NASA Technical Memorandum 4779

ARL Technical Report 1402

Quasi-Static Viscoelasticity Loading

Measurements of an Aircraft Tire

Angela J. Mason and John A. Tanner

Langley Research Center • Hampton, Virginia

Arthur R. Johnson

Vehicle Technology Center

U.S. Army Research Laboratory

Langley Research Center • Hampton, Virginia

National Aeronautics and Space Administration

Langley Research Center • Hampton, Virginia 23681-2199

September 1997
Available electronically at the following URL address: http://techreports.larc.nasa.gov/ltrs/ltrs.html

Printed copies available from the following:

NASA Center for AeroSpace Information

800 Elkridge Landing Road

Linthicum Heights, MD 21090-2934

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 487-4650
Abstract

Stair-step loading, cyclic loading, and long-term relaxation tests were performed

on an aircraft tire to observe the quasi-static viscoelastic response of the tire. The

data indicate that the tire continues to respond viscoelastically even after it has been

softened by deformation. Load relaxation data from the stair-step test at the 15000-1b

loading was fit to a monotonically decreasing Prony series.

Introduction

Aircraft tires are composite structures made of

carbon-filled rubber, nylon cords, and steel wires. Under

normal loading conditions, tires are subjected to large

deformations with the constituents experiencing moderate strains. During aircraft ground operations and landings, the dynamic deformations of tires result in

dissipative internal stresses. Tread friction and wear performance are affected, and heat is generated in the tire

carcass. (See rcfs. 1 and 2.) Computational models that

predict the dynamic responses of aircraft tires should

address their viscous characteristics. The material properties needed in the viscoelastic constitutive models are

determined by testing both coupons and full-size tires.

(See refs. 3 to 9.)

The objective of this research activity is to expand

the database on viscoelastic loading of full-size aircraft

tires. An experimental program to establish the quasistatic mechanical response of the Space Shuttle orbiter

nose-gear tire subjected to combined inflation pressure

and vertical loading conditions is conducted. Stair-step

loading, cyclic loading, and long-term relaxation tests are

performed. Viscoelastic relaxation loads for the tire are

approximated by least-squares fitting a Prony series to

the load relaxation data. The least-squares fit is performed with the constraint that the coefficients of the

exponential terms in the Prony series be positive (ref. 3).

The Prony series model is intended for use in a separate

effort in which viscoelastic finite element analyses are

carried out to model the tire loading experiments.

Test Apparatus

The aircraft tire used in this effort is a 32 × 8.8, type

VII, bias-ply Shuttle nose-gear tire which has a 20-ply

rated carcass and a maximum speed rating of 217 knots.

The tread pattern consists of three circumferential

grooves and the rated inflation pressure is 320 psi. The

tire was inflated to 300 psi, which is consistent with

previous tests performed on the tire. (See refs. 4, 10,

and 11.) The rated operating load for the tire is 15 000 lb.

A schematic of a typical bias-ply aircraft tire of similar

construction is shown in figure 1.

The tire vibration stand (TVS) shown in figure 2 was

used to perform the experiments. This equipment has

been used in a number of studies to determine tire

damping characteristics (refs. 7 and 9) and tire footprints

(refs. 10 and 11). The main structure of the TVS consists

of two three-bay portal frames joined above by four

beams (not shown in fig. 2) and along the floor by a thick

plate. The tire rim is clamped between vertical supports

to prevent rotation. A special feature of the TVS is the

supporting of the test platen by four 5/8-in. wire rope

cables. Each cable is suspended from a force-measuring

load cell. The four load cells are connected through

screw jacks to a frame with miter gears and worm-gear

actuators. The frame is mechanically driven by an electric motor such that the four cables move simultaneously;

thus, the platen is displaced in the vertical direction to

load and unload the tire. A more detailed description of

the TVS is found in reference 7.

