1、TECHNICAL REPORT R-64MECHANICAL PROPERTIES OF PNEUMATIC TIRESWITH SPECIAL REFERENCE TOMODERN AIRCRAFT TIRESBy ROBERT F. SMILEY and WALTER B. HORNELangley Research CenterLangley Field, Va.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHS
2、Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTENTSPageSUMMARY . lINTRODUCTION . 1SYMBOLS 2DEFINITIONS . 3RATED PRESSURE . 4RATED AND BOTTOMING DEFLECTIONS . 4SLIP RATIO 4TIRE CONSTRUCTION AND NOMENCLATURE (See also fig. 1.) 4GENERAL DISCUSSION 4SPECIFIC NOMEN
3、CLATURE 5PROPERTIES OF A STANDING OR NONROTATING TIRE (See also figs. 2 to 37.) 6PURE VERTICAL LOADING (See also figs. 2 to I6.) . 6Geometric Properties of Footprint Area (See also figs. 2 to 7.) . 6Footprint length (See also figs. 2 to 4.) 6Footprint width (See also figs. 2 and 5.) . 7Gross footpri
4、nt area (See also figs. 6 and 7.) . 7Net or bearing footprint area 7Pressure Rise (See also figs. 8 and 9.) . 8Vertical-Force-Deflection Variations (See also figs. 10 to 14.) 9Static-force-deflection variation (See also figs. 1i to 13.) . 10Dynamic-force-deflection variation (See also figs. 10 and 1
5、4.) 12Gross Footprint Pressure (See also fig. 15.) 13Average Bearing Pressure (Set also fig. 16,) 13COMBINED VERTICAL AND LATERAL LOADING (See also figs. 17 to 25.) 14Ltteral Spring Constant (See also figs. 18 to 21.) . 14Vertical-Force Center of Pressure (See also figs. 17 and 22.) . 17Vertie-d Sin
6、king (See also fig. 23.) . 18Lateral Deformation (Static Relaxation Length) (See also figs. 17, 24, and 25.) . 18COMBINED VERTICAL LOADING AND TWISTING ._OMENT (See ,dso figs. 26 to 29.) 19General Observations (See also figs. 26 and 27.) 19Torsional Spring Constant (See also figs. 28 and 29.) 20COMB
7、INED VERTICAL AND FORE-AND-AFT LOADING (See also figs. 30 to 33.) 21Fore-and-Aft Spring Constant (See also figs. 31 and 32.) 22Vertical-Force Center of Pressure (See also figs. 30 ,_nd 33.) . 24Vertical Sinking . 24Circumferential Distortion 24COMBINED VERTICAL LOADING AND TILT (See als0 figs. 34 to
8、 37.) 25Laterd Force (See flso figs. 34 to 36.) 25Vertical-Force Center of Pressure (See also figs. 34 and 37.) . 26PROPERTIES OF A ROLLING 02 ROTATING TIRE (Sec also figs. 38 to 59.) . 26ROLLING RELAXATION LENGTIIS (See also figs. 38 and 39.) . 26Unyaw(,d-Rolhlg Relaxation Length (See also fig. 38.
9、) 26Y,_wvd-l_olling Relaxation Length (See Mso fig. 30.) 27IOLLING RADIUS (See also figs. 40 and 42.) 28Effect of Vertical Deflection (See also figs. 40 -rod 41.) 28Effect of Braking 28Effect of Yaw (See also fig. 42.) 30YAWED-ROLLING CIIARACTERISTICS (See also figs. 43 to 52.) . 30General Observati
10、ons (See also fig. 43.) . 30Steady-State Conditions (See also figs. 44 to 52.) . 30Normal force (See also figs. 44, 46, and 47.) . 30Cornering force (See also fig. 45.) . 33Cornering power (See also figs. 48 and 49.) 33Self-alining torque (See also fig. 50.) 35Pneumatic easter (See also fig. 51.) .
