LDTP - 78-01
Technical Report
Tire Test Variability
by
Richard N. Burgeson
March, 1978
Notice
Technical reports are intended to present a technical analysis of
an issue and recommendations resulting from the assumptions and constraints
of that analysis. Agency policy constraints or data received subsequent
to the date of release of this report may alter the conclusions reached.
Readers are cautioned to seek the latest analysis from EPA before using
the information contained herein.
Standards Development and Support Branch
Emission Control Technology Division
Office of Mobile Source Air Pollution Control
Office of Air and Waste Management
U.S. Environmental Protection Agency
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Table of Contents
Page
I. Introduction
II. Summary and Conclusions
III. Technical Discussion
A. Program Objectives
B. Program Design
C. Equipment
D. Tires
E. Data Collection
F. Analysis
G. Test Procedure
IV. Results
V. Conclusions/Recommendations
Appendices
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Tire Test Repeatability
I. Introduction
In order to determine the effects of the twin small-roll dynamometer on
tire rolling resistance, EPA has undertaken a program to measure tire
rolling resistance on both a twin small-roll dynamometer and a single
large-roll dynamometer. The results generated on the single large-roll
dynamometer will then be corrected to a flat surface (the road) and a
correlation between the twin small-roll dynamometer and the road estab-
lished with regard to tire rolling resistance. In order to estimate the
accuracy of these measurements, three (3) sets of tires (2 tires are a
set), each set of different construction type (radial, bias belted, and
bias ply), were tested repeatedly under the same conditions (vertical
load, cold tire pressure, etc.) on the single large-roll dynamometer.
The results of these tests are discussed in this report.
II. Summary and Conclusions
To estimate the test-to-test variability of our tire rolling resistance
test method, a set of tires representing each construction type (radial,
bias belted, bias ply) were chosen for repeat testing. All the tires
selected were of the "78" series, 15 inch nominal diameter and "H" load
carrying capability. Prior to testing, each tire was set to a cold
inflation pressure of 26 psig which was unregulated throughout the test
(trapped air method). The vertical load was fixed as the rear axle
weight of the test vehicle to include a full tank of fuel. Each tire
test was preceeded by a warm-up cycle which consisted of the vehicle
being operated according to the current Federal Test Procedure (3-bag
Urban Speed-Time Driving Cycle). The vehicle was then accelerated to
and maintained at 50 mph for a period of 15 minutes, during which time
data were collected (all tests were conducted on the large (48" dia-
meter) single-roll dynamometer). The power absorbed by the tire was
obtained by monitoring both the power transmitted from the vehicle and
the power received by the dynamometer and computing the difference. The
tire rolling resistance was then determined from this differential
quantity.
From the data collected, it was found that the test-test variability is
approximately 9.16% for the radial tire, 7.57% for the bias belted and
10.01% for the bias ply tire. Vehicle speed fluctuations, dynamometer
residual friction, and the vehicle differential power losses are iden-
tified as the primary sources of this variability. An investigation
into other possible sources failed to result in any significant con-
clusions.
III. Technical Discussion
A. Program Objectives
To determine the variability associated with the tire and tire rolling
resistance test procedure currently used by EPA.
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B. Program Design
Tire rolling resistance measurements were conducted on three (3) sets of
tires, each set representing a popular construction type (radial, bias
belted, bias). The initial cold inflation pressure was set at 26 psig
and allowed to increase during testing. Each set of tires was mounted
on an instrumented vehicle and the vehicle operated first, over the
Federal Test Procedure (speed-time) driving schedule as a warm-up and
second, at a velocity of 50 raph for 15 minutes. It was during the
latter vehicle operation that tire rolling resistance measurements were
conducted. Each set of tires was tested in this manner seven (7)
times. An individual set of tires was not retested until at least a
period of four (4) hours [1] had elapsed to permit the tires to return
to ambient temperature. All tests were conducted on the large single-
roll dynamometer.
C. Equipment
1. Test Vehicle
A 1971 Ford stationwagon equipped with a driveshaft torque sensor and
optical speed pick-up was utilized for this program. The combination of
these two sensor outputs provide a measure of the power transmitted from
the vehicle to the tire. By measuring the driveshaft torque and the
driveshaft speed the power to the rear axle of the vehicle may be
computed as follows:
P = T W 1
Engine Engine E
where
?„ . = Power generated by the engine
t-j in K in &
T_, = The torque measured at the driveshaft
Engine
W = Angular velocity of the driveshaft.
