APPENDIX A
APPENDIX A DESCRIPTION OF LANDING GEAR m m\ _i ft} TD.
T
Sketch (a) The important geometric characteristics of the landing-gear shock strut are illus- trated in sketch (a). The computer program input parameters follow: Shock strut: 2 2 Pneumatic area, A , m (ft ) 0.00535 (0.05754) 2 2 Hydraulic area, AI, m (ft ) 0.00317 (0.03409) 2 2 Primary orifice area, A , m (ft ) 0.00008 (0.00085) Fluid volume in piston below orifice plate, Vj 3 3 (gear extended), m (ft ) 0.00074 (0.0260) 3 3 Pressurized pneumatic volume, V2 (gear extended), m (ft ) . . 0.00122 (0.0432) Volume between cylinder and piston, V$ (gear extended), 3 3 m (ft ) 0.00011 (0.0040) Charging pressure, p , kPa (psfg) 1850.2 (38 643) Q a Bearing separation for fully extended shock strut, l\, m (ft) . . . 0.1544 (0.5065) Axial length from hub to lower bearing for fully extended shock strut, 1 , m (ft) 0.6727 (2.2071) Drop mass (mass acting on gear), kg (Ibm) 1490 (3280) Hub mass (wheel, tire, and piston), kg (Ibm) 25.3 (55.7) Maximum shock strut stroke, m (ft) 0.229 (0.75) m ft Fully extended length of shock strut, Z s,e. ( ) • • • 1.1135 (3.65334) S 2 2 Area between piston and cylinder, A , m (ft ) 0.00151 (0.01626)
APPENDIX A
APPENDIX A 3 3 Specific weight of hydraulic fluid, y , N/m (lbf/ft ) 8226 (52.36) R Dynamic viscosity of hydraulic fluid, JLIJJ, 2 2 N-sec/m (lbf-sec/ft ) 0.00862 (0.00018) 3 3 Mass density of hydraulic fluid, pjj, kg/m (slugs/ft ) 838 (1.626) 3 3 Volume of hydraulic fluid, V , m (ft ) 0.00164 (0.05801) H Wheel and tire: Wheel flange diameter, m (ft) 0.2954 (0.9692) Unloaded diameter of tire, d, m (ft) 0.552 (1.81) Maximum width of undeHected tire, w, m (ft) 0.175 (0.5735) Unloaded rated inflation tire pressure, p , kPa (psf) 55.16 (1152) r Unloaded tire inflation pressure, p , kPa (psf) 413.7 (8640) o Pressure rise parameter, K 0.62 Vertical force coefficient, GZ 0.03
APPENDIX B
APPENDIX B APPARATUS, TEST SETUP, AND PROCEDURE FOR PSEUDOSTATIC TESTS Gear Fore-and-Aft Spring Constant The basic configuration of the gear with mounting fixture for both the fore-and-aft spring constant and axial-friction tests is shown in figure 12. In order to compute the spring constant, the gear was mounted horizontally as a cantilever and tip drag loads were applied for 10-, 50-, and 90-percent extensions of the shock strut. Maximum tip load ranged from 3.56 kN (800 Ibf) for 90-percent shock strut extension to 6.23 kN (1400 Ibf) for a 10-percent extension. Deflections were measured with a sensitive dial gauge indi- cator. The relation between drag load and gear bending deflection for the three shock strut extensions is plotted in figure 13. Taking the slope of each line allowed derivation of the elastic spring constant for each extension. The three points were plotted on a graph (fig. 8) with spring constant as the ordinate and shock strut extension as the abscissa. The spring constant is seen to vary from 342 kN/m (23 400 Ibf/ft) for 90-percent extension of the strut to 644 kN/m (44 100 Ibf/ft) for a 10-percent extension. Although the spring con- stant variation with strut extension is nonlinear, a linear fit can be made to the points with little loss of accuracy.
Brake Torque as a Function of Brake Pressure The experimental setup to determine maximum brake torque as a function of hydrau- lic brake pressure is illustrated schematically in figure 14. Instrumentation required for this test consisted of a load cell for measuring applied force (and hence torque) and a mechanical pressure gauge for measuring applied brake pressure. The test procedure was first to apply a known hydraulic brake pressure and then to measure the force level necessary to initiate rotation of the wheel. This force multiplied by the length of the torque arm gave the maximum brake torque for the set hydraulic brake pressure. The procedure was repeated three times for each pressure, and the average values were plotted as shown in figure 9.