11、35Coefficient of friction (See also fig. 52.) 37IIIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTENTSPROPERTIES OFAROI,LING OR ROTATING TIRE Continued lageBRAKING F()RCE FOR SMALI, SLIP RATIOS (See also figs. 53 and 54.) 37TURNING MOMENT FOR CU
12、RVILINEAR ROI,I,ING . 38ROLLING CIIARACTERISTICS OF A TILTED TIRE (See also figs. 55 and 56.) 40Lateral Force (Se_ also fig. 55.) . 40Turning Moment (See also fig. 56.) . 41VERTICAL-FORCE-DEFLECTIC)N VARIATII)N (See also figs. 57 to 59.) 42Apparmlt and Effcctivc Tire Doflections . 42St atic-Forcc-Dv
13、floetion Variation . ,12Force-Deflection Variation for Slow Rolling (See aso fig. 57.) -13Force-Deflection Variation for I,anding Impact (See also fig. 58.) . 43Inertia effects . 43.Drag and side-loM effects . 44ltysteresis effects 4 1Illustrative data (See also fig. 58.) . -t4Foree-Defloction Varia
14、lion for Prcrotation Drop T_sts (See also figs. 58 and 59.) . 45MISCELI,ANEOITS TIRE PROPERTIES (See also figs. 60 to 65.) . 4,5CENTRIFUGAL GROWTH OF TIRE RADIUS (See also figs. 60 and 61.) . 45WIEEL ANI) TIRE INERTIA PROPERTIES 46TIRE IIYSTERESIS PROPERTIES (See also figs. 17 and 62 to 65.) 47Preli
15、minary Discussion (Sec also fig. 17.) i9Evahmlion of Lateral IIyst(,resis Paramct(r rh (See also figs. 62 to 65.) . 4949Free-vibration tests (See also fig. 62.) .Static wsts (See .dso fig. 63.) . 5050Mean value of r/x Ev,duation of Vertical Hysteresis Parameter _7_ (See also fig. 64.) . 50Evaluation
16、 of Fore-and-Aft Itystcresis Parameter “q_ (See also fig. 65.) 51Evahmtion of Torsional Itysteresis Parameter “q. 51CONCLUDING REMARKS . 52APPENDIX A-SAMPLE OF METIIOD OF DETERMINATION OF EMPIRICAL EQUATIONS . 53APPENDIX B-MEASUREMENTS OF TIRE GROWTIt DVE TO CENTRIFUGAL FORCES 5,1APPENDIX C-I)ETERMI
17、NATION OF IIYSTERESIS CONSTANTS FROM FREE-VIBRATION TESTS_ 55REFERENCES . 56IVProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHNICAL REPORT R-64MECHANICAL PROPERTIES OF PNEUMATIC TIRES WITH SPECIAL REFERENCETO MODERN AIRCRAFT TIRES 1By ROBERT F. S
18、taLEr and WALTER B. ttORNESUMMARYA .,tudy i._ pre._ented of mo._t of the propertie.; q/pneumatic tires which are of i.terext to aircraft de-_igner,_. The principal topic,s di,_eu,_._ed are tirevertieal:foree-d_fleetion eharaeteristie,_; lateral, fore-and-aft, aim tor._ional ._pring eonxta_ts; footpr
19、int-area propertie,_; rehtxation length,_; rolling radiu,_;cornering f.rce, cornering power, ,_elf-alining torque,and pneumatic caster .tim yawed rollD_g condilion,_;_fleets q wheel tilt; a.d tire radial growth under thei.fluenee of eentr(fugal.force,_.For each tire property eon,_idered, ,_emiempiri
20、ealequation,_ are set up which lake i_+to aecou.t tt+emajor factors pertine,_t to the property. Wl_erererpo,_sible each equation is compared with the arailablec,rperimental data to exlablish il,_degree of reliability.A ,small amount _!f preciou,dy unpublished exper-imental data i._ i_cluded, mo.stly
21、 o7_ the subjects oftire tilt,.fore-an :t-aft st(fine,% and con tr(fugal grmeth.INTRODUCTIONIn ordt, r to cope adequately with the landingatul taxiing problems of present-day aircraft, thoseengaged in landing-gear design need inforinationon a large nmnber of pneumatic-tire properties.At present some
22、 information can be obtained fromsuch sources as referenees 1 to 64 flw a number ofobsolete or foreign types of tires and for a fewmodern American tires. Ilowever, it is doubtfulwhether the landing-gear designer will find in theliterature experimental data which are directlypertilwnt to the particul
23、ar tire or tires in which heis interested. Moreover, the scale laws which tireproperties obey have not been thorougldy inves-tigated, and, for at least a few important tirei ,%lpersedes NACA Technical N*oie 4110 by “Robert F. Smile5“ and Walter B.properties, these scah, laws are not at all obvious;i
