ISSN: SIMULATION AND ANALYSIS OF PASSIVE SUSPENSION SYSTEM FOR DIFFERENT ROAD PROFILES WITH VARIABLE DAMPING AND STIFFNESS PARAMETERS S.

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1 Journal of Chemical and Pharmaceutical Sciences ISSN: SIMULATION AND ANALYSIS OF PASSIVE SUSPENSION SYSTEM FOR DIFFERENT ROAD PROFILES WITH VARIABLE DAMPING AND STIFFNESS PARAMETERS S. Prabhakar *, Dr.K.Arunachalam 1 Department of Automobile Engineering, Anna University-M.I.T Campus, Chennai, India *Corresponding author: prabhakarucevmec@gmail.com, ABSTRACT The main aim of this paper is to simulate the passive suspension system for quarter car model with variable damping and stiffness parameters. Recent automotive suspension systems uses passive components utilize only fixed rate of spring and damping parameters. Vehicle suspension systems are characterized by its ability to provide good ride comfort and handling improvisation. Conventional passive suspension offers a compromise between these two conflicting criteria. The stiffness more widely variable by virtue of having controllable air springs in parallel along with conventional suspension and also if the stiffness varies in accordance to that a small amount of damping also varies. Using variable damping and stiffness parameters the suspension can provide optimal performance. The disturbances are mostly in the form of various modelled road profiles (terrains) that the unsprung mass (wheel) comes in direct contact with and which in turn are transmitted to the sprung mass (body) of the system causing undesirable vibration or shaking that may cause discomfort to passenger. Thus the idea behind this study is to come up with the solutions that can minimize this discomfort condition as well as with better road holding. Comparison between conventional passive suspension system and passive suspension with variable damping and stiffness parameters is done with the help of different types of road profiles simulations. Finally the results are compared with the help of graphs. Keywords: Quarter Car model, Passive Suspension system, Road Profile, Variable Damping INTRODUCTION coefficient Conventionally Automobile suspension strategies have been a compromise among three contradictory criteria of road holding, rattle space requirements and ride comfort of passenger. The suspension arrangement need to take care of the vehicle handling parameters during vehicle moving over a terrain and be responsible for effective separation of passengers from road disturbances (Robert L.W 1997). Though a passive suspension system has the capacity to collect the energy through a spring and to drive away it via a shock absorber, their factors are normally fixed. These fixed parameters support to attain a definite level of settlement among road holding and comfort by the selection of different stiffness and damping parameters (Robert L.W 1997). The problem of passive suspension is if its design is heavily damped or too hard suspension occurs, it will either transfer a lot of road input or throw the car on unevenness of the road (Abdolvahab, 212). The ride comfort is improved by means of the reducing the car body acceleration caused by the irregular road disturbances (Sharp, 1986). Works in literature has been done to analyze and optimize the performance of passive suspension for a particular road response by means of different methods viz. examination through the state space modelling in MATLAB and in conclusion through physical modeling using Adams (Yue, 1988; Changizi, 211). State Space modeling of passive suspension: The vehicle model considered in this study is quarter car model. The quarter car model suspension system consists of one-fourth of the body mass, suspension components and one wheel (Thompson, 21) for passive suspension system is shown in Figure 1. The assumptions of a quarter car modelling are as follows: 1. The tire is modeled as a linear characteristics spring deprived of damping, 2. There is no rotating motion in wheel as well as frame, 3. The performance of spring and damper remain linear characteristics, 4. The road wheel is continuously in contact with the lane surface and result of resistance is ignored so that the residual essential damping is not taken into vehicle modelling (Thompson, 21; Sun, 22). Figure 1 shows a basic two-degree-of freedom system representing the model of a quarter-car. The model consists of the sprung mass m s and the unsprung mass m u. The tire is modelled as a linear spring with stiffnessk t. JCHPS Special Issue 7: 215 NCRTDSGT 215 Page 32

