19-01-2013, 03:43 PM
MATHEMATICAL ANALYSIS OF HYDROPNEUMATIC SUSPENSION SYSTEMS
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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.
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.
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
Theoretical determination of hydropneumatic spring characteristics
In the following development the gas is considered to be inert so that it would not react with the sides and thereby change its characteristics during working. The ideal gas model is considered and an isothermal process as well. This assumption does not represent exactly the realistic conditions due to the heating of gas during the process. If the system is running at a very high frequency, there isn’t time to allow
heat exchange with the environment, and a hysterises phenomenon will occur. This effect will not be considered once the energy starts to dissipate from the system.
Definition of initial gas volume and dimensions:
The geometric suspensions of all components are keys to the suspension system design. These parameters, including other like tire stiffness, mass of wheel define the vehicle response to external stimulation. In order to optimize the configuration the manufacturers usually confront responses from systems empirically adjusted. For hydropneumatic suspensions, the non-linear stiffness is a function of pressure and volume of gas and the area of the cylinder. Assuming the cylinder area as already specified, the gas volume at the atmospheric pressure will define the stiffness of the system.
Recent trends in Hydropneumatic Suspension Systems:
Recent developments - which have seen a shift toward active, individually adaptable hydropneumatic suspension systems - have extended the range of available solutions.
In order to be able to use the diaphragm accumulator at both maximum and minimum axle loads, a hydraulic opposite load is built up in the cylinder ring chamber and generally controlled at a constant level.
The Simrit system uses a pressure control valve to keep the ring chamber pressure at a constantly low level and regulate it with every new control procedure. This allows for two different strategies.
The first generation hydropneumatic suspension system works as follows: the pressure level in the ring chamber is adapted by the structure in such a way that the components and accumulator design are harmonized for completely different types of vehicles. This reduces the number of part designs and increases quantities in an economical way. The size of the suspension cylinder is adapted in such a way that the reduced difference in pressure at the cylinder seals is beneficial for the suspension function as it creates low frictional behaviour. Moreover, this variant is not dependent on maximum pump pressure.
Conclusion:
In the present paper, the damping behaviour has been studied. Using basic Mathematical analysis the spring stiffness of the hydropneumatic system has been calculated and its effects have been thereby stated. Thus for optimal performance of hydropneumatic suspension systems, a damping control must be done. Thus, the uses of this kind of suspension system are vast and a goldmine to explore. Hopefully, in the future we may see more and more vehicles using such kind of suspension systems and thereby increase the efficiency of the vehicle and simultaneously increase the ride comfort.