1、0)NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSi_TECHNICAL NOTE 3235LOW-SPEED YAWED-ROLLING MiD SOME OTHER ELASTICCHARACTERISTICS OF TWO 56-DVCH-DIMVIETER,24-PLY-RATING AIRCRAFT TIRESBy Walter B. Home, Bertrand H. Stephenson,and Robert F. ,., . .Provided by IHSNot for ResaleNo reproduction or networkin
2、g permitted without license from IHS-,-,-NACA TN 3235.Inasmuch asetilly very welJreader.rDEFINITIONS OF CONCEPTSsome of the quantitiesused in this paper areWown, the following definitions are given toFootprint area.- The tire contacts theground in a finite5not gen-aid thearea theshape of which is il
3、lustrated in figure 1. Because the tires tested hada rib-_ however, becausethis theory is not completely rigorous, it is not unexpected that thedifferentdefinitions to be given will not lead to precisely the samevalue of relaxation length. In order to distinguish these differentvalues of relaxation
4、length to be discussed, they are assigned differentnames and -01 mibscripts.Static relaxation length Ls.- Consider the experimentwhere theground-contactarea of a stationarytire is deflected lateralJywithrespect to the wheel plane. The different parts of the center band orequator of the tire are then
5、 deflected sidewise from the wheel centerplane in the manner iJJurated in figure.2. From the available experi-mental data, it is found that, except in and near the edge of the ground-contact area and near the top of the tire, this distortion curve isessentially an exponential curve of the form(2)whe
6、re 1 is the lateral distortion of the tire equator, A2 is a con-stant, and s is the circumferentialdistance about the tire. Theexponential constant Ls is called the static relaxation length of thetire.Unyawed-roll.ing-deflectionrelaxation len that is, the side force FYi builds up with dis-tance x ro
7、lled according to a relation of the form/%-xFyi = Fy - Ape (5)where the constant general views of this vehicle areshown in figures 3 to 5. The airplane was towed tail first by a tractortruck at an attitude such that the original airplane shock struts werevertical. This attitude was necessary in orde
8、r to use the existingtiding-gear structureand still.keep the tires in a vertical plane atvarying angles of yaw. The originalyokes and torque links of thelanding-gear struts along with the wheel assemblieswere replacedbysteel wheel housings which held the tires and wheels tested. A rigidtruss pinned
9、at four points to the two wheel housings held the wheelhousings in a ftied relative position during towing operations. Holeslolocated in the wheel ho-psingsat angular intervals of permitted thewheel frames to be rotated through a nominal yaw-ane range of 0 to21$0. Actual measurements on the complete
10、d test rig, however, showedr,the yaw-angle range tobe from 0.35 to 24.90.The towing loads were takenby two steel cables attachedbetweenthe wheel housings and the tow truck chassis. At high yaw angles withthe heavy-weight condition,an additional truck was attached to the towtruck to provide increased
11、power for towing. The mximum towing forcereqfired was approximately 8,OOO pounds.The airplane tail was supportedby the original swiveling tail-wheel-stnrt asseniilywhich was modified so that the tail-wheel assenkd.yrotated about a vertical axis. The tie rested in a slot on the top ofthe tow-truck su
12、pport structure. Tbis slot and pin arrangementpermittedthe entire towing load, with the exception of a relatively small amountof friction force, to be carriedby the drag cables.The weight of the test vehicle acting on the tires was approximately20,0 pounds in the lightest condition. This weight was
13、varied in incre-ments by the addition of six steel and concreteweight cans (eachweighingabout 8,0 pounds) which were mounted on the airplane structure as shownin figure 3. Additional weights were also added in the fuselage to obtainthe heaviest weight ction of ,0 pounds. 4. .Provided by IHSNot for R
14、esaleNo reproduction or networking permitted without license from IHS-,-,-K.(.NACA TN 3235 9For the locked-wheel drag-force investigation,the test setup wasas shown in figure 5. The drag cables were disconnected from the towtruck and attached to a hydraulic ram which was anchored to several sta-tion
15、ary heavy vehicles. The airplane wheels were locked by means of rodspassing through the spokes and bearing on the wheel frames. Pressure wassupplied to the ramby the electrically driven pump shown in figure 5. .InstrumentationThe test vehicle was equipped with instruments for measuring sideforce, se
16、)f-aliningtorque, drag, vertical tire deflection, horizontaltranslation,and wheel rotation. An explanation of the method by whicheach of the quantitieswas measured is given in the following sections.Measurements of these quantitieswere recorded simultaneouslyon a14-channel oscillographmounted in the