24、n some cases, simph, and accurate scah, laws ap-parelltly cannot be estal,lished at all. Conse-quently, the air(raft desio_ner cannot confidentlyscah, the results of tire tests in order to apply themto tires in which he is interested.Some useful studies have been made in regardto theoretical i lffor
25、mation on tire properties; mostof these studies are contained or summarized inreferences 18 and 46. llowever, these l|leoreticalstudies, although enlightening in some respects,are usually based on oversimplified concepts and,almost inevitably, involve some empirical con-stants which have not. yet be
26、en evahtated.Th(,se observations indicate a need to assess timpresent state of the art for prediction of tire prop-erties I)3“ a. comprehensive study of the awfilabletheoretical and experimental information on tireproperties. The present paper presents suchstudy which has as its primary aims the det
27、ermi-nation of the most important variables which in-fluence the various tire properties and the estab-lishment of some simple quantitative equationsfor most of these properties.Since it is improbal_le that many readers of tiffspaper will be interested in all the properties dis-cussed herein, each t
28、ire property is considered ina separate section with as little cross-correlationbetween sections as appears necessary.For each tire property considered some equat ionis obtained, either from a previous paper, by acrude theoretical deriva.tion, or by purely empiricalmeans. (For example, see appendix
29、A.) Valuescalculated by these equations are then comparedwith the available experimental data, which areIIorne, 1958.1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHNICAL REPORT R-64-NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONused to establish
30、 any empirical constants needed G,Fzin the equations. It should be emphasized that F_the theoretical derivations that are presented areintended largely to give some idea of the basicphenomena, to demonstrate the major variables F_involved, and to suggest some promising form forempirical equations. I
31、n general, the equations F_._resulting from these derivations are far from rig-orous; however, by judicious insertion of empirical F_,_constants into these equations, it is believed thatmost of them can give at least a fair correspond- Fu,_ence to reality. F_,Although ahnost all the discussion in th
32、is paper F_,xdeals with previously published experimental data,a small amount of new data is presented princi- F,pally on the suljects of tire tilt, braldng, and F:,ocentrifugal-growth effects. F+Ag.(t _tb_xC- tCXc_c.dD,( )SYMBOLSratio of net footprint area to gross foot-print area, A,j.lgvertic_d s
33、inking of tire per unit lateral Hdistortion I_,_oss footprint areanet footprint areawidth of tire-ground contact area (foot- Iv,tprint)change in fore-and-aft position of centerof pressure of vertical force per unit of lv,_fore-and-aft deflectionchange in lateral position of center of Jpressure of ve
34、rtical force per radian of letwheel tiltchange in lateral position of center of kwpressure of vertical force per unit oflateral distortion k,braking-force coefficientcornering-power coefficientvertical-force coefficient (see eq. (24) K,outside diameter of free tire If_differential operator with resp
35、ect to time, K,d( )dt K, _base of natural logmithmsefat )=t0.96( )-_-0.216( )2/C,2.4( )- C.F forcef_,r_,r,eLL,.L,L_drag forces for two narrow couph, d wheelsinstantaneous drag or fore-and-aft force(ground force parallel to direction ofmotion)lateral or cornering force (perpendicularto direction of m
36、otion)lateral force resulting from wheel tilt forstanding tirelateral force resulting from wheel tilt, forrolling tirelateral hysteresis forcelateral spring forcelateral force resulting from elastic andhysteresis effectsvertical force acting on tire from groundaverage or reference verlic_d forcenorm
