Effect of joint nonlinearities on the dynamic performance of machine tools

Evaluating the dynamic performance of machine tools at the design stage requires prediction of Frequency Response Functions (FRFs) and Stability Lobe Diagrams (SLDs). This is, however, a challenge because of nonlinearities in the machine joints. Here we address this challenge by providing a method to identify such joint nonlinearities and use them to predict the FRFs and SLDs for a machine tool design concept.; An experimental study was undertaken to understand the relationship between the machine structure and its dynamic characteristics during cutting using the Arch-Type Reconfigurable Machine Tool. It has been experimentally determined that the machine performance is insensitive to the structural changes if the dominant frequency in the machine's FRF arises primarily due to the tool-tool holder-spindle assembly. The FRFs and the analytical SLDs for the Arch-Type Reconfigurable Machine Tool were evaluated and it was found that the machine had similar characteristics at various reconfiguration positions.; Linear techniques to predict FRFs at the design stage can be inaccurate as even weak nonlinearities in machine tool joints can lead to significant changes. Identification of machine joint nonlinearities is difficult as they are typically very stiff and, thus, any dynamic experiment to identify joint nonlinearities has to be done at very high frequencies where the results are sensitive to small errors in calibration and geometry. Guidelines to carry out such experiments have been discussed, and the experiments were carried out on a translational guide of the type often used in machine tools. Both a parametric and nonparametric approach has been used to determine the nonlinear restoring force relationship for the translational guide. This relationship is then converted into the frequency domain using describing functions. A derivation is presented to convert the two dimensional polynomial result for determined nonlinear restoring force relationship from nonparametric approach into a closed-form describing function expression.; Finally the effects of the experimentally determined nonlinearities in the translational guide on overall machine structural dynamics is determined using the nonlinear receptance coupling approach. Significant variations are observed in both FRFs, as well as the SLDs for a column-spindle head machine structure even with weakly nonlinear joints. Such variations in natural frequency and response of the FRF, and in the location of stability lobes with respect to the spindle speed, were also experimentally observed for the Arch-Type Reconfigurable Machine Tool.