17、.test vehicle. This oscillographwas equippedwith a O.01-second timer. A sample oscillograph record fora yawed-rolling series B represents conditionsfor a later period of time,and so forth.The change in tire-tread pattern due to tire wear throughout thetests is illustrated h figure 9. At the beginn o
18、f the tests bothtires had a rectangular cross-sectionaltread pattern (fig. 9(a) andthis pattern was mibstantiallypresemed throughoutmost of series Ato c. Tawsrd the end of series C, however, the side of the tread in$nthte contact with the ground began to wear away and produced thetread pattern illus
19、trated in figure 9(b). This wesr increased substan-tially during series D and for series E to G the tire profile remainedbapproximatelyas indicated in figure 9(c). The small projecting edgesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3235
20、 11.of the tread were then cut off and for the reminder of the tests(seriesH and I) the tread cross section was again essentially rectan-gular with rounded-off corners, as shown in figure 9(d).Tire radius.- The variation of the unloaded tire radii with infla-tion pressure and tire wear is shown in f
21、igure 10. Each measurementshown was taken after the tires had been left at constant pressure forat least 24 hours. For test series E to H, the radius of the tires isdefined as the maximum rwlius less the height of the small projectingedge shown in figure 9(c); thus, the indicateddifference in tire r
22、adiusfor series A to C and E to I is largely due to the wearing off of thetread. It should also be noted that the tire radii during the laterstages of this investigation (seriesE to I in fig. 10) differ sghtlyfrom the radii measured after the conclusion of the tests (tableI andfig. 8). The differenc
23、e, approximately 1 percent, is probably due tothe fact that the earlier measurements were made during a period oftime when the tires were being regularly subjected to severe loadingswhereas the later measurements were made after the tires had been com-pletely unloaded for a long period of time.A rad
24、ius-pressurehysteresis loop for tire B is shown in figure 11.The elapsed time from start is shown for a-few of the measurements pre-sented. The variation in tire radius for a given pressure is seen toamount to as much as 1 percent for this relatively slow rate of changeof pressure (roughly,four hour
25、s for most of the cycle).Tire width.- The variation of msximum tire width with inflationpressure is shown in figure 12 for both tires. These measmements werealJ made after the conclusion of testing (tireswell worn) and eachmeasurement was taken after the tires had been kept at constant pressurefor a
26、t least 24 hours in order to mimbnize hysteresis effects.Test SurfaceAJJ yawed-rolling and drag tests were conductedby towing the testvehicle along the center of a 9-inch-thickreinforced-concretetaxi strip.This taxi strip had a slight crown such that the tires on the test vehi-cle were subject to a
27、slight tilt. However, this tilt was less than 1.The texture of the taxi strip, a boarded”concrete surface, as determinedfrom plaster casts, is shown in figure 13 for three random positions onthe strip. All other tests were conducted on a much smoother, level,reinforced-concretesurface.a71a15a14a13.-
28、 . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACA TN 3235“Precision of DataThe instrumentsused in these tests and the methods of reducing.data are believed to yield results usually accurate within the followinglits :Vertical load on tires, F
29、z, percent . . . . . .Cornering force, Fy, percent . . . . . . . . .Force perpendicular to wheel plane, F*, percentDrag force per tire, Fx, lb . . . . . . . .Measured moment, , lb-in. . . . . . . .Tire inflation pressure, p. or p, lb/sq in. . .Freeradius,r, in. . . . . . . . . . . . . .Rol.lidi,re,
30、h. . . . . . . . . . .Horizontal translation, x, in. . . . . . . . .Vertical the deflection, 50 or 5, in. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Yawangle, $, deg . . . .TES
31、TThe present tivestigationof. . . . . . . . . . . . . . . . *0.1 .tire characteristicsis divided intothe follohowever, the vertical load on the tires decreased slightlywith increasingdrag force as a consequenceof the moment prcihced by the drag force. Thischange in vertical load was taken into accou
32、nt in the computation of fric-tion coefficients. (Itwas not taken into account in the other testssince the effect was very small for those conditions.). .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 5235 15Supplementary Tests and Measureme
33、nts”In addition to the tests just described, several supplementarytests were made. These tests included vertical-load-deflectionmeasure-ments and footprint-areadeterminations. The vertical-load-deflectioncharacteristicsof the two tire specimenswere determined for one infla-tion pressure (about220 lb
