1. 《 Elementary Vehicle Dynamics 》 （《汽车理论》）

2. Preface What can we learn from this course? The six fundamental performances of vehicle( 六项基本性能 ) Acceleration Performance( 动力性） Economical Performance （经济性） Braking Performance （制动性） Passing Ability （通过性） Handling Performance( 操 纵稳定性 ) — Connering&Rollover Ride Performance( 行驶平 顺性）

3. What ’ s the aim of this course To find out the reasonable method to design and use vehicle according to the relationship among the parameters of structure and performance of vehicle. （通过车辆结构参数与性能之间的关系， 找到正确设计汽车的方法和合理使用汽 车的途径）

4. Development of Automobile 1886,Daimler (invent carburetor) & Benz ( invent two- stroke engine). In 30~40 ’ s of the 19th century —— Acceleration Performance In 60~70 ’ s of the 19th century —— Economical Performance (Because of Petroleum Crisis ) In 80~90 ’ s of the 19th century —— Handling Performance 、 Ride Performance (Because of development of the electronic technology ) Economize resources 、 Environmental protection 、 Safety —— Forever Subject of Development

5. 汽车的发展 1886,Daimler & Benz, 前者发明了化油器， 后者发明了二冲程三轮车。 第一、二次世界大战，以动力性，可驾 驶性为主。 60-70 年代，石油危机，经济性 80-90 年代，计算机技术发展，操纵稳定 性，平顺性。 节能、排放、安全是永恒的发展主题。

6. Chapter 1 Acceleration Performance §1.1 Evaluation Index （评价指标） 1.Maximum Vehicle Speed (Velocity) 最高车速 —— (km/h): （ 1 ） Definition ： The maximum speed which the vehicle can get under good and flat road with rated load （额定载荷 ). （ 2 ） Actual Measurement of ： ( 实验方法 )

7. 2. Acceleration Ability （加速能力） （ 1 ） The acceleration ability for starting( 原地起步加 速能力 ) Test Condition ( 实验条件 ) : Full engine power （节气门全开） ; Optimal shift point between gears （最佳换档时机） which are from low gear （第Ⅰ档） for start-up to high gear （最 高档） for fuel economy. Evaluation Index — T T is the time needed by the vehicle to accelerate from 0 to 80%Uamax under the above test condition or the time needed to pass through a fixed distance （ 400 m or ¼ mile(402.5m) ）. （用Ⅰ档起步，按最佳换档时间，逐次换至高档，节气门全开，以最大加速度行驶，全力 加速至 80%Uamax 所需时间，或通过某一预定距离所需时间）

8. 2. Acceleration Ability （加速能力） （ 2 ） The acceleration ability for high speed driving ( 超车加速能力 ) Test condition: Full engine power ; High gear （最高档） or inferior high gear （次高档） Evaluation index——T T is the time need to accelerate from the minimum stable speed of high gear ( 最高档的最小稳定车速） to 80%Uamax or the time needed to pass through a fixed distance （ 400 m or ¼ mile ）. ( 在直接档 ( 在很多车辆中是最高档 ) 工作时，节气门全开，由该档的最小稳定车速全力加速 至 80%Uamax 所需时间，或通过某一预定距离所需的时间）

9. 3. Maximum Gradeability of Vehicle —— i max （最大爬坡度） （ 1 ） Definition ： The maximum grade which the vehicle can climb in the first gear （Ⅰ档） under good road condition with fully rated load （额定满载）. i=tanα EQ140 i max =28% EQ240 i max =58% α=30° （ 2 ） Actual Measurement of i max

10. §1.2 Driving Mechanics of Vehicle To analyze the balance between Total Road Load force （行驶阻力） and Tractive Force （驱动力） along one degree of freedom （自由度） that is longitudinal direction （纵向）. 1. Tractive Force （驱动力） — Torque of Engine Flying Wheel ( 发动机转矩 ) — Numerical Ratio of the Transmission ( 变速器传动比 ) — Numerical Ratio of the Final drive ( 主减速比 ) — Total efficiency of driveline ( 传动系机械效率 ) — Torque of Driving Wheel ( 驱动轮转矩 )

