SDSB 79-10
Technical Report
•-February 1979
Computer Simulation of Tire Slip On
A Clayton Twin Roll Dynamometer
by
John Yurko
NOTICE
Technical Reports do not necessarily represent final EPA decisions
or positions. They are intended to present technical analysis of
issues using data which are currently available. The purpose in
the release of such reports is to facilitate the exchange of
technical information and to inform the public of technical devel-
opments which may form the basis for a final EPA decision, position
or regulatory action.
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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Abstract
Due to the occurrence of tire slip on a Clayton twin roll
dynamometer, there is a difference between the velocities of
the front and rear rolls of the dynamometer. This slip can be
modeled by the method described in the following report. The
results of this theoretical modeling show that, over the LA-4 and
the HWFET driving schedules the velocity of the rear roll (which is
currently used to determine the vehicle speed) exceeds the velocity
of the front roll (which determines the power abosrbed) by an
average of approximately 1%. From this difference in velocities of
the two rolls, a computation of the total energy effect, over
transient driving cycles, can be obtained. Approximately a 2% to
5% increase in total energy dissipated over the city (LA-4) or
highway driving schedules is predicted from the use of the front
roll velocity to determine the vehicle speed, as compared to the
currently used velocity of the rear roll.
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I. Introduction
When a vehicle is operated on a twin roll dynamometer the
velocities of the front and rear rolls differ. This difference, or
tire slip, is important because the tractive load imposed on the
vehicle is dependent on the velocity and acceleration of the front
roll, while the velocity of the rear roll is used to determine
the vehicle speed. This report discusses a theoretical model
of this tire slip phenomenon and investigates its effect on
the EPA measurements of fuel economy and emissions.
II. Discussion
Historically, the term tire slip has been used to describe
several physical phenomena and hence is somewhat ambiguous.
For the purpose of this report, which only considers the twin
roll dynamometer, slip is defined as the difference between
the velocities of the front and rear rolls of the dynamometer.
That is:
Slip = V - U (1)
V = velocity of the rear roll
U = velocity of the front roll
This slip has been observed in an EPA tire test program
which showed that at steady-state 50 MPH, the front roll consis-
tently travels at a slower speed than the rear roll (1). This was
confirmed for several different tires at five different power
absorber settings.
This phenomenon is significant, since the tractive load
imposed on the vehicle is dependent on the velocity and acceler-
ation of the front dynamometer roll, however, the vehicle is driven
over a speed versus time schedule based on the velocity of the rear
roll. Consequently, the difference in the roll velocities may
cause the vehicle to be underloaded with respect to the loading
which would be imposed if the same speed schedule were followed on
the road. Under steady state conditions, tests have shown that
this under loading may be more than 1/3 HP (1). (FY78 program
plans include an investigation into the relationship between
the occurence of slip on the twin roll dynamometer and the actual
road experience of the vehicle.)
It is also important to consider the effect of tire slip under
transient conditions. Since it is difficult to monitor slip during
a transient cycle, a theoretical model was proposed as the most
appropriate method of investigation. The subsequent subsections of
the discussion consider the development of the tire slip model, a
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comparison of some empirical slip results with the predicted
results, a computation of the energy effects, and an estimate of
the effect on fuel economy and emissions testing.
A. Theoretical Model
In order to theoretically model the tire slip that occurs on a
twin roll dynamometer, a model equation which couples the slip to a
dynamometer or cycle parameter must be chosen. Steady-state tests
show that the difference between front and rear roll velocities
increased as the dynamometer power setting increased. Conse-
quently, it is assumed that tire slip is directly proportional to
the force across the tire roll interface.
Slip = sF (2)
or
V - U = sF (3)
where
s = coefficient of slip
F = force at the tire/roll interface
The basic model equation 2, assumes that tire/roll slip is
caused by a tire deformation resulting from the tangential forces
that exist at the tire/front-roll interface.
Slip, during transient driving, can be calculated from the
model equation (3) if the force across the interface is known. The
force at the tire/front roll interface includes the dynamometer
force and the inertial force.
F = Dyno Force + Inertia Force (4)
The dynamometer force is assumed to be proportional to the
square of the vehicle velocity, that is:
2
Dyno Force = b u (5)
where
b - proportionality constant dependent on the total dyna-
mometer absorbed power.
