MATHEMATICAL SHAPING OF THE SUSPENSION SYSTEM OF MACPHERSON TYPE

Abstract

In the engineering road vehicles, simulating the dynamic behavior is very important because it allows us to study real-world systems without making changes in their actual development, the ultimate goal being to find the ideal configuration. Mathematical models simulate physical tests that allow engineers to see similar results from testing of motor vehicles, but can be obtained repeatedly, safe and much faster than is possible by performing physical tests. We use virtual simulations for the CarSim software, which is a commercial software package that provides efficiency vehicle response to the driver's commands (steering, throttle, brakes or clutch shift) in a given environment (road geometry, coefficients of friction and wind).

Headnote

Abstract: In the engineering road vehicles, simulating the dynamic behavior is very important because it allows us to study real-world systems without making changes in their actual development, the ultimate goal being to find the ideal configuration. Mathematical models simulate physical tests that allow engineers to see similar results from testing of motor vehicles, but can be obtained repeatedly, safe and much faster than is possible by performing physical tests. We use virtual simulations for the CarSim software, which is a commercial software package that provides efficiency vehicle response to the driver's commands (steering, throttle, brakes or clutch shift) in a given environment (road geometry, coefficients of friction and wind).

Keywords: road vehicles, testing of motor vehicles, CarSim software, MacPherson suspension

(ProQuest: ... denotes formulae omitted.)

1 INTRODUCTION

In the engineering road vehicles, simulating the dynamic behavior is very important because it allows us to study real-world systems without making changes in their actual development, the ultimate goal being to find the ideal configuration. In our experiments we use the virtual simulations offered by the CarSim software (Figure 1), which is a commercial software package that provides efficiency vehicle response to the driver's commands (steering, throttle, brakes, clutch shift) in a given environment (road geometry, coefficients of friction, wind) [1], [2].

To validate simulation models we considered the case of a small car compact coupe class. The feature of this class is the body in two-door, fixed roof and trunk of a sedan shorter than the same model.

The configuration of the Ford Puma is all face 2 + 2-seater, based on the Ford Fiesta platform, but increased track width, aerodynamic bodywork, suspension and stiffer gearbox with shorter ratios.

2.MATHEMATIC MODEL OF THE MACPHERSON SUSPENSION

For a dynamic simulation of a MacPherson suspension it is necessary to identify its mathematical model; mainly, the MacPherson suspension is composed of a damper and a spring element fitted to a link mechanism (Figure 2) [3], [4]. The sizing mechanism is made for each vehicle individually. The mathematical equations describing the dynamics of the system are the following [5], [6]:

... (1)

... (2)

The status variables are: [x1 x2 x3 x4]T = [ZS ZS в в]T

... (3)

where: Zs is the vertical displacement of the vehicle body weight; Żs is the speed of vertical motion of the vehicle body (bodywork, engine, passenger); в is the movement of the control arm; в is the angular speed of movement of the control arm.

The system of nonlinear equations is:

... (4)

Where: A is the matrix of the parameters of the suspension; B1 is the matrix of the active force; B2 is the matrix that takes into account road profile;B3 is the matrix that takes into account the force applied to the vehicle chassis.

...

The software test route is an uneven road which frequency is regular, so the shocks felt by the mechanism of suspension of the car have a sinusoidal distribution. In this paper we will focus on three characteristic parameters: angle of fall coefficient of compression springs and ride height [7].

3.RESULTS ANALYSIS

The results of the simulation are shown in graphical form as follows:

- Forces on the vertical oscillation (Figure 3)

- Angle of fall according to the damping stroke (Figure 4)

- Damping force (Figure 5)

- Spring compression (Figure 6)

4.CONCLUSIONS

Mathematical models reproduce the behavior of the system at high fidelity. They contain major effects that determine how the tire comes into contact with the road and how the forces resulting from the interaction tire / road transferred through the chassis suspension. However, they do not provide details about transmission connections or compliance structure. The models were validated repeatedly by the manufacturers for the reproduction of motor vehicles, generally the movements necessary for assessing handling (stability, braking and acceleration). On the other hand, these do not include the details necessary for determining the durability of components, fatigue or high-frequency vibration

References

References

[1 ] https://www.carsim.com/products/carsim/index.php

[2] https://www.carsim.com/products/supporting/simulink/index.php

[3] Keum-Shik Hong, Dong-Seop Jeon and Hyun-Chul Sohn, (1999). A New Modeling of the Macpherson Suspension System and its Optimal Pole-Placement Control, Proceedings of the 7th Mediterranean Conference on Control and Automation (MED99) Haifa, Israel - June 28-30

[4] H. Chen, Z. Y. Liu and P. Y. Liu, Application of Constrained H8 Control to Active Suspension Systems on Half-Car Models, ASME Journal of Dynamic Systems, Measurement, and Control September 2005, Vol. 127 / 345

[5] Patil, A., Mathematical Model for Kinematic Analysis of McPherson Strut Suspension, SAE Technical Paper 2016-28-0184, 2016

[6] http://www.minitab.com/en-US/default.aspx

[7] W. Gao, N. Zhang and H. P. Du, A half-car model for dynamic analysis of vehicles with random parameters, 5th Australian Congress on Applied Mechanics(ACAM 2007),Brisbane, Australia