11. (1)Torque of Engine Engine maybe characterized by its torque and power curve as a function of rotate speed. Figure 1. shows typical curves for gasoline engine. Figure 1. Performance characteristics （外特性曲线） of gasoline

12. Full performance and Full performance with all the accessories ( 外特性与使用外特性 )

13. Useful formulas for Power calculation Unit: 发动机功率 P e [kW] ； 发动机转矩 T tq [Nm] ； 发动机转速 n[r/min] Clew : ， Unit ： P e [W] ； T tq [N·m] ； n[m/s], Unit ： P e [kW] ； T tq [N·m] ； n[r/min] 。

14. （ 2 ） Efficiencies of Driveline The necessity of the introduction of : The inefficiencies due to mechanical and viscous losses in the driveline components （ transmission; driveshaft; final drive; differential and axles ） have not been taken into account. These act to reduce the engine torque in proportion to the products of the efficiencies of the individual components. （ combined efficiency of driveline ） consists of four primary parts: 离合器 变速箱 传动轴 驱动桥 Generally, equal to 0.9~0.92 for a car; equal to 0.82~0.85 for a truck or a bus;

15. （ 3 ） Tire Radius Definition: Nominal Radius （自由半径）： the radius of tire without load (spare tire 备胎 radius). Static Loaded Radius （静力半径） — ： the distance from the center of static tire to the contact point with ground under vertical load only. Rolling Radius （滚动半径） — ： the radius which is measured by S (distance passed by vehicle ） and n (rolling numbers). r——tire radius, 统称车轮半径

16. （ 4 ） Graph of Tractive Force （驱动力图） How to make tractive force-vehicle speed characteristics graph ： 1 ） Mathematical conversion between n (engine revolution speed [r/min]) and (vehicle speed [km/h])

17. 2 ） Make the graph Two basic formulas for making the graph: Make the tractive force line of each gear （ given ） of the vehicle （ given & given r and given ）：

18. Make all the curves of the vehicle figure1.2: Figure 1.2 Tractive force-speed characteristics for a manual transmission

19. 3) Conclutions from the graph of tractive force: “ Constant Engine Power ” is equal to the maximum power of the engine; which is the upper limit of tractive force available, less any losses in the driveline.( 发动机最大动力线是可获得的驱动力的极限 ) The curves illustrate visually the need to provide a number of gear ratios for operation of the vehicle ( low gearing for start-up, and high gearing for high-speed driving).( 驱动力图表明汽车需要变速器来提 供不同传动比 ) For maximum acceleration performance the optimum shift point between gears is the point where the line cross.( 最佳的换档时刻在各 档驱动力线的交点处 ) The area between the lines for the different gears and the constant power curve is indicative of the deficiencies of the transmission in providing maximum acceleration performance.( 发动机最大动力线和 各档驱动力线的区域表明变速器各档提供的最大加速能力未能充 分利用发动机的最大动力 )

20. 2. Road Load force （行驶阻力） （ 1 ） Rolling Resistance Force —— （滚动阻力） Energy losses: Due to the deflection of tires: Due to the deflection of road surface: converted into the heat within the tires caused by the friction of rubber particles Rolling resistance torque — （滚动阻力偶矩）

21. The mechanics analysis of driven wheel with constant revolution assume — Rolling Resistant Force of driven wheel （从动轮的滚动阻力） ∴ assume a/r = f （ — Coefficient of rolling resistant ） 滚动阻力系数 ∴ conclusion: under given conditions( stiff road; constant vehicle speed)

22. The mechanics analysis of driving wheel with constant revolution total rolling resistance— : assumed : —driving force —rolling resistance force of driving wheel ∴

23. Note: 1. Rolling resistance force is present from the instant the wheels begin to turn.( 只要车轮滚动，滚动阻力就存在 ) 2. Rolling resistance force is the primary motion resistance force. ( 滚动阻力是主要的运动阻力 ) 3. For off-high way, level ground operation, the rolling resistance force is the only significant retardation force. ( 在平直路面，车速较低工况，滚动阻力几乎是唯一的 阻力 ) 4.usually is equal to 0.012. (note ： influenced factor ： vehicle speed ， type and model of tyre 、 steering of vehicle)

