Analysis of the Influence of Structural Parameters on the Modes of a Gantry Machine Tool Crossbeam Based on Analytical Method

Modal analysis and structural parameters selection are essential in the structural design of the crossbeam of a gantry machine tool. In order to explore an efficient modal analysis method, the analytical method of modes of the beam with variable cross-section is derived based on the Euler beam theory and transfer matrix method. By dividing the machine tool crossbeam into 27 segments, the crossbeam modes are obtained analytically, which is validated by the finite element method. Compared with the FEM, the analytical method shows high efficiency. On this basis, the influence of various structural parameters, including bending stiffness and linear density, on the crossbeam mode is explored, and the sensitivity analysis is carried out. The results show that the first-order bending frequency of the crossbeam is mainly affected by the bending stiffness in the middle part of the crossbeam, followed by the linear density in the middle and end part. The first-order bending frequency of the crossbeam increases by increasing the bending stiffness in the middle part and decreasing the linear density of the crossbeam. The linear density both in the middle and end part has a great effect on the mode shape of the crossbeam. This study can provide a reference and method for structural design and modal analysis of machine tool crossbeams.