THE UNIVE R S I TY OF M I C H IGAN COLLEGE OF ENGINEERING Department of Applied Mechanics & Engineering Science Technical Report No. 14 TESTING TECHNIQUES FOR DETERMINING STATIC MECHANICAL PROPERTIES OF PNEUMATIC TIRES. R. N. Dodge R..B. B Larsbn *S.S K. Clark G. H.y Nybakken - * supported by: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GRANT No. NGL 23-005-010 WASHINGTON, D.C. administered through: DIVISION OF RESEARCH DEVELOPMENT AND ADMINISTRATION ANN ARBOR July 1973

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TABLE OF CONTENTS Page SUMMARY 1 INTRODUCTION 3 SYMBOLS5 TEST PROCEDURES AND RESULTS 6 CONCLUDING REMARKS 43 REFERENCE 44 DISTRIBUTION LIST 45 iii

LIST OF ILLUSTRATIONS Table Page I. Tire Descriptions 11 II. Tire Operating Conditions 12 III. Summary of Static Fore-Aft Stiffness, k (lb/in.) 16 IV. Summary of Static Lateral Stiffness, k (lb/in.) 30 V. Summary of Static Vertical Stiffness, k (lb/in.) 39 V.Figuremmary of Static Figu reions. 1. Tire coordinate directions. 6 2. Photograph of fore-aft test apparatus for model tires. 8 5. Photograph of fore-aft test apparatus for full size tires. 9 4. Typical fore-aft, increment load, force-deflection plots for model and full size tires. 18 5. Fore-aft force-deflection loops illustrating effect of loop size for a model tire. 20 6. Fore-aft force-deflection loops illustrating effect of loop size for a full size tire. 21 7. Dimensionless plot of fore-aft stiffness versus loop size for all tires. 24 8. Fore-aft force-deflection loop illustrating tire slippage during testing of a model tire. 25 9. Fore-aft force-deflection loop illustrating small, unidirectional slippage during testing of a model tire. 25 10. Lateral force-deflection loop illustrating dog leg type loop generated during testing of a full size tire. 26 11. Photograph of lateral test apparatus for model tires. 29 iv

LIST OF ILLUSTRATIONS (Concluded) Figure Page 12. Photograph of lateral test apparatus for full size tires. 29 13. Typical lateral, increment load, force-deflection plots for model and full size tires. 32 14. Lateral force-deflection loops illustrating effect of loop size for a model tire. 34 15. Lateral force-deflection loops illustrating effect of loop size for a full size tire. 35 16. Dimensionless plot of lateral stiffness versus loop size for all tires. 36 17. Photograph of vertical test apparatus for model tires. 37 18. Typical vertical force-deflection loop for a model tire. 40 19. Typical vertical force-deflection loop for a full size tire. 41 v

TESTING TECHNIQUES FOR DETERMINING STATIC MECHANICAL PROPERTIES OF PNEUMATIC TIRES By R. N. Dodge, R. B. Larson, S. K. Clark, and G. H. Nybakken SUMMARY Fore-aft, lateral, and vertical spring rates were three static mechanical properties selected for this program to determine the effect of testing techniques on the measured values of these pneumatic tire properties. Of these three mechanical properties, the fore-aft stiffness property was affected the most by different testing techniques used to obtain it. Appreciable differences in the fore-aft spring rates occurred using increment loading techniques and continuous loading techniques. However, varying the fore-aft force loop size had the most significant effect on the values for fore-aft stiffness. The most consistent and usable technique for determining a value for foreaft stiffness was based on generating and recording a continuous full cycle force-deflection loop. The stiffness value was then determined by measuring the slope of the line connecting the end points of the loop. To achieve consistent stiffness values, it was necessary to closely monitor operating conditions during the test, particularly the size of the force-deflection loop. The dependence of lateral stiffness values on testing techniques followed the same trends as fore-aft stiffness values, except to a lesser degree. However, vertical stiffness values were found to be nearly independent of testing procedures and techniques. Due to a characteristic initial "soft" portion in 1

the vertical load-deflection curve, consistent values of vertical stiffness can only be obtained when its value is determined from a definition that bypasses the initial nonlinear portion of the force-deflection curve. 2

INTRODUCTION Engineers measure and evaluate static mechanical properties of pneumatic tires for various reasons. Often the numerical values of these properties are exchanged among many engineering groups. This flow is an admirable exchange of technical knowledge and an economic use of time and effort. However, the indiscriminant use of such information can be unwise if these numerical values are not measured and interpreted consistently from one source to another. Thus, there is a definite need to investigate the effects of testing procedures and techniques on the static mechanical properties of pneumatic tires. Also, if it is evident that some properties are highly susceptible to testing techniques, it is possible that guidelines could be established for such measurements. The general purpose of the test program discussed here was to systematically investigate the effects of testing techniques on three important static mechanical properties of pneumatic tires. These effects were to be studied on both scaled model aircraft tires as well as full size tires. In addition, it was hoped that this work would be useful in establishing criteria for measuring those properties that are highly influenced by testing techniques. The static mechanical properties chosen for this study were vertical, lateral, and fore-aft spring rates. Each of these properties was to be measured and evaluated by various techniques and their results compared with one another. The techniques were to be varied according to the numerous methods used in the past by various testing groups. The research group concerned with this program has been actively involved

in establishing structural modeling laws of pneumatic tires [1]. Some validity has been established for these laws by showing favorable correlation between some mechanical properties of prototype and model aircraft tires constructed according to the modeling laws. These model aircraft tires are used in this investigation as well as a variety of full size automobile and aircraft tires. 4

