Simulation and comparison of quarter-car

passive suspension system with Bingham

and Bouc-Wen MR semi-active suspension
models
Cite as: AIP Conference Proceedings 1564, 22 (2013); https://doi.org/10.1063/1.4832791
Published Online: 13 November 2013

A. Perescu, and L. Bereteu

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© 2013 AIP Publishing LLC.

 Simulation and Comparison of Quarter-Car Passive
Suspension System with Bingham and Bouc-Wen MR Semi-
Active Suspension Models

A. Perescu*, L. Bereteu*

*
Mechanical and Vibration Department, University “Politehnica”, M. Viteazu 1, RO-300222, Timișoara,
Romania

Abstract. In this paper we want to transposion the suspension system in MATLAB, Simulink®, based on
equation of motion. Consider only vertical movement of the car, neglecting roll and pitch. All movements of the car axes
are modeled as having equal amplitude. The characteristic equations that describe the behavior of dynamical systems
based on FBD (Free Body Diagram) of automotive suspension. It will make two models, one passive and one Bingham
semi-active. Their responses will be compared between them, and with another Bouc-Wen semi-active model, more
complex.
Semi-active suspension systems have received significant attention in recent years because they offer the
adaptability of active control devices without requiring large power sources.
Given that both passive and semi-active dampers are in mass production will follow the normal parameters and
their economic efficiency.
These models are used for initial design of suspension system.
Keywords: automotive suspension, quarter-car, passive, semi-active.

INTRODUCTION

The function of automotive suspension system is not only to isolate the effect of road surface irregularities on
the passengers to improve the ride comfort but also it has to control the dynamic tyre load with acceptable
suspension working space to enhance the vehicle stability and safety.[5]
The passive suspension’s drawbacks can be overcome by resorting to one of three techniques, adaptive, semi
active or fully active suspension. A semi-active suspension utilizes a passive spring and an adjustable damper with
fast response (less than 10 ms) and the damping force is controlled in real time to improve the control of ride and
handling.
Various semi-active dampers are being employed in different vibration isolation systems. Two such dampers
are the newly conceived Electro-Rheological (ER) and Magnetorheological (MR) dampers. MR Fluid is composed of
oil, usually mineral or silicon based, and varying percentages of ferrous particles that have been coated with an anti-
coagulant material. Engineering notes by Lord Corporation (Ahmadian, M., 1999) have reported that when
unactivated, MR Fluid displays Newtonian-like behavior when exposed to a magnetic field, the ferrous particles that
are dispersed through out the fluid form magnetic dipoles. These magnetic dipoles align themselves along lines of
magnetic flux.[1]

SUSPENION MODELS

Figure 1 (a) shows a simplified passive suspension system with two-degrees-of-freedom (2-DOF) quarter-
vehicle model.

TIM 2012 Physics Conference

AIP Conf. Proc. 1564, 22-27 (2013); doi: 10.1063/1.4832791
© 2013 AIP Publishing LLC 978-0-7354-1192-0/$30.00

22
 FIGURE 1. (a) Quarter-car suspension model (Chi et al., 2008); (b) Passive suspension system in Simulink

The governing equations of motion of the 2 DOF quarter-vehicle model are:

­ ..
§ . . ·
°° m1 y1  c¨ y1  y2 ¸  k  y1  y2  0
© ¹ (1)
® ..
§
°m2 y2  ct ¨ y2  z ¸  kt  y2  z   c§¨ y1  y2 ·¸  k  y1  y2  0
·
. . . .

°¯ © ¹ © ¹

Final model of the passive suspension system in Simulink is shown in Figure 1 (b).
There are three main types of MR dampers. These are the mono tube, the twin tube, and the double-ended MR
damper. Of the three types, the mono tube is the most common since it can be installed in any orientation and is
compact in size.[1]
A magnetorheological damper (MRD), shown in Figure 2, is not very different from a conventional viscous
damper. The key difference is the magnetorheological (MR) oil and the presence of a solenoid embedded inside the
damper which produces a magnetic field.

FIGURE 2. Principle of a magnetorheological damper[2]

The behaviour of MR fluids is often described as a Bingham plastic model having a variable yield strength,
which depends upon the magnetic field H. At fluid shear stresses above the field-dependent yield stress τy(H) the
fluid flow is governed by the Bingham plastic equation. At fluid stresses below the yield stress the fluid acts as a
viscoelastic material. This behaviour is described by equation (2):

23
 ­° .

