Transportation Research Record 1070 9

Experimental Determination of Pressure Distribution of Truck Tire-Pavement Contact KURT M. MARSHEK, HSIEN H. CHEN, RICHARD B. CONNELL, and W. RONALD HUDSON

ABSTRACT

The results are presented of an experimental determination of pressure distribu­tions beneath statically loaded truck tires using a pressure-sensitive film. A load frame fitted with a hydraulic ram was used to statically load a bald and treated 10-20 bias ply truck tire. The use of pressure-sensitive film allowed the net contact area--as well as the entire pressure distribution--to be captured, and the data to be stored by using an automated print reading system. The results indicate that the treaded tire produced the highest pressures in the tire shoulder region for the cases studied, except for the overinflated case. High inflation pressures caused the peak pressures to move from the tire shoulder toward the tire centerline. The results also indicate that heavy axle loads produced regions of high pressure in the tire shoulder region. Experiments conducted on bald tires show similar trends; however, the overall pressure distribution is more continuous because of the lack of treads.

One of the major costs incurred by highway depart­ments in the United States is maintaining public roads in a serviceable condition. A variety of fac­tors are known to contribute to pavement damage, in­cluding climate, traffic density, and the loads from automobile and truck tires. Historically, the subject of contact pressure distribution between a tire and pavement has received little attention for several reasons, including the following: (a) simplifying assumptions made in past road design work have made knowledge of the actual pressure distribution un­necessary, and (b) measurements of the contact pres­sure at all locations (points) in the tire footprint are difficult to make. The actual contact pressure distribution between the tire and the pavement will undoubtedly play a larger role in highway pavement design.

The common assumption is made that the contact pressure is uniform and equal in magnitude to the tire inflation pressure, and that it acts on an area that is circular in shape <!l· The theoretical rela­tionships used by highway engineers in design work are simplified considerably by this assumption. However, previous investigations have demonstrated that the actual pressure distribution deviates con­siderably from the uniform pressure model (~ 1}).

To determine the shape and size of the contact pressure area, Flugrad and Miller modeled the tire as a modified standing torus in their finite element analysis and predicted an elliptical contact pressure area <.!l. Another study, by Mack et al., also modeled the tire as a standing torus, and predicted an el­liptical contact area as did Flugrad and Miller (5).

O'Neil determined experimentally the net contact pressure area of a statically loaded tire by coating the tire with oil, loading the tire on paper, and allowing graphite particles to stick to the oily

K.M. Marshek, H.H. Chen, and R.B. Connell, Mechani­cal Engineering Department, University of Texas at Austin, Austin, Tex. 78712. W.R. Hudson, Center for Transportation Research, University of Texas at Aus­tin, Austin, Tex. 78712.

parts of the paper (l_) • Tracing of the image obtained then gave the desired net contact area.

For statically loaded tires, O'Neil used a nylon pin and proving ring assembly to determine the normal and tangential pressure distributions exerted by the tire <ll • A study by Marshek et al. in progress at the University of Texas at Austin uses a digitizing camera and data acquisition system to determine the contact pressur.e distribution and the net contact area from pressure-sensitive film prints of stati­cally loaded truck tires. The camera digitizes the print and then, using this data base (a) displays the pressure distribution, and (b) calculates the net contact area by summing the picture elements on the television monitor (pixels) on the digitized image, the color intensity of which defines them as a con­tact area. Clark demonstrated that the pressure dis­tribution for a statically loaded tire is a good ap­proximation for the pressure distribution of a freely rolling tire <.~).

Lippmann and Oblizajek used specially designed microtransducers mounted in a ground steel bed to record three components (normal, radial, and tangen­tial) of the pressure distribution under freely rolling tires (7). Shimada et al. conducted a study using piezoelectric sensors mounted in a rotating drum to measure various contact pressure forces at high speeds (2).

The objective of this study is to determine the contact pressures that exist beneath statically loaded truck tires using pressure-sensitive film. The data obtained will indicate what effect the tread pattern, tire inflation pressure, and axle load have on the resulting tire-pavement contact pressure dis­tribution.

EXPERIMENTAL APPARATUS

The experimental apparatus used in this study con­sisted of the following components: a load frame for statically loading tires, pressure-sensitive film for capturing the pressure distribution, an optical device (densitometer) for converting color intensity

10

to pressure, a bidirectional (X-Y) table for precise movement of the print beneath the densitometer, and an HP 3054A data acquisition system.

