THE UNIV ER SIT Y OF MI CHI GAN COLLEGE OF ENGINEERING Department of Engineering Mechanics Department of Mechanical Engineering Tire and Suspension Systems Research Group Technical Report No. 1 PRELIMINARY MEASUREMENTS ON HEAT BALANCE IN PNEUMATIC TIRES G. H. Nybakken D. Collart R. J. Staples J. I. Lackey S. K. Clark R. N. Dodge supported by: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION LEWIS RESEARCH CENTER GRANT NO. NGR 23-005-417 CLEVELAND, OHIO administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1971

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS iv I. INTRODUCTION 1 II. SUMMARY OF RESULTS 2 III. THERMOCOUPLE MEASUREMENTS 6 IV. TEMPERATURE SENSOR MEASUREMENTS 24 V. SCRATCH PLATE MEASUREMENTS 36 VI. MODEL TIRE STUDIES 38 VII. THERMAL ANALYSIS 60 VIII. REFERENCES 67 IX. APPENDIX 68 iii

LIST OF ILLUSTRATIONS Table Page I. Summary of Experiments with Free Rolling Tires 14 II. Summary of Experiments with Yawed or Braked Tires 15 III. Summary of Experiments with H78-15 Tire at 30 mph 16 IV. Summary of Experiments 17 Figure 1. Thermocouple locations relative to cross section for G78-15 #5 and #8 6JK rim. 18 2. Thermocouple relative to cross section for H78-15 on 6JK rim (shown on a tracing of a G78-15 on a 6JK rim). 19 3. Temperature build-up around cross section. 20 4. Temperature build-up within crown. 21 5. Temperature profiles at crown. 22 6. Heat generation profile at crown. 23 7. Detail of sensor construction. 31 8. Sensor mounted on pavement. 31 9. Sensor array on pavement. 32 10. Bridge circuit for sensor. 32 11. Schematic instrumentation for experiment. 33 12. Trigger circuit and balancing circuit. 33 13. Treadless test tire mounted on truck. 33 14. Temperature/flux as a function of time. 34 iv

LIST OF ILLUSTRATIONS (Continued) Figure Page 15. (a) and (b) Positional information for surface temperature measurements; (c) tire as viewed from top. 43 16. Surface temperatures at various positions vs. speed on cast iron at 00 yaw. 44 17. Surface temperatures at various positions vs. speed on sanded Safety Walk at 0~ yaw. 45 18. Surface temperatures at various positions vs. speed on cast iron and sanded Safety Walk at 0~ yaw. 46 19. Temperature change of tension shoulder after going through contact patch vs. speed. 47 20. Temperature change of center tread after going through contact patch vs. speed. 48 21. Temperature difference between compressed shoulder and tensioned shoulder vs. speed. 49 22. Temperature difference between compressed sidewall and tensioned sidewall vs. speed. 50 23. Center tread temperature entering contact patch. 51 24. Center tread temperature leaving contact patch. 52 25. Compression sidewall temperature entering contact patch. 53 26. Tension sidewall temperature entering contact patch. 54 27. Compression shoulder temperature entering contact patch. 55 28. Tension shoulder temperature entering contact patch. 56 29. Temperature difference of center tread (and tension shoulder) between cast iron and sanded Safety Walk,. 57 30. Drag load in wheel plane vs. speed. 58 31. Drag load in direction of motion vs. speed. 59 v

LIST OF ILLUSTRATIONS (Concluded) Figure Page 32. Detail of sensor installation. 65 33. Schematic of sensor installation. 65 34. Analog of sensor installation for theoretical analysis. 65 35. Temperature/flux in nickel as a function of time. 66 vi

I. INTRODUCTION The purpose of the analysis and measurements outlined in this report is to give a clearer picture of the origin of heat generation in a pneumatic tire, and of the way in which the heat leaves the tire. In more detailed form, this question breaks down into several individual questions or research studies, each worthy of substantial effort. These may be expressed as: (1) To what extent is heat generated by hysteresis within the tire tread and side walls, and to what extent by mechanical scuffing bttween outer tread surface and roadway? (2) What is the distribution of release of heat by hysteresis relative to depth beneath the outer tread surface? (3) To what extent does the total heat generated flow to the atmosphere, and to what extent does it flow through the contact patch into the roadway? Subsequent sections of this report attempt to throw light on these questions by both analytical and experimental means. 21

II. SUMMARY OF RESULTS Research on this problem has been directed along three major lines of activity. These are: (1) An analytical study of -the problem of heat conduction in the rolling tire as it contacts the roadway. (2) Experimental measurements on full sized tires. (3) Experimental measurements on small scale, model tires. In regard to these three phases of effort, the analytical studies so far have been the least productive, at least in terms of generating new information. They have, however, been extremely helpful in interpreting the results of some of the experiments carried out under this program. For example, a, number of analytical solutions to thermal conductivity problems have been developed during the course of this one year of effort. In particular, the problem of' two-body contact has been studied in some detail and a, computer program written to give the temperature distribution in two bodies in contact for a short period of time, under conditions of heat release at the surface of Chese two bodies and under conditions of an elevated temperature of one body with respect to the other. In general this work shows that for the velocities and thermal conductivities encountered by an aircraft tire operating on a runway, the temperature profile caused by surface heating is that of an extremely thin skin on both surfaces, with the proportion of heat flowing into the concrete runway and into the tire being governed by their relative thermal conductivities and specific heats. This gives rise to the expectation that such 2

a thermal proportioning could be radically affected by controlling the thermal properties of the runway itself, even in the form of a very thin skin or sheet. So far, however, it has not been possible to calculate in any reasonably sound way the degree of heat released from the tire due to surface scrubbing on the runway, and so one must rely upon measured values of this quantity in order to examine the various temperature profiles exhibited. Experiments on fully instrumented passenger car tires were carried out at the Texas Transportation Institute using The University of Michigan Highway Safety Research Institute Mobile Tire Tester. Instrumentation in these tires consisted of a. large number of thermocouples embedded throughout the thickness of the tread and carcass at two regions, as well as an array of thermocouples around the meridional section of the tire. These tires were run for fairly long periods of time at a speed of 50 mph, and both the initial transient temperature rise profile as well as the near-equilibrium temperature distribution were measured. From the results of the transient temperature work it has been possible to show that a very large fraction of the total work done in rolling the tire under straight line, unbraked conditions is made up of hysteretic heat distributed throughout the tire carcass. However, far and away the largest fraction of this heat appears to be located close to the tread surface of the tire, opening up the possibility that it could be removed by some highly conductive surface mechanism. The exact fraction of heat so generated cannot be defined quantitatively until further experiments accurately define the total drag force of the tire

at the velocity and load conditions used in the thermocouple measurements. These conclusions based on thermocouple measurements are substantiated by thin film temperature sensor measurements taken directly on the highway. A series of these measurements show that the temperature rise associated with a freely rolling tire of typical passenger car size, at a speed of 50 mph and loaded with a, vertical load of 1000 lb, was so small as to be barely measurable. The sensitivity of these sensors is less than 10F, so that we can state with certainty that the temperature rise is less than this 10F limit. Calculations are not yet complete on this data., but it strongly implies that surface scrubbing itself plays a very small part in the rolling loss process. Slow speed scratch measurements were made using the same tire as used in the thermocouple measurements. These were carried out on the flat plank tire testing machine at The University of Michigan Highway Safety Research Institute, also under the same vertical load as was used on the highway tests. These measurements showed that the drag force associated with surface scrubbing of the tire was less than 10% of the total drag force of the tire. This implies that less than 10o of the energy used to move the tire forward is released in the form of surface heat scrubbing. This confirms the two previous experimental conclusions, but still leaves the possibility open that the hysteretic portion of the tire loss, which appears to be the largest portion by far, has its origin very close to the surface. Recent computational studies on the stress states near the surface of rolling tires, such as that of Yandell [1], reinforces the idea that the distribution of hysteretic and frictional losses may be radically different in a 4I

pure rolling and a pure sliding tire. Therefore, the conclusions reached so far in this work must be considered only for the case of the rolling tire and not as general statements good for all operating conditions.

