CHAPTER IV DRIVELINE DYNAMICS I. II. III. IV. ENGINE DYNAMICS DRIVELINE AND EFFICIENCIES GEAR BOX AND CLUTCH DYNAMICS GEAR BOX RATIO I. ENGINE DYNAMICS For indirect injection For direct injection Diesel engines Diesel engines A sample of power and torque performances for a spark ignition engine I. ENGINE DYNAMICS An example of power performance in a spark ignition engine with constant efficiency contours II. DRIVELINE AND EFFICIENCIES 2.1 Driveline Driveline components of a rear wheel drive vehicle II. DRIVELINE AND EFFICIENCIES 2.1 Driveline The input and output torque and angular velocity of each driveline component III. GEAR BOX AND CLUTCH DYNAMICS 3.1 Velocity and Traction Force III. GEAR BOX AND CLUTCH DYNAMICS 3.2 Velocity and Traction Force - example III. GEAR BOX AND CLUTCH DYNAMICS 3.2 Velocity and Traction Force - example A sample of a gear-speed plot for a gearbox III. GEAR BOX AND CLUTCH DYNAMICS 3.2 Velocity and Traction Force - example Wheel torque-speed at each gear ni of a gearbox III. GEAR BOX AND CLUTCH DYNAMICS 3.3 Acceleration capacity at different speed An example for the acceleration capacity ax as a function of forward speed vx III. GEAR BOX AND CLUTCH DYNAMICS 3.4 Gear box stability condition When we shift the gear to ni−1 the engine speed ωe jumps to a higher speed ωe = ωi−1 >ωT at the same vehicle speed The stability condition requires: A simple rule for a stable gearbox design III. GEAR BOX AND CLUTCH DYNAMICS 3.5 Example - Gear box stability condition Transmission ratios and stability condition The stability condition requires that ni−1/ni = cte III. GEAR BOX AND CLUTCH DYNAMICS 3.5 Example - Gear box stability condition Using n1 and n6 IV. GEAR BOX RATIO used to calculate the gear ratios of a gearbox as well as vehicle performance - Engine should work at its maximum power to have the best performance. - To control the speed of the vehicle, we need to vary the engine’s angular velocity. - The engine’s working range: (ω1,ω2) around ωM, which is associated to the maximum power PM. Recommendations to design the transmission ratios of a vehicle gearbox 1.Design the differential transmission ratio nd and the final gear nn such that the final gear nn is a direct gear, nn=1, when the vehicle is moving at the moderate highway speed. 2.Same as item 1, however, when the vehicle is moving at the maximum attainable speed. 3.The first gear n1 may be designed by the maximum desired torque at driving wheels, (determined by the slope of a desired climbing road). 4.The gear stability condition is used to find the intermediate gears. 5.The value of cg for relative gear ratios, can be chosen in the range 1≤cg≤2. To determine the middle gear ratios, there are two recommended methods: 1 - Geometric ratios 2 - Progressive ratios IV. GEAR BOX RATIO 4.1 Geometric Ratio Gearbox Design Geometric gearbox: the jump of engine speed in any two successive gears is constant at a vehicle speed. The engine’s speed jump is kept constant for any gear change from ni to ni+1 IV. GEAR BOX RATIO 4.1 Geometric Ratio Gearbox Design A gear-speed plot for a geometric gearbox design IV. GEAR BOX RATIO 4.2 Progressive Ratio Gearbox Design Progressive gearbox: the speed span of a vehicle in any two successive gears is kept constant. IV. GEAR BOX RATIO 4.2 Progressive Ratio Gearbox Design A gear-speed plot for a progressive gearbox design IV. GEAR BOX RATIO 4.3 Example 1: A gearbox with three gears Consider an m = 860 kg car having an engine with η = ηdηg = 0,84 and the powerspeed relationship We define the working range for the engine, when the power is 100kW ≥ Pe ≥ 90 kW IV. GEAR BOX RATIO 4.3 Example 1: A gearbox with three gears The power performance curve and its working range At the maximum speed vx=50 m/s, the engine is rotating at the upper limit of the working range ωe = 524 rad/s and the gearbox is operating in third gear. IV. GEAR BOX RATIO 4.3 Example 1: A gearbox with three gears The gear-speed plot for a three-gear gearbox IV. GEAR BOX RATIO 4.4 Example 2: Better performance with a four-gear gearbox The gear-speed plot