A displacement transducer shown in figure 3 is

mounted to the platen and affixed to the right adapter

plate. This device measures the vertical displacements of

the tire. The displacement transducer has a measuring

span of + 10 in. and a measurement accuracy of +0.00657

in. The four TVS load cells are connected in parallel,

have a range of 0 to120 000 lb, and have a measurement

accuracy of +134 lb. A digital data acquisition system

was used to collect the data at a recording rate of

5 samples/sec.

Test Procedures

Three different experimental procedures were used.

The first is referred to as "stair-step load relaxation testing"; the second, "cyclic testing"; and the third, "longterm relaxation testing." These procedures are described

in the following paragraphs. In each test discussion, the

targeted peak loads and time intervals are referenced.

The targeted loads are 5000, 10 000, 15 000, 20 000, and

25 000 lb. Note, if the targeted peak load is 25 000 lb but

the actual load reached is 25 300 lb, the discussion of the

test procedure refers to the targeted load of 25 000 lb.

Stair-Step Loading Test

The purpose of the stair-step loading test was to

obtain a database for the time-dependent viscoelastic

characteristics of the Shuttle nose-gear tire when subjected to incremental loading and unloading. Prior to

starting this procedure the tire was inflated to 300 psi and
maintainedinanunloadedconditionforatleast24hours

to helpensurethatthetirewasfullyrelaxedinthepressurizedstateprior to startingtheincremental loading

tests.Thedesiredtimeintervalbetweenloadingincrementswas190sec.Thetechniqueusedforthetestconsistedof loadingandunloadingthetireto averticaload

of 25000lb at 5000-1bincrements. At eachincreasing

loadstep,theverticaldisplacement washeldconstant

andtheloadrelaxationwasrecordedfor 190sec.A time

of approximately 7 to 10 sec was required to increase

(ramp up) the vertical load. After the peak load of 25 000

lb was reached, the process was reversed and the load

was decreased to 0 lb in 5000-1b increments. Again, at

each decreasing load step, the vertical displacement was

held constant and the load rebound was recorded for

190 sec.

Cyclic Loading Test

The second category of testing consisted of cyclically loading and unloading the Shuttle nose-gear tire.

The primary focus of this test was to exercise and soften

the tire. Tire hysteresis measurements were then made.

The tire was again inflated to 300 psi and maintained in

an unloaded condition for at least 24 hours prior to starting this procedure. The cyclic tests involved loading the

tire from 0 lb to predetermined peak load and then

unloading the tire as quickly as possible. There was no

pause at the peak load during these tests and it took

approximately 70 sec to complete one 25 000-1b cycle.

The sequence of testing was initiated with ten 25 000-1b

cycles followed by a series of tests wherein the tire was

incrementally loaded and unloaded through the sequence

of 5000, 10 000, 15 000, and 20 000 lb. The testing was

conducted in one continuous operation.

Long-Term Relaxation Test

The long-term relaxation test was performed to

examine the relaxation behavior of the Shuttle nose-gear

tire over long time intervals. Within 1 minute of the completion of either the stair-step test or the cyclic test, the

tire was ramp loaded to a vertical load of 20 000 lb, the

displacement was held constant, and the load relaxation

was recorded for 900 sec. A variation of this test procedure included loading the tire to 25 000 lb and holding

the displacement constant for 3200 sec. During these

tests, the data acquisition system recorded continuously

so that a complete time history could be obtained.

Experimental Results

Stair-Step Loading Test

Time histories of the tire vertical load and displacement are presented in figure 4. The figure shows time

2

histories of load and displacement for the stair-step test

and a 20 000-1b, 900-sec, long-term relaxation test. The

load time history (fig. 4(a)) and the displacement time

history (fig. 4(b)) show the stair-step patterns associated

with the test. The load time history exhibits relaxation

during increasing load increments. This relaxation is

indicated by load reduction over the 190-sec interval at

each increasing load step. This effect is most pronounced

at the higher load conditions. The load time history also

exhibits load rebound during decreasing load increments

of the test as indicated by a load increase over the

190-sec interval at each decreasing load step. This effect

is most pronounced at the lower load conditions. The displacement plateau at each load step is flat; this indicates

that the desired constant displacement test conditions

were in fact achieved.

