轮胎力

TireForceTireForce轮胎坐标与轮胎力轮胎坐标与轮胎力外倾角侧偏角SAE轮胎运动坐标系前视图（FrontView）俯视图（TopView）()zzzFfzCz=Δ≈Δ()0limzzzfCzΔ→∂=∂Δ轮胎刚度轮胎刚度轮胎变形与轮胎力轮胎变形与轮胎力()xxxFfxKx=Δ≈Δ()0limxxxfKxΔ→∂=∂Δ()yyyFfyKy=Δ≈Δ()0limyyyfKyΔ→∂=∂Δ纵向变形轮胎力纵向变形轮胎力侧向变形轮胎力侧向变形轮胎力纵向位移刚度纵向位移刚度侧向位移刚度侧向位移刚度滚动阻力滚动阻力„Thenormalstresswillmoveforwardwhenthetireisturningonaroad.„Byincreasingthespeed,thenormalstresswillshiftmoreandconcentrateinthefirsthalfofthetireprint,causinglowstressinthesecondhalfofthetireprint.„Highstressinthefirsthalfalongwithnostressinthesecondhalfissimilartohammeringthetirerepeatedly.RzMFx=Δ滚动阻力矩滚动阻力RRZFfF=firsthalfsecondhalftireprint滚动阻力滚动阻力————能量耗散能量耗散阻尼结构阻尼结构弹簧结构弹簧结构滚动阻力系数滚动阻力系数RRZFfF=滚动阻力系数201RRRxfffv=+仿真中可近似计算：4012RxxFCCvCv=++滚动阻力系数随车轮载荷的增加而减小；随胎压的升高而减小；随车速的增加而增加；还与轮胎的材料、结构等有关；•Thetirematerialandthearrangementoftirepliesaffecttherollingfrictioncoefficientandthecriticalspeed.•Radialtireshavearound20%lowerrollingfrictioncoefficientand20%highercriticalspeed.•Generallyspeaking,therollingfrictioncoefficientdecreaseswithwearinbothradialandnon-radialtires,andincreasesbyincreasingtemperature.Criticalspeedisthespeedatwhichstandingcircumferentialwavesappearandtherollingfrictionincreasesrapidly.201RRRxfffv=+Rf车速与滚动阻力系数车速与滚动阻力系数滚动驻波滚动驻波StandingWavesStandingWaves•Thewavelengthofthestandingwavesareclosetothelengthofthetireprint.•Abovethecriticalspeed,overheatinghappensandtirefailsverysoon.胎压与负载对滚动阻力的影响胎压与负载对滚动阻力的影响525.5109011000.03885.11000zzRxFFKfvpp⎛⎞×++=++⎜⎟⎝⎠Radialtires：K=0.8;Nonradialtires:K=1.0Rf纵向轮胎力纵向轮胎力{}max,dwdwrusruωω−=纵向滑移率(Slipratio)：rd—滚动半径ω—轮胎旋转角速度uw—轮心速度s0—驱动加速(Driving)s0—制动减速(Braking)[1,1]s∈−()xxzFsFμ=纵向轮胎力(Longitudinalforce)：轮胎纵向力的饱和与非线性特性轮胎纵向力的饱和与非线性特性0100%sBrakingxμxpμs*xsμ-s*xpμxsμDrivingSlidingSlidingxxFCs≈xC—轮胎纵滑刚度[0.2,0.2]s∈−纵向轮胎力的线性近似:侧向轮胎力侧向轮胎力()arctanywvuα=轮胎侧偏角(Slipangle)：vy—轮胎侧滑速度uw—轮心速度[1,1]α∈−侧向轮胎力：()yyzFFμα=回正力矩：zyMzMFa=侧向力的饱和与非线性特性侧向力的饱和与非线性特性-0.6-0.4-0.200.20.40.6-4000-3000-2000-100001000200030004000轮胎侧偏角(rad)轮胎侧向力(N)轮胎侧向力：()yyzFFμα=yyFCα≈yC—轮胎侧偏刚度[0.15,0.15]α∈−侧向轮胎力的线性近似:附着条件的影响附着条件的影响轮胎规格轮胎规格回正力矩与侧偏角回正力矩与侧偏角轮胎负载的影响轮胎负载的影响综合分析综合分析外倾侧向力外倾侧向力xC外倾侧向力与回正力矩yFCγγ≈zyMzMFa≈Cr—外倾角刚度(CamberStiffness)外倾侧向力与