Numerical solution of problems on the position of a five-link mechanism of an automobile suspension

Abstract

A multilink structure of an automobile suspension can offer a better relationship between controllabil ity, safety, comfort, and occupied space. This structure ensures high lateral rigidity and sufficient longitu dinal compliance. The first 5 stage (5 link) suspension was patented by Mercedes Benz in the late 1980s. Since then, the use of multilink suspensions in modern sedans and coupes, both at rear and front axles, have gradually increased. Its design has not been precisely outlined and differs depending on the model of a car. The present paper covers the design of the Honda Accord suspension, which is an evolution of the double wishbone suspension.Computational simulation of automobile suspension motion allows one to make the process of its design automatic and reduce the number of in situ tests. For example, in [1] the maneuver of changing a traffic lane was simulated to optimize criteria of comfort and controllability. In [2, 3] elasto kinematic and dynamical characteristics of the 5 link suspension were optimized.The present paper covers some important kinematic characteristics of the automobile suspension, such as toe and camber angles, longitudinal and lateral displacements [4,5]. Values of these characteristics and the way they change during compression and rebound travels affect controllability, transverse stability of the automobile, comfort, tires and wear, etc.A kinematics analysis of the suspension mechanism requires the solution of a system of polynomial equations. In [6], the authors made an overview of three accurate computational methods for solving these systems of equations. These are Groebner basis (analytical), polynomial continuation (numerical), and dialectic elimination The procedure of dialectic elimination is very useful only for problems with a small number, up to six, of variables. A disadvantage of the method of building the Groebner basis is a large vol ume of calculation due to a large number of generated intermediate polynomials.Nevertheless, in [7] the authors managed to build the Grobner basis for triangulation of equations of kinematic limitations. Their approach was applied to the Stewart Go platform and the 5 link suspension. As these mechanisms are similar in topology it makes sense to consider them in parallel. Though pregen eration of the Groebner basis is attractive from the point of view of real time applications, it requires com putational costs and an individual approach to each problem.In [8], interval analysis was used to build all possible trajectories corresponding to a certain range of values of a free parameter. It was shown that calculation of analytical expressions for output parameters is not practical even for the easiest McPherson mechanism.Let us find kinematic characteristics by following the trajectory of the suspension mechanism from compression to rebound. The system of polynomial equations generated during the analysis of kinematics of the 5 link mechanism will be solved numerically with use of the Newton multivariable method. This is a standard appro...