| In ultra-precision machining (UPM), aerostatic bearing spindle vibration plays a major part among many factors that directly degrades the surface quality of fabricated components. There has been still a lack of investigation into dynamic characteristics of spindle vibration under the excitation of cutting forces in UPM and its effects on surface generation. In this regard, this study develops a theoretical dynamic model to characterize the basis mechanism of spindle vibration and sheds light on the effects of spindle vibration on surface generation. The theoretical results are identified by a series of experiments.;Firstly, a five-degree-of-freedom dynamic model is expressed by NewtonEuler equations. The analytic solutions are provided for the equations. The theoretical and experimental results reveal that (i) the motion of spindle vibration consists of periodic, sub-harmonic, quasi-periodic and coupled-periodic components; (ii) the frequency characteristics of spindle vibration possess radial, axial and coupled tilting frequencies accounting for radial, axial and coupled-tilting motions, respectively; (iii) the coupled tilting frequencies (CTFs) are influenced by the spindle rotational frequency (SRF); (iv) the spindle vibration is determined by its inertial moments and force, and influenced by the external cutting forces and torques; and (v) the factors of spindle speed, cutting forces and contact time produce quasi-quadratic, quasi-linear and linear impact on the dynamic responses of spindle vibration, respectively.;Secondly, a surface generation model integrated with the dynamic model of spindle vibration is developed. For ultra-precision diamond tool (UPDT), the simulated periodic concentric, spiral, radial, and two-fold patterns (PCSRPs) are further confirmed by the measured surface topographies. In ultra-precision raster milling (UPRM), the simulated and measured aliased or lattice-like patterns, ribbon-stripe patterns and aliased tool loci (run-out) are caused by the spindle-vibration-induced profiles (SVIPs). Moreover, the established prediction and optimization models show that the phase shift of 0.5 and the half shift length are optimal to achieve the best surface quality in UPM and the optimal selection of spindle speed to minimize surface roughness in UPRM is to avoid that the intermittent cutting forces synchronously excite the spindle. |
