entire rotor-hammer assembly is rotating (usually at about
1,000 to 1,500 rpm), the hammers fly perpendicularly to the rotor
Upon impact with objects being size-reduced, each hammer is free
to move in a 180° arc within the plates of the rotor. In a
typical commercial installation, the motor is usually attached to
the rotor shaft by means of a steel flex coupling. Materials to
be size-reduced enter the machine through an infeed chute and
interact with the hammers and each other until at least one
dimension of the objects has reached a size small enough to fall
through the grates in the bottom of the machine.
Experience has shown that refuse is an abrasive material
that does not directly conform to the previously mentioned grind-
ability types and is relatively difficult to size reduce. As a
result, the comminution processes cause considerable wear to the
machine elements, particularly the hammers. The problem of wear
is considered in detail in a later section of the report. The
19
-------
residence time of material in the mill and subsequently the size
distribution of the product are largely determined by the grate
spacing. In addition, other comminution parameters such as
feedrate, moisture content, mill speed, etc. influence the product
size distribution. The effect of these variables is also consid-
ered in detail in another section of the report. There are several
safety precautions that must be included in the design of_size-
reduction installations that involve the use of a hammermill. ^In
this regard, it is important to note that because of the rotating
hammers, certain types of large objects (metal objects, for
instance), tend to be thrown out or ejected because of impact
with the swinging hammers. These airborne objects, which leave
through the input opening, are potentially dangerous to the^
operators of the equipment, especially to the operator loading
refuse or to the input conveyor. A chain curtain is often hung
over the input opening to deflect the objects that are ejected.
In the vertical shaft machines, the rotor is placed in a
vertical position, with the input material moving parallel to the
shaft axis, assisted by gravity. Several hammermill-type machines
using the vertical principle are being used. A variation of the
vertical principle is embodied in a relatively new machine known
in the industry by its commercial name - the Eidal grinder or
shredder. The principle followed in the design of the machine
differs from that of the hammermill in that size-reduction is
accomplished by a set of gear-like teeth installed in a rotor
(see Figure 4) that fits in a stationary ribbed housing. After
the material to be ground is introduced into the upper part of
the machine, it passes a set of breaker bars by means of which
large objects are torn apart. The material then enters the space
between the rotor teeth and the housing ribs. Size reduction
occurs in this part of the machine as a result of the induced
shear and the mutual self-comminution interaction between the
various types of materials. Since the space between the rotor and
the housing is tapered, smaller objects are continually worked
downward and eventually exit via a peripheral opening at the
bottom. The dimension of the opening in this extraction area can
be varied. Therefore, it theoretically is possible to adjust the
size of the product. Measurements of the size distribution of
refuse ground under both the coarse and fine settings show that
there is no significant difference in the size distribution of
the product leaving this type of grinder. The power requirements
of the Eidal grinder are similar to those of the hammermill-type
grinder. This machine is relatively slow turning and does not
tend to reject objects in the manner of the hammermill.
Additional aspects of size reduction equipment, including
installation and material handling, have been previously
considered (12, 13).
20
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Utilization and Location of Shredders
An appreciation of the degree to which shredders are being
utilized in the solid waste processing industry can be obtained
from a recent compilation prepared by Waste Age (14). In 1971,
the Waste^Age survey revealed 27 municipal-scale waste shredding
installations. The number had increased to 87 by 1974 and to
134 by 1975. Table 4 shows the states that have municipal-scale
shredding operations and the dates of first installation.
TABLE 4. MUNICIPAL-SCALE SHREDDING OPERATIONS, BY STATE OR COUNTRY
AND DATE OF FIRST INSTALLATIONa
State or
country
* Alabama
California
Colorado
Connecticut
Delaware
Florida
Georgia
Illinois
Indiana
Iowa
Kentucky
Louisiana
Maine
Massachusetts
Michigan
Missouri
Montana
Nebraska
Date
1965
1969
1972
1972
1972
1967
1963
1970
1970
1973
1962
1975
1972
1973
1967
1969
1973
1974
State or
country
New Jersey
New York
North Carolina
North Dakota
Ohio
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Texas
Vermont
Washington
West Virginia
Wisconsin
Canada
Jamaica
Date
1974
1969
1974
1975
1968
1973
1966
1972
1973
1975
1965
1968
1970
1975
1958
1970
1962
aData from Waste Age (14)
The Cal Waste Processing Facility
Scientific studies require the ability to systematically
modify and control the conditions and parameters germane to a
particular investigation. Consistent with this requirement, a
size-reduction facility capable of operating on a scale resembling
a commercial installation and yet able to produce laboratory
quality data was developed for the purposes of conducting the
comminution studies sponsored by EPA. The waste processing
facility is located at the University of California's (Berkeley)
Richmond Field Station. Although the initial emphasis of the
21
-------
laboratory was on size reduction, the facility was later expanded
to include complete front end dry processing as well as certain
types of back end processing for material and energy recovery.
Since the system is modular and differs in many aspects from other
waste processing schemes, this processing facility has been^called
the Cal Recovery System as a means of providing it with an iden-
tity. A brief description of the features of this facility
follows.
The comminution device is a 10 ton/hr Gruendler Model 48-4
hammermill with 44 free-swinging manganese steel hammers. This
machine was formerly at the Johnson City Tennessee Compost Plant
and was moved to the Richmond Field Station site after the size
reduction in refuse processing research had gotten underway.
Power to the hammermill is supplied through a variable speed
drive system from a motor rated at 250 hp, 480 V, 3 phase,
310 amps, and 1,200 rpm; the electrical power consists of 480 volts
supplied by three 100-kilovoltamps (KVA), 400-amp transformers.
A motor starter provides starting, stopping, and overload protec-
tion. With the starter, the large current draw (1,600 to 1,800
amps of a 250-hp induction motor) during direct line startup at
480 volts is reduced to a workable draw of 800 to 900 amps by
initially providing a reduced voltage (285 volts) to the motor.
After a period of about 10 seconds, full voltage is applied. In
essence, the overload protection consists of overload relays with
heater coils sized to 310 amps and a thermal protection device to
guard the autotransformer against overheating. In addition in
this installation, an A.C. load current relay and timing relay
were included to prevent "blowing" of 12 12,000-volt fuses
protecting our 300 KVA transformer bank should a blockage occur
in the grinder. The power cable consists of three lines of 500-
mcm cable.
The variable speed drive consists of two Gates Super HC
Powerbands (four strands each) and five Gates Super HC QD
sheaves and bushings (see Figure 8). The speed ratios are 1:1,
1.22:1, 1.52:1, and 2.16:1, and they correspond to 1,200, 985,
790, and 555 rpm at the grinder shaft, respectively. In most
commercial installations, the motor is attached directly to the
rotor shaft with a Falk steel flex coupling or some type of
hydraulic coupling. Here the variable speed drive was required
because grinding speed is an important comminution parameter and
documenting its effects was part of the study. In certain
instances, however, space or equipment layout considerations may
make it advantageous to use a belt drive. But the motor, and in
some cases the grinder bearings, usually are not sufficiently
sturdy to handle the radial load caused by the belt tension (on
the order of 4,400 Ib in our case). A jackshaft and bearing
assembly can be inserted to compensate for this lack. Again, as
a design guideline, in this installation 8V-type v-belts were
needed to transmit the 250 hp from motor to grinder. An inherent
22
-------
Discharge
Conveyer
SrinderSs!
Shaft
Alternate
Sheaves
Figure 8 Overall View of the V-belt (Alternate Driven
Sheaves are shown in Foreground)
-------
disadvantage of a belt drive system is that it requires a movable
motor base so that the position of the motor can be adjusted to
apply the necessary belt tension. On the other hand, a chain
drive would require a lubrication system.
Mounting the grinder is an important aspect of developing a
trouble-free facility. For example, the grinder must be mounted
on a foundation structure massive enough to absorb a high degree
of vibration and thus result in a smooth-running system. The
foundation must be suitably isolated from the enclosing structure
so as to avoid transmitting the vibration to the building. In
constructing the foundation, sufficient clearance must be allowed
between the output of the grinder and the discharge conveyor to
prevent the ground material from jamming. A clearance of 4 ft
was provided between the grate bars and the discharge conveyor.
The base of the foundation is a solid concrete mass extending,
6 ft below the floor level. A low water-to-cement ratio concrete
(4-in. slump) with 3/4-in. reinforcing iron was used. Although
this is a "thick" concrete and somewhat hard to place, it allows
a high compressive stress. The full strength of about 3,000
lb/in.2 cannot be reached until the concrete has cured for_several
weeks. The grinder is secured to the foundation through six 1-in.
bolts present in the concrete. Isolation material was placed
between the foundation and the existing floor of the building.
Steel belt, piano-hinge-pusher, flight-type conveyors were
selected for both the feed and discharge. To accommodate the
grinder, the feed conveyor was arranged to have a 22° angle of
incline. Its belt is 4 ft wide. As a design guideline, a belt
speed of 7 ft/min would be required to deliver 12 tons/hr with an
18-in. depth of refuse on the belt. Since effects of feedrate were
part of the investigation, the input conveyor has a variable belt
speed. The variation in belt speed (from 1.8 to 7.0 ft/min),
accomplished through the use of a variable-pitch drive sheave and
two interchangeable driven sheaves, enables the feedrate to be
governed from 1 to 10 tons of packer truck refuse per hour. The
controls of the conveyor in this installation are such that the
feeding action is synchronized with the power demand of the grinder.
The synchronization was such that feeding was stopped when the
electrical current demand of the grinder reached a preset level.
The discharge conveyor used to remove the ground refuse has a 30°
angle of incline. (The ground material has a particle size such
that 80% of it passes through a 2-in sieve.) Since the belt width
is 3 ft, a belt speed of about 10 ft/min is required to remove
12 tons/hr of the ground material.
Instrumentation is available for continuous monitoring of
power consumption and surges, and also rotational speed of the
grinder shaft. A 480-V, 5-amp, 3-phase watt hour meter is used
to measure the energy consumed by the grinder motor. To study
the power surges, the current from one motor leg is monitored
24
-------
using a strip chart recorder. The rpm of the grinder shaft is
measured electronically using an electromagnetic pickup and a
Hewlet Packard Counter.
The size reduction portion of the Cal Recovery System is
shown in Figure 9. A working relationship established with a
local scavenger company (Richmond Sanitary Service) allows a
variety of waste streams such as domestic and commercial packer
truck refuse to be analyzed and processed. The laboratory has
also processed the University waste stream generated on the
Berkeley campus. This is a unique stream in that it contains on
the order of 90% high-grade paper fraction. This material can
subsequently be processed into a high-grade mixed paper waste.
The additional features of the system, which were developed after
the size reduction studies matured, are described as follows.
The next stage of processing involves air classification,
where the stream is separated into light and heavy fractions -
the so called lights and heavies. A schematic representation
of the basic dry process is given in Figure 10. Air classifi-
cation and heavies processing equipment is shown in Figure 11.
Here the air classifier is fed directly from the grinder discharge
conveyer. With typical packer truck refuse, the split of the
incoming material stream after air classification is about 70%
lights and 30% heavies. The heavy fraction, essentially devoid
of fiber, is further processed into its components, which consist
of ferrous and nonferrous metals, glass, and organic and miscel-
laneous compounds. Referring to Figure 10, this processing can
be delineated as follows: The heavies, conveyed from the bottom
of the classifier, first pass under a ferrous magnet whose belt
travels perpendicularly to the discharge conveyor causing the
ferrous scrap to be ejected into an adjacent bin. The stream then
proceeds into a trommel screen, where the minus fraction is
conveyed to a device that results in the separation of this stream
into a glass-rich fraction and an organic fraction. The plus
fraction component of the trommel screen contains aluminum,
organics, and other miscellaneous materials (Figure 11).
The air-classified light fraction ("lights") exits the top
of the classifier and is de-entrained from the air stream by
means of a cyclone separator. As seen in Figure 12, the lights
are pneumatically conveyed to the top of the cyclone, where the
material and air are separated. The duct leading to the fan as
well as the fan discharge can also be seen. Basically, the air-
classified light stream is predominantly fiber, but it is
contaminated with plastics and fines composed of myriad substances,
principally fine glass, dirt, some fine organic components, etc.
The contaminating material is removed by screening (see Figure 13).
Here the light fraction is removed from the cyclone by means of a
rotary air lock feeder and then conveyed to a trommel screen for
removal of the fine contaminants. A number of options are
25
-------
variable speed
.drive system
Figure 9 Input Conveyor and Grinder
(Size Reduction Unit)
26
-------
Solid
Waste
Size
Reduction
Ferrous
Mixed
Paper
Non-Ferrous Digestible
Heavy Fraction Rejects
Figure 10 Basic Dry Plant
available for processing the cleaned light fraction (Figure 14).
They are essentially as follows: 1) The material can be baled
and sent away to be used as a fuel supplement, or it can be
shipped to a paper mill equipped for handling secondary fiber
contaminated with plastic, hot melt, etc. Since almost all of
the organic substances have been removed, the baled material will
not deteriorate when stored - that is, it has a long "shelf-life."
2) The material can be subjected to further size reduction and
used as a fuel for certain types of combustion applications.
This option is attractive in view of the present demand for
energy sources - as contrasted with the existing uncertain second-
ary fiber market. 3) The material can be further processed by
way of a wet processing step. At this point, it should be noted
from the preceding description that the system has followed a
basic principle of subjecting as little as possible of the incoming
waste stream to the wet phase of the process, which is the subject
of the following paragraph. It is important to note that when the
material is used as energy (item 2), the subsequent fuel has a
heating value on the order of 7,300 BTU/lb, an ash content of 5%
to 10%, low sulfur content, and combustion compatibility with
coal, gas, or oil. The further densification of this material
into pellets enhances its transportation, storage, and in some
cases its feeding characteristics.
The wet phase of the system, shown schematically in Figure
15, is designed so that contaminants remaining after the dry
processing of the lights are efficiently removed. The wet phase
is begun by pulping the cleaned light fraction from the dry
27
-------
t .1
00
1 ight fraction air
classifier discharge
air
classifier
•r <-
ferrous recovery
V,
discharg
conveyor
heavy fraction
trommel screen
.
glass fraction-
recovery
Figure 11 Grinder Discharge into Air Classifier and
Heavies Recovery
-------
air classifier 1ight
fraction to cyclone
•
cyclone
air
discharge
fan discharge
Figure 12 Light Fraction Processing Facility - Air Classifier
Light Fraction Discharge, and Cyclone
-------
bottom cere .
of cyclone •
rotary air-lock
feeder
! t I
1ight fraction,
trommel screen
/w»
....
Figure 13 Components of the Light Fraction Processing
Facility
30
-------
Screened Lights
(From basic dry
plant)
Fiber—^
Fiber
Market
Fuel
Fuel
Fuel
•—ijDensI fieri-
Fuel
Figure 14 Alternatives for Screened Lights
process at a consistency of about 3% in a manner that allows the
fibers to be slurried while the plastic component retains its
large particle size. A conventional ragger can be incorporated
into the pulping operation. Plastic removal follows pulping.
The pulper discharges into the head tanks, which feed the plastic
removal screen. This operation is designed to dilute the fiber
slurry to a consistency of about 0.5% at the time the plastic is
being removed. A 0.5% concentration is compatible with centrifu-
gal cleaning. The fiber slurry after plastic removal is pumped
to the first holding tank. Each tank communicates with the first
and second stage of centrifugal cleaning where "triclean-type"
cleaners are used. In the first step, very fine glass, grit,
and dirt contaminants as well as fiber bundles and some usable
fibers are removed. These materials exit through the bottom of
the cyclone with which centrifugal cleaning is accomplished,
while hot melt, wax, and some remaining fine plastics are dis-
charged through the center probe of the cleaner. Since the reject
stream contains usable fibers, a separate step is used to clean
it. The accepts from the reject cleaner are combined with the
first stage cleaner accepts. The rejects from the reject cleaner
are discharged from the system and constitute a fiber loss of
about 5% of the total fiber entering the system. A similar
procedure is followed in the second cleaning step. However,
because the center probe and bottom rejects are considerably less
contaminated than those from the first step, the stream is
returned to the beginning of the first stage and reprocessed. In
some cases, it may be desirable to include a large holding tank or
31
-------
AIRBORNE POSSIBLE
PARTICULATES AIR POLLUTION
DUST
—PARTICLE SIZE FLOW RATE
FIBER
RAW MAT
CLASSIFICATION OF
INPUT 8 OUTPUT
WATER
U)
ro
GRINDER SIZE
ENVIRONMENT
^ACCEPTS
(ORGANICS)
NATURE
OF REJECTS
POSSIBLE
AIR POLLUTION
TREATED
WATER
REJECTS T GRIT
LANDFILL
POSSIBLE USEFUL
APPLICATION
GRIT-LANDFILL
POSSIBLE USEFUL
APPLICATION
SUPERNATANT
DIGESTED
SLUDGE
Al
POSSIBLE
REJECTS
GARDEN
DEBRIS
POSSIBLE USEFUL APPLICATION
SOIL CONDITIONER
Figure 15 System Flow Diagram
-------
pond between the first and second cleaning steps. This would
allow dirt loosened in the centrifugal cleaner and carried with
the accepts to be floated off and thereby removed from the system.
A noticeable brightening of the fiber takes place after the first
stage of the cleaning process.
After the two cleaning steps, only an occasional small
contaminant is present. The fiber produced in the two steps is
suitable as a secondary stream for media and liner board manu-
facture. The addition of yet another cleaning step would lead to
the production of a fiber slurry having only occasional speck
contaminants. The final step in the fiber processing involves
the use of conventional dewatering, and possibly of drying and
baling for shipment. All of the process water is recirculated
within the system. After each pass, 25% of the water is subjected
to a conventional primary and secondary activated sludge waste-
water treatment process. Makeup water is introduced at the pulp-
ing stage. Samples of the fiber recovered by way of the system
have been subjected to rigorous analyses and found to be satis-
factory by potential users in the paper-making industry.
Another module of the Cal Recovery System involves the
anaerobic digestion of the light fraction rejects and the heavy
organic fractions, shown schematically in Figure 16. After removal
of the inerts, these two fractions are combined and mixed with
sewage sludge and are introduced into an anaerobic digester in
which a gas mixture composed primarily of methane (55% to 65%) and
carbon dioxide (35% to 45%) is produced. The gaseous product can
be used directly by way of injection into existing natural gas
pipelines, or it can be scrubbed to remove the CC>2 and other
impurities and used directly as a substitute for natural gas.
Digestion results in a significant volume reduction of the heavy
and light organic fractions and the production of a relatively
stable sludge. The sludge can be used as a soil conditioner or
as a burner fuel. It has a heating value of approximately 4,800
BTU/lb. r Water -jf needed
Digestible
Rejects
Sewage Sludge
Agricultural Waste
Gas
Digester
Figure 16 Anaerobic Digestion
--> Digested Sludge
33
-------
SECTION 2
SIZE DISTRIBUTION
The waste stream contains a multitude of different-sized
objects. Collectively, they give rise to a material, the size of
whose components usually spans an order of magnitude. Thus, the
material is said to have a certain size distribution. Several
modern solid waste management practices dealing with materials
and energy recovery take advantage of the existence of the material
size distribution. Certain types of materials in both the raw and
processed waste stream tend to occur within various size-range
bands within the overall size distribution spectrum. Distributions
for various states of the waste stream are given. These include
the raw unprocessed packer truck refuse, the waste stream after
being subjected to various shredding or size-reduction operations,
and the waste stream components after recovery with a dry, front-
end processing system.
RAW REFUSE
Characterization of the raw waste stream's size distribution
is important for several reasons, which include the ability to
successfully use analytical predictive methods for determining
processed product size distributions, the successful operation of
certain types of recovery schemes that involve the raw waste
stream, etc. Detailed studies of the composition and size of the
raw waste stream on an item-by-item basis have been performed by
Winkler and Wilson (15). They examined form samples totaling
1,152 Ib from high-, middle-, and low-income neighborhoods. These
samples were collected in January in such a manner that a 600-lb
sample came from one source, and 175-lb samples came from other
sources. No statistically significant differences were found.
In this area there is also a separate municipal collection for
food waste (garbage) that would tend to affect relative amounts
in each waste category. This group also examined 915 Ib of waste
from Middlebury, Vermont, which was collected from mid March to
June. This sample contained a large fraction of commercial refuse.
