?Elementary Vehicle Dynamics ?汽车理论?PrefaceWhat can we learn from this course?The six fundamental performances of vehicleAcceleration Performance(动力性）动力性）Economical Performance （经济性）（经济性）Braking Performance（制动性）（制动性）Passing Ability（通过性）（通过性）Handling Performance(操纵稳定性操纵稳定性)Connering&Rollover Ride Performance(行驶平顺性）行驶平顺性）Whats the aim of this courselTo find out the reasonable method to design and use vehicle according to the relationship among the parameters of structure and performance of vehicle.l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Chapter one Acceleration Performance1.1 Evaluation Index评价指标 1.Maximum Vehicle Speed (Velocity)最高车速uamax (km/h):1Definition：The maximum speed which the vehicle can get under good and flat road with rated load 额定载荷). 2Actual Measurement of uamax2. Acceleration Ability加速能力1The acceleration ability for starting(原地起步加速能力) Test Condition : Full engine power 油门全开; Optimal shift point between gears最正确换档时机 which are from low gear 第档 for start-up to high gear 最高档 for fuel economy. Evaluation IndexT T is the time needed by the vehicle to accelerate from 0 to 0.8Uamax under the above test condition or the time needed to pass through a fixed distance 400 m or mile(402.5m).用档起步，按最正确换档时间，逐次换至高档，油门全开，以最大加速度行驶，全力加速至 0.8uamax所需时间，或通过某 一预定距离所需时间2The 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 indexTT 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 0.8Uamax or the time needed to pass through a fixed distance 400 m or mile.(在直接档工作时，油门全开，由该档的最小稳定车速全力加速至 0.8Uamax所需时间，或通过某一预定距离所需的时间3.Maximum Gradeability of Vehicle imax最大爬坡度1Definition： The maximum grade which the vehicle can climb in the first gear档 under good road condition with fully rated load额定满载. i=tg EQ140 imax=28% EQ240 imax=58% =302Actual Measurement of imax1.2 Driving Mechanics of Vehicle To analyze the balance between Total Roads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 Numerical Ratio of the Transmission Numerical Ratio of the Final drive Total efficiency of driveline Torque of Driving Wheel(1)Torque of Engine Engine maybe characterized by its torque and power curve as a function of speed. Figure 1. shows typical curves for gasoline engine. Figure 1. Performance characteristics 外特性曲线 of gasolineFull performance and Full performance with all the accessories(外特性与使用外特性外特性与使用外特性)Useful formulas for Power calculationUnit: Pe (kW) ;Ttq (Nm); n(r/min)。2Efficiencies of DrivelinelThe necessity of the introduction of T: l The inefficiencies due to mechanical and viscous losses in the driveline componentstransmission; driveshaft; differential and axleshave not been taken into account. These act to reduce the engine torque in proportion to the products of the efficiencies of the individual components.l T combined efficiency of driveline consists of four primary parts:l l l 离合器 变速箱 传动轴 驱动桥 l l 3Tire RadiusDefinition: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 vehicleand n (rolling numbers). 4Graph of Tractive Force 驱动力图lHow to make tractive force-speed characteristics graph：l1Mathematical conversion between nengine revolution speed) and l vehicle speed lNote: (km/h) ; n (r/min); r (m)l 2Make the graphlTwo basic formulas for making the graph:lMake the tractive force line of each gear given of the vehiclegiven & given r and given ：l l lMake all the curves of the vehicle figure1.2: Figure 1.2 Tractive force-speed characteristics for a manual transmission3)Conclutions from the graph of tractive force:l“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.lThe 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).lFor maximum acceleration performance the optimum shift point between gears is the point where the line cross.lThe area between the lines for the different gears and the constant power curve is indicative of the deficiencies of缺乏，缺乏 the transmission in providing maximum acceleration performance.2. Road Load force 行驶阻力1Rolling Resistance Force F f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 T f 滚动阻力偶矩 T f = F zaThe 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 conclution: under given conditions( stiff road; constant revolution speed) assumed : driving force rolling resistance force of driving wheel total rolling resistance : The mechanics analysis of driving wheel with constant revolutionNote:1.Rolling resistance is present from the instant the wheels begin to turn.2.The rolling resistance is the primary motionresistance force. 3.For off-high way, level ground operation, the rolling resistance is the only significant retardation force.4. usually is equal to 0.012.2Aerodynamic Drag(空气阻力)Aerodynamic Drag （空气阻力）（空气阻力）Pressure Drag（压力阻力）（压力阻力）Vicious Friction（摩擦阻力）（摩擦阻力）Form Drag-形状阻力形状阻力 58%Total Protuberance Drag-干扰阻力干扰阻力 14% Total Internal Drag-内循环阻力内循环阻力 12%Induced Drag-诱导阻力诱导阻力 7%lAerodynamic forces interact with the vehicle causing drag，lift or down load，lateral forces，and their individual moments.lThe Aerodynamic forces produced on a vehicle arise from two sources：lNote: 1Total Internal Drag comprises of air flow management of cooling system and l inside ventilation of the body.