The first tire studied was a smooth 10-20 bias ply truck tire used for skid testing. The data from this tire will represent one extreme in the range of tread patterns found in use (as with a tire worn bald) and will thus allow broader conclusions to be drawn about tread patterns and the resulting pressure dis­tributions. The second truck tire studied was a used 10-20 bias ply tire with 3/8 in. of tread depth re­maining. This tire is representative of the type of tire and tire condition commonly found on highways today.

Load Frame

The truck tires studied were statically loaded with the load frame shown in Figure 1. This frame was designed so that a hydraulic ram mounted above the tire assembly could deliver a load to the tire through a shaft running through the tire hub. This design allowed the tire to be loaded to better simulate actual use, in contrast to loading the tire, for example, by placing weights on the top of the tire.

MTS Control System

•• • . . . .

·~

FIGURE 1 Tire load frame.

Pressure-Sensitive Film

A pres s ure-sensi tive film was used, which is capable of capturing the sta t ic pressure distribution betwee n contacting bodies. This film consists of an A-sheet and a C-sheet, as shown in Figure 2, the A-sheet containing capsules of developer and the C-sheet providing a developing layer on which the developer acts. The capsules are made in a variety of sizes so that they break when exposed to a certain pressure level. Statistical distribution of the different capsule sizes allows a range of pressures to be cap­tured.

When the two sheets are in their proper orienta­tion and subjected to a pressure, a number of the capsules break and release the developer onto the developing layer1 the developer from the A-sheet produces a red spot on the C-sheet, with the inten­sity of color obtained being proportional to the ap­plied pressure.

Densitometer

The prints developed are read with an optical device called a densitometer (shown in Figure 3). The den-

Transportation Research Record 1070

A-Sheet

C-Sheet

FIGURE 2 Pressure-sensitive film.

Re6ding He6d

Vol lmeter ~Light Sources

l j Photocell

@-- Re6ding Are6

Re6ding Heed

FIGURE 3 Densitometer and schematic diagram of densitometer reading head.

sitometer consists of the reading head and a chassis that contains a voltmeter and calibration controls.

The reading head consists of two symmetrically placed light sources and a photocell. The light sources project beams of light, which pass through a circular opening (0.118 in. in diameter) in the base of the head, striking the print directly below the head, and then reflecting back to the photocell an amount of light proportional to the intensity of color on the print. The photocell outputs a voltage that is proportional to the pressure that was applied to the film: the response of the photocell is that of a first-order system with a time constant of 0.8 sec. The output of the densitometer photocell was connected to a precision voltmeter located in a data acquisition system.

The print developed can be read with the densi­tometer to determine the pressure at any point or region desired. One important advantage gained by using the densitometer is that a grid reading reso­lution can be specified, that is, the user can divide the resulting contact area into a grid size with step sizes as small or large as required. This character­istic is important because large pressure gradients occurring in extremely small distances are conunon­place, particularly when dealing with bodies such as treaded tires the contact surfaces of which contain numerous discontinuities.

X-Y Table

The small measuring area (0.044 in.') of the den­sitometer compared with the large contact area of the truck tire footprint made it necessary to devise a means for automating the print reading process. This was accomplished in part through the use of a bidirectional (X-Y) table that featured high-speed, precision stepper motors driven by an on-board digi­tal control unit. An RS232 interface in the control unit permitted direct control of the X-Y table and data taking by the HP 3054A data acquisition system described in the next section. Errors resulting from miscommunication between the densitometer and the X-Y table controller were avoided because of the ex­clusive control of the HP3054A over the data-taking process: the pr int reading time also was kept to a minimum.

Marshek et al.

Data Acquis i tion Sys tem

An HP 3054A data acquisition system was used exten­sively throughout all phases of this study. It con­sisted of the following components: an HP 9816S com­puter, a dual disc drive, a data acquisition unit, a dot matrix printer, and a multiple pen plotter.

Because of the small measuring area of the densi­tometer, approximately 6, 000 points were measured for each truck tire print in order to map the entire pressure distribution in the contact area. Figure 4 shows the schematic diagram of the pr int reading system.

Densitometer Chossis

HP 9B 16S

FIGURE 4 Print reading system.