Ci
In order to determine the power at the tire, however, the amount of
power lost due to differential bearing friction and to brake drag must
be subtracted from the power generated by the engine, P_ . . In this
study break drag was minimized by disablement of the self*aSjustors and
readjustment of the brakes. The following equation assumes zero brake
drag.
P = P - P 2
Tire Engine Diff
where
P .f, = Power required to revolve the rear axle and associated
bearings and gearing which compose the differential.
PD'ff was Previ°usly determined by measuring the driveshaft torque and
speed while the vehicle's rear wheels were raised off the ground. These
data were collected by sampling these parameters while the vehicle was
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operating at velocities from 10-60 mph. The vehicle velocity was in-
creased and then decreased in 10 mph increments between 10 mph and 60
mph. Thirty seconds of data were collected at each velocity increment.
A regression line defining P^jff as a function of driveshaft speed was
then computed.
2. Dynamometer
A large (48" diameter) single-roll LABECO dynamometer was utilized for
this experiment. The dynamometer roll was equipped with a magnetic
proximity detector so that roll revolutions (roll RPM) could be moni-
tored. In addition, the torque load cell sensor output was recorded
simultaneously. The product of these two variables is the power re-
ceived by the dynamometer through the tire. However, since the dyna-
mometer is an electro-mechanical device, a certain amount of power is
consumed by bearing friction. Therefore, the power at the tire/roll
interface is as follows:
P = P + P 3
R LC BL
where
P = Power measured as a function of the torque load cell sensor
IjO
PDT = Power consumed by bearing friction
tlL
The power consumed by bearing friction was determined by dynamometer
coastdown on a daily basis after a 30 minute warm-up period at 50 mph.
Prior to this program, a study was conducted to determine the test-test
variability of the dynamometer residual friction. After a warm-up
period of 30 minutes at 50 mph, five (5) successive coastdowns of the
dynamometer were performed. The dynamometer roll speed, load cell
torque and real time were recorded during each coastdown.
D. Tires
Three (3) sets of tires (2 tires constitute a set) of various manu-
facture were chosen for this program. All tires were of the same size
(15" nominal diameter), series ("78") and load carrying capacity ("H").
Each set of tires represented one of the common construction types
(radial, bias belted, bias) and had at least 400 miles of tread wear.
E. Data Collection
During the 15 minute test period, data were collected and recorded at a
frequency of once per second. Vehicle and dynamometer-roll speeds,
vehicle and dynamometer torques, real time, test code, tire manufacturer
code and a size code were recorded on 7-track magnetic tape utilizing a
Kennedy 7-track tape transport and a Datum digital data acquisition
system. Only those data recorded while the vehicle was operating at a
velocity of 50 mph were utilized for this program (approximately 900
data points per test).
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F. Analysis
The power absorbed by the tire was computed for each data point (each
second) recorded during testing. This quantity was calculated according
to the following equation:
P=P -P -P-P
AT Engine Diff LC BL
where
P. = Power abosrbed by the tire
P,, . and P^. ,.,. are as defined in 2,
Engine Diff
and PT and P,.. are as defined in 3.
LL. rSL
The force required to roll the tire was then derived from PAT- In act
ality, PA is the product of the torque at the tire/roll interface and
P = T w 5
FAT VT D
The torque at the tire/roll interface is defined as the product of the
tire rolling force, F and the rolling radius of the tire, r,
K.
TT = FR x r 6
By substituting for T in equation 5, the following equation results;
PAT = (FR x r)WT 7
Since the angular velocity of a rotating body is the ratio of the body's
linear velocity to its radius of rotation, P.T can be expressed as a
function of the linear velocity of the tire,
(F x r)V
P = — - - - = F V 8
AT r R T
where V is the linear velocity of the tire and F and r are defined in
6, above. The linear velocity, V , is in actuality the ground or test
surface velocity. Therefore, eitner the test vehicle speed or the
dynamometer roll speed can be utilized for the determination of F . For
this experiment the vehicle speed was utilized for this computation.
