Quarter Car Model

Simulink simulation of a 1-DOF Quarter Car Model analyzing vehicle body displacement in response to road surface profiles.

1. OverviewThis project presents a Quarter Car Model developed in Simulink. It simulates the vertical dynamics of a vehicle body as it traverses road irregularities. This model is essential for engineers studying vehicle comfort and suspension design.

2. Mathematical FoundationThe simulation solves the second-order differential equation for a single-degree-of-freedom system:

• Equation: m*x'' + c*x' + k*x = c*y' + k*y
• Rearranged for Acceleration: x'' = (1/m) * [(c*y' + k*y) - (c*x' + k*x)]

3. Model ParametersThe blocks in the provided model use the following values:

• Body Mass (m): 100 kg
• Damping Coefficient (c): 200 Ns/m
• Spring Stiffness (k): 10,000 N/m
• Input (y): Sine Wave (Road Profile)

4. Key Features

• Dynamic Response: Real-time calculation of Velocity and Displacement.
• Road Excitation: Includes both displacement (y) and velocity (y') of the road profile.
• Visual Output: Scope block for analyzing the stability and settling time of the suspension.

5. How to Use

1. Download and open the .slx file.
2. Double-click the Sine Wave block to change road frequency.
3. Run the simulation and observe the Scope to see the car body's reaction.