This neglects the constant characteristic of the dynamometer
bearing force, however, this is not critical since the velocities
squared characteristics of the power absorber dominate over most of
the speed regions. Hence minor variations in the assumed dyna-
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mometer curve shape should not significantly affect the accuracy of
the model results.
The inertia force is the mass effect of the vehicle.
inertia force = m a
= m (du/dT) (6)
where :
m = dynamometer simulated inertia of the vehicle.
a = du/dt = acceleration
Substituting equations 5 and 6 into equation 4.
F = b u2 + m (du/dT) (7)
using the model equation 3 this becomes:
v - u = s(b u2 + m (du/dT)) (8)
A linear approximation is used to calculate du/dt for each one
second interval of the given speed versus time schedule. That is;
du/dt = u2 - Uj (9)
where :
T = 1 second.
This acceleration is assumed to be the acceleration at the
midpoint of the time interval. Therefore the midpoint velocities
are used in the model equation:
v = (v2 + Vj)/2 (10)
-u = (u2 + Uj)/2 (11)
Substituting 5, 6 and 7 equation 8 becomes:
(v2 + Vl)/2 - (u2 + Uj)/2 = s(b((u2 + u^/2) + m(u2 - Uj)) (12)
Expanding and regrouping terms in order to use the quadratic
formula:
2
(sb/2) u2 + (sbu. + 2 sm + I)u2 + (-(v2 + Vj ) + (sbu./2 + 2 sm + l)u,) (13)
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Using the quadratic formula to solve for u~
u2 = (-B + (B2 - r AC)1/2)/2A (14)
Where:
A = sb/2 (15)
B = sbuj + 2 sm + 1 (16)
C = (sbUj/2 - 2 sm + l)ux - (vj + v2) (17)
In order to utilize this model for computer simulation u, and
vj are initialized to zero, since the cycle begins with an idle.
vo is entered as the next speed point from the given driving
schedule (see Appendix A for computer program "slip"). Each time a
U2 is calculated, v2 and u2 are replaced by v^ and uj respec-
tively and the next v2 is entered. This iterative process is
continued for the entire driving schedule.
B. Theoretical vs. Experimental Results
The model was used to compute the dynamometer slip, using
input parameters estimated to reflect the vehicle parameters of a
1978 Mercury Zephyr. The Zephyr was chosen since this vehicle was
used in a recent test program on a Clayton dynamometer in which the
difference between the front and rear roll velocities was recorded
over an LA-4 driving cycle. Therefore, this allows a direct
comparison between the theoretical tire slip model and experimen-
tally measured dynamometer slip.
A mean coefficient of slip was calculated from the data
acquired from steady-state tire tests (1).
s = 0.0008 sec/kg
This program also requires the vehicle frontal area as an
input parameter to calculate the appropriate force coefficient. In
this case, the actual dynamometer power absorber setting used to
test the Mercury Zephyr, was used to back calculate for the appro-
priate frontal area, according to the equation given in the Federal
Register for non-fastback vehicles (2).
HP at 50 mph = 0.50 (Frontal Area) (18)
Where :
Actual Dynamometer HP at 50 mph = 9.7 HP
therefore;
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Frontal Area = 19.4 square feet.
The dynamometer power at 50 mph is then used to calculate the
proportionality constant (b) using equation 5.
2
Dyno Force = bv
Dyno Power = bv
therefore
b = (Dyno power @ 50 mph)/(50 mph)
50 mph = 22.35 m/s
745.7 watts = 1 hp
b = 0.648 kg/m
The input parameter for the vehicle inertia (m) was the same
as that used in the dynamometer tests with the Mercury Zephyr.
m = 1600 kg
With these parameters the theoretical slip was then computed
for the entire LA-4 and Highway Driving cycles.
The results of the tire slip modeling showed that the rear
roll travelled, on the average, 0.09% faster than the front roll
over the LA-4 driving schedule. Over the highway cycle the rear
roll averaged 1.4% greater speed than the front roll.
These results can be compared to the results of a test con-
ducted on a Clayton twin roll dynamometer with the Mercury Zephyr
(Figure 1 shows both the actual and theoretical slip for the first
130 seconds of the LA-4 cycle).
