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

Figure 4-2: The deflection of tyre and rolling resistanceThe torque caused by shifted ground reaction force is:T r= P × a( 4-2)In order to compensate this torque, a torque should be applied to the wheel with theopposite direction so:FTr P × a= = = P Cr( 4-3)r rRolling×d dWhich Cr is called the rolling resistance coefficient and P is the normal load on thewheel. The rolling resistance force is in the opposite direction of the vehicle movementand if the vehicle is climbing a grade the normal force will decrease so the aboveequation should be multiplied by Cosα which α is the angle of the grade in degree. Therolling resistance of the vehicle is not constant and there are so many factors affecting itsvalue including tyre pressure, tyre temperature, tyre material, road material and vehiclespeed of which speed is more important than the other ones. The rolling resistancecoefficient will change according to the following equation with speed especially in lowspeeds for a passenger car [10].VCr = 0.01(1 + )( 4-4)100The other resistance is the aerodynamic resistance which is caused because of two things.Shape drag and skin effect. [11], [14], [10].The aerodynamic force is calculatedaccording to the following equation.16