Suspension Systems: Some New Analytical Formulas for Describing the Dynamic Behavior

The paper presents some new and unreferenced analytical formulae describing the dynamic behaviour of the suspension system of road or off-road vehicles. The quarter car model (2 degrees of freedom) is considered, the suspension can be either passive or active. Passive suspensions can be simplified as the spring-damper combination or the spring-damper combination with an additional in series spring (representing, e.g., the rubber bushing at the top of a McPherson strut or the rubber bushing at the end joints of the damper). The mathematical system is linear and the excitation is given by a random stationary and ergodic process. The standard deviations in analytical form are given referring to, respectively, the vehicle body acceleration, the relative displacement between sprung and unsprung mass, and the force at the ground. The so called invariant points of the frequency response functions are derived for both active and passive suspension. Unreferenced sub-invariant points are derived which give hints on the performance of suspension systems. The analytical expressions of the Pareto-optimal solutions for selecting proper suspension parameters and the preferred performance are given, when possible, in analytical form. Analytical formulae are useful to understand qualitatively the behaviour of suspension systems. Despite their simplicity, they appear to be useful during testing.