Experimental Determination of Tire Force-Deflection Characteristics The determination of nonrolling tire force-deflection characteristics was accom- plished by use of a compression loading machine. The tire (an 8-ply, 6.50-10, type m aircraft tire) and wheel were mounted on the test-fixture axle (fig. 15) which was attached to the upper platen of the testing machine. The tire was loaded to a maximum force of
APPENDIX B
APPENDIX B 13.34 kN (3000 Ibf) in increments of 0.22 kN (50 Ibf) initially and in 1.33-kN (300-lbf) increments after the curve had begun to level off.
The experimental loading and unloading curve and the semiempirical curve (ref. 4) F = 2.4|p + *p „(£•) + O.OSpJwtfwd L^r - CT; 1 - e rt L o,a\w/ rj are plotted in figure 10. The above terms are: F load, N (Ibf) 6 tire deflection, m (in.)
w maximum width of undeflected tire, m (in.)
d unloaded tire diameter, m (in.)
p absolute tire pressure, Pa (psi) K pressure rise parameter p initial inflation pressure, Pa (psi) p rated tire pressure, Pa (psi) GZ vertical force coefficient As can be seen from figure 10 the agreement is excellent in loading. The loading rate was slow and the deflections were read using a dial gauge. Some tire hysteresis is present in the unloading cycle.
Axial Friction Due to Applied Drag Loads To determine the axial friction Ff due to applied drag loads, the gear and test fixture were mounted horizontally on a vertical backstop (fig. 12). The gear was drained of hydraulic fluid and the filler plug (with air valve) was removed.
Deadweight drag loads were applied (up to 1.33 kN (300 Ibf)) for 10-, 50-, and 90-percent extensions of the shock strut. An external hydraulic cylinder was used to
APPENDIX B
APPENDIX B
initiate axial motion, and the force necessary was read using a load cell. The axial motion
was limited to approximately 2.5 cm (1.0 in.); the motion took place in most cases at a
very slow rate. The friction obtained by this method was probably static, not kinetic, because the motion was abrupt and jerky instead of smooth and continuous.
Equilibrium of vertical forces on the lower mass (piston and hub) gives the normal
force on the lower bearing N2
N = N! + W + D (Bl)
where
NI normal force on upper bearing
W weight of lower mass (hub plus steel test cylinder); total 0.18 kN (40 Ibf)
D applied load on lower mass (drag load)
Equilibrium of moments about the lower bearing is used to give the upper bearing normal
force
D (B2)
*1
with
j?D distance from lower bearing to point of external load application
j? distance from lower bearing to center of gravity of lower mass
w
#1 distance from lower bearing to upper bearing
Finally if the friction coefficient Cf is the same for both bearing surfaces, then Ff, the
shock strut axial-friction force, is
'n /> \
(B3)
The experimental axial-friction force as a function of drag load D is shown, in fig-
ure 11 for 10-, 50-, and 90-percent extension of the shock strut. The analytical curve can
be calculated from equation (B3) with a constant friction coefficient of 0.27. This value
gives the best average fit to the experimental data. Values used in the equation were
measured values and are given in table I.
REFERENCES
1. DC-10 Landing Gear Modified. Aviat. Week & Space Technol., vol. 98, no. 12, Mar. 19, 1973, p. 181.
2. Ropelewski, Robert R.: Airbus Test Tempo Quickening. Aviat. Week & Space Technol., vol. 98, no. 10, Mar. 5, 1973, pp. 32-35.
3. McGehee, John R.; and Garden, Huey D.: A Mathematical Model of an Active Control
Landing Gear for Load Control During Impact and Roll-Out. NASA TN D-8080, 1976.
4. Smiley, Robert F.; and Horne, Walter B.: Mechanical Properties of Pneumatic Tires
With Special Reference to Modern Aircraft Tires. NASA TR R-64, 1960. (Super-
sedes NACA TN 4170.)
5. Milwitzky, Benjamin; and Lindquist, Dean C.: Evaluation of the Reduced-Mass Method
of Representing Wing-Lift Effects in Free-Fall Drop Tests of Landing Gears. NACA
TN 2400, 1951.
6. Westfall, John R.; Milwitzky, Benjamin; Silsby, Norman S.; and Dreher, Robert C.: Summary of Ground-Loads Statistics. NACA TN 4008, 1957.
