《汽车理论》课程教学课件（英文讲稿）第4章 汽车制动性 Braking Performance 4.2 Braking Mechanics（制动时车轮的受力）

4.2 Braking Mechanics1.Ground Braking ForceuaMT,uF0XbrFpFXbFZ

a u FP FZ FXb T W Xb  T F r   1 . Ground Braking Force 4.2 Braking Mechanics 1

1.Ground Braking ForceF小Ground Braking ForceFxb (frictional coupling betweenthe tire and road)> Definition: It is the braking force acting on the tires fromground along the X-direction.Z1WLXbrFpNote:1) Compared with the greatly increasing T,other torques are little enough to be ignoredwhen brakes work.2) T, is the braking torque from brakes2

 Ground Braking Force—— FXb (frictional coupling between the tire and road)  Definition: It is the braking force acting on the tires from ground along the X-direction. Xb T F r   1. Ground Braking Force—Fxb Note: 1) Compared with the greatly increasing Tμ , other torques are little enough to be ignored when brakes work. 2) Tμ is the braking torque from brakes. 2

2.BrakesBraking ForceF.> Brakes Braking Force-Fu(frictional coupling between theshoes and drum)> Definition: It is the braking force arising from the torque of thebrakes. acting on the edge of tire along the X-directionZFWurNote :1) F. is the test result on the test-bed2) F, has nothing to do with road condition.3

 Brakes Braking Force——Fμ (frictional coupling between the shoes and drum)  Definition: It is the braking force arising from the torque of the brakes, acting on the edge of tire along the X-direction. 2. Brakes Braking Force—Fμ Note : 1) Fμ is the test result on the test-bed. 2) Fμ has nothing to do with road condition. r T F    3

3.The relationship Between Fxb, F, and F0FLCFFxb=FPedal Force-Fp, NFxb ≤F,= Fz -0Pedal Force-F,, NLFxb = FlXxbmax = Fz βFis the limited force applied on the tires bythe ground foranti-skidpurpose.>Fxb can only increase to the limit of the frictional couplingbetween the tire and road

- Pedal Force FP，N F F F F Xb   F F Xb   C Pedal Force-FP，N 3.The relationship Between FXb, Fμ and Fφ Fφ is the limited force applied on the tires by the ground for anti-skid purpose. FXb can only increase to the limit of the frictional coupling between the tire and road. max Xb Z Xb Z F F F F F         F 4

4. Slip of Tire(1)Definition> Slip of tireis defined by the ratio of slip velocity in the contactpath(forwardspeedminus(减去）tirecircumferential speed)to forward speed :usu...0roMSE0WuWwWWN00roV10小0usrolling : uw = Owro = s = 0Orolling & slipping : uw>Ow'rroslipping : w =0= s =100%(full locking)5

（1） Definition  Slip of tire is defined by the ratio of slip velocity in the contact path (forward speed minus(减去) tire circumferential speed) to forward speed : 0 0 = w w r w w w r w r w u u r s u u r r u         0 0 : 0 & : : 0 100%( ) w w r w w r w rolling u r s rolling slipping u r slipping s full locking            ＞ 4. Slip of Tire 5

rolling,s = 0rolling & slipping0<s<1slipping, s =100%( full locking)Different slip ratioand tire trace

Different slip ratio and tire trace , 100% ( ) slipping s full locking & , 0 rolling slipping ＜s＜1 rolling s, 0  6

(2)TheRelationshipBetweenBrakingCoefficient（，制动力系数）andSlipRatioNote: Surface Coefficient changes with the change of Wheel Slip> Surface Coefficient reaches its maximum value-Pp at 15%~20% s.（PeakCoefficient峰值附着系数）> Surface Coefficient reaches its minimum value-P, at 100% s.（SlideCoefficient滑动附着系数）> Conclusions: 1)pp corresponds to the highest brake force that can beobtained from the particular tire-road friction pair.2)p is only theoretically possible to achieve because it is unstable at thispoint. Only a brake release (as in an anti-lock control) can return thewheel to operation at Pp1.09pX-Coordinate0.8nX-Coordinates0.6SurfaceCoefficientversus SlipRatio0.4Pb ~S0.2010040608020SlipRatios(%)

(2)The Relationship Between Braking Coefficient (φb ,制动力系数) and Slip Ratio Note: Surface Coefficient changes with the change of Wheel Slip.  Surface Coefficient reaches its maximum value—φP at 15%~20% s. (Peak Coefficient峰值附着系数)  Surface Coefficient reaches its minimum value—φs at 100% s. (Slide Coefficient滑动附着系数)  Conclusions: 1)φP corresponds to the highest brake force that can be obtained from the particular tire-road friction pair. 2) φP is only theoretically possible to achieve because it is unstable at this point. Only a brake release (as in an anti-lock control) can return the wheel to operation at φP . X-Coordinate Surface Coefficient versus Slip Ratio φb ~s 7

(3)TheRelationshipBetweenCoefficientofLateralForce（o，侧向力系数）andSlipRatiosP, =Pss = 100% =easilydriftingtoside9=0Where : Pb— Braking Coefficient or X-coordinate Surface CoefficientPr Side Friction Force Coefficient or Y-coordinate Surface Coefficient1.0PpBX-Coordinate0.8Fabo0.6Coefficient of LateralForceversus Slip0.4RatioP0.2Pi ~s110806020401008Slip Ratio s(%)

(3)The Relationship Between Coefficient of Lateral Force (φl ,侧向力系数) and Slip Ratio easily drifting to side Where : φb— Braking Coefficient or X-coordinate Surface Coefficient φl —Side Friction Force Coefficient or Y-coordinate Surface Coefficient b s 100% 0 l l s s                 Coefficient of Lateral Force versus Slip Ratio φl ~s 8

1.21.0Pp6F一X-Coordinate0.8XbA-0Pr =Pb9FzFo0.60.4Pp= PbmaxP0.2Ps = Pb(S=100%)L11060804010020Slip Ratio s(%)P ~S、P ~SC

  b l ~ ~ s、 s   S  b(S 100%)  Xb b Z F F   Y l Z F F     P b  max 9

各种路面平均附着系数路面pps0.75沥青或混凝土（干）0.8~0. 9沥青 (湿)0.5~0.70.45~0.60. 80. 7混凝土（湿）砾石0. 60. 55土路 (干)0. 680. 65土路 (湿)0.550.4~0.5雪 (压实)0. 20. 15冰0. 10. 0710

各种路面平均附着系数 10 路面 φ p φ S 沥青或混凝土（干） 0.8～0.9 0.75 沥青（湿） 0.5～0.7 0.45～0.6 混凝土（湿） 0.8 0.7 砾石 0.6 0.55 土路（干） 0.68 0.65 土路（湿） 0.55 0.4～0.5 雪（压实） 0.2 0.15 冰 0.1 0.07