Vibration Control of Automobile Suspension System using ...ijens.org/Vol_19_I_01/191001-6464-IJET-IJENS.pdf · compared with other types of dampers. suspension system Index Term--Suspension

International Journal of Engineering & Technology IJET-IJENS Vol:19 No:01 1

SI J E N IJENS © February 2019 IJENS -IJET-6464-011910

Abstract-- In general, the objective of suspension systems of

automobiles is to isolate the vibrations produced due to road

disturbances from transfer to driver and passengers. The

design of a hydraulic control valve to improve the performance

of the damper of automobile suspension system is focused in

this paper. . The proposed control valve makes the damper of

suspension system to behave as a smart damper. A quarter

automobile model of two degrees of freedom is adopted.. The

parameters of the proposed control valve are optimized

according to settling time and peak overshoot. The efficiency of

this valve is tested by evaluating the response of the sprung

mass when the automobile excited by step and impulse

functions. The results show that the smart damper attenuates

the vibrations of the sprung mass in a short period when

compared with other types of dampers.

Index Term-- Suspension system, smart damper, control

valve, ride comfort, control strategy.

I- INTRODUCTION

One of the most important problems in automobile

suspension design is the vibration control which depends on

the damping system. The study of automobile dynamics has

special importance since it helps automobile designers to

produce an automobile that capable of achieving ride

comfort to passengers according to the international

standards. The main purpose of the vehicle suspension

system is to support and separate automobile body from the

wheels and relatively allows for movement between the

components. It is certainly rated by its ability to achieve

suitable ride comfort and good automotive holding from

road disturbance and improve passenger comfort. There are

many reasons cause the disturbance such as road surface

unevenness, aerodynamic forces, non-uniformity of the

wheel, tire assembly, and even or braking forces [1].

The study of the vibration control of automobile

suspension has been treated by many investigators using

different methods for passive, active and semi-active

suspension system types of control technique. All the studies

in this field pointed to how providing best comfort of riding,

and /or stability of riding.

G. Verros et. al [2] presented the optimization of

suspension parameters, damping factor and spring stiffness

for non-linear quarter –car model when excited by random

input from road profile. Firstly, the study starts with passive

damping, then involving the selection of damping

coefficient to produce results which approximated to that for

active suspension. The suspension characteristic was

optimized with respect to passenger comfort and automobile

handling. The method is to select the optimal damping

factor and stiffness constant of the suspension.

P. Sharma et. al [3] used a two degree of freedom

system for a quarter car model. The ordinary differential

equations were solved by Mat lab program to compute the

displacement of sprung mass and unsprung mass. The

solution of the mathematical model also gives the velocities

for suspension and travel response when the vehicle passes

over bump with damping ratio of 0.078. It was found that

the overshoot was about 70% and the amplitude of

acceleration was found to be 1.7m/s2. This value of

acceleration of the spring mass is very high and undesirable

for the automobile. With respect unsprung mass, the

maximum overshoot is 30% and the acceleration is reduced

from 4 to 0.7 m/s2 and it is undesirable.

V. Popovic et. al [4] studied a quarter automobile

suspension system through two stages. They investigated

the passive suspension system as a first stage, then studied

the active suspension system with external actuator

excitation. They used Mat lab program to solve the state

space model.

A. Krishnan [5] solved the equations of motion of

the mathematical model of passive suspension system and

the control strategies that used for semi-active suspension

system, for 2DOFquarter automobile model. The solution

was performed by using the Simulink program. This paper

concluded that skyhook control can achieve more reduction

of resonant peak of the body mass than of passive

suspension and gives good ride comfort.

Gabor Licsko et. al [6] dealt with the study of

single stage relief valve embedded within a simple hydraulic

circuit. The goal is to catch the mechanism of instability of

such valves, taking into account both fluid compressibility

and the chattering behavior that can occur when the valve

poppet impacts with its seat. This study concluded that these

systems may lose their stability in case of self-excited limit

cycle vibrations. From this study and when using linear

stability analysis, it was obtained a criterion for stability

related with flow rate and damping coefficient. It was also

found that an increasing of damping coefficient makes the

system to be more stable, and if the damping is moderate, it

leads to avoidance of unstable limit cycle.