W W y (H )  K J W ! W y (2)
®
°̄ GJ W Wy

.
where H is the magnetic field, J is the fluid shear rate and η is the plastic viscosity (i.e., viscosity at H = 0), G is the
complex material modulus (which is also field dependent).
Based on this model of the rheological behaviour of smart fluids, an idealised model, known also as Bingham
model, was proposed in 1985. This model consists of a Coulomb friction element placed in parallel with a viscous
dashpot. In order to obtain a better approximation of the experimentally measured data, an elastic element was added
in parallel with these two elements (Figure 3.a.). In the model, the damping force is generated by:

. .
Fmr Fc sgn x  c0 x  F0 (3)

where c 0 is the damping coefficient, fc is the frictional force directly related to the yield stress, f0 is the offset force,
.
x is the imposed relative displacement and x its time derivative.[3]
The Simulink model of the Bingham system is shown in Figure 3. (b).

(a)

(b)
FIGURE 3. Bingham mechanical model[8] and Bingham Simulink model

A model that can capture a large variety of hysteretic behaviour is the Bouc–Wen model. A schematic
representation of a Bouc-Wen based model of an MR damper is shown in Figure 4. (a)[3]. The Bingham model is
clearly linear and since the MR damper is highly nonlinear, this model will not be an area of focus and detailed
study.[8]
The model equation is given by:
. . . .
n 1 n
z J x z z vx z  Ax (4)

By changing the parameters γ , ν and A, the shape of the evolutionary variable z can vary from a sinusoidal to
a quasi-rectangular function of the time. When the model is completed with viscous dashpots or springs the system
response can predict a wide range of hysteretic behaviour. The damping force is given by:

24
 .
Fmr c 0 x  k 0 ( x  x 0 )  Dz (5)
where the parameter α determines the influence of the model on the final force value.[3],[6]
Bouc-Wen model reproduced in Simulink is presented in Figure 4. (b).

(a)

(b)
FIGURE 4. Bouc-Wen mechanical model[3] and The physical system with the MR damper[8]

The Bouc-Wen model is the most commonly used model to capture the behavior of non-linear hysteric
systems such as the MR damper. This model can produce a variety of hysteric patterns.

RESULTS AND DISCUSSIONS

Typical features of the different types of suspension are the required energy and the characteristic frequency
of the actuator as visualized in Figure 5.
The response of passive system in Simulink shown in Figure 6. The response in Simulink of second system,
with Bingham characteristic is shown in Figure 7.
The Bouc-Wen model were compared with the models above, achievement in Simulink, is shown in Figura 8.

FIGURE 5. Comparison between passive, adaptive, semi-active and active systems[7]

25
 FIGURE 6. Passive resonse in Simulink

FIGURE 7. Bhingam characteristic in Simulink

FIGURE 8. Bouc-Wen model[8]

CONCLUSIONS

The study of rheology as such, the theory behind rheological fluids, their properties and their application to
vibration control. The design and fabrication of MR damper suited to vehicle suspensions were carried out.[1]

26
 REFERENCES

1. A. Ashfak, A. Shaeed, K. K. Abdul Rasheed, J. Abdul Jaleel, Design, Fabrication and Evaluation of MR Damper, Academy of
Science, Engineering and Technology, 53, 2009, pp. 358-363.
2. B. F. Spencer, Jr., S. J. Dyke, M. K. Sain, J.D. Carlson, Phenomenological Model of a Magnetorheological Damper, Journal of
Engineering Mechanics, Vol. 123, No. 3, 1997, pp. 230-238.
3. E. Guglielmino, C. W. Stammers, T. Sireteanu, G. Ghita, M. Giuclea, Semi-active Suspension Control, Springer, London 2008.
4. G. Verros, S. Natsiavas, C. Papadimitriou, Design Optimization of Quarter-car Models with Passive and Semi-active
Suspensions under Random Road Excitation, Journal of Vibration and Control, Vol. 11, No. 5, 2005, pp. 581-606.
5. M. El-Kafafy, S. M. El-Demerdash, A. M. Rabeih, Automotive Ride Comfort Control Using MR Fluid Damper, Enineering, 4,
2012, pp. 179-187.
6. M Giuclea, T. Sireteanu, D. Stancioiu, C. W. Stammers, Modelling of Magnetorheological Damper Dynamic Behaviour by
Genetic Algorithms Based Inverse Method, Proceedings of the Romanian Academy, Series A, Vol. 5, No. 1, Bucharest, 2004.
7. T. Ram Mohan Rao, G. Venkata Rao, K. Sreenivasa Rao, A. Purushottam, Analisys of Passive and Semi Active Controlled
Suspension System for Ride Comfort in an Omnibus Passing Over a Speed Bump, IJRRAS 5, 2010.
8. Y. Iskandarani, H. R. Karimi, Vibration analysis for the rotational magnetorheological damper, GEMESED, 2011, pp. 486-
492.

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