III. THERMOCOUPLE MEASUREMENTS A series of experiments was conducted to examine the internal heating of a tire carcass under various conditions. The tires were instrumented with thermocouples bonded into the carcass. The temperature was recorded as a function of time and from this data the rate of heat generation could be calculated. This rate of heat generation can be compared to the mechanical power dissipated. The experiments were conducted on regular roads using The University of Michigan Highway Safety Research Institute Mobile Tire Tester, a truck modified to carry a tire under various loads and alignments at normal highway speeds. A total of three tires wa~s instrumented a~nd yielded useful information in the tests. Two of the tires, identical B. F. Goodrich G78-15 bias belted tubeless tires mounted on 6JK pressed steel rims, were instrumented in the same way. They bore code numbers DG24-0026-5 G598 and DG24-0026-8 G598 and are identified by the abbreviations G78-15 -f5 and G78-15 #8, respectively. 'lhese two tires had a. solid tread surface with the same gross contour as the standard production tire, but without grooves or sipes. The third tire was an H78-15 of the same construction as the G78-15 tires and was mounted on the same rim. This tire had a standard production tread. All three tires were load range B tires and the two sizes are both common on domestic intermediate size automobiles. 6

The thermocouple locations relative to the cross-section for the G78-15 tires and the H78-15 tire are shown in Figures 1 and 2, respectively. A fourth tire, a B. F. Goodrich 7.75-14 bias belted tubeless tire (code number R86-4079-3 U304) was instrumented but was not used because a leak developed during preliminary testing. The tires carried 1000-lb vertical load and were inflated.to 24 psi except as otherwise noted. The thermocouples were installed in the following way: the immediate area of the chosen location was frozen with liquid nitrogen, a 1/8 in. hole was drilled to the proper depth, the tire was allowed to return to room temperature and, after the thermocouple was inserted, the hole was potted with Duro Plastic Rubber (T.M.). The Plastic Rubber was injected with a. syringe to avoid trapping air pockets. All holes were drilled from the inside of the tire. In those locations where the thermocouple was within or beyond the ply structure, the fabric was also drilled. Those thermocouples located on the interior wall of the carcass were glued using Plastic Rubber in-to shallow dimples machined into the surface. The thermocouples were made from 28-gauge copper-constantan twin lead wire with plastic insulation. The junctions were butt-welded electrically and that region stripped of insulation during the welding process was coated with "Gaugecoat," a thin latex rubber waterproofing agent. The wire leads were taken from the point where they emerged from the rubber, around the inside of the tire to the common exit holes in the rim.

There were two such exit holes for the G78-15 tires and one for the more lightly instrumented H78-15 tire. The wires passed through the holes in a bundle and the hole region was potted with Plastic Rubber which served as a grommet, seal, and mechanical reinforcement. The lead wires were fastened to the inside of the tire at 6-in. intervals using tape secured with Eastman 910 adhesive. Preliminary experiments showed that a, small amount of slack between these fastening points was necessary to permit the lead wires to flex with the tire and to prevent breakage. The constantan lead wires were fastened to a common junction inside the tire cavity and a, single constantan lead wire was brought out from this junction. After passing through the exit holes the wire bundle was brought to a slip ring assembly, thence to a, 32~F ice bath reference junction located on the rear of the truck, and finally to the instrumentation in the cab of the truck. The instrumentation in the truck consisted of a, low resistance multipole switch, a, digital microvolt meter, a stop watch, and a tape recorder. The switch position and corresponding voltage and time were read verbally into the recorder for later transcription. The experiments reported here were performed on three occasions. The experiments using the H78-15 tire were performed on November 19, 1970, and December 3, 1970, at Ann Arbor, Michigan, on concrete roads with air temperatures between 40~ and 45~F. The experiments using the G78-15 tires were performed March 1, 1971, through March 3, 1971, inclusive, at College Station, 8

Texas, on asphalt roads with air and road temperatures in the ranges 40~-70~F and 450-900F, respectively. The experiments were conducted by bringing the truck to the appropriate speed, at which point the tire was lowered to the pavement and run under load at a constant speed until the appropriate data had been taken. The tire was then lifted and allowed to reach a uniform temperature as determined by the thermocouples before a second experiment was conducted. The recorded thermocouple potentials were transcribed and converted to degrees Fahrenheit and plotted as temperature vs. time. The data for the initial 1 to 2 min were examined to determine if conduction, diffusion, and convection effects were sufficiently small to warrant further processing of the data. If the graphs were sufficiently straight and did not exhibit curvature or the exponential leveling off associated with heat flow, then it was assumed that the rate of temperature increase was representative of the initial input of heat. It should be noted that, barring heat flow, the conversion of a constant mechanical power input to thermal energy yields a constant rate of temperature increase independent of initial temperature of the tire, and the ambient road and air temperatures. The rate of temperature increase was determined by fitting a straight line to the temperature vs. time graph and determining the slope of this line or by taking the temperature difference between two data points spaced 60 or 80 sec apart and directly calculating AT/At. The two methods are almost equivalent and the choice of method was made subjectively according to the 9

almost the same value and because the first scheme was much easier to use and because the difference between the values obtained using the two schemes was less than the overall projected uncertainty in the whole experiment, it was decided to use the first scheme for all the calculations of heat influx. The second scheme is illustrated in the Appendix. The partitioned sections used are shown in Figure 1 which also shows thermocouple locations. Experiments were conducted with the tires rolling free, with the tires at yaw angles of 4~ and 80, and with brake torques yielding drag forces up to 460 lb. The speeds used were 30 and 50 mph. Drag force could be measured for either nonzero yaw or nonzero brake torque but was too small to be measured for the free rolling case. The drag of the free rolling tire was assumed to be 20 lb, equal to 2% of the 1000-lb vertical load. Samples of the data and the graphs derived from them are shown in the figures and tables. Figure 3 gives an example of the temperature vs. time data for thermocouples located around the cross section and Figure 4 gives an example of temperature vs. time data for points within the crown. Both these figures refer to a free rolling tire. Figures 5 and 6 show sample temperature and heat generation profiles, respectively, through the crown of the tire. The specific rate of heat generation is the product of the rate of temperature increase and the specific heat capacity. The total heat generation data for the free rolling tire is presented in Table I along with the power input based on 20 lb drag and 50 mph forward 11

speed. The heat generation is calculated according to Eq. (1). Despite the extent of the assumptions involved there is surprisingly close agreement between the heat generated and the mechanical energy expended. The mean deviation for the AT/At data is 90 and it follows that the same mean deviation is applicable for the Q values. If the drag was indeed constant for all the experiments the average Q/P value has a mean deviation of 9%. This fact coupled with the average Q/P value of 1.035 indicates that the majority of mechanical energy used to drive a free rolling tire is converted to heat via tire rubber and fabric hysteresis. The data in Table II represents the heat generation around the cross section for various yaw and braking conditions for the G78-15 #5 tire. The drag was measured using the equipment on the Mobile Tire Tester. The power expenditure is meaningful only for the yawed experiments because in the braked experiments the brake mechanism absorbs an unknown fraction of the total mechanical energy. However, the yawed experiments may be compared with the unyawed experiments. Here we see that only 36% of the mechanical energy is converted into carcass heat whereas the figure for an unyawed tire was close to 100l. The difference is apparently due to the increased scrubbing in the contact patch in the yawed case. Table III contains a summary of some pertinent experiments with the H78-15 tire which was instrumented in the shoulder region. The experiments were all conducted at 30 mph with the standard 1000-lb vertical load and 24 psi inflation pressure. The heat generation rate Q was determined by using 12

Eq. (1). The thermocouple locations are referenced in Figure 2. The power figure for the free rolling tire corresponds to 20 lb drag. Note that the drag force may be under-estimated because the Q/P ratio indicates a surplus of 13o. However, the Q/P data for both the free rolling and yawed rolling tests compare well with the data for the corresponding tests with the G78-15 tires considering the extent of the uncertainties involved in the tests. Most of the experiments were of less than 5 min total duration because diffusion and convection effects would only complicate the determination of heating effects as explained previously. However, one experiment was conducted for a. time sufficient to reach thermal equilibrium. Temperature profiles through the crown showing the approach to equilibrium are shown in Figure 5. Note that as diffusion within the tire and heat transfer out of the tire become important, the hottest point in the crown moves from the region close to the surface inward toward the middle of the cross section. The profile yields temperature gradient data, which indicates that at equilibrium about 78%o of the radial heat flow is toward the outer surface and the remaining 22o is toward the inner surface. 13

TABLE I SUMMARY OF EXPERIMENTS WITH FREE ROLLING TIRES 0O yaw, no braking; 50 mph Test #8 with G78-15 #8; all other tests with G78-15 #5 Location Test 1 2 3 4 5 6 7 8 9 Avg. ftlb/sec t lbse of 1-9sec ft lb/sec 6.o875.1875.2000.1250.1188.1250.2063.1250.1570.1570 1760 1468 1.200 7.0625.1438.1313.1188.o688.0938.1688.2250.1000.1263 1 416 1468.965 11A.1175.2050.1250.0900.1250.2050 *.1900.1511 1692 1468 1.152 13.0775 *.1613.1188.1025.1238.1950 *.1088.1268 1420 14168.968 1.0688.1375.1250.1000.1063.1125.1688.2063.1125.1264 1417 1468.965 8.0625.1750.1063.1188.1313.1375.1500.1438.1375.1290 1446 1468.986 Avg. Average of six experiments -*.1357 1520 1468 103.5 Q is calculated according to Eq. (1). It is the rate of increase of the total heat energy within the tire structure. P is the product of the total drag and velocity. *Thermocouple inoperative. This location omitted from average.

