Analysis of the Dynamic Behavior of a Vehicle Suspension when Passing over a Bump

Passing a vehicle over bumps generates sudden variations in acceleration with effects on passenger comfort. In this paper we aim to model the movement of a vehicle, considering only vertical movements, neglecting the movement of roll and pitch. Based on differential equations that govern dynamic behavior, a simulation model of motion is built in MATLAB, the Simulinkˇ module. Suspensions of the vehicle will be considered as passive and semi-active. Passive and semi-active are still the most common suspensions, although active suspensions have been used lately, with mechanical parameters that characterize suspensions, stiffness and dampers being controlled. The paper analyzes the responses given by the suspensions to the passage over bumps, and how they can be mitigated.


Introduction
the single wheel movement, i.e. the movement of the axle and the vehicle assumed to be only vertical and the perturbation to be identical on each wheel [4]. The main requirements for a suspension are: to isolate the car from road disturbances, ensuring passenger comfort; maintaining good manoeuvrability; maintaining a good road; supporting the static weight of the car. A simulation and analysis model (SAM) requires information on the mechanical parameters used [5]. Measurement of the mechanical characteristics of the suspension requires a static test facility. The simulation and analysis model (SAM) used in the work has 17 degrees of freedom, of which 6 degrees of freedom are required for the rigid body motion of the vehicle, and each wheel is considered to have two degrees of freedom, one for rotating the wheel the other for its vertical movement relative to the vehicle. Suspension modelling has been made so that they are pivoted relative to an instant centre. In this paper, the Simulink software is used to simulate possible laboratory or field tests. It demonstrates the ease with which they can reproduce the tests, regardless of their complexity, both under laboratory conditions and in field conditions.

Mathematical models
In Fig. 1 there is presented a very simplified model of a vehicle with one degree of freedom (1-DOF) that takes into consideration only the vertical movement, the pitch and roll movement are not taken into account. The vertical movement of the car is done at a height of 0.15 m. The car tire is considered to have 0.305 m, and the bump is modeled by a step input function. After a horizontal movement over 450 m, less 0.15 m from the zero level, it returns to this level over a distance of 1 m, as shown in  Simplified model of suspension To obtain the differential equations of the movement of a car, two cases are considered. In the first case, the mass of the tire and its damping and stiffness properties are negligible in relation to the mass of the vehicle and the elastic properties of the spring, and the damping properties of the damper. In this case, the simplified model is that of Fig. 2 [6]. In Simulink, the model considered with 1DOF, can be simulated starting from the expression of acceleration given in equation (1).  In order to realize the Simulink simulation scheme of the system with two degrees of freedom, the expressions of the two accelerations given in the equation (2) are explained from the differential equations of the movement.
To simulate the equations (2) in Simulink, it is necessary to give the initial conditions corresponding to the geometric form of the bump, which in this case are given by equations (3).

RESULTS
The results obtained from the simulation are given in the graphic form registered by Scope. For each of the two car models with 1-DOF and 2-DOF, three regimes were analyzed according to different values of the damping coefficient. For second, regime with damping close to the critical damping of the mass-springdamper system, the following damping coefficients were considered: 1 c 1000Ns / m = for 1-DOF system, and for 2-DOF system consider c 600Ns / m = and t c 500Ns / m = .

CONCLUSIONS
The results obtained from the simulation lead to the conclusion that in the analysis and design of a suspension one can go from modeling the car as a system with a degree of freedom, although the system with two degrees of freedom has a more complete response and more closer to reality. It is found that in the system response with two degrees of freedom two frequencies are present.
For small dampers or lack of damping in the system, an uncomfortable ride is obtained. Improved comfort is obtained around optimum damping. For some damping values, reverberations are produced. High damping diminishes the effect of reverberation. Simulink software can be used to simulate different situations in the real world.
In order to achieve optimum damping regimes, different semi-active dampers with electroreological or magnetoreological fluids can be used. Using Simulink to simulate the behavior of these dampers can be useful in identifying rheological parameters of fluids.