Experimental Identification of the Nonlinear Parameters of an Industrial Translational Guide for Machine Performance Evaluation

Prediction of machine dynamics at the design stage is a challenge due to lack of adequate methods for identifying and handling the nonlinearities in the machine joints, which appear as the nonlinear restoring force function of relative displacement and relative velocity across the joint. This paper discusses identification of such a nonlinear restoring force function for an industrial translational guide for use with the Nonlinear Receptance Coupling Approach (NLRCA) to evaluate machine dynamic characteristics. Translational guides are among the most commonly used joints in machine tools. Both parametric and nonparametric techniques have been employed to identify the nonlinearities. A novel parametric model based on Hertzian contact mechanics has been derived for the translational guide. A nonparametric method based on two-dimensional Chebyshev polynomials is also used. The models derived from the two techniques, i.e., parametric and nonparametric, are fitted to the experimental data derived from static and dynamic tests to get the restoring force as a function of relative displacement and relative velocity across the joint. The nonlinear representation obtained from both techniques is later converted into the describing function representation which is needed for evaluation of machine dynamic characteristics using the NLRCA. The describing function representations obtained from the two approaches are compared. The design of experiments for evaluating the nonlinearities in such industrial machine tool joints is a challenge, requiring careful alignment and calibration, because they are typically very stiff. This constrains the dynamic experiments to be carried out at high frequencies (e.g. 2000—7000 Hz) where the experimental readings are very sensitive to errors in geometry and calibration.