SYMBOLS English Letters D - tire diameter F - tire fore-aft force x F - maximum tire fore-aft force xm F - tire lateral force y F - maximum tire lateral force ym F - tire vertical force z F - maximum tire vertical force zm k - tire fore-aft elastic stiffness x k - tire lateral elastic stiffness y k - tire vertical elastic stiffness z p - tire inflation pressure o x,y,z - tire coordinate directions (see Figure 1) Greek Letters b - tire fore-aft deflection x 6 - maximum tire fore-aft deflection xm 6 - tire lateral deflection y - maximum tire lateral deflection ym 6 - tire vertical deflection z - maximum tire vertical deflection zm 5

TEST PROCEDURES AND RESULTS The two coordinate system used in this work is shown in Figure 1. The mechanical properties discussed are described in terms of these coordinates* The x-direction is referred to as the fore-aft direction, the y-direction as the lateral direction, and the z-direction as the vertical direction. ical) z Tire coordinate directions. Figure 1. The stiffnesses or spring rates in these directions are defined in terms of the ratio of applied force to resulting deflection. The fore-aft stiffness k is defined in terms of the fore-aft load F and the corresponding deflection x x 6 obtained when a stationary time is first inflated and loaded vertically and x then subjected to a varying fore-aft load. The lateral stiffness k is defined Y in terms of the lateral load F and the corresponding deflection 6 obtained Y Y 6

when a stationary tire is first inflated and loaded vertically and then subjected to a varying lateral load. The vertical stiffness k is defined in z terms of the vertical load F and the corresponding deflection 5 obtained z z after a stationary tire is first inflated and then subjected to a varying vertical load. Data necessary to investigate these properties were collected for both model and full size tires. The model aircraft tires were built according to the modeling laws and procedures discussedbyClark, Dodge, Lackey, and Nybakken [1]. The model tires used in these tests were scaled from 40x 12-14 PR Type VII and 49 x 17-26 PR Type VII aircraft tires. The full size tires ranged from a foreign made 155 mm x 15 radial passenger car tire to a 24x 7.7-10 PR Type VII aircraft tire. Fore-Aft Stiffness The test apparatus used to obtain fore-aft data for the model tires is shown in Figure 2. This apparatus is a revision of the Static Testing Device described in [1]. Its basic structure consists of a tire holding yoke attached to a counterweighted 90-degree elbow arm which in turn is attached to a fixed base through a steel pointed hinge. The yoke assembly is loaded vertically with dead weights, causing the tire to bear against a movable steel bearing plate. This plate is supported by three ball bearings rolling in steel guides. The bearing plate has a high friction surface bonded to it to minimize tire slippage. The tire was positively locked in the yoke assembly to minimize 7

Figure 2. Photograph of fore-aft test apparatus for model tires. wheel windup during the fore-aft tests. The three ball bearing supports had low friction characteristics and the effective friction coefficient of the total apparatus was 0.0138. This friction coefficient also held for the lateral tests. Fore-aft data for the model tires were generally obtained by inflating the tire to a prescribed internal pressure and loading the tire vertically with a prescribed load. A varying fore-aft load was applied to the bearing plate through the screw assembly. Force was monitored by a calibrated force transducer located between the screw assembly and the bearing plate. Displacement was monitored by a Linear Variable Differential Transformer located between the yoke and the bearing plate. The placement of the LVDT is important, especially in fore-aft stiffness tests where the spring rate of the tire is high. The spring rate of the tire in the fore-aft direction can easily be of the same 8

order as the support structure. Measurement of the true tire deflection requires the relative displacement of the wheel hub and tue bearing plate. Because of the positive locking procedures used in these tests, wheel windup was found to be negligible. Thus, the relative displacement between the wheel yoke and the bearing plate was used as the measure of tire deflection. The output signals of both transducers were amplified througn carrier preamplifiers and recorded on a x-y plotter to give a force-deflection record. The test apparatus used to obtain fore-aft stiffness data for the full size tires is shown in Figure 3. The apparatus is a modification of a, Riehle Figure 3. Photograph of fore-aft test apparatus for full size tires. Tensile Test Machine into a slow-rolling flat plank mach ine. The wheel is bolted to the axle, which is rigidly bolted to the yoke whiCl i s bolted to the loading head of the testing machine. The tire is loaded vertically through 9

the loading mechanism of the machine, causing the tire to bear against a movable flat plank. The top surface of the plank directly under the tire has a number 80 grit sanding belt bonded to it. The plank is supported by low friction rollers located directly under the loading area and is guided by ball bearings located along the length of the plank and running against a stationary steel angle guide. This plank arrangement results in low friction characteristics and has an effective friction coefficient of 0.006, considerably lower than the model tire system. The fore-aft load is applied to the end of the movable plank. A tension-compression load cell is placed between the loading screw and the plank. The displacement is measured with the same LVDT used in the model tests. Again the LVDT is located between the plank and the yoke, since wheel-axle windup was negligible with the rigid system used in these tests. The fore-aft data for the full size tires were obtained in the same manner as the data for the model tires. One minor difference was caused by the nature of the two loading systems. The model tires were always operating under a fixed vertical load while the full size tires were always operating under fixed vertical deflection. However, the basic operation of the full size test apparatus was very similar to that used for the model tires. A brief description of the model and full size tires used in these tests is given in Table I. The A-series model tires are scale models of 40x 12-14 PR Type VII aircraft tires with a scale factor of 8.65 and the B-series model tires are scale models of 49x 17-26 PR Type VII aircraft tires with a scale factor of 12. Each model tire had been run through a break-in period before 10