The load relaxation and rebound curves at the

15 000-1b loading (fig. 4) are enlarged and shown in

figures 5 to 8. Figure 5 shows time histories of load and

displacement as the load is increased from approximately

10 000 to 15 000 lb. The displacement time history

(fig. 5(b)) indicates a constant displacement of 1.8 in.

once the 15 000-1b level is reached. The load ramp and

relaxation shown in the load time history in figure 5 is

examined more closely in figure 6. The load ramp time

history (fig. 6(a)) indicates that the load was increased

from a starting point of about 9800 lb to a peak load of

15 400 lb in 7 sec. The load relaxation time history

(fig. 6(b)) indicates a drop from 15 400 lb at the beginning of the 190-sec time interval to about 14 860 lb at the

end of the time interval, a load relief of about 540 lb.

Figure 7 shows time histories of load and displacement

as the load is decreased from approximately 20 800 to

15 000 lb. The displacement time history (fig. 7(b))

indicates a constant displacement of 1.9 in. once the

15 000-1b load is reached. The load ramp and rebound

shown in the load time history in figure 7 are examined

more closely in figure 8. The load ramp time history

(fig. 8(a)) indicates that the load was decreased from a

starting point of about 20 800 lb to a minimum load of

14730 lb in 7 sec. The load rebound time history

(fig. 8(b)) indicates an increase from 14 730 lb at the

beginning of the 190-sec time interval to about 15 030 lb

at the end of the time interval. These load tests showed

that there was a load rebound of about 300 lb.

Relaxation characteristics for each of the increasing

load step cases are displayed in figure 9. This figure

shows time-dependent load relaxation curves for each

increasing load step from 5000 to 25 000 lb. The timedependent load for each load step was derived by subtracting the minimum load from each point on the load

relaxation time history for that load step and then adding

70 lb to the result. The data were initialized to 70 lb arbitrarily to compare the relaxation data. The Prony series
takesaninfiniteamountof timetorelaxto0; therefore,

the data were adjustedso that the Prony series

least-squares fit algorithmcouldfunctionproperly.Other

positivevaluesselecteddid notsignificantlyaffectthe

data.Forexample,inthe15000-1bloadsteprelaxation

datashowninfigure6,thetime-dependent loadcurvefor

15000Ibinfigure9is610lbatthebeginningofthetime

intervalandisreducedto 70lb in 190sec.Thedatain

figure9 indicatethatthe magnitudesof therapidly

decayingviscousloadincrementsincreasedasthetotal

loadlevelincreased.

Reboundcharacteristicsfor eachof thedecreasing

loadstepcasesaredisplayedin figure10.Thefigure

showstime-dependent load reboundcurvesfor each

decreasingloadstepfrom20000to5000lb.Thetimedependent loadfor eachloadstepwasderivedbysubtractingtheminimumloadfromeachpointontheload

reboundtimehistoryforthatloadstepandthenadding

70lb to theresult.Again70lb wasselectedarbitrarily.

Thusforthe15000-1bloadstepreboundatashownin

figure8,thetime-dependent load,showninfigure10,is

70lbatthebeginningofthetimeintervalandincreased

to370lbin 190sec.Thedatapresentedinfigure10indicatethatloadreboundforthe20000-1bloadstepisabout

60percentof theloadreboundobservedfor theother

decreasingloadsteps.

The time dependencyof thetire load-deflection

characteristicsis furtherillustratedby displayingthe

incremental loadingdataversusdisplacement asgivenin

figure 11.The 190-secpausesallowthe materialto

recover(relax)whichproducesa substantial hysteresis

loop.

