Modeling and prediction for frequency response functions of parameter-varying mechanical systems based on generalized receptance coupling substructure analysis

Most machining systems such as machine tools and robots are parameter-varying mechanical systems, which show different dynamic characteristics under different parameters. Generally, a large number of modal tests are required for parameter-varying mechanical systems to obtain frequency response functions (FRFs) under different system parameters, which reduces efficiency. Receptance coupling substructure analysis (RCSA) provides ideas for solving such problems. In this study, the generalized RCSA (GRCSA) was proposed. The coupling method of two sub-structures at arbitrary pairs of nodes was derived, and a more general coupling method of mul-tiple substructures at arbitrary pairs of nodes was further elaborated, which provides a complete set of theories and methods for the modeling and prediction of FRF of general parameter-varying mechanical systems. Based on the derivation process and results of the GRCSA, the parameter -varying mechanical systems are classified into three basic categories: variable interface sys-tems, variable spatial attitude systems, and variable substructure systems. Typical cases of three basic categories in engineering practice were selected for studying, and the prediction models for FRFs of various parameter-varying mechanical systems were derived in detail. The calculation methods for FRF matrices of various substructures and the calibration methods for interface parameters are given. The validity of the prediction models was verified by experiments and simulations. The relative errors of the established prediction models under most system variables are less than 1% for the natural frequency, and the maximum relative error of the prediction models is 3.775% for the natural frequency. Finally, based on the prediction models, the FRFs under different system variables were predicted, and the variation laws of the natural frequencies with the system variables were analyzed. The modeling processes based on the GRCSA for the FRFs of typical parameter-varying mechanical systems are general, and can provide references and ideas for the study of frequency response characteristics of other complex parameter-varying mechanical systems.