Chapter 8 Dynamics of Vehicles Sectionl Traveling Principle Overall dynamics of vehicles discuss all the forces vehicles beard and the transfer and balance laws of them. The driving equation is:FF (7-) F--driving force, Fall the driving resistance 1.Driving Force The driving force of vehicles: T--Torque acting on the driving wheels (N.m), r--Wheel radius (m) Figure 8-1 The driving force of vehicles 机械与电子工程学原 Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles Overall dynamics of vehicles discuss all the forces vehicles beard and the transfer and balance laws of them. The driving equation is: 1. Driving Force The driving force of vehicles: （ ） （ ） Wheel radius m Torque acting on the driving wheels N m , − − − − • = r T r T F t t t driving force, all the driving resistance (7 1) − − − − = − F F F F t t Section1 Traveling Principle Figure 8-1 The driving force of vehicles
Chapter 8 Dynamics of Vehicles Sectionl Traveling Principle Since the torque T:acting on the wheels is produced by the engine and transmitted to the wheels through the driven system,therefore: T:=Tigigion T--Engine torque ig--Transmissi on ratio; io--Final drive ratio; --Mechanical efficiency of transmiss ion. The above equation should be included corresponding gear ratio and mechanical efficiency for vehicles with devices such as transfer case,wheel reduction and dydraudynamic drive unit,thus the driving force is: Ta●ig●i●n 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 Since the torque Tt acting on the wheels is produced by the engine and transmitted to the wheels through the driven system, therefore: Final drive ratio Mechanical efficiency of transmiss ion . Engine torque Transmissi on ratio 0 0 − − − − − − − − = • • • T t q g t t q g T i T i T T i i ； ； ； The above equation should be included corresponding gear ratio and mechanical efficiency for vehicles with devices such as transfer case, wheel reduction and dydraudynamic drive unit, thus the driving force is: r T i i F t q g T t • • • = 0 Section1 Traveling Principle
Chapter 8 Dynamics of Vehicles Sectionl Traveling Principle Two requirements of generation driving force: (1)Engine torque is transmitted to the driving wheels as the driving moment after changing the magnitude and direction by the transmission,and then it provides the applied force along the tangential directions of the tires,which is the internal conditions of generating the driving force. (2)Depending on the interaction between the ground and driving wheels,the applied force that the driving wheels act on the ground is changed to the ground reacting force along the tangential directions of the tires,which is the external conditions of generating the driving force. 机被电子工程学聚 Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles Two requirements of generation driving force: (1) Engine torque is transmitted to the driving wheels as the driving moment after changing the magnitude and direction by the transmission, and then it provides the applied force along the tangential directions of the tires, which is the internal conditions of generating the driving force. (2) Depending on the interaction between the ground and driving wheels, the applied force that the driving wheels act on the ground is changed to the ground reacting force along the tangential directions of the tires, which is the external conditions of generating the driving force. Section1 Traveling Principle
Chapter 8 Dynamics of Vehicles Sectionl Traveling Principle 2.Driving Resistance The total driving resistance is ∑F=F+Fn+E+E, (7-5) F--Rolling resistance; F。--Air resistance; F--Slope resistance F--Accelerating resistance. By(7-1)and(7-5): F=F-E+E+) 械电子工程学度 Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles 2. Driving Resistance The total driving resistance is : 。 ； ； ； Accelerati ng resistance Slope resistance Air resistance Rolling resistance (7 5) − − − − − − − − = + + + − j i w f f w i j F F F F F F F F F By (7-1) and (7-5): ( ) Fj = Ft − Ff + Fw + Fi Section1 Traveling Principle
Chapter 8 Dynamics of Vehicles Sectionl Traveling Principle 3.The Driving and Adhesion Conditions of Vehicle Traveling 3.1 Driving Conditions The first condition of the vehicle traveling: ,≥Fr+Fw+F 3.2 Adhesion Conditions The second condition of the vehicle traveling E≤F。=Fop --Coefficien t of adhesion F--Weight beard by driving wheels; The driving and adhesion conditions of the vehicle traveling (necessary and sufficient conditions) F+Fn+F≤F≤Fo·p Automobile and Tractor Northwest A&F University
Automobile and Tractor Northwest A&F University Chapter 8 Dynamics of Vehicles 3 . The Driving and Adhesion Conditions of Vehicle Traveling 3.1 Driving Conditions The first condition of the vehicle traveling: 3.2 Adhesion Conditions The second condition of the vehicle traveling: The driving and adhesion conditions of the vehicle traveling: (necessary and sufficient conditions) —— ； —— ； Weight beard by driving wheels Coefficien t of adhesion z t z F F F = F • Ft Ff + Fw + Fi Ff + Fw + Fi Ft Fz • Section1 Traveling Principle
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