X. Xu, et. al [7] focused their study on modeling

and analysis of solenoid valve to improve performance of

shifting control system. The energy loss and dynamic

characteristics of this system are the important parameters to

improve the performance and operation of this valve. The

valve was considered as a potential component applied in

the shifting control system. The study presented a numerical

approach for solving the multi –domain problem of the

valve. The results of simulation agreed with that picked

from experimental data thus the mathematical model was

accurate and effective. Both the viscous and magnetic forces

were found to be influenced on the pressure response, when

the magnetic force responded quickly or the viscous force

Vibration Control of Automobile Suspension

System using Smart Damper

Abdulkareem Abdulrazzaq Alhumdany Ahmed Abdullah Hassan Al-Rajihy/University of Babylon, College

of Engineering/Almussyab, Ali T. Hassan / University of Kerbala/ College of Engineering



was increased, the pressure response time would be

decreased.

I. Mihai and F. Andronic [8] studied the semi-

active suspension system to remove undesirable oscillations.

Different kinds of control system have been developed

lately in order to obtain adjustable suspension. The

viscosity of the working fluid is altered using magneto

rheological or electro-rheological liquids. This study

concluded that, using semi-active system instead of passive

system leads to an almost total elimination of the system

oscillations. A reduction in the amplitude of the oscillatory

phenomenon and a reduction in the disruptive time,

constitutes a great advantage.

Barbara Zardin, et. al [9] proposed a two-stage

On/Off cartridge valves for automobile applications,

because of simplicity of this valve. The goal of this study is

for improving the performance characteristics of the valve,

allowing the managing of increased pressure and flow rate

levels, without changing the valve size. This study proposed

a new geometry to reduce the flow forces. The dynamic

behavior of the valve has been studied with a lumped

parameters model.

G.K. Sinha and U. Prasad [10] studied the quarter –

automobile model to investigate the response of suspension

system and to improve the vehicle handling, ride comfort for

large automobile such as bus. The improvement of

performance was done by using many controllers such as PI,

PID and H∞, based on step input signal. The study

concluded that for passive suspension system, the overshoot

observed as 0.08m from 0.1 m and settling time is 35 sec,

which means that the passengers feel low oscillation for

long time. Using PI controller, the overshoot reduced to

0.0058m and the settling time to 6 sec. Using PID controller,

the overshoot reduced to 0.0039 and the settling time to 2

sec.

This work investigated the efficiency of a proposed a smart

damper via a control valve, Fig. 1, to attenuate the

vibrations of automobiles due to road surface profile. The

idea based on dominating the flow rate of the hydraulic fluid

via the proposed control valve. The flow rate of the

hydraulic fluid is controlled by controlling the flow area

which depends on the dynamic characteristics of the control

valve. The mathematical model, which based a quarter

automobile model, is solved by Mat lab/Simulink programs

to compute the response of the control valve and automobile

body. The efficiency of the control valve is tested by

observing the response of automobile body when subjected

to step and impulse inputs.

Fig. 1. Schematic diagram of the proposed smart damper consist of main

damper (1), directional valve (2), and control valve (3) which represent the

main objective of this investigation.

II- MATHEMATICAL MODELLING

II-a- Modelling of a Quarter –Automobile

Suspension System

The mathematical model of the two DOF quarter –

automobile model is defined by two differential equations

which obtained by applying Newton's second law of motion

taking into account the following assumptions [2] and [3];

Vehicle moves as a rigid body with respect to

suspension system.

Suspension system consists of linkage, sprung,

damper, sprung mass, and un-sprung mass.

Tire stiffness and damping are considered

separately [3].

In this study, a quarter automobile model is considered

which is composed of main sprung, main damper, tire

stiffness and tire damping. The model is represented

schematically in Fig. 2.



According to the coordinates shown in Fig. 2, the equation of motion of the sprung mass of a quarter automobile model can

be written as [3];

(1)

The motion of the wheel set (unsprung mass) is given by the following equation,

(2)

The above two equations are two ordinary differential equations coupled by y1 and y2 coordinates can be solved by many

methods of solutions. One of the powerful methods used to solve such equations in the field of control is the "State Space"

method, which has a very good flexibility to deal with wide range of differential equations of input-output systems.

To represent equations (1) and (2) in the state-space, assume [4]:

(3)

(4)

Also it is assumed;

(5)

Where zr is the input disturbance and y is the output.

Using Eqns. (3), (4) and (5) into Eqns. (1) and (2), the input/output relations can be represented by the following two

relations as;

Fig. 2. Schematic diagram coordinates of a Quarter-automobile model



(6a)

) (6b)

Where x, is the vector of states, A and B are the system matrices which are given by;

(7a)

(7b)

C: Represent the output matrix and written as;

(7c)

D: represent the disturbance matrix which is;

(7d)

The set of equations (6) and (7) can be solved by Mat lab/Simulink programs to find displacements, velocities and

accelerations of sprung and unsprung masses[5], [11] and [12].

