Modelling the static stiffness and dynamic frequency response characteristics of a leaf spring truck suspension
Authors: Hoyle J B 
Published: March 2004

The suspension characteristics of a 10 ton truck with a highly non-linear leaf spring suspension have been investigated. The acceleration transmissibility frequency response characteristics of the truck were first investigated. Results showed that whereas the bounce (sprung mass) resonant frequency was quite close to that expected, the wheel-hop (unsprung mass) resonant frequencies were roughly twice that expected. As no obvious mechanism for this effect was evident, the static stiffness characteristics of the suspension were measured in an attempt to understand this phenomenon. A simple plot of the resulting suspension-generated force against suspension deflection showed that two distinct stiffness regimes were present; the first, which was associated with small suspension deflections of between 2 and 4 mm, was significantly greater than the second, which was associated with larger suspension deflections.

A state-variable linear 5 degree-of-freedom spring mass damper model of the vehicle was created within MATLAB in an attempt to predict the frequency response characteristics of the vehicle. The state-variable model predictions were close to those seen experimentally for the sprung mass at frequencies below 3 Hz, but were quite incorrect for both the sprung and unsprung masses above this frequency. The state-variable model was then used again with increased values of suspension stiffness and results showed that using these higher values led to a more accurate predicted response for both the sprung and unsprung masses above 3 Hz, whereas below this frequency their responses were clearly incorrect. Comparison of experimental and predicted results showed that the vehicle frequency response was dominated above 3 Hz by the low suspension deflection-high stiffness regime identified in the static stiffness results, whereas below this frequency, the high suspension deflection- low stiffness regime tended to dominated the response.

To overcome the problem of the transition from the low to the high stiffness regimes when predicting the frequency response characteristics, a non-linear model was created using MATLAB and SIMULINK. Results showed that the model was able to capture this transition, with resulting frequency response curves for both the sprung and unsprung masses being very similar to the experimental results. Further refinements to the model were able to account for additional discrepancies between predictions and experimental results.

The non-linear nature of the spring stiffnesses, resulting in a very useful hysteresis damping effect at the sprung mass resonant frequency, meant that for most normal road conditions the vehicle would ride on a near solid suspension. The apparent advantages of the extra damping would therefore be o set by a significant decrease in ride quality, and this was especially evident in respect to road noise and vibration-a finding borne out in practice.

This paper establishes the principal characteristics of the truck suspension and goes on to describe the linear state-variable and non-linear models created to simulate the frequency response characteristics of the vehicle suspension.