This paper investigates the GENSIS air spring suspension system equivalence to a passive suspension system. The SIMULINK simulation together with the OptiY optimization is used to obtain the air spring suspension model equivalent to passive suspension system, where the car body response difference from both systems with the same road profile inputs is used as the objective function for optimization (OptiY program). The parameters of air spring system such as initial pressure, volume of bag, length of surge pipe, diameter of surge pipe, and volume of reservoir are obtained from optimization. The simulation results show that the air spring suspension equivalent system can produce responses very close to the passive suspension system.
Suspension system design is a challenging task for the automobile designers in view of multiple control parameters, complex objectives (often conflicting), and stochastic disturbances. The problems stem from the wide range of operating conditions created by varying road conditions, vehicle speed, and load [
One of the advantages of air springs is that the energystorage capacity of air is far greater per unit weight than that of mechanical spring material, such as steel. Because of the efficient potential energy storage of springs of this type, their use in a vibrationisolation system can result in a natural frequency for the system which is almost 10 times lower than for a system employing vibration isolators made from steel springs [
As discussed above, the air spring suspension has a number of advantages in real application. However the design suspension system with air springs has been studied extensively. On the contrary, the design and analysis of the passive suspension system are fully established. Therefore, the air spring suspension system design problem can be converted to a model which produces suspension performance the same as a passive suspension system when using it without active controller or it can produce more efficient suspension system when use it with active controller. It is possible to convert a passive suspension system to an air spring suspension system and vice versa [
There have been some researches on the use of air spring for suspension systems. For example, Toyofuku et al. showed that the auxiliary chamber has a smaller effect on the system [
The main objective of this study is to obtain an air spring suspension system which can replicate the passive suspension system in terms of the suspension performance. In this research, an air spring suspension system is to be found which can produce the performance better than VAMPIC model [
The basis for mathematical models of air springs is to measure its mechanical properties. The mechanical behavior of air springs is often very complicated. The behavior is mainly based on fluid dynamic and thermodynamic mechanisms, where important quantities in such mechanisms are pressure, volume, temperature, mass flow rate, density, and energy of the air as well as shape of the air volume. For most air springs, these quantities should be expressed for both the air spring itself and its reservoir volume, as shown in Figure
Air spring suspension system: (1) reservoir, (2) controlled valve, (3) surge pipe, (4) air bag, and (5) tire.
There are many different kinds of air spring models, such as a simple model for vertical air spring dynamics (Nishimura [
In order to consider the change in the gas state in the two volumes, an approximation has been introduced by implementing a mechanical barrier (fictive piston) in the pipeline. The mechanical barrier is considered to be with neglected mass and equivalent fluid mass that is moving through the pipeline is added to the barrier [
The following analysis follows the method of calculation in [
Modeling of air suspension spring.
The GENSYS model of the air suspension system as shown in Figure
The mechanical model of air suspension system [
The quarter car model of passive suspension system of vehicle is shown in Figure
Quartercar model and relevant free body diagram.
Nonlinear equations of the sprung mass and unsprung mass motions can be derived in two parts as follows [
Sprung mass equation:
The idea of equivalent model is to find an air spring suspension system configuration which produces the same suspension performance (displacement) as a passive suspension system count part with the same road profile inputs (if the passive mode is selected that means without controller). This is achieved by finding air spring system model parameters by minimizing the performance difference.
The process of obtaining the equivalent model is illustrated by Figure
The lower bound and the upper bound of the constraint parameters.
Parameter  Lower bound  Upper bound  Unit 

Initial pressure (in bag and reservoir)  100000  700000  kPa 
Bag diameter  0.05  0.2  m 
Bag height  0.1  0.75  m 
Reservoir volume  0.01  0.3  m^{3} 
Length of surge pipe  1  5  m 
Diameter of surge pipe  0.003  0.025  m 
Finding equivalent model using SIMULINK simulation and OptiY optimization.
The parameter values of the quarter passive vehicle model used in the simulation are taken from [
The numerical values of the passive suspension system.
Notations  Description  Values  Units 


Frontleft and frontright suspension stuffiness, respectively  19960  N/m 

Rearleft and Rearright suspension stuffiness, respectively  17500  N/m 

Frontleft and frontright and rearright and rearleft tire stuffiness, respectively  175500  N/m 

Frontleft and frontright suspension damping, respectively  1290  N·s/m 

Rearleft and rearright suspension damping, respectively  1690  N·s/m 

Frontleft and frontright and rearright and rearleft tire damping, respectively  14.6  N·s/m 

Sprung mass  1460  Kg 

Frontleft and frontright tire mass respectively  40  Kg 

Rearleft and Rearright tire mass respectively  35.5  Kg 

Moment of inertia 
460  Kg·m^{2} 

Moment of inertia 
2460  Kg·m^{2} 

Distance between the center of gravity of vehicle body and front axle  1.011  m 

Distance between the center of gravity of vehicle body and rear axle  1.803  m 

Width of track  1.51  m 
The system responses for passive and optimized air spring suspension systems are presented in Figure
The results of OptiY software with MATLAB/Simulink.
The response of optimization technique with sine wave road profile.
The response of optimization technique with square wave road profile.
The response of optimization technique with saw tooth wave road profile.
The optimization technique available in OptiY with SIMULINK simulation was successfully used in this paper to find the equivalent air spring suspension model with the optimized parameters. The results are shown that the equivalent model can produce the suspension response similar to the passive suspension system. In future studies, the model can be used in active air suspension system design for better handling and stability properties. The nature of low resonance frequency in air spring can be exploited by frequency domain controller design methods such as H∞ methods [
The authors declare that they have no conflict of interests regarding the publication of this paper.