24. （ 2 ） Aerodynamic Drag( 空气阻力 ) Aerodynamic Drag ( 空气阻力 ) Pressure Drag( 压力 阻力 )91% Form Drag- Form Drag- 形状阻 力 58% Total Protuberance Drag- 干扰阻力 14% Total Internal Drag- Total Internal Drag- 内循环阻力 12% Induced Drag- Induced Drag- 诱导 阻力 7% Vicious Friction( 摩 擦阻力 )9% Aerodynamic forces interact with the vehicle causing drag ， lift （ or down load ）， lateral forces ， and their individual moments. The Aerodynamic forces produced on a vehicle arise from two sources ： next

25. Note 1)Total Internal Drag comprises of air flow management of cooling system and inside ventilation of the body. With no attention to the need for air flow management, the air entering through the radiator dissipates much of its forward momentum against the vehicle components in the engine compartment before spilling out through the underside openings. The momentum exchange translates directly into increased drag. （发动机冷却系、车身通风等所需空气流经车体内部时的阻 力称为内循环阻力。其主要部分是空气在散出到车身下部 之前流经发动机舱的水箱散热器消散了较多的动量造成的， 这些动量的交换直接导致了阻力的增加。） Return

26. 2 ） Bernoulli ‘ s Equation ： P - 大气压； ρ- 空气密度； C- 常数 Zero underbody air speed produces the pressure difference Lift Force unsmoothed underbody panel Induced Friction （ the projection of lift force along the longitudinal direction ） （ minimizing underbody drag is the use of a smooth underbody panel ） Return 伯努利方程 车身底板几乎为零的空气流动速 度产生压力差 升力 诱导阻力 升力在水平方向的投影，采用光滑的车身底板可大大降低该阻力 3 ） For minimizing Form Drag we adopt the body of streamlined shape ( 流线形） which is usually be described as drop-like （雨滴状） body.

27. Semi-empirical models ： Where: Aerodynamic drag coefficient （空气阻力系数） Frontal area of the vehicle （迎风面积） Air density （空气密度） Relative Velocity （相对速度） International C D : China C D Cars 0.25~0.35 Cars 0.3~0.4 Vans 0.33~0.35 Vans 0.5~0.6 Pickup trucks 0.42~0.46 Pickup trucks 0.5~0.6 Because of u a [km/h] ； u r [m/s] ； u r =u a /3.6 [m/s] (no wind) So Calculation of Aerodynamic Forces ——F W

28. （ 3 ） Uphill Grade Resistance Force — F i （坡道阻力） Define: — Road Resistance （道路阻力） Define: Road Resistance Coefficient （道路阻力系数）

29. （ 4 ） Acceleration Resistance——F j 1.Translational mass inertial force —— F j1 （平移质量惯性 力） G/g —— mass, 质量 [kg] du/dt —— translational acceleration, 行驶加速度 [m/s 2 ] 2.Rotational mass inertial force (moment) —— （ F j2 ; T j ） （回转质量惯性力 / 力矩） (rotating components comprise of fly wheel, gear system, shafts&axles, wheels) I —— moment of inertia, 转动惯量 [kg · m 2 ] dω/dt —— angular acceleration, 角加速度 [1/s]

30. Rotational mass inertial force (moment) 1) Inertial moment for fly wheel ω e —— angular velocity of fly wheel( 飞轮旋转角速度 ) ω w —— angular velocity of wheel( 车轮旋转角速度 ) u—— vehicle speed r—— radius of wheel I f —— moment of inertia for fly wheel Deliver T f to driving wheel —— T fw 2) Total inertial moment for wheel and rotational mass inertial force ——∑T j ； F j2 飞轮的惯性力矩 车轮的惯性力矩和旋转质量惯性力 I w —— moment of inertia for wheel

31. 3. Total Inertial Force ——F j Assumed : δ —— rotational mass coefficient （回转质量换算系数） So

32. 3.Driving Equation （汽车行驶方程式） 1)General model of driven wheel: (acceleration) 2) General model of driving wheel: (acceleration)

