Modeling and Simulation of Vehicular Power Systems - webfiles its ...

4.1.1 Normal load on each wheel.The normal load on each rear and front axles for a passenger car depends on thedimension and shape of it. The normal load for a passenger car is found according to thefollowing equation [11].LhbgrddVWf= MvgCosα− ( Fgrade+ FAerodynamic+ MvgCrCosα+ Mv)LLhdtWr=LaLMvhggCosα− ( FLgrade+ FAerodynamic+ MvgCrrhdggCosα+ MvdVdt)( 4-13)Where h g is the height of vehicle center of gravity from the ground, L a and L b are thedistances of the front axle and the rear axle from the center of gravity respectively. L isthe total distance between front ant rear axles. The dimensions are shown in figure 4-1.As in passenger vehicles the center of application of aerodynamic force, h w and thegravity force are near the same height, h g , so the above equations are simplified toWWfr==LLbLaLMMvvhggCosα− ( FtLhggCosα− ( FtLrd− Fr(1 − ))hr− Fr(1 −hdgg))( 4-14)Where F t is the sum of front and rear tractive forces and F r is the sum of front and rearrolling resistance. r d is the effective radius of the wheel.4.1.2 Friction coefficient and slip modelingExperimental studies have produced several clearly defined friction/slip characteristicsbetween the tyre and road surface for a variety of different driving surfaces andconditions [12]. For the purposes of simulation, four types of road condition are modeled:• Normal: The road is dry and maximum traction is theoretically possible.• Wet/Raining: Overall traction is reduced by about 20 %.• Snow: Un-packed snow lies on the road surface. Maximum traction reduced by 65 %.• Ice: Packed frozen snow and black ice lie on the road surface. Highly dangerous –maximum traction reduced by 85 %.Graphically, these four conditions are shown in figure 4-5 below:20