Effects of nonlinear behaviour of linear ball guideway on chatter frequency of lathe machine tool

Abstract

Linear ball guideways (LBGs) have several advantages for the precise positioning control of machine tools. However, the ball-groove contact behaviour leads to poor dynamic compliance, which induces a significant nonlinear behaviour of the guideway and a poor chatter stability. Accordingly, the present study first employs Hertzian contact theory to describe the ball-groove contact behaviour in the LBG of a lathe machine. Two static models are then derived to predict the LBG stiffness under different cutting loads. For simplicity, the first model ignores the effects of the contact force on the deformation of the guideway components. By contrast, the second model adopts a dynamic sub-structuring co-simulation method to incorporate the effects of structural deformation into the analysis. For both models, a linearisation approach is employed to analyse the dynamic behaviour of the system under static loading and define the dynamic compliance. The chatter frequencies of the LBG are estimated using the second model and are shown to be in good agreement with the experimental results. In general, the analysis results show that fundamental shifts in the frequency response of the LBG occur under specific values of the cutting force and load. In other words, the results confirm the need to take the nonlinear behaviour of the LBG structure into account in the design of lathe machine tools.