Influence of Tire Stiffness on Automotive Quarter Car Suspension System

 

Patel Sanjay M.^1*, Dr. Patel A. D.²

¹Ph.D. Scholar, CSPIT, CHARUSAT University, Changa-388421, India

²Principal, CSPIT, CHARUSAT University, Changa-388421, Gujarat, India.

 

ABSTRACT:

Quarter car automotive suspension model is the model with two degrees of freedom system, which is used for the analysis of ride comfort and vertical movement of the vehicle. It represents the analysis of vehicle suspension system at any one wheel out of all four wheels; it means the vertical motion of the vehicle body at any one wheel of the vehicle is being analyzed to check the performance. Automotive suspension designs have been always compromise between road handling, road holding and passenger comfort. This paper describes the dynamic model of quarter car automotive suspension system for bump condition prepared in MATLAB using Simulink. The influence of varying values of tire stiffness on vertical acceleration of the vehicle has been discussed in this paper. The results obtained from the simulation of simulink model are used for performance investigation and analysis of the dynamic behavior of the vehicle.

 

 

 

INTRODUCTION:

Road handling, comfort of passengers, and load carrying capacity are three conflicting criteria, which are very important during automotive suspension designs. So, the designers have to always compromise between these three criteria during design synthesis process. The suspension system provides directional control [1] by using different handling characteristics and ultimately prevents the transfer of forces from road surfaces to vehicle body.

 

A soft suspension gives good ride comfort and on the other hand, a stiff suspension provides better road handling with less settling time. So, the design of suspension must be an optimized compromise between these criteria [1, 2]. Tianbing et al. studied the vibration characteristics of the vehicle, and formulated equations of motion [3]. Natural frequencies, damping ratio, transfer function and state space formulation for quarter car model can be determined by mathematical modeling and vertical acceleration can be determined by simulation of simulink model prepared in MATLAB.

 

VEHICLE SUSPENSION:

The typical function of a vehicle suspension system is to provide isolation to a vehicle body from different kind of road disturbances to enhance the ride quality of passengers. For the purpose of luxury in automobiles, a suspension with lightly damped softer springs is designed for comfortable ride. On the other hand, for better stability and handling, the sports cars are designed with heavily damped stiff springs at the cost of luxury and comfort [4]. The ideal suspension is one which gives optimum result between conflicting parameters like ride comfort and road holding [5]. Safety is also a prime issue at the same time which can be achieved by keeping wheels always in contact with the road surfaces in all kind of situations by providing road holding characteristics. When a vehicle is in motion, it could slip, skid, overturn or experience other forms of dynamic behavior. The problem of evaluating dynamic behavior of a vehicle then could cover a very wide scope. The major factors affecting the vehicle dynamics and stability include vehicle geometry, weight distribution, suspension system, tires, maneuvering condition (lane changing, cornering, accelerating, decelerating etc.), road condition and applied external forces. Any combination of these factors can make the problems quite complicated [6, 7]. Vehicle dynamics research is generally focused on specific subset of overall vehicle operation, such as acceleration or braking performance in a straight line, handling characteristics at constant forward speed, roll dynamics and ride quality etc. The formulation of an adequate vehicle dynamic model is essential for any simulation which reliably predicts the dynamic behavior of vehicles under different operating conditions. The simulation models used can range widely in complexity and accuracy for evaluating the dynamic response of a single vehicle or an articulated vehicle [8, 9]. Current systems of vehicle dynamics were generally developed by considering vehicles driving on a level ground. However, when a vehicle is driving on an inclined or banked road surface, additional longitudinal or lateral weight transfer is introduced. On the other hand, the total vertical load imposed on the wheels is also reduced. These effects will change the distribution of the vertical load on each tire and will, in turn, affect the dynamic properties of the tire and the dynamic behavior of the vehicle [10].

 

QUARTER CAR SUSPENSION MATHEMATICAL MODEL:

The conventional quarter car automotive suspension model can be mathematically and graphically represented as shown in figure 1.