There is a very close comparison between the theoretically
modeled slip and the experimentally measured slip. The regions of
positive slip correspond to accelerations or steady-state modes in
the driving schedule, while the regions of negative slip correspond
to decelerations. A minor discrepancy in the magnitudes of the
modeled slip and the actual slip is mainly due to the use of a mean
value for the slip coefficient, which appears to be slightly low
for this particular vehicle. There are a few minor discrepancies
in peak locations which are probably caused by transmission shift
points. Also, a very slight shift in the data is observed which
may be due to a slight miscalibration of the chart recorder.
Since the purpose of this report is to estimate the total fuel
economy and emissions effects, these slight inaccuracies are not a
major concern. During rapid decelerations an actual mechanical
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slippage has also been observed. This phenomenon may result in a
significant discrepancy when comparing actual slip to theoritical
slip. However, since mechanical slip (actual sliding of the roll
surface across the tire surface) primarily occurs during closed
throttle modes it will not have a significant effect on fuel
economy results. Thus the theoretical model may be used to accur-
ately predict the effect of slip on EPA fuel economy and emissions
testing.
C. Computation of Energy Effects
In order to estimate the energy effect of the tire slip over a
transient cycle, a second computer program is developed. This
model utilizes the total road load equation of the vehicle on the
dynamometer (see appendix B for program "LA4FORCE").
f = rr + b v2 + m(dv/dT) (19)
Where:
rr = rolling resistance (tire force).
o
b v = dynamometer force.
m(dv/dT) = inertial force
The input velocity (v) can be either the front roll velocity
or the rear roll velocity, for any given driving cycle.
The power dissipated (P) is then calculated
P = F * V (20)
Finally the power is summed each second over the entire
driving schedule to yield the total energy dissipated. However, if
the power is negative the vehicle is assumed to be braking and this
is summed as a separate quantity referred to as "Brake Energy".
This program may then be used to calculate the total energy
that is assumed to be dissipated, over a driving cycle, using the
rear roll velocity. Simultaneously, it may be used to calculate
the actual energy that the vehicle has dissipated, by inputting the
front roll velocity, that has been calculated by the tire slip
model, for the same cycle.
This program was utilized in conjunction with the tire slip
program in order to calculate the energy effects of this tire slip
phenomenon. Once again, the input parameters were those of the
Mercury Zephyr. In addition, a rolling resistance coefficient is
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required in order to calculate the tire energy dissipated. A mean
rolling resistance coefficient was used, typical of that particular
tire type and size on the Mercury Zephyr(S).
rr = 0.010
coef
The total energy dissipated over the LA-4 cycle was calculated
using the veloctiy of the rear roll, and then the computation was
repeated using the velocity of the front roll (as computed from the
tire slip program). The results showed that 4.3% more energy was
calculated using the velocity of the rear roll as compared to that
calculated from velocity of the front roll (see Table 1). The same
procedure was repeated using the highway driving cycle and the
results showed a 4.1% greater total energy absorbed by the dynamo-
meter was calculated using the velocity of the rear roll as com-
pared to using that of the front roll.
III. Conclusions
There is a difference in the velocities of the front and rear
rolls of a Clayton twin roll dynamometer due to tire slip. This
slip is directly proportional to the tangential force at the front
roll/tire interface. It accounts for approximately a 1% greater
velocity of rear roll than the front roll, during transient driving
cycles. This difference in velocities can be modeled approximately
by the method as described in this report. A computation of the
total energy dissipated, by a vehicle over an LA-4 or HWFET driving
schedule indicates that approximately a 2% to 5% increase in energy
will result from using the front roll velocity to determine vehicle
speed rather than the currently used rear roll velocity.
IV. Recommendation
It is important to determine if this occurrence if slip on the
twin roll has a significant effect on fuel economy or emissions
testing. It is most important to compare this phenomenon to the
actual road experience of the vehicle. If such studies show that
slip is an undesirable factor during vehicle testing, some possible
alternatives are: to couple the front and rear rolls of the
dynamometer; use the front roll to determine vehicle speed, or look
to the possible use of flatbed dynamometers.
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References
1. Richard Burgeson, Myriam Torres, "Tire Slip on the Clayton
Dynamometer," EPA Technical Support Report, LDTP 78-02, March
1978.
2. "Control of Air Pollution from New Motor Vehicle Engines,"
Federal Register. Vol. 42, No. 176, September 12, 1977.
3. Richard N. Burgeson, "Clayton Dynamometer-to-Road Tire Rolling
Resistance Relationship," Technical Report, LDTP 78-09.
