Jawaharlal Nehru Technological University Hyderabad B.Tech IV ELECTRIC AND HYBRID VEHICLES Previous Question Paper (July/August - 2022 - R16)

The performance of a conventional vehicle is primarily determined by its internal combustion engine (ICE) and the mechanical transmission system. The engine produces power and torque that vary significantly with rotational speed, necessitating a transmission to match these characteristics to the requirements of the vehicle at different road loads.

The performance is governed by the following key factors:

• Engine Characteristics: An ICE has a limited speed range and produces zero torque at zero speed. It requires a clutch or torque converter to decouple the engine from the wheels during idling.
• Tractive Effort: The force available at the wheels is the product of engine torque, gear ratio, and final drive ratio, divided by the wheel radius. As the gear ratio increases (lower gears), the tractive effort increases, allowing for acceleration and hill climbing.
• Transmission Role: The transmission provides multiple gear ratios to keep the engine operating within its efficient speed range (the 'sweet spot') across varying vehicle speeds.
• Road Load: The vehicle must overcome aerodynamic drag, rolling resistance, and gravitational forces. The intersection of the tractive effort curve and the road load curve defines the vehicle's maximum speed and acceleration capability.

The transmission characteristics are represented by a plot of Tractive Effort (F) on the y-axis against Vehicle Velocity (v) on the x-axis. This graph typically shows a series of hyperbolic curves, each corresponding to a specific gear ratio. As the gear ratio decreases (shifting from 1st to higher gears), the maximum tractive effort drops, but the maximum achievable vehicle speed increases. The envelope of these curves represents the maximum performance capability of the vehicle across its entire speed range.

In this relationship, T_engine is the engine torque, i_gear and i_final are the gear and final drive ratios, η_transmission is the efficiency, and r_wheel is the effective radius of the tire. The transmission characteristics ensure that the engine remains within its peak power band while providing the necessary torque multiplication for starting and climbing.

The mathematical model of a vehicle's performance is based on the longitudinal dynamics of the vehicle, which balances the tractive effort provided by the powertrain against the resistive forces acting on the vehicle. The fundamental equation of motion is derived from Newton's second law:

Where the individual forces are defined as follows:

• Tractive Effort (F_t): The force delivered by the motor/engine to the wheels, calculated as F_t = (T_m × G × η_t) / r, where T_m is motor torque, G is gear ratio, η_t is transmission efficiency, and r is tire radius.
• Rolling Resistance (F_r): The resistance due to tire deformation and friction, given by F_r = C_r × M × g × cos(θ), where C_r is the rolling resistance coefficient, M is vehicle mass, and θ is road gradient.
• Aerodynamic Drag (F_ad): The force due to air resistance, calculated as F_ad = 0.5 × ρ × A × C_d × v², where ρ is air density, A is frontal area, C_d is drag coefficient, and v is vehicle velocity.
• Grading Resistance (F_g): The force required to climb a slope, given by F_g = M × g × sin(θ).
• Inertial Force (F_ia): The force required to accelerate the vehicle, defined as F_ia = M × δ × (dv/dt), where δ is the mass factor accounting for the rotational inertia of rotating parts.

By rearranging these components, the vehicle acceleration can be expressed as:

This model allows for the simulation of vehicle performance, such as maximum speed, acceleration time, and gradeability. By integrating this equation over time, one can determine the velocity profile and distance traveled, which are essential for evaluating the energy consumption and range of electric and hybrid vehicles under various drive cycles.