发动机冷却、车身通风l With no attention to the need for air flow management, the air entering through the l radiator dissipates much of its forward momentum against the vehicle components in the l engine compartment before spilling out through the underside openings. The momentum l exchange translates directly into increased drag. 2Bernoullis Equation： P -大气压； -空气密度；C-常数 Zero underbody(车身底板) 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 panel3For minimizing Form Drag we adopt the body of streamlined shape ( 流线形which is usually be described as drop-like body.Calculation of Aerodynamic Forces FwSemi-empirical models：Where: Aerodynamic drag coefficient空气阻力系数空气阻力系数 Frontal area of the vehicle迎风面积迎风面积 Air density 空气密度空气密度 Relative Velocity相对速度相对速度 International CD: China CD Cars 0.300.35 Cars 0.4 Vans 0.330.35 Vans 0.6 Pickup trucks 0.420.46 Pickup trucks 0.8Because of ua (km/h) ；ur(m/s)；ur=ua/3.6 (m/s) (no wind)So 3Uphill Grade Resistance Force F i坡道阻力Define: Road Resistance 道路阻力道路阻力Define: Road Resistance Coefficient 道路阻力系数道路阻力系数 4Acceleration ResistanceFj1.Translational mass inertial force 平移质量惯性力Fj1G/g质量 du/dt加速度2.Rotational mass inertial force (moment) 回转质量惯性力or 力矩Tj; Fj2(rotating components comprise of fly wheel, gear system, shafts&axles, wheels)I转动惯量 d/dt角加速度Inertial moment for fly wheel e angular velocity of fly wheel w angular velocity of wheel Ua vehicle speed r radius of wheel Deliver Tf to driving wheel Tfw2) Total inertial moment for wheel and rotational mass inertial force Tj；Fj23. Total Inertial Force FjAssumed : rotational mass coefficient 回转质量换算系数So 3.Driving Equation行驶方程1)General model of driven wheel: 2) General model of driving wheel:3General model of vehicle:Note: Fjw2 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 ; For general model of the vehicle ,Fp and Ft are considered as internal forces ,so there is no Fp and Ft on the graph. Ft and Ff are the result of assumption , so there is neither Ft nor Ff on the graph.1.3 Traction-Limited Acceleration1Driving Condition of AccelerationWhen Level road: Constant speed: Level road & Constant speed: For constant speed: 匀速 acceleration: 加速 deceleration: 减速So Driving Condition驱动条件 is 2Limited 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 drive wheels 驱动车轮上道路垂直反力 3Traction-limited Acceleration 驱动附着条件4Traction 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)(求矩求矩)2 when: 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: 5percentage of utilization of maximum tractive force 附着利用率Definition: 汽车附着力汽车附着力/全轮驱动汽车附着力全轮驱动汽车附着力=附着利用率附着利用率Where: Maximum tractive force of front-wheel-drive cars Maximum tractive force of rear-wheel-drive cars Maximum tractive force of four-wheel-drive carsFor front-wheel-drive cars: rear-wheel-drive cars: four-wheel-drive cars: Graph of ：Note: increase leads to decrease in the case of fron-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； 前部轴荷后部轴荷前部轴荷后部轴荷1.4 Tractive Force & Driving ResistanceSpeed Characteristics 驱动力-行驶阻力平衡图From Drivng 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.1Maximum 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. 2Maximum Gradeability of Vehicle The maximum uphill grade resistance force which the vehicle could overcome F i坡道阻力3Acceleration AbilityEstimate ： The acceleration ability of the vehicle at any speed(ua1). the tractive force which the vehicle need to drive with constant speed (ua1). the maximum tractive force which could be used to accelerate at this speed (ua)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)1.5 Dynamic Character of Vehicle 汽车的动力特性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.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 vehicleG/g ) Definition: So: where: Ddynamic factor 动力因数 road resistance coefficient 道路阻力系数 Note : D=f when : constant speed du/dt=0 level road =0 f=0.012 under the most situation f0.02 when ua50 km/h where f0=0.012 ua fAnalyze：1Maximum Vehicle Speed (Velocity) (km/h): So is the corresponding x-coordinate of the cross point of f curve and D curve of the fourth (high-speed) gear.2 Maximum Gradeability of Vehicle So when climbing the soft grade (坡度小坡度小) because cos=1, sintgi, D=f+i when climbing the big grade坡度大坡度大 because 3Acceleration ability： driving on the level road So How to calculate T which is the evaluation index of acceleration ability ? 1.6 Power Equilibrium1.Equation of Power Equilibrium：2. How to make the Graph of Power Equilibrium: because : (功率平衡图 abreverse supply of power(后备功率)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.3. -The maximum difference between the resistance power curve from the full power curve of the first (-speed) gear