TABLE II SUMMARY OF EXPERIMENTS WITH YAWED OR BRAKED TIRES Tilre-G78-15 #5, 50 mph Values of At/At, OF/sec TestYaw, B e Dr*ag Avg... P. Test Yawl Brake* Avg. deg No. 1 3 4 5 6 9 ft lb/sec ft lbec Q/ 10 4 0 70.1750.2875.1613.1175.1600.1650.0900.1652 1850 5140.360 12A 8 0 112.2375.3613.2575.2238.2963.2838.1988.2656 2970 8210.362 11A 0 V/ 70.0775.1475 1050.0o863.1050.1913.1000.1161.290 5140**.252** 12B 0 i/ 112.0775.1.100.o650.0500.o663.1125.0688.0786 870 8210**.106'* Q is calculated according to Eq. (1). It is the rate of increase of the total heat energy within the tire structure. P is the product of the total drag and velocity. *A check (/) indicates that the brake ^was applied. **No attempt has been made to determine the power dissipated in the braking system. Hence, this P does not represent power absorbed by the tire.

TABLE III SUMMARY OF EXPERIMENTS WITH H78-15 TIRE AT 30 MPH AT/At, OF/sec Location Yaw, Drag Qp deg No. 1 2 3 4 5 6 7 8 9 Avg. ft lb/sec ft lb/sec Q/P of 1-9 18 0 0 Dob.0875.1125 X**.1250.0750.0625.0792.0792.0708.0865 969 880 1.111 22a 0 0 Dob.1083.1125.1250.1167.0833.0708.0750.0667.0625.0912 1042 880 1.182 15 0 l/ 100.0778.1278 **.1444.0944.0778.0889.0889.0778.0972 1090 4400.248 24a 0 100.0611.o833 *.0944.0611.0389.0500.0500.0444.0o604 628 4400.154 17 4 0 90.0944.1000 **.1667.0722.1556.1722.1444.1444.1312 1470 3960.371 16 4 0 165.1056.1000 x-.2111.0944.2333.2278.2056.2056.1729 1935 7250.267 23a 8 0 go90.0889 o833.1556.0667.1667.1566.1167.1222.1195 1340 3960.338 Avg. of 18, 22 0 0.0889 995 880 1.130 Q is calculated according to Eq. (1). It is the rate of increase of the total heat energy within the tire structure. P is the product of the total drag and velocity. *A check ( /) indicates that the brake was applied. **Thermocouple inoperative. This location omitted from average. aThese tests were conducted with an improperly sealed system. Pressure dropped from 29 psi to approximately 24 psi for these tests. bDo is taken to be 20 lb equal to 2% of 1000-lb vertical load.

TABLE IV SUMMARY OF EXPERIMENTS Data + Sd Data ~~Yaw, k Drag,+ S ide 'eo re, Toad' Tair, Load, Pressure, Page Date Tire* Yeg Brake l*gb Force, Velocity., TLo -deg lb.9~l mph 'OF OF lbps No. lb 1 3/ 1/71 8 0 - Do 0 50 90 70 1000 22 2 3/ 1/71 8 4 64 647.5 50 95 70 1000 22 3 3/ 1/71 8 -? 50 95 70 1000 24 4 3/ 2/71 14 0 Do 0 50 51 43 1000 24 5 3/ 2/71.14 0 Do 0 50 51 43 1000 24 6 3/ 2/71 5 0 Do 0 50 46 40 1000 24 7 3/ 2/71 5 0 - Do 0 50 46 40 IO00 24 8 3/ 2/71 5 0 - Do 0 50 46 40 1000 24 9 3/ 3/71 5 0 - Do 0 50 54 34 1000 24 10 3/ 3/71 5 4 - 70? 50 65 41 1000 24 11A 3/ 3/71 5 0 - Do 0 50 65 41 1000 24 11B 3/3/71 5 0 V 70 0 50 70 46 1000 24 12A 3/ 3/71 5 8 112 0 50 70 46 1000 24 l2B 3/13/71 5 0 112 0 50 70 46 1000 24 13 3/ 3/71 5 0 Do 0 50 54 34 1000 24 14 3/ 3/71 5 0 Do 0 50 54 34 1000 24 15 12/ 3/70 H 0 / 100 0 30 54 34 1000 24 16 12/ 3/70 H 8 - 165 814 30 54 34 1000 24 17 12/ 3/70 H 4 - 90 555 30 54 34 1000 24 18 12/ 3/70 H 0 Do 0 30 54 47 1000 24 19 This data page blank 0 1000 24 20 12/ 3/70 H 0 V 460 0 40,50 54 47 1000 24 21 12/ 3/70 H 10 377 560 50 54 47 1000 24 22 11/19/70 H 0 Do 0 30 54 -4o 1000 28-18 23 11/19/70 H 4 90 555 30 54 -4c 1000 29-22 24 11/19/70 H 0 V 100 0 30 54 -40 1000 29-? 25 11/19/70 H 8 165 814 30 54 N4o 1000 24 *G78-l5 #5 + 5 G78-15 #8 + 8 H78-15 H 7.75-144 14 **A check (7) indicates that the brake was applied. +Do = Drag under free ieolling conditions. This is assumed to be 20 lb and could not be measured accurately. ++Side force is assumed to be zero in all unyawed cases.

18 X 'I 6 1 I 4 16 e 1 12 T.C. No DEPTH FROM INSIDE WALL INCHES 1-9 1/4 I 0 10-12 0 13 1/4 14 3/8 15 1/2 16 5/8 17 3/4 18 — 13/16 Figure 1. Thermocouple locations relative to cross section for G78-15 #5 and #8 on 6JK rim.

1.5 9 T. CN DEPTH FROM INSIDE WALL INCHES. I 0 2.3 3.6 4.9 5 0 6.3 7.6 8.9 9 0 Figure 2. Thermocouple locations relative to cross section for H78-15 on 6JK rim (shown on a tracing of a G78-15 on a 6JK rim).

85- G 78-15 No. 5 Tire Free Rolling, 50 mph 80 Refer to Figure 1 for Thermocouple Locations a: 70 20 w 9..9 60 Thermocouple No. Air Temp. - 400 Road Temp.- 460 20 40 60 s80I00 120 ELAPSED TIME (Sec) Figure 3. Temperature build-up around cross section. 20

75 GG 78-15 No. 5 Tire Free Rolling, 50 mph 70- Refer to Figure 1 for Thermocouple Locations 14 20 40 60 80 100 120 13 21 W 55 Thermocouple No. Air Temp. - 400 45 20 40 60 80 I00 120 ELAPSED TIME (Sec) Figure 4. Temperature build-up within crown.

120 110 L00 -o 24 'C - M16.2 0 8 0.0 0 r | ir| X8 w X w 50 5' —NITIAL 5/ 3 TE Fi p 60ro ximate2/3 oat DEPTH FROM INIEWA n —INITL TEMe I' —ROAD TEMP. -460 Outside Wall 40 --—.'AIR TEMPR- 400,,Approximate Location 30- 1 I I Iof Plies 0 0.25 0.50 0.75 DEPTH FROM INSIDE WALL (Inches) I I I I I I 12 5.13 14 15 16 17 18 THERMOCOUPLE NUMBERS Figure 5. Temperature profiles at crown.

Z 0.8 G 78-15 No.5 Tire o 0.18- Free Rolling, 50mph 1 Weg c 0.008 w a. I 0.16 < Q~O 0.007 W.o I 0.14 z z [,> 0.06t~nside~al | 0.006 0 oz o <J~ Isd W 0.00 2 z,-,r -— nOutside Wall u~~W C r. ~~0.00 o 0. 0.002 0 J E<: I,Approximate Location I" U ---~ 0.02- j of Plies 0.001 w 0 0.25 0.50 0.75 1.00 DEPTH FROM INSIDE WALL (Inches) I I I I I I 12 5.13 14 15 16 17 18 THERMOCOUPLE NUMBERS Figure 6. Heat generation profile at crown.