This, along with the fact that an alternate site for disposing
yard and garden wastes was available, had a tendency of diluting
the domestic waste contribution. Waste stream objects were
categorized by weight, dimension (length, width and height), and
material composition. In this study, objects were defined as
items that would be expected to remain intact after a reasonable
34
-------
amount of mechanical handling. Plastic bags were allowed to rip
open after they were grasped at two points and shaken; in effect,
this was considered mechanically breakable. Size analysis went
down to 1 in., with the remainder being considered as miscella-
neous. Since their findings indicated that many objects in the
waste steram are composite materials, secondary and tertiary
material composition classifications were performed. Although
some 50 categories were established, the bulk composition of their
material was reported in terms of 9 principal categories (see
Table 5) .
TABLE 5. BULK COMPOSITION (WEIGHT PERCENT) OF REFUSE SAMPLES
(Percent by weight, wet basis)
Constituent Cambridge, Mass. Middlebury, Vt.
Paper
Newsprint
Metals
Ferrous
Nonferrous
Glass
Plastics
Cloth, rubber, leather
Wood
Food
Yard and garden
Misc. and uncategorized
35.8
7.8
9.2
8.3
0.9
18.6
4.1
5.2
1.1
5.9
0.5
19.6
100.0
48.9
3.0
9.1
8.8
0.3
16.6
2.4
2.5
0.4
4.7
0.3
15.1
100.0
The sample size and the manner in which it is obtained are
important aspects of properly categorizing the waste stream.
Wilson (15) found and reported that perhaps the most satisfactory
method of obtaining a typical sample of manageable volume is to
take material from the lengthwise side of the pile dumped by a
packer truck instead of choosing a sample from one end. In this
manner, Wilson claims a sample of the entire load may be obtained.
Other investigators have obtained samples by randomly grabbing
them from conveyor belts or by using such procedures as the
quartering technique, in which a sample of only several pounds is
eventually obtained from a large sample of several thousand pounds.
Both the American Society for Testing and Materials (ASTM) and
American Public Works Association (APWA) have put forth procedures
dealing with the use and application of the quartering technique.
In general, adaptation of this procedure does not favor materials
with large particles. Further, most of these procedures have been
applied in the analysis of homogeneous, usually brittle materials
where the sample size is considered to be related to the
35
-------
characteristics of the material, the available form, and the
requirements of the analysis and subsequent sample processing.
Our experience with categorizing raw refuse is consistent with
that of Wilson, and the sample used to obtain the size distribu-
tion of our raw waste was obtained in a similar fashion.
Some of the results of the Winkler and Wilson study (15)
are given in Figures 17 and 18. Size distribution information
is given in Figure 19, where the cumulative weight is given versus
the longest dimension and also mesh size. The latter was calcu-
lated from the fact that an object must have at least two dimen-
sions smaller than a given mesh size to pass through it. This,
in effect, corresponds to a 100% screening efficiency._ Histograms
given in Figure 20 show the relation of objects and weights per
ton versus size. Some of the interesting results of this work
indicate that 70% of the objects have a length greater than 5 in.
Also, half of the total weight of metallics, mostly cans, occurred
in the 3- to 5-in. range and accounted for 40% of the refuse in
this range. Approximately 94% of the bottles remained intact,
caused a peak in the 5- to 10-in. range, and made up 38% of the
refuse in this range. Further, paper objects predominated in the
size range greater than 12 in. This material was estimated to
have a high recycle value.
Both the composite and component size distributions of raw
refuse have been reported by Ruf (8). His samples averaged from
4.7 to 16.5 Ib and were obtained from the Gainesville, Florida,
compost plant. This work used the random collection and a
quartering procedure. In his thesis, Ruf presents an extensive
review of sample selection and screening procedures. The results
of his work for raw refuse size distributions are given in
Figure 21.
The raw refuse size distribution can be compared to that ob-
tained by Wilson and at the Richmond Field Station laboratory (Fig-
ure 41 p.74). Those given by Wilson fall in a larger size range
than the Richmond and Gainesville data. Also, the Wilson data
are approximately linear on a log-log plot of percent passing
versus screen size, whereas, the other data tend to be more sig-
moidal in character. These differences may have arisen because
the Richmond and Gainesville data may be more representative of
domestic packer truck refuse or the geographic variation of the
waste stream.
SHREDDED REFUSE
After the raw waste stream has been processed through a
comminution device such as a hammermill, its size distribution
will be reduced by several orders of magnitude. At this point,
expedient characterization must be by mechanical means rather
than hard measurement. As mentioned previously, sample size
36
-------
100
0
Figure 17
5 10 15
LENGTH (in.)
Cumulative Weight (% Raw Refuse
Total) of Objects With Longest
Dimension Greater than Given Lengths
100,
h-
x
to 80
5
_i
fe 60
LJ
O
(X
40
20
MIDDLEBURY, VT.
CAMBRIDGE,
MASS.
0
10 15
MESH SIZE (in.)
20
25
Figure 18 Cumulative Weight (% Raw Refuse
Total) of Objects that Will Pass
Through a Square Mesh, Plotted vs.
Mesh Size
37
-------
PAPER
2 5
15 20 >20
§2oo^
H
cn
s
£ o
ioo H
p_.
I
METALS
1
I;****. « ,,1..,
UJ
O
UJ
Q.
100-L
O
>s.
en
UJ
.5
GLASS
25 10 15 20 >20
PLASTICS
25 10 15 20 >20
LENGTHUn.)
CLOTH,
RUBBER,
LEATHER
NONE
2 5 10 15 20 >20
1500-
ALL MATERIALS
25 10 15 20 >20
LENGTH (in.)
TOTAL.
MIDDLEBURY, VJ.
CAMBRIDGE, MASS.
Figure 19 Number of Objects per Ton of Raw
Refuse vs. Length (Longest Dimension
of Object) for Principal Categories of
Refuse. Total Height of Each Bar Gives
Weighted Average of Cambridge and
Middlebury data, with Relative Contribu-
tions Indicated by Shading. Note
Different Vertical Scales.
38
-------
80-
i«M
>40H
m
20-
0
PAPER
122
25 10 15 20 >20
40
5
CO
20-
METALS
15
.
25 10 15 20 >20
GLASS
25 10 15 20 >20
PLASTICS
0
25 10 15 20 >20
LENGTH (in.)
8-1
CLOTH,
RUBBER.
LEATHER
25 10 15 20 >20
FOOD
WASTES
25 10 15 20 >20
ALL
MATERIALS
25 10 15 20 >20
LENGTH (in.)
TOTAL
MIDDLEBURY, VT.
CAMBRIDGE, MASS.
Figure 20 Total Weight per Ton of Raw Refuse of
Objects in Given Length Ranges for
Principal Categories of Refuse. Note
Different Vertical Scales.
39
-------
100
*>.
O
SAND
AND
ROCK
J- FERROUS
NON-FERROUS
GARDEN
X
FOOD
COMPOSITE
0.02
PARTICLE SIZE (in.)
Figure 21 Cumulative Distributions of
Raw Waste
-------
determination and screening procedures have been established for
characterizing homogeneous brittle materials such as ores, coal
etc. Shredded refuse, having only 25% brittle materials, poses'
certain additional problems in performing a size distribution
analysis. The general area of screening materials has been
reviewed in the thesis of Ruf (8). Details of sample size, sample
preparation, screening times, peculiarities of various screens,
etc. are given. In addition, Ruf elaborates on the fact that
sieves classify particles according to geometric similarity
regardless of the density and that both the shape of the particles
and the shape of the openings affect the size of the particle that
can pass through a given opening. The probability that a particle
will present itself at an aperture depends on a number of factors,
including the particle size distribution of the material, the
number of particles on the sieve, the physical properties of the
particles, the method of shaking the sieve, the dimension and
shape of the particles, the geometry of the sieving surface (open
area/total area), etc. In addition, the distribution given by
the sieving operation also depends on the duration of sieving,
the variation of sieve aperture, wear, errors of observation and
experiment, errors of sampling, effects of different equipment
and operations, etc. These factors suggest that there may be
doubt in comparing the size distribution results obtained in
various laboratories that follow widely differing procedures.
DISTRIBUTIONS OBTAINED AT THE CAL WASTE PROCESSING FACILITY
Extensive size distribution measurements of shredded refuse
were made as a part of the comminution studies conducted at the
University of California, Richmond Field Station laboratory. The
details of the shredding and screening procedure are summarized
as follows: Refuse was loaded onto the feed conveyor with a
tractor loader. After some experimentation, a feeding procedure
was established that produced a relatively constant feedrate. It
is important to note that since feedrate is one of the comminution
parameters, it must be known and controlled when the effects of
other parameters are being determined. Thus size distributions
must be reported for a feedrate as well as in terms of the other
comminution parameters if they are to be completely meaningful.
In our experiments, feedrate control was achieved by having the
loader-operator concentrate on picking up the same volume of
material each time, dumping the bucketfuls side by side on the
belt, and using a mirror and levelling board on the conveyor.
A value for feedrate is determined by weighing a size-reduced
sample from a 3-ft section of the discharge conveyor. This was
chosen as a matter of convenience, since the discharge conveyor
has 4-in. cleats at 36-in. spacings on the belt. Knowing the
sample weight, section length, and belt speed, the feedrate (m)
can be computed as follows:
41
-------
A = sample weight x belt d
section length
Preliminary analyses of size distributions were performed as
a means of determining what constitutes an appropriate sample
size and what effects the various sieving parameters have_on the
size distribution. Initially, measurements of size distribution
were performed by shaking a sample in a series of Tyler standard
screens using a Ro-Tap testing sieve shaker. The sample size for
a given run is a function of the material and the volume that can
fit into the screens. In general, for ground refuse materials,
the sample sizes were on the order of 100 to 200 g. Later, a
Sweco 18-in. rotary screen was used to perform the size distribu-
tion analysis. The side parts on each deck of the screen were
blocked so that all materials were required to remain on their
appropriate screen in the screen deck assembly. In general,; the
sample sizes were larger (on the order of 5 Ib) than those used
with the Tyler screens. Typical screening times were 20 min
with the Tyler screens and 5 min with the Sweco screens.
A moisture loss generally occurs during sieving, which has
an effect on the percent passing a given sieve size. In other
words, it is possible to define the percent passing as either (a)
percent passing equal to the ratio of weight passing over sample
weight before sieving (which reflects the initial moisture content
of the material) or (b) percent passing equal to the ratio of
weight passing over sample weight after sieving (which reflects
the water loss during sieving). Again a correlation of experimen-
tal data requires that the basis on which percentages are calcu-
lated be given. Both methods of analysis have been presented
here for comparison, and a distinction is made between them where
appropriate.
A detailed description of the experimental procedure used in
the field station studies is given below:
1. The hammermill was run at prescribed speeds, and the
freewheeling power was measured by timing a number of
revolutions of the meter disc.
2. The output conveyor belt was run at its fixed speed
of 10 ft/min, and the input conveyor belt was run
at a speed commensurate with the required feedrate.
The raw material was then loaded onto the input
conveyor belt for grinding.
3. The energy measurements were again carried out after
steady state grinding process had been achieved
(usually from 15 to 30 min) and generally were
recorded over a period of 1/2 hr. The actual power
for grinding the material was obtained by subtracting
42
-------
the freewheeling power from the new power measure-
ment. During this time, the feedrates were being
monitored from the discharge end of the grinder.
A steady state is established when approximately
equal and consistent values are obtained over a
period of 1/2 hr for the recorder readings, power
measurements, and weights of product samples taken
from 3-ft sections between the cleats of the dis-
charge conveyor; the values of power and feedrates
must line within the limits given in Table 6.
4. Two samples of the product were taken at different
times from the output conveyor belt. Each sample
was divided into two parts - one part for wet
sieve analysis and the other for dry sieve analysis
and moisture content determination. The part for
the wet sieve analysis was screened immediately
and that for dry sieve analysis was predried
before sieving.
The term "wet sieve analysis" used here is different
from the usual meaning in the terminology of the
sieving process where the material is sprayed with
water in damp screening. In this thesis it is
used to denote the case in which the product to be
screened is not predried but retains its own
moisture from the grinding process.
5. The sieving was done in two stages. The very coarse
and relatively large materials were removed from
the sample by shaking the sample over 4-, 2-, 1-,
and 3/8-in. wire mesh. Weights of the materials
retained on these screens were recorded and included
in the overall size distribution analysis.
6. The undersize from the 3/8-in. sieve was screened
in batches of approximately 200 g on a Ro-Tap
sifter for 20 min using a standard Tyler series
(geometric ratio of 1/2) of sieves from 9,423
microns to 147 microns (100 mesh).
7. Weighings were made on a two-place Mettler balance.
The weight of each fraction was determined by the
difference between sample plus sieve weight and
the weight of the empty sieve. This procedure was
adopted to prevent errors introduced by transferring
each fraction from the sieve to the balance before
weighing.
8. To ensure the proper drying period of the sample
43
-------
TABLE 6. ANALYSIS OF EXPERIMENTAL ERROR: FEEDRATE (TON/HR) ;
Sample mean Standard deviation Coefficient of variation
x a C.V. = a /x
1.20
1.95
2.70
4.20
5.08
9.05
0.1414
0.2828
0.4243
0.4243
0.3889
0.9899
0.1179
0.1451
0.1571
0.1010
0.0766
0.1094
Approximate 95% confidence interval for a single observation,
Feedrate = (Feedrate) (1.0 ± t C.V. )
observed 0.025 average
= (Feedrate) (1.0 ± 0.303)
observed
bC.V. = 0.1178
average
44
-------
for the dry sieve analysis, this sample was
dried under the same conditions as the sample
for moisture content determination in a thermo-
statically controlled, heated room at an average
temperature of 80°F.
9. The moisture content was determined from weighing
the wet sample initially and then subsequently
over a period of time (24 to 36 hr) until no
change in the weight of the sample was not-iced in
consecutive measurements. The percent moisture
content given in this study was computed as
percent moisture = /"(wet weight) - (final dried
weight)_7/wet weight.
Figure 22 shows a typical graph that was drawn
to monitor the moisture content. A sample for
moisture content analysis is split into two
parts; the moisture contents for these parts
are determined independently and the average
value of these results is accepted as a
representation of the condition of the experiment
if these individual results lie within prescribed
confidence intervals. Differences in the
results of 1A and IB arise from incomplete
mixing of the product and also from differences
in the proportions of the various material
components in each part.
10. To study the effect of variations of moisture
content on the grinding of refuse, the feed
was sprayed with water at the inlet of the
hammermill. Different moisture contents for
different runs were obtained by varying the
rate of water supply to the spray (2, 4, and
8 gal/min were found to be adequate to attain
different conditions).
11. The whole procedure from 1 to 10 was repeated
when the product from a primary grinding process
was used as the feed for a secondary grind,
and also when the product from a secondary
grinding was the feed for a tertiary grinding
process.
12. The precision of sieving was determined by
splitting the primary product from preliminary
grinding of raw packer truck refuse into 10
portions and sieving these as described above.
The sample means and standard deviations and
coefficients of variation were determined for
45
-------
SPRAY
WATER
gol/min
FINAL
MOISTURE LOSS
40.45
39.13
45.64
43.93
20 30 40
DRYING TIME (hours)
50
60
Figure 22 Moisture Content Analysis.
Loss vs. Drying Time
Percent Moisture
46
-------
the nine size fractions - 2-in., 1-in., and
1 x 2, 3 x 4, 6 x 8, 10 x 14, 20 x 28, 35 x 48,
and 65 x 100 mesh.
The overall precision of experiments was prelim-
inarily estimated by conducting six independent
experiments under the same conditions. The
data for these experiments were pooled to obtain
estimates of overall sample means and variances.
For example, we notice that the coefficient of
variation does not depend strongly on the mean
moisture content with which it is associated;
that is, they are all of the same order of
magnitude. Thus it is reasonable to approxi-
mate the coefficient of variation for all
moisture contents by the mean value of the seven
moisture contents examined, C.V. average.
Similar averages can be used for particle size,
feedrate, and power consumption.
Some typical size distribution results are presented for
representative grinding conditions in Figures 23-28. These
curves show a downward concavity for primary, secondary, and
tertiary grinding products. In addition, plots of ln(l/l-Y)
vs. sieve size for the dry analysis indicate that these size
distributions conform to the Rosin-Rammler distribution equation
(Figure 29) . The average value of the index n of the Rosin-
Rammler equation for the size distributions of the primary
grinding was found to be 0.99 (with a standard deviation, a =
0.13), and 0.87 (with a = 0.07) for secondary grinding, and 0.75
for tertiary grinding. The corresponding average values of the
characteristic particle size, x (size at 63.2% cumulative passing)
for the primary, secondary, and tertiary grindings were 0.61,
0.33, and 0.23 in., respectively.
The graphs for the wet sieve analysis show a similar shape
to those of the dry sieve but have greater slopes in the smaller
size range. The differences between the curves for the two
analyses can be explained by the fact that, in the wet analysis,
some of the smaller particles agglomerate with the bigger ones.
This gives a higher percentage of retained weight on the bigger
sieves and smaller values for sieves with small openings.
Moisture losses during sieving of the wet samples also contribute
to the differences between the results of the two analyses.
DISTRIBUTIONS OBTAINED AT. MADISON
A project demonstrating the use of shredded refuse in land-
filling was initiated by the EPA at Madison, Wisconsin, in 1966
(2) . The shredding facility contains both a horizontal and a
vertical hammermill. The former is a Gondard mill with free
47
-------
295 589
SIEVE SIZE (microns)
1168 2362 4699 9423
25x10 5lx|pv
PRIMARY GRINDING
MOISTURE CONTENT -22.0%
FEED RATE
ton/hr
DRY ANALYSIS
WET ANALYSIS
4.1 (dry)
5.3 (wet)
0.001
0.01
SIEVE SIZE (inches)
Figure 23 Product Size Distribution for the
Primary Grinding of Municipal Refuse
with 22.0% Moisture Content
48
-------
UJ
M
cn
Q
UJ
?
cn
•z.
QC
Ul
LL
O
h-
o
tr
u_
UJ
_
ID
O
295 589
SIEVE SIZE (microns)
1168 2362 4699 9423
25x10 5UICT
0.001
PRIMARY GRINDING
MOISTURE CONTENT-40.4%
FEED RATE
ton/hr
DRY ANALYSIS
O WET ANALYSIS
0.01
0.01
1.0
SIEVE SIZE (inches)
Figure 24 Product Size Distribution for the Primary
Grinding of Municipal Refuse with 40.4%
Moisture Content
49
-------
UJ
M
cn
Q
LU
i
z
<
X
a:
UJ
o
o
cc
U.
UJ
15
o
295 589
SIEVE SIZE (microns)
1168 2362 4699 9423
25*I03 5UI03
0.001
PRIMARY GRINDING
MOISTURE CONTENT-55.3 %
FEED RATE
(ton/hr)
50 (dry)
35 (wet)
• DRY ANALYSIS
O WET ANALYSIS
0.01
0.01
.0
SIEVE SIZE (inches)
Figure 25 Product Size Distribution for the Primary
Grinding of Municipal Refuse with 55.3%
Moisture Content
50
-------
.295 589
SIEVE SIZE (microns)
1168 2362 4699 9423
NJ
o
LoJ
1-
O
0.001
SECONDARY GRINDING
MOISTURE CONTENT - 21.0%
FEED RATE
ton/hr
("2.7 (dry)
I 3.4
DRY ANALYSIS
WET ANALYSIS
0.01 —
0.01
SIEVE SIZE (inches)
Figure 26 Product Size Distribution for the Secondary
Grinding of Municipal Refuse with 21.0%
Moisture Content
51
-------
LU
M
Q
LU
cn
(T
LU
Z
o
h-
o
tr
u.
LU
H
_i
r>
2
O
1.0
295 589
SIEVE SIZE (microns)
1168 2362 4699 9423
25x10° 51x10*
O.I
0.01
0.001
SECONDARY GRINDING
MOISTURE CONTENT -19.6 %
• DRY ANALYSIS
O WET ANALYSIS
FEED RATE
ton/hr
6.60 (dry)
8.25 (wet)
J L
J—L
0.01
O.I
SIEVE SIZE (inches)
1.0
Figure 27 Product Size Distribution for the Secondary
Grinding of Municipal Refuse with 19.6%
Moisture Content
52
-------
UJ
N
cn
Q
LL)
I
I-
QC
111
h-
O
I-
-------
SIEVE SIZE (microns)
295 589 1168 2362 4699 9423 25xl03 5lxl03
>-
i
0.001
MOISTURE CONTENT
19.6% 22.0%
PRIMARY
SECONDARY
TERTIARY
0.01 —
0.01
O.I
SIEVE SIZE (inches)
Figure 29 Plot of In . 1 vs. Sieze Size for Primary,
II-Y'
Secondary, and Tertiary Grinding of Municipal
Refuse
54
-------
swinging hammers and a bottom grate. It operates at 8 tons/hr,
150 hp, 1,200 rpm, and at 12 Kwh/ton milled. The vertical
machine is a Tollemache with no retaining grate to control particle
size and has the following operating data: 15 tons/hr, 200 hp,
1,300 rpm, and 7 Kwh/ton milled. The composition of the raw waste
stream at Madison is given in Table 7.