33. 3 ） General model of vehicle: (acceleration and uphill) Note: ⒈ F jw2 comprises of two parts :1 ） the rotational mass inertial force of fly wheel that is delivered into the driving wheel; 2 ） the rotational mass inertial force of the driving wheel itself. ⒉ For general model of the vehicle, F p and F t are considered as internal forces, so there is no F p and F t on the graph. ⒊ F t and F f are the result of assumption, so there is neither F t and F f on the graph. Return

34. §1.3 Traction-Limited Acceleration and Adhesion Ratio （ 1 ） Driving Condition of Acceleration （驱动条件） When Level road : Constant speed: Level road & Constant speed: For constant speed: （匀速） acceleration: （加速） deceleration: （减速） So Driving Condition is 汽车行驶的驱动附着条件和附着率 1. Traction-Limited Acceleration

35. （ 2 ） Limited Condition of Acceleration （附着条件） Presuming there is adequate power from the engine, the acceleration may be limited by the friction that is between the tire and road for anti-skid purpose. In this case is ： （限制车轮打滑的极限力） Where: Coefficient of friction （道路附着系数） Weight on driving wheels （驱动轮上道路垂直反力） usually ranges from 0.7-0.8 （ 3 ） Traction-limited Acceleration （驱动附着条件） 地面对轮胎切向作用力的极限值

36. 2. Adhesion Ratio （ 1 ） Define: （ When front wheel is the driving wheel ） （ When rear wheel is the driving wheel ） Note: So is the minimum coefficient of friction which vehicle needed to use driving adequately. ( 附着率是汽车充分发挥驱动力作用时要求的最低附着系数。 ) （ 2 ） （驱动轮上的道路切向反力 ） When front wheel is the driving wheel ： When rear wheel is the driving wheel ： ( is small)

37. Note: is the coefficient of lift force for front; is the coefficient of lift force for rear. （ 3 ） （驱动轮上的道路垂直反力 ） A. static part: B. dynamic part: Note: Ignore Rotational mass inertial moment C. lift force: D. the part produced by rolling resistance torque : this part is very small and is ignored.

38. （ 4 ） analysis A. Acceleration and uphill (front wheel drive cars): measure : Note: q is the equivalent grade( 等效坡度 ) ； ， so the which vehicle needed is big and the front driving wheel is easy to skid. B. high speed (rear wheel drive cars): speedstate small0.28smallno skidding 250km/h0.280.57just meet the need 300km/h0.280.99 don ’ t meet the need

39. （ 4 ） Traction Limits (maximum tractive force) — （最大牵引力） Clew : Independent front drive axle → (maximum tractive force for front drive axle) Independent rear drive axle → (maximum tractive force for rear drive axle) 1 ） by(equilibrium of static equilibrium)( 求矩 ) 2 ） when: graph

40. For rear drive axle(rear-wheel-drive cars) : Also in the case of front drive axle(front-wheel-drive cars): In the case of four-wheel-drive cars:

41. 5 ） percentage of utilization of maximum tractive force—— （附着利用率） Definition: （ 汽车附着力 / 全轮驱动汽车附着力 = 附着利用率） Where: Maximum tractive force of front-wheel-drive cars Maximum tractive force of rear-wheel-drive cars Maximum tractive force of four-wheel-drive cars For front-wheel-drive cars: rear-wheel-drive cars: four-wheel-drive cars:

42. Graph of ： Note: increase leads to decrease in the case of front-wheel-drive ; is the percentage of utilization of cars’ weight on the drive axle ； Forward longitudinal weight transfer → and increase in the case of front-wheel-drive car ； （质心偏移） For cars the load on the front (drive) axle is usually higher than the load on the rear axle ； （前部轴荷＞后部轴荷）

43. §1.4 Tractive Force & Driving Resistance—Speed Characteristics （驱动力 - 行驶阻力平衡图） From Driving Equation: when level road & constant speed To (Driving Resistance comprises of and ) Analyze : Acceleration Performance of the vehicle through Tractive Force & Driving Resistance-Speed Characteristics ： （ 1 ） Maximum Vehicle Speed (Velocity)—— (km/h): So is the corresponding x-coordinate of the cross point of the driving resistance curve and the tractive force curve of the fourth (high-speed) gear.