Cyclic Loading Test

Figure 12 presents time histories of load and displacement for the cyclic loading test and a 25 000-1b,

900-sec, long-term relaxation test. The load time history

(fig. 12(a)) and the displacement time history (fig. 12(b))

show a total of ten 25 000-1b loading and unloading

cycles that were completed in about 700 sec. These

cycles were followed by four cycles with peak loads that

were changed in increments from 5000 lb to 20 000 lb

over a period of about 150 sec. Finally, a 25 000-1b,

900-sec, long-term relaxation test completed this test

sequence. The load time history exhibits load relaxation

during the 25 000-1b relaxation test as indicated by load

reduction over the 900-sec time interval. Again, the displacement plateau for the relaxation test is flat.

Load-deflection curves from the first, second, and

tenth cyclic tests are presented in figure 13 to demonstrate the effect of conditioning on the hysteresis characteristics of the tire. Each test was conducted without any

pauses; approximately 70 sec was required to complete

each cycle. The load-deflection curves are developed in a

clockwise sense as indicated by the arrows in figure 13.

The vertical load-deflection curves denote the commonly

observed tire stiffening as the load and tire deformation

become large. The initial cycle exhibits a well-defined

hysteresis loop throughout most of the load range. Hysteresis losses for subsequent loading cycles were much

less pronounced.

To better illustrate the effect of the cyclic loading

history on the viscoelastic response of the tire, the thin

hysteresis loops in figure 13 were least-squares fit to

cubic polynomials. The plots of these polynomials are

presented in figure 14. They demonstrate that the hysteresis loops are migrating to the right which is a measure

of the viscoelastic softening of the tire. Immediately following the ten 0- to 25 000-1b load cycles, a series of four

load cycle tests were conducted at loads ranging from

5000 to 20 000 lb. Load-deflection curves from these

tests are presented in figure 15. These load-deflection

curves are similar. They exhibit the low hysteresis characteristic associated with a work-conditioned tire, and

each curve defines a similar nonlinear load-displacement

response.

Long-Term Relaxation Test

The long-term relaxation behavior of the tire is

shown in figure 16. Time histories of viscoelastic load

are presented for the 190-sec stair-step loading test at

20 000 lb (denoted by the solid line) and a 3200-sec,

20 000-1b relaxation test (denoted by the dashed line).

Note that in figure 16, the curves were adjusted so that

the maximum relaxation loads were equal at Time = 0.

The 20000-1b, 3200-sec relaxation test was initiated

approximately 60 sec after the 900-sec relaxation test

shown in figure 4. The data presented in figure 16 indicate that load relaxation characteristics for the stair-step

test are similar to the characteristics for the first 190 sec

of the long-term relaxation test. Furthermore, the longterm relaxation data demonstrate load relaxation

throughout the entire 3200-sec time interval.

Prony Series Relaxation Model

Constitutive models for viscoelastic materials are

often expressed in their relaxation form. Consider a

Maxwell material model (ref. 1), which is represented by

a Prony series (also referred to as a "Dirichlet series").

The series is defined as follows:

n

f v(t) = Z Ai e-t/xi

i=1
where the coefficients A i > 0 (to ensure monotonic relaxation at all times) and xi represents time constants. In the

case of a constitutive model, A i represents moduli. Here,

we explore modeling the tire relaxation loads with a

Prony series. The algorithm described in reference 3 was

used to determine a Prony series for the 15 000-1b tire

relaxation load shown in figure 6. A total of 24 time

constants

{ xi}i241 = { 10-9/4,10-2,10-7/4 ..... 1013/4,107/2}

were considered and an optimal fit to the relaxation data

was made with the constraint that A i >_O. The magnitudes

of the coefficients are shown in the top plot of figure 17,

and the Prony series representation of the load relaxation

is shown in the bottom plot of the figure. There were five

nonzero coefficients in the resulting series which produced an excellent representation of the data.

Concluding Remarks

Tests were conducted to determine the quasi-static

viscoelastic characteristics of the Space Shuttle orbiter

nose-gear tire. The following observations are noted:

The initial load cycle for a tire which has been

unloaded for 24 hours exhibits a well-defined hysteresis loop. Hysteresis losses for subsequent loading

cycles were much less pronounced.

