Optimal Design Of Multibody Systems

Abstract

Dynamic simulation is often used to predict the behaviour of multibody systems but, it should be sometimes completed to optimize the choice of the design parameters by taking into account the expected performances of the mechanism. The aim of this paper is to propose an optimal design method adapted to mechanisms containing close loops and submitted to dynamic criteria. A formulation based on relative coordinates and Newton-Euler laws has been chosen, the constraint equations being expressed by the closing of the loops. A single value decomposition method is used to divide the set of differential and algebraic equations into two sub-spaces associated to the dependent and independent parameters. The equations of motion are integrated by the Newmark algorithm in its residual formulation. The optimization step is performed by the steepest descent method with constraint compensation. A special design sensitivity analysis has been developed by considering time dependent constraints, including first and second derivatives of the configuration parameters. The primary problem is reformulated so that integrals replace the time dependent functions. The classical adjoint variables are introduced to eliminate the state variables in the sensitivity formulation. The method has been applied to optimize the suspensions of an urban railway vehicle.