II-b- Modeling of the Control Valve

The function of the control valve is to restrict the flow rate of the hydraulic oil during rebound stroke to give variable

damping effect. Accordingly, the displacement of the control valve nose is related to the speed of the rebound of piston of the

main damper and in turn the speed of the main damper affected by the displacement of the control valve nose. In other words,

the rebound speed and displacement of the control valve nose are interrelated.

The mathematical modeling of the control valve lies in two lines which are the "Flow rate conservation" line and the "Valve

dynamics" line.

II-b-1 Flow rate conservation

To derive the relations of the flow rate of the hydraulic oil, four assumptions are documented to simplify the complexities of

the problem mathematics. These assumptions can be summarized, as;

No leakage of hydraulic oil to the surrounding of damper or between compression and rebound states.

Incompressible fluid.

Constant density of oil.

Constant viscosity of oil.

The direction of flow of the hydraulic oil is regulated by the direction switching valve (one-way valve which allow free flow

during compression state), while the amount of flow rate of the hydraulic oil is controlled by the "control valve". According

to the above assumptions, the equation of continuity can be applied to the flow rate that swept by damper piston which passes

through the control valve.

This continuity is;



(8)

Where represent the flow rate swept by damper piston during rebound, and is the flow rate passes through the

control valve.

The flow rate that swept by damper piston through the rebound stroke is given by the following equation;

(9)

Where, represent the annual area of damper, and Cf is the ratio between the area of the piston to the area of

flow and taken to be 0.8 [13].

The swept flow rate given by (9) is the same that passes through the control valve, thus the flow rate through the control valve

is written as:

(10)

According to the assumption of density constancy, the solution of Navies-Stoke equation gives the flow drag force created by

oil flow faced to the valve nose. This drag force is given by [7, 9]:

(11)

The flow velocity through the control valve is given by:

(12)

Where, is the area of flow through the control valve which it is given by;

(13)

Substituting Eq. (12) in Eq. (11) results in;

(14)

The face of the control valve nose also subjected to a force (Fh) delivered from the hydraulic pressure equal to;

(15)

Where is the projected area of valve nose that faced to hydraulic flow, and P is the hydraulic pressure.

Now, the nose of the control valve will be subjected to both the flow drag force given by Eq. (14), and the pressure force

given by Eq.(15). The summation of these two forces gives the total force that generated on the face of the valve nose which

is written as;

(16)

The effective area of hydraulic flow through the control valve according the geometry shown in Fig. 3 is given by;

(17)

The area Ap is given by:

(18)

The pressure delivered in the main damper during rebound state is;

(19)

Now, the pressure force, Fh is;



(20)

The total force generated on the face of the valve nose, Eq. (16), will take the force;

(21)

II-b-2 Dynamics of the Control Valve:

The equation of motion of the control valve nose can be derived by using Newton's second law based on the coordinates

shown in Fig. (3);

(22)

The right hand side of Eq. (22) is the total force applied on the face of valve nose that given by Eq. (21).The interaction

between Eqns. (1), (2) and (22) relate the dynamics of the control valve and the motion of suspension system.

Fig. 3. Schematic diagram coordinates of a Quarter-automobile model

III-Vibration Control of Automobile Suspension Strategies

The vibration control strategy is the technique that used to achieve the controlling for automobile suspension. When the

automobile match over different road profile, the disturbance transmitted to the sprung mass and then transmitted to the

passengers inside the automobile. To get the suitable ride comfort for the passengers and good road handling for the vehicle

and high stability, it must reduce the vibration of sprung mass to be minimum. This can be achieved by choosing one strategy

of control figure (4) illustrated the diagram of system control.



Fig. 4. Vibration Control of Automobile Suspension Strategies

IV- Optimization of Control Valve Parameters

The process of optimization is applied to the parameters of

the control valve in order to obtain the best damping effect

to the suspension system. This process includes the moving

mass of the control valve, stiffness of valve spring, and

diameter of valve throat.

The optimization process is done by solving the governing

equation of the control valve, Eq. (22), using unit step input.

The optimization process of the parameters of the control

valve is based on time response of the control valve. The

optimum value for each parameter is selected when the time

response of the control valve reaches minimum overshoot,

minimum steady state error and settling time [2], [14].

The response of the moving part (nose) of the control valve

is plotted in Fig. 5 as a function of its mass. From this figure

the optimum mass of the moving part of the control value is

found to be (70) grams. This value is taken when the settling

time reach unnotable change with changing mass value. The

optimum value of valve spring stiffness is estimated from

Fig. 6 by drawing the displacement and settling time of the

moving part of the control valve as a function of valve

spring stiffness. From this figure one can select the optimum

value of the valve spring stiffness at the point of intersection

between the displacement curve and settling time curve. The

intersection point show that the valve spring stiffness is

11000 N/m. The best value of the control valve orifice is

drawn from Fig. 7 when the displacement and settling time

reach maximum values.