The vertical load-deflection curves for the tire demonstrate a nonlinear stiffening behavior as the load is

increased.

During the stair-step loading test, each successive

increasing 5000-1b load increment resulted in a

larger component of rapidly decaying load than that

produced by the previous load increment. A similar

pattern was not obtained for decreasing load

increments.

The relaxation curves obtained in the stair-step loading test are similar to the load relaxation curve for

the first 190 sec of the long-term relaxation test.

Furthermore, the long-term relaxation test data demonstrated load relaxation throughout the entire

3200-see time interval.

An optimization algorithm was used to least-squares

fit relaxation data 1o a monotonically decreasing

Prony series. The Prony series approximation is in

excellent agreement with the experimental data.

NASA Langley Research Center

Hampton, VA 23681-2199

May 20, 1997

References

I. Clark, Samuel K., od.: Mechanics of Pneumatic 7ires. U.S.

Dep. Transportation, 1981.

2. Futamura, S.: Effect of Material Properties on Tire Performance Characteristics--Part II: Tread Material. Tire Sci. &

Technol., vol. 18, no. 1, Jan.-Mar. 1990, pp. 2-12.

3. Johnson, A. R.; Quigley, C. J.; and Mead, J. L.: Large Strain

Viscoelastic Constitutive Models for Rubber Part I: Formulations. Rubber Chem. & Technol., vol. 67, no. 5, Nov.-Dec.

1994, pp. 904-917.

4. Johnson, Arthur R.; Tanner, John A.; and Mason, Angela J.: A

Kinematically Driven Anisotropic Viscoelastic Constitutive

Model Applied to Tires. Computational Modeling of Tires,

Ahmed K. Noor and John A. Tanner, eds., NASA CP-3306,

i 995, pp. 39-51.

5. Kumar, M.; and Bert, C. W.: Experimental Characterization of

Mechanical Behavior of Cord-Rubber Composites. T/re Sci. &

Technol., vol. 10, nos. 1-4, Jan.-Dec. 1982, pp. 37-54.

6. Quigley, Claudia J.; Mead, Joey; and Johnson, Arthur R.:

Large Strain Viscoelastic Constitutive Models for Rubber--

Part II: Determination of Material Constants. Rubber Chem. &

Technol., vol. 68, no. 2, May-June 1995, pp. 230-247.

7. Sleeper, R. K.; and Dreher, R. C.: lire Stiffness and Damping

Determined From Static and Free-Vibration Tests. NASA

TP-167 l, 1980.

8. Johnson, A. R.; Quigley, C. J.; Young, D. G.; and Danik, J. A.:

Viscohyperelastic Modeling of Rubber Vulcanizates. 7ire Sci.

& Technol., vol. 21, no. 3, July-Sept. 1993, pp. 179-200.

9. Davis, Pamela A.: Quasi-Static and Dynamic Response Characteristics of F-4 Bias-Ply and Radial-Belted Main Gear

7ires. NASA TP-3586, 1997.

10. Howell, William E.; Perez, Sharon E.; and Vogler, William A.:

Static Footprint Local Forces, Areas, and Aspect Ratios for

Three Type VII Aircraft Tires. NASA TP-2983, 1991.

11. Tanner, John A.: Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear

Tire. Ph.D. Thesis, George Washington Univ., Jan. 1993.

4
Fabric tread

reinforcement

Undertread

Sidewall

Plies

Chafer stri

Ply turnups

Beads

Figure 1. Aircraft tire construction.

Bead fiat

Bead toe

Cord body

(carcass plies)

5
Figure 2. Tire vibration stand.

6
Figure3. Displacement measurement device.

7
30000-

25000

20000

Load,

lb 15000

10000

5000

Seefigures [ [ R_.e.fic,,l_

5 and_,.6_1_ _ -- 7-a_nd_ _

I I

500 1000 1500

Time, sec

(a) Load.

