The difference, comparing with conventional suspension system is the gas spring instead of a mechanical spring, and the hydraulic fluid passing through the valve, where the energy is dissipated without using additional dampers, achieves the damping.
The most important item of this system is the gas chamber, therefore the stiffness will be defined basically, by the pressure and volume contained within the chamber. In some vehicle (like the Citroen® CX series), the chamber is built from two different parts that then join to take the shape of a sphere, and the gas is separated hydraulic fluid by a flexible diaphragm. This diaphragm avoids gas leaks even having hydraulic fluid losses, if the system is not sealed Fig-2: Arrangement of Hydropneumatic Suspension System
perfectly. The hydraulic fluid that drains out of the system is stored in a reservoir and thereby returned to the system using a hydraulic pump, keeping the vehicle height constant throughout. A semi active control can be done through an adjustable valve that increases or decreases the damping. Controlling the level of the hydraulic fluid either manually or automatically may do an active suspension.
One or two of the more obvious ones are that since the system is hydraulic, the ride height can easily be altered, a trend low riders are now following on with in California, nearly fifty years later. Also, they could link the four corners together to make a system that prepared the car for the bump to keep it even and offer the passengers a smoother ride. Basically they put fancy valves called height correctors on the anti-roll bar. These were mounted in such a way that as the suspension twisted, this operated the valves that controlled the transfer of fluid to the struts.
It was possible to isolate the front and rear systems and have the front suspension set at a height which required 'x' litres. So when the front nearside wheel takes a knock compressing its sphere, x/2 L is lost in the sphere, then the height correctors allow another x/2 L in, to inflate the offside strut by that much. This
keeps the front part of the car, always level in a horizontal plane.
As the car clears the bump, the reverse happens; the sphere displaces that fluid, the strut returns to its own height pulling the anti roll bar back true with it which in turn tells the height corrector to lose that extra x/2 litres of fluid from the other side. As one side extends its strut in reaction to clearing the bump, the other is retracting by the same amount to return the car to its set height above the road.
A further mechanical advantage of hydraulic suspension is that the car is able to link its braking effort to the weight on the wheels.
In the Citroën® CX, the rear braking effort comes from the pressure exerted on the LHM fluid by the weight on those struts. This means that as the weight travels forward under braking, there is less pressure on the back suspension. The suspension is the able to exert less pressure on its fluid, and as weight and grip diminish on the wheels, so does the braking effort, thus the hydropneumatic system prevents rear wheel lock ups. This flexibility in operation is one of the outstanding advantages of the hydropneumatic suspension system.
In this paper, a methodology for primary specification of critical parameters of a hydropneumatic suspension system is presented.
3.0 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.
According to the hypothesis mentioned above,
PV=nRT & …(1)
PV=constant …(2)
Where P is the pressure, V is the volume and T is the temperature of the gas.
To find the spring stiffness function which represents a force (F) done by the hydraulic cylinder as a function of displacement (x) must be developed. The initial state is where the force is zero for null displacement. This condition only occurs when the gas pressure inside the chamber is equal to the atmospheric pressure. The figures (a) and (b) show the forces and pressures for the initial condition and generic condition respectively.
Fig-3 (a) (b)
Let the initial volume of the gas be V0. To each piston displacement, due to force acting on the vehicle wheel an oil volume will be displaced to inside or outside the chamber, which will decrease or increase the gas volume.
Let the volume displaced be Vd,
Vd=Acx …(3)
Where Ac is the piston area, the final gas volume V inside the chamber is
V=V0-Acx …(4)
From equations (2) & (4)
PoVo=P (Vo-xAc) …(5)
The force acting on the wheel changes the gas pressure inside the chamber to
P=Po+ …(6)
Fro equations (5) & (6)
+Po= …(7)
F= …(8)
This equation shows that force as a function of piston displacement has a non-linear behaviour. Therefore the spring stiffness co-efficient is not constant, as in the conventional systems.
Ks (x)= …(9)
This equation shows that the spring stiffness does not depend on the chamber shape where the gas is confined, but depends on the initial pressure, initial gas volume and the variation of gas volume. As the gas pressure depends on the piston area and the vehicle load, the easiest way to modify the spring stiffness is by changing the initial gas volume and is comparatively cheap rather than changing the hydraulic cylinder. The local stiffness is usually intended as the derivative of the force function with respect to displacement x. Deriving equation (8) we get,
Kl(x)= …(10)
Therefore it’s interesting to see that this stiffness is used only in the local incremental analysis. The product Kl (x). x doesn’t give the value of F(x), due to non linearity. Then this definition is not adequate for suspension analysis.
Hence it is convenient to work with new displacement variable z with origin at the static equilibrium position Xs and defines stiffness variable constant K (z).
Z=X-Xs …(11)
K(z)= = …(12)
Where F(x) & F(Xs) can be calculated using equation (8).
With this definition is satisfied that ΔF(z)=K(z).z for all z.
3.1 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.