EXPERIMENTAL PROCEDURE

The load application was divided into three parts. The first part was a load ramp in which the load on the tire was increased linearly from zero to full load over a 2-min time period. Part two of the load­ing consisted of maintaining the full tire load on the paper for 2 min. After this, the tire load was quickly released, the A-sheet was separated from the C-sheet, and the C-sheet was set aside to finish developing. All prints obtained during a testing session were read within l hr after the session ended because it was believed that the color intensity on the film might fade with time.

To obtain a pressure print, the A-sheet and c-sheet were taped firmly in their proper orientation to the flat steel plate to prevent erroneous pressure values from being recorded due to the presence of shear forces between the sheets. Also, a piece of shimstock (with a thickness of 0.001 in.) was placed between the tire and the top piece of pressure paper so that expansion of the tire on application of the load was restrained by the shimstocki therefore, only the normal tire load was transmitted to the paper (see Figure 5).

To keep the calibration and experimental proced­ures as similar as possible, a scheme was devised whereby a known load could be applied to a rubber cube with 1-in. sides (and a Young's modulus roughly equal to the moduli of the truck tires tested) by

Pressure Sensitive Film

FIGURE 5 Shimstock and pressure-sensitive film configuration.

lnstron Compression Tester

Shims lock

Rubber Block

Pressure Sensitive Film

FIGURE 6 Calibration test equipment.

11

using an Instron compression tester, as shown in Figure 6. Examples of calibration prints obtained with the rubber block and a complete description of the calibration procedure are given by Connell (8).

The data points used to construct the calibration curve were obtained by using the same loading pro­cedure as was used for the tire. The same steel plate and pressure-sensitive film configuration was used, the only difference being that the face of the rubber block touching the shimstock was lubricated to achieve a more uniform pressure distribution. The uniform distribution of known pressure intensity was desired for the calibration prints because the aver­age voltage measured by the densitometer in each of these prints was used as a data point on the cali­bration curve.

Data points were obtained for each pressure level by averaging voltages in the calibration prints. A second-order polynomial was fitted through the data points to obtain the calibration curve used to con­vert the voltage arrays to pressures. Because of the sensi ti vi ty of the film to its environment, careful attention was paid to ensure that the atmospheric conditions (temperature and relative humidity) were sufficiently close for both calibration and experi­mental test sessions.

Experiments were conducted with truck tires to demonstrate the effect of tread pattern, tire infla­tion pressure, and axle load on the resulting contact pressure distribution. Because the pressure-sensitive film is expensive, and because it required about 6 hr to read a developed pr int, a minimum number of tests were conducted that would still satisfy the goals of this study.

Experiments were conducted by using three differ­ent tire inflation pressures (75, 90, and 110 psi) to demonstrate the effect the inflation pressure had on the distribution of pressure in the tire foot­print. Two different axle loads were used with this studyi the first was a 4,500-lbf load and the second was a 5,400-lbf load (a 20 percent overload).

EXPERIMENTAL RESULTS

The data read by the densitometer from the six pres­sure prints were stored on disc in the form of ar­rays of voltages. From the voltage data base, various parameters could be determined, including the net contact area of the tire footprint and the pressure distribution throughout. In addition, the data base could be reduced or converted into equivalent forms (such as equivalent but smaller arrays of pressures and forces) i this made it possible to use the data (a) as a means of drawing pressure distributions, (b) to substantiate conclusions about the distribu­tion, and (c) as input to computer programs analyzing pavement performance.

The first form of output used consists of numeri­cal prints that show the pressure that acts on each

12 Transportation Research Record 1070

grid area in the contact patch; Figure 7 shows a sample numerical pressure print for treaded tire at 90 psi inflation pressure and an axle load of 4,500 lbf, The numerical prints were made by printing the arrays of pressures values in matrix form. General trends in the pressure distribution are difficult to determine from the numerical pr in ts because of the overwhelming amount of data presented for each test conducted. The prints do, however, give a location and the individual pressures that exist in the con­tact patch.

to obtain a single pressure or force acting on each unit area. The plots shown in Figure 8 optimize the viewing variables so that the pressure changes in the contact patch along the two axes and the presence of high pressures at the tire shoulder and along tread gaps can clearly be observed,

Operations were performed on the data to reduce the data from an array of 6,000 points (either pres­sure or force) per print to a number of points ap­propriate to the applicat ion . In general, the opera­t i ons on the data were performed to accomplish one of two goals: the first goal was to reduce the data to a form suitable for plotting, and the second was to convert the data to an equivalent form compatible with the input requirements of pavement analysis programs.