4. Glenn D. Thompson, "Investigation of the Requested Alternate
Dynamometer Power Absorption for the Ford Mercury Marquis,"
EPA Technical Report, LDTP 78-06.
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Figure 1
- - - - Actual slip
Theoretical slip
CO*
0.0
20.0
40.0
60.0
TIME
80.0
(SEC)
100.0
120.0
140.0
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Table 1
LA-4 Cycle
(1) Rear Roll
(2) Front Roll
(1-2) Difference
.-2)/2 % Diff.
Highway Cycle
(1) Rear Roll
(2) Front Roll
(1-2) Difference
L-2)/2 % Diff.
Total Distance
(meters)
11987.5
11877.4
110.1
0.93%
16496.2
16254.3
242.2
1.47%
Avg. Velocity
(m/sec)
8.74
8.65
0.09
1.00%
21.5
21.2
0.3
1.42%
Total Energy
(Joules)
X 10
504.0
483.0
21.0
4.3%
807.0
775.0
32.0
4.10%
Tire Energy
(Joules)
X 10
153.0
151.0
2.0
1.30%
210.0
207.0
3.0
1.45%
Aerodynamic
Energy (Joules
X 10
170.0
163.0
7.0
4.30%
552.0
527.0
25.0
4.70%
Brake Energy
i (Joules)
X 10
-181.0
-169.0
- 12.0
7.10%
-448.0
-400.0
48.0
12.00%
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Appendix A
A-l
C
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C
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C
C
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C
c
10'-
600
c
r:
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C
c
C
C
pPOf.RAM JO CAl'/iLATF THF TOTAL F OPCEC> » PnwE-c , AND ENERGY QISSIPA.TEO
n\/FP THF LA4 S-!-"En
V^. TIMF SCHEDULE
^'DITTEN BY JOH-.i YUPKQ
THF FOLLOWING •'"•', T a MUST RF SI IP'--L UTi'i : VFHICI..E MASS (KC-)« FRONTAL
(FT**?) , POLL I
COEFFICIENT (D^
FOP
ftY r-ir>T f1>>TC^ T-iE TEP'^S IN' THIS REPOPTt
FAREA ....... FP?V--;TAL
PAUCOF ...... CO^'FTCTFA'T ^F AEP-OYMAf-'IC HRAr,
VE-jlCi. F MASS (w)
EF ...... POl.i I\'G RrST^TAMCF COEFFICIENT
r) I MFNS I OKJ V ( 1 0 n 0 0 ) . T T ( 1 0 n o 0 )
H (5»100) VMJ.sS.F.A
(?F in. I.? !0.3)
A T ( ] X , ?F 1 0 . 1 » F 1 0 . 1 , / / )
FRONTAi APFA TO A n
"FDFRAL REG
FOR
= n.sn*FA".- A
'1 = 0.0
= PwATT"/ (??
IN VELOClTr-,TIME. AMD
LOAD COEFFICIENT USING THF
DV/DT
99
•10 ?o 1 = 1.1372
-VFAD (5»?On.FMD = c:'9Q) TT ( I ) . V( I )
20
FORMAT
. 1 )
30 "> FORMAT ( • 1 • . T6« »T!MF. i . Tl?. • VFLO-TTY* *T22.»ACCELFR.'«T33»
1 i TTRFFORCF1 . T44. » AFROFnRr;r i . T55 , • TMEPTIM..' «T^7.
? 'TrTAL'»T7°, if>0'Jc.R« . //I X »T5, i (S~C) • «T12. • (M/SFC)
1 • (HV/DT) » .T33» ' f^EMjOHS) ' . T44. • t ME '--'TOMS) •
.T67.tFO»CEi.T7P,ifwATTS)«.//)
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r.
c
C
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r
C
r
r
c
c
r,
C
40
70 n
CALCULATE OOLLIMG RESISTANCE (T*»EF> , AERODYNAMIC
IMEPTIAL FORCE (p
JMO TOTAL
TTRFF =
^FP.OE = 0.0
fMEPF =0.0
TJPFNG = 0.0
FMFPGY = n.o
;.1P Q 1 = ] ,M
CONVERT VFLOflrv FROM MP^ TO M-Tt'RS/SEC
V ( T )=.447*\/ (T)
.1=1-1
If (T.FQ. 1 )GO TO 5
= V ( ! )-V ( 0
TO 6
CALCULATE POWF° AMH FNFO-Y OIS-TPATEO
POWFP = FHPCF*-" 'EftM
JJPFP = TTPF.F*l'"EAM
T i PFNG =
AFPOF = A.FPOF + .'