34、/sq in.) with the tires mounted on the testvehicle. Tire-contact or footprint-areameasurements were made for thetire specimens at several inflationpressures and vertical tire deflec-tions. These measurements were obtained from the imprint left on apiece of heavy paper placed between a chalked portio
35、n of the tires anda snmoth concrete hangar floor.figure 1.lwsmrs,-. . .Several typicalAND DISCUSSIONMost ofpresented inthe experimental data obtained fromtables IIto VI and figures 8to 47.imprints are shownthis investigationinare., Yawed-Rolling TestsTable 11 contains all test data obtained during t
36、he final steady-state stage of each yawed-rolling run. Data are presented for 9 differ-ent test series (A to I) which represent either different verticalloadings, different the wear, r different orientation of the tires.The variation of normal force F*, self-aliningtorque , and pneumaticcaster with
37、yaw angle are shown in figure 14 for all vertical loadsand inflationpressures. Some details pertinent to the interpretationof these data are discussed in the appendix. Sample rolling-radius datafor two typical test conditions are plotted in figure 15 as functions ofyaw angle and vertical tire deflec
38、tion.The buildup of cornering force with horizontal distance rolledduring the initial stages of the yawed-rolling runs is illustrated infigure 16 for typical runs at several pressures and for three testseries. Inasmuch as for most runs there was an initial residual forceor preload in the tires, the
39、original test curves did not usually passthrough the origin. In order to take this fact into consideration,thetest curves shown in this figure have been horizontally shifted (if neces-sary) so that the extrapolation of each curve is made to pass throughthe origin. For most of these curves, the initi
40、al rate of buildup appearsto increase with increasingyaw angle (as is predicted by theory, that is,ref. 5) and that the force generally approaches close to its maximum valuebefore the tires have rolled more than 6 feet. . ._Provided by IHSNot for ResaleNo reproduction or networking permitted without
41、 license from IHS-,-,-16.Relaxation-LengthNACA TN 3235!kSt6Samples of the test data obtained from the four different methodsused to determine the relaxation length of the tire specimens are shownin figure 17 for test”seriesA, B, and E. In parts (a), (b),and (c) offigure 17, these data are plotted in
42、 semilogarithmiccoordinates in orderthat the expected exponential curves (accordingto theory) should appearas straight lines. The relaxation lengths,for the conditions shown hereand for all other conditions of this investigationwere obtainedbyfitting straight lines to such semilogarithmicplots for e
43、ach test runand are tabulated together in tables II to IV.It is seen from figure 17 that usually the test results do”appearto give substantiallystraight lines in these semilogarithmicplots;thus, the theoreticalexponentialvariation of force with distancerolled (forthe rolling relaxation lengths) or d
44、istance around the tireperiphery (forthe static relaxation length) is supported. The samedata shown for series B in figure 17(b) is replotted in linear coordi-nates in figure 17(d). The solid lines drawn on these plots (fig.17(d) -are the same solid faired lines which were fitted through the data in
45、figure 17(b).It shouldbe noted that, for the static-relaxation-lengthdata, theNtest data do not aee well with the assumed exponentialvariation nearthe two endpointconditions at the edge of the tire footprint and at thetop of the tire (for example, see fig. 17(a). This discrepcy iS duelargely to the
46、finite bending stiffness of the tire which reqd.res thatthe slope of the tire-distortioncurve must be zero at the edge of thetire footprint (s = h) and also at the top of the tire and both of thesefactors conflictwith an exponentialvariation.Locked-WheelDrag TestsMost of the experimental data obtain
47、ed from the locked-wheeldragtests sre presented in table V. Also, pical data are shown in fig-ure 18 forpulled forthe buildup ofseveral runs.fore-and-aftforce-with horizontal distanceSupplemen_ however, reversing the tire tread(reversingthe tires ti the wheel housings) decreased the maximum normalfo
48、rce considerablyas is illustrated in figure 28. A likely explanationfor this phenomenon could lie in the fact that the tire-treadbeadsresulting from unsymmetrical tread wear (seefig. 9) fold over on topof the treads lx.xlertowing conditionswith the tires reversed as is shownschematicallyh figure 29.
49、 Such a folding of the tread bead would tendto reduce the tread-contactarea considerablyand thus increase thebearing.pressurebetween the tire and the ground. This increase inbearing pressure wouldrestit in a reduced friction coefficient (tobediscussed later) and would thus reduce the mximum attainable normalforce.Maximum sel.f-alinhgtorque