TABLE I TIRE DESCRIPTIONS Model Tires A24 A23P B21 B23 B26 B29' 2-ply bias model of 40 x crown angle 39~, 840/2 2-ply bias model of 40 x crown angle 36~, 840/2 2-ply bias model of 49 x crown angle 42~, 840/2 2-ply bias model of 49 x crown angle 42~, 840/2 2-ply bias model of 49 x crown angle 41~, 840/2 2-ply bias model of 49 x crown angle 34~, 840/2 12-14 PR Type VII, Nylon, 10 EPI 12-14 PR Type VII, Nylon, 10 EPI 17-26 PR Type VII, Nylon, 28 EPI 17-26 PR Type VII, Nylon, 28 EPI 17-26 PR Type VII, Nylon, 10 EPI 17-26 PR Type VII, Nylon, 10 EPI Full Size Tires 1 2 3 4 5 6 7 8 9 10 1OM 24 x 7.7-10 PR Type VII, aircraft 8.00 x 14, 4-ply bias, automobile 7.50 x 14, 2-ply bias, automobile 7.50 x 14, 4-ply radial, foreign, automobile 5.90 x 15, 4-ply bias, foreign, automobile 155 x 15, radial, foreign, automobile 215 R 15, radial, automobile 7.50 x 14-8 PR Type III, aircraft H78-15, belted bias, automobile G78-15, belted bias, smooth tread, automobile G78-15, belted bias, smooth tread, automobile being used in any test. Most of the full size tires had not gone through such a break-in period. The operating conditions for the model and full size tires are given in Table II. For the model tires, the vertical force is prescribed while the vertical deflection is prescribed for the full size tires. The full size tire vertical deflections were obtained by loading the tires to the approximate rated load as specified by the Tire and Rim Association and then measuring the 11

TABLE II TIRE OPERATING CONDITIONS Tire A24 A23P B21 B23 B26 B29' 1 2 3 4 5 6 7 8 9 10 10M D (in.) 4.55 4.55 4.00 4.00 4.00 4.00 25.7 25.1 27.9 26.9 25.8 24.5 28.2 27.5 28.4 27.7 27.7 Po (psi) 20 20 25 25 25 25 85 24 24 24 20 20 24 87 24 24 24 (lb) 41.6 41.6 51.6 51.6 51.6 51.6 4800* 1175* 1085* 1085* 770* 770* 1510* 5400* 1510* 1380* 1380* 6z (in.).527*.519*.211*.216*.224*.197* 1.90 1.125 1.00 1.54 1.00 1.25 1.75 1.70 1.24 1.00 1.00 Fxm (lb) ~ 6 6 6 6 6 ~ 6 ~225 ~275 +250 ~200 +175 ~300 ~500 ~500 ~250 +250 (lb) ~ 5 + 5 + 5 + 5 + 6 + 5 +200 ~225 ~200 ~150 ~150 ~250 ~500 ~250 ~230 +230 *Approximate values. deflections. Also shown in Table II are the maximum and minimum fore-aft load F and lateral load F used for most of the tests. xm ym Eight different testing techniques were used to obtain fore-aft stiffness data. Each of these techniques is described below by number and the results from their use are discussed. All of the tires listed in Tables I and II were not subjected to all eight testing techniques. For tests 1-7, the model tires were run on number 220 grit silicon carbide sandpaper and the full size tires were run on number 80 grit sanding belt. Test 1 - Increment loads, half cycle, slow loop. The tire was pressurized and vertically loaded to the conditions given in 12

Table II. An increment of fore-aft load was applied to the system and held constant for one minute, at which time the resulting fore-aft deflection was recorded. The fore-aft load was then increased by the same increment and the procedure repeated. This incremental loading was continued until the fore-aft load had reached the maximum F given in Table II. The fore-aft loads were xm then decreased in a similar manner until the fore-aft load returned to zero. The resulting force-deflection data were plotted and the fore-aft stiffness k x determined by averaging the best straight line fits to the increasing and decreasing portions of the plots. These best fit straight lines were obtained "by eye." The fore-aft stiffness k was also determined by forming the ratio x of the maximum fore-aft load F and its resulting deflection 5 to obtain xm xm (F /5 ). The waiting time of one minute between increments of load was a xm xm controlled attempt to allow the tire to reach equilibrium before recording the deflection. This test procedure, Test 1, is representative of those used by testing groups that only have the facilities for taking half-cycle, increment load data. Test 2 - Increment loads, full cycle, slow loop. This test procedure was identical to Test 1 except the load cycle was continued in both directions, thus generating a full cycle of fore-aft loaddeflection data. The fore-aft spring constant k was determined by measuring x the slope of the line joining the end points of the fore-deflection loop. This determination of k eliminates the observers "eye" approximation used in Test 1. Again the maximum and minimum fore-aft forces are those given in Table II. Again the maximum and minimum fore-aft forces are those given in Table II.