A computer graphics program was used to convert each data base of numerical pressure values into discrete points of color on a graphics terminal; controls in the graphics program associated a par­ticular pressure level with a specific color (e.g., yellow points might indicate pressures between 120 and 140 psi) • After the entire data base for each print had been read into the graphics program, plots on the color graphics terminal were photographed with a 35-mm camera. Pr in ts made from the slides give a striking summary of the experimental results, showing both the localized pressures and the general trends in pressure found in the contact patch beneath stat­ically loaded truck tires. Prints of the 35-mm slides are given by Connell (.!!_) •

DISCUSSION OF RESULTS

A three-dimensional plot was chosen over a two­dimensional plot despite the usual assumption that the pressure distribution varies little along the length (in the direction of travel) of the tire. The three-dimensional plots were rotated so that the view chosen best illustrates the pressure profiles along both axes of the footprint (see Figure 8).

The grid dimensions used to make the three-dimen­sional plots were made nonuniform to preserve regions of high pressure that were isolated because of the presence of the tire shoulder or a tread gap. A mov­ing average scheme was then used to reduce the data

The tread type, that is, the particular pattern of treads, plays a dominant role in the determination of the shape of the pressure distribution. The bald tire represents one end of the tread spectrum, the treaded tire the other. The plots shown in Figure 8 illustrate that a bald tire produces a uniform pres­sure distribution with significant gradients only at the tire center and shoulder.

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" FIGURE 7 Sample numerical pressure print.

Marshek et al. 13

"~ ~~ 4500 lbf 4500 lbl

TREAD 75 4500 lbf

1'EAD~ 4500 lbl

FIGURE 8 Three-dimensional plots of pressure distributions.

With a treaded tire, the pressure distributions have large discontinuities at the tread gaps, within which the pressure is zero. The gaps separate regions of significantly different nonzero pressure levels. Th is can clearly be observed on the copies of the pressure prints, particularly for the overloaded case (treaded tire at 90 psi and 5,400 lbf), where the circumferential tread gap separates high pressures on the shoulder from medium pressures directly on the other side, This region between the shoulder of the tire and the circumferential gap usually carries the highest pressures.

For a given load, inflation pressure determines the regions of high pressure. Increasing the infla­tion pressure reduces the crown curvature, thus shifting the high-pressure regions at the tire shoulder to the center of the contact patch.

One other effect of inflation pressure was ob­served with the treaded tire that supports the use (by highway engineers) of the inflation pressure as the magnitude of the uniform pressure delivered by a tire. The region in the center of the tire, bounded by a circumferential gap on either side, consistently maintained pressures close to the inflation pressure (plus or minus 15 psi) for all of the tests con­ducted. The high pressures occurred near a tread gap or in the shoulder region where the stress concen­tration drove the pressures above the range stated.

The axle load is the final parameter the effect of which on the contact pressure distribution was studied. A comparison of the numerical and three-di­mensional plots obtained for the treaded tire at rated inflation pressure but for two different axle loads immediately makes clear the following: the pressures in the center region of the tire remain relatively unchanged whereas pressures in the shoulder region increase dramatically.

SUMMARY

The results of this study can be summarized as fol­lows:

l . The tread pattern on a tire was found to have a significant effect on the size of the contact area and the shape of the pressure profiles. Smaller con­tact areas for treaded tires were observed because the presence of the tread gaps reduced the number of contact points in the tire footprint. The tread gaps

were also demonstrated to separate adjacent regions of vastly different pressure levels. High pressures were consistently found at tread-gap interfaces and at the tire shoulder. As the tread wears, three re­sults can be expected: an increase in the net contact area, a reduction of the peak pressures, and a more continuous distribution.

2. The tire inflation pressure, in general, determined the location of regions of high pressure in the contact patch. Low inflation pressures re­sulted in large contact regions and high pressures near the tire shoulder region. High inflation pres­sures produced a significant reduction in contact area and a shifting of high pressures toward the center region of the contact patch.

3. The axle load also affected the contact area and pressure distribution. The 4,500-lbf axle load saturates the center region of the tire footprint with contact pressures approximately equal to the tire inflation pressure. The 5,400-lbf axle load caused deformations in the tire sidewalls and an in­crease in the load carried by the tire shoulder region.

