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