Test 3 - Increment loads, full cycle, fast loop. This test was a. repeat of Test 2 except the loads were held constant for 15 seconds instead of one minute. This procedure was a controlled attempt to determine time effects on increment load tests. Test 4 - Continuous loads, slow loop. This test was also a repeat of Test 2 except the loads were continuously applied from zero to the maximum F, back through zero to the minimum F and xm xm back to zero. However, the test was not stopped after one cycle, but continued for several loops. In these tests, the loops were continued until the generated loop "homed in" on a single path. In most cases the single path was generated on the second or third cycle. The time for one complete cycle was approximately one minute. The value of the fore-aft stiffness k was again dex termined by measuring the slope on the line joining the end points of the forcedeflection loop. This test procedure, Test 4, is representative of those testing groups that have the capabilities of obtaining a full loop of forcedeflection through a continuous loading system. Test 5 - Continuous loads, fast loop. This test was identical to Test 4 except the load cycle was completed in approximately 10 seconds instead of one minute. This test was included to determine time effects for continuous loading conditions. Test 6 - Continuous loads, slow loop, plate deflection. This test was also identical to Test 4 except deflections were measured between the fixed base and the bearing plate. This test was included to illustrate possible errors when the wheel, yoke and support mechanism are assumed rigid. 14

Test 7 - Continuous loads, varying force loop size. This test was basically tne same as Test 4 with a complete loop generated in approximately 20 seconds. In this test, the maximum fore-aft force applied F was varied over a range of values. This procedure resulted in 4 or 5 difxm ferent size force-deflection loops. The fore-aft stiffness k was determined x using the Test 4 procedure of connecting the end points. Test 8 - Continuous loads, varying contact surface conditions. This test was also basically the same as Test 4. The high friction surface test was the same as in Test 4. After this test the tire was thoroughly cleaned. The high friction surface was removed from the bearing plate and the metal surface of the plate was cleaned thoroughly. The test procedure described in Test 4 was then repeated. Next an oiled surface and then a dirty surface (oil mixed with grit and sand) were tested in the same manner. Finally, the plate and tire were thoroughly cleaned and the tire bonded to the bearing plate with methyl-2 cyanoacrylate. At the instant of bonding, the tire was maintained at the prescribed operating conditions given in Table II. The test procedure was then repeated, again using the force loop size given in Table II. Due to the possibility of tire damage during the unbonding, the tires used in this test, Test 8, were different than the tires used previously in Tests 1-7. The results of Tests 1-8 are summarized in Table III. The friction forces of the testing apparatus have not been taken into account in arriving at the fore-aft stiffnesses given in this table. The results given in the table indicate that all tires, both model and full size, have the same general trends. However, the different in stiffness values between Test 5 and the preceding 15

TABLE III SUMMARY OF STATIC FORE-AFT STIFFNESS k (lb/in.) Test 1 2 3 4 5 6 7 8 Fxm k k k k k k Force Loop Size High Clean il Oil + Bonded Tires\ x x x x x Value of kx Friction Metal Grit A24 319 554 346 348 376 381 247 -2 4 -- -6- --- 457 402 577 568 355 A25P --- --- --- --- --- --- --- --- --- --- --- --- 326 328 --- 335 384 ~2 + 4 ~6 ~ 8 ~ 10 B21 320 3554 337 370 396 413 -- 441 420 95 69 --- - - B23 --- --- --- --- --- --- --- --- --- --- --- - 5365 349 --- 357 466 B26 300 342 3517 340 551 3653 - ~84 44 6 -- -- - 424 384 564 344 333 2 + 4 ~ 6 ~ 8 + 10 B29' 526 34 6 43 336 362 378 388 - 44 4 595 575 549 454 412 393 373 349 50 100 ~ 150 + 200 + 225 2 2620 2880 28820 040 5870 0 4140 2550 6190 00 4470 220 4160 6195 5000 4470 4220 4169 50 ~100 ~ 150 + 200 + 250 2990 0 04080 3 40 240 5440 3660 4940 460 4100 800 - - - 494o 456o 4100 3800 36 ~ 5+ 100 + 150 + 200 + 250 4 1680 1750 1690 1780 1780 1810 - 00 200 - -- -- -- ~ 50 + 100 + 150 + 200 5 3020 2680 313 300 3690 5790 50 0 4070 --- 6 1380 1410 1410 1470 1550 1560 - 50 ~ 100 150 ~ 175 1720 1650 1560 1560 + 50 + 100 + 150 + 200 + 3500 7 1400 1320 146 50 1630 1650 -- 2160 180 170 1690 1630 100 ~200 ~100 400 + 500 8 5210 5700 5860 6190 6670 6800 900 7950 7580 690 681 - - - - 9300 7950 7580 6930 6810 + 50 + 100 ~ 150 + 200 + 300 9 3410 5720 3460 3610 5820 3950 50 4900 0 2 30 - --- -1 - - 5302 4go0 4480 4210 3920 + 500 + 200 + 250 10 417 0 4000 4130 4170 ~ 50 0 2 - -- --- 2 - 60 1480690 4520 4480 loM --- --- --- --- --- --- --- --- --- --- --- --- 4960 4950 4910 4750 5060 + 50 + 150 + 200 + 250~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

four tests is somewhat greater for Tire 2 than any other tire. A number of specific observations can be made concerning the fore-aft stiffness tests: (a) The values of k determined from increment load tests, with the exx ception of Tire 2, ranged from 5-15X lower than those determined from continuous load tests. See the results for Tests 1-5. (b) The values of k determined from full cycle increment load data from x model tires were 2-7% less than those determined from half cycle increment load data. On the other hand, the full cycle values for the full size tires ranged from + 10% of the half cycle values. A further indication of the differences encountered in determining k from half cycle and full cycle increment x data is shown in Figure 4. This figure presents typical increment load forcedeflection plots for a model tire and a full size tire. The friction force is indicated by the bar in the figure, but has not been subtracted from the data presented. It is apparent from these plots that the various interpretations of k mentioned previously can lead to different values of k x x (c) The slope of the line from the origin to the maximum force-deflection point, F /6, was usually lower than either of the values of k determined xm xm x from the increment load techniques on Tests 1 or 2. (d) The values of k determined from the fast increment loading loops x were 0-90 higher than those determined from the slower increment loading loops. See the results of Tests 2 and 5. (e) The values of k determined from the faster continuous loading loops, x with the exception of Tire 2, were 0-6% higher than those determined from the 17