外倾角外倾侧向力与外倾角外倾侧向力与轮胎负载外倾侧向力与轮胎负载外倾侧向力与侧偏角、外倾角外倾侧向力与侧偏角、外倾角摩擦椭圆摩擦椭圆221yxyMxMFFFF⎛⎞⎛⎞+=⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠shearzFFμ=xMxzyMyzFFFFμμ==轮胎力模型轮胎力模型轮胎模型分类轮胎模型分类9预测联合工况下的轮胎力与力矩，可以同时预测纵向力、侧向力和回正力矩等力学特性；9车辆动力学仿真研究中常用的综合轮胎模型：“魔术公式”（MagicFormulaTireModel,Prof.Pacejka,Delft工业大学,Netherlands），Fila轮胎模型（Japan），Dugoff模型（Dugoff，Japan），平方轮胎模型，立方轮胎模型等；„综合轮胎模型„单一性能轮胎模型：9纵滑模型：预测车辆驱动与制动工况时的纵向力；9侧偏模型：预测车辆纯转向时的侧向力；纵滑纵滑““MagicFormulaMagicFormula””模型模型sin(arctan())xxxxxFDCB=Φ(1)()arctan()xxxxxEsEBBsΦ=−+1.65xC=212xxzxzDaFaF=+5234xFzxzxzxaxxaFaFBCDe+=2678xxzxzxEaFaFa=++121.3xa=−21144xa=349.6xa=4226xa=50.069xa=60.006xa=−70.056xa=80.486xa=-1-0.500.51-8000-6000-4000-200002000400060008000滑移率轮胎纵向力(N)sin(arctan())xxxxxFDCB=Φ纵滑纵滑““MagicFormulaMagicFormula””模型模型分段线性纵滑模型分段线性纵滑模型xbzFFμ=()(),,11pbbpspsbbssssssssssμμμμμμμ∗∗∗∗∗∗⎧=≤⎪⎪⎨−−⎪=−⎪−−⎩sμpμs∗1.0μs0wbbwursuω−=侧偏侧偏““MagicFormulaMagicFormula””模型模型sin(arctan())yyyyyFDCB=Φ(1)()arctan()yyyyyEEBBααΦ=−+1.30yC=212yyzyzDaFaF=+345sin(arctan())yyyzyyyaaaFBCD=2678yyzyzyEaFaFa=++122.1a=−21011a=31078a=41.82a=50.208a=60.000a=70.354a=−80.707a=-0.6-0.4-0.200.20.40.6-4000-3000-2000-100001000200030004000轮胎侧偏角(rad)轮胎侧向力(N)sin(arctan())yyyyyFDCB=Φ侧偏侧偏““MagicFormulaMagicFormula””模型模型纵滑与侧偏联合工况纵滑与侧偏联合工况““MagicFormulaMagicFormula””模型模型0xxxFFσσ=−0yyyFFσσ=−1xssσ=−+tan()1ysασ=−+22xyσσσ=+Fx0—纯纵滑轮胎力Fy0—纯侧偏轮胎力-0.8-0.6-0.4-0.200.20.40.60.801000200030004000500060007000滑移率轮胎侧向力(N)α=20degα=10degα=4degα=2degDugoffDugoff非线性经验轮胎模型与计算非线性经验轮胎模型与计算()1xiixwiiCsFfSs=−tan()1yiiywiiCFfSsα=−222222(1tan)(1)2tanzirxiiixiiyiiFvsSsCsCμεαα−+=−+11()(2)1SfSSSS⎧⎪=⎨−⎪⎩纵向力：侧向力：-0.4-0.200.20.40.6-8000-6000-4000-200002000400060008000Tireslipangle(rad)Corneringforce(N)DugoffTiremodellongitudinalsliprate=0.2Fz=1500NFz=4500NFz=8500N参考文献参考文献[1]Bakker,E.,Pacejka,hbandLidner,L.,Anewtiremodelwithapplicationinvehicledynamicsstudies.SAEpaper890087,1989.[2]Pacejka,H.B.andBesselink,I.J.M.,Magicformulatyremodelwithtransientproperties.VehicleSystemDynamicsSupplement.27(1997)234–249.[3]DUGOFFH,FANCHERPS,SEGALL.Ananalysisoftiretractionpropertiesandtheirinfluenceonvehicledynamicperformance.SAEPaper70037,1970.