Sensitivity Analysis Approach to Multibody Systems Described by Natural Coordinates

作     者：LI Xiufeng WANG Yabin 

作者机构：State Key Laboratory of Electromechanical Dynamic Control Beijing Institute of Technology 

出 版 物：《Chinese Journal of Mechanical Engineering》 (中国机械工程学报（英文版）)

年 卷 期：2014年第27卷第2期

页      面：402-410页

核心收录：

学科分类：0817[工学-化学工程与技术] 08[工学] 0807[工学-动力工程及工程热物理] 080203[工学-机械设计及理论] 0802[工学-机械工程] 0811[工学-控制科学与工程] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by National Defense Pre-research Foundation of China during the 12th Five-Year Plan Period(Grant No.51036050107) 

主　　题：sensitivity analysis direct differentiation method natural coordinates multibody systems 

摘      要：The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.