Analysis And Optimization Of Multibody System With Uncertain Parameters

Multibody systems are commonly described by mathematical mdoels,and the parameters in the models are assumed as deterministic parameters.However,practical mechanical systems often operate with some degree of uncertainty.The uncertainty can result from poorly known or variable parameters.The uncertainty can be expressed by interval parameters or random parameters.For realistic predictions of the multibody system behavior and perfromacne,mathematical models should account for these uncertainties.The major contents of this study are summarized as follows:(1)Kinematics of spatial mechanism with a large number of interval parameters is analyzed.It is implemented in three steps:(i)development of a map between the end-effector position error and geometric source errors within the kinematic chains using homogeneous transformation matrix;(ii)selection of geometric errors which have significant effects on endeffector positioning accuracy by error analysis;(iii)kinematic analysis of the mechanism within which the geometric errors are modelled as interval variables.The computational algorithms are presented for positioning accuracy analysis and workspace analysis in consideration of geometric errors.The analysis results show that the key factors which have significant effects on end-effector position error can be identified efficiently,and the uncertain motion trajectory and workspace can also be calculated efficiently.(2)Multibody dynamics with interval parameters is investigated.A new method termed as Legendre metamodel(LM)method is presented.The implementation of Legendre metamodel model involves two steps.The first step is to approximate the original multibody model using Legendre polynomial approximation.Then take the interval parameters into consideration,and the Legendre metamodel model with interval parameters is obtained.The second step is to calculate the bounds of Legendre metamodel model using interval arithmetic or Monte Carlo.Chebyshev interval method,LM and Monte Carlo are applied into typical multibody systems including a vehicle multibody system.The Legendre metamodel method shows high accuracy and efficiency.(3)Multibody dynamics with random parameters is investigated.Gear rattle dynamics of an automotive driveline system at idle condition is investigated in the presence of random uncertainty using PC method.A driveline model is presented including the flywheel,the clutch damper,seven gear pairs,and input,intermediate and output shafts.The rotation speed of flywheel is measured and used as the input of driveline model.In the gear contact model,gear backlash and time-varying mesh stiffness are modelled.The random uncertainties of gear backlashes and clutch damper properties are systematically investigated using generalized polynomial chaos method.The simulation results of polynomial chaos method are compared with Monte Carlo simulations.(4)Flexible multibody system dynamics with hybrid uncertainties(interval parameters and random parameters)is investigated.A new method termed as polynomial-chaos-Legendremetamodel(PCLM)method is presented.Flexible multibody system is establised using Abosulte Nodal Coordinate Formulation(ANCF)method.The PCLM is a combination of PC and LM.The engineering examples are employed to demonstrate the effectiveness of the proposed methods.The uncertainties resulting from geometrical size and material properties are studied.(5)Multi-objective optimization for multibody dynamics with interval uncertainty is investigated.The optimization model with interval uncertainty and corresponding solution strategy is presented.This interval uncertain optimization methodology is appled for a vehicle multibody dynamics multi-objective optimization problem,including several bio-objective optimization problems and one ten-objective optimization problem.The methodology shows its effectiveness in the numerical example.