Chapter 8 Dynamics of Vehicles Section2 Force Analysis of automobiles 1.The External Forces the Vehicle Bear When Uphill With Acceleration Figure 8-2 The free-body diagram of the automobile when uphill with acceleration G:Gravity of the automobile; a:road grade; Tfl,Tf2:rolling resistance moment acting on the front and rare wheels; Tji,Ti2:inertia resisting moment acting on the front and rare wheels; Tz,T2:normal counterforce of the ground acting on the front and rare wheels; Fx1,F:tangential counterforce of the ground acting on the front and rare wheels; hg:barycentre height of the automobile; hw:height of center of air pressure L:wheel base; a,b:the distances between the automobile barycentre and front and rare wheels; 机械电子工程二 Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles 1. The External Forces the Vehicle Bear When Uphill With Acceleration Figure 8-2 The free-body diagram of the automobile when uphill with acceleration G: Gravity of the automobile; α: road grade; Tf1,Tf2: rolling resistance moment acting on the front and rare wheels; Tji, Tj2: inertia resisting moment acting on the front and rare wheels; Tz1, Tz2: normal counterforce of the ground acting on the front and rare wheels; Fx1, Fx2: tangential counterforce of the ground acting on the front and rare wheels; hg: barycentre height of the automobile; hw: height of center of air pressure ; L: wheel base ; a,b: the distances between the automobile barycentre and front and rare wheels; Section2 Force Analysis of automobiles
Chapter 8 Dynamics of Vehicles Section2 Force Analysis of automobiles d Gcosa(bfr)-Ghg sin a-mhs ∑I-Fh F= L F2= a+列-Gnr+空+7+5人 L Simplified as: (Ghg sin amdi F-G du) b(Ghg sin am di F2=G LL ) Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles F ) dt du (Gh α m L h L b F G F ) dt du (Gh α m L h L b F G L T F h dt du G a f r G h m h F L T F h dt du G b f r G h m h F g w g z g w g z g g i w w z g g i w w z = + + + = − + + + + + + + = − − − − − = sin sin Simplified as cos ( ) sin cos ( ) sin 2 1 2 1 ： Section2 Force Analysis of automobiles
Chapter 8 Dynamics of Vehicles Section2 Force Analysis of automobiles 1.1 Rolling Resistance 20 W(N) 15 (NX) 10 h(mm) B 203040 (a) (b) h(mm) Figure 8-3 Radial deformation Figure 8-4 Resilient wheel rolling on curve of 9.00 to 20 tires the hard pavement 业机械电子工学度 Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles 1.1 Rolling Resistance Figure 8-3 Radial deformation curve of 9.00 to 20 tires Figure 8-4 Resilient wheel rolling on the hard pavement Section2 Force Analysis of automobiles
Chapter 8 Dynamics of Vehicles Section2 Force Analysis of automobiles (a) (b) Figure 8-5 Free-body diagram of driven Figure 8-6 Free-body diagram of wheels rolling on the hard pavement driving wheels rolling on the hard pavement Rolling resistance equal to the product of the rolling resistance coefficient and the wheel load: F,=Wf Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles F Wf f = Rolling resistance equal to the product of the rolling resistance coefficient and the wheel load: Figure 8-5 Free-body diagram of driven wheels rolling on the hard pavement Figure 8-6 Free-body diagram of driving wheels rolling on the hard pavement Section2 Force Analysis of automobiles
Chapter 8 Dynamics of Vehicles Section2 Force Analysis of automobiles 1.2 Air Resistance It is the component force of the applied air force in the driving direction when the vehicles travel straightly. F.-CoAp C--Coefficien t of air resistance: p--Air density; A--Frontal area; u,--Relative speed. 1.3 Acceleration Resistance F=oin du --Auto rotating mass conversion coefficien t m--Mass of vehicle du dt _-Accelerati on; Empirical estimation value of 8=1+8+6g In the formula:d≈6，=0.03~0.05， i-Transmissi on ratio 械电子工程学 Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles 1.2 Air Resistance It is the component force of the applied air force in the driving direction when the vehicles travel straightly. u Relative speed. A Frontal area; Air density ; Coefficien t of air resistance 2 1 r 2 − − − − − − − − = D ； w D r C F C A u 1.3 Acceleration Resistance In the formula 0.03 ~ 0.05 Transmissi on ratio . 1 Empirical estimation value of m Mass of vehicle Accelerati on Auto rotating mass conversion coefficien t 1 2 2 1 2 ： ， —— ： ； ； g g j i i dt du dt du F m = = + + − − − − − − = Section2 Force Analysis of automobiles