IV. TEMPERATURE SENSOR MEASUREMENTS The purpose of the experiment is to measure the heat flux, if any, caused by the scrubbing of the tire and the road in the contact patch area. It is believed that the presence of very small sensors bonded to the road does not change the geometry of the deformation of the tire in the contact patch region. Therefore the heat flux measured by the sensor is due to scrubbing of the tire on the polyimide surface of the sensor. This heat flux and the heat flux between tire and road are proportional to the respective friction coefficients, tire-to-sensor and tire-to-road. The experiment was performed on an asphalt taxiway at Willow Run Airport, Ypsilanti, Michigan. The sensors used for these measurements were thin film nickel resistors sold under the designation type ETG-50B by Micro-Measurements, Inc., Romulus, Michigan. Their measuring area is 1/8 in. x 1/8 in., and their thickness approximately.001 in. Four sensors were bonded to the road with a thin layer of epoxy cement. The sensors used are made of a thin film of nickel between two layers of polyimide. The film is practically insensitive to strain but very sensitive to temperature. Figure 7 shows the dimensions and geometry of these sensors. Figure 8 shows the sensor bonded to the asphalt road. Figure 9 shows the four sensors in place. On that figure notice: (a) the white arrow indicating the direction of travel of the tire over the sensors, 24

(b) the four sensors 2.5 in. apart, (c) the crack of the runway in which all wires are glued, and (d) the triggering mechanism for the oscilloscope. Each sensor was part of a bridge circuit shown in Figure 10. The sensitivity was found experimentally to be 0.77 mV/OF for E = 1.500 V and e = 0.00 at 75~F. A constant voltage power supply was used. Two sensors at a time were used. Figure 11 shows the complete circuit. Figure 12 shows the trigger and zero balancing circuit. A G78-15 patternless tire was used for the experiment, with inflation pressure of 24 psi and load of 1000 lb. The tire was mounted on the Highway Safety Research Institude truck and was in straight ahead free rolling position (see Figure 7). The tire was run at 50 mph and dropped on the road at fixed distances from the sensors. A device was put on the road in order to check the lateral position of the tire when passing over the sensors. Numerous tests were run between June 1 and July 27 in order to determine the best experimental conditions. Sensitivity of the sensors to sun radiation necessitated the running of the experiment very early in the morning of a cloudy day. The results of these tests are as follows: (1) When the tire was dropped as close as possible to the sensors (bouncing of the tire limited this distance to a minimum of 100 ft) with an initial temperature equal to the temperature of the road, as appreciable heat flux could be detected. 25

(2) When the tire was rolled for a fixed distance of 1 to 2 miles before passing over the sensors, it was possible to pick up the surface temperature of the tire which was apparently due to heat build-up caused by hysteresis inside the tire. (3) It is not feasible to run the tire under braking or yawed conditions because of the difficulty of dropping the tire at a distance less than a circumference before the sensors, and then the heat pulse measured is a combination of surface temperature and friction heat. Two typical trials are shown: (1) Trial 6 shows a slight cooling effect due to our initial temperature of the tire slightly less than the road temperature. (2) Trial 8 shows the typical data when the tire has been run for 1 mile before passing over the sensors. The computer program given subsequently in this section relates the temperature observed in the nickel film to the heat flux at the outer surface of the sensor. Prints of the contact patch show a length of 5.5 in. and a total 2 area of 29.6 in.. Therefore the time of contact of the tire with the sensor is: L 5.5 x 36oo00 V 50 x 5280 x 12 = 0.00625 sec The computer program is run for a unit heat flux pulse at the outer surface of the sensor for a duration of 6.25 x 103 sec and with the thermal 26

DATA FORM 036390 TRIAL NO. 6 OVERALL EEE E SENSITIVITY.26 _OF ruuu/cmu SENSOR # SENSOR *ih 2 -ms/cm SWEEP RATE INSTRUMENTATION: ATTEN X SCOPE SENS.2 mV/cm VELOCITY 50 mph TIRE: I.D. G 78-15 #5 LOAD 1000 lb PRESSURE 24 psi TEMPERATURES OF AIR 67 ROAD TIRE NOTES: All speeds so far: 50 mph 27

DATA FORM 036390 Duration of contact based on contact TRIAL NO. 8 patch length and velocity. SEN SIT IVIITY.26 -oF//cm SENSOR # 2 SENSOR # 2 ms/cm SWEEP RATE INSTRUMENTATION ATTEN X SCOPE SENS -mV/c VELOCITY 50 mph 678-15 #5 TIRE: I. D. LOAD 1000 lb PRESSURE 24 psi TEMPERATURES OF AIR 69C Bench 68TC ROAD 77 TC TIRE 84 TC NOTES: Tire down for / as in trial 8 28

characteristics of polyimide and asphalt. The thermal characteristics of asphalt were calculated from the composition furnished by the builder of the asphalt taxiway used in the experiment. A graph and table of the computer program are shown in Figure 14. The maximum ratio of temperature to flux is found to be 0.622 x 10-3 oF-ft2-hr/Btu. From the results of the experiments it was found that no increase in temperature could be found. As a way of checking, it is assumed that a 0. ~F increase could be found, and calculations are conducted to find out what this increase would represent in terms of drag losses: we have G/q = 0.622 x 10 3 ~F-ft -hr/Btu and G = 0.50F therefore q = 0.80 x 103 Btu/ft 2-hr q corresponds to the part of F (total heat flux generated at the interface of tire and sensor) flowing into the polyimide. We have therefore q + Fo kl, a1 conductivity and diffusivity 1 r and q - qr k 1 r F r 1 +Ea1 kkr1 ]~- ~~ 3.87 x l0.16 1 k] q 4 46 x 1o-3.o895.30 x 10 = 2.13 x 103 Btu/ft -hr f asphalt Therefore Q of friction between asphalt and rubber is Q = F x polyimide 29

f: coefficient of friction between asphalt and rubber asph f: coefficient of friction between polyimide and rubber poly The measured coefficients of friction were found to be f = o.80, f = 0.64 as pol -3 o.8o 3 2 Q = 2.13 x 10 3 x 064 = 2.66 x 10 Btu/ft -hr But the contact patch area is 29.6 in., therefore the heat due to friction is 2.66 x 103 x 29.6 D = 144 x 6oo = 0.152 Btu/sec And for a total drag of 25 lbf at 50 mph, the power loss in the tire is 25 x 50 x 5280 = 2.32 Btu/sec 778 x 3600 and D is 6% of total drag loss We see from our experiments and calculations that the friction heat generated at the interface of road and tire is a very small percentage of the total losses of the tire. Therefore all losses have to occur within the tire itself as hysteresis losses. 3o

Micro-Measurements ETG-50B Option W.24" Nickel.0002"i.0005" Figure 7. Detail of sensor construction. Figure 8. Sensor mounted on pavement. 31

Figure 9. Sensor array on pavement. Trigger is located at end of rule. 150R 25 150: 00'--- o_ 0 o 0o SI |o Sensor E 50~2 50Qa 500Q T Figure 10. Bridge circuit for sensor. 32

Triggetr([, ~~~~~~~~Trigg r~~~er~ ~Trigger Circuit S~~~~~~~~Eensors.5V BR Tridge ~~o i| ~ innput L- ~ -, ---- - — I-~IC''C~i'~L I c~-~z~Circuit sn1 2 ~~~~(ciof Iscope Figure 1. SchTrigg er circuit and batioancing for experiment. Fiur 1 Triggero Figure 11. Trigger circuit and balancing circuit. Figure 1 Treadless test tire mounted on truck bonded to the r55

++ ++ + + + + + + ++ -":3 + + ++ w. + 5~~ Legt ofteHa us Ir + + i ++ ~LL 0, ++ b. + X +xS +WyII I I LLI. 32 LI + — l t Length of the Heat Pulse + - 2 3 4 5 6 7 8 9 10 TIME (Milliseconds) Figure 14. Temperature/flux as a function of time.