I ,

2000

i i , I ,

2500

! i L I

3000

3.0

2.5

2.0

Displacement,

in. 1.5

1.0

.5

See figure 5

0 500 1000 1500 2000 2500 3000

Time, sec

(b) Displacement.

Figure 4. Time histories of load and displacement for stair-step and long-term relaxation load tests.

8
Load,

lb

16000

15000

14000

13000

12000-

11000-

10000-

9000

450

, , i i I L J i , I , , , , I , , i J I , L i , I

500 550 600 650 700

Time, sec

(a) Load.

1.9 --

1.7 -

Displacement,

in. 1.6 -

1.5 -

1.4 -

1.3 .... I .... I .... I .... i .... I

450 500 550 600 650 700

Time, sec

(b) Displacement.

Figure 5. Time histories of load and displacement for incremental loading from 10 000 to 15 000 lb.
16000-

Load,

lb

15000

14000

13 000

12000

I1 000

10 000

9000

460

lllllllllJ,i,an,nnal,IIi i Inanlllai,ai,llla,alllll[

462 464 466 468 470

Time, sec

(a) Load ramp.

15 500 -

Load,

lb

15400

15300

15 200

15100

15000

14900

14800 , i , , I , , , , I , i , , I , , , , I , , L I I

450 500 550 600 650 700

Time, sec

(b) Load relaxation.

Figure 6. Time histories of load ramp and load relaxation for incremental loading from 10 000 to 15 000 lb.

10
21000 -

20000

19000

18000

Load,

lb 17000

16000

15000

14000

1200

.... I .... I .... I , , , , I , , , I I

1250 1300 1350 1400 1450

Time, sec

(a) Load.

2.4

2.3

2.2

Displacement,

in. 2.1

2.0

1.9

1.8

1200 1250 1300 1350 1400 1450

Time, sec

(b) Displacement.

Figure 7. Time histories of load and displacement for incremental loading from 20 000 to 15 000 lb.

11
Load,

lb

21000

20000

19000

18000

17000

16000

15000

14000

1220

i [ , l _ , , I , _ , I _ , , I , _ , I , , , I , _ _ I

1222 1224 1226 1228 1230 1232 1234

Time, sec

(a) Load ramp.

Load,

lb

15050

15000

14950

14900

14 850

14800

14750

14700 , I

1200 1450

I

.... I .... I , , , , [ J _ , , I _ , I

1250 1300 1350 1400

Time, sec

(b) Load rebound.

Figure 8. Time histories of load ramp and load rebound for incremental loading from 20 000 to 15 000 lb.

12
A load,

lb

80O

Increasing load, lb

700 /-- 25 000

/

V_ /-_oooo

_oo\/ f,_ooo

/ f,oooo

400

300

200

100

,,,I,,,I ,,,I,,, I,,,t,,,I,,,I,, ,I,_1_1

0 20 40 60 80 100 120 140 160 180 200

Time, sec

Figure 9. Stair-step test with increasing load viscoelastic results.

A load,

ib

400

350

300

25O

200

150

100

50

Decreasing load, lb

15 0O0

10000

20 000

5 000

0 20 40 60 80 100 120 140 160 180

Time, sec

Figure 10. Stair-step test with decreasing load viscoelastic results.

200

13
30000

Load,

lb

25O00

20000

15000

10000

5000

190-secdiplacement

pause

0 .5 1.0 1.5 2.0 2.5

Displacement, in.

Figure11. Load-deflectioncurveassociatedwithstair-steptest.

3.0

14
Load,

lb

30 000 /

lOcycles _ _1_[

4 cycles

25 000

20 000

15000

10000

5OOO

I

0 500 1000

Time, sec

Relaxation test

, , , I , , , , _1

1500 2000

(a) Load.

Displacement,

in.

