Modeling and experimental investigation of wheel spindle vibration and surface generation in ultra-precision grinding

Abstract

Ultra-precision grinding is primarily employed to manufacture high-precision components made from hard and brittle materials with high machining quality and efficiency. An aerostatic bearing spindle is widely applied to provide the rotary motion of the grinding wheel for its high accuracy and high speed capacities. It is prone to vibrating under mass eccentricity, bearing forces, and grinding forces, degrading the quality of ground surfaces. Though many studies have focused on the influences of various factors on surface generation, there is still a lack of investigation into the spindle dynamics and its effects on surface topography in ultra-precision grinding. In this thesis, an investigation of the vibration mechanism of the aerostatic bearing wheel spindle and the surface generation mechanism under the vibration has been made through modeling and experimental approaches, and is divided into three parts. In the first part, a mathematical model is established for studying the dynamic characteristics of aerostatic bearings by solving the Reynolds equation and the equation of motion to simulate the orbits of the rotor center. The model suggests that the bearing reaction forces could be considered linear at small eccentricity when analyzing vibrations with small amplitudes. Further, nonlinear analysis of dynamic responses provides a comprehensive understanding of the characteristics of aerostatic bearings. At the same rotor speed, the rotor mass at the instability threshold is nearly 4 times the mass corresponding to the resonance. The influences of supply pressure, orifice diameter, bearing clearance, and eccentric