FIRST MATERIAL: CONI ALPI THICKNESS O.5350E-O1 0.3R70E-02 0.1250E-03 SECND MATERIAL: CON2 ALP2 0.5600E 00 0.1760E-01 POSITION OF NICKEL/INTERFACE- 0.0333F-04 ASPAIA SHAPE OF HEAT FLUx TIME MA'NITIlDE 6.250 0.I0000E 01 TAPLE OF TEMPERATURE OVER FLUv" TIME IN MSEC TEMP/FLl!y I! NICKEL TE'1P/FLUX AT SURF "F FT2 HR/BTU F FT2 HR/BF U 0.125 0.044466E-0O 0.1/561/7E-03 0.250 0.746536E-05 0.2 0C64E-03 0.375 0.200160 E-0 0.253135E-03 0.500 0.35A733E-0O 0.2'22,05E-03 0.625 0. 5?2452 E-Oh 0.320706E-03 0.750 0.,<?5470E- - 0.357F7 E-03 0.R75 0.: S. 74''- 0 Z 0.33q.670E-03 1.000 0.! 043 15 E-03 CO. 13367E-03 1.125 0. 1 I 51 E-t03 0.4 3 A2 E-03 1.250 0. 3R321E-03 0C.S5215PE-03 1.375 0. 1543R42-03 0.3. 716 E-03 1.500 0.1711552-03 0.5062s3E-03 1.625 0.! 7101 -03 0.520?30 E-03 1.750 0.202'732E-03 0.54 r527E-03 1.g75 0.21 g53E-03 0.56S014E-03 2.000 0.2330722E-03 0.5g4567E-03 2.125 0.24777E —03 C.0C25430-03 2.250 0.26 2234 — 03 0.61 0 - 03 2.375 0.27 6394 E-03 0. 63 6'Q50 F-03 2.500 0.220242 -03 0.653A57E-03 2.625 0.3030 12E-03 0. 543 - 0- 3. 750 0.3172q E-03 0. 6523A- -03 2.F75 0.330417E-03 0.70055AE- 03 3.000 0.3,3303'- 03 0.715523E-03 3.125 0.3555"67E-03 0.73010 1 E-03 3.250 0.3 Sg' 02 -03 C. 7F z 31 E:- 0-3 3.375 0.3C061' -C03 CO.7550C <E- 03 3.500. 0.3 2 2 Z E-03 C. 77221 1 E-03 3.625 0.o 0?4 E- -03 C. 75702 - 03 3.750 0.1603E-03 C. 7 00 E-03 3.c75 0.427,??E-03 0.1 I z44E-03 A.000 0. 63q,- 03 0. 2 5 55E-03.125 O.t9 7 —03 0.370 1I -03 A.250 0.h A52zE-03. C251 -E- 03 4.375 0.a 71 0c20- 03 0. 2 1?72 E-03.50Q 0Q.a171 -' 03 0. 7301IE-03 h.625 0.A2056E-03 0.340352-03 4.750 0.502237E-03 0.?000 E-03 A. 75 0.5122!1 0E-3 0.073022-03 5.000 0. 52 131 E-03 0. 132 7 E-03 5.125 0.531?51 -03 0.9.?2 170 E-03 5.250 0.51zI '2E-03 093a37E-03 5.375 0.550057'-03 0.^50332E-03 5.500 0.560150E-03 0.906559 E-C3 5.f25 C.50S30 7E-C3 0. 7012AE-03 5.750 0.573331 '-03 0.9031 E- 03 5.g75 0.597225 -03 0. 99 0 3 E-0 3 6.000 0.595093E-03 0. 10003 E-02 6.125 0.604637E-03 O.10094E-02 6.250 0.613161E-03 0.101235E-02 6.375 0.620921 E-03 0.382476E-03 6.500 0.622410E-03 0.831072E-03 6.625 0.61gO016E-03 0.703629 E-03 6.750 0.610624 E-03 0C. 7 633 42 E-03 6.375 0.6011 I E-03 0.737529E-03 7.000 0.592361E-03 0.715021E-03 7,125 0.52 062 E-03 0. 94 0 g4Q0 F-03 7.250 0.572 0 E-03. 7 IS 52 7 E-03 7.375 C.5.3 A 03 3-023 0,., 50 72 0 - 03 7.500 0. 5530e4 -03 0C. 1 f;O'- 03 7.625 0.54 76 E- 3 2,2C 4 E-03 7.750 0.535771 0E-3 C.61 i033 E- 03 7.375 0.52 S3? E- 03- 0. 6 03 1? E - 03.000 0.51451 E-03 051035E-0 03 P.125 0.510125 E-03. 5 7 75 E- 03.250 0. 5 02 0 1 7 E-03 0. 5 F 5 1 -03.8375 0., 120?-0 3 C. 557600E- 03 3.500 0.66427E- 03 0.5477:6E-03 g. 625 0. 7q31 -03 0. 5 3 0 E-03 3.750 0.471 27E-03 0. 52 072,E-03 3.g75 0. C50 E-03 0.51 705F-03.000 0. 45754S E-23 0.510 o I E-03,.125 0.1z 5C702 E-03 0. 50 5,53 E-03 0.250 0.44 1 7E-03 0.44402E-03 0.375 0.4377 I E-3 0.4'64~0E-03. 500 0.43 144 4 -03 0.4733 11E-03 9.625 0. 2530Q -03 0.4713502-03 9.750 0. 310E- 0 03 0.. 1 I IE-03 0.375 0., 1 3 52 E- 03 0.4;57068E-03 1 0. 0 0 0 0.40772E-03 0.450 20! E-03 RE'.AR1. UN.IT OF TErMP/FLUY IS F-FT**2-FOR/' TIJ #EXECUTION TERMI']ATE Figure 14. (Concluded) 35

V. SCRATCH PLATE MEASUREMENTS One relatively simple mechanical method for measuring the energy losses at the surface of a rolling tire is to cause the loaded tire to roll over a smooth metallic plate upon which carborundum particles have been sprinkled. The grit embeds itself in the tread rubber and causes scratch marks on the plate surface as the grit particles pass through the tire contact patch. These scratch marks are indications of the amount of surface scrubbing present in the tire contact patch area. It is difficult to assess the accuracy of this method. Insofar as is known there is no study presently available comparing the measured deflections obtained from scratch records with those obtained from more sophisticated instrumentation. It must be surmised that the scratch records could not, in general, be larger than the displacements undergone by the tire surface in the absence of the grit, provided that the friction coefficients between the actual road surface and the metallic plate were the same. This is because the embedding of the grit particles into the rubber surface would, in general, cause scratch records to be equal to, or smaller than, the actual distances moved. In view of the uncertainty between the actual distances and the resulting scratch records, and the additional uncertainties concerning equality of the friction coefficient between a real roadway and a metallic plate, these scratch records can only be used as an indication. In the specific work reported here, 8.25 x 14 size bias belted passenger tires furnished without tread pattern by the B. F. Goodrich Tire Company were 36

used on The University of Michigan Highway Safety Research Institute flat plank tire testing machine in order to produce such scratch records. The plates used were.005-in. brass, and the grit material was carbotundum. The load on the tires was 1000 lb at an inflation pressure of 24 psi. These are standard conditions which have been used on these same tires for other tests. The tires were rolled in straight line, nonbraking, fashion over the scratch plates in three separate tests. The scratch plates were observed under a medium power microscope and the length of the resulting scratches were measured. These lengths were averaged over the width of the contact area and the total length of scratch, on the average, was found to be 0.02 in. Assuming a pressure distribution equal to the inflation pressure of 24 psi, assuming a contact patch width of 6 in., and further assuming a friction coefficient between the tire and brass plate of 0.8, a total drag force associated with these tires, due to surface scratching alone, can be computed. This gives a value of drag force due to surface scrubbing - 2.0 lb. In view of the fact that other measurements indicate that the total drag force associated with these tires at slow speeds is at least 20 lb, then one must conclude from these scratch records that the surface effects cause a contribution to the total energy loss which is approximately 10% or less of the total. This means that only a very small portion of the total losses can be ascribed to surface scrubbing directly, at least at these low speeds. 37

VI. MODEL TIRE STUDIES Two basic types of experiments were carried out on a 4.5 in. diameter tire, scaled down from a Type VII 40 x 12-14 PR aircraft tire. The tire model and its construction are described in Ref. [3]. One experiment was to measure the drag force of the free-rolling tire, while the other experiment was to measure the surface temperature of the free rolling tire. Both experiments were performed on a 30 in. diameter road wheel using two different surfaces of contact for the tire. One surface was the cast iron of the roadwheel itself, while the other surface was Safety Walk.* In a separate experiment these two surfaces exhibited similar static coefficients of friction. However, since the Safety Walk is made up of abrasive sand grains bonded by a glue to cloth backing, it is clear that their thermal properties are quite different. No formal attempt was made, however, to measure the thermal characteristics of the Safety Walk. Drag-force measurements were made on the freely rolling tire by use of small force transducers located in the axle between the tire and its supporting yoke. At the same time the side force perpendicular to the wheel plane was measured as a function of yaw angle. Bearing drag was estimated and subtracted from the drag-force measurements by use of a Plexiglas model wheel of the same size as the tire, but of essentially rigid construction and with extremely low loss characteristics. By subtracting this bearing drag component, the actual tire drag could be obtained for any set of conditions. *Trade Mark.