A24 Po= 20 psi Fz = 41 lbs. F (lbs.) 6 - 4 Friction I Force 2 -0.02 0.01 0.02 6xtin.) -6 Fx( TIRE 8 500 7.50 x 14 Type mI Po = 87 psi 400 6z = 1.70 in. 300 Friction - 200 Force 100 Ibs.) -r -0.10 -0.06 0.04 0.06 0.08 0.10 6x(in.) - 400 - 500 Figure 4. Typical fore-aft, increment load, force-deflection plots for model and full size tires. 18

slower continuous loading loops. See the results of Tests 4 and 5. (f) The values of k determined by measuring the plate deflection and x assuming it to be equal to the tire deflection were 25-40O lower than those obtained using the relative displacement between yoke and plate. See tne results of Tests 5 and 6. This result is a clear indication of the role of yoke and support deflections in measuring the relatively stiff fore-aft spring rate of a tire. (g) The values of k decreased from 12-50% as the force loop size was inx creased from a small value to a maximum value. See the results of Test 7. A further indication of this significant difference is clearly illustrated in Figures 5 and 6. Figure 5 shows a typical composite force-deflection plot for two different loop sizes for a model tire. Figure 6 shows the same type of plot for a full size tire. Again the friction force is indicated on the two figures, but is not subtracted from the data shown. (h) The values of k varied less than 5% for the tests conducted under x various surface conditions. However, when the model tires were bonded to the surface, the value of k increased 16-2X while the full size tire value inx creased only 5%. It is not clearly understood why the increase is so different between the model tires and the full size tire. The reason may be in the difference between the contact patch geometries. The model tire has a typical aircraft tire geometry, with circumferential grooves and little rubber buildup at the tire shoulders. When loaded to 30-355 vertical deflection, the tire has a rounded contact patch [1]. The full size tire is a typical automotive tire with pronounced shoulders but with no tread pattern. The resulting 19

Fx(lbs.),I/% /' A24 lU.U PO =20 psi Fz 41.6 Ibs. 7.5 5.0 Friction Force 2.5 -1 Fx +~ 10 Ibs. Fx-+ 4 lbs. Xc- -0.0250 0.0125 0.0250 6x (in.) -7.5 - 10.0 Figure 5. Fore-aft force-deflection loops illustrating effect of loop size for a model tire. 20

I TIRE 8 F7.50 x 14 Type Ii Po = 87 psi 6z = 1.70 in. 500 Friction 250 Force x(Ibs.) Fx + ~ 500 x Fx - +200 -0.100 0.050 0.100 6x (in.) -500 Figure 6. Fore-aft force-deflection loops illustrating effect of loop size for a full size tire. 21

contact patch is almost a perfect rectangle. These contact patch geometry differences may cause different deformation patterns when the tire is bonded to the plate and distorted in the fore-aft direction. The fact that the fore-aft stiffness does increase with bonding may have two possible explanations. The first possible reason may be based on the restraining of the tire contact patch from stretching when the tire is bonded. The net deflection for a given load is less, resulting in a higher spring rate. The second reason is based on the restraining of local slip in those regions of the contact patch where the vertical pressure distribution is small. This restriction on the bonded tire again results in a smaller deflection and a higher spring rate. From the results and observations discussed above, it seems there are several important suggestions to be made in regards to obtaining and interpreting static fore-aft mechanical properties of pneumatic tires. First, if k is meax sured by loading a locked tire against a movable plate which in turn is loaded in the fore-aft direction, care should be taken to measure relative deflection between the plate and the wheel and not between the ground and the plate. Even using apparatus that appears to be fairly rigid can lead to substantial errors in deflection measurement, as the results of Test 6 illustrate. Secondly, a crude estimate of a tire's fore-aft stiffness can be obtained by applying a single fore-aft load and measuring the resulting deflection. The ratio of these two values gives a reasonable estimate for k. In general, this estimate will be less than the true value. Finally, it might be recommended that the most consistent and useful method for measuring k is with a system that allows full cycle, continuous X 22

load loops to be generated and recorded in the form of x-y plots. There are several reasons for this recommendation. First, a consistent interpretation of the value for k is possible if a full force-deflection loop is available. x This interpretation specifically defines k as the slope of the line joining x the end points of the loop. This method eliminates the need for best fits or other approximations. However, as the discussion above indicates, a value of k can only be used and interpreted in a consistent manner if the operating x conditions for which the value was measured are well monitored and clearly indicated. In particular, the inflation pressure, the vertical load, and the fore-aft load loop size should be clearly defined. The inflation pressure and vertical load can be fixed in relation to an easily obtainable rated condition. However, no such specification exists for the fore-aft loop size. The effect of fore-aft loop size on the measured value of the fore-aft stiffness can be clearly seen in Figure 7. Figure 7 is a composite plot of, k as a function of X varying force loop size in dimensionless form for all the tires tested in Test 7. The results shown in Figure 7 indicate the size of the fore-aft loading loop must be taken into account when comparing fore-aft stiffnesses of different tires. A standard loop size might be defined as a fixed percentage of the vertical load or the vertical deflection. The continuous loading full loop also has the advantage of displaying unusual and, usually, unwanted characteristics of the load-deflection data. Figures 8, 9, and 10 are examples of force-deflection loops with undesirable features. Figure 8 shows a fore-aft force-deflection loop where slippage has occurred between tire and plate. Comparing Figure 8 with the usual loops in 23