The results of the size distribution of shredded refuse
processed at the Madison facility have been reported by Gawalpanchi,
Berthouex and Ham (16). In their work, a standard U.S. sieve
series was used to analyze dried, shredded refuse. This sieving
procedure involved the use of 7-lb samples dried in 200-g lots
to a constant weight for 18 to 24 hr at 104°C, and sieved in a
13-sieve column in 60- to 100-g batches. They tested the accuracy
of sieving with hand ruler measurements and found that discrepan-
cies can occur in the size range of particles larger than 1/2 in.
The shaking time was on the order of 100 to 125 shakes, or about
2 min. Comparative tests performed on the method of shaking the
sieves showed that the shaking motion was unimportant. In general,
they found sieving reproducibility to within the estimated variance
because of experimental error of 3.82%, and accuracy of the esti-
mated mean percentage of material passing a sieve to within
approximately 2%. Their conclusion is that the simple sieving
method is sufficiently accurate to serve as a tool to evaluate
operational factors. Typical size distribution data from the
Madison site are given in Figure 30.
DISTRIBUTION OBTAINED AT GAINESVILLE
Results of the size distribution of refuse shredded at the
Gainesville, Florida, composting plant are reported in the thesis
of Ruf (8). This plant was constructed in 1967 and began
processing municipal refuse the following year. The facility has
TABLE 7. COMPOSITION OF MADISON'S SOLID WASTE,a NOVEMBER 1968
(% wet weight basis)
Category Minimum Maximum Average
Food wastes
Garden wastes
Paper products
Plastics, rubber, leather
Textiles
Wood
Metals
Glass , ceramics
Rock, ash, etc.
4.4
0.0
35.1
0.3
0.1
0.0
5.0
4.4
0.6
28.9
31.1
53.2
3.7
7.8
2.6
14.5
17.6
17.6
15.3
13.8
42.4
1.8
1.6
1.1
6.7
10.1
7.2
Determined by Federal solid waste management personnel.
55
-------
primary and secondary Williams swing hammer hammermills rated
at 30 and 20 tons/hr, respectively. Each machine has a 400-hp
motor directly coupled to the rotor shaft with a flexible coupling.
The grate openings in the primary shredder were 4 1/2 x 8 in. for
the grate box near the breaker plate and 12 x 8 in. at the opposite
end. In the secondary shredder, the grate spacing was 3 1/2 x 10
in. throughout, and each grate box had six openings. The breaker
plates in these machines were periodically adjusted to the point
of nearly touching the hammers. The typical waste stream composi-
tion is given in Table 8. About 10% of the incoming waste was
manually removed as bulky materials before shredding. This
included such items as mattresses, sofas, tires, large pieces of
wood, heavy metal and appliances, etc.
As part of his thesis, Ruf (8) surveyed the various types of
screens and considered their suitability for analyzing shredded
refuse. He selected the Gilson mechanical testing screens (Model
No. CL-325) from Soil Test, Inc. This machine holds six screen
trays and the dust pan simultaneously. The screens are stacked
vertically, 4 in. apart, with a clear space of 1 3/8 in. between
them for observation. The screens operate with a vertical
agitation and a 7/16-in., 10-cycle/sec oscillation. The test
samples ranged from 2 to 8 lb, and screening time was about 5 min.
In addition, some particles in the 2- to 4-in. range were tested
by hand to see if they would fit through the openings. The
detailed procedures used by Ruf are given in his thesis. He
considers the effect on the size distribution of a host of screen-
100
o
to 80
UJ
tsj
CO
60
CC
UJ 40
a:
UJ
CL
20
0
•AUG., SEPT.
-DEC.2
10
O.I
0.01
MESH SIZE (in.)
Figure 30 Typical Particle Size Distributions for
Milled Refuse from both Mills in 1972
56
-------
TABLE 8. SUMMARY OF REFUSE COMPOSITION AT GAINESVILLE, FLORIDA
Refuse category
Weekly average
Range , % %
(wet wt. basis) (wet wt. basis)
Food waste
Garden waste
Paper products
Salvageable3
Cardboard
Other
Nonsalvageable
Plastic, leather, rubber
Textiles
Wood, limbs, sawdust
Miscellaneous combustibles
Metal
Ferrous
Nonferrous
Glass and ceramic
Ash, earth, rock, etc.
0.31 -
0
22.69 -
1.43 -
0
0
8.94 -
0.26 -
0
0
0
0.33 -
0.26 -
0
0
0
21.96
55.19
91.55
63.18
57.45
26.13
48.90
21.94
7.31
29.11
5.39
20.51
20.26
2.42
19.12
27.60
5.23
12.71
49.65
23.64
14.95
8.69
26.01
4.61
1.61
6.20
0.30
8.04
7.44
0.60
7.06
4.59
Total
100.00
aAs used here, the term "salvageable paper" refers to those
pieces of paper that appear to.be large enough, dry enough, and
clean enough to be separated at the sorting platform for
subsequent sale.
ing variables, which include screening time, overloading the
screens, screening efficiency, etc. He further undertook component
classification studies in which the screened fractions were
classified into 13 different categories. The size distribution
results of this work are given in Figures 31 and 32 for primary
and secondary shredded waste, respectively. Ruf also analyzed
primary shredded waste from the Don-Oliver Rasp located at the
Johnson City, Tennessee, compost plant. This machine has a rasp
that revolves at 8.3 rpm, is designed for 10 tons/hr, is driven
by two 40-hp motors, and passes material through a perforated
plate grate with 1 1/4-in. openings. The size distribution
results for the rasped waste are given in Figure 33.
57
-------
100
U1
00
.
MISCELLANEOUSV'-..
FERROUS '7... __
I i i i i i i i i I i Pr-i"-i-7cT!
20 15 10
I O.I
PARTICLE SIZE (in.)
0.02
Figure 31 Cumulative Distributions of
Primary Waste
-------
100
en
\\
FERROUS:
•. \
TEXTILES
20 15 10
O.I
0.02
PARTICLE SIZE (in.)
Figure 32 Cumulative Distributions of
Secondary Waste
-------
100
2 80
.5*
'5
DC
UJ
UJ
o
a:
20
CARDBOARD
PLASTIC
TEXTILE
WOOD
NON-FERROUS
GLASS
i i i i I I
•-.. ^<*.
i i i i l i "\ f
20 15 IO
I
PARTICLE SIZE (in.)
O.I
0.02
Figure 33 Cumulative Distributions of
Rasped Waste
-------
RECOVERY SYSTEM COMPONENT SIZE DISTRIBUTIONS
Although data have been presented that deal with the shredded
waste stream component size distribution, this may not be entirely
useful to predicting the material flow characteristics of a
resource recovery operation. As a means of aiding the clarifica-
tion of this problem, the component size distributions, after each
stage of processing in a typical front-end recovery system, were
studied in the Cal Recovery System. The light fraction recovered
in this process is suitable for use in a fiber recovery process
or for use as a refuse-derived fuel. The description of the
system has been given previously. Briefly, the resource recovery
system consists of a horizontal swing hammermill, air classifier,
and rotary cylindrical (trommel) screen for screening the air-
classified light fraction and is capable of handling a throughput
of up to 2,722 kg/hr (3 tons/hr) on a continuous basis. The
shredded refuse is fed by conveyor into a vertical air classifier.
The heavy fraction falls to the bottom of the air classifier
chamber and is removed by a conveyor. The light fraction is
carried by fan suction through the top of the air classifier and
removed from the air stream by a cyclone separator. A rotary air
lock valve discharges the light fraction from the cyclone onto a
conveyor, which subsequently feeds the trommel screen. The
recovery system has been optimized for recovery of magnetic metal
and glass from the air-classified heavy fraction and paper fiber
from the air-classified light fraction.
Samples of refuse from various stations of the recovery
system have been analyzed for size distributions and composition.
The size distribution analyses were carried out using a Sweco
0.457-m (18-in.) rotary screen. Samples having a weight of 2.3 kg
(^5 Ibm) were screened for 15 min and were subsequently hand
picked to determine sample compositions. Because of the difficulty
of differentiating components at small sizes, no attempt was made
to determine compositions below 14-mesh, 1.3-mm (0.051-in.) screen
opening.
SHREDDED COMPONENT SIZE DISTRIBUTIONS
A comparison of raw and shredded refuse size distributions
(Figure 34) shows that size reduction has the deleterious effect
of increasing the number of particles and the homogeneity of the
product. With an arbitrary cumulative percent-passing range of
1% to 95%, it can be seen from Figure 34 that the overall size
distribution of the shredded refuse spans three orders of magni-
tude - 0.076 mm (0.003 in.) to 76 mm (3 in.). On the other hand,
the size distribution of municipal solid waste as dumped from a
packer truck occupies roughly two orders of magnitude - 2.54 mm
(0.1 in.) to 0.254 m (10 in.). This order of magnitude increases
in the nonuniformity of particle sizes and the added degree of
mixing enhances the randomness of the system of particles and
61
-------
100
o
z
en
en
UJ
o
-------
therefore makes separation more difficult. This consequence
suggests that shredding should be as coarse as possible to main-
tain maximum efficiency in the down-stream separation processes.
Of course, the size distribution must be consistent with the type
of equipment being used in the processing line.
Size reduction of raw municipal solid waste shredded at
1,200 rpm through 63.5-mm x 152-mm (2.5-in. x 6-in.) grate openings
yields the component size distribution shown in Figure 34 as a
log-log cumulative percent passing versus screen size plot. The
major constituents worth recovering, either because of quantity
or economic value (aluminum, magnetic metals, glass, plastic,
and paper fiber), and a miscellaneous fraction called "other"
are shown to occupy distinctive regions of the size spectrum. In
the coarser sizes, the "other" fraction contains leather goods,
rubber, wood, rags, nonferrous/nonaluminum metals, and organic
matter. As seen from the curve, the "other" fraction also
contains most of the finer material (< 14 mesh) - namely, dirt,
lint, and other material unidentifiable to the naked eye because
of its small size. The glass size distribution essentially
exists in the range of 1.3 mm (0.05 in.) to 25 mm (1.0 in.). In
the larger sizes (> 9.5 mm, or 3/8 in.), the glass particles are
flat and perhaps 3 mm (1/8 in.) in thickness. Particles roughly
cubic in shape characterize the pieces less than 4 mesh. The
fiber and plastic fractions tend to be much larger than the glass.
The size distributions of fiber and plastics tend to be similar,
with the latter being slightly coarser. The size distribution of
the fiber fraction is between 2.5 mm (0.1 in.) and 50 mm (2 in.);
for plastics it is between 6.4 mm (1/4 in.) and 76 mm (3.0 in.).
The coarsest products are the ferrous and aluminum fractions.
The aluminum fraction, 6.4 mm to 76 mm, undergoes the least
amount of size reduction, presumably because aluminum is so mallea-
ble . The smaller particles of aluminum are generally flat and
irregularly shaped. The larger particles are mostly the twisted
remains of aluminum cans. The ferrous materials exist in the
range of 5 mm to 76 mm. As with the aluminum, the finer ferrous
particles are irregularly shaped flat pieces, and the coarser
particles are the larger remains of bar stock, wire, and tin cans.
AIR-CLASSIFIED FRACTIONS SIZE DISTRIBUTIONS
Direct processing of the shredded refuse (whose size distribu-
tion is shown in Figure 34) through a vertical air classifier
produces a "heavy" fraction and a "light" fraction (Figures 35
and 36, respectively). Under optimum conditions for recovery of
paper fiber or a lights fuel fraction, a flow split of 70% lights
and from 30% heavies is typical for raw solid waste moisture
contents in the range of 20% to 30%. Higher moisture contents
reduce the ratio to 60%/40%. Conversely, lower moisture contents
increase the ratio to 85%/15%. Thus, in general, higher moisture
contents tend to produce a higher percentage of heavy fraction,
63
-------
100
en
en
2
UJ
o
DC
tt
UJ
O
0.254
(0.01)
SCREEN SIZE, mxlO'5, (in.)
-3
Figure 35 Component Size Distribution of Air-
Classified Heavy Fraction
64
-------
100
CD
z
en
3 10
Q_
o
oc
UJ
a.
UJ
<
1''°
o
O.I
OTHER
I
I
0.254
(0.01)
2.54
(O.I)
25.4
(1.0)
254
(10)
SCREEN SIZE, mxlO~3,(in.)
Figure 36 Component Size Distribution of Air-
Classified Light Fraction
65
-------
and lower moisture contents tend to result in a lower heavy
fraction. Ideally the heavies fraction would contain the densest
components of refuse such as ferrous, aluminum, other metals,
ceramics, stones, and glass. Practically, however, the heavies
consist of those components just mentioned plus paper, plastics
(other than film), and other materials such as wood splinters,
garbage matter, leather, rubber, and rags. The degree of contami-
nation of the heavies depends on the air flowrate through^the air
classifier, the moisture content of the refuse, and the size
distributions of the various refuse components.
With a 70%/30% split, the density of the heavy fraction is
typically 400 kg/m3 (25 lb/ft3), and that of the light fraction
is 80 kg/m3 (5 lb/ft3). The size distributions for various compo-
nents of refuse after air classification at a 70%/30% split are
shown in Figures 35 and 36. Comparing the size distributions of
the feed (Figure 34) to that of the air~classified heavies
(Figure 35), several conclusions can be drawn. First, the ferrous,
aluminum, and glass (> ~ 10 mesh) size distributions remain the
same after air classification because essentially all these
components report to the heavies fraction. Second, the paper and
plastic particles present in the heavies tend to be the finer
pieces. The coarser particles of paper and plastic tend to be in
the light fraction (Figure 36). Comparison of the "other"
fraction after air classification shows that the coarser particles
fall out with the heavies (Figure 35) and the finer particles are
carried away in the air stream (Figure 36).
The relative amounts of various components of air-classified
solid waste as a function of screen size are given in. Figure 37.
The dark bands represent that portion of a particular component
that falls out with the heavy fraction. The remaining (or light
bands) material reports with the light fraction. The potentially
recoverable materials - ferrous, aluminum, and glass - account for
62.6% of the heavy fraction. Paper fiber represents 60.2% of the
light fraction, with plastic and other material accounting for the
remaining 39.8%. Table 9 presents a detailed breakdown of the
heavy and light fractions of air-classified shredded solid waste.
SCREENED LIGHT FRACTION SIZE DISTRIBUTION
Further treatment of the air-classified light fraction
employing a rotary cylindrical (trommel) screen results in a
screened light fraction usable in a fiber recovery system or as
refuse-derived fuel. Size distributions of oversized and under-
sized material obtainable using a 9.5-mm (3/8-in.) wire mesh trom-
mel screen are shown in Figures 38 and 39, respectively. As shown
in Table 10, the +9.5-mm material essentially contains paper fiber
(78.8%), plastics (7.8%), and other material such as hair, string,
wood, etc. (13.4% by weight). The -9.5-mm fraction is composed
of 78.7% other material (dirt and glass fines, string, lint,
66
-------
tr
UJ
CD
20
18
16
•- 14
0) '^
12
O
LL
O
I-
Z
UJ
O
DC
UJ
Q.
10
8
0
HEAVY FRACTION I
LIGHT FRACTION D
+1.6 +0.95 +0.51 +0.28 +0.13 -0.13
(+5/8) (+3/8) (+0.20) (+0.11) (+0.05) (-0.05)
SCREEN SIZE, m x I0"2,(in.)
Figure 37 Composition of Air-Classified Shredded
Solid Waste - 70%/30% Split
67
-------
TABLE 9. COMPOSITION OF AIR-CLASSIFIED
SHREDDED SOLID WASTE, 70/30 SPLIT
Component
Heavy fraction:
Magnetic metals
Glass
Aluminum
Paper fiber
Plastic
Other
Total
Light fraction:
Paper fiber
Plastic
Other
Total
Weight %
24.2
36.1
2.3
3.6
1.7
32.1
100.0
60.2
5.7
34.1
100.0
organic matter, etc.), 19.9% paper fiber, and 1.4% plastics,
percent by weight. The composition of the +9.5-mm and -9.5-mm
material is shown in Figure 40. Paper fiber dominates each screen
size from +25 mm down to +9.5 mm. Below 5 mm (0.2 in.), dirt,
glass fines, and stringy materials, which compose the "other"
category, dominate the composition of the -9.5-mm fraction.
Elimination of this material enhances fiber or fuel recovery. If
such fine materials were allowed to remain in the light fraction,
serious cleaning and water treatment problems would occur in any
subsequent fiber recovery process. Similarly, these fines would
also lead to scaling, furnace contamination problems, and dilution
of the heating value if the light fraction were used as a refuse-
derived fuel.
68
-------
100
CD
2
CO
en
UJ
O
OL
UJ
Q_
UJ
>
O
.0
O.I
0.254
(0.01)
PLASTIC
I
2.54
(O.I)
25.4
(1.0)
254
(10)
SCREEN SIZE, mxICT3, (in.)
Figure 38 Component Size Distribution of Oversize
from 9.5 x 10~3m (3/8 in.) Trommel Screen
69
-------
100
o
2
CO
CO
Q.
t-
2
UJ
O
DC
UJ
Q.
UJ
O
0.254
(0.01)
2.54 25.4
(O.I) (1.0)
SCREEN SIZE , m x IO'3, (in.)
254
(10)
Figure 39 Component Size Distribution of Undersize
from 9.5 x 10~3m (3/8 in.) Trommel Screen
70
-------
TABLE 10. COMPOSITION OF SCREENED,
AIR-CLASSIFIED LIGHT FRACTION
Component
Weight %
+9.5-mm material:
Paper fiber
Plastic
Other
Total
-9.5-mm material:
Paper fiber
Plastic
Other
Total
78.8
7.8
13.4
100.0
19.9
1.4
78.7
100.0
71
-------
20
18
16
•5 14
Z 12
fe
u_
O
h-
LU
O
QC
10
8
2
0
IT
LU
03
+9.5xlO"3m MATERIAL
-9.5xlO"3m MATERIAL i(-3/8in.)
o
cn
UJ
I
Jl
U.Q.
+2.54
(+1)
+ 1.6 +0.95 +0.51 +0.28 +0.13 -0.13
(+%) (+3/8) (+0.20) (+0.11) (+0.50) (-0.50)
SCREEN SIZE, mxlQ-2, (in.)
Figure 40 Composition of Screen Air-Classified
Light Fraction
72
-------
SECTION 3
BEHAVIOR OF THE COMMINUTION PARAMETERS
Shredder performance can be characterized through the param-
eters that effect the comminution process. In addition, the
capability for control and predictability of the size distribution
of the ground product is vital to the successful performance of
the subsequent stages of processing and can only be achieved
through understanding of the behavior of the comminution variables.
The three quantities that taken collectively characterize
the ability of a particular comminution device to size reduce
refuse are the specific energy consumption (Kwh/ton), the product
size distribution, and the machine wear. In effect, these
quantities are manifestations of the physics of the comminution
mechanisms. The important operating parameters that influence
these three dependent variables are the set of five independent
variables - the feed size distribution, the flow of material
through the device, the moisture content of the materials, the
grate or extraction spacing, and the relative velocities of the
size reduction apparatus in the machine, such as the rpm or tip
speed of the hammermill hammers. The interrelationship between
these variables and their influence on quantities characterizing
a comminution process will be discussed first in terms of their
effect on the product size distribution and then their effect on
the energy consumption.
FACTORS AFFECTING SIZE DISTRIBUTION
The measurement of raw and shredded refuse size distribu-
tions has been considered in a previous section. Since they
characterize the feed and product respectively, both are important.
Even though the size distribution of the incoming raw refuse feed
is a significant variable in the comminution process, it is
perhaps the most poorly measured and least controllable parameter.
It can span a two- to three-order-of-magnitude size range and vary
between successive packer trucks. From the previously discussed
comparison of raw refuse size distributions (Figure 41), a range
of 90% cumulative passing between 12 and 25 in. can be expected.
Furthermore, there is a significant difference between residential
and commercial solid wastes; the latter tend to be bulkier and
have a generally coarser size distribution because of the large
amounts of packaging and cardboard present (approximately twice
as much).