TABLE I.- DISTANCES USED TO DETERMINE STRUT
AXIAL-FRICTION COEFFICIENT
Shock strut Stroke
*w
*1
V
extension, cm in. cm in. cm in. cm in.
percent
20.57 36.04 27.64 46.69
10 8.1 14.19 10.88 18.38
50 11.43 4.5 27.15 10.69 36.53 14.38 55.58 21.88
90 2.29 .9 17.78 7.00 45.87 18.06 64.92 25.56
Air valve and filler port
Cylinder
O r i f i c e tube hole
Orifice tube
Upper bearing
Lower bearing
Orifice plate
Piston
Piston plug
Fork
Figure 1.- Internal view of landing gear.
Stationary • I Honeycomb ( l i f t simuiat Hydraulic pressure transducer Hub accelerometer § • Tire deflection s l i d e wire
L-76-3532.1
Figure 2.- Dynamic drop test setup.
/
\
\
/
\
/
\ /
\
\
I n c l i n e d impact surface
Figure 3.- Drawing of dynamic drop test setup
for inclined surfaces.
Pneumatic pressure transducer Cyli nder Pi ston — Hydraulic pressure transducer Pi ston piug
Figure 4.- Location of hydraulic and pneumatic
pressure transducers.
L-76-3536
Figure 5.- Instrumentation rack and oscillograph.
-.Analytical predictions —i2.0 O D O Experimental values 1.6 1.2 1.2 m/s (U f t / s ) .It I I I I I I I I L g> o° oBo 1 - 5 m/s _ 1.2 (5 f t / s ) Tire deflection, Tire d e f l e c t i o n .
.8 .(( I I I I L 2.0 1.6 1.2 .8 .it .02 .01* .06 .08 .10 .12 .!"» .16 .18 .20 -22 ,2k .26 .28 . 3« Ti me, s (a) Tire deflection.
Figure 6.- Parameter time histories for drop tests (three runs per test)
onto level impact surface.
12.5 Analytical predictions Experimental values O Cj 0—*•* u L*> e 1.2 m/s Ct ft/s) J I I I L I I I I I I I I I 1.5 m/s Shock strut (5 ft/s) Shock strut stroke, 2 stroke, i n, -1 J I I I I I I I I I I I I O D D D D k 1.8 m/s (6 ft/s) -1 I I I I I I I I I I I I_ I_ L 0 .02 .Olt .06 .08 .10 .12 .11) .16 .18 .20 .22 .2k .26 .28 .30 Time, s (b) Shock strut stroke.
Rgure 6.- Continued.
i.s r
n 200
Analytical predictions Experimental values
i.o -
Hydraulic Hydraulic pressure, MPa 1,0 - pressure, psig 2.0 r- 2W 1.5 - 1.0 o gOJ I I I I I I I I I .02 .Qi» .06 .08 .10 .12 .lit .16 .18 .20 .22 .2it .26 .28 .30 Time, s (c) Hydraulic pressure.
Figure 6.- Continued.
i.s
- Analytical predictions
i.o
OD<> Experimental values 120
8 8 m/s
^ ' -
1 . 5 1.0 Pneumati c o o° Pneumati c pressure, MPa pressure, psig 1.5 m/s (5 ft/s) .5 ko I I I I I I I I I I I I 04 .06 .08 .10 .12 .l<i .16 .18 .20 .22 .24 .26 .28 .30 (d) Pneumatic pressure.
Figure 6.- Continued.
D
o o
0^*0
° - n 3 r * r, r,njWT— A «T. °ar
{? o a __^ 5*"-"° 9 ^oo "" 6 & ffi o g^>_^tr°
1.5 m/s -2 (5 f t / s )
-It
Hub acceleration, _ & O D ll» 1 1 1 1 1 1 1 1 1 1 02 .C* .06 .08 .10 .12 .lit .16 .18 .20 .22 .21* .26 .28 .30 (e) Hub acceleration.
Figure 6.- Continued.
1.2 m/s ft ft/s) Analyti cal predi ct ions Experimental values Upper mass acceleration, I I I I I I I I I I I I I 1 1 0 .02 . 0 1 ( .06 .08 .10 .12 .1<t .16 .18 .20 .22 .2k .26 .28 .30 (f) Upper mass acceleration.
Figure 6.- Concluded.