10 9 8 7t 6 kx PoD 5 4, A24 & B21 x B26 o B29' o 2 3 + 4 o 5 * 6 v 7 8 * 9 10 "} Bias (4 Ply) Belted Bias ----- Bias (2 Ply) N\odels,. r — +: + 3 Aircraft (Type I.) 2 1 0.05 0 0.01 2 0.03 FX I Po~2 0.04 fore-aft stiffness 7 Dimensionless plot of Figure 7. all tiresversus loo 7 s. e for all tiresversus IOOP 1 24

F (lbs.) 4 2 -I X /72 -0.0250 -0.0125 1 -4 - 0.0250 6x (in.) Figure 8. Fore-aft force-deflection loop illustrating tire slippage during testing of a model tire. Fx (lbs.) 6 4 2 - 0.0250 0.0250 0.0375 6x(in.) -6 Figure 9. Fore-aft force-deflection loop illustrating small, unidirectional slippage during testing of a model tire. 25

Fy (Ibs.) 200 t 100 -0.250 0.125 0.250 6 (in.) Y - 200 Figure 10. Lateral force-deflection loop illustrating dog leg type loop generated during testing of a full size tire. 26

Figure 5 and 6 illustrates the large flat portions at the high loads where large deflections are occurring witn no increase in load. Also, the absence of a homing in on a single loop indicates that more slippage has occurred in one direction than the other. Figure 9 illustrates this same effect, even though the slippage is not obvious. In this case, the lack of a homing in on a single path is caused by improper locking of the wheel in the yoke. Even though the force continues to rise with deflection, a slight slippage has occurred between the axle and the yoke. This slippage is unidirectional and results in the absence of a final, single loop. Figure 10 illustrates a dog-leg type feature of a force-deflection loop. In this case, the dog leg was generated by running the plate into an unnoticed obstruction. The obstruction acted like a stiff spring in series with tire at one end of the loop and caused the stiffer portion of the loop. Dog-leg loops can also be caused by measuring the deflection with respect to ground and having a support structure that is stiffer in one direction than the other. In this case the structure acts like a spring in series with the tire but with asymmetric force-deflection properties. The resulting force-deflection loop will have a dog leg at the origin. Although the undesirable characteristics of a fore-aft test might be obvious when one looks at the resulting force-deflection loop, these characteristics might go unnoticed in half cycle or increment loading tests or at least go unnoticed until the data are plotted after the test. The simultaneous x-y recording of the force and the deflection during the actual test can indicate test difficulties immediately and obviously, especially when continuous loading, full loops are generated. 27

Lateral Stiffness The testing apparatus used to obtain lateral stiffness data for the model and full size tires was the same as that used in obtaining the fore-aft data. The only change in the model and full size equipment was to position the tire holding yoke such that the tire was 900 from its orientation used in the foreaft test. Figures 11 and 12 show the model and full size lateral testing apparatus. This arrangement provided a lateral force and deflection on the tire as load was applied through the screw mechanisms of each apparatus. The forces and deflections were measured in the same manner as in the fore-aft tests. The same eight test techniques described for tne fore-aft tests were used for the lateral tests. The same tires and operating conditions listed in Table II were also used, except for the standard lateral force magnitudes F, which are also listed in Table II. The results of the various lateral tests are summarized in Table IV. Again, friction forces of the testing apparatus have not been taken into account for these values. Several observations can be made from these results: (a) The values of lateral stiffness k determined from increment load Y tests were 5-15%e less than those determined by continuous load tests. See the results of Tests 1-5. This result was very similar to that observed for foreaft tests. (b) The values of k for the model tires determined from full cycle inY crement load data were 6-10% greater than those determined from half cycle data. This result is in direct contrast to that observed for the fore-aft tests. 28

Figure 11. Photograph of lateral test apparatus for model tires. Figure 12. Photograph of lateral test apparatus for full size tires. 29

TABLE IV SUMMARY OF STATIC LATERAL STIFFNESS ky(lb/in.) est 1 2 3 4 5 6 7 8 \ Fym k k k k ky k Force Loop Size High Clean Oil + Tires 5ym Y Y Y Y Value of ky Friction Metal Grit + 2 + 4 ~ + 8 A24 78 73 80 84 85 85 2 8 - - - --- 95 85 83 80 A23P --- -- -- - --- - -- --- --- --- --- 80 80 --- -- 90 + 2 + 4 + 6 + 8 + 10 B21 97 95 106 110 114 116 956 - 11 0 - --- 129 1 ig 116 113 log B23 -- - --- --- - -- --- --- --- --- --- -— 116 114 --- 116 125 + 2 + 4 + 6 + 8 + 10 B26 --- --- -- 101 102 105 --- 4 6 ~ 8 -- --- 116 108 100 96 93 + 2 + 4 + 6 + 8 + 10 B29' 86 84 89 93 95 9798 94 90 87 - 105 98 94 90 87 + 50 100 + 150 + 200 2 640 710 680 710 740 780 - ~- -- - - --- 930 870 800 770 +0 + 100 + 150 + 200 + 225, 610 640 610 620 660 680 - - 0 +1 ~15 ~ 200 - - - - - 810 740 6o90 690 660 + 50 100 + 150 + 200 4 590 580 560 560 580 590 - 620 590 -90 680 620 590 590 + 50 + 75 100 ~ 150 5 560 600 540 610 600 620 530 50 660 ~ ~ - - - 710 660 660 620 + 50 + 100 + 150 + 200 + 250 7 500 500 520 530 550 560 - 60 60 600 ~570 560 - 680 620 6oo 570 560 + 100 + 200 + 300 + 400 + 500 8 1800 1740 1850 2040 2010 2040 -- 20 2200 2180 o - -- 2390 2200 2180 2120 2070 + 50 100 + 150 + 200 + 250 9 670 670 680 690 740 740 -0 50 70 760 740 - - 980 850 790 760 740 + 50 ~ 100 + 150 + 200 + 230 10 690 700 700 760 790 800 970 890 830 810 790 970 890 830 810 790 o

