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Hydro-pneumatic suspension systems have been used increasingly in recent times because of the well known advantages they offer. It is equally well known that the spring force is time- and temperature dependent, resulting in varying ride height and ride comfort of vehicles equipped with hydro-pneumatic suspension systems. In the present study, the temperature- and time dependent characteristics of hydro-pneumatic springs are modelled mathematically. This is done in order to investigate the effect of heat transfer on the spring characteristic so that it can be taken into account during the design of such systems. The mathematical analysis is based on the solving of the energy equation of a gas in a closed container by using the Benedict-Webb-Rubin equations for real gas behaviour. This differs from the traditional method which makes use of the ideal gas approach and polytropic processes to determine the spring characteristic.

A modified Nelder & Mead (N&M) algorithm (Simpleks algorithm) is used, with the Vibration Dose Value (VDV) as optimisation parameter, to optimise the springs and dampers, functioning in unison with defined suspension bump stops, of the suspension system of a vehicle. The teqnique for determination of VDV's was origionally developed for use during physical testing of vehicles where it was used as a single number to provide an objective assesment of the severity of the vehicle ride as experienced by the driver and passengers of a vehicle. However, the VDV has proved to be ideally suited as optimisation parameter during the development of new vehicles and during investigations into existing vehicles and vehicle upgradings as regards the optimisation of the springs and dampers of their suspension systems.