73
-------
lOOr—
2
UJ
O
tr
LU
0-
UJ
O
AVG.790RPM
AVG. 555 RPM
PRIMARY
SECONDARY
TERTIARY
0.01
SCREEN SIZE ( in.)
Figure 41 Size Distribution Comparison for Raw
Municipal Refuse and Residential Refuse
Shredded at 1,200, 790, and 5S-5 rpm.
Effect of Moisture Content (MC) and
Secondary and Tertiary Grinding
-------
Because the product size distribution can be represented
analytically, a semi-empirical predictive theory has been developed
in terms of breakage and selection functions to allow prediction
of the product size distribution for any input feed. Although
this theory can be further used to study the interrelation and
effects of the comminution variables, examination of the size
distribution itself provides useful insights into the behavior of
these variables. Our experience, as well as that obtained at
other shredding installations, indicates that product size
distributions can be represented by a Rosin-Rammler relation of
the type
y(x) = 1 - exp [-(x/xo)n] (1)
where y(x) is the cumulative percent passing screen size x. The
exponent n (sometimes referred to as the n index) is essentially
the slope of the line ln[l/(l-y)J versus x on log-log coordinates.
Also, the value of xo is the size corresponding to 63.2% cumulative
passing or, alternatively, the value of x where ln[l/(l-y)j = 1.0.
It is interesting to note that the individual values of n obtained
for all grinding conditions lie between the limits (0.5 < n < 1.3)
of the values for the grinding of brittle materials in hammermills.
Lower values of n are usually associated with a more scattered
distribution over a wider size range, while higher values of n are
associated with uniform particle structure over a narrow size
range. Also, the Rosin-Rammler distribution physically indicates
that for a particular value of xo, as the value of n increases,
the cumulative percent passing a size x (i.e., [y(x)]) decreases,
a result that can be interpreted as larger size particles or a
coarser product. Operating at 1,200 rpm, values of the character-
istic size (XQ) in the range of 0.6 to 1.0 in. were obtained for
primary grinding. Values previously given for xo and n for
primary, secondary, and tertiary grinding of the product (xo = 0.. 6
to 1.0, 0.33, and 0.23, respectively; and n = 0.99, 0.87, and 0.75,
respectively) indicate that when the number of grinding cycles
increases, the product size distribution shifts toward the finer
sizes and a higher percentage passes at lower sizes. In short,
a finer product is obtained with successive cycles of grinding,
as would be expected (Figure 41).
A study of the effect of comminution speed on the product was
conducted by operating the shredder installed with a belt-pulley
drive system at 1,200 (rated speed), 790, and 555 rpm. For the
case of primary grinding, the resulting product size distributions
for these three speeds (Figure 41) yield values of the n index of
0.81, 0.97, and 0.91, respectively. The respective corresponding
average values of the characteristic particle size (xo) are 0.78,
1.08, and 0.88 in. In general, the decreased speed produces a
coarser product, or, conversely, the higher speeds should yield
a finer product because of a greater number of impacts per unit
time. A definitive differentiation of the product size distribu-
75
-------
tion at the two lower speeds was not possible, suggesting that
when a minimum speed is attained, the speed variable does not
participate in a dominant manner in the overall description of
the comminution process.
It was found that the increase of moisture in the range of
37% to 63% had the effect of producing a coarser size distribu-
tion as shown in Figure 41 for both the 1,200 and 790 rpm speeds.
At a feedrate of 1.8 tons/hr (790 rpm) and a moisture content of
25%, the n index has a value of 0.82 in. The effect of doubling
(57%) the moisture content is to increase the values of n and XQ
to 1.06 and 1.1 in., respectively. On the other hand, data
obtained from the Madison facility for a moisture content of 46%
to 92% indicated the opposite trend (Figure 42). The Madison
group (16) indicates that for a given refuse composition, an
increase in moisture content tends to yield a smaller average
particle size and a more uniform size distribution. Two hypotheses
regarding the moisture content effect are advanced by the Madison
group. They claim that certain refuse components, principally
the fibrous ones, become weaker when wet and are more readily
torn apart; moisture also increases frictional resistance of the
refuse and thus allows greater shearing forces to develop. It is
important to note that the ability to accurately measure the
size distribution at high moisture contents (around 60%) is
diminished because of coagulation, clumping, and balling of the
shredded material. In the high moisture state, the shredded
refuse product will have a certain size distribution, but after
drying, the size distribution may be considerably different because
of clumping - most noticeably, the shredded paper components.
For these reasons, results of experiments that interpret size
distribution at moisture contents over 60% are not reported here.
In general, it has been found that smaller grate spacings
will produce a finer product size distribution. This has been
demonstrated on the Gondard mill at Madison, which operated with
grate spacings ranging from 3 1/2 to 6 1/4 in. (Figure 43). The
effect of grate spacings on particle size can also be considered
in terms of the characteristic particle size (Figure 44). Here
a trend is established by comparing the data obtained for various
model shredders. Data for St. Louis (17) are not predicted by
this trend, either because of a difference in raw refuse composi-
tion or, more significantly, by the fact that the St. Louis machine
has 3-in.2 grate openings, whereas the others (with the exception
of the Eidel, which does not have grates but an extraction opening
at the bottom) have rectangular grates, with the smallest dimension
occurring perpendicular to the axis of the rotor.
The effect of hammer wear has been studied at the Madison
site (Figure 45). Their experience indicates that a coarser size
distribution results as hammer wear increases. The change is
greatest immediately after installation of new hammers because the
76
-------
$ too
CO
UJ
80
IT
LU
60
40
20
10
46.3%M.C.
-91.5% M.C.
-66.2%M.C. -
I O.I
SIEVE SIZE(in)
0.01
Figure 42 Effect of Moisture Content (MC)
on Particle Size Distribution
OC
UJ
Z
u_
I-
z
UJ
o
cr
UJ
a
100
80
60
40
20
0
•3'/2" GRATE
5" GRATE
61/4 GRATE
10 5
1.0 0.5 O.I 0.05
PARTICLE SIZE (in.)
0.01
Figure 43 Effect of Grate Size on Particle
Size Distribution at Madison
77
-------
7r-
x 4
UJ
5 3
o
z ~
8
Q. -
tn I
UJ
C£
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_ ACTUALLY USED IN
ST. LOUIS
rPREDICTED BY TREZEK
EIDEL 100
HEIL-GONDARD
GRUENDLER
O.I
0.2 0.4 0.6 0.8 1.0 2.0
CHARACTERISTIC PARTICLE SIZE, X0 (in.)
4.0 6.0
Figure 44 Characteristic Particle Size vs.
Grate Spacing
clearance between the hammer tips and the housing is progressively
enlarged, and worn edges do not shred as effectively. The wear
effect on size distribution is described by the Madison data in
terms of an exponential decay with time (Figure 46). Their rela-
tion for percent passing (p) takes the form
(2)
where t is the cumulative tons of refuse shredded since the
installation of new hammers. Furthermore, the Madison group
indicates that hammer wear is a more significant variable then
moisture content in affecting the product size distribution.
FACTORS AFFECTING ENERGY CONSUMPTION
A range of n values from 0.7 to 1.3 resulted from the
previously discussed size distribution analysis. In this range,
it was found that the specific energy consumption was a function
of the characteristic size x only (Figure 47) (18). The zero
energy reference XQ equal to°6.0 in. was obtained from the raw
refuse feed size distribution analysis. These results further
indicate that the specific energy gradient is greater for small
values of xo. For the coarser values of xo, the amount of energy
needed to produce a given percent in xo is less than that required
for a similar amount of size reduction at the finer sizes. For
example, 50% reduction in characteristic particle size from 6.0
to 3.0 in. would require about 2.2 Kwh/ton compared to 6.5 Kwh/ton
78
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100
0.3 O.I
SIZE OF MESH
0.03
0.01
Figure 45 Effect of Hammer Wear on Particle
Size Distribution - Tollemache Mill
100
A MARCH 22-23
O APRIL 7-12
200 400
TONS MILLED
Figure 46 Changes in Particle Size Distribution
as a Result of Cumulative Hammer Wear
79
-------
26
22
o
z
o
h-
CL
z
o
o
o
oc
LU
z:
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18
14
10
i—r-| 1 1—
6RUENDLER HAMMERMILL
I200RPM
1-7 TPH, 19-35% MC
0.7-1.3 n, INDEX
RAW REFUSE
ZERO ENERGY
REFERENCE
O.I
1.0
X0(in.)
10
Figure 47 Specific Energy Consumption to Achieve
a Given Characteristic Particle Size
80
-------
for a similar percent reduction of XQ from 0.6 to 0.3 in.
The specific energy consumption is affected by the feedrate
in the manner shown in Figure 48. As the feedrate increases beyond
2 tons/hr, the energy consumption increases significantly at higher
grinding speeds. At a feedrate of 6 tons/hr, energy savings on the
order of 48% can be realized by grinding at the lower speed of
790 rpm. The penalty is in the resulting coarser size distribu-
tion, which is evidenced by the fact that a 118% increase in
specific energy was needed to obtain a size distribution at 790 rpm
that is nearly identical to that at 1,200 rpm (Figure 49). In this
case, both size distributions were obtained under nearly identical
feedrate and moisture conditions. Specifically, for a dry feed-
rate of 6.4 Kwh/ton, whereas 27.2 Kwh/ton is required for grinding
at 790 rpm to obtain the same size profile. Figure 49 also shows
that a portion of the 555 rpm size distribution coincided with
the 1,200 and 790 rpm distributions at the larger screen sizes.
Thus, less material is contained in the finer size ranges, and
slightly less energy was used (22.4 Kwh/ton) than at 790 rpm.
The finer size distribution obtained at 790 rpm (Figure 49) at
the same feedrate and moisture content required an increase in
specific energy consumption from 10-7 to 27.2 Kwh/ton. Even though
there was a significant increase in specific energy consumption, it
seems somewhat anomalous that two different size distributions can
be obtained under the same conditions of feedrate and moisture
content. The physics of the comminution process determines the
amount of energy required for size reduction. In this case, the
raw refuse size distribution may have been different in each
instance or the physical mechanisms of comminution may have been
different, perhaps because of a difference in refuse composition.
The amount of moisture contained in refuse also has an effect
on the comminution energy consumption. This effect is shown in
Figure 50 for a range of moisture content conditions between 20%
and 60% or feedrates from 1 to 7 tons/hr (dry weight) or from
1 to 13 tons/hr (wet weight). A minimum energy consumption occurs
at moisture contents in the 35% to 50% range. These results are
consistent with the tendency of lower grinding speeds to require
less specific energy consumption and yield coarser size distribu-
tions. Furthermore, these results appear to agree with data
obtained at Madison on the Tollemache mill. Here moisture contents
of 24% and 36% gave specific energy consumptions of 10.9 Kwh/ton
and 8.8 Kwh/ton, respectively. These results lie in our range_of
moisture content where specific energy consumption decreases with
increasing moisture content.
Since the characteristic particle size (x ) of commercial
refuse is two to five times that of residential refuse, the
specific energy consumption required to reduce commercial
81
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00
24
20
I l6
12
6
JC
5
~~l f 1 1 I
— O—I200RPM
—£*— 790 RPM
• PERCENT DECREASE IN ENERGY CONSUMPTION
BY LOWERING SPEED FROM 1200 TO 790 RPM
4
TON/HOUR (D.W.)
50
40
30 I
20 £
10
0
8
Figure 48 Specific Energy Consumption at Different
Grinder rpm (Dry Weight Basis)
-------
100
o
CO
en
g
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o
cc
UJ
CL
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O
10
FEED RATE = 6.4 TPH
J L
0.02
O.I
1.0
SCREEN SIZE (in.)
Figure 49 Influence of Grinder Rotor Speed on
Energy Consumption vs. Size Distri-
bution of Residential Refuse
4.0
83
-------
CO
Q
1200 RPM
•^—790 RPM
5 12-
Figure
30 40 50
MOISTURE CONTENT (%)
50 Effect of Moisture Content on Specific Energy
Consumption for Grinder Rotor Speeds of 1,200
and 790 rpm
-------
refuse, the specific energy consumption required to reduce
commercial refuse to an equivalent residential size distribution
must increase. For example, a comparison between grinding resi-
dential and commercial refuse to nearly the same size distribution
yields energy consumption values of 13.5 Kwh/ton (n = 1.0, xo = 0.9)
and 19-0 Kwh/ton (n = 0.96, xo = 1.1), respectively. This result is
further illustrated in Figure 51.
The correct placement of hammers in certain machines can also
have an effect on reducing the specific energy consumption.
Investigators at Madison report that with the vertical Tollemache
mill, the original 54-hammer configuration could be replaced with
34 optimally positioned hammers, resulting in increased production
and decreased specific energy consumption.
COMPARISON OF SOME COMMERCIAL GRINDERS
The shredded refuse size distributions obtainable from several
commercially available grinding machines are shown in Figure 52.
The relative position of each size distribution is mainly a func-
tion of the grate spacing, or exit clearance dimension, of a
particular grinder. Grinders that produce size distributions at
the finer end of the spectrum consequently have smaller exit
openings. Using the average size distributions obtained from
different grinding machines for size reducing residential solid
waste, a correlation between specific energy consumption and
characteristic particle size (xo) (Figure 53) was established. It
is interesting to note that the data obtained at the St. Louis
facility and analyzed by the Midwest Research Institute are in
excellent agreement with prediction of specific energy consumption
from characteristic particle size.
Observations of the performance of vertical and horizontal
shredders at Madison indicate that for machines of comparable size,
operating under comparable conditions, specific energy consumptions
of 7.2 Kwh/ton and 12.5 Kwh/ton, respectively, were obtained. This
result tends to suggest that horizontal shaft hammermills require
more energy. However, the vertical Eidel machine shows the
highest energy consumption (Figure 53) and correspondingly the
smallest characteristic particle size. Consequently, comparison
of energy consumption of various machine configurations should be
in terms of comparable particle sizes.
85
-------
03
a\
SPECIFIC ENERGY (Kwh/TON) SPECIFIC ENERGY
RESIDENTIAL COMMERCIAL INCREASE (Kwt/TON)
4.O
7. I
8.5
9.0
8.6
I I
1.0 10
SCREEN SIZE (in.)
Figure 51 Comparison of Characteristic Particle Size (XQ)
and Specific Energy for Commercial and
Residential Solid Waste
-------
100-
o
h-
z
Ld
O
CE
LJ
13
O
I 1 I I
El DEL 100
I I
894 RPM
I I T
RABCO GRINDER
GRUENDLER
HAMMERMILL
HEIL GONDARD
HAMMER MILL
J I L
J.
0.01
O.I 1.0
SCREEN SIZE (in.)
Figure 52 Size Distribution of Refuse from
Various Shredders
87
-------
D EIDEL 100
HEIL-GONOARD
GRUENDLER
A RABCO
X0 = 6.0 CORRESPONDS TO
THE ZERO ENERGY REF-
O VALUES OBSERVED
IN ST. LOUIS STUDY
PREDICTED BY
TREZEK
CHARACTERISTIC PARTICLE SIZE, X0 (in.)
Figure 53 Characteristic Particle Size vs.
Specific Energy Consumption
88
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SECTION 4
WEAR, MAINTENANCE, AND SHREDDER SELECTION ASPECTS OF REFUSE
COMMINUTION
Not only do comminution variables play a role in refuse size
reduction, but they also give rise to a number of maintenance or
operational considerations. These factors are usually reflected
in the economics of the size reduction process or, depending on
the accounting procedure, contribute to the cost of feeding
material into the shredder. The following discussion first
considers the question of hammer and grate bar wear and then other
areas that have a bearing on maintenance considerations.
WEAR ASPECTS
Data related to hammer and grate bar wear were routinely
monitored as part of the experimental protocol used in systemati-
cally studying the nature and behavior of the parameters involved
in refuse comminution in our laboratory (19). In essence, the
comminution parameter study involved the collection of a series of
data sets where a particular data set consisted of runs at various
feedrates for each of a specified series of moisture contents all
at a constant grinder speed. Additional data sets were generated
by changing the grinder speed and then repeating the feedrate-
moisture content procedure. After the completion of a data set,
the hammers and grates were removed and checked for wear.
At the beginning of the first data set experiment (1,200 rpm),
8 new, non-hard-faced hammers and 36 face-hardened hammers
(Figure 54) were weighed, identified, profiled on paper, and placed
in the grinder as depicted in Figure 55. All the new hammers were
placed in the same row so that a representative wear pattern could
be established for the new hammers. Opposing rows of hammers were
carefully balanced to eliminate dynamic imbalance while the grinder
was operating. Similarly, the 3-in. grate bars were weighed,
identified, and placed in the grinder. Thus the grinder wear
investigation included the determination of the parent hammer
material and hardfacing material, the material loss of the face-
hardened hammers, the non-hard-faced hammers, and the 3-in. grate
bars.
The hammer material was an austenitic manganese steel contain-
ing 12.65 wt. % manganese. Such a steel (commonly called Hadfield's
89
-------
Figure 54 Manganese Steel Hammer with Hard Facing
Weld Material Applied About the Crushing
Face
90
-------
Rows
37 38
39 40
43 44
27 28
29 30
Axis of Rotation
[21 22
9)10
Columns •* AB CD EF GH IJ KL MN OP QR ST UV
Figure 55 Hammer Configuration
-------
manganese steel) is extremely tough and is used in applications
where heavy impact and abrasion are present. The Brinell hardness
ranged from 179 to 209 over the surface of the hammers.
The face-hardening material applied to worn hammers was an
austenitic manganese steel containing 10.5% manganese, 8.14%
chromium, and trace amounts of nickel and molybdenum. This
particular alloy belongs to the 2c subgroup of hard facing alloys
and is used in applications where severe impact (greater than
1,000 ft-lb/in2) and abrasion are encountered. The Brinell hard-
ness of the hard facing welds varied from 321 to 385 over the sur-
face of the weld deposit.
On the average, bare hammers weighed 9,464 g (20.85 Ib) , and
the hard-faced hammers weighed 9,251 g (20.38 Ib). Although there
is no way of accurately determining the amount of hard facing that
was present on the face-hardened hammers, an estimate of about
1 Ib of weld material per hammer seems realistic.
MEASUREMENTS OF WEAR
During the first data set, the hammers and grate bars were
exposed to the processing of 69 tons of municipal solid waste. A
wide range of moisture (17.7% to 62.5%) and feedrates (1.75 to
8.10 tons/hr, wet weight basis) were presented to the wearing
elements in the grinder. Likewise, the hammers and grates during
the second data set were exposed to 50 tons of refuse ranging from
14.8% to 56.7% moisture and feedrates of 1.10 to 11.0 tons/hr.
According to the procedure previously mentioned, at the
conclusion of the first data set, the grinder was disassembled,
and the hammers and grate bars were removed. The individual
hammers were weighed, photographed, and examined for metal failure
and wear. The grate bars were also weighed and examined. The
wear that the hammers and grate bars experienced during each data
set is summarized in Tables 11 and 12.
TABLE 11. HAMMER WEAR
Item
Non-hard-faced
hammers (Ib)
Hard-faced
hammers (Ib)
1,200 rpm Operation:
Max. wt. loss per hammer/ton
Min. wt. loss per hammer/ton
&T7rr T.H- loss per hammer/ton
wt.
790 rpm Operation:
Max. wt. loss per hammer/ton
Min. wt. loss per hammer/ton
Avg. wt. loss per hammer/ton
0.00290
0.00159
0.00245
0.00158
0.00128
0.00138
0.00222
0.00088
0.00155
0.00140
0.00084
0.00106
92
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TABLE 12. GRATE BAR WEAR
Item Amount (Ib)
1,200 rpm Operation:
Total wt. of grates 1,427.0
Total wt. loss 3.6
Wt. loss/ton 0.053
790 rpm Operation:
Total wt. of grates 1,423.4
Total wt. loss 1.7
Wt. loss/ton 0.034
The grate bars in the vicinity of the entering refuse stream
were subjected to the greatest amount of wear. Less wear was
apparent further away from the entering refuse stream. This trend
was evident in the data collected from both experimental sets.