However, the full cycle values of k for the full size tires were within + 10%0 y of the half cycle values, as they were for the fore-aft tests. Figure 13 shows typical increment lateral load-deflection plots for a model and a full size tire. Again the friction force is indicated on the plot, but is not subtracted from the data. Again it is apparent that different values of k can be detery mined with different interpretations of the data. (c) Unlike the fore-aft results, the ratio of F /ym was usually between ymi ym the values of k determined for Tests 1 and 2. y (d) The values of k determined from fast increment loading loops were y 0-11% greater than those determined from the slower increment loading loops. Again this result agrees with the fore-aft test results. (e) The values of k determined from fast continuous loading loops were Y 0-5Ai greater than those determined from slower continuous loading loops. Again this result agrees with the fore-aft test results. (f) The values of k determined by measuring plate deflection and asY suming it to be tire deflection were 12-17% lower than those determined by measuring the relative displacement between plate and yoke. This result is lower than that obtained from the fore-aft tests and might be expected. Although the testing system has the same effective stiffness as before, the lateral stiffness of the tire is approximately 1/5 the fore-aft stiffness. Thus, the percentage of the total lateral deflection due to the structure is lower than in the case of the fore-aft deflection. (g) The values of k decreased 13-24% as the force loop size was inY creased from a small prescribed value to a maximum size. This difference is 31

Fy (lbs.) A24 6 PO = 20 psi Fz =41 bs 4 Friction 2 Force -0.08 -0.06 -0.04 0.02 0.04 0.06 0.08 y (in.) -4 -6 Fy (Ibs) TIRE 8 500 7.50 x 14 Type Il P = 87 psi 400 6 - 1.70 in. 300 300 -- Friction 200 -Force 100 -0.3 -0.2 -0.1 0.1 0.2 0.3 6 (in.) - 300 - 400 - 500 Figure 13. Typical lateral, increment load, force-deflection plots for model and full size tires. ) 32

clearly seen in Figures 14 and 15. Figure 14 is a typical composite forcedeflection plot for two different size loops for a model tire. Figure 15 is a similar plot for a full size tire. A dimensionless plot of lateral stiffness versus lateral loop size for all the Test 7 results is shown in Figure 16. (h) For the model tires, the value of k varied less than 2% for the dify ferent surface conditions tested and increased 9-11% when bonded to the surface. A comparison of the lateral stiffness results with the fore-aft stiffness results indicates that, generally, the effects of testing techniques on these two mechanical properties are similar in nature, although the degree of influence on fore-aft properties appear to be greater. Thus, the observations and recommendations made for fore-aft stiffness can also be made for lateral 'stiffness. Vertical Stiffness The test apparatus used to obtain vertical stiffness data for the model tires is shown in Figure 17. This apparatus is yet another adaptation of the Static Testing Device described in [1]. In its use as a vertical stiffness test stand, the wheel and yoke were rigidly blocked up off the movable bearing plate. A "vertical" load was then applied horizontally to the tire by loading a rigid vertical surface against the tire. The vertical wall was attached to the bearing plate and the load was applied through the screw mechanism. The resulting "vertical" deflection was measured by the LVDT mounted between the bearing plate and the yoke. The force was measured with the same force 33

B29' Fy (Ibs) Po: 25 psi Fz= 31.6 Ibs 7.5 -5.0 F - O. 075 -0.050 -0.025 0.025 0.050 Fy-,2 Figure 14. Lateral force-deflection loops illustrating effect of loop size for a model tire. ^+8 0.075 6 (in.) Y 34

TIRE 8 Fy (lbs) 7.50 x 14 Type m P = 87 psi 6z= 1.70 in. 500 Friction I 250 Force Fy - 500 -0.250 0.125 0.250 6y (in.) F +~ 200 y -500 Figure 15. Lateral force-deflection loops illustrating effect of loop size for a full size tire. 355

1.61 * A24 b B21 x B26 o 829' o 2 * 3 + 4 o 5 a 6 I 7 4, 8 * 9 ol0 1.3 1.2 Po D 0O 0.8 0.7 0.6 0.4 0.2 o.05 0.1 0 f I Po02,s-fiffnes of lter& t ionless plot er DsUenso al% tires. FX ure lo6 - e for v ersus l00 36

