The existing micro-spindle systems equipped with micro-tools compromise micro-machining accuracy and efficiency due to their large error. In this study, the radial error of micro-tool tip was classified into static mechanical offset, thermally induced error, and radial motion error. The micro-tool tip, having the smallest stiffness, was the major error source of radial mechanical offset. A stiffness-based error model was proposed to predict the radial mechanical offset of micro-tool tip, and the predictions were well consistent with the measured values. The front bearing, due to its large thermal loss, had lower temperature than the rear bearing at nearly all rotational speeds. The difference of thermal growths between the two ball bearings resulted in the thermally induced error. The thermally induced error increased rapidly with running time within the first hour and then entered into a relative stable state, which was modeled by the least square method. The proposed model of thermally induced error also considered exponential characteristic of spindle thermal growth in nature. It agreed well with the measured values. The radial motion error increased with the over-hang length of micro-tool, but decreased with the rotational speed. It was modeled by the least square method and validated by the measurements. The micro-grinding tests were conducted to further verify the proposed predictive models of static mechanical offset, thermally induced error, and radial motion error. With the error compensation, the micro-grinding thickness was close to the required value, which showed the error predictive models and compensation scheme were effective.
The presented work is funded by the National Science Foundation of China (51505140, 51675170), China Postdoctoral Science Foundation (2016T90749, 2015M570676), and Natural Science Foundation of Hunan Province, China (2016JJ3037).