Fig. 5. Optimization process of Mass of the control valve nose.



Fig. 6. Spring constant optimization of control valve

The performance of the control valve affects on the efficiency of the suspension system. This can be illustrated by the

response of the sprung mass to the road profile (bumps), compared with other published work. The response of the suspension

system is performed according to the optimized parameters of the control valve which are listed in Table 1. The values of the

parameters of the suspension system are given in table 2.

Fig. 7. Diameter optimization of control valve.



Table I

Optimum values of the control valve parameters.

No. Parameters Value Unit

1 Diameter of control valve 0.015 m

2 Spring stiffness of control valve 9768 N/m

3 Damping coefficient of control valve 10 N.s/m

4 Mass of moving part of the control valve 70 Gr

5 Density of hydraulic oil 890 kg/m3

6 Angle of control valve nose, θ 45 Degrees

7 Area factor, Cf 0.7 -

Table II

Parameters of suspension system [3]

No. Parameters Value Unit

1 Sprung mass, m1 275 kg

2 Unsprung mass, m2 27 kg

3 Spring stiffness of suspension, K1 150000 N/m

4 Damping coefficient of suspension, B1 1120 N.s/m

5 Tire stiffness, K2 310000 N /m

6 Tire damping coefficient, B2 3100 N.s/m

7 Annual area, (AP-AR) 7E-7 m2

V- RESULTS AND DISCUSSIONS

The results of the analysis of the suspension system of the

quarter automobile represent the response of the sprung

mass based on the optimized parameters of the control

valve. The optimized parameters of the control valve and

others are listed in table 1, and the parameters of the

suspension system are listed in table 2.

Figure 8 shows the response of the control valve nose when

subjected to a step pressure input delivered from the main

damper of suspension system during the rebound stroke. It is

seen that the settling of the control valve nose is about 0.07

sec. This value of settling time reflects the fast steady state

damping control for the suspension system. The effective

area of flow of the hydraulic oil through the valve is plotted

in Fig. 9. When the valve nose subjected to the same input

used in Fig. 8. It can be deduced from Figs. 8 and 9 that the

effective area of flow is proportional to the displacement of

the control valve nose.

The displacement of the control valve nose and the

corresponding effective area of hydraulic oil flow are shown

in Figs. 10 and 11 respectively when the valve subjected to

pressure impulse input. These two figures show that the

valve return to its initial state in a short period after input

termination. The fast response of the control valve and its

short settling time reflects the efficiency of the control valve

in controlling the hydraulic oil flow which in turn reflects in

turn an efficient vibration control to the sprung mass.

Figures 12 and 13 show the response of the sprung mass

(body of automobile) when the tire of automobile excited by

a 0.1m step input and 0.1m impulse input respectively.

These results represent the present work (smart damper)

and those for the traditional passive damper given by[3].

From these figures it can be seen that the smart damper

presented in this work, makes a notable improvement for

the response of the sprung mass by the fast and hard

attenuation compared with that for passive damper.

The fast attenuation of response of the sprung mass to the

external excitation is due to the smart resrtriction of

hydraulic oil flow through the control valve. The smart

restriction of the hydraulic oil flow makes the damping of

the suspension system to be varied in strength and softness

as the input excitation strengthed or softened. Figure 14

shows the response of the sprung mass to random excitation

for both the traditional passive damper given by [8] and the

smart damper presented in this work.

From the ride comfort point of view, the fast attenuation of

the sprung mass to the external excitation gives an

indication for ride comfort for both driver and

passengerswhich is the main objective of this investigation.



Fig. 8. Displacement response of control valve nose when subjected to step pressure input.

Fig. 9. Effective area of flow through control valve subjected to step pressure input.



Fig. 10. Displacement response of control valve nose when subjected to impulse pressure input.

+

Fig. 11. Effective area of control nose valve subjected to impulse pressure input.



Fig. 12. Response of sprung mass to step input of 0.1 m amplitude.

Fig. 13. Response of sprung mass to impulse input of 0.1 m amplitude.



Fig. 14. Response of sprung mass to random input.

VI- CONCLUSIONS

In this paper, the performance of a proposed smart

damper used to control vibrations of automobiles is

investigated. The mathematical model is based on a

quarter automobile model. From the simulation

results, the following important conclusions can be

withdrawn:

Fast attenuation of vibrations induced by

disturbance excitations due to irregular

road surface.