For each test, the following mean values were computed; vehicle speed,
V , power absorbed by the tire, PAT, rolling force, F , power absorbed
by the dynamometer, PTr, and the power out of the vehicle engine,
P . . Each test mean value was then considered to represent one test
engine —
point. For each tire type, a weighted mean, x , and pooled standard
deviation, s , were calculated from the test point mean values and then
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a coefficient of variability, in percent, was derived. The x and s
values were computed according to the following equations :
n..x.. + n_x. + . . . + n.x
2 - . . . ± -
g _ ^ - - - - - J -^Q
p n1 + n- + . . . + n. - i
where;
i = number of tests
n = the number of observations in the i test
N = total number of observations
s. = the variance of the i test
x = the mean value of the i test
The coefficient of variability was calculated as follows:
s
coefficient of variability = -^ x 100% 11
x
P
G. Test Procedure
Prior to testing each day, the vehicle and dynamometer were warmed-up
for 30 minutes at a steady state 50 mph. The vehicle tires used for
warm-up were then removed and a pair of test tires installed. A cold
tire pressure of 26 psig was set upon installation of the test tires.
The vehicle was then driven in accordance with the current Federal Urban
driving (3-bag speed-time) schedule used for vehicle certification.
Upon completion of this schedule the vehicle was then accelerated to and
then maintained at 50 mph for 15 minutes. The performance of the Federal
Driving Schedule was considered to be the tire warm-up period. At the
completion of each test, the vehicle fuel tank was refilled and a dif-
ferent set of test tires were installed and the above process repeated.
Once tested, a given set of tires was not retested unless a minimum of
four (A) hours [1] had elapsed. A minimum of six (6) tests per set of
tires were conducted in the above manner.
IV. Results
The values for rolling force, F , for all the tests conducted were
analyzed to determine the variability of the current tire test pro-
cedure. The coefficient of variability was computed by tire type
according to equation 11. These results are presented in Table 1.
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Table 1
Coefficients of Variability for
Tire Rolling Force, Fn , by Tire Type
Tire
Type
Radial
Bias Belted
Bias
Weighted
Mean F *
(Newtons)
117.09
167.78
167.97
Pooled
Standard
Deviation
10.72
12.70
16.81
Coefficient of
Variability (%)
9.16
7.57
10.01
* Rolling 'force mean values for two (2) tires.
An Analysis of variance (ANOVA) was performed on the above data to
determine if any significant differences could be detected with respect
to tire type. The results of this analysis indicated that the mean
rolling force displayed by the radial tire tested was significantly
different from that displayed for the bias belted and bias ply tires.
However, no significant difference was detected between bias belted and
bias ply tire rolling force means. This result is not unusual and is
due to the small sample and the magnitude of the variability displayed.
Possible sources of this variability are instrumentation calibration
errors, dynamometer repeatability, the frictional losses within the
vehicle differential, and vehicle speed fluctuation. Each item is
discussed separately below.
A.
Instrumentation Calibration
Prior to the commencement of the program, the driveshaft torque trans-
ducer, dynamometer load cell and the vehicle and dynamometer-roll speed
sensors were checked to establish linearity. It was found that all the
sensors, including associated electronics, conformed with the precision
specified by their respective manufacturers. Set points for each sensor
were determined at that time and were checked during the calibration
procedure. Since each set point calibration was recorded on magnetic
tape, any errors which may have occurred during the procedure would have
been detected during data review. It is assumed that the variability
contributed by the instrumentation and associated sensors is no greater
than the basic design precision and is negligible.
B. Dynamometer .
A study was conducted to determine the test-test variability of the
dynamometer residual friction. After a warm-up period of 30 minutes
at 50 mph, five (5) successive coastdowns of the dynamometer were per-
formed. The dynamometer roll speed, load cell torque and real time
were recorded during each coastdown.
The bearing losses, P , was computed for each coastdown (see Appendix
B for a derivation of P ). All PB and roll speed data were then
combined and a regression analysis was performed. The value of P
BL
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—7—
at 50 mph was then calculated from the regression equation and a coef-
ficient of variability computed as follows:
c.. . . . ,.,... Regression Standard Error ,nn
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Vehicle Speed
0.92
1.02
0.83
p
Engine
4.43
4.44
5.35
PLC
2.70
3.27
2.23
-8-
D. Vehicle Speed
Analysis of the vehicle speed data for each tire type indicated that the
variability of this parameter was small. However, even small fluctua-
tions produce large effects on F variability. From the "Analysis"
portion of this report, it can be seen that the vehicle speed influences
each variable comprising the computation of F . Statistically, it is
almost impossible to estimate the exact magnitude of the effect on F of
this variability. However, the coefficients of variability for the
major parameters affected can be calculated using equation 11 and are
presented below in Table 4. Also included is the coefficient of vari-
ability for the vehicle speed itself.
Table 4
Coefficients of Variability for Major Parameters in the
Tire Rolling Force Computations
Percent Variability
Tire Type
Radial
Bias Belted
Bias
If all parameters except vehicle speed were assumed to remain constant,
an estimate of the effect on F variability of the vehicle speed vari-
ability can be computed. These esimates are presented in Table 5.
