S 1.4 Traction-Limited Acceleration and AdhesionRatio汽车行驶的驱动-附着条件和附着率l.Traction-LimitedAcceleration（1）DrivingConditionofAcceleration（驱动条件）F =0When Level road:Constant speed: F, = OLevel road & Constant speed: F = F, + FwF=F+Fw+F+Fdu= SmF-(F,+Fw+F)dtChapter1 AccelerationPerformance
Chapter 1 Acceleration Performance §1.4 Traction-Limited Acceleration and Adhesion Ratio汽车行驶的驱动-附着条件和附着率 （1）Driving Condition of Acceleration（驱动条件） When Level road: Constant speed: Level road & Constant speed: Fi 0 Fj 0 F F F t f W 1. Traction-Limited Acceleration ( ) t f W i j t f W i F F F F F du m F F F F dt 1
（1）DrivingConditionofAcceleration（驱动条件）(等速）F=F,+Fw+FFor constant speed:（加速）acceleration:F,>F,+Fw+F（减速）deceleration:F,<F,+Fw+FSoDriving Condition isF≥F,+Fw+FTqigionrtqgF7rig 个or 个or n 个orTaor r→F2Chapter1AccelerationPerformance
Chapter 1 Acceleration Performance （1）Driving Condition of Acceleration（驱动条件） For constant speed: （等速） acceleration: （加速） deceleration: （减速） So Driving Condition is F F F F t f W i F F F F t f W i ≥ F F F F t f W i ＞ F F F F t f W i ＜ 0 0 , tq g T t g T tq t T i i F r i or i or or T or r F 2
（附着条件）(2)LimitedConditionofAcceleration> Presuming there is adequate power from the engine, theacceleration may be limited by the friction that is F。（附着力)between the tire and road for anti-skid purpose附着力：地面对轮胎切向作用力的极限值In this case F, is :F=F=FβXmax0T-Tf2 = Fx2 ≤F,= Fzo0（后轮驱动，限制车轮打滑的极限力）r（道路附着系数）Where: ΦCoefficient of adhesionusually p ranges from 0.7~0.8FzeWeight on driving wheels（驱动轮上道路垂直反力）3Chapter1 AccelerationPerformance
Chapter 1 Acceleration Performance Presuming there is adequate power from the engine, the acceleration may be limited by the friction that is Fφ（附着力） between the tire and road for anti-skid purpose. In this case Fφ is ： （后轮驱动，限制车轮打滑的极限力） Where: φ——Coefficient of adhesion （道路附着系数）, usually φ ranges from 0.7~0.8. FZφ —— Weight on driving wheels （驱动轮上道路垂直反力） F F F X z max X Z t f F F F r T T 2 2 附着力：地面对轮胎切向作用力的极限值 （2）Limited Condition of Acceleration （附着条件） 3
Average Coefficient of Frictionfor Common RoadRoadCondition（路面条件）CD0.7~0.8DryBlacktop（干沥青路面）0.5~0.6WetBlacktop（湿沥青路面）Drygravelroad（干燥的碎石路）0.6~0.7Dryearthroad（干土路）0.5~0.6Wetearthroad（湿土路）0.2~0.40.2~0.3Rollingsnowroad（滚压后的雪路）4Chapter1 AccelerationPerformance
Chapter 1 Acceleration Performance Road Condition(路面条件) φ Dry Blacktop（干沥青路面） 0.7~0.8 Wet Blacktop（湿沥青路面） 0.5~0.6 Dry gravel road（干燥的碎石路） 0.6~0.7 Dry earth road （干土路） 0.5~0.6 Wet earth road （湿土路） 0.2~0.4 Rolling snow road（滚压后的雪路） 0.2~0.3 Average Coefficient of Friction for Common Road 4
Tyre of Formula 1 racing carwettyre雨地胎Intermediatetyre中性胎dry tyre or Slicktyre干地胎5Chapter1AccelerationPerformance
Chapter 1 Acceleration Performance Tyre of Formula 1 racing car wet tyre雨地胎 Intermediate tyre 中性胎 dry tyre or Slick tyre干地胎 5
（3）Traction-limitedAcceleration（驱动附着条件-充分必要条件）: Fx2 = F, - Ff2 ≤ pFz2→ F,≤(f +β)Fz2and f <<Φ.:. F ≤@Fz2 = FQF,+Fw+F≤F≤F16Chapter1AccelerationPerformance
