# VEHICLE DYNAMICS - MATHEMATICAL ANALYSIS OF HYDROPNEUMATIC SUSPENSION SYSTEMS

VEHICLE DYNAMICS

MATHEMATICAL ANALYSIS OF

HYDROPNEUMATIC SUSPENSION SYSTEMS _

MATHEMATICAL ANALYSIS OF

HYDROPNEUMATIC SUSPENSION SYSTEMS

Abstract:

Every one of us might have seen the heavy trucks running on the roads. These vehicles have efforts on their axles very close to the allowed limits, mainly driving on rough roads or during cornering. In this case, the use of conventional suspension systems like those using McPherson Struts, Multi Link Suspension, Trailing Arm Suspension, 4- bar suspension etc. can increase the axle’s overload phenomena. Hydropneumatic suspension system, when used in these vehicles, takes an asset in providing a better load distribution per axle, decreasing the overload problem and thereby increasing the ride comfort. The well known problem of the damper co-efficient changes due to load variation in vehicles using conventional suspension system is even more observable when a hydropneumatic spring is applied due to its non linearity, as opposed to the several advantages this spring type brings. This problem is more emphasized in vehicles with a large mass range when they pass from a no load condition to a full load condition.

In this study, a Mathematical model of the hydropneumatic spring stiffness behaviour was developed. The various factors or parameters that influence the spring stiffness behaviour have been mathematically found out. Also in this paper, a methodology for primary specification of critical parameters of a hydropneumatic suspension system is presented.

Keywords:

Vehicle, active suspension, axle displacement, Isothermal process, Spring Stiffness Factor.

1.0 Introduction:

Vehicles used for transport of loads have their efforts on the axles very close to the allowed or critical limits mainly during its travel on a bumpy surface or during cornering. In such cases the use of conventional suspension systems can increase the axle’s overload phenomena. Hydropneumatic suspension leads to an even distribution of load per axle, thereby decreasing the overload problem and simultaneously increasing the efficiency and comfort levels.

2.0 About the Suspension System:

This suspension system was invented in the late 50’s by Citroen® and has been fitted to many of their cars since. As its name suggests, its core technology and mainstay of its functionality is hydraulics. Superbly smooth suspension is provided by the fluid’s interaction with a pressurized gas. This system is powered by a large hydraulic pump operated directly by the engine in much the same way as an alternator or an air- conditioner is, and provides fluid to an accumulator at a pressure, where it is stored ready to be delivered to servo a system.

The spheres are like the springs on your cars, and the struts and the hydraulic components that make the fluid act like a spring. There is a hydraulic component

called an accumulator, which is gas under pressure in a bottle contained

within a diaphragm, effectively a balloon which allows pressurized fluid to compress the gas, and then as pressure drops the gas pushes the fluid back to keep the system's pressure up. As you can see in the drawing, the pink gas(Nitrogen) is compressed when the pressure in the green fluid overcomes

the gas pressure and pushes back the diaphragm, which compresses the gas. Then as the pressure of the fluid decreases, the gas pushes back the diaphragm and as the gas overcomes the fluid, it expels the fluid from the sphere, returning gas and fluid to equilibrium.

Fig-1