Dynamic modelling of a flexure-based mechanism for ultra-precision grinding operation

This paper presents the dynamic modelling and performance evaluation methodologies of a flexure-base mechanism for ultra-precision grinding operation. The mechanical design of the mechanism is briefly described. A piezoelectric actuator is utilized to drive the moving platform. A flexure-based structure is utilized to guide the moving platform and to provide preload for the piezoelectric actuator. By simplifying the Hertzian contact as a linear spring and damping component, a bilinear dynamic model is developed to investigate the dynamic characteristics of the flexure-based mechanism. Based on the established model, the separation phenomenon between the moving platform and the piezoelectric actuator is analyzed. The influences of the control voltage and the preload stiffness on the maximum overshoot are extensively investigated. The slope and cycloidal command signals are utilized to reduce and/or avoid the overshoot of such flexure-based mechanism for rapid positioning. The effects of the rising time of the command signals on the maximum overshoot and the settling time are also explored. Experiments are performed to verify the established dynamic model and the performance of the developed flexure-based mechanism.