A multi-segment two-point receptance coupling method for FRF prediction of holder–tool assemblies

Abstract

This study presents a multi-segment two-point coupling method for predicting the frequency response functions (FRFs) of a holder–tool assembly. The assembly is modeled as a structure consisting of two substructures—an outer tube and an embedded inner cylinder—with a coincident neutral axis, and is then divided axially into multiple segments. For each assembly segment, the FRFs of its substructural components, i.e., the tube and cylinder segments, are theoretically calculated using Timoshenko beam theory. A new receptance coupling principle is established at the two endpoints of each assembly tube and cylinder segment based on their deformation and compatibility conditions. The overall FRFs for each assembly segment are synthesized from the theoretically calculated values of its corresponding tube and cylinder segments. By employing classical receptance coupling substructure analysis (RCSA), the FRFs of the entire assembly are obtained by coupling the individual segment FRFs. Unlike traditional multi-point coupling methods, which generate intermediate matrices strongly dependent on the number of coupling points, the proposed method yields a fixed 4 × 4 intermediate matrix, fully independent of the coupling points. This feature simplifies the calculation procedure to a summation across all segments, eliminating the need for complex iterations required by conventional methods. The proposed method is numerically validated and experimentally verified.