2 Journal of Chemical and Pharmaceutical Sciences ISSN: The suspension system consists of a passive spring K s and a damper C s. System of equation about sprung mass (m s) and unsprung mass (m u) are shown in equation 1 and equation 2 respectively. m s. x s + C s (x s x u) + K s (x s x u ) = (1) m u. x u + C s (x u x s) + K s (x u x s ) + K t (x u x r ) = (2) Figure 1.Quarter car model The State space model of the quarter car automotive suspension system is given by the equation 3. x = Ax + B. F a + L. x r (3) For passive suspension Fa=.The states of the system is given by x 1 = x s x u, Suspension deflection x 2 = x s, Absolute velocity of Sprung mass x 2 = x u x r, Tire deflection x 4 = x r, Absolute velocity of unsprung mass Values of State Space model is represented as shown in equation B = A = 1 M s K s B s M s M s 1 [ K s B s K t B s M s B s + B t ] (5) (4) { 1 } L = 1 (6) B t { } The following three transfer functions (equation 7, 8 and 9) are of interest and their attenuation will be used to judge the effectiveness of the suspension system: Acceleration Transfer Function: H A (s) = Z (s) (7) Z r (s) Rattle space transfer function: H RS (s) = Zs(s) Zu(s) (8) Z r (s) Tire deflection transfer function: Zu(s) Zr(s) H TD (s) = Z r(s) (9) JCHPS Special Issue 7: 215 NCRTDSGT 215 Page 33

3 Journal of Chemical and Pharmaceutical Sciences ISSN: III. Simulation of passive suspension using MATLAB The following values of parameters are typical for a passenger sedan: Cs=1; Suspension Damping value in N-s/m. Ks=16; Spring Stiffness N/m. Ms=25; Sprung mass in kg. Mu=45; Unsprung mass in kg. Kt=16; Tire stiffness in N/m. Ct=; Tire Damping value in N-s/m. The above values are given as the input to the simulation. The obtained results from simulation are discussed as below. The road bump (step input) can be described using the following equation (6). Its value is 1 only when the value of t is greater than or equal to 1. For other values the value is. Figure 2 depicts the road profile for 1-step input X r = { 1, t 1, otherwise (6) Sprung mass accelaration(m/s 2 ) Frequency response-effect of various damping on Sprung Mass Accelaration Cs=5 Cs=1 Cs=15 Cs=2 Figure 2: Road profile 1-step input Figure 3: Sprung mass velocity for different damping values (Road Profile1) Figure 4: Frequency response of sprung mass acceleration for different damping values (Road Profile 1) Figure 5: Frequency response of suspension deflection for various damping parameters Figure 8: Frequency response of Suspension deflection for various suspension stiffness values (Road Profile 1) Figure 6: Frequency response of Tyre Deflection for various Damping values Tyre Deflection(m) Frequency response-effect of Spring stiffness on tyre deflection Kt/Ks= Frequency (rad/sec) Figure 9: Frequency response of Tire deflection for various suspension stiffness values Figure 7: Frequency response of sprung mass Acceleration for Various Spring Stiffness values (Road Profile1) Frequency response-effect of various Tyre Stiffness on Sprung mass Accelarataion 1 2 Sprung mass accelaration(m/s 2 ) Kt/Ks= Figure 1: Frequency response of sprung mass Acceleration for various Tyre Stiffness values JCHPS Special Issue 7: 215 NCRTDSGT 215 Page 34