^aLC'ILATF TMF TOTAL
E TP4VELt"0 RY THE ROLL
IF(FOPCF.LF.n.n»Go TO 7
FMFDGY = FMFPGV+PPWFD
GO TO R
"PPAKE" REPRESENTS \/EHjri E
r-'PlTE (6*400) I • v ( I ) .nv^T, TJOFF. •• c"POF . r'lrj^P
F OPM A T(io«.4x,Tu»Fin.?,FT0.2»FH.?.F12.?.Fll.2,Fin.2.Fl3.2)
F (6,FOO) TJ-Jl- NG.FIMEP. AEROE.f.^AKt .E'-.'FPGY
»0» »^X« 'TlPE EMEPr'Y = ' . F 1 0 . 3./4X , ' TNERTI AL EMERGY = ',
FH .3»/4X« 'AFRni-YMAMir FMFPAY - ' *El?.3«/4v. »PPAKE EMERGY = '»
r1 ?.3*/4X, iTOTM. FiVFPGY = ' « E 1 '-• . 3 )
-•'PITE (6.700)0
COP.WAT(FX. • 01 ST^Nrp = '.-10.1)
STOP
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Appendix B
B-l
C POnGBAM TO C*LC!'LATE THE \/ELOCI T Y (II?.) OF THE FRONT POLL FOR A TWIN
C ' P'UL DYNAMOMETER
C GIVEN THE ^EAP -'vLL VELOCITY (V2) : THAT IS THE VELOCITY FROM THE
C l_a<. SCHEDULE
C W'-'TTTEN PY JOHN vURKO
C
C THE FOLLOWING DATA MUST RF SUPPi TED: VEHICLE MASS (VM) IN KG*
C FRONTAL A^EA (F.'iPEA)
C IM FT**2, POLLl"-'^ RESISTANCE COEFFICIENT (RP). VELOCITY (V?) IN
C A^-Jn SLIP
C COFFFICIFNT (S)
c
r"
o
c CALCULATE COEFFTCIFNTS e AND M -OR ROAD LOAO EQUATION:
C (C"rft + R»V**?t-^J->n.//DT)
r C«"'MSTANT "A" REPRESENTS POLLING RESISTANCE AND HOES NOT
r C'iNTPIRUTF TO S! ?P
c THERFORE THIS TC VM T«; IGMPRED
r
OlfFNSlON V2(lOOnO) .IT (10000)
RE -'\n ( 5 , 1 0 0 ) \/M , F A -' - A , pp , s
DO ?n 1=1.132
DEin(R,?00»EMD=9^g) IT(T) .V'(T)
200 FO.'vAT(I4,F6. 1 )
20 C"J!-.iTlNllE
990 \|=T-1
10^ FO-'^'AT(2F10.1 tFlrt.3.E14.3)
WRITE (ft » 100) V/M»P"At-E/i ,RR.S
vi=n.o
u l=o.o
c
C CALCULATE" REAR PnLL VELOCTTY
C
no 9 1=1, N
c
C CONVERT V2 FROM '-••PH TO M
C
*1 .n
<-»C= (R*S*U 1/2.0-2. 0*S of* "I .p) *U1-V ( T) -VI
l(p= (_QP + SQRT (GR?-4.n«-OA*OC) ) / (•-•.0*0 A)
IP" (UP. RE. 0.0) GO TO ?
U?=0.0
Vl=V2(I)
r*
-------
e-2
c c-n CMLATF TOTAL USTANCF TRAVELS ON EACH ROLL
r
\/?U )=V2(T) /
TSl. TPrV?(I)-U?
AQ TO 21
W«TTP(6,300) IT (I) ,U?,V2(I) .TSL IP
30 r FORMAT (J4,F6.1 .Fl •••.] ,FIO. D
?i w»iTf:(A.,7nn) IT (H ,TSLTP
700 FORMAT ( I5.F5. 1 )
C
C THIS PROGPAM OUTPUTS THE rRQNT wOLL V^LrrHY IN (>'PH) IN /
C FOPMflT THAT
C CAM PF DIPFCTLY r
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