Tire surface temperatures were measured with an Ircon model CH-34L infrared radiation thermometer which has been previously calibrated for the emissivity of rubber. For these experiments, the average image size was approximately 3/16 in. in diameter so that the temperatures recorded represent averages over that area of the tire. Although a single individual operated this instrument throughout most of the experiments reported here, several people made check measurements from time-to-time to establish that there was no gross biasing in the temperature measurements. Figure 15 shows the location of the positions at which temperature was measured. The procedure for recording drag forces and tire temperatures was kept constant throughout these experiments. Each test was begun with both tire and rim allowed to cool to equilibrium temperature before beginning the test. The tire was allowed to run 4 min at the first test speed (500 rpm) at which time data was taken for drag load and temperature. Each successive speed value was then run for 2 min before data was again recorded. This procedure was followed for all yaw angles, and under a vertical load of 38 lb and with a 20 psi inflation pressure for this particular model tire. While considerable care was taken in measuring the steer angle values quoted in the subsequent figures, the mechanism for this was not as accurate as desired and so one must interpret the resulting yaw angle data as subject to an error of approximately +1~. Considerable care was also taken to insure that the measurements of temperature with the two different surface coatings on the roadwheel were taken under identical yaw angle conditions. This was accomplished by setting 39

the test tire at a particular yaw angle and carrying out the measurements of temperature on both surfaces without changing this yaw angle setting. Figures 16, 17, and 18 are typical surface temperatures measured at the three basic positions on the tire for zero yaw angle. On all three figures, it will be noticed that for both surfaces on the roadwheel, the center tread position is the coolest, the sidewall is the hottest while the shoulder surface temperature is intermediate. As is to be expected, the temperatures and temperature differences at the three positions increase with speed. Figure 18 is particularly interesting in that it can be seen that both the center tread and shoulder positions exhibit higher temperatures while running on the Safety Walk surface than they do when running on the cast iron surface. However, the sidewall temperatures are the same for both roadwheel surfaces. Figures 19 and 20 show the temperature change through the contact patch for the center tread and shoulder positions. Shoulder temperature is taken on the so called tension shoulder as shown in Figure 15. The tension shoulder temperature shows a definite tendency to increase on both road surfaces for both the 0~ and 2~ yaw angle conditions, but not for the other yaw angle conditions. There does not appear to be a great deal of speed dependence on this data. There is little strong evidence here that the tread either cools or heats in passing through the contact patch. Unfortunately the arrangement of the experimental apparatus did not allow us to measure the temperature on the compression shoulder of the tire as it passed through the contact patch. Consequently, little can be concluded about this particular position on a yaw tire. Figure 21 shows temperature difference 40

between the compressed shoulder and the tension shoulder at the entrance to the contact patch of a yawed tire. On both roadway surfaces the compressed shoulder is hotter than the tension shoulder in general. Figure 22 shows the temperature difference between the compression sidewall and the tension sidewall under identical running conditions. Here, the compressed sidewall is always hotter than the tension sidewall, with little influence of roadwheel surface apparent here. Figures 23 through 28 illustrate particular temperature levels for various positions on the tire under different yaw angles and speeds, using the two different roadwheel surfaces. In general, study of this data leads one to the following conclusions: (1) Temperatures increase in the tire with an increase in yaw angle. (2) Temperatures increase in the tire with an increase in speed. (3) Sidewall temperatures are independent of the roadwheel surface. (4) Points on the tire coming into contact with the road surface are hotter when run on the Safety Walk than on the cast iron. This latter point is quite clearly demonstrated in Figure 29, which shows the difference in temperature between the two surfaces for the center tread and tension shoulder positions. Figures 30 and 31 illustrates drag force in the wheel plane and drag force in the direction of motion, respectively, as a function of speed at several yaw angles. The nonlinearity of the data with yaw angle probably indicates errors in the measurement of 0~ yaw angle position, as previously mentioned. In examining this data, there appears to be little difference 41

between drag forces measured on the Safety Walk or cast iron, indicating minor effects from scrubbing contact. This is substantiated by Ref. [5]. Finally, it should be noted that examination of this data seems to indicate that the temperature difference between entering contact and leaving contact, as measured on the tread of the tire, seems to be approximately independent of the surface material upon which the tire runs, but to the best of these measurements is a very small quantity, thus not clearly substantiating the hypothesis of Schallamach concerning temperature rise in the contact region of the tire. 42

Portion of Tire in Contact (a) Patch. Excellent Demarcatio Lines Could be Seen on LRolling Tire. (o) Road Wheel 2, 1, 7 6, 5 FRONT VIEW REAR VIEW Positional Data was (b) w w. Always Taken in the Following Sequence: I, 2, 3, 4, 5, 6,2,1, 7,8 Thus Positions I 8 2 REAR FRONT REAR Gave a Fairly Good w~ ~ Check on Consistency FRONT of Temperature 4.~~3~ *sd~~ 8. Measurements. Road Wheel (c) TOP VIEW TENSION COM PRESSION SIDE SIDE DI RECTION' OF TRAVEL I_ I YAW ANGLE Figure 15. (a) and (b) Positional information for surface temperature measurements; (c) tire as viewed from top. 43

180 " 170 YAW ANGLE: 0~ 160 L ROADWHEEL SURFACE: Cast Iron w 160 Sidewall 150 nc i 140 W130 -H~~~~~~~~~~~~~ 130 | ~~Contact,~~~~~~~~~~ 1200~~~~ 1~ |Patch I 110 oShoulder _P- uc Center u100 / O_ Tread ~~~~~F 90C~~~~ J~ AGlazed Rubber LU 90 n| / 0- | Surface of 80 _ 00-1 Tread oa/3 Contact =E 70c Area 60 500 1000 1500 2000 2000 3000 3500 MODEL TIRE SPEED (rpm) Figure 16. Surf'ace temperatures at various positions vs. speed on cast iron at 0~ yaw.

180 L 170 YAW ANGLE: 0~ 0 160 ROADWHEEL SURFACE: Sanded Safety Walk LLJ W' Sidewall 150 ~l40 Entering L 130 E 130 Contact Shoulder wi. 120 o Center Tread v I100 _ 90 W 80 0 70 60 500 1000 1500 2000 2500 3000 3500 MODEL TIRE SPEED (rpm) Figure 17. Surface temperatures at various positions vs. speed on sanded Safety Walk at 00 yaw.

180 170 YAW ANGLE: 0~ MOO ROADWHEEL SURFACE: o Cost Iron wrr 160 o Sanded Safety Walk i 150 POSITION ON TIRE: o 0 Center Tread,0 < e Shoulder Lw 140 0 Sidewall XE | Leaving 130 t~ > Contact o r - o I Patch w 120 -w // 500 1000 1500 2000 2500 3000 3500 MOnFI TIRF SPEED (rpm) Figure 18. Surface temperatures at various positions vs. speed on cast.iron and sanded Safety Walk at 0f yaw Figure 18. Surface temperatures at various positions vs. speed on cast.iron and sanded Safety Wal at01 y w

CAST IRON SANDED SAFETY WALK ANL I0 10 I 0O 5r 0 _ -5Y -5.. w 10 10 -5 5 010 0 040 1 0 60 1000 2000 3000 1000 2000 3000 rpm rpm Figure 19. Temperature change of tension shoulder after going through contact patch vs. speed.

CAST IRON SANDED SAFETY WALK 5. 5 0 ' ~cC~- ~ ~____~_ O' `4~L~C~LC ~~ 00 5 -5 O IJ i 5I 'I I -5 -5 '~ 0 60 C5 L5 1000 2000 3000 1000 2000 3000 rpm rpm Figure 20. Temperature change of center tread after going through contact patch vs. speed.

30 Li 2-020 I 0~~~~~~~~~~~~IO w 01 0 20 YawAngle 0 30 A 40 060 ~ ao~ SANDED - 1 0 H C 500 1000 1500 2000 2500 3000 3500 rpm Figure 21. Temperature difference between compressed shoulder and tensioned shoulder vs. speed.