Figure 17. Photograph of vertical test apparatus for model tires. transducer used for the previous tests. Again the output signals of the transducers were amplified and recorded on an x-y plotter. The Riehle test machine used to obtain vertical stiffness for the full size tires was basically that illustrated in Figure 3. In this test the vertical load was applied through the movable loading head of the test machine and the resulting vertical deflection measured with a dial gage. For the vertical tests, four testing techniques were used to obtain vertical stiffness data. These techniques are described below as Tests A, B, C, and D. Test A - Increment deflections. The tire was inflated to the value listed in Table II. An increment of vertical deflection was applied and held constant for one minute at which time the vertical load was recorded. An identical increment of deflection was then applied and the procedure repeated. This test procedure was continued until

the maximum desired deflection was obtained. The increment deflections were then decreased to zero. The value of the vertical stiffness k was then deterz mined by measuring the slope of the line joining the maximum end point of the force-deflection loop and the point whose coordinates were one half the maximum deflection and the average force of the increasing and decreasing portions of the loop at this deflection. Test B - Continuous slow loop. This test was a repeat of Test A except the vertical deflection was applied in a continuous manner. The time for one complete cycle was at least one minute. Test C - Continuous fast loop. This test was a repeat of Test B except the loop was complete in approximately 15 seconds. Test D - Looping about a predeflection. The tire was inflated to the specified value in Table II and deflected to one half of its maximum vertical deflection 6. This deflection was taken as zm the center of a force-deflection loop. The loop was obtained by starting at this point as zero reference and slowly and continuously applying an increasing vertical deflection to a value short of 6 and then decreasing the deflection zm back through the reference point towards the real zero deflection, but reversing the deflection before zero was reached and increasing the deflection to the reference point. The value of k was then determined by measuring the z slope of the line joining the end points of the loop. A summary of the results from these four tests is shown in Table V. Again 38

TABLE V SUMMARY OF STATIC VERTICAL STIFFNESS k (lb/in. ) z Test A Test B Test C Test D Tires Fzm k Fzm k Fzm k Fzm k 5 6zm zm m zm A24 140 160 140 160 140 160 150 160 B21 170 220 170 220 170 220 180 210 B26 180 230 180 230 180 230 190 220 B29' 180 230 190 240 190 240 200 230 1 2650 3260 2660 3260 2650 3240 2890 3290 2 1000 1210 1030 1290 1040 1300 1180 1320 5 1030 1200 1050 1260 1060 1260 1130 1290 4 810 900 810 900 820 920 850 920 5 750 840 760 870 780 900 850 880 6 610 690 610 700 620 720 660 700 7 840 950 850 980 860 970 920 990 8 3060 4070 3090 4120 3130 3980 3420 4140 9 1210 1470 1220 1500 1240 1570 1320 1580 10 1380 1410 1400 1460 1420 1460 1550 1490 some general the values of observations can be made. First, in general, th k from Test A through Test D was less than 5%. z e variation of Secondly, in general, the ratio of the maximum load to the maximum deflection, F /6, was zm zm appreciably less (5-20%) than the value of k. See the results of Tests A, B, z and C. This result is clearly indicated in Figures 18 and 19, which snow typical vertical force-deflection curves for the model and full size tires, respectively. In these figures a definite nonlinearity is evident in the lower portion of the curve. This nonlinearity diminishes as the contact patch becomes fully developed under the influence of the vertical deflection. Thus, the ratio of F /6 was less than k because the F was proportionately zm zm z z smaller for the first half of the loop than for the second half. 59

40 35 30 25 20 B29' Po = 25 psi Fz (Ibs.) 15 10 5 0 ---- Looping around fixed deflection 0 0.05 0.10 0.15 0.20 6z (in.) Figure 18. Typical vertical force-deflection loop for a model tire.

5000 TIRE 1 24 x 7.7 - 10PR TypeZl PO = 85 psi 4500 4000 3500 - 3000 2500 Fz (Ibs) 2000 1500 1000 - 500 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 6 (In.) Figure 19. Typical vertical force-deflection loop for a full size tire.

Finally, the value of k was not appreciably changed when determined from z the slope of the line through the end points of the loop generated by cycling about 6 /2. Tiis result is obvious after observing a typical loop and its zm corresponding full loop shown in Figure 18. It is evident in this figure that looping about a predeflection point does not effect the value of k as long as the loop does not extend significantly into the lower nonlinear region. From these observations it might be recommended that the most consistent way to evaluate k is to establish a definition which will eliminate the iniz tial "soft" portion of the vertical load-deflection curve, such as the definition of k used in this study. The technique used to obtain the forcez deflection information seems to make little or no different in the value for k. z 42

CONCLUDING REMARKS The research program described in this paper indicates that testing techniques do have an effect on the measured values of the three static stiffnesses studied. As more tire user groups demand to know more tire characteristics, the need for a uniform criteria to measure and interpret values for these tire characteristics grows. It is hoped that this study might be used as a preliminary indication of how such a criteria may be formulated. Eventually, slow rolling properties such as cornering power, self-aligning torque, pneumatic trail, and relaxation length must also be exhaustively studied if the values of these tire parameters are to have meaning to the tire user group. However, the basic static tire properties covered in this report are probably the most amenable to some sort of measurement and interpretation standard. It is hoped that the results given in this report might provide some indication of the type of measurement and the difficulties of measurement interpretation that must be thoroughly investigated before such a standard can be proposed.

REFERENCE [1] Clark, S. K., Dodge, R. N., Lackey, J. I., and Nybakken, G. H., "Structual Modeling of Aircraft Tires," NASA CR-2220, National Aeronautics and Space Administration, Washington, D. C., 1973. 44

DISTRIBUTION LIST No. of Agency Copies Scientific and Technical Information Division Code US National Aeronautics and Space Administration Washington, D.C. 20546 25 NASA Headquarters Langley Research Center Dynamic Loads Division Hampton, Virginia 23365 Attn: Mr. Walter B. Home 5 45

UNIVERSITY OF MICHIGAN 3 9015 02844 9208111 11 I 3 9015 02844 9208