After completion of the first data set, there was evidence
of abrasive wear on the bare hammers. A comparison of the worn
non-hard-faced hammers against their original cast profiles
(Figure 56) illustrates the general rounding of the edges of the
hammers. The majority of the material loss, usually 1/2 to 9/16
in., occurred on the bottom edge of the hammer's crushing face,
whereas the top edge sustained a material loss of about 1/8 to
3/16 in. (Figure 57). This pattern of wear, in which the bottom
edge of the crushing face sustains the greatest amount of material
loss, is consistent with the fact that the bottom edge of the
hammer shreds and crushes the refuse against and through the grate
bars. Some of the face-hardened hammers showed areas of severe
impact. These impacts were marked by gouges, indentations, and
suspicious flat surfaces on and about the crushing face of the
hammers. The worn surfaces of the hard facings were indicative of
abrasive wear, as was the case with the new hammers. A general
rounding of edges and overall smoothness of the hard facing led to
this conclusion. Nevertheless, areas of severe impacts were also
present on some of the hard-faced hammers.
Upon termination of the 790 rpm data set, the hammers and
grates were again subjected to physical examination. The bare
hammers still exhibited the characteristic abrasive wear noticed
in the first data set. As noticed after completion of the first
data set, physical examination of the hammers showed few areas o£
severe impacts. Indications are that impact plays an insignificant
destructive role compared to the abrasive forces at work during the
comminution of refuse.
93
-------
Figure 56
Non-Hard-Faced Hammers After Grinding
70 Tons of Refuse at 1,200 rpm
94
-------
The wear pattern for the hammers used in each data set was
established and exhibited an asymmetric profile about the grinder
centerline. Both hard-faced and bare hammers on one side of the
grinder experienced more wear than those on the other side. This
pattern may be somewhat explained by the procedure used to load
refuse on the input conveyor to the grinder. A front-end loader
dropped refuse over the side hopper wall onto the conveyor belt.
As a result of the restricted movement of the loader bucket, more
refuse may have been dumped onto the near side of the conveyor,
and thus the hammers on this side of the grinder may have sustained
more wear (Figure 58).
This irregular wear of the hammers points out the importance
of feeding the grinder uniformly across its width. Both machine
rotor imbalance and premature hard facing or hammer replacement
are possible penalties for a haphazard or poorly engineered
grinder feeding system.
DISCUSSION OF WEAR PARAMETERS
The above experimental data provide an insight into the effect
of shredding speed on the wearing properties of hard-faced and
non-'hard-faced hammers and the wearing durability of hard facing
under different operating speeds. The important influence of speed
on wear can be evaluated by referring to Table 11. For operation
at 1,200 rpm, based on an average weight loss per hammer for the
face-hardened and non-face-hardened hammers, the latter lost 57%
more material under the same conditions and during the same time
period. Compared to the average material loss of the hard-faced
..
8 16
Figure 57 Summary of Worn Hammer Profiles
95
-------
0.30
v>
§ 0.25
.+M.
O
o
tf)
.o
-------
hammers, the range of increased wear for new hammers varied from
3% to 87%.
If the average weight loss per non-hard-faced hammer/ton of
refuse is extrapolated to a full set of non-hard-faced hammers for
this particular grinder, the estimated hammer weight loss per ton
would be 0.107 Ib/ton. Similarly, for a full set of face-hardened
hammers, the weight loss per ton would be 0.068/ton. Hence the
face-hardened hammers should exhibit about 37% less wear than
hammers that are not face-hardened.
To estimate the actual grinder wear, both the hammer wear and
the wear of the grate bars must be combined. The grate bar wear
expressed in pounds of material lost per ton (0.053 Ib/ton) can be
expected to be about equal to the weight loss per ton for a full
set of face-hardened hammers (0.068 Ib/ton), or roughly half the
weight loss per ton of a full set of non-face-hardened hammers
(0.107 Ib/ton). Therefore, the estimated wear for a grinder
employing non-face-hardened hammers is 0.160 Ib/ton; and for a
grinder using face-hardened hammers, it is 0.120 Ib/ton. Thus
when the total wear of the hammers and grates is combined, face
hardening of the hammers results in 25% less wear in the grinder.
Results at 790 rpm were similar to those at 1,200 rpm; the
hard-faced hammers exhibited less material loss on the average
(0.00106 Ib/ton) than the non-hard-faced hammers (0.00138 Ib/ton).
Based on the average weight loss per hammer, the non-hard-faced
hammers lost 30% more material than the hard-faced hammers under
the same conditions and during the same time period. The range
of increased wear for the non-hard-faced hammers when compared to
the average material loss for the hard-faced hammers varied from
a high of 49% to values that were actually lower than the average
for the hard-faced hammers.
If the average weight loss per ton for non-hard-faced hammers
is extrapolated to a full set of non-hard-faced hammers operating
at 790 rpm, the estimated hammer weight loss per ton would be
0.061 Ib. Similarly, for a full set of hard-faced hammers, the
weight loss per ton would be 0.047 Ib. Hence the hard-faced
hammers would exhibit 23% less wear than hammers that are not
hard-faced.
To estimate the total grinder wear, both the hammer wear and
the grate bar wear for machine operation at 790 rpm must be
combined. The grate bar wear produced at 790 rpm was 0.036 Ib/ton.
The grate wear can be expected to be about half the wear of the
hard-f.aced hammers (0.061 Ib/ton), or about 70% of the wear of the
non-hard-faced hammers. The combined grate bar and hammer wear
for the hammermill equipped with non-hard-faced hammers and operat-
ing at 790 rpm was estimated to be 0.095 Ib/ton. On the other
hand, total wear when hard facing is used is decreased to 0.081
97
-------
Ib/ton. The use of hard-faced hammers would represent a decrease
of 11% in total grinder wear.
SIGNIFICANCE OF LOWER OPERATING SPEED
A definite reduction in hammer wear occurred while operating
at the lower grinder speed of 790 rpm (Figure 58). The decrease
in material loss was apparent in both non-hard-faced and hard-
faced hammers. On the average, hammers with hard facing exhibited
a decrease of 31% in material loss when the grinder speed was
reduced from 1,200 rpm to 790 rpm (Table 13). At the same time,
the bare hammers showed a 43% reduction in material loss. Grate
wear also decreased by 36% as a result of operating at the lower
speed.
At 1,200 rpm, the non-hard-faced hammers lost 57% more
material than the hammers with hard facing, and at 790 rpm, the
bare hammers lost 30% more material than their face-hardened
counterparts. Thus there was a reduction in the performance of
hard-faced hammers with respect to bare hammers of approximately
50% when the grinder speed was reduced. This finding indicates
that at lower grinder speeds, expensive hard facing may be
unnecessary, and that a less expensive material applied less
frequently would appear to be a beneficial alternative.
Perhaps the most significant finding of this study involves
the tempering of the wearing mechanisms on the non-hard-faced
hammers through a reduction in operating speed. As Table 13
shows, the average hammer wear for bare manganese steel hammers
at 790 rpm is 10% less than that for hard-faced hammers whirling
at 1,200 rpm. This fact along with knowledge that the non-hard-
faced hammers exhibited a decrease in wear of 43% point to the
adoption of lower grinding speeds for the size reduction of
refuse. Reduction of machine speed would appear to present a
viable alternative to the costly and time-consuming maintenance
required for hard facing grinder hammers.
At the reduced rpm, there was a slight shift in the size
distribution towards a coarser product and a decrease in energy
consumption that varied with feedrate. This is mentioned in
passing to indicate that the reduction in speed from 1,200 rpm
to 790 rpm had no significant effect on grinding efficiency or
throughput capacity.
WEAR INFORMATION FROM VARIOUS SHREDDING FACILITIES
Though there is a general paucity of quantitative wear data,
the operation of some shredding facilities over the past decade
and the establishment of new facilities for energy and material
recovery offer the potential for alleviating this situation. The
98
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TABLE 13. AVERAGE WEAR FOR HAMMERS AND GRATE BARS AT DIFFERENT
GRINDER OPERATING SPEEDS
Average wear % Decrease in
(Ib/ton) wear at
Item 1,200 rpm 790 rpm lower speed
Full set of
hammers
Full set of
hard-faced
non-hard-
0.
0.
068
107
0
0
.047
.061
31
43
faced hammers
Grate bars
0.
053
0
.034
36
correlation of wear data is hampered by the fact that standard
procedures for measuring and evaluating wear are not used in the
industry. In some cases, wear is simply measured as the length
of hammer recession or the number of inches of hammer tip lost
after a certain number of tons of refuse have been processed.
Some specific information regarding the amount of metal removal
revealed the following facts: a) Correspondence with Mr. L.C.
Herbert, Director, Municipal Machinery Ltd., Kent, England,
manufacturers of the Gondard equipment, indicated that hammers
tend to wear at a constant rate at any one plant. Furthermore,
hammer wear can be expressed as 0.5 Ib of hammer material/10
tons of refuse when the plant averages 1,500 tons/set of 48
hammers. Also of interest is his suggestion that hammer retipping
may not necessarily be in the best economic interest. Principally,
the custom of adding weld material or tipping was adopted as a
means of keeping large rotors in balance once wear started to
occur. Economics may be more favorable toward replacement rather
than retipping. b) Some data from the Madison project indicated
a hammer material loss of about 0.1 Ib/ton of refuse. Other
information from this site indicates a weight loss/100 tons on
the order of 0.36%. The Madison investigators also question the
idea of using hammer weight loss as the sole criteria for measur-
ing hammer life. The validity of this criticism is somewhat
substantiated by the fact that for some hammer configurations, a
considerable wear or degradation of the cutting surface can take
place with a relatively small loss in weight. In essence, eyen_
though hammers are heavy, a small weight loss may still_result in
a hammer that is considerably less effective. Hard facings have
been reported to increase hammer life by a factor of nearly 5 for
the Gondard mill. c) Some information °\^inding_parameters is
also available in the joint EPA - New Jork City grinding study
conducted on the Jeffrey Swing Hammer B3, 150 hp machine Values
of hammer wear reported as % weight loss/100 tons range from 0 3
to 1.0; a value of 0.8 corresponds to new hammers, and 0.3 to 0.4
99
-------
appear to be more typical of used hammers. Investigators at this
site also indicate that the hammer wear problem is sensitive to
the nature and type of hard facing applied to hammer tips. Severe
problems of rotor imbalance occurred as a result of rapid wear
that was due to the loss of hard face material.
In summary, our wear measurements of 0.068 Ib/ton and 0.107
Ib/ton for hard-faced hammers and 0.047 Ib/ton and 0.061 Ib/ton
for non-hard-faced hammers operating at 1,200 and 790 rpm,
respectively, indicate that the range of 0.05 to 0.10 Ib/ton (or
in some cases slightly higher - 0.30 Ib/ton) can be expected for
haramermills shredding refuse.
HARD FACE COATINGS
Research into the area of hard facing has produced several
avenues that could lead to improved life for grinder hammers. A
base hammer material of an austenitic manganese steel appears to
be the best choice among materials that could be considered for
use in refuse grinding applications. Its toughness and abrasive
resistance makes this steel a logical choice for the combined
effects of abrasion resulting from glass, dirt, and paper, and
of impact that is due to the presence of concrete, metal, etc.
in refuse.
There are basically five groups of hard facing alloys. Each
group has a given resistance to impact, abrasion, erosion,
corrosion, and heat. Cost, ease of application, availability,
compatibility with the base hammer material, abrasion, and impact-
resistant properties of the weld material must all be considered
when determining which hard facing alloy will give the most
economical and best wearing service. As mentioned earlier, our
hammers are coated with a typical Subgroup 2c alloy (basically
impact resistant, but good abrasion resistance). Insofar as
abrasion may be the predominant wearing process in the size
reduction of solid waste because of the cumulative weight per-
centages of glass and paper (65% to 80%) in refuse, an abrasion-
resistant alloy with good impact-resistance qualities may prove
to be the best choice among alloys. Moving up to a Group 3 or 4
hard facing alloy would increase the abrasion resistance of the
hammers, but it would also cost more. The cost of the hard facing
material ranges from $0.50 to $9.00/lb over the span of the five
hard facing groups. Group 3 or 4 alloys cost $5/lb; Group 5
alloys, the hardest and most wear-resistant of all hard facing
materials, cost $9/lb.
Since physical examination of the worn hammers indicates that
hammer wear is primarily abrasive and not representative of wear
resulting from continual impact, hard facing alloys in Groups 3f
4, or 5 may substantially increase hammer life. However, experi-
mentation would be necessary to determine if the increased life
100
-------
was worth the cost of these more exotic abrasion-resistant
alloys. A Subgroup 2c alloy yielded 57% longer life at 1,200 rpra
and 30% more life at 790 rpm; a Group 3, 4, or 5 alloy could
conceivably result in a 100% to 150% longer life.
Various hard facing alloys are compatible with a manganese
steel base material (Table 14) . It should be pointed out that the
application of the hard facing to a manganese steel requires care
in welding. Manganese steel is unusually sensitive to reheating.
Embrittling, transformations, or carbide precipitation resulting
from heating can drastically reduce the characteristic toughness
of the parent material. To prevent this undesirable effect,
properly handled electric arc welding is necessary.
GRINDER MAINTENANCE
This discussion will focus on vertical and horizontal hammer-
mills since these compose the majority of size reduction machines
used in solid waste processing. Grinding maintenance can be
broken down into two general areas: 1) rebuilding or replacing
internal grinder parts (i.e., hammers, breaker bars, breaker
plates, grates, wear plates, etc.); and 2) servicing the grinder
drive system (i.e., grinder and motor bearings, couplings, etc.).
The latter maintenance area requires a diligent servicing schedule
with frequent inspections of the critical drive components,
particularly the rotor bearings. For all components of the drive
assembly, manufacturer's maintenance instructions should be
conscientiously followed. Preventive maintenance significantly
reduces the risk of premature failure of drive train components.
For example, a premature rotor bearin'g failure can take days
or weeks to properly diagnose. After diagnosis, proper remedial
action must be taken or the bearing may destructively fail.
Unfortunately, most bearing failures are terminally diagnosed.
That is, destructive failure occurs before any prior warning of
imminent failure is noticed (e.g., increased operating temperature,
unusual noise, etc.).
The replacement of a rotor bearing is usually a very time-
consuming operation. Besides tearing down the grinder, examining
the old bearing, and locating a replacement, the cause of the
failure must be discovered. These operations usually shut down a
shredding operation for 3 to 5 days. Obviously, the need for
proper drive train component maintenance is very explicit.
Both rebuilding and replacement of the grinder's internal
wear surfaces are accepted practice. Although each grinder and
its mode of operation should be considered separately, experience
has generally pointed toward some degree of hammer resurfacing
(retipping) as being the preferred hammer wear maintenance
technique.
101
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TABLE 14. SUITABILITY OF HARD FACING COATINGS FOR VARIOUS BASE MATERIALS
Facing alloys
Iron-base
Base material to
be hard faced
Cobalt
To 20% alloy Above 20% base
Tungsten carbide
Nickel
base Inserts Deposits
Carbon steels:
0.10 to 0.35% C
0.35 to 1.0% C
Yes
Yesa'b
Yes Yes
Yesa'b Yesa'b
Yes Yes Yes
Yesa'b Yesa'b Yesa<
o
NJ
Low-alloy structural
and constructional
steels; 0.30% max C Yes
Gray, malleable and
nodular irons Yesb'c
Yes
Yes
Yesb'c Yesb'c
Yes
Yes
Yes
Yesb/c Yesb'c
Low-hardenability
martensitic stain-
less (410,403) No
High-hardenability
martensitic stain-
less (420,440) No
Yesa'f Yesa'f Yesa'f Yesa'f Yesa'f
Yesa'c/f Yesa'f Yesa'f Yesa'f Yesa'
-------
TABLE 14 (Continued) . SUITABILITY OF HARD FACING COATINGS FOR VARIOUS BASE MATERIALS
o
u>
Facing alloys
Iron-base
Base material to
be hard faced
Type 321 austenitic
Type 347 austenitic
All other type 300
austenitic
Monel
Nickel
13% Mn steels
To 20% alloy
No
No
No
No
No
Yese
Above 20%
Yesc
Yesc
Yesc
Yesc
Yesc
Yese
Cobalt
base
Yesd
Yes
Yes
Yes
Yes
Yese
Nickel
base
Yes
Yes
Yes
Yes
Yes
Yese
Tungsten carbide
Inserts
Yes
Yes
Yes
Yes
Yes
No
Deposits
Yes
Yes
Yes
Yes
Yes
Yese
^Preheat.
'••'Gas welding preferred.
GFor limited applications only.
<%se type 347 interlayer.
eUse nickel-base interlayer.
fPost-isothermal anneal.
-------
The other components that are subjected to significant wear
are the breaker bars, breaker plates, wear plates, and grates.
Not all of these may be incorporated into the same grinder. These
components generally require replacement or resurfacing with hard
facing during the lifetime of the grinder. Replacement or
resurfacing, as in the case of hammers, is usually process
specific. That is, for a particular shredding operation, conve-
nience and economy dictate which maintenance method (replacement
or resurfacing) is most appropriate.
FACTORS AFFECTING GRINDER MAINTENANCE
Several factors relating to the grinder and drive system can
have a significant impact on the performance of maintenance and
maintenance costs, and these should be considered during the size
reduction facility design phase and before grinder selection.
Since wear of the internal grinder components is inherent in
the grinding process, consideration should be given to grinders
that allow easy accessibility to the parts subjected to wear
(e.g., hammers, grates, wear plates, etc.). Grinders that possess
this accessibility feature will provide reduced maintenance costs
for replacement or resurfacing as opposed to grinders that do not
provide easy accessibility.
Hydraulic or pneumatic systems that open -up or separate the
grinder housing eliminate the need for overhead or portable cranes
to disassemble the machine. Walkways and scaffolding built around
the grinder allow workmen to move freely about and service the
machine. In addition, sufficient headroom (above and below) and
clearance around the other equipment should be incorporated into
the design and layout of the grinder and its ancillary equipment.
Last, the necessary clearance for part removal (e.g., hammer pins,
grate bars, etc.) must be contemplated early in the design phase.
Since a rotor bearing replacement can be a time-consuming
operation, a grinder that possesses easily accessible bearings is
preferable over one that requires complete dismantling of the
machine to free the bearings. In this regard, a horizontal mill
may prove more convenient than a vertical mill. Removal of the
bottom bearing(s) in a vertical hammermill usually requires dis-
assembling the grinder and pulling out the rotor and hammers
assembly.
MAINTENANCE COSTS
The prediction of hammermill maintenance costs is a very
nebulous area. The costs are highly dependent on a number of
factors. Some of the more important of these are:
1. Grinder model,
104
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2. Composition and size distribution of the raw refuse
3. Hammer tip speed, '
4. Type of hardfacing,
5. Retipping schedule,
6. Part replacement schedule.
Because of the multiplicity of variables, two identical grinders
operating under slightly different conditions (e.g., at different
tip speeds or with different weld material as the hardface) can
have significantly different maintenance costs. Most grinder
manufacturers are very reluctant to forecast specific maintenance
costs because of the unknown nature of the actual grinder opera-
tion and maintenance program.
Some manufacturers, however, have suggested a range in
maintenance costs of $0.25 to $0.75/ton of refuse. Interest-
ingly, the Madison hammermills, a Gondard mill, and a Tollemache
mill had maintenance costs of $1.27/ton and $0.98, respectively.
The Gainesville primary hammermill experienced maintenance costs
of $0.76/ton. The Midwest Research Institute (17) estimated
maintenance costs to be a function of hammermill capacity.
Maintenance costs ranged from $0.30/ton for a throughput of
10 tons/hr to $0.70/ton for a throughput of 100 tons/hr.
GRINDER DESIGN AND SELECTION
The previously developed material in this report can be help-
ful in forming a firm background in MSW size reduction principles.
In this section on grinder design and selection, the experimental
results, variable interdependence, and other theoretical develop-
ments of the previous sections will be extended to actual grinding
practice - namely design and selection considerations. Material
presented here should provide the reader with the necessary infor-
mation to 1) extend MSW grinding research data to "practical"
use, 2) esimate the grinder power requirements for desired through-
puts and product sizes, and 3) estimate the grate size required to
furnish a desired size distribution.
Before further discussion, some other factors important in
grinder selection should be considered, even though they do not
involve feedrates, power requirements, and product size distribu-
tions. These factors concern the mill and the services that the
manufacturer will deliver. Due consideration should be given_to
the manufacturer's knowledge and experience in the hammer retip-
ping area. Since hammer resurfacing work contributes significantly
to the total cost of grinder operation, the correct hardfacing
material can generally reduce maintenance cost. Usually the manu-
facturer supplies the mill hammers already hardfaced. Consequently,
a knowledgeable grinder manufacturer can save the grinder operator
money by providing the hammers properly hardfaced. Proper hard-
facing includes selection of a weld material that will provide
105
-------
good wearing characteristics and correct application of the weld
material to the hammer base material. In addition, if in. opera-
tion the hammer wear is unsatisfactory, the experienced manu-
facturer can recommend alternative weld materials that will provide
better wear resistance and will be compatible with the hammer
base material.