ACKNOWLEDGMENTS

The authors are pleased to acknowledge the combined efforts and support of the Center for Transportation Research and the Mechanical Engineering Department at the University of Texas at Austin and the Texas State Department of Highways and Public Transporta­tion, in cooperation with the FHWA, U.S. Department of Transportation.

REFERENCES

l • K. B. Woods (ed. ) • Highway Engineering Handbook. McGraw-Hill, New York, 1960,

2. T. Shimada, T.S. Furuya, and K. Ikehara. A Study of Contact Forces of a Radial Tire at High Speed. Bridgestone Tire Company, Inc., Akron, Ohio, 1984.

3. E.W. O'Neil, Jr. Measurement of Pneumatic Tire Contact Pressure for Static Loading. M.S. thesis. North Carolina State University, Raleigh, 1969.

4. D.R. Flugrad and B.A, Miller. Experimental and Finite Element Study of a Standing Torus Under Normal and Tangential Loads. Iowa State Univer­sity, Ames, 1981.

14

s. M.J. Mack, Jr., D.E. Hill, and J.R. Baumgarten. Analytical and Experimental Study of a Standing Torus with Normal Loads. Tire Modeling, NASA Con­ference Publication 2264. National Aeronautics and Space Administration, Washington, D.C., 1982.

6. S.K. Clark. Mechanics of Pneumatic Tires. Report NBS-Mono-122. Michigan University, Ann Arbor, Nov. 1971,853 PP•

7. S.A. Lippmann and K.L. Oblizajek. The Distribution of Stress Between the Tread and Road for Freely Rolling Tires. Transaction 740072. Society of Automotive Engineers, Warrendale, Pa., 1974.

8. R.B. Connell. Experimental Determination of Truck Tire Contact Pressures and Their Effect on Flex-

Transportation Research Record 1070

ible and Rigid Pavement Performance. M.S. thesis. University of Texas at Austin, Austin, 1985.

The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the FHWA. This paper does not constitute a standard, specification, or regulation .

Publication of this paper sponsored by Conunittee on Strength and Deformation Characteristics of Pavement Sections.

Effect of Truck Tire Inflation Pressure and Axle Load on Flexible and Rigid Pavement Performance

KURT M. MARSHEK, HSIEN H. CHEN, RICHARD B. CONNELL, and CHHOTE L. SARAF

ABSTRACT

Results are presented of an investigation into the effect of truck tire infla­tion pressure and axle load on flexible and rigid pavement performance as determined by using computer analysis programs. The flexible and rigid pavement analyses were conducted with both an experimental nonuniform contact pressure distribution and a uniform circular contact pressure distribution as input to the computer programs. The results indicated for the flexible pavement analysis that high inflation pressures and heavy axle loads cause higher tensile strains at the bottom of the surface course, but that only heavy axle loads and not increased inflation pressures are responsible for higher compressive strains at the top of the subgrade course. The rigid pavement analysis indicated an in­significant difference between results obtained by using an experimental and a uniform contact pressure distribution model.

A variety of factors are known to contribute to pavement damage, including climate, traffic density, and the loads from automobile and truck tires. His­torically, the subject of the effect of truck tire inflation pressure has received little attention for several reasons, including the following: (a) simpli­fying assumptions made in past road design procedures have made knowledge of the actual pressure distribu­tion unnecessary, and (b) it is difficult to make measurements of the contact pressure over the entire contact area. The influence of tire inflation pres­sure as well as the contact pressure distribution between the tire and the pavement will both un­doubtedly play a larger role in highway design after

K.M. Marshek, H.H. Chen, and R.B. Connell, Mechanical Engineering Department, University of Texas at Austin, Austin, Tex. 78712. C.L. Saraf, Center for Transportation Research, University of Texas at Austin, Austin, Tex. 78712.

their role in causing pavement damage is better understood.

The contact pressure distributions for truck tires loaded at various axle loads and tire inflation pres­sures were obtained experimentally by using a pres­sure-sensitive film technique (1). These experimental data were used to determine the effects that the magnitude and shape of the truck tire contact pres­sure distribution have on the stresses, strains, and deformations developed in the pavement. Computer programs, typical of those used by highway engineers in pavement analysis and design work, are used to determine the strains and stresses of interest for both flexible and rigid pavements. The strains and stresses for an experimental contact pressure dis­tribution will be compared with those obtained by using a uniform pressure model.

The objective of this paper was to determine the effect of tire inflation pressure, tire axle load, and tire pressure distribution model on the strains