Ongoing aircraft tire experimental programs are reported. These programs are designed to measure profile growth due to inflation pressure and vertical loading, contact pressures in the tire footprint, and a number of tire mechanical properties including spring, damping, and relaxation characteristics

Tanner, J. A.

English

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OVERVIEW OF NASA T1R.E EXPERIMENTAL PROGRAMS 
John A. Tanner 
NASA Langley Research Center 
ABSTRACT 
The experimental measurement of various tire properties is an important step in 
the tire modeling process. Some properties are needed to define the complex loading 
distributions that must be imposed on a tire model to simulate typical operational 
environments. Others, such as tire stresses and displacements resulting from 
various loading conditions, can be used to assess the accuracy of candidate finite 
element codes. In many cases these properties are used to establish the tire 
response characteristics which are useful in the simulation of operational problems 
and support the design of vehicle suspension systems and aircraft landing gear sys- 
tems. 
This paper reports on the interim results from a number of ongoing aircraft 
tire experimental programs. These programs are designed to measure profile growth 
due to inflation pressure and vertical loading, contact pressures in the tire 
footprint, and a number of tire mechanical properties including spring, damping, 
and relaxation characteristics. 
163 
https://ntrs.nasa.gov/search.jsp?R=19830013127 2020-03-21T03:38:51+00:00Z