THE USE OF SPECIFIC ENERGY AND THE CHARACTERISTIC PARTICLE SIZE
FOR DETERMINING GRINDER POWER REQUIREMENTS
Information developed in this report can be used to ascertain
the net motor power required to achieve a given degree of size
reduction. Determination of the net power requires specification
of the product size distribution expressed as the characteristic
particle size, XQ. Once the characteristic particle size has been
chosen, the net horsepower can be calculated using the curve in
Figure 59.
For example, consider a grinder that would be required to
size reduce six tons of municipal refuse per hour to 90% passing
1.5 in. To use Figure 59, an xo value must be estimated for the
anticipated size distribution (i.e., 90% passing 1.5 in.).
Estimating xo requires some preliminary calculations. First, the
value of £n(l/(l-y)) must be calculated for use in conjunction
with Figure 59:
£n(l/(l-0.9)) = Jln(10) = 2.3 (3)
Second, a value of the n-index must be assumed for estimating
purposes. An average value for municipal refuse shredding would
be n = 1.0. The values for the £n(l/(l-y)), 2.3, and the screen
size, 1.5 in., specify a point on the graph in Figure 59.
An n-index of 1.0 implies a 45° slope through the point
(1.5, 2.3). Intersection of this slope with the line Jin (l/(l-y)) =
1.0 provides the characteristic particle size, xo, corresponding
to a screen size of 1.5 in. In this case, the XQ value would be
0.65 in. Figure 59 indicates that a characteristic particle size
(x0) of 0.65 in. implies a specific energy consumption of 18 Kwh/
ton.
The net power can be expressed as
KW = (E )(tons/hr) (4)
n o
where KW = net power in kilowatts; EQ = specific energy, Kwh/ton;
and tons/hr = tons of refuse per hour. In this instance, En = 18
Kwh/ton and tons/hr = 6.0- Therefore,
106
-------
10,000
yj
5
LJ
DC
D
O
IU
oc
(£.
UJ
8
QL
LU
cn
cr
O
S
lOOOh-
lOO—
100
FEEDRATE (tons/hour)
Figure 5i
Horsepower Required for Size Reduction of
MSW as a Function of Feedrate and Desired
Product Size
107
-------
KWn = (18 Kwh/ton) (6 tons/hr) (5)
KWn = 108 Kw (6)
For this example, the net power required for size reduction is
108 Kw.
To this net power consumption must be added the power required
to overcome the bearing friction and the air resistance of the
whirling hammers. For instance, our Gruendler mill (44 hammers,
36-in. tip-to-tip diameter) consumes approximately 30 Kw or 40 hp
when operated at 1,200 rpm. Consequently, the actual motor horse-
power is always larger than the net horsepower required solely for
size reduction.
RELATIONSHIP OF GRINDER HORSEPOWER, FEEDRATE , AND PRODUCT SIZE
To introduce the jargon of the grinding industry, namely
grinder horsepower and the 90% cumulative passing size (which
henceforth will be abbreviated as X^Q) , the kilowatt power
consumption and characteristic particle size (xo) , discussed
previously, must be converted to the aforementioned industry-used
terms. The kilowatt conversion is straightforward; that is,
1 hp equals 1.34 Kw. Likewise, 1 horsepower-hour/ ton equals
1.34 Kwh/ton.
The conversion of xo to xgg can be shown analytically to be
solely a function of the n-index. In fact, the relationship of
xo, n, and the screen size corresponding to a given cumulative
passing percent can be expressed as
(7)
n - .-, -
° UnO/0-y.)}l/n
where xo = characteristic particle size, x^ = screen size for a
given cumulative passing percent (y.^) , and n = the slope of the
curve of the £n(l/(l-yjj) versus the screen size x^. Equation
(5) reduces to
*° =
when the 90% cumulative passing size is used. If Equation 6
is solved for XQQ, any xo value can be converted to the equivalent
xgg value,
108
-------
X90
As mentioned previously, a value of n = 1.0 can be used for
estimations of feedrates and power consumptions when dealing with
MSW. Equation 7, therefore, reduces to
X90 = 2'3 X0 (10)
Using these conversions (hp = 1.34 Kw and x90 = 2.3 xo) , a
functional relationship among net horsepower, feedrate, and xg0
has been established and is presented graphically in Figure 59.
This figure may be used to estimate the net horsepower required
to size reduce MSW at a given feedrate to a specific xgg size.
As an example , to estimate the net horsepower required for a
feedrate of 25 tons/hr and 90% passing 2.0 in., consult Figure 59
and follow these steps :
1. Locate the feedrate, 25 tons/hr, on the horizontal
axis ;
2 . Find the intersection of the line corresponding to
25 tons/hr and the line X
-------
UJ
O
z
-------
SECTION 5
ANALYTICAL ASPECTS OF COMMINUTION
The design of advanced refuse processing technology aimed
at material and/or energy recovery can be advanced by a funda-
mental understanding of how to control waste stream comminution.
Although refuse comminution is an emerging technology, it is
becoming widely adapted in the industry. Analytical modeling of
comminution processes for a heterogeneous mixture of brittle and
nonbrittle materials, which is the nature of refuse, has hereto-
fore not been the subject of extensive investigation. In fact,
because of its complex nature, the predominant tendency has been
to rely on empiricism rather than to pursue the fundamental
approach. Advanced processing, often involving multiple comminu-
tion events that require control and manipulation of the subsequent
product size distributions, along with process scaling cannot be
optimally designed with only empirical means. A general comminu-
tion theory depends on a variety of factors. For example, the
dominant mechanism of size reduction in any grinding machine
influences the final product size distribution and is itself
dependent on machine design and particle characteristics. The
particle size distribution produced by a comminution device is
the summation of the many single event distributions occurring
as a result of the particular grinding action peculiar to the
mill. The analytical approach developed for refuse comminution
has its roots in the vast amount of experience and analysis
already accumulated in the field of comminution of brittle
materials. Consequently, a brief overview of the past brittle
material work is germane.
Relating breakage energy of homogeneous brittle materials
(rocks, coal, etc.) to the performance of size reduction machines
has been the goal of much of the previous comminution research.
Typically, grinding data were interpreted in terms of empirical
energy-size relationships [Charles (20), Schuhmann (21)J or "laws
of comminution" [Bond (22), Harris (23,24)] that were based on
highly oversimplified descriptions of the fracture process.
A common failing of all the so-called laws is that they do not
give information on the size throughput relations of a mill or on
optimum operation conditions. A breakage process effects changes
throughout all sizes of a complete size distribution, and a
single parameter (such as surface area) cannot by itself describe
111
-------
changes of such complexity (25,26). Gaudin (27), Rosin and
Rammler (28) , Bennet (29) , and Schuhmann (30) have advanced
comminution theory by recognizing the frequently observed
regularities of milled product size distributions and their_rela-
tion to breakage mechanisms. Such experimental and theoretical
studies are fundamentally of a statistical nature (31,32) and
require the concepts of distribution and of averages. Various so-
called laws, generally expressed in terms of a cumulative weight
fraction smaller than any size x as a function of x raised to
some numerical power, have been proposed as governing the size
distributions of brittle material.
Formulations that account for repeated breakage, a normal
occurrence in mills, have been advanced by Epstein (33), Bass (34),
Broadbent and Callcott (35) , and Brown (36) . The basic concept
involved is to characterize the operation by two parameters -
the selection function and the distribution function. Basically,
the selection function represents the fractional amount of any
given size present in the mill that is selected for breakage in
a differential increment of grinding; the distribution function
represents the primary breakage distribution of a given size on
breakage.
Bass (34) presented a mathematical theory for the milling
process and was the first to derive the fundamental mass balance
for batch grinding as an integrodifferential equation. Under
certain restrictions he showed that the formal solution to the
basic equation yields an expression equivalent to that of the
previously semi-empirical Rosin-Rammler size distribution.
Using time-continuous population balance models, Austin and
his co-workers [Gardner and Austin (37), Austin et al. (38JTJ and
Fuerstenau and his co-workers [Herbst and Fuerstenau (39), Grandy
et al. (40), Gumtz and Fuerstenau (41), Herbst and Mika (42)]
have successfully simulated, on a laboratory scale, batch ball
mill behavior for a range of operating conditions. An experimental
study of breakage in a continuous grinding system was reported by
Kelsall (43) in 1964 and led to a search for a workable mathemat-
ical representation for continuous grinding. By accounting for
the residence time distribution of particles in the mill, Kelsall
and Reid (44,45) and Kelsall, et al. (46,47,48) extended these
models to simulate laboratory scale, continuous ball milling
systems.
Other investigators [Broadbent and Callcott (35,49),
Callcott and Lynch (50), Lynch and Rao (51), Lynch et al. (52),
Meloy and Bergstrom (53), and Mori et al. (54)^ have used discrete-
time, steady state matrix models to develop mathematical descrip-
tions of comminution devices. The main criticism of the latter
approach is that the matrix models do not provide an adequate
description of the dynamic behavior in a mill since time is not an
112
-------
explicit variable and material transport is (implicitly) assumed
to occur by plug flow (55).
Other more recent comminution studies have been reported
(56-70), including a review by Snow (71). Studies dealing with
complex minerals, mixtures, and specially designed heterogeneous
materials (72-74) have been reported.
Some details of the concepts discussed here will be given to
elucidate the possible extensions from the field of size reduction
of brittle materials to the comminution of nonbrittle heterogeneous
materials.
INITIAL ENERGY COMMINUTION RELATIONS
The early energy size reduction laws attempted to determine
an index for any given material that could be related to a
standard range of size reduction and that could be used to
compute the energy required to produce any other range of size
reduction. This index c, depending physically on material
properties and mill operating variables, is mathematically
described by the following relation:
dE c
dx ~ ~Vn (11)
j\
where E is the net energy required per unit weight in a given
process of comminution, x is a factor related to size, and n is
an exponent. Difficulties arise in expressing the size in a
mathematical form, since in any actual process, the material being
comminuted has a considerable range of size on entering and
leaving the process; also, it is impossible to denote this size
by a single index because of variations in the shapes of the
particles.
The three most frequently quoted, so-called general laws of
comminution, derived from Equation 11, are those attributed to
Rittinger (75), Kick (76) and Bond (22). These are obtained as
follows: When n = 2, integration of this basic equation gives
Rittinger's law:
When n = 1, integration gives Kick's law:
AE = CK log (*-)
113
-------
Bond's third theory of comminution (22) is obtained by substi-
tuting n = 1.5 in Equation 11, integrating, and rearranging:
-J/2 , lnn 1/2
AE = W. ^ll (M) (14)
1 R1^ X2
where W^ is a work index-and R is the size reduction ratio,
xi/Xo. Obviously, energy requirements for Bond's law lie between
those predicted by the earlier two laws.
It is important to note that the three laws differ in their
definitions of x^ and x2- Rittinger's (75) statement of his law
claimed that the energy consumed in comminution is proportional
to increase in surface area produced (surface theory). It follows
from this that xj and X2 must be defined as the particle sizes
that have a surface area such that it is equal to the total surface
area of a unit mass of feed or product divided by the total number
of particles contained in that mass. Kick's (76) statement of
his law - that analogous changes of configuration of geometrically
similar bodies vary as the volumes of the bodies (volume theory) -
implies that Xj and x2 are particle sizes that have their mass
equal to the mean mass of the particles in the feed and product.
Bond (22) defines his particle sizes as the apertures through
which 80% by weight of the feed or product pass.
Before Bond's law appeared, it was known that Rittinger's
law applied primarily in crushing relatively small particles, and
Kick's law generally held for large particles. The evidence
indicated that the value of n depended not only on the material
crushed, but also on the kind of crusher used. Bond's equation
made allowance for this variation in the work index, W^, whose
evaluation for any given material involved using arithmatic
mean value energy per ton based on data accumulated from many
kinds of crushers and grinding equipment of different efficiencies.
As Bond (22) has indicated, these data are sometimes so widely
scattered as to seem unsuitable for taking the arithmatic mean.
Nevertheless, taking n as 1.5 proves more workable than either
Kick's or Rittinger's laws in correlating many data from various
types of crushing devices. Bond's law must be considered as an
empirical rule of thumb that is principally useful as a means of
codifying a mass of industrial experience so that interpolation
and limited extrapolation can be made for known materials and
equipment (25).
Using different approaches, Charles (20), Holmes (77), and
Schuhmann (21) indirectly show that energy-size relations can
have as a common base the simple relationship
AE = Ck"m (15)
114
-------
where C is a machine constant, k is the size modulus (theoretical
maximum size from size distribution curve) , and m is a constant.
Recent work of Tanaka (78) relates the constant C of Equation
15 with collision, critical stress, and crack-tip propagation
probabilities. Based on this work, Suzuki and Tanaka (79) find
the relation between crushing efficiency and some operational
variables and material constants.
The energy-size relationship does not provide a complete
theoretical analysis of the comminution process; in some instances,
this kind of approach has provided a basis for partial correlation
of experimental data, but it is inadequate for meaningful process
simulation (25,56,66,77).
SIZE DISTRIBUTION RELATIONS
Several empirical size-distribution equations have been
proposed as a means of describing the physical nature of a
comminuted product. Among them are the Gaudin-Schuhmann equation
(27,30) and the Rosin-Rammler equation (28). The Gaudin-Schuhmann
equation
a
Y(x) = (f) (16)
relates the fraction of undersize Y(x) to relative size x/k. In
this relationship, Y(x) is the cumulative fraction by weight
finer than the stated size x, and k is a quantity called the size
modulus (theoretical maximum size), which together with the slope
parameter, a, characterizes the product. The slope parameter is
usually close to unity (25,30,74,80).
The Rosin-Rammler equation relates the same relative fraction
of undersize to the relative size modulus by an equation of
different form
Y(x) = 1 - exp[-(—) ] ^17'
xo
where n is some numerical constant, and xo is a characteristic
particle size (63.2% cumulative passing).
Gaudin and Meloy (31) derived a theoretical size-distribution
equation for single fracture in the form
Y{x) - 1 - (1 - f I" (18)
0
In this equation, xn is a characteristic dimension of the feed
particle before fracture, and r is the size ratio, which is a
measure of the number of breaks in the particle. Bergstrom (81)
115
-------
modified the Gaudin-Meloy equation empirically by adding another
parameter. He pointed out that the modified form
Y(X) = [!-(!- -*-nq (19)
Xo
combines the fine and coarse size curve-fitting capacities of the
Gaudin-Schuhmann and Gaudin-Meloy equations, respectively.
Other size distribution equations (60,67,68) have been proposed
with additional parameters, ostensibly for greater curve-fitting
flexibility, as further generalizations of the above relations.
Because refuse is a heterogeneous material, it is unlikely
that a single breakage law can describe all types of breakage.
There are some difficulties in the applications of these various
laws characterizing size distribution. One of the major defi-
ciencies is that, although it seems natural to suppose that a
breakage process operates according to some law, our experimental
results indicate that the feed cannot be characterized by any of
the previously derived size distribution relations. Thus when
the process is supplied with some unusual distribution of feed,
like refuse, it seems that the product need not obey any of the
usual laws. The analysis of a breakage process by matrix method
offers an excellent approach to overcome this difficulty, espe-
cially in the case of the simulation of a breakage process whereby
the feed and discharge size distributions can be obtained.
MATRIX ANALYSIS OF THE BREAKAGE PROCESS
The principles of the matrix method of analysis of comminution
processes leading to the simulation models developed for refuse
are reviewed. In the matrix method, the size distribution given
by the sieve analysis is replaced by a vector by considering the
size range of the assembly of particles to be subdivided into n
intervals, with maximum size x^ and minimum size x n+]_- The ith
size fraction is bounded by x^ above and x^+^ below and Xj_ =
rxi+l ^ = !'2'3' --- ' n~l)/ with r (>1) being the geometric sieve
ratio. Where it is necessary to specify the size of particles in
a particular size fraction by a single number, the geometric mean
is taken. When the size scale is logarithmic, this geometric
progression of sizes appears as equally spaced points on the
abscissa.
Pj_ designates the cumulative mass fraction of product material
below X-L, and Fj_ is the cumulative mass fraction of feed material
below size xi where i = 1,2,3, --- , n. Then the feed and product
size distributions can be described by n x 1 column vectors f and
p with elements fj_ and p^, where fj_ and p^ are, respectively! mass
fractions of feed and product materials that fall between x-j_ and
tnus:
116
-------
f =
B =
(20)
with
V Fi -
(21)
(22)
The percentage or fraction of material under the smallest size,
the undersize, is described by
'n+1
Vl
— C
n+1
= P
n+1
= ] - e'f
= 1 - e'g
(23)
(24!
where e' is the transposition of the n x 1 column vector e with
unity elements. The transformation of the feed to the product
is thus expressed mathematically by a matrix algebra:
p=Xf (25)
where X expresses the breakage process.
The sequence of rows and columns in the matirx, X, describing
a transformation of a size distribution bears definite relations
to particle size. Let i and j refer to the ith row and jth _
column of X, with elements X±,. Then X±j denotes the proportion
of particlis that were initially in sizejrange D and afterwards
in product size range i.
For size reduction, X is lower triangular (35,55,57), and a
knowledge of the n elements of p and the n elements off does not
suffice to enable a unique solution from the n equations of the
n(nH-l) unknowns X^ (i*j). Several authors (37 f^'55,81,82) have
2 discussed the Impirical evaluation of the ^"J.^ *n°^ibed
circuit grinding process. Their approach is essentially described
by the following equation:
117
-------
Ej = I §.. (j = 1,2,34 ..., n) (26)
where X is unknown and e . is the unity vector with all elements
zero except the jth element (=1), the experimental determination
of p. gives the jth column of X. If particle interaction is
absent, and if it is possible to use graded feeds (e.) down to
the smallest size x , the experimental evaluation of X. should
satisfactorily predict the output size distribution (p) obtained
on feeding ungraded material (f ) - that is, Equation 15.
Though the above approach does not disclose the mechanism
determining the numerical values of the overall matrix, X, a
mathematical model can be set up to describe the action In the
mill, based on the concept of the probability of breakage accord-
ing to Epstein (33). This concept has provided a convenient basis
for the formulation of detailed comminution models (55). In these
treatments, the process is represented by a series of discrete
breakage events characterized by a probability of breakage for a
given size particle (y) in any given event, which is called the
selection function, S(y), and a resultant product size distribution
from that breakage event, which is called the breakage function
or redistribution function., B(x,y) (i.e., the proportion of the
product whose size is less than x) .
Instead, of using continuous functions as done by Epstein,
Broadbent and Callcott (49) cast the weight size distribution into
finite intervals. Instead of using B(x,y), a parameter b-^j was
defined as the fraction of material in size interval j that falls
into size interval i after breakage. Thus the product of break-
age of size 1 material is distributed - k>21 into interval 2,
into interval 3, etc., and bn^ into the last interval of smallest
particle size. The sum of the values of b^j over all the values
of i is one. Similarly, breakage of the second size interval
yields products distributed - bg2/ ^42' etc. The selection func-
tion was again defined as the fraction of any size interval
selected for breakage, but it was expressed generally as a function
of size, S j .
According to Broadbent and Callcott, consider the mass
fraction f.: of a size range i. If S^ is the appropriate value of
the selection function, a proportional amount (1 - S^) of the size
will remain unbroken in the grinding process and a fraction S^
will be broken. The way in which the material is broken is de-
scribed by the breakage function B^ j . This is a size-discretized
form of B(x,y) obtained by replacing x and y with the geometric
mean sizes of the size intervals i and j, respectively* in the
"general" breakage function (49)
118
-------
B(x,y) = [1 - exp(-x/y)]/[l - exp(-l)]
0 (i = j, attrition is negligible)
= 0 , (i < j, no agglomeration)
In all instances where the appropriate information has been
obtained (37,38,44), breakage functions have been found to be
normalizable in the sense of Epstein (33); that is,
B(x,y) = B(x/y) (29)
or, equivalently, in the case of a size discretized representation
with a constant sieve ratio, r (x^ = rx^+^)
Bij = B(i-j+l)l 1=J'» •••» n-1 (30)
The assumption of geometric similarity** for both the breakage
function and the grade sizes implies that particles of every size
break in the same way. Thus,
(3D
* The values of Sj_ and B^, determined experimentally and using
discrete size intervals, are not the same numerically as S (x)
and B(x,y), which are point values (38); in general, the values
of Sj_ and Bji change as the size interval used changes.