Chapter 1 Acceleration Performance （3）Traction-limited Acceleration (驱动附着条件-充分必要条件) F F F F F f W i t 2 2 2 2 2 ( ) X t f Z t Z t Z F F F F F f F and f F F F 6
Pmax≤0.8,Howcould off-roadvehicle climbfhinking?100%grade？越野车如何爬上100%的坡道？FF =Gsin αxmax =F, = Gβ cos αneed: F,≥Fi=100%即α=45Gocosα≥Gsinαneed :β≥1Chapter1 AccelerationPerformance
Chapter 1 Acceleration Performance sin FXmax Fi G G cos F F i need: G cos G sin need : 1 ≥ o i 100% 45 即 ， How could off-road vehicle climb 100% grade？越野车如何爬上100％的坡道？ max Thinking? 0.8 F 7
2.AdhesionRatio（附着率）(1)Define:Te驱动轮上的道路切向反力K10驱动轮上的道路垂直反力(When front wheel is the driving wheel)FnFy(When rearwheelisthedrivingwheel)2Fz2Note:FX2H≤F= Fz。β= Fz2 β=≤β=C≤βX1Fz2So C.isthe minimum coefficient offriction whichvehicleneededtousedrivingadequately.（附着率是汽车充分发挥驱动力作用时要求的最低附着系数。8Chapter1 AccelerationPerformance
Chapter 1 Acceleration Performance 2. Adhesion Ratio（附着率） （1） Define: Z F F X C 驱动轮上的道路切向反力 驱动轮上的道路垂直反力 X1 1 Z1 F F C （When front wheel is the driving wheel） X2 2 Z2 F F C （When rear wheel is the driving wheel） Note: 2 2 2 2 2 X X Z Z Z F F F F F C F ≤ ≤ ≤ So Cφ is the minimum coefficient of friction which vehicle needed to use driving adequately. (附着率是汽车充分发挥驱 动力作用时要求的最低附着系数。) 8
> front wheel is the driving wheel: if Fx1↓、Fz1T、Co1↓ 'easy to meet the needs of limited condition>good road condition, ua ↓, Ff ↓ ; Fw ↓ ;Fx1 ↓flat road,F ↓; smooth acceleration, F↓ 。slickroad湿滑路面noteasyto meet theneeds ofice and snow roadlimitedconditionwhichroad?sand roadstanding start on ice andbe in high gear and stepsnowroadhighgearorlowgear?accelerator pedal slightlynot easy to meet the needs ofslamaccelerationfromlimitedcondition→whichstandingstart起步急加速working condition?9Chapter1 AccelerationPerformance
Chapter 1 Acceleration Performance front wheel is the driving wheel：if FX1↓、FZ1↑、Cφ1↓ ， easy to meet the needs of limited condition. FX1 ↓ good road condition，ua ↓，Ff ↓ ；Fw ↓ ； flat road，Fi ↓ ； smooth acceleration ，Fj ↓ 。 not easy to meet the needs of limited condition→which road? slick road湿滑路面 ice and snow road sand road standing start on ice and snow road→high gear or low gear? be in high gear and step accelerator pedal slightly not easy to meet the needs of limited condition → which working condition? slam acceleration from standing start起步急加速 9
（2）Fx。（驱动轮上的道路切向反力）When front wheel is the driving wheel:duGFxi =Fx2 +Fw +F +dtgduGFf2+Fw+F+FW2gdt(Fw2 is small)=F2+Fw+F+FWhen rear wheel is the driving wheel:duHx2=Fx +Fw+Fg dtduGFx2=Fr1+Fw+F+F'note :dtg10Chapter1 AccelerationPerformance
Chapter 1 Acceleration Performance （2）FXφ（驱动轮上的道路切向反力 ） When front wheel is the driving wheel： 1 2 2 2 1 2 X X W i f W i jw X f W i j G du F F F F g dt G du F F F F g dt F F F F F When rear wheel is the driving wheel： 2 1 2 1 X X W i X f W i j G du F F F F g dt F F F F F ( is small) Fjw2 : j G du note F g dt 10