44. （ 2 ） Maximum Gradeability of Vehicle —— — The maximum uphill grade resistance force which the vehicle could overcome — F i （坡度阻力） （ 3 ） Acceleration Ability Estimate ： T he acceleration ability of the vehicle at any speed——( u a1 ). the tractive force which the vehicle need to drive with constant speed (u a1 ). the maximum tractive force which could be used to accelerate at this speed (u a1 ) Conclusion: The acceleration ability changes with the change of gear. Higher gear leads to lower acceleration ability. Changing the position of pedal make the constant speed drive possible because the tractive force-speed curve would move up and down vertically with the change of injection system. (the force-speed curves shown above is the upper limit ones of the vehicle)

45. 1.AimAim 2.How to get D （动力因数） ?How to get D 3.Dynamic Characteristic Graph （动力特性图）Dynamic Characteristic Graph 4.Analyze the evaluation Index of dynamic performance with Dynamic Characteristic Graph （ 1 ） Maximum Vehicle Speed (Velocity) Maximum Vehicle Speed (Velocity) （ 2 ） Maximum Gradeability of VehicleMaximum Gradeability of Vehicle （ 3 ） Acceleration ability Acceleration ability Note §1.5 Dynamic Character of Vehicle （汽车的动力特性）

46. 1. Aim In order to make the analysis of dynamic performance simpler,we use another group of characteristic curves which comprise the Dynamic Characteristic Graph （动力特性图） of the vehicle. B ） We can compare the dynamic performance of different vehicle which mass is not equal with Dynamic Characteristic Graph. A ） Tractive Force & Driving Resistance—Speed Characteristics （驱动力 - 行驶阻力平衡图） is not simple to analyze and.驱动力 - 行驶阻力平衡图

47. 2. How to get D （动力因数） ? Method: The right side of the equation concerns the grade ability and acceleration ability only, it has nothing to do with the mass of the vehicle—G/g. Definition: So: where: D——dynamic factor （动力因数） —— road resistance coefficient （道路阻力系数）

48. when : constant speed → du/dt=0 level road → α=0 Note : so D=fD=f where f=0.012 under the most situation f≈0.02 when ua>50 km/h ua↑ f↑↑ （ show in the figure ） 3. Dynamic Characteristic Graph （动力特性图）

49. 4. Analyze the evaluation Index of acceleration performance with Dynamic Characteristic Graph （ 1 ） Maximum Vehicle Speed (Velocity)—— (km/h): is the corresponding x-coordinate of the cross point of f curve and D curve of the fourth (high-speed) gear.

50. （ 2 ） Maximum Gradeability of Vehicle —— So when climbing the soft grade ( 坡度小 ) because cosα=1, sinα≈tgα≈i, D=ψ=f+i when climbing the big grade （坡度大） because

51. （ 3 ） Acceleration ability driving on the level road So How to calculate T which is the evaluation index of acceleration ability ?

52. Note A.We can compare the different vehicle which mass is not equal with Dynamic Characteristic Graph （动力特性图）. B.Dynamic Characteristic Graph is convenient for analyzing and. C.Analyzing methods is similar to the methods with Tractive Force & Driving Resistance — Speed Characteristics( 驱动力 - 行驶阻力平 衡图）.

53. §1.6 Power Equilibrium 1.Equation of Power Equilibrium ： 2. How to make the Graph of Power Equilibrium: because : ( 功率平衡图） ab—reserve supply of power( 后备功率 )

54. (3). ------The maximum difference between the resistance power curve from the full power curve of the first ( Ⅰ -speed) gear. 3. Analyze the evaluation Index of acceleration performance with Power Equilibrium Graph (1). is the corresponding x-coordinate of the cross point of the resistance power curve and the full power curve of the fourth (high-speed) gear. (2). The reverse supply of power changes with the change of gear.------ Higher gear leads to lower reverse supply of power and acceleration ability.