A total elimination of the system

oscillations.

The proposed smart damper satisfy ride

comfort to the driver and passengers.

The damping which is controlled by the

control valve is not constant as that for

traditional passive damper, but it is a

function of disturbance excitation.

REFERENCES

[1] O. Ghasemalizadeh, S. Taheri, A. Singh, and J. Goryca, “Semi-

active Suspension Control using Modern Methodology: A

Comprehensive Comparison Study,” in 2014 NDIA GROUND VEHICLE SYSTEMS ENGINEERING AND TECHNOLOGY

SYMPOSIUM MODELING & SIMULATION, TESTING AND

VALIDATION (MSTV) TECHNICAL SESSION, 2014, no. August, pp. 1–24.

[2] G. Verros, S. Natsiavas, and C. Papadimitriou, “Design

optimization of quarter-car models with passive and semi-active

suspensions under random road excitation,” JVC/Journal Vib.

Control, vol. 11, no. 5, pp. 581–606, 2005. [3] P. Sharma, N. Saluja, D. Saini, and P. Saini, “Analysis of

Automotive Passive Suspension System with Matlab Program Generation,” Int. J. Adv. Technol., vol. 4, no. 2, pp. 115–119,

2013.

[4] V. Popovic, B. Vasic, M. Petrovic, and S. Mitic, “System approach to vehicle suspension system control in CAE

environment,” Stroj. Vestnik/Journal Mech. Eng., vol. 57, no. 2,

pp. 100–109, 2011. [5] A. Rijumon K, Murtaza M A, Krishnan, “a Comparison Between

Passive & Semi Active Suspension Systems,” Int. J. Innov. Res.

Sci. Eng. Technol., vol. 2, no. 6, pp. 2412–2416, 2013. [6] Gábor Licskó, Alan Champneys and Gsaba Hos, “Dynamical

Analysis of a Hydraulic Pressure Relief Valve,” in Proceedings

of the World Congress on Engineering 2009 Vol II WCE 2009, July 1 - 3, 2009, London, U.K., 2009.

[7] X. Xu, X. Han, Y. Liu, Y. Liu, and Y. Liu, “Modeling and

Dynamic Analysis on the Direct Operating Solenoid Valve for

Improving the Performance of the Shifting Control System,”

Appl. Sci., vol. 7, no. 12, p. 1266, 2017.

[8] I. Mihai and F. Andronic, “Behavior of a semi-active suspension system versus a passive suspension system on an uneven road

surface,” Mechanika, vol. 20, no. 1, pp. 64–69, 2014.

[9] B. Zardin, M. Borghi, G. Cillo, C. Alberto Rinaldini, and E. Mattarelli, “Design of Two-Stage On/Off Cartridge Valves for

Mobile Applications,” Energy Procedia, vol. 126, pp. 1123–

1130, 2017. [10] G. K. Sinha and U. Prasad, “Vibration Control of Car Suspension

System Using Different Controllers,” in International conference

on Emerging Trends in Engineering, Technology, Science and Management, pp. 20–30.

[11] R. Herman, S O LV I N G D I F F E R E N T I A L E QUAT I O N



S U S I N G S IMU L I N K. 2017.

[12] D. I. Wilson, Advanced Control using MATLAB or Stabilising the unstabilisable. 2016.

[13] Csaba Bazso Csaba Hos, “On the Static Instability Of Liquid Popet Valves,” Periodical Polytechnica Mechanical

Engineering,59(1), pp. 1-7, 2015.

[14] Sung Won Kum, Youngmin Seo, Manjin Ahnaand and Yoonseok Jang, “Optimization of Poppet Shape to Minimize Override on

Direct acting Relief Valve,” Proceedings of the 9th JFPS

International Symposium on Fluid Power, Matsu, 2014, Oct. 28-31, 2014, 2014, vol. l, pp. 254–260.

Professor Ahmed Abdullah Hassan Al-Rajihy, Staff member in University of Babylon, College of Engineering-Almusayab. PhD. In

Mechanical Engineering, Applied mechanics. Interested in system

dynamics, vibrations, and dynamics of fluid-structure system interaction. Official E-mail;

[email protected]&[email protected]

m

Assistant Professor Abdulkareem Abdulrazzaq Alhumdany Staff member

in University of Babylon, College of Engineering-Almusayab. PhD. In Mechanical Engineering, Applied mechanics. Interested in

vibrations and tribology. E-mail;

[email protected] [email protected]

Ali T. Hassan, Mechanical Engineering, Applied Mechanics.

mailto:[email protected]



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