Simulating Vehicle Suspension with a Simplified Quarter-Car Model

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The simplified quarter-car suspension model is basically a mass-spring-damper system with the car serving as the mass, the suspension coil as the spring, and the shock absorber as the damper.


This Demonstration lets you explore the affect of different suspension parameters and road conditions on the vertical motion of the car.

The mathematics of the system are based on the differential equation of the spring-damper suspension: , which, after a Laplace transform, results in the transfer function . The Mathematica 8 functions TransferFunctionModel and OutputResponse were used to calculate the car movement with no need to solve the differential equation.


Contributed by: Erik Mahieu (March 2011)



Snapshot 1: very hard suspension with a light car gives excessive shaking

Snapshot 2: the damping ratio is 1 and gives optimal comfort

Snapshot 3: at resonant frequency, a maximum car movement is obtained