0 e 30 r-m3 - — uaI 6~ e 20 4C 2Oi CAST I: 20 Q- 20 IRON Ia: 40 w- 60 0 30 40 SANDED 20 SAFETY I1 20 WALK I0 I I I I I I I 500 1000 1500 2000 2500 3000 3500 rpm Figure 22. Temperature difference between compressed sidewall and tensioned sidewall vs. speed.

CAST IRON SANDED SAFETY WALK 180 L 170, 3500 a1 6L 3000 <150~ ~~~~~/ /2500 LU 140 2000 a./ 3500 w 130 - 300 10000 u1 500 90 I000 I3 I 0 I0.(. I I I I 0I0 o 70 0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) Figure 23. Center tread temperature entering contact patch.

CAST IRON SANDED SAFETY WALK 180 L 170 / 3500 " 160 3000 < 150 / a / 3500 2000 140 200(20oo Q, 130' 3000 ~ 1200 9 I 1000 80w 500 0 70 - o 0 0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) Figure 24. Center tread temperature leaving contact patch.

CAST IRON SANDED SAFETY WALK 180 3500 3000 /3500 "Om! 3000 2 170 -200 2 46 0 2000 o: 160:::). 2000 a 140 w:3 ~~~0~~~~~~~~1000 w 1000 1270 Ila 0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) Figure 25. Compression sidewall temperature entering contact patch.

CAST IRON SANDED SAFETY WALK 180 U-I170 3500 0~~~~~~~~~~~~30 w 160 3500000 sop 3500 P 50 150 3000 w 140 2 2000 w 130 I- ~ 2000 w 120:.Utr IIIor V) 100 F~9- 1000 1000 ar~~~~~~~ 90 j5lk 500 0 70 0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) Figure 26. Tension sidewall temperature entering contact patch.

CAST IRON SANDED SAFETY WALK 180..170, " 3500 X::30 /,, 3000 or 160 < 150 a: / 3500 L 140 3000- 2000 130 2500.3o 120 OF U. 00000-2000 1000 w 1 Fg 1000 M(/') 90oQ 500 __ j v,500 970 0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) Figure 27. Compression shoulder temperature entering contact patch.

CAST IRON SANDED SAFETY WALK 180 10170- / 3500 // 3000 n/ i-1650-o a,>150 3 2000 I40 / 3500 140 _ a. / 3000 w 130 I'uJ 120 2000 1000 C) W 100 500 90 w 80 0 2 4 6 0 2. 4 6 YAW ANGLE (Degrees) Figure 28. Tension shoulder temperature entering contact patch.

CENTER TREAD ~ 40r Entering Contact Patch Leaving Contact 3000 3000 Patch 000 gg30 't'cj ~ ~ ~ l a 02000 <'20 1000 _ua,9~~ 1(S1000 0 ~. I — cI0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) TENSION SHOULDER 50 Entering Contact Patch Leaving Contact Patch 4 - 3000 - 3000 -30 2000 2000 a ~~~~20 1000 I~Vj 1~~~~~~~~~~000 0 2 4 6 0 2 4 6 YAW ANGLE (Degrees) Figure 29. Temperature difference of center tread (and tension shoulder) between cast iron and sanded Safety Walk.

1.6 w z 1.4.4.4 LIJ 1.0A20 w _ r ~~~~~~~~~P — r~x — -wx wo -- ~ o 0.8 CAST 0I6.4 1.4 IF~~l~~ll~~~~~~II~C~ll 3 40 w 1. 00 a 2 0 0~~~~~~~~~~~~~~~~2 0 Oi SANDED 0. 66 _ A L 500 I0 0 150 2000 25oo 30O0 35Oj MODEL TIRE SPEED (rpm) Figure 30. Drag load in wheel Plane vs. speed

1.8 o -' —' --- —- ~ 40 1.6 0:2 1.4 U. CAST Z'~ 1.2 IRON Z '. 2~ o j 0o O 1.0 -0.8 zp0.6 c: 1.8 001 40::=.I SANDED Ie 1.4 SAFETY -i 1.2WALK O ~~~~~~~~~~~~~~0 1.0 o0.6 500 1000 1500 2000 2500 3000 3500 MODEL TIRE SPEED (rpm) Figure 31. Drag load in direction of motion vs. speed.

VII. THERMAL ANALYSIS This analysis is conducted in order to determine the temperature induced in the thin film of nickel of a sensor by the passage of a heat flux of length L at speed V at the outer surface of the sensor. The sensor is made of a thin film of nickel between two polyimide films, and this sensor is bonded to the road of different materials (see Figure 32 for dimensions). The idealization of the problem is shown in Figure 33. q(t) represents the heat flux generated at the interface of tire with sensor, and we are looking for the temperature inside the layer of nickel due to the heat flux q(t). The function q(t) depends on the contact between tire and sensor, and if we assume a uniform heat flux q, we have L: length of contact patch t = V: speed of the vehicle t: time of contact tire-sensor The following assumptions are made in the analytical treatment of the problem: (1) The problem is unidimensional. (2) The thin flim of nickel is so thin and such a better conductor than polyimide that it can be eliminated. (3) The layer of epoxy is supposed to be thin enough to be integrated to the road material. The final model is shown in Figure 34. We are looking for an expression of Gl(x,t). 60

Equations and Solutions Let us call e + e = L 1 3 the equations of conduction are r as a22 1 = 1 -L < x < O (2) "2 a2 2 x>O at 2 X>~ the boundary conditions are - 1k a) q (step function) "ICDCx=-L -k I = -k '1 axx=o Jx=O (3) 1(O,t) = 2(0,t) 1(x,O) = G 2(x,O) = 2(+o,t) = O Solving by Laplace transforms gives us __x _six X2(x,s) = C e2 +De 2 61

A, B, C, D are determined with the boundary conditions and finally 2 +00 2 2 9 e1x (2n+l)L, +- exp )(2n+l _ l(xt) = q 1 exp(-lt) 1 kn k4 1t -4 1 exp(2n+l)Lsc -( 2n+l)] n=0 k x-(2n+l)L erfc (2n+l)L-x x+(2n+l)L erf (2nl)L + x L 1 - erfc j () Computer Program The computer program calculates G1(x,t) for x = -L (outer surface) and x = -a (any position in the polyimide). The inputs are (1) all thermal characteristics of the polyimide and the road material; (2) the value L (called TH in the program) thickness of the polyimide; (3) the value a (called POS in the program) position of the nickel film in the polyimide; and (4) the shape of the heat flux q(t) in the form of a series of heat pulses (up to ten). The program computes 1 (-TH,t) and G1(-POS,t) using Duhormel's superprosition theorem. The program itself and typical results are shown for a step function for q and different road materials: copper, aluminum, concrete, asphalt, micarta, in Figure 35. 62

FUrTRANiA IV G COMPILER MAIN 03-26-71 13:29.54 PAGE 0001 0001 REAL*8 D,EQKF,GtO,PtQHRTtDEXPtDERFCtDSQRT,DABSSTtTL 0002 DIMENSION X(2),T(90),F(200),Q(500).RES(90,2,21htST(90)tFRES(90t2), 1TP(20),U(20),V(21,TL(90,21' ) 0003 DA'TA V U/21.*0, 20*O./ 0004 1 READ ( 5 100END=999 ) (O4ALPL,CON2 ALP2, THPOS TSVP NP 0005 i00 FORMAT ( 2E l4/2E1.4/2E1 14/.El11 L.4 I2) 0006 READ (5 201) M 0007 201 FORMAT(I2) 008Ci DO 35 I =i. 0009 READ(59,202) TP(I),V(I) 0010 202 FORMAT(2Ell 4) 0011 35 CONTINUE Oi)12 W=. 0013 DO 36 I=ltM 0014 W=W+TP( I )* (V( I)'V ( I+1' ) 0015 36 CGNTINUE 016 IF(W.NE.TP(M)) GO TO 37 0017 r I=TSVP/NP O018 X(1)=-POS 0019 X(2)=-TH 0020 A=SQR' ( AL P1 )/CON1 0021 B=2./SQRT(3.141596) 002 2 C=CON2*SQRT (ALP) 1 /(CON1*SQR T(ALP2 ) 0023 QK=( 1.+C) / (1.-C) 0024 D0'3 J=I NP 0025 ST(J)=J*T1 0026 TL( J,21)=ST (J)/0.36E7 0027 DO 3 K=1,M o028 IF(ST(J).LE.TP(K)) GO TO 4 0029 TL( J,K)=TL( J,21 )-TP(K)/0.36E7 0030 GO TO 3 003L 4 TL(J,K)=O. 0032 3 CCNTlNUE 0033 00 10 J=1,NP 0034 K=21 0035 63 T(J)=TL(J,K) 0036 62 DC 1 1 I=1,2 0037 IF(T(J).EQ.0.) GO TO 12 0038 G=O. 0039 H=O. 0040 R=AX( I) (**4'2)/( 4.*ALPI4T( J) ) 0041 DE 15 L=1,200 0042 N=L-1 0043 0=2.*N+1. ) *TH*X(I)/( 2.*ALP*T(J ) ) 0044 E=( (2**N+1. )**2*Th**2 )/ 4.*ALPL*(J ) 0045 F(L)=(UEXP(D-E)/QK+DEXP(-D- ))/QK**N 0046 G=G+F(L) 0047 IF(L.EQ.1) GO TO 15 0048 iF(DABS(F(L)).L'.DA3BSG)/1000.) GO TO 17 0049 15 CONTINUE 0050 WRITE(6, 01) ST(J I 0051 101 FORMAT('IFIRST SERIES NON CONVERGENT AT TIME: ',F7.3,'ON I='ll.) 0052 GO TO 79 0053 17 00 20 L=1,500 0054 N=L-1 63

