4-5BrakingProportioningBalancing the brake outputs on both the front and rear axlesis achieved by“proportioning"the pressure appropriatelyforthe foundation brakes installed on the vehicle.It is well recognized that the preferred design is to bringboth axles up to the lockup point simultaneously.1.Vertical forces given by the ground when vehicle brakes-FziandFz2GFw(ignored)F(b+zh.)2g2duGF-zh.zgZ2OLdt6FxblaXb2FwhereZBrakingIntensityZ2F7
4-5 Braking Proportioning • Balancing the brake outputs on both the front and rear axles is achieved by “proportioning” the pressure appropriately for the foundation brakes installed on the vehicle. • It is well recognized that the preferred design is to bring both axles up to the lockup point simultaneously. 1 2 ( ) ( ) Z g Z g G F b zh L G F a zh L 1.Vertical forces given by the ground when vehicle brakes ——FZ1 and FZ2 FZ1 FZ2 FXb1 FX 2b G hg F ignored W ( ) Fj L a b du zg dt where z— Braking Intensity 1
Vertical forces given by the ground when vehicle brakesFziandFz2FFw(ignored)h60GFbFXb2aXb1F12LFZ12
FZ1 FZ2 FXb1 FX 2b G g h F ignored W ( ) Fj L a b Vertical forces given by the ground when vehicle brakes ——FZ1 and FZ2 2
1.Vertical forces given by the ground when vehicle brakes-Fziand Fz2if front lockup and rear lockup occur at the sametime or oneafteranother:GFw(ignored)FFboh.+ZPduLpg三dtphOTFxb2hFxblaFZ2F7
1 2 ( ) ( ) Z g Z g G F b h du L g dt G F a h L 1.Vertical forces given by the ground when vehicle brakes ——FZ1 and FZ2 if front lockup and rear lockup occur at the same time or one after another： FZ1 FZ2 FXb1 FX 2b G hg F ignored W ( ) Fj L a b 3
正常制动一条制动管路失效
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e"l"curve2.Idealproportioningcurve-Definition: A special curve which present therelationship between front and rear brakes brakingforce determined by the pressure applied to eachbrake and the gain of when front and rear lockupsoccurtogether"I"curveFu2欧5
2. Ideal proportioning curve——”I” curve Definition: A special curve which present the relationship between front and rear brakes braking force determined by the pressure applied to each brake and the gain of when front and rear lockups occur together. F1 F 2 " "I curve 5
How to get the "I"' curve?If front and rear brakeslockups together bothFuand Fμ2 could meet thedemands of these eguationsF+Fu2 = GplFu +F.Fu2 = GpFui = FziCb+phFZ1Fμ2 = Fz29Fa-phZ2substitution4h.LmgbmgFF+2Fu2ulul2Gh606
1 2 1 1 2 2 Z g Z g F F G F F b h F F a h How to get the “I” curve? If front and rear brakes lockups together bothFμ1 and Fμ2 could meet the demands of these equations. 2 2 1 1 1 4 2 2 g g g mg mgb h L F b F F h G h 1 2 1 1 2 2 Z Z F F G F F F F substitution φ 6
(1)Fun + Fu2 = GpLb+ph(2)Ha-ph.u2Steps:1.From the first equation-(1)we can get a group of lines which andthe same slope of 45 degree, each line presents the differentfriction coefficient.2.From the second equation-(2)we can get a group of lines startingat the origin and extending upward and to the right, each linepresents the different friction coefficient.3.Finding out the cross points of the first group lines and the secondgroup lines with the same coefficient.4.Connecting the cross points mentioned above all together, we canget the ideal "l" curve.NDifferent point of the curve has its own friction coefficient andthecorrespondingEuandFu2:7
Steps: 1.From the first equation—(1)we can get a group of lines which and the same slope of 45 degree, each line presents the different friction coefficient. 2.From the second equation—(2)we can get a group of lines starting at the origin and extending upward and to the right, each line presents the different friction coefficient. 3.Finding out the cross points of the first group lines and the second group lines with the same coefficient. 4.Connecting the cross points mentioned above all together, we can get the ideal ”I” curve. Different point of the curve has its own friction coefficient and the corresponding Fμ1and Fμ2 . 1 2 1 2 (1) (2) g g F F G F b h F a h 7
0.3F+F=GΦu2ul0.4F0.5F2b+phμl0.6Fa-ph0.7u2@=0.8curve叉=0.87Q0.60.3Q50Y40.2F1g1
＝0.8 ＝0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.7 0.6 0.3 0.4 0.5 0.2 0.1 " " I curve F1 F 2 1 2 1 2 g g F F G F b h F a h 8
3.RealproportioninglineβGenerally the traditional vehicle has a fixed.constant, and straight proportioning line.FFulμulFF+Fuuu1Fβulwhere βbraking proportioning coefficient（制动分配系数）
2 1 1 1 F F 3. Real proportioning line——β Generally the traditional vehicle has a fixed, constant, and straight proportioning line. where β—— braking proportioning coefficient （制动分配系数） 1 1 1 2 F F F F F 9
4.Synchro-adhesion coefficientPo（同步附着系数）Definition : The friction coefficient of the cross pointbetween“I"curve and“β"”line.How to get o?(1) Method OneGraph Method(2) Method TwoAnalytic ApproachFb+ohgul: for"I "Fa-Pohg42Fβfor"β"F1-β112b+PohgβLβ-b 1-βMoa-Pohg10
Definition : The friction coefficient of the cross point between “I” curve and “β” line. 4. Synchro-adhesion coefficient—— φ0 （同步附着系数） How to get φ0 ? （1）Method One ——Graph Method （2）Method Two——Analytic Approach 1 0 2 0 " " g g F b h for I F a h 1 2 " " 1 F for F 0 0 0 1 g g g b h L b a h h 10