Jawaharlal Nehru Technological University Hyderabad B.Tech IV Year ELECTRIC AND HYBRID VEHICLES Previous Question Paper (September - 2020 - R16)

Vehicle motion is governed by various resistive forces that oppose forward movement. The two primary components at higher speeds are rolling resistance and aerodynamic drag.

Rolling Resistance: This force arises primarily from the deformation of the tire as it contacts the road surface. As the tire rotates, energy is dissipated due to the hysteresis of the rubber material. It is defined as:

Where C_rr is the rolling resistance coefficient, M is the vehicle mass, and g is the acceleration due to gravity.

Aerodynamic Drag: This force is caused by the resistance of the air through which the vehicle travels. It depends on the vehicle's shape, frontal area, and speed. It is expressed as:

Where ρ is air density, A_f is the frontal area, C_d is the drag coefficient, and v is the vehicle velocity.

Derivation of Translational Speed:

The total tractive force F_t required to move the vehicle at a constant speed on a level road is the sum of resistive forces:

To derive the translational speed v, we consider the power balance where the power at the wheels P_w equals the product of tractive force and velocity:

Solving for v involves rearranging the equation into a cubic form:

This cubic equation can be solved for v using Cardano's method or numerical iteration, providing the steady-state translational speed for a given power input.

To model the performance of an electric vehicle (EV), we must analyze the forces acting on the vehicle during motion. The fundamental equation of motion is derived from Newton's Second Law, where the tractive force provided by the electric motor must overcome various resistive forces.

The total tractive force F_t required at the wheels is expressed as:

Where the individual resistive forces are defined as follows:

• Rolling Resistance (F_rr): Caused by tire deformation and friction with the road surface. It is modeled as:
  F_rr = M × g × C_rr × cos(θ)
• Aerodynamic Drag (F_ad): Resulting from air resistance against the vehicle body. It is modeled as:
  F_ad = 0.5 × ρ × A × C_d × v²
• Gradient Force (F_gd): The force required to climb an incline of angle θ:
  F_gd = M × g × sin(θ)
• Inertial Force (F_ia): The force required for linear and rotational acceleration:
  F_ia = M × (1 + δ) × (dv/dt)

In these equations, M is the vehicle mass, g is acceleration due to gravity, C_rr is the rolling resistance coefficient, ρ is air density, A is the frontal area, C_d is the drag coefficient, v is velocity, and δ is the mass factor accounting for rotating parts.

The power requirement P_t at the wheels is obtained by multiplying the total tractive force by the velocity:

To determine the electrical power input from the battery P_bat, we must incorporate the efficiency of the transmission η_t and the motor-controller system η_m:

This model allows for the simulation of vehicle speed, acceleration, and energy consumption profiles over standard drive cycles, providing the basis for sizing the battery pack and electric motor.