15th Symposium: Dynamics of vehicles on roads and tracks [antikvár]

Optimization design of multibody systems by using genetic algorithms. S. DatoussaYd, R. Hadjit, 0. Verlinden, C. Conti Faculté Polytechnique de Mons Service de Mécanique Rationnelle,Dynamique et Vibrations Boulevard Dolez, 31, 7000, MONS (BELGIUM) Abstract The designing step of multibody systems requires in somé specific cases an optimization process, where the design parameters have to be determined by taking into account the expected kinematic or dynamic performances. The aim of this paper is to propose an optimál design method adapted to multibody systems containing closed loops and submitted to kinematic and/or dynamic time-dependent criteria. The optimization process is based on genetic algorithms, using a natural evolution concept leading to stochastic optimization techniques that can often overtop classical optimization methods when applied to real-world problems. Illustrative examples are given in the context of the optimization of the kinematics of the suspension of a motorcar and the lateral dynamics of an úrban railway vehicle. 1 Introduction When designing a multibody system, the dynamic analysis step predicts the behaviour of the mechanism for a special set of design variables. These ones have to be optimized to improve the performances of the system without passing the conceptual or technological boundaries. Nevertheless when dynamic behaviour is taken into account, the optimization process becomes harder because both performances and constraints are explicitly time dependent. The purpose of this paper is to describe a generál method for the optimization of the dynamic behaviour of multibody systems. A stochastic search method based on genetic algorithms has been applied as optimization engine. The dynamic analysis uses a residual formulation in relative coordinates. 2 Optimization of multibody systems The optimization of the dynamic behaviour of multibody systems becomes a complicated task because of the explicit time dependency. At one hand, the equations of motion, so-called state equations, are time dependent, as well as the objective and constraint functions. On the other hand, the configuration parameters q, so called state variables, describe the motion of the multibody system and cannot be considered as design variables because their values are obtained from the integration of the state equations. The system of differential equations of motion (1) is expressed in its residual form by [3]. F(q(t),q{t)1q{t),t) = 0 (1) Usually the optimization process deals with extreme dynamic response, subject to performance constraints that must hold over the entire time interval [Or]. The objective function which has to be maximized is written as : *0= max {M - fo(b,q(t),q{t),q\t),t)) M» 0 (2) í 6(0 r] ~ ~ - The criterion /0 can be for example the maximum acceleration of one of the bodies of the multibody system under operating conditions. The scalar M is chosen in such a way that is positive. The constraints are usually time dependent and express, for example, the limited rangé of the relative distance between two bodies during their motion : / o \