FORTKAN IV G COMPILER MAIN 03-26-71 13:29.54 PAGE 0002 U055 U= (X ( I-2.*N+1.)TH)/SQRT( ALP ) 0056 P=( X i) +(2.*N+1.)*TH)/SQRT (ALP1) 0057 QL)=( O*DERFC ( 1.-O ) / (2.*DSQRr ( J )/QK-P*DERFC(P/t 2.*D.SQRT(T(J) ) 1 ) )) /QK**N 0058 H=H-+Q(L) 0059 IF(L.EQ.1) GO TO 20 0060 IF(DAbS(Q(L)).LT.DABS(H)/1000.) GO TO 22 0061 20 CCNTINUE 0062 WRITE(6,102 ) STIJ),11 U003 l02 FURMAT('ISECNO SERIES NONCONVERGENT AT TIME:',F7.3,'ON 1=e,1I) 0064 79 RES(J,I,K)=O. 0065 GO TO 11 0066 22 RES(JI,K)=A*(B*'DS'iRT(T(J} })*EXP(-R)*G+H) 0067 GC TO 11 0068 12 RES(J,I,K)=O. 0069 11 CONIINUE 0070 IF(K.EQ.21) K=O 0071 K-K+1 0072 IF(K.LE.M) GU TO 63 00'73 10 CONTINUE 00'74 IF(ST( l).GT.TPI ) ) GO TO 37 00:75 00 41 K=1,M 00/6 U(K)=VK+1 )-V(K) 0077 41 C.CNTINUt 007 JK= 1 0079 DO 43 J=1,NP 0080 IF(JK.Et.M) GO TO 45 0061 IF(ST'(JJ).GT.TP(JK)) JK=JK+.l 0082 45 DC 43 I=1,2 008 3 W=0. 0084 0DC 44 K=1,JK 0085 W=W+RE-S( JtI,K)U (K) 0066 44 CGNTINUE 0087 FRES(JJI)=V(1)'*RES(J, I,21)+W 0088 43 CONTINUE Od89 WRI TE(6, 106) CN,ALPI, 1 TH, CN2, ALP2,POS 0090 106 FLRKAMAT('1''FIRST MATERIAL:CONI',8Xt'ALPI',X, ' THICKNESS /' 't15X, 13El1.4/' SECND' MATERIAL:CON2',8X ' ALP2', 8X/' ' 15X,2ELl.4/ ' POSITI. 20N OF NICKEL/INTERFACE=', E l.4J 0091 WRITE6,204 ) 0092 204 FORMAT{'OSHAPE OF HEAT FLUX' J '0 SXt'TIME'tlOXt'MAGNITJDE/'. '1) 009.3 DC 71 K=1,M 0094 R ITE(6,205) TP(K. ),V K, 0095 205 FORMAT( ', 5XF7.3,6XE13. 6) 0096 71 CLNTINUE 0097 WRITE(6,103) 0098 103 FORMAT('0,19OX,'TABLE OF -TEMPERATURE OVER FLUX'/'OTIME IN THSEC', 14X,'TTEMP/FLUX IN NIGKEL',4X,'TEMP/FLUX AT SURF'/'O') 0099 DO 50 J:1,NP 0100 WRITE(6,104) ST(J) FRES( J,FRES( J2 ) 0101 104 FCRMAT(' ' 2X,F7.3t9X,E13.6, LOX, E13.6) 0102 50 CONTINUE 0103 WRITE(6,105) 0104 1'05 FORMATI'-','REMARK: UNIT OF TEMP/FLUX IS F —FT**2-HR/BTU') 0105 GC TO 81 0106 37 WRITE(6,203) 0107 203 FORMAT('IERROR ON FORM OF HEAT FLUX') 0108 81 GO TO 1 0109 999 CALL EXIT 0110 END 64

Polymide ez.0005" ______......______ _ -—.. Nickel e.0002" / Polym ide ea.0010" Epoxy Figure 32. Detail of sensor installation. (t) Polymide 0 e(:.0005" Nickel 2. e.oo000o2" Polymide ( e3 =.0010" Epoxy ) 4 Rood 5) Figure 33. Schematic of sensor installation..qtt) 'A Polymide 00 ~~K, Qa. 0 I. 0 "4 Concrete (or asphalt etc...) K2' (2' 82 Figure 34. Analog of sensor installation for theoretical analysis.

15- 0 ~ 010 0o 00 02 14- oo 8 3 B 12 -m 1O- x a,+ o3 Concrete Asphalt a- 6 + + Copper w + 5 9 2 -+ 0 5 10 15 20 25 30 35 40 TIME (Milliseconds) Figure 35. Temperature/flux in nickel as a function of time. First material: polyimide. Second material: as indicated. 66

VIII. REFERENCES 1. Yandell, W. O., "The Use of a Mechano-Lattice Analogy for Determining the Abrading Stresses in Sliding Rubber," Rubber Chemistry and Technology, 44, no. 3, June 1971, p. 758. 2. Viehman, W., "Surface Heating by Friction and Abrasion by Thermal Decomposition," Rubber Chemistry and Technology, 31, no. 4, 1958, p. 925. 35. Clark, S. K., R. N. Dodge, J. I. Lackey, and G. H. Nybakken, The Structural Modeling of Aircraft Tires, AIAA Paper No. 71-346, AIAA/ASME 12th Structures, Structural Dynamics, and Materials Conference, Anaheim, California, April 19-21, 1971. 4. Schallamach, A., "A Note on the Frictional Temperature Rise of Tyres," Journal of the IRI, 1, no. 1, January/February, 1967. 5. 'Seki, K., S. Sasaki, and H. Tsunoda, "Tyre Rolling Resistance," Automobile Engineer, pp. 88-91, March, 1969. 67

IX. APPENDIX The second scheme for determining the total rate of heat generation involves partitioning the tire cross section into elements centered about their representative thermocouples. The elements are delineated by dashed lines in Figure 1. The sketch below illustrates this partitioning and the names assigned to the elements. crown The elements as well la midregion as the tire are mid region symmetric. shoulder - sidewall \\ | --- bead + C/. This region is motionless and is not represented by a thermocouple. The areas of the elements and the approximate distances of the centroids from the scle center can be used to calculate the representative volumes. The percentage of the total volume represented by each element becomes a weighting factor in calculating a weighted sum of the rates of temperature increase. The tire is assumed to be homogeneous so that volume fractions are equivalent to mass fractions and the specific heat capacity is taken to be that of the rubber. The figures given are for a G78-15. All thermocouples are 1/4 in. deep. The tire weighs 30 lb. The data is for a free rolling, 50 mph experiment. 68

Location %,l Total Volume Thermocouples AT OF/sec (Left + Right Sides) Averaged At avg Actual Bead 5.1 none 0 Bead 8.7 1.9.1063 Sidewall 22.3 2.8.2125 Shoulder 26.9 3.7.2032 Mid region 22.0 4.6.1250 Crown 15.0 5.1188 The weighted average is (5.1 x 0 + 8.7 x.1063 + -— ) - 100 or.1566 OF/sec. Then Q =.1566 x 30 x (.48 x 778) = 1750 ft lb/sec. The average of all the thermocouples 1-9 =.1570 Q = 1759 ft lb/sec. The agreement is quite good, compared to the nonweighted method of Section III of this report. 69

UNIVERSITY OF MICHIGAN 3111111111111111111111111111111 11111110 3 9015 03483 0458