3.0

2.5

2.0

1.5

1.0

.5

, , , J I , J _ _ I

0 500 1000 1500 _000

Time, sec

(b) Displacement.

Figure 12. Time histories of load and displacement for cyclic loading and long-term relaxation load tests.

15
Load,

lb

25000

20000

15000

10000

5000

.5 1.0 1.5 2.0 2.5

Displacement, in.

Load,

lb

25000

20000

15000

10000

5000

.5 1.0 1.5 2.0 2.5

Displacement, in.

Load,

lb

25000

20000

15000

10000

5000

0 .5 1.0 1.5 2.0 2.5

Displacement, in.

Figure13.Typicalload-deflectioncurvesforcyclicloadingtest.

16
Load,

lb

25 000

20 000

15 000

10000

5000

Figure 14.

First cycle /

Second cycle //

Tenth cycle /_

J

/f'

f

f

f

J

f

/

.5 1.0 1.5 2.0 2.5

Displacement, in.

Least-squares approximation of hysteresis loops for cyclic loading test.

17
Load,

lb

200O0

18 000

16 000

14000

12OOO

10000

8 000

6OO0

4 000

2 000

15O0

10

.5 1.0 1.5 2.0

, I

2.5

Displacement, in.

Figure 15. Hysteresis curves for loads from 5000 through 20 000 lb.

18
Viscoelastic

load,lb

1400

1200

1000

800

600

400

200

190-secrelaxation

(20000-1bstair-steploadingtest) 3200-secrelaxation

(20000-1blong-termrelaxationtest)

\

\

\

\

.... I .... I , , i , I .... I .... I .... _ .... I

500 1000 1500 2000 2500 3000 3500

Time, sec

Figure 16. Long-term relaxation and stair-step tests results.

19
Pronyseries

coefficients,

A i, lb

400

300

200

100

)

Prony series

fv(t) = _,A i e-t/'ci

10-2 10-1 100 101

0 O' 0"_ 0 0 ...... I

10-3 102 103 104

Time constant, x i, sec

Viscoelastic

load, lb

700

600

500

400

300

200

100

I Experiment

......... Prony series

approximation

iii I , , , I, , , I , , , I , , , I , , , I * , ,I, , _ I _ , I , , ,I

20 40 60 80 100 120 140 160 180 200

Time, sec

Figure 17. Prony series approximation of tire relaxation characteristics.

2O

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND )ATES COVERED

September 1997 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Quasi-Static Viscoelasticity Loading Measurements of an Aircraft Tire

6. AUTHOR(S)

Angela J. Mason, John A. Tanner, and Arthur R. Johnson

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS{ES)

NASA Langley Research Center Vehicle Technology Center

Hampton, VA 23681-2199 U.S. Army Research Laboratory

NASA Langley Research Center

Hampton, VA 23681-2199

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

and

U.S. Army Research Laboratory

Adelphi, MD 20783-1145

WU 505-63-50-19

PR A5008

8. PERFORMING ORGANIZATION

REPORT NUMBER

L-17609

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4779

ARL-TR- 1402

lt. SUPPLEMENTARY NOTES

Mason and Tanner: Langley Research Center, Hampton, VA; Johnson: Vehicle Technology Center, ARL, Langley

Research Center, Hampton, VA.

12a.DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 05

Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Stair-step loading, cyclic loading, and long-term relaxation tests were performed on an aircraft tire to observe the

quasi-static viscoelastic response of the tire. The data indicate that the tire continues to respond viscoelastically

even after it has been softened by deformation. Load relaxation data from the stair-step test at the 15000-1b loading

was fit to a monotonically decreasing Prony series.

14. SUBJECT TERMS

Aircraft tire properties; Viscoelasticity; Relaxation; Hysteresis; Tire load deflection;

Stair-step tire loading

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

24

16. PRICE CODE

A03

20. LIMITATION

OF ABSTRACT

Standard Form 298 (Rev. 2-89)

Prescribed by ANSi Std. Z39-18

298-102