Ps= & …(13)
Ps= …(14)
Where W is the load on each wheel, Ps is the pressure in static equilibrium and Vs is the corresponding volume. The criteria used in this study to define the hydropneumatic spring stiffness and the initial gas volume assumes a maximum axle displacement Xm, relatively to the vehicle frame, at the maximum attended load. The most severe load condition considered happens when the vehicle has its maximum static load. The figure (4) shows the initial, transition and final states.
Fig-4 (i) (ii) (iii)
The condition (i) means zero force is acting on the suspension. In other words the pressure acting inside the cylinder is atmospheric. At condition (ii) the maximum static load that the vehicle will transport is acting, resulting in a pressure Ps & volume Vs. the static displacement in this condition is Xs. At condition (iii), the dynamic load condition is acting that results in a pressure Pm and a volume of gas Vm inside the chamber. The displacement Xm is considered to be maximum as it allows the maximum displacement of the axle.
Considering conditions (i) & (ii) and equation (2), is obtained:
PoVo=PsVs=Ps(Vo-Acxs) & …(15)
Vo= …(16)
To determine the Xs, the condition (i) & (iii) must be considered, since Xm is known,
PoVo=PmVm=Pm(Vo-Ac(Xs+Xm)) …(17)
Isolating Xs of equation (17) and from equation (16), the initial volume is obtained as,
Vo= …(18)
Ps= & …(19)
Pm= …(20)
Figure (5) shows the theoretical curves of hydropneumatic spring stiffness considering 4 different load conditions as function of displacement in the range –50mm to 150mm. The parameters used to define the initial volume are: diameter of cylinder as 0.05m,Maximum Vehicle static load (W) = 8829 N, Maximum allowed displacement (Xm) as 0.05m and dynamic load factor (fd) as 3. Equation (18) gives an initial volume Vo=0.0067 m3.
Figure 5(a) shows stiffness obtained when vehicle is empty. Figure 5(d) when the vehicle is fully loaded and figures (b) & (c) at intermediate conditions. The cylinder displacement equals zero means that it’s at equilibrium position (the vehicle is at correct height). Positive values means that the gas is being compressed and expanded for negative values.
Fig: 5 (a), (b), (c), (d)
4.0 Results:
In practice, for each increase of vehicle static load and consequent displacement of piston to new position, the oil volume must be increased to make the piston come back to zero. Another important point is the addition of oil in the system does not change its stiffness, since this will not change the pressure and volume of gas inside the chamber. The stiffness rises drastically when the piston is achieving its end as the volume becomes very small. This is an advantage because if there’s a displacement of the wheel bigger than previewed the suspension becomes tight very fast, avoiding the piston achieve its end, which can result in damage to the vehicle.
Thus, in this way the damping behaviour is analyzed mathematically. Thus, this analytical study predicts that the vehicle becomes over damped very fast when the load decreases. Thus, to obtain optimum performance a damping control must be done.
5.0 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.
The second-generation hydropneumatic system was developed for suspension systems whose axles are actually subjected to some really very high load ratios.
Here, the pressure level in the cylinder ring chamber is automatically controlled by the axle load.
Once the minimum axle load falls below a structurally fixed level, the pressure is automatically raised to a higher level. Similarly, once the minimum axle load is exceeded, the pressure is reduced to a lower level.
The fact that the pressure in the ring chamber can be adjusted means that load ratios of up to 1:20 can easily be managed very easily by changing the ring chamber pressure
Changing the ring chamber pressure influences the axle's elastic spring rate so that the functions can accurately be adapted to suit the operating conditions.
This innovative suspension system's variety of adaptation possibilities allows more effective use to be made of the functional advantages of a hydropneumatic suspension system no matter what the operating conditions.
In short, Simrit offers two different types of hydropneumatic suspension system, both of which allow different types of vehicles to fine tune differently at variable pressure ranges
The standardization of components also allows samples to be produced very quickly.
The self-adapting settings of these intelligent, active systems open up completely new opportunities.
Consequently, planned developments such as combined front axle, cab and rear axle suspension will exploit the full safety potential that is of such vital importance for tractors that are travelling at ever-increasing speeds.
6.0 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.
7.0 References:
Inman DJ., 1996, “Engineering Vibration”, Prentice Hill, Englewood Cliffs, New Jersey.
Els, P.S., Grobberlaar, B., 1993, “Investigation of Time and Temperature Dependency of Hydropneumatic Suspension System”, SAE Technical Paper Series, SAE Publications.
Shearer, J.L., T.M. Arthur, H.H. Richardson, “Introduction to System Dynamics”, Addison-Wesley Publishing Co., 1967.
Dr.Kirpal Singh., “Automobile Engineering Vol-2”, A.K.Jain Publishers
8.0 Acknowledgements:
The authors wish to support the acknowledgement of :
Mr. P.S.Kishore, Assistant Professor, Mechanical Department, G.I.T.A.M
Dr. M.R.S. Satyanarayana, Assistant Professor, Mechanical Department, G.I.T.A.M.