4 Journal of Chemical and Pharmaceutical Sciences ISSN: Suspension deflection(m) Frequency response-effect of Tyre stiffness on Suspension deflection 1 Kt/Ks= Figure 11: Frequency response of Suspension deflection for various Tyre Stiffness values Figure 12: Frequency Response of Tyre Deflection For various Tyre stiffness values Figure 13: Random Road Profile (Road Profile 2) Figure 14: Suspension deflection for Road Profile 2 Figure 15: Suspension velocity response for Road Profile 2 Figure 16: Sprung mass Acceleration for Road Profile 2 The observation obtained from figure 3 is that whenever there is smaller amount of damping, the sprung mass displacement is higher. If the damping is too higher the force transferred to the sprung mass is damped so the sprung mass movement is restricted. If the suspension is provided with too higher damping it damps the vibration of the system within shorter period but the problem associated with this is the direct transfer of initial stage forces occurs. If the initial force transfer is high then it produces discomfort of passengers present inside the vehicle. So the optimization of damping and stiffness is required. In order to study the various effects of specific suspension parameters on the suspension performance, we analyze the system in the frequency domain. The mode corresponding to the first natural frequency predominantly consists of sprung mass motion. This mode is therefore called the sprung mass mode. The mode corresponding to the second natural frequency is called the unsprung mass mode. The effects of increasing suspension damping only are studied by varying the damping C s as follows 5,1,15,2. From figure 4, the higher damping is seen to reduce the resonant peak of the acceleration transfer function but at the cost of high frequency harshness i.e. slower roll-off in sprung mass acceleration at high frequencies. From figure 5, we can observe that the higher damping reduces the resonant peaks in the suspension deflection transfer function thus leading to significant overall improvement in suspension deflection performance. The observation from figure 6 is that higher suspension damping also lead to the increasing damping ratios for both peaks in the tire deflection function i.e. Reduction of both natural frequency of the system occurs. The softer suspension is seen to provide better vibration isolation i.e., provides better reduction on the resonant frequency of sprung mass mode (can be seen graphically in figure 7). But there is no effect on the unsprung mass mode frequency. At high speeds on smooth roads, the low stiffness and light damping suggested from the conventional passive suspension may be such that the directional stability is poor, and if so, increase in damping should be made first, followed by switching immediately to the high stiffness (if needed) to correct matters, ride comfort being sacrificed. However the softer suspension provides better vibration isolation but the problem associated with this is, softer suspension requires higher rattle space requirements (Refer figure 8). The tire deflection performance with the variable suspension stiffness is shown in figure 9. Tire deflection is significantly reduced at sprung mass natural frequency. However it appears to have a higher peak at the unsprung mass resonant frequency due to reduced damping, since the tire by itself has little damping but we did not considering that for simplified analysis. By providing stiffer tire the resulting suspension is seen to provide significantly reduced tire deflections and hence better road holding and cornering performance. But the second JCHPS Special Issue 7: 215 NCRTDSGT 215 Page 35

5 Journal of Chemical and Pharmaceutical Sciences ISSN: resonant frequency gets increases. Also there is a little increase of sprung mass acceleration due to roll-off of the sprung mass acceleration transfer function occurring at higher frequency. From figure 11, the tire stiffness has the same effect on the suspension deflection as like the effect of tire stiffness on sprung mass acceleration. This is due to the increase in unsprung mass resonant frequency. The effect of tire stiffness on the tire deflection is shown in figure 12. Stiffer tire has reduced sprung mass mode frequency. But it has increased effect on unsprung mass mode frequency. A new road profile is generated randomly and shown in figure 13. Figures 14 to 16 show the response of the new random system. Analysis results of suspension system for ¼ car model for random road excitation shows that vehicle Suspension deflection (figure 14) has overshoot of 7% and peak amplitude of.8 m. These values are very low and suspension able to provide good comfort. Suspension velocity as shown in (figure 15) varies from.2 m/s to.4 m/s.the sprung mass acceleration having considerable lower values. The settling time is quite satisfactory. RESULTS AND DISCUSSION In addition to providing vibration isolation for the vehicle body, an automotive suspension strongly influence the cornering, traction and handling parameters as well as the rattle space requirements of the vehicle. Results of the MATLAB simulations are compared with the ADAMS model results. From that the optimized value for the ride comfort as well as handling for the typical passenger car is Cs=15 N-s/m, Ks= N/m, Kt=192 N/m. And for the better rattle space requirements optimized values are given as Cs=2 N-s/m, Ks= N/m, Kt=24 N/m. REFERENCES Abdolvahab, Agharkakli, U. S. Chavan, and Dr S. Phvithran, Simulation And Analysis Of Passive And Active Suspension System Using Quarter Car Model For Non-Uniform Road Profile, International Journal of Engineering Research and Applications, 2(5), 212, Changizi, Nemat, and Modjtaba Rouhani, Comparing PID and fuzzy logic control a quarter-car suspension system, The Journal of Mathematics and Computer Science, 2(3), 211, Robert L.W. & Kent L.L, Modeling and Simulation of Dynamic System, Second Edition, Prentice-Hall, Sharp, R.S. and Hassan, S.A, Evaluation of Passive Automotive Suspension Systems with Variable Stiffness and Damping Parameters, Vehicle System Dynamics, 15(6), 1986, Yue, C., Butsuen, T. and Hedrick, J.K, Alternative Control Laws for Automotive Suspensions," Proceedings of the American Control Conference, 1988, JCHPS Special Issue 7: 215 NCRTDSGT 215 Page 36