- A n a l y t i c a l predictions, C^ = 0 . 1 5 O D O Experimental values Level surface — .14 I I I I I 2.It - 1.6 Ti re dcf 1 ecti on, -3 _ Tire deflection, in.
I I I I I I I I I I I I 0 .02 Time, s (a) Tire deflection.
Figure 7.- Parameter time histories for drops at 1.5 m/s (5 ft/s) onto 0°, 5°, and 10° inclined surfaces. Cf is bearing friction coefficient.
12.5 A n a l y t i c a l predictions , C = 0.15 O D O Experimental values * H>g.(>uS 0 1u • 7.5 Level surface 2.5 0 0 I I I J L I I I I -2.5 -1 12.5 5 it 7.5 Shock strut Shock strut stroke, stroke, cm in.
2.5 1 0 0
I I I I I I I I I I I I I -1-
-2.5 "15 12.5 7.5 2.5 I I I I I I I I I I J L .02 .Ol» .06 .08 .10 .12 .11* .16 .18 .20 .22 .24 .26 .28 .30 Time, s (b) Shock strut stroke.
Figure 7.- Continued.
201- Analytical predictions, C = 0.15 f Experimental values <tO 20 r- 0 0 ° Hydraulic —°~o—""— pressure, Ufa Hydraulic ° °° n° on pressure, psig 1*0 I I I I I I J I I 02 .04 .06 .08 .10 .12 .14 .16 .18 .20 .22 .24 .26 .28 .30 (c) Hydraulic pressure.
Figure 7.- Continued.
Analytical predictions, C, = 0.15 r Q Q <^> Experimental values w
o " <r o "o
Level surface kO J L J I I L 0 i5 Pneumati c ^ -» <> Pneumatic pressure, MPa o o o o o o ° n pressure, psig kO I I I I I I 1 1 1 L '5 0° -I D I I I I I I I I 0 .02 ,0l» .06 .08 .10 .12 .lit .16 .18 .20 .22 .21* .26 .28 .30 Time, s (d) Pneumatic pressure.
Figure 7.- Continued.
Level surface A n a l y t i c a l p r e d i c t i o n s , c, = 0.15 er menta OU O ExP ' ' values I I I I I I I J 1 I I I I I -2 - Hub acceleration, .(, -Jl* I I I I I I I I I I 1 .02 .01* .06 .08 .10 .12 .1<t .16 .18 .20 .22 .2 * .26 .28 .30 (e) Hub acceleration.
Figure 7.- Continued.
Analytical predictions , C = 0.15 f Level surface O Q O Experimental values Upper mass acceleration, g
I I I _l I I I I
.8 .it 10" -.It -.8 -1.2 -1.6 -2 I I I I I I I I I I I I I I I .02 .OU .06 .08 .10 .12 .lit .16 .18 .20 .22 .-2l» .26 .28 .30 Ti me, s (f) Upper mass acceleration.
Figure 7.- Concluded.
c ID 4-1 cn -KI C •*.
0 \ u uC -Q 01 — J-
.._
r o
a
o
.2
CO
a
_ o cr> CD CO
U
O CO
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U <a a.
I
CO
rt
c
o
o
bfl o J-
a
CO rt i
•o
rt
cu
rt
cu
O
i
oo
cu
C at
s
c U
a
S-, CO
JS
rt
c
o
«iH •+J O
a
a
rt
0) 0) S I • rH X rt I OJ Deflection, in.
1.0 1.25
•5 .75 •25 15 r
- 2500
- 2000 Force, kN Force, tbf - 1500 - 1000 Figure 10.- Tire force as function of tire deflection.
O • |H W
c
o>
CD
•s
a)
o
t-i
CD
a
' o
Oi ^ 0) I O
o o
•O -r
g -
rt 0) J2 O
O
w
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a
<u
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rt -i->
cu
0)
o
o
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.2
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bJD
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.a
a
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.2
-i->
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I
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cu
O
<3
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fn
0, OJ
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S
^i
0) 4-> 0> T5 ^ O «*H Q, 0) CO CO 0) ID U 0) >s I/I 1) •<-» as C "a.
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0) fn fafl \ NASA-Langley, 1977 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON. D.C. 2O546 POSTAGE AND FEES PAID NATIONAL AERONAUTICS AND SPACE ADMINISTRATION OFFICIAL BUSINESS PENALTY FOR PRIVATE USE S3OO
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