PROFILE GROWTH DUE TO INFLATION PRESSURE 
Typical profile growth data for the 40 x 14 aircraft tire during inflation 
are presented in figure 3. For this particular test the tire was inflated to 
1.17 MPa (170 psi) from an uninflated state and the arrows in the figure denote 
the direction of growth for selected points on the tire periphery. The profile 
growth involved both radial and tangential tire displacements. The tire inflation 
problem is axisymmetric and the tire displacements are symmetric about the 
tire equator. 
I 
/ 1.17 MPa 
b l 
0 MPa ’ 
&- (170 PSI) 
L .4- 
I 
\ -w-c 
G R I M CENTERLI NE \ --- 
I 
b-- 
’ WY 
b-r, 
- RIM FLANGE 
Figure 3 
165 
PROFILE GROWTH DUE TO COMBINED INFLATION PRESSURE AND VERTICAL 
LOADING 
Typical growth measurements of a 40 x 14 aircraft tire for vertical loads 
ranging up to 89 kN (20 000 lbf) are presented in figure 4. For this test the 
inflation pressure was 1.07 MPa (155 psi) and the profile measurements were along 
a line which was displaced 5" from the contact centerline as shown in the sketch. 
The ground lines for each of the vertical loading conditions are also shown in 
the figure. The arrows again denote the direction of growth and in this case 
depict the growth of the sidewall bulge for increasing vertical load. The dis- 
placement data from these loading conditions should exhibit symmetry about the tire 
equator but the axial symmetry associated with the inflation process is now lost. 
TIRE SIDEWALL DISPLACEMENT DUE TO VERTICAL LOAD, INFLATION PRESS., 1.07 MPa (155 PSI) 
RIM CEN TERL ,INE 
v') ++- f’5’IcNM) . . 
I 5 
. . 
v 
f 
I 
. \*' 
GROUND LINE, Fz = 89 kN (20 KIPS) ------------ 
t l 
,I -I--------- . 68 kN (15 KIPS) 
t < 44 kN (10 KIPS) ---------. 
-w 
22 kN ( 5 KIPS) ---v-m- \ 
0 kN i;. __.-----. -- - - 
RIM FLANGE 
Figure 4 
166 
TIRE FOOTPRINT 
The forces and moments developed in the tire footprint must be modeled 
accurately to simulate the tire operational environment. Figure 5 is a typical 
footprint from a 40 x 14 aircraft tire inflated to 1.07 MPa (155 psi) and subjected 
to a vertical load of 89 kN (20 000 lbf). Instrumentation is currently under 
development to measure the pressure distribution and tangential friction force 
variation throughout the tire/surface contact region. 
Figure 5 
167 
FOOTPRINT LENGTH 
The length of the tire footprint Lf for two tire sizes is presented as a 
function of tire vertical deflection 6 in figure 6 where both parameters have been 
nondimensionalized by the tire outside diameter d. The data for the two tire sizes 
can be faired in a least squares manner by a single-valued, nonlinear curve defined 
by the following expression (ref. 1), 
, 
Lf/d = 1.66 
J 
(6/d) - GM2 (1) 
This expression is similar to an expression in reference 2 for various type 
VII aircraft tires. Also included in the figure is the curve for the expression 
which defines the relationship between footprint.length and vertical deflection if 
the tire is not distorted by the vertical load: r 
Lf/d = 2 
J 
(6/d) - @/d12 (2) 
Without distortion the footprint length equals the length of the geometric 
chord formed by the intersection with the ground plane of a circle having a 
diameter equal to that of the tire. The data for both tires indicate that the 
footprint is about 83 percent of the geometric-chord length. 
.6 
.5 
.4 
Lf/d -3 
I I I I I I 
.04 .05 .06 .07 .08 .09 
6/d 
Figure 6 
168 
STATIC LOAD-DEFLECTION CHARACTERISTICS 
Typical lateral load deflection curves for an aircraft tire are presented in 
figure 7. This family of curves was generated by varying the later& load while 
holding the vertical load constant. For this test the lateral loading was decreased 
with each successive cycle as identified by the numbers in the figure which denote 
the loading sequence. The tire response to this loading condition is characterized 
by a number of large hysteresis loops. The area enclosed within each loop is a 
measure of dissipated energy or hysteresis loss and the slope of the load deflection 
curve is a measure of the tire spring characteristics. Similar load -deflection 
curves can be generated in the vertical and fore and aft or braking directions to 
establish additional tire response characteristics. 
LATERAL LOAD 
7 LATERAL DEFLECTION 
Figure 7 
169 
HYSTERESIS LOSS 
The static lateral hysteresis loss of a tire can be obtained from.load 
deflection curves such as that shown in figure 7 by measuring the area enclosed 
within the lateral loading and unloading cycle. Typical values of the lateral 
hysteresis loss ratio are plotted as a function of lateral load in figure 8. The 
lateral hysteresis loss ratio, the ratio of hysteresis loss to total energy input 
to the tire, is obtained by dividing the area within the hysteresis loop by the 
area under the load deflection curve including the hysteresis loop. The data in 
the figure indicate that increasing the lateral load increases the energy input 
lost to hysteresis, and the influence of vertical load is inconsequential. 
LATERAL 
HYSTERESIS 
RATIO 
61 
5( 
4i 
3( 
2( 
l( 
( 
Fz, kN 
0 200 
: ::i 
10 20 30 40 
LATERAL LOAD, kN 
50 60 70 
Figure 8 
170 
STATIC AND DYNAMIC LATERAL SPRING RATES 
Typical tire lateral spring rates obtained from static and dynamic tests are 
plotted in figure. 9. as a -function of vertical load. As shown in the sketch, two 
spring rate values were obtained from the 'static tests. One spring rate corresponds 
to the linear 'portion of the load-deflection curve during load application and is 
denoted by the short dashed line in the figure.. The other static spring rate 
approximates the slope of the load-deflection curve at initial load relief and is 
denoted by the long dashed line. These two static spring rates represent the 
lower and upper bounds for each vertical loading condition. The dynamic spring rates 
were determined from free vibration tests described in reference 3 and are denoted 
by the solid line. The data presented in the figure indicate that dynamic spring 
rates lie between the two bounds established by the static tests. 
SIZE 49 x 17 TIRE 
LATERAL 
SPRING 
RATE, 
kNIM 
16 
12 
8 
4 
0 
STATIC LOADING 
4 
DEFL 
50 100 
VERTICAL LOAD, kN 
Figure 9 
150 200 
171 
LATERAL DEFORMATION OF TIRE PERIPHERY 
Another parameter available from static tests is the static relaxation length 
which is obtained from displacements of the tire equator at various angular positions 
around the circumference. Such measurements taken on a 49 x 17 aircraft tire under 
four combinations of vertical loading F, and lateral loading Fy are presented in 
figure 10. Lateral deformation of the tire equator X is plotted as a function of 
the tire peripheral angle 0 measured from the footprint centerline. The lateral 
displacement of the free-tread periphery of the tire near the edge of the footprint 
varies exponentially with circumferential angular position and can be expressed 
in the following form: 
X = Ae -s/L S (3) 
where A is a constant, s is the circumferential distance from the footprint edge, 
and L 
S 
is called the tire static relaxation length. 
0, DEG 
A, cm 
Figure 10 
172 
VARIATION OF STATIC RELAXATION LENGTH WITH 
VERTICAL DEFLECTION 
Relaxation lengths computed from data such as that presented in figure 10 are 
plotted in figure 11 as a function of tire vertical deflection; Both parameters 
are nondimensionalized by the tire width w.. Data from two tire sizes are presented 
and faired by separate linear curves. Relaxation lengths from both tires tend to 
decrease-with increasing tire deflection. 
2.5 
2. (I 
1.5 
L*l w 
1.0 
.5 
TIRE SIZE 
n 18x5.5 
-+J-- 49x17 
0 .05 . 10 .15 
61 w 
.20 .25 .30 
Figure 11 
173 
CONCLUDING REMARKS 
Some of the data reviewed in this paper are typical of the experimental measure- 
ments necessary to verify the performance of tire analytical models and to establish 
footprint loading conditions for tire contact problems. Other data presented are 
used in defining tire spring and damping properties and the transient response 
characteristics necessary to model the tire's role as a component of a vehicular 
suspension system or an aircraft landing gear system. Experimental measurements of 
tire properties will continue to be an important step in the tire modeling process, 
regardless of the level of sophistication of the modeling technique. 
REFERENCES 
1. 
2. 
3. 
Tanner, John A.; Stubbs, Sandy M.; and McCarty, John L.: Static and Yawed- 
Rolling Mechanical Properties of Two Type VII Aircraft Tires. NASA TP-1863, 
1981. 
Smiley, Robert F.; and Horne, Walter B.: Mechanical Properties of Pneumatic 
Tires with Special Reference to Modern Aircraft Tires. NASA TR R-64, 1960. 
Sleeper, Robert K.; and Dreher, Robert C.: Tire Stiffness and Damping Determined 
from Static and Free-Vibration Tests. NASA TP-1671, 1980. 
174 


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