** The breakage functions used here are of the geometric similarity
form.
119
-------
Consequently, bj_-; are the elements of a breakage matrix B.. The
matrix B is similar to the breakage matrix X except that B is used
in conjunction with a selection matrix | to characterize the size
reduction process. The selection matrix § is a diagonal matrix
with entries S-,, S2, ..., Sn along the diagonal and zeros_else-
where. Normally both matrices B and S are not known a priori,
and so the b.: • and S-L must be estimated from experimental results.
If some particles are selected for size reduction according to B,
and if § defines the proportions of each size grade of f that is
selected, then Sf are reduced according to B, and naturally (I-S)f
describes the distribution left unbroken, where I is the identity
matrix. If the broken and unbroken parts are combined, then the
final product is
P. = iSf + (I-S)f
that is, P = (BS + (J-S)}f (32)
Thus Equation 25 is replaced by Equation 32, in which trans-
formation of the feed to the product proceeds in accordance with
the breakage matrix B and selection matrix S; a single cycle of
selection and breakage according to B is said to have occurred.
BREAKAGE PROCESS MODELS
A matrix method similar to that employed by Callco.tt (82) for
the comminution of coal in a swing hammermill was used to analyze
the size reduction of refuse. Observations of refuse size reduc-
tion in the swing hammermill-indicate that in general, the majority
of material tends to pass through the mill without being subjected
to repeated fracture. It is possible that mill operating condi-
tions differing widely from those considered here will give rise
to greater mill recirculation. Furthermore, unlike the process in
a batch grinding system, the residence time of material in the
hammermill is small. Estimates yield a residence time on the order
of 1/80 records for a rotor speed of 1,200 rpm (28,29,32). In any
event, similar to the procedure used by Broadbent and Callcott
(49), the swing hammermill can be reasonably considered as a once-
through grinder for the simulation of the refuse comminution
process. Four simulation models summarized in the following sub-
sections have been evaluated (83).
it-Breakage Process
The simplest breakage process is w-breakge in which the
selection function S (y) = IT for all sizes y - i.e. a proportion ir
of the particles, independent of particle size, is broken accord-
ing to the breakage function B(x,y). In matrix terms, §_ = irl, and
the equation describing the process is: ~ ~
120
-------
P = {-rrB + (l-7r)I}f (33)
The parameter w then completely describes the process if B is
assumed to be known; it is a useful measure of the breakage
effected by the process. The techniques for back-calculating the
value of TT from known feed and product distributions have been
indicated by Broadbent and Callcott (36). They also pointed out
that the simple simultaneous solution of elements of Equation 33
is not generally possible because of errors in measurement, and a
least-squares technique was outlined.
TT, K-Breakage Process
This is similar to the it-breakage process except that the
breakage matrix is replaced by B«, K > 1 on the basis that some
machines would cause more severe"degradation on breakage than
others, corresponding to repeated breakage of the particle products
without their moving away from the grinding action and having to
wait for reselection for breakage. We infer that a proportion IT
of the feed is selected for breakage, just as in it-breakage, but
that the product of this breakage is rebroken. This is repeated
until breakage has been effected K times. The unbroken material
passing through the grinding zone unaltered is, of course, (1-ir)
of the feed. The process is characterized by two parameters, IT
and K, and the matrix equation describing the process is:
p = {rrBK + (l-TT)I} f (34)
IT , K , co-Breakage Process
This process involves the case where the probability of
particle selection for breakage varies with some power v of the
particle size. Thus, the proportion of particles in the ith size
range selected for breakage is
S. = S (r)"v1 <35>
If a) = r~v and the probability is IT for the first size range, it
is TTO,, Tro)2,..., and rr^-1 in the ranges that follow. If n is the
matrix with 1, o>, u>2, ... a)0'1 along the main diagonal and zeros
elsewhere, the selection matrix is irfi. The equation of the process
is:
(36)
121
-------
Repeated Breakage Cycles
When the feed and product size distributions do not cover
the same sizes and the size ranges differ considerably, one may
be able to assess the breakage process in terms of a series of
cycles of mild breakage. The description may be written (50,82)
N
P = C TT (BSu + I - §u)>f (37)
h=1 - n n
where h = 1,2,..., N refers to the hth cycle in which the probabi-
lity of breakage is Sh. Given only p, f, and B, the evaluation of
each Sh and of N is not possible (507817. We will adopt the
following sequential model to simplify the analysis:
We assume that the probability of breakage Sh is the same for
all the cycles, hence Equation 37 becomes: ~
P = (BS + I-S)Nf (38)
where S is the selection matrix common to all the N cycles. If
D = (BS + I-S) (39)
then
p = D f (40)
The whole process in the mill is treated as a sequence of
operations in which the product from the jth cycle becomes the
feed for the (j+l)th cycle. To ensure that the undersize from
any cycle of the process is correctly described, we make p and f
(n+l)-column vectors, with the last elements, p , and f ~,,
describing the undersize for the product and feed, respectively.
We write D as a (n+1) square matrix, with the (n+l)th row
describing~the proportions of the various size ranges that end up
as undersize.
The number of cycles, N, is associated with the "stages of
grinding" (55). Callcott (82) considered the hammermill to be
made up of N obstructions or grinding zones (see Appendices).
The product from the jth zone in passing through the (j+l)th zone
is said to have undergone a single cycle of breakage. In the
present model, the number of cycles, N, is not identified with
the grinding zones, but it is introduced artificially as a means of
122
-------
repeatedly applying the single matrix D to the feed vector f in
order to obtain p when the top sizes of the feed and product
distributions ditfer considerably. if Xl is the maximum size
of the initial feed and x the maximum size of the final product
(where x± = rx±+1, i = 1,2,..., m,...,n-l), then N is estimated
from
N = (m - 1) (41)
SIMULATION RESULTS
Because present comminution theories are not sufficiently
developed, selection and breakage functions, particularly for a
heterogeneous refuse material, cannot be obtained from first
principles. Thus to use the previously described simulation models,
these quantities were determined with an indirect estimation or
semiempirical technique similar to that proposed by Broadbent
and Callcott. Two forms of the breakage function were selected.
The first, after a modified form of Broadbent-Callcott, was
B(x,x ) = {1 - exp[- (^-)n]}/[l - exp(-l)] (42)
o XQ
where n is some positive index. Experimental results indicated
that certain products of the size reduction conformed to the
Rosin-Rammler distribution with an n index varying between 0.845
and unity. The second form of the breakage function was after
the Gaudin-Meloy distribution equation:
B(x.xQ) = B(x/xQ) =!-(!- x/xQ)r (43)
This additional relation was necessary since, as will be shown,
Equation 42 did not simulate primary grinding. The elements bj_j
of the breakage matrices are calculated from Equations 28,30,
and 31 using the various breakage functions in Equations 42 and
43. The values of these elements are tabulated in Table 15.
The selection functions were determined with the least-squares
procedure for the ir-breakage, •n , K-breakage and TT ,K^,U> -breakage
processes for integer values of K f rom 1 to 5 and to - 1, 0.9,
0.8,..., to 0.1 using the experimental feed and product size
distributions. The "best" selection functions and the breakage
aistriDUtions. me we&u oca.cwt-.i.«« - .uZ«
matrices (i.e., those that yield least squared errors) are then
used to calculate the product size distributions for the Particular
breakage model. For the repeated breakage cycles model values of
,=0102 to 1 are chosen and used together with the
Jreakge matrices to compute product size distributions. The
123
-------
TABLE 15. BREAKAGE FUNCTION ELEMENTS OF THE FIRST COLUMN
i
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
B-C
n=l
0.10027
0.19037
0.16588
0.13599
0.10676
0.08129
0.06057
0.04444
0.03226
0.02323
0.01664
0.01188
0.00845
0.00600
0.00426
0.00302
0.00214
j i
B-C
n=0.845
0-08484
0.16336
0.14746
0.12684
0.10524
0.08500
0.06728
0.05247
0.04045
0.03093
0.02350
0.01778
0.01340
0.01007
0-00756
0.00566
0.00424
G-M
r=10
0-00000
0.00012
0.00417
0.02513
0-06516
0.10573
0.02944
0.13261
0.12088
0.10189
0.08142
0.06271
0.04708
0.03472
0.02529
0.01826
0.01310
G-M
r=5
0.00010
0.01087
0.05450
0.10605
0.13602
0.14001
0.12668
0.10573
0.08373
0.06402
0.04780
0.03511
0.02549
0.01837
0.01316
0.00939
0.00668
aSince the breakage matrix is a step matrix, i.e., b.^- = t>i+i/-;+]_*
all the other elements of the breakage matrix B can Be calculated
from the elements of the first column. A geometric sieve ratio
of /2~ is used in the computation of bj^. That is, X/X = ^2.
124
-------
particular selection function that gives the least-squared error
is chosen as the parameter to represent the model, in all the
above cases, computations were performed with a systematic varia-
tion of combinations of the selection breakage function so that
the reported simulation results are those that yield the least-
squared errors. The actual results of the simulation can be
summarized according to the following.
ir-Breakage Process
Figure 61 shows the comparison between the computed and
experimental product size distributions for primary, secondary,
and tertiary grindings using the ir-breakage model for various
selection and breakage functions. Here the breakage function
based on Equation 43 with the index r = 7 predicts the primary
product size distribution very well within experimental errors.
Also, the breakage functions obtained from Equation 42 give better
results for the secondary and tertiary grinding processes than the
predictions from Equation 43.
ir ,K-Breakage Process
Figure 62 shows the comparison between the computed and
experimental product size distributions for primary grinding using
this model. The results for K = 2 and 3 using the modified
Broadbent-Callcott equation represent the best among a host of
other computed product size distributions, and since the above
results do not in any way predict the actual experimental product
size distribution, the ir ,K-breakage process model is rejected as
a representation of the refuse size reduction process in the
hammermill. With K = 1 (i.e., ir-breakage process), Equation 32
does not come any closer in predicting the product size distribu-
tion. The computations based on the ir,K-breakage process model
for the secondary and tertiary grinding conditions do not give any
better results than those predicted with the simple ir-breakage
process model.
IT , K , a)-Breakage Process
This model is also rejected as a mathematical representation
of the breakage process in the mill. The values of IT for u> < 0.9
are found to be greater than unity. Values of IT greater than
unity cannot be accepted because they violate the definition of ir
as a probability of a certain-sized particle being broken in
passing through a process. If the values of ir greater than unity
were accepted, it would just mean that we were merely curve-fitting
the computed results to the experimental data and the model would
not be amenable to any physical interpretations.
125
-------
to
O
1.0
UJ
M
V)
Q
UJ
I
I-
z Q
OL
O
O
<
QC
U_
UJ
0.01
GRIND
FEEDRATE,
TON/HR
MOISTURE DRY WET
(7T)
(SS)
iwnpy SELECTION SQUARED
INDEX FUNCTION RESIDUAL
OPR I MARY
SECONDARY
A SECONDARY
D TERTIARY
• TERTIARY
22.0%
PRODUCT
PRODUCT
FEED
PRODUCT
FEED
INITIAL SOLID WASTE FEED-PACKER
TRUCK REFUSE
21.8%
18.5%
20%
4.10
6.55
5.55
7.35
6.55
5.30
8.15
7.08
9.05
8.15
A
B
C
D
E
• r=7
- r = IO
•n=Q845
• r = 5.0
e nsl.O
0.93
0.89
0.814
0.365
0.07
0.44
0.0049
0.0447
0.0011
0.0256
0.0274
0.0012
EQUATION
GAUDIN-MELOY S
BROADBENT- CALLCOTT's
BROADBENT- CALLCOTT'S (MOD.)
1 I
I
I
_L
I I I
0.01
0.1 1.0
PARTICLE SIZE (in.)
10
Figure 61 Comparison Between Computed and Experimental
Product Size Distributions for Primary,
Secondary, and Tertiary Grinding Using the
ir-Breakage Process Model
-------
LU
rsl
CO
Q
CO
j? o.i
cr
LU
2
U_
i
h-
o
i
§
13
2
ID
Q
0.001
0.(
u / X / /
t / / 1 mrr
/ REFUSE """'"
- / / 1 f *
- / I i
I/ I j EXPERIMENTAL, PRIMARY GRINDING
/ / / M°'f7URE FET§N/RSTRE' "
r \ 1 % DRY WET
/ — O— 22.0 4.10 5.30
1
~ ' BROADBENT-CALLCOTT'S EQUATION"
(7T) (SS)
INDEX SELECTION SQUARED -
n =0.8 45
K = 1
K =2
K =3
1 1 J 1 1 1 111 • ...
FUNCTION RESIDUAL
1.27 0.7562
0.98 0.0829
0.90 0.2104
1 11^
Dl O.I 1.0 10
PARTICLE SIZE (in
.)
Figure 62 Comparison Between Computed and Experimental
Product 'Size Distributions for Primary Grinding
Using the ir, K-Breakage Process Model
127
-------
The Repeated Breakage Cycle Model
Figure 63 shows the partial success of this model in computing
product size distributions for primary, secondary, and tertiary
grinding processes. Breakage functions based on Equation 20 yield
good results for the primary grinding process for sizes down to
0.2 in. (5,080 y), with about 32% passing stated size; below this
size, the computed and experimental values diverge. There is a
considerable improvement in the results of this model for the
secondary and tertiary grinding process. The computed results
are close to the experimental ones down to sizes as low as 0.02
in. (508 y), with about 12% passing the stated size. In all the
above cases, the breakage functions based on the modified
Broadbent-Callcott equation or normalized Rosin-Rammler equation
(Equation 42) give better results than those of the Gaudin-Meloy
equation (Equation 43). The Gaudin-Meloy equation fails to
predict well in the small size ranges.
In summation, a good model will include the most important
features of the process, will be mathematically simple (if
possible), will provide a minimum of assumptions, and will be
fruitful for purposes of prediction and theoretical speculation.
In the simulation of the various results in this paper, the two
models, ir ,<-breakage and ir ,K,u>-breakage, are found to be untenable
because they fail to predict the product size distributions within
any reasonable accuracy. The ir-breakage model is clearly superior
to the repeated breakage cycle model; however, both give very good
results for the products of primary, secondary, and tertiary
grinding processes. The ir-breakage model is clearly superior to
the repeated breakage cycle model because it gives better results
for all the three grinding conditions.
128
-------
1.0
LU
N
cn
Q
£
fe
<
Q
o
UJ
p
_1
ID
2
o
o.i
B
GRIND
FEEDRATE,
TON/HR
MOISTURE DRY
0.0
PRODUCT
PRODUCT
FEED
PRODUCT
FEED
INITIAL SOLID WASTE FEED-PACKER
TRUCK REFUSE
O PRIMARY
A SECONDARY
A SECONDARY
D TERTIARY
• TERTIARY
22.0%
20%
21.8 %
18.5%
20%
4.10 5.30
6.55 8.15
5.55 7.08
7.35 9.05
6.55 8.15
A-
B-
C"
D-
£•
F-
INDEX
r =5.0
n = 1.0
n = 1.0
r =10.0
n - 1.0
r =10-0
(TT)
SELECTION
FUNCTION
O.I
0.2
0.2
O.I
0.20
0.10
(SS)
SQUARED
RESI DUAL
0.0928
0.0216
0.0073
0.0181
EQUATION
GAUDIN-MELOY S
BROADBENT-CALLCOTT'S (MOD.)
j L
I i I
_L
_L
J I
0.01
O.I I.O
PARTICLE SIZE (in.)
10
Figure 63 Comparison Between Computed and Experimental
Product Size Distributions for Primary Grinding
Using the Repeated Breakage Cycle Model
-------
REFERENCES
1. Ham, R.K., "The Role of Shredded Refuse in Landfillings,"
Waste Age, Vol. 6, No. 12, December 1975, pp. 25-30.
2. Final Report on a Demonstration Project at Madison,
Wisconsin, Vol. 1, 1966-1972, EPA Report, March 1973.
3- Resource Recovery from Municipal Solid Waste. National
Center for Resource Recovery, Inc., Lexington Books, B.C.
Heath & Co., Lexington, Mass., 1974, 182 pp.
4. Decision-Makers Guide in Solid Waste Management, U.S.
Environmental Protection Agency, Second Ed. (SW-500), 1976.
5. Fan, Dah-Nien, "On the Air Classified Light Fraction of
Shredded Municipal Solid Waste - Composition and Physical
Characteristics," Resource Recovery and Conservation, Vol. 1,
No. 2, 1975, pp. 141-150.
6. Trezek, G.J. and G. Savage, "MSW Component Size Distributions
Obtained from the Cal Resource Recovery System," Resource
Recovery and Conservation (In Press), 1976.
7. Trezek, G.J., D. Howard, and G. Savage, "Mechanical Properties
of Some Refuse Components," Compost Science, Vol. 13, No. 6,
Nov.-Dec. 1972, pp. 10-15.
8. Ruf, J.A., "Particle Size Spectrum and Compressibility of
Raw and Shredded Municiple Solid Waste," Ph.D. Thesis,
University of Florida, 1974.
9. The Feasibility of Baling Municipal Refuse. Prepared by
Project Personnel of the Public Works Dept. of the City of
San Diego, Calif, for the Solid Waste Program of the U.S.
Public Health Service, April 1968, 123 pp.
10. High-Pressure Compaction and Baling of Solid Waste. Prepared
by the American Public Works Assoc. for the Solid Waste
Management Programs of the U.S. Environmental Protection
Agency, EPA Publication No. SW-32d. Washington, D.C.: U.S.
Government Printing Office, 1972, 163 pp.
11. Taggart, A.F., Handbook of Mineral Dressing, Wiley Handbook
Series, John Wiley & Sons, Inc., 1945.
130
-------
12. Trezek, G.J., "Size Reduction Equipment," Compost Science
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131
-------
27. Gaudin, A.M., "An Investigation of Crushing Phenomena,"
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32. Klimpel, R.R. and L.G. Austin, "The Statistical Theory of
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33. Epstein, B., "Logarithmico-Normal Distribution in Breakage
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34. Bass, L., "Zur Theorie der Mahlvorgange," Zeits. Angew,
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36. Brown, R.L. J. Inst. Fuel, 14, 1941, p. 129.
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Part II: The Prediction of Size-Weight Distributions from
Selection and Breakage Data," Symp. Zerkleinern, 1st Eur.
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Weinheim, 1962, pp. 217-248.
38. Austin, L.G., R.R. Klimpel, and A.M. Beattie, "Solutions
of Equations of Grinding," Zerkleinern, 2nd European Symp.
on Comminution, Edit. H. Rumpf and W. Pietsch, Amsterdam,
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39. Herbst, J.A. and D.W. Fuerstenau, "The Zero Order Production
of Fine Sizes in Comminution and its Implications in Simula-
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132
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40. Grandy, G.A. , G.D. Gumtz, J.A. Herbst, T.S. Mika, and D.W.
Fuerstenau, "Computer Techniques in the Analysis of Laboratory
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Industry, Edit. A. Weiss, AIME, New York, 1969, pp. 765-788.
41. Gumtz, G.D. and D.W. Fuerstenau, "Simulation of Locked Cycle
Grinding," Paper presented at 98th Ann. AIME Meeting,
Washington, D.C., February 1969.
42. Herbst, J.A. and T.S. Mika, "Mathematical Simulation of
Tumbling Mill Grinding: An Improved Method," Rudy, No. 3/4,
1970, pp. 70-75-
43. Kelsall, D.F., "A Study of Breakage in a Small Continuous
Open-Circuit Wet Ball Mill," Proceedings of VII International
Mineral Processing Congress, New York, 1964, Edit. N.
Arbiter, Gordon and Breach, New York, 1965, pp. 33-42.
44. Kelsall, D.F. and K.J. Reid, "The Derivation of a Mathematical
Model for Breakage in a Small Continuous, Wet, Ball Mill,"
in Application of Mathematical Models in Chemical Engineering
Research, Design and Production, AIChE-Inst. Chem. Eng.
Symposium Series, No. 4, 1965, pp. 14-20-
45. Kelsall, D.F. and K.J. Reid, "Some Effects of a Change in
Environment Size Distribution on the Grinding Behavior in a
Continuous Wet Ball Mill," Trans. Inst. Min. & Met.,
Section C, 7j8, 1969, pp. C198-205.
46. Kelsall, D.F., K.J. Reid, and C.J. Restarick, "Continuous
Grinding in a Small Wet Ball Mill. Part I: A Study of the
Influence of Ball Diameter, " Powder Tech. , i, 1968, pp. 291-
300.
