Dynamic modeling of spindle vibration and surface generation in ultra-precision machining

Abstract

Ultra-precision machining (UPM) typically includes ultra-precision diamond turning (UPDT) and ultra-precision raster milling (UPRM) for the manufacture of symmetric and non-symmetric profiles, such as spherical, aspheric and freeform components for optical, medical and telecommunication applications etc. They require extremely high geometrical accuracies in sub-micrometric form error and nanometric surface finish. In UPM, an aerostatic bearing spindle is popularly employed as only one power source to remove surface material of components due to its low friction, low heat generation, low contamination, and high accuracy. However, its vibration (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. In this thesis, the theoretical and experimental investigation is divided into two parts. In the first part, a five-degree-of-freedom dynamic model has been built up based on the linear and angular momentum principles. Newton-Euler equations for spindle vibration are developed to explore its dynamics under the excitations from continuous and intermittent cutting forces in UPDT and in UPRM, respectively. With the linearization of the Newton-Euler equations, the analytic solutions are sought to describe and characterize the spindle vibration under different machining processes. The solutions are further verified by the experimental and simulated results. Based on the power spectral density (PSD) analysis of the acquired cutting forces and the measured surface topographies, the dynamic characteristics of spindle vibration from the proposed dynamic model are identified with 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. In the second part, a surface generation model integrated with the dynamic model of spindle vibration is developed to simulate the formation of surface topographies in UPM. In the surface generation model for UPDT, the spindle vibration is considered with the effects of its damping ratio and phase shift. The periodic concentric, spiral, radial, and two-fold patterns (PCSRPs) are concluded at the simulated surface topographies, which are further confirmed by the measured surface topographies in the cutting trials. In UPRM, the aliased or lattice-like patterns, the ribbon-stripe patterns and the aliased tool loci (run-out) are evidently observed at both the simulated and measured surface topographies. The patterns are caused by the spindle-vibration-induced profiles (SVIPs), which are determined by the dynamic responses of the spindle excited by intermittent cutting forces of UPRM. Moreover, the prediction and optimization models for surface generation of UPM are established to predict surface roughness and optimize surface quality, respectively. The theoretical and experimental results present that the phase shift of 0.5 and the half shift length are optimal to achieve the best surface quality in UPM, and surface roughness increases with depths of cut and contact time. The results also reveal that the prediction models can precisely predict surface roughness as considering spindle vibration. Especially, the optimal selection of spindle speed to minimize surface roughness in UPRM can effectually improve surface quality by avoiding the 'resonance' phenomenon induced by the intermittent cutting forces synchronously exciting the spindle. The thesis presents an original study of spindle vibration and its effect on surface generation. It significantly contributes to (i) further understanding of dynamic characteristics of spindle vibration in the perspectives of an aerostatic bearing spindle in UPM, (ii) the predication and optimization of surface generation in UPM zeroing in on the improvement of surface quality, and (iii) the development of ultra-precision machine tools with enhanced precision to meet future demands for the manufacture of components with ever-stringent tolerance requirements.