Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems

Abstract

Increasing attention is paid to modeling flexibility of individual components in the multibody simulation of large-scale mechanical systems. Nevertheless, the high model order of common methods such as FEA restricts efficient explorations, especially in dynamic design and iterative optimization. In this paper, a rigid multibody modeling strategy (RMMS) with low DOFs and explicit physical meaning is proposed, which directly discretizes a continuous structure into a number of rigid finite elements (RFEs) connected by spring-damping elements (SDEs). In the RMMS, a new identification method from the perspective of the inverse vibration problem is particularly put forward to resolve the parameters of SDEs, which is crucial to the implementation of RMMS in complex flexible structures. With decoupling and linearization, this nonlinear problem is transformed into solving the incompatible linear equations in Rn2 vector space based on vectorization operator and Kronecker product, and optimal parameters are obtained by calculating the Moore–Penrose generalized inverse. Finally, the comparison of the experimental results with the simulated ones by the RMMS strongly validates the feasibility and correctness of the RMMS in predicting the dynamic behaviors while with few DOFs and explicit physical meaning; the application in a lithography system exhibits the applicability of the RMMS for dynamic modeling of large-scale mechanical systems.

Mechanical system and dynamic control in photolithography for nanoscale fabrication: A critical review

“…If the changes in the refractive index of the air are not compensated, they will cause measurement noise and errors, especially in the region 0.5-50 Hz. 47 Even in a system with a very stable environment, these noise and errors will 42 Copyright 2020, The Authors, published by Hindawi Publishing Corporation still be larger than 1 nm. They are mainly cause by complex physical processes during the movement of stage itself.…”

“…Compared with the traditional FEM, RMMS would regard a complex flexible component as a few rigid finite elements connected by spring‐damping elements (SDE). Finally, by solving the dynamic characteristics of a few rigid finite elements connected by SDE or multibody systems, the dynamic characteristics of the original model can be obtained 42 …”

“…Finally, by solving the dynamic characteristics of a few rigid finite elements connected by SDE or multibody systems, the dynamic characteristics of the original model can be obtained. 42…”

“…FE, finite element; MBS, multibody systems; RMMS, rigid multibody modeling strategy; SDE, spring‐damping element. Reproduced under terms of the CC‐BY license 42 . Copyright 2020, The Authors, published by Hindawi Publishing Corporation…”