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On The Analysis and Design of Vehicle Suspension System Going over Speed Bumps

by Alireza Mohammadzadeh & Salim Haidar Grand Valley State University

Overview

In this paper, we discuss a novel framework in the form of a classroom project in which clients in first courses on vibrations would learn in an effective manner about basic elements of vibrations such as transient load, field equations, simulation, and design. We also note that the problem we present in this paper cannot be solved by existing techniques such as proportional damping through modal analysis.

In effect, to teach transient vibrations to our students in vibrations class the authors gave them a project, in which the students analyzed and studied the ensuing motions of a vehicle passing over a speed bump. Students used a 2-degree of freedom model to simulate the motion of the vehicle going over the bump. They studied the effect of vehicle speed, speed bump’s geometry on the subsequent bounce and pitch motions of the vehicle. Once they understood the underlying physical concepts of transient vibrations, the students then modified the original system’s parameters to reduce the respective amplitudes of the bounce and the pitch motions of the vehicle at a given vehicle speed and a set bump geometry.

After deriving the equations of motion, we had students use MATLAB and SIMULINK in this project to overcome the mathematical difficulties inherent in the solution of the physical problem of transient response, to simulate its behavior, and to design the corresponding system.

Problem Statement

An automobile such as the one shown in the Figure 1, exhibits bounce, pitch, and roll on top of its rigid body motion as it goes over a speed bump. In this analysis, we assume that the rolling motion compared to the two other types of oscillatory motions is negligible. Neglecting the rolling motion and mass of tires, and combining the stiffness and damping effects of tire and suspension system into an equivalent damping and stiffness system, a preliminary model for automobile’s suspension system is presented in the Figure 2. Initial values for the respective inertias, damping coefficients, and spring rates are as follows:

m = 2000 kg J = 2500 kg.m2 k1 = k2 = 30000 N/m c1 = c2 = 3000 N.s/m

l1 = 1 m and l2 = 1.5 m

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Mohammadzadeh, A., & Haidar, S. (2009, June), On The Analysis And Design Of Vehicle Suspension Systems Going Over Speed Bumps Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5368