Driven by the ever increasing demand in function integration, more and more next generation high value-added products, such as head-up displays, solar concentrators and intra-ocular-lens, etc., are designed to possess freeform (i.e., non-rotational symmetric) surfaces. The toolpath, composed of high density of short linear and circular segments, is generally used in computer numerical control (CNC) systems to machine those products. However, the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration, which will decrease the machining efficiency and product surface finish. Driven by the ever-increasing need for high-speed high-precision machining of those products, many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry, aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods. This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications. The advantages and disadvantages of these approaches are discussed. Possible future research directions are also offered.

In ultra-precision machining field, the air motorized spindle which is composed of a motor and an air bearing, plays a major role. In air motorized spindle, the motor eccentricity between the stator and the rotor is inevitably introduced during the manufacturing process, which directly affects the machining results of workpiece surface, and this phenomenon is particularly unwanted in machining. However, little attention has been paid to the motor eccentricity of air motorized spindle. In this paper, a new integrated electromechanical coupling method for estimating unbalanced force in air motorized spindle is presented, and the effects of motor rotor eccentricity on surface topography in ultra-precision processes are analyzed. An electromagnetic-mechanical method is used to study the coupling effects between the motor rotor and the aerostatic spindle. Meanwhile, the motor rotor and the aerostatic spindle are analyzed as a whole. In order to clearly describe the electromagnetic–mechanical method, the ultra-precision spindle for potassium dihydrogen phosphate crystal machining tool is selected as the research object, and the model of air motorized spindle and motor rotor eccentricity are presented. Besides, in order to assess the impact of the radial magnetic force caused by motor rotor eccentricity on the spindle performance, a range of rotor eccentricities is calculated. Additionally, the influence of the motor rotor eccentricity on the dynamic response of spindle is further analyzed. It is found that motor rotor eccentricity has a significant influence on the spindle vibration, which dramatically reduces the processing quality. Finally, the machining experiments are carried out, and the flatness errors of the workpiece caused by the motor rotor eccentricity are obtained by the wavelet method. The experimental results are consistent with the analysis results, which verifies the reliability of this method. This study is quite meaningful for deeply understanding the influence of motor rotor eccentricity on the machined surface.