Nonlinear micro-dynamic behavior of a ball-screw driven precision slide system

Abstract

An essential ingredient in diamond turning is a slide system that can respond quickly and precisely to very small input signals. In this paper, a study is carried out to characterize the micro-dynamic (or small motion) behavior of a ball-screw driven precision slide. First, it is observed that the dynamics of the slide system change significantly from a nominal linear approximation as the commanded input signal decreases. This apparently nonlinear phenomenon can be attributed mainly to the presence of the nonlinear friction and local elastic deformation plus other residual effects due to a higher noise-to-signal ratio for a smaller input signal, the digitization of the servo error, etc. Specifically, for small input signals, a local elastic deformation at the ball-screw interface prior to stiction breakaway resulted in a secondary resonant peak in the frequency response. As the magnitude of input signal increased, the peak showed a decrease in its frequency as well as the magnitude, and finally disappeared completely beyond a certain input signal magnitude. The presence of the peak is a strong indication that the micro-dynamics of the system are nonlinear, and the gradual shift and eventual disappearance of the peak indicate that the behavior is characterized by varying spring and damping constants. A nonlinear model has been developed based on this observation, and simulated time response matched accurately the actual micro-dynamic response of the system.