Table 5
Effect of Vehicle Speed Variations
on Tire Rolling Force
Tire Type Percent Increase in Fn Variability
— — K
Radial 1.43
Bias Belted 1.41
Bias 1.17
The above estimates are based on the vehicle speed variabilities pre-
sented in Table .4. It must be noted, however, that the displayed
variations in speed also affect the torque measurement variability due
to the inertia of the system, i.e., torque spiking occurs on accelera-
tions and decelerations. The above estimates also ignore the additional
variability in the dynamometer portion of the tire rolling force compu-
tations which would also be affected by the vehicle speed fluctuations.
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It is generally accepted that a given tire is repeatable to less than
1 percent and is a function of the accuracy of the instumentation used
to measure the force. By summing the variabilities identified thus
far and subtracting these totals from the variabilities presented in
Table 1, an estimate of the remaining unidentified variability can be
determined. These results are shown in Table 6.
Table 6
Unidentified Variability
Tire Type Percent Variability
Radial 3.09%
Bias Belted 2.61%
Bias 5.29%
It is believed that if the variability associated with the interactive
effects of vehicle speed vaiations on the vehicle-dynamometer power
relationships could be quantified, the remainder of the test variability
shown in Table 6 can be explained.
E. Other Parameters Investigated
In an effort to identify other possible sources of test variability,
many of the parameters recorded during testing were analyzed for pos-
sible correlation with tire rolling force. The following is a list of
the parameters investigated.
1. Vehicle Differential Temperature
2. Wet Bulb Temperature
3. Dry Bulb Temperature
4. Barometric Pressure
5. Test Date
6. Test Time-of-Day
7. Tire Test Sequence
8. Test Driver
The results of these analyses indicates that the above parameters inves-
tigated were not correlated with tire rolling force.
V. Conclusions/Recommendations
The above analyses indicates that the test-test variability of the
present tire test procedure is larger than one might desire for an
engineering experiment. The method of determining the tire rolling
force via the subtraction of two large quantities (the power transmitted
by the vehicle and the power received by the dynamometer) to obtain a
relatively small quantity tends to create variable results. Small
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deviations in the large quantities produce large deviations in the
difference. The variability of the results is compounded further by
uncontrollable parameters such as the losses in the vehicle differential
and the bearing friction in the dynamometer.
In order to reduce the variability of future results several improve-
ments to the current test procedure can be made. Since a driver is only
capable of controlling the vehicle speed for a short period of time, the
sample period of each tire test can be shortened to 30-60 seconds,
instead of 15 minutes. An alternative to this method is to install an
automatic speed controller with drivetrain feedback. This would permit
a longer sampling period and reduce the variability due to speed fluctu-
ations. The speed controller would also permit better estimates of the
differential losses, again reducing the test variability. A moderately
expensive method of variability reduction would to be eliminate the
vehicle altogether. This could be accomplished by modifying the existing
dynamometer. A shaft torque sensor could be installed between the B.C.
motor and the rolls, in addition to the installation of low friction
bearings. A test stand could then be constructed and used to support
the test tire and vary vertical loading. The dynamometer could then be
used to control the tire test according to whatever type of speed cycle
is chosen. The ultimate method of reducing the test variability is to
construct a tire test machine specifically designed to reduce frictional
forces and to accurately control test speed. This machine would be
equipped with precision sensors so that the tire rolling force could be
measured as accurately as possible.
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References
[1] D.A. Clemming and P.A. Bowers, "Tire Testing for Rolling Resistance
and Fuel Economy", Tire Science and Technology, TSTCA, Vol. 2, No.
4 November 1974, pp. 286-311.
[2] D.J. Schuring, "The Energy Loss of Tires on Twin Rolls, Drum, and
Flat Roadway - A Uniform Approach", SAE Paper 770875, Society of
Automotive Engineers, New York, September 1977.
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APPENDIX A
Tire Descriptions and Test Data
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Table A-l
Tire Description
Tire ID Manufacturer Size Model/Type
090 Goodyear HR 78X15 Custom Polysteel Radial
13A B.F. Goodrich H 78X15 Custom Long Miler
ISA B.F. Goodrich H 78X15 Silvertown Belted
Table A-2
Ambient Tire Test Data
Tire
ID
090
090
090
090
090
090
13A
13A
13A
13A
13A
13A
13A
15A
15A
15A
15A
15A
ISA
Diff.