37、al force (ground force perpendicularto wheel plane)instantaneous normal forcesteady-state normal forcehalf-length of tire-ground contact area(footprint)tire radius minus rim radiuspolar moment of inertia of wheel and tireabout axis perpendicular to the wheelaxlepolar moment of inertia of tire and tu
38、boabout wheel axle (excluding solid wheelparts)polar moment of inertia of tire, tube, andwheel about wheal axlecircumferential decay lengthradius of g3.ration of tire and tube aboutthe wheal axle, _7_. ,/m,radius of gyration of wheel and tire _tboutthe wheel axle, _:_, w/mwradius of gyration of whee
39、l and tire aboutan a:vis perpendicular to the wheel axle,3,:/z_w_ r/_ wfore-and-aft spring constanttorsional spring constantlateral force per radian tilt angle forstanding tire with Xo=Olateral force per radian tilt angle for roll-ing tirelateral spring constantrelaxation lengthunyawed-rolling-force
40、 relaxation lengthstatic relaxation lengthyawed-rolling-relaxation lengthProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Lxm_Dl tM,31, _nNPAppopo ,a_bP_P_pnPrPqrroArrere,ore.Dre,2R881t_oV_VqJ)XYMECHANICAL PROPERTIES OF PNELVMATICunyawed-rolling-deflc
41、ction relaxation alength .ymass of tire, tube, and wheel 8mass of tire and tube 8oturning or twisting moment about a ver-tical axis through the wheel centerturning moment rcsulting from pathcurvature 80turning moment resulting from wheel tilt, 8_polytropic exponent 8_cornering power, _/_-_tire infla
42、tion pressure (ixpressure rise, P-Potire inflation pressure at zero vertical load _(gage) E_tire inflation pressure at zero vertical load(absolute) wtire bursting pressure n,average gross footprint pressure, FjA_ n.additional pressure resulting from centrif- yxugal forces Oaverage tire-ground bearin
43、g pressure, O_F)An Ktire rated inflation pressure Xtire parameter defined by equation (96) Xoor (97)pneumatic caster, _ll,._/F._ or 3,._.JFt X_outside fice radius of tireinitial tire radiusincrease in tire radius resulting from cen-trifugal-force effectsrolling radiusrolling radius for unyawed and u
44、nbrakcdrolling _+rolling radii for two narrow coupledwheels rxradius of curvature of tire rolling pathperipheral distance around tire 4slip ratio _btimeperipheral displacement _oovertical velocity at ground contacthorizontal rolling velocityinside volume of tireinitial volume of tiremaximum width of
45、 undcflccted tiredisplacement in fore-and-aft direction orin direction of motiondisplacement perpendicular to directionof motionTIRES (MODERN AIRCRAFT TIRES)tire twist, angletilt of wheel pla, ne, radiansvertical tire deflectionvertical tire deflection for pure verticalloading conditions (F_= F_=0)_
46、, 82 vertical tire deflection for two narrowcoupled tiresvertical deflection at tire bottomingeffective vertical tire deflectionrated vertical tire deflectionvertical sinkiug of tire resulting fromapplication of fore-and-aft ground forcevertical sinking of tire resulting fromapplication of lateral g
47、round forceelongation strain produced by drag forceelongation strain produced by verticalforce (always negative)fore-and-aft hysteresis parametervertical hysteresis parametertorsional hysteresis parameterlateral hysteresis parameterwheel rotation, radiansperipheral angle, degpressure-rise parameterl
48、ateral distortion of tirc equatorlateral distortion of tire equator at centerof the-ground contact areafore-and-aft distortion of tire-ground con-tact area,g_ drag coefficient of friction. maxinmm drag coefficient of friction forlocked-wheel testsu_,_ sliding-drag eocfi3cient of friction forlocked-w
49、heel testsyawed rolling coefficient of frictiontilt paramctcr (sce rcf. 53)lateral-spring-constant coefficientNyaw-angle parameter, _ _byaw angh,wheel angular velocity, radians/seewheel angular velocity for unbrakedrolling, radians/sceSubscripts :max maximum valuest staticDEFINITIONSThe following terms are defined for use in manyparts of this paper. Other terms which arc us
