Prediction of dynamic behavior for different configurations in a drilling–milling machine based on substructuring analysis

Abstract

Dynamic models of machine tool structures are essential instruments to evaluate structural performance in cutting operations. In order to fully exploit these models, they must meet three critical requirements such as accuracy, computational efficiency and multi-configuration machine behavior predictability. These virtues are hard to combine in one single model, as the improvement of one feature can easily involve a negative effect in the others. This paper deals with this problem and presents a robust procedure to develop reliable, efficient and versatile dynamic models. First, the machine tool structure is split up in several components. For each component, a finite element model is developed and the necessary corrections are made comparing the numerical results to the experimental data obtained from a modal analysis test. Once suitable numerical definitions of the components are available, substructures are defined, considering some components individually and grouping those with no relative movement. In this process, the connection between components is accurately modeled, checking the resulting substructures experimentally. Secondly, the order of the substructures is reduced using a Component Mode Synthesis approach based on Craig–Bampton method. Traditionally, when working with movable substructures, the order reduction capability has been limited by the large amount of connection degrees of freedom which must be kept in the reduced representation to cover all possible positions of substructures. This paper presents a procedure to solve this issue, where these degrees of freedom are eliminated from the reduced model as the substructures are assembled sequentially. Finally, in order to evaluate the reliability of the resulting model, the dynamic characteristics of the structure in various configurations are calculated and the results are compared with the experimentally obtained natural frequencies, mode shapes and frequency response functions for the same configurations. Results indicate that the proposed method predicts correctly the position-dependent dynamic behavior of a machine, validating the developed procedure.