Global Journal of Researches in Engineering, A: Mechanical & Mechanics, Volume 22 Issue 1

road excitation to the tire of a vehicle used as part of a quarter car model. This method has been applied in many previous studies such as Florin et al. [14] and Mehdi et al. [15]. Magnetorheological (MR) is one of the most recent and widely used applications in semi-active suspension systems. It consists of an intelligent device whose function is to dampen the vibrations to reach a relatively acceptable vibration amplitude that meets the requirements for vehicle ride comfort. Usually, the magnetorheological is based on the generation of a magnetic field using a direct current from the controller affecting the coil in the magnetorheological MR, and this causes the MR fluids to change from a viscous liquid state to a semi-solid state in the resistance gap [16-18] . The active suspension system is characterized by the presence of a linear actuator beside the spring and damper. The linear actuator can be either a hydraulic actuator or an electric motor. The role of the linear actuator is to generate the force required for the suspension system to be more comfortable and the vehicle more stable during varied driving conditions [19- 21]. Modelling of vehicle suspension systems can be simulated as a quarter car, which deals with two degrees of freedom [22]. Two masses are used in the quarter-car model: a sprung mass and an unsprung mass. The sprung mass includes the chassis, body, engine, and cabin. The sprung mass is carried over the spring and damper system [23]. Un-sprung masses are the axle and tire masses and are installed down the spring and damper system [24]. The quarter model of vehicle suspension system performance can be introduced with sprung mass vertical acceleration, tire dynamic load, and suspension working space ] 25 .[ To evaluate the vibrational behaviour of the vehicle while traveling over the bumps, Fakhraei et al. [28] assumed that the hump function is part of a sinusoidal wave for the circular humps, while for the rectangular humps, it was expressed as a function of the amplitude (height), the length of the bump and the frequency (vehicle speed). They studied the effect of traveling over humps on non-linear dynamic behaviours as well as ride comfort for the vehicle and driver. A mathematical model was presented, by solving the differential equations and then evaluating the ride comfort by calculating the RMS value of the vertical displacement of the vehicle body and the driver . Other works have presented theoretical research aiming to reduce the cost of that which uses magnetorheological MR damper such as Ghoniem et al. [32] who have used a new, low-cost damper for the application of the vehicle's semi-active suspension systems. The strategy of this system is based on changing the damping coefficient is adapted using an artificial neural network controller by controlling the throttle opening area. A controller was trained based on the data obtained from the PID controller. The results showed that the proposed new suspension system provides a cheaper alternative to commercially available semi-active suspension systems based uses magnetorheological MR damper. The proposed new semi-active suspension could cost up to 20% of the cost of the magnetorheological MR damper. In this work, to study the vehicle's vibrational behaviour, a mathematical model for a quarter of a vehicle was designed using the MATLAB Simulink program. Three models of passive, semi active and active suspensions were presented for use in this study. Comparison of the vibrational behaviour of the three types will be introduced when the vehicle is travelling over different types of road humps such as circular, trapezoidal, and cat eye hump to achieve the most ride comfortable system . II. M ethodology To study the vehicle's vibrational behaviour, a mathematical model for a quarter of a vehicle was designed using the MATLAB Simulinkprogram. Three models of passive, semi active and active suspensions were presented for use in this study. Comparison of the vibrational behaviour of the three types will be introduced when the vehicle is travelling over different types of road humps such as circular, trapezoidal, and cat eye hump to achieve the most ride comfortable system . MATLAB Simulink will be used in this study; a quarter car model will be investigated to achieve vibrational behaviours of the vehicle and these effects on vehicle ride comfort . Moreover, a comparison between the three models will be introduced . From the simulation results, we assume to find the following data for each case : • Body Vertical Acceleration (m/s2) . • Tire Dynamic Loads (N) . • Suspensions Working Space (m) . • Body Displacement (m) . Where these four outputs are directly affecting the ride comfort and stability of the vehicle. Moreover, the vibrational behaviours of the three types of suspension systems will be investigated . A semi active suspension system is normally characterized by the presence of a control system. Mostly PID controller is used to adapt the body vertical acceleration within minimum level. The damping coefficient is used as the controller action. The proportional parameter K P is firstly tuned. Then, the integrator factor K I is adapted until the system noise reached until minimum levels and the error becomes too low. The differential parameter K D is then adjusted to damp the noise of the signal. Saad et al [22] and Hanafi Global Journal of Researches in Engineering (A ) Volume XxXII Issue I Version I 47 Year 2022 © 2022 Global Journals Vibrational Behaviour of a Quarter Car Travelling over Road Humps with Different Suspension Systems