CHAPTER-VIRESPONSE OF PASSIVE AND SEMI-ACTIVE SUSPENSION SYSTEMS______________________________________________________________6.1 Introduction In order to compare the performance of semi-active suspension system using Sky-hook control algorithm and passive suspension system a 2 DOF quarter car model is considered with the following parameters mentioned in the Table. 6.1.

Table 6.1 Parameters of the passenger car model with various sizesParameters (symbols)Values

HeavyMediumLight car

Sprung mass (M)8200 kg1010 kg656 kg

Spring stiffness of front axle suspension (Ks) 0.4MN/m35,000 N/m15,000 N/m

Damping coefficient of axle suspension (Cs) 5kN-sec/m2kN-sec/m1189 N-sec/m

Stiffness of front tires( Ku)0.1MN/m0.25MN/m0.15MN/m

Damping coefficients of front tires (Cu)01,000 N-sec/m1500N-sec/m

Mass of front axle (M1)100 kg90 kg41kg

By using above parameters a study has been conducted to find out the Sky-hook response in terms of displacement, and acceleration of the three systems in Table 6.1.

6.1.1 Response study of heavy vehicle system Displacement response of the heavy vehicle system for a Sky-hook control strategy in a semi-active and passive suspension systems is shown in Fig. 6.1 which is simulated using MATLAB/SIMULINK for a quarter model with the dimensions given in Table. 6.1. Similarly, acceleration response of heavy vehicle quarter car model in frequency domain is plotted in Fig. 6.2. Fig. 6.1 Displacement response of heavy vehicle Time domainFrom the above Fig.6.1, the plot is observed between time and displacement for bump profile, displacement of sprung mass for passive and semi-active suspension system. For passive system maximum amplitude is 0.04m and for the semi-active system maximum amplitude occurred is 0.03m.

Fig. 6.2 Acceleration response of heavy vehicle frequency domainFrom the Fig. 6.2, acceleration amplitude of the sprung mass for passive and semi-active suspension are 0.23 m/s2 and 0.16 m/s2. It is observed that there is a shift in the peak for semi-active suspension system occurred due to variable damping.

6.1.2 Response study of medium vehicle systemDisplacement response of the medium vehicle system for a Sky-hook control strategy in a semi-active and passive suspension systems is shown in Fig. 6.3 which is simulated using MATLAB/SIMULINK for a quarter model with the dimensions given in Table. 6.1. Similarly, acceleration response of medium vehicle quarter car model in frequency domain is plotted in Fig. 6.4.

Fig. 6.3 Displacement response of medium vehicle Time domainFrom the Fig. 6.3 response of a sprung mass is observed in time vs displacement domain. It is found that maximum amplitude occurred at 0.025m and 0.019m for the passive suspension system and semi-active suspension system.

Fig. 6.4 Response of medium vehicle frequency domainFrom the Fig. 6.4 the acceleration response for the sprung mass is studied in frequency domain for the medium car model. It is found out that maximum response occurred at the natural frequencies of bounce mode of sprung mass i.e., at 1.2Hz for passive system with an amplitude of 0.27m/s2 and 1.4Hz for semi-active suspension system with an amplitude of 0.38m/s2 respectively. The shift in the peak occurred due to the with variation in damping coefficient in the semi-active suspension system.6.1.3 Response study of small vehicle systemDisplacement response of the small vehicle system for a Sky-hook control strategy in a semi-active and passive suspension systems is shown in Fig. 6.5 which is simulated using MATLAB/SIMULINK for a quarter model with the dimensions given in Table. 6.1. Similarly, acceleration response of small vehicle quarter car model in frequency domain is plotted in Fig. 6.6. Fig. 6.5 Displacement response of small vehicle Time domainFrom the Fig. 6.5 time displacement response of a sprung mass is studied, it is found out that the response of the passive system is slow and it took more to settle down when compared with that of the semi-active suspension system.

Fig. 6.6 Acceleration response of small vehicle frequency domain From Fig. 6.6 the acceleration response of sprung mass is studied in frequency domain for the small car model. It is found that maximum response occurred at the natural frequencies of the system for the bounce mode of sprung mass i.e., at 1.2 Hz with an amplitude of 0.39 m/s2 for passive suspension system and 1.4 Hz with an amplitude of 0.26 m/s2 for semi-active suspension system. From above analysis of quarter car models it is found that with sky-hook control strategy in semi-active suspension system the improvement in acceleration of sprung mass is 38 %, 32% and 30% respectively for heavy, medium and small vehicle models. A penalty of 8% is taken into account for the small car model while adopting sky-hook control strategy to find the response of the sprung mass for ride comfort traversing over various road profiles.

6.2 Various road testsA comparison is drawn between passive suspension system and semi-active suspension system by considering different road excitation for a full car model.6.2.1 Response to circular bump excitationTransient excitation in the form of a circular bump is given as road input for full-car model moving at 20 kmph and simulation is carried out using MATLAB/SIMULINK in time domain for studying the displacement of the sprung-mass for passive and semi- suspension as shown in the Fig. 6.7

Fig. 6.7 Displacement of sprung mass passing over a circular bump - Time domain

From the Fig. 6.7,Sprung mass displacement magnitude for semi-active suspension system based on Sky-hook control algorithm is low when compared with passive suspension system. Also the maximum displacement of the sprung mass occurs earlier than that of the passive suspension system and there is no negative displacement. This shows that semi-active suspension system gives lower value of maximum sprung mass displacement for given bump road excitation hence compared with passive suspension system with less suspension travel. Using FFT the time domain data for acceleration of the sprung mass is converted into frequency domain. In the frequency domain maximum sprung mass acceleration amplitude of semi-active suspension system is less than that of the passive system. So, it shows that semi-active suspension system gives good ride comfort when compared to passive suspension system

Fig. 6.8 Acceleration response of sprung mass passing over a circular bump - Frequency domain Also, from the Fig. 6.8, in the mid-range frequency of 4-9Hz, where the natural frequencies for various parts of human body lie, we find that there is decrease in the amplitude, which reflects the increase in human comfort. Hence, semi-active suspension system with Sky-hook control is showing favourable results in terms of human comfort.

6.3 Response to pot-hole excitationSometimes will come across pot-holes on the rural roads. So, pot-hole excitation is given as input for the full-car model and simulation is carried out to find out the sprung-mass displacement for active and semi-active suspension systems.

Displacement (m)Time(s) Fig. 6.9 Displacement of sprung mass for pot-hole excitation - Time domain

From the above Fig. 6.9, it can be observed that semi-active suspension shows good vibration isolation characteristics by reducing the displacement of sprung-mass when compared to passive suspension system.

Fig. 6.10 Acceleration response of sprung mass for pot-hole excitation - Frequency domain Also, from Fig.6.10 frequency domain analysis for acceleration of sprung-mass it can be observed that there is decrease in amplitude of sprung mass acceleration at frequency of 1.2Hz, which indicates frequency corresponding to natural frequency of bounce of sprung-mass.

6.4 Response to harmonic road excitationA sinusoidal input as developed in chapter-3, Fig. 3.10, with amplitude of 0.01m is given as road excitation to the full-car model, where a passive and semi-active suspension system sprung mass displacement responses are compared.

Time ( s) Displacement (m) Fig. 6.11 Displacement of sprung mass for harmonic excitation - Time domainFor harmonic road excitation as represented in the Fig. 6.11, a comparison is drawn between passive and semi-active suspension system for the sprung mass displacement. From the Fig. 6.6, for passive suspension system the sprung-mass displacement is higher than the road excitation amplitude and for the semi-active suspension system there is decrease in displacement amplitude for sprung mass.

Fig. 6.12 Acceleration of sprung mass for harmonic excitation - Frequency domainFrom the Fig. 6.12, frequency domain analysis for harmonic road excitation, we can see the representation of passive and semi-active suspension system acceleration response. For, passive system there is a peak value of acceleration amplitude which is much higher compared to that of semi-active suspension system.6.5 Response to random road excitationThe full car model is fed with random road profile shown in Fig. 3.12 and the displacement response of the sprung mass is studied in the time domain analysis.

Fig. 6.13 Displacement of sprung mass for random excitation - Time domainFrom the Fig. 6.13, displacement of sprung mass with respect to time is studied for passive and semi-active suspension system. It is found that for semi-active suspension system there is decrease in amplitude of vibration to the sprung mass when compared with that of passive suspension system.

Accleration(m/s2)Frequency(s) Fig. 6.14 Acceleration of sprung mass for random excitation - Frequency domainFrom Fig. 6.14, frequency domain analysis of random road excitation, we can observe various peaks occurring due to bounce, rolling and pitching. Due to experiencing of random vibration rolling and pitching which are predominant during steering and accelerating conditions are also occurring in this excitation. From the above Fig. 6.14 frequency peaks are occurring at 0.8, 1.2, 1.5 Hz which indicates the natural frequencies for mode of vibration of rolling, bouncing and pitching. Also, from the figure we can conclude that there is decrease in the amplitude of vibration to sprung-mass when compared to passive suspension system.So, therefore from the above analysis of semi-active suspension and passive system we can observe that there is decrease in amplitude of vibration transmitted to the sprung-mass for semi-active active when compared with passive suspension system.

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