47. Kelsall, D.F., K.J. Reid, and C.J. Restarick, "Continuous
Grinding in a Small Wet Ball Mill. Part II: A Study of the
Influence of Hold-Up Weight. " Powder Tech. , 2, 1969, pp- 291
300.
48. Kelsall, D.F. , P.S.B. Stewart, and K.J. Reid, "Confirmation
of a Dynamic Model of Closed-Circuit Grinding with a Wet
Ball Mill," Trans. Inst. Min. & Met., 1J_, 1968, Section C,
pp. C120-127.
«»•
209, 1964, pp. 109-131.
133
-------
51. Lynch, A.J. and T.C. Rao, "Digital Computer Simulation of
Comminution Systems," Proc. VIII Commonwealth Mining and
Metallurgical Congress (Australia and New Zealand, 1965) -
General, Edit. J.T. Woodcock, R.T. Madigan and E.G. Thomas,
Eight Comm. Min. and Met. Congress, Melbourne, 1966,
pp. 587-595.
52. Lynch, A.J., W.J. Whiten, and N. Draper, "Developing the
Optimum Performance of a Multi-Stage Grinding Circuit,"
Trans. Inst. Min. & Met., Section C, 76, 1967, pp. C169-
C181.
53. Meloy, T.P. and B.H. Bergstrom, "Matrix Simulation of Ball
Mill Circuits Considering Impact and Attrition Grinding,"
Proc. of the VII Int. Min. Proc. Cong., New York, 1964,
Edit. N. Arbiter, Gordon and Breach, New York, 1965,
pp. 19-31.
54. Mori, Y., G. Jimbo, and M. Yamasaki, "Flow Characteristics
of Continuous Ball and Vibration Mill Mixing Size Distribu-
tion, Dynamic Response of Flow Rate and Application,"
Zerkleinern, 2nd Eur. Symp. on Comm., Edit. H. Rumpf and
W. Pietsch, Amsterdam, 1966, Dechema-Monographien, 57, 1967,
Part II, pp. 605-632.
55. Austin, L.G., "A Review Introduction to the Mathematical
Description of Grinding as a Rate Process," Powder Technol.,
5_, 1971/72, pp. 1-17.
56. Austin, L.G., P.T. Luckie, and R.R. Klimpel, "Solutions of
the Batch Grinding Equation Leading to the Rosin-Rammler
Distributions," Trans. AIME, 252, 1972, pp. 87-94.
57. Klimpel, R.R. and L.G. Austin, "Determination of Selection-
for-Breakage Functions in the Batch Grinding Equation by
Nonlinear Optimization," I.E.&C. Fundamental, 9, 1970,
pp. 230-237. ~
58. Rampf, H., Fracture, Vol. 2, Edit. H. Liebowitz, Academic
Press, New York, 1969.
59. Shoenert, K., "Role of Fracture Physics in Understanding
Comminution Phenomena," Trans. AIME, 252, 1972, pp. 21-26.
60. Harris, C.C., "The Application of Size Distribution Equations
to Multi-Event Comminution Processes, Trans. AIME, 241,
1968, pp. 343-358.
134
-------
61. Harris, C.C. , "Deficiencies in Two-Batch Grinding Hypotheses,
Powder Technol . , _3, 1970, pp. 309-311.
62. Horst, W.E. and E.J. Freeh, "Mathematical Modeling of a
Continuous Comminution Process," Trans. AIME, 252, 1972,
pp. 160-167.
63. Herbst, J.A., G.A. Grandy, and T.S. Mika, "On the Develop-
ment and use of Lumped-Parameter Models for Continuous
Open- and Closed-Circuit Grinding Systems," Trans. AIME,
Section C, 8£. 1971, pp. C193-C198.
64. Luckie, P.T. and L.G- Austin, "A Review Introduction to the
Solution of the Grinding Equations by Digital Computation,"
Mineral Science and Engineering, 4_, No. 2, April 1972, p. 24.
65. Herbst, J.A. and D.W- Fuerstenau, "Influence of Mill Speed
and Ball Loading on Parameters of the Batch Grinding
Equation," Trans. AIME, 252, 1972, pp. 160-167.
66. Austin, L.G. and P.T. Luckie, "Grinding Equations and the
Bond Work Index," Trans. AIME, 252, 1972, pp. 259-266.
67. Harris, C.C., "A Method of Determining the Parameters of the
3-Parameter Size Distribution Equation," Trans. AIME, 244,
1969, pp. 187-190.
68. Harris, C.C., "Relations for the xYt Comminution Surface,"
Trans. Inst. Mining Met., 7_9, 1970, pp. C157-158.
69. Kelly, F.J. and R.F. Pilgrim, "Simulation of a Grinding
Circuit and Encountered Problems," Trans. AIME, 252, 1972,
pp. 366-371.
70. Hogg, R. and D.W. Fuerstenau, "Power Relationships for
Tambling Mills," Trans. AIME, 252, 1972, pp. 418-423.
71. Snow, R.H., "Annual Review of Size Reduction," Powder
Technol., _5, 1971/72, pp. 351-364.
72. Fuerstenau, D.W. and P. Somasundaran, "Cinetique de la
Fragmentation," in 6th Congres International de la Prepara-
tion des Minerals (Cannes), Edit. ?aint-Etienne, 1963,
DD 39-48 (cf also "Comminution Kinetics," in Mineral
Processing, Edit. A. Roberts, Pergamon Press, Oxford, 1965,
pp. 25-34.
"• ^i-i
1961, p. 69.
135
-------
74. Kinasevich, S.R., "Application of the Schuhmann Single Event
Hypothesis to Comminution," M.S. Thesis, Univ. of California,
1962.
75. Von Rittinger, R.P., "Lehrbuch der Aufbereitungskunde,"
Ernst und Korn, Berlin, 1857.
76. Kick, F., "Das Gesetz der Proportionalem Widerstand und
seine Anwendung," Leipzig, 1885.
77. Holmes, J.A., "Contribution to the Study of Comminution -
Modified Kick's Law," Trans. Inst. Chem. Engrs., 35, 1957,
pp. 125-141.
78. Tanaka, T., "Comminution Laws," I & EC Process Design and
Development, J5, No. 4, October 1966.
79. Suzuki, A. and T. Tanaka, "Crushing Efficiency in Relation
to Some Operational Variables and Material Constants,"
I & EC Process Design and Development, ~T_, No. 2, April 1968.
80. Crabtree, D.D., S.R. Kinasevich, A.L. Mular, T.P. Meloy, and
D.W. Fuerstenau, "Mechanisms of Size Reduction in Comminution
Systems," Parts I and II, Trans. AIME, 229, 1964, pp. 201-210.
81. Bergstrom, B.H., "Empirical Modification of the Gaudin-Meloy
Equation," Trans.AIME, 235, 1966, p. 45.
82. Callcott, T.G., "A Study of the Size Reduction Mechanisms of
Swing Hammer Mills," J. Inst. Fuel, 33_, 1960, pp. 529-539.
83. Obeng, D.M., "Comminution of a Heterogeneous Mixture of
Brittle and Non-Brittle Materials," Ph.D. Dissertation,
University of California, Berkeley, 1973.
84. Bennett, J.G., J. Inst. Fuel, 10, 1936, p. 22.
136
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APPENDICES
APPENDIX A. MILL MATRIX CIRCUIT ANALYSIS
Callcott (82) assumes that a mill has N obstructions formed
by breakage bars and grids (or screen) . A symbolical representa-
tion is given by Figure A-l in which
mj represents the new feed vector to the jth stage
Cj ,Dj represent the classification and "mill" matrices
for the jth stage
qj represents the output vector of the jth stage
or zone
E-: represents the diagonal matrix of which the
= elements express the proportions of each size
range of q^ that pass on to form m-+1
g.: represents the vector of material discharged
- between the jth and (j+l)th zone.
Mass flow rates are represented by M . , Qj
E .
The subscript j ranges over 1, 2, 3, --- , N for all symbols,
except that if some of the material characterized by N is returned
to mix with the mill feed (m, M) j ranges from zero up to N + 1.
Thus in N (equal or unequal,, finite or infinite) steps, the mass
of material with vector m is eliminated from the system.
The discharge of the jth ejection has a size distribution
given by
q. = g./e'g.*
"j -J - -J
and the size distribution of the entire output from m is
q - " 9i
"
%' - [1, 1, —
137
-------
m, M
Figure A-l Hammermill Analysis
138
-------
Two simple cases arise:
(i) No material is discharged until after the Nth obstruction
and none is returned to the starting point. That is,
jj-j = I (J = 1, 2, 3, — , N-l), EN = g.
(ii) Some discharge occurs after each obstruction, and none
returns to starting point. That is,
| ? I, (j = 1, 2, 3, — , N-l), EN = 0.
The general equation describing the transition from m to the
mill discharge q for case (i) is
N -1
g, = q = { TT {{I-C,} D. {I-C.D-.} '}}m (A3)
n _ j_-j = =J =J - -J-J
Now suppose that C- = C, D. = D for all j; then
=J = =O =
§N = 5 = {{H} ^
For case (ii) , the entire output from m is
N j-1
q = { £ ({I - E.}X. { £ E.X, }}}m (A5)
j=l = =J =J k=i=K k -
The above equation is obtained by considering the local grinding
circuits of the various grinding zones. Thus Q- and D^ become
the local or internal classification and "mill" matrices,
respectively. Using the results of the simple grinding closed-
circuit analysis (84), we get the local discharge to be given by
q, = (I - C,) D (I - CjD.rV - X m
-------
By definition
m. = E. q. 9j
j-i
= {(I - E.)}X. E X.} m
J J k_l K. K - I
(All)
The entire output from the mill is obtained by summing up the
individual discharges from the various grinding zones. Thus
= <
If we put EJ = E,Xj = X for j=l, 2, --- , N, we get
- ,-_-, N_i
q = { E {{I-E} X {E X}J '}} m + X {E X}1^ m
j=1 = _ = = = - = - -
= {I-E} X {I-E X}"^! - {E X}N}m + {E X}N m
= = = = = = = == _ == - (A13)
and noting 0 < Eii < 1, 0 < X-. < 1, Xnn =1, if i > j and the
eigen values of E X~are less than unity, {E X}N •> 0~as N -> «>;
even for relatively large N this will apply." ~
140
-------
Hence
9 = {H} X U-E X}"1 m (A14)
and so is identical in form with the closed-circuit equation
developed earlier.
Another special case of example (ii) arises when EH = I for
j = 1, 2, --- , r; Ej = 1 if j =r; Xj = g; namely ~J
q = {I-E}Xr{I-E X}"1 m (A15)
This approach enables us to define any part of the grinding
system using convenient if arbitrary decisions on the correspond-
ing intervals j = --- , etc., and defining E j , £• correspondingly.
Equation 34 in this report is obtained by considering the
hammermill as a once-through grinder and neglecting any internal
classification of the material. Thus if we put £ = g in Equation
A 4 we get
q = gN m (A16)
Similarly, if E = I, Equation A13 becomes
q = XN m (A17)
Both D and X now represent the overall "mill" matrices that may
be defined In terms of the breakage matrix | and selection
matrix S .
141
-------
APPENDIX B. SOME SIZE DISTRIBUTION RELATIONS PREPARED BY
D.M. OBENG (83)
Size Distribution Equations (for Brittle Materials)
Since the 1920's, repeated attempts have been undertaken by
research workers to arrive at a mathematical description of the
distribution of comminuted brittle materials. In the following
paragraphs, a brief outline is given of some of the relations
most frequently quoted in the literature.
Gaudin-Schuhmann Distribution Function—
Plotting on a log-log paper oversize particle weights
retained by a successive series of /2~ quotient Tyler screens,
Gaudin observed frequency distribution to form a straight line in
the finer particle ranges, leading to the discovery of the j
relationship
AY = cxa (Bl)
where AY represents the fractional weight of oversize particles
between two successive-Tyler screens.
Based on the findings of Gaudin, Schuhmann succeeded in
deriving a cumulative distribution formula in the following manner:
Let the quotient of screen series be p; then, summing up
over-size weights retained on the successive sieves according to
Equation Bl, we get
-a
and thence conveniently combining the constants
Y = (jl)a (B2)
where
-a
(B3)
142
-------
By transforming Equation B2 into
log Y = a(1og x - log k)
it may be represented on log-log paper as a straight line having
inclination a. Parameter a is referred to by Schuhmann as the
distribution modulus, and k, having a dimension of length, as a
size modulus.
Substituting x = k we get Y = 1; that is, k will be the
largest particle size, and a sieve with an aperture of that size
will let the complete charge pass.
Beyond Y = 1, the distribution formula will lose its validity,
and at this point, a break will occur in the straight line contrary
to the postulate that a distribution curve has to approach the
100% pass point asymptotically. In the coarse particle ranges,
therefore, the line will decline downwards, implying that with
unclassified ground products, Equation B2 will be valid up to a
certain limit only, as suggested by Gaudin's original paper.
For the last 30 years or so, most of the vast experimental
work conducted by American research workers has been based on the
Schuhmann formula.
Rosin-Rammler Distribution Function—
The Rosin-Rammler empirical formula, the most widespread
in European laboratory practice and research, can be written as
follows:
Y (X) = 1 - e-bxn
-------
For the same output T and different screen apertures they derive
pl
T = cR ' =
and therefore
1
k, pi^y
(B8)
,
R = (-1)
Variations of parameter p had to be determined as a function
of screen aperture (particle size) x. Experimental results have
shown that
p(x) -
and therefore n
X
k ^2
R=£-) (BIO)
and, finally, substituting e for k,
R = ]_Y = e-b)
-------
As shown by this equation, the relation can be plotted as a
straight line by a coordinate system made up from a log scale
abscissa on one hand, and an ordinate with a double logarithmic
scale of the reciprocal (J^yon the other. The slope of the
straight line is n to be intercepted by particle size x on the
horizontal line representing 63.2% undersize. Lower va?ues of n
are to be associated with a more scattered distribution, whereas
higher values of n will imply an increasingly uniform particle
structure. Size xo may be referred to as the absolute size
constant or characteristic particle size, and n as the uniformity
coefficient of the particle pattern. In reality., n varies from
0.5 to 1.3 for brittle materials.
Gaudin-Meloy Size Distribution Function—
Gaudin and Meloy present a theoretical derivation of the
distribution equation for single fracture that agrees with
experimental results better than either the Gaudin-Schuhmann
equation or the Rosin-Rammler equation. This equation is:
Y = = -i _ (1 _ _) (B13)
0 0
where MQ is the total weight of crushed sample, M(x) the weight
of undersize contained, x the size considered, x the feed size,
and r the size ratio (to be explained further below) .
The above equation is used in this thesis as a breakage
function B(x, xo) for the simulation of the process in the hammer-
mill, and we find it instructive to give here its derivation as
presented by Gaudin and Meloy in their paper.
It is assumed that the solid to be broken is isotropic,
homogeneous, and that the fracture is a single event. The model
of the fracture is as follows: Surfaces randomly oriented in
position and direction pass through a crystal. The crystal
fractures randomly along segments of these surfaces. All fragments
have the same shape. The assumption that all fragments have the
same shape puts constraints on how the surfaces cut the character-
istic dimension of the feed crystal.
Consider a line segment xo in length cut by r surfaces.
The first goal is to determine the frequency distribution of z,
the distance between any two adjacent cuts.
145
-------
1 2 3 n-1 n n+1 r-1 r
1 '' ! ; ; i ' M i
_ xn —>u
Vi
L
•^ x
0
dx
The probability of any cut being at a fixed point is xo.
Specifically, for a cut being at xn, it becomes ^xn . Similarly,
xo
the probability of another cut being at xn+1 is dxn+l.
o
If the cut at distance xn from 0 is the nth cut, then there
are (n-1) cuts preceeding it. Therefore the probability of the
cut ^ from the origin being the nth cut is /^n)11"1, and likewise
the probability of the cut x ., being the (n+l)th cut out of the
r cuts is /xo~xn+l\r~n~1.
xo
The probability Pj_(xn, xn+1) of having all of these events
happen simultaneously is the product of their individual
probabilities,
P fx x 1 - fV"1 ^" dX"+1 fWl/"""1
1 ' xQ- XQ ' (-I;-) (B14)
Equation (B14) gives the probability that there will be (n-1)
cuts between 0 and xn, one cut at xn+i, and (r-n-1) cuts between
xn and x0. Since the r cuts were ordered after the event took
place, a multinomial coefficient must be used to determine all
possible ways r cuts can cut a line with only the nth and (n+l)th
cuts having fixed positions. Since there are (n-1) cuts below
xn, and (r-n-1) above xn+i, the multinomial coefficient y is
A = /„ -,\.rL , -.M (B15)
146
-------
Thus, the probability ?2(xn, xn+i) of having r cuts at
a line segment x0 in length, with the nth and (n+l)th c
random on
cuts
fixed is ^ °r
(x "^Hx -x )r"n"1
_ , ri ^n "VVl . ,
(n-1): (r-n-l)l Y r dxn dVl (B16)
xo
We are interested in the distribution of the distance Z
between the nth and (n-J-l)th cuts. We have
Vi = z + \ (B17)
Regarding xn as fixed, while x ., varies we get
dxn+l = dz
Substitute this value of dxn+i and the value of y into Equation
B16 to obtain
P3(z,xn) = YX^" (xo - Z - xn)dzdxn (B18)
Since Equation B18 is a joint distribution of two independent
variables, it can be integrated with respect to xn within the
limits 0 < xn < x0 - z, thereby eliminating it. Hence
VZ> = ^ f V~X'Z V^X (B19)
The form of the integral can be changed by defining a new
variable y such that
Xn = (Xo - Z)y ; dxn - (XQ - z)dy (B20)
Substituting the above values into B19, we get
'-"-1 «•»>
147
-------
The integral in the preceding equation is the familiar 3
function
1 n_i r_n_i J . ,
/ y (l-y) dy = B(n,r-n) (B22)
0
and can be expressed in terms of r functions:
6(n, r-n) = r(n^n)
Since both r aitd n are integers,
r(n)rfn-l) _ (n-1): (r-n-D! (B24)
r(r) (?=17!
Substituting the results of Equations B23 and B24 into
Equation B21, we get
P4(z) = -~ (x -z)1""1 dz (B25)
xo
From Equation B25, we can derive the size distribution
equation. The relative volume of a fragment of size z to the
original size x0 is , z3 . Hence the abundance, dN(z), of
xo
particles of size z is
XQ3 r r_-,
dN(z) = (—) —- (x -z) dz (B26)
xo
The corresponding mass may be obtained by multiplying by the mass
of each z particle, Xp3, in which p stands for density, and X
for a shape factor. Hence
dM(z) = ApxQ3"r r(xo-z)r"]dz (B27)
integrating between the limits of 0 and x
M(x) = Xpxn3"r r ( (x -z)r"]dz (B28)
o J
148
-------
gives the mass contained between zero and x. On completing the
integration, inserting limits, and simplifying, we get
1 y r
M(x) = XpxAJ [1 - (1 - 7^ ] (B29)
0 xo
Since the initial weight is Mo = Apxo , then
Y = M(x) = i _ (] _ JL) (B30)
o xo
This equation is identical with Equation B13.
149
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-77-131
2.
4. TITLE AND SUBTITLE
Significance of Size Reduction
in Solid Waste Management
6. PERFORMING ORGANIZATION CODE
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
July 1977 (Isssuing Date)
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
George J. Trezek
9. PERFORMING ORGANIZATION NAME AND ADDRESS
The Regents of the University of California
University of California
Berkeley, California 94720
10. PROGRAM ELEMENT NO.
1DC618
11. CONTRACT/GRANT NO.
R804034
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laboratory—C1n.,OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
FINAL
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Project Officer - Carl ton C. Wiles, Phone 684-7881
16. ABSTRACT
This report provides information from laboratory research conducted
to characterize the size reduction of Municipal solid waste (MSW).
Results and data are presented on the relationships between refuse
size distribution, particle size, grinding speed, moisture content,
energy consumption, and feed rate. Also presented are some basic
considerations useful for designing solid waste shredders.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Comminution
Waste Treatment
Refuse
Size Reduction
Solid Waste
(Theoretical Relation-
ships)
Shredder Design
13B
3. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (ThisReport)
UNCIASSTFTED
21. NO. OF PAGES
164
20. SECURITY CLASS (Thispage)
:LASSTFTFn
22. PRICE
EPA Form 2220-1 (9-73)
150
• U. S. GOVERNMENT PRINTING OFFICE: l977-757-056/6't75 Region No. 5-11
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