Temp.
139.80
138.30
135.10
139.15
136.10
135.70
140.75
139.15
139.45
136.95
137.55
135.80
139.95
140.40
138.55
134.95
138.25
138.40
Dry
Bulb
73.5
72.0
73.0
72.5
73.5
73.5
74.0
73.0
72.5
75.5
73.5
74.0
72.0
72.0
72.5
71.0
74.0
73.5
72.5
Wet
Bulb
63.5
61.5
64.0
63.5
64.5
63.5
65.0
62.0
61.0
65.0
63.0
64.0
60.0
60.5
63.5
61.7
64.0
62.5
63.5
Baro.
Press.
29.10
29.05
29.11
29.02
29.08
29.02
29.05
29.10
29.11
29.11
29.06
29.10
29.02
29.00
29.10
29.06
29.10
29.10
29.00
Test
Time
1040
1310
930
1035
910
905
1015
1035
1440
1440
1435
925
1440
1500
1040
1430
900
1020
920
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Table A-3
Tire Test Data
Tire
ID
090
090
090
090
090
090
13A
13A
13A
13A
13A
13A
13A
ISA
ISA
ISA
ISA
ISA
ISA
N
891
940
859
893
942
923
917
936
914
913
922
901
928
870
887
908
927
908
877
p
Engine
X
5422.186
5431.267
5501.703
5524.109
5545.504
5432.466
6496.567
6733.672
6713.409
6384.386
6922.609
7032.563
6548.309
6569.348
6716.341
6551.850
6359.213
6724.486
6594.408
a
219.745
267. 323
255.473
215.412
157.695
310.642
356.475
534.912
444.015
217.222
196.461
331.529
295.495
252.440
236.653
208.066
352.204
434.141
183.688
p
LC
X
1433.869
1341.797
1389.574
1434.324
1447.653
1388.097
1398.335
1375.443
1467.492
1487.961
1464.225
1437.751
1456.060
1367.694
1365.728
1405.039
1399.000
1470.095
1389.559
a
31.372
27.328
65.839
25.976
33.416
31.090
31.282
26.811
41.738
23.448
24.731
25.162
44.696
28.580
24.890
32.903
26.208
93.108
24.443
p
F
DIFF
X
1072.485
1036.208
1066.361
1069.518
1062.383
1068.828
1068.359
1070.710
1090.410
1076.499
1081.616
1070.353
1067.095
1068.868
1046.294
1076.227
1068.616
1070.293
1056.749
a
7.369
8.241
30.823
5.767
8.737
9.895
16.695
7.601
13.603
17.944
6.158
6.561
16.431
7.700
14.133
10.449
8.727
32.104
6.853
X
113.149
121.210
116.343
115.847
116.682
119.014
161.598
177.212
165.567
148.863
175.236
184.850
162.118
170.425
175.116
166.492
155.416
170.301
169.530
R
a
9.706
12.533
9.272
9.344
7.216
14.493
13.521
24.208
22.536
10.322
9.730
14.791
16.570
11.151
11.057
10.849
16.306
15.413
9.603
Vehicle Speed,
X
50.350
49.193
50.105
50.256
50.030
50.234
50.218
50.294
50.914
50.475
50.638
50.283
50.178
50.235
49.516
50.468
50.227
50.274
49.851
a
.233
.265
.992
.182
.278
.314
.534
.241
.431
.578
.194
.208
.522
.244
.460
.330
.277
1.017
.218
-p-
I
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APPENDIX B
Dynamometer Bearing Loss Computations
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B-2
Dynamometer Bearing Loss Computations
The power losses within the dynamometer due to bearing friction, PBT, is
the difference between the power at the dynamometer roll surface and
that measured by the dynamometer load cell. This may be expressed as a
function of torque as follows:
where
p = (T - T )W B-l
BL v R LCT R
T = the torque at the tire/roll interface
K
T _ = the torque measured by the dynamometer load cell
and W = the angular velocity of the dynamometer roll.
K.
During a coastdown, T can be computed by knowing the amount of inertia,
I, that is rotating and the time it takes this inertia to traverse from
one velocity to another.
T = la = I-r~R - I—R B-2
where a = the angular acceleration of the inertia.
For this program, a At of 30 seconds was utilized. The velocity of the
dynamometer roll at the center of this 30 second interval was then
defined as W and substituted into equation B-l. The value of T at
the appropriate W was then subtracted from the computed T and a value
for P at W results from equation B-l. Each P value was then re-
gressed against the appropriate W and a defining equation derived.
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