 

Figure 1: Quarter car suspension model

The quarter car model represents the motion of the vehicle at any of the four wheels. It means, the analysis of any one wheel out of four wheels of the vehicle is done for the performance analysis. The tire is considered as a spring in the system. The suspension is converted as spring and damper for the modeling purpose. This spring and damper is taken in parallel. The vehicle body represents the sprung mass, and the mass of the vehicle which is not supported by suspension system represents unsprung mass. So, axle and tire mass is taken as unsprung mass in modeling. In mathematical model, Zs, Zu, and Zr represent vertical motion of sprung mass, unsprung mass, and road respectively. This type of investigation provides more understanding of vehicle dynamics and allows the vehicle designers to build more powerful and safer vehicles [7].

 

QUARTER CAR SIMULINK MODEL:

A Simulink model of quarter car suspension system for bump type of situation was developed for the analysis using simulink in MATLAB.

 

Figure 2: Block of Sprung Mass for Quarter Car Bump Model

 

Figure 2 shows the block diagram of sprung mass for quarter car bump model prepared in simulink using Matlab.

 

Figure 3: Block of UnSprung Mass for Quarter Car Bump Model

Figure 3 shows the block diagram of unsprung mass for quarter car bump model prepared in simulink using Matlab.

 

For the simulation purpose, different data sets were used mentioning different parameters of the suspension. From the simulation results the dynamic behavior of vehicles for different parameters and conditions can be analyzed.

 

SIMULATION RESULTS & DISCUSSION:

Data Set 1:

Table 1: Parameters for data set 1

 

 

Figure 4: Vertical acceleration Vs Time for data set 1

 

Figure 4 shows simulation results for data set1 for quarter car suspension bump model. The value of vertical acceleration varies between 0.2254 to -0.2782 m/s² for data set1. Mean value of vertical acceleration found to be -0.0181. Total range of movement is 0.5036.

 

Data Set 2:

Table 2: Parameters for data set 2

 

 

Figure 5: Vertical acceleration Vs Time for data set 2

Figure 5 shows simulation results for data set2 for quarter car suspension bump model. The value of vertical acceleration varies between 0.6641 to -1.442 m/s² for data set2. Mean value of vertical acceleration found to be -0.016. Total range of movement is 2.106.

 

Data Set 3:

Table 3: Parameters for data set 3

Parameter	Value
Body Mass (Sprung)	2500 Kg
Mass of wheel/axle (unsprung)	320 Kg
Tire Stiffness	1000000 N/m
Suspension Stiffness	30000 N/m
Suspension Damping	2500 NS/m

 

Figure 6: Vertical acceleration Vs Time for data set 3

 

Figure 6 shows simulation results for data set3 for quarter car suspension bump model. The value of vertical acceleration varies between 0.6759 to -1.663 m/s² for data set 3. Mean value of vertical acceleration found to be -0.0157. Total range of movement is 2.339.

 

CONCLUSION:

In this paper, an attempt has been made to prepare the mathematical and simulink model of quarter car suspension system. Simulink model of quarter car suspension system for bump kind of situation has been prepared in MATLAB for analysis. The values of vertical acceleration can be found from the simulation of the model by substituting values of tire stiffness. The results show that the dynamic system of the vehicle should have low overshoot and the system should have small settling time so that it settles quickly. Better handling performance and minimum vertical car body acceleration for ride comfort can be achieved by having low overshoot and less settling time which is complimented by simulation results. The simulink model can be used with different input parameters to predict the dynamic behavior of the vehicle. 

 

ACKNOWLEDGEMENT:

We are thankful to Charutar Vidya Mandal (CVM), A.D. Patel Institute of Technology, and Charotar University of Science and Technology (CHARUSAT) for supporting this research work.

 

REFERENCES:

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9.       Jaitwar R. Sliding mode control of an active suspension system. MTech Thesis, IIT Guwahati, Ind. 2011.

10.     Creed B., Kahawatte N. and Varnhagen S. Design of an LQR Control Strategy for Implementation on a Vehicular Active Suspension System. University of California, Davis. 2010.

 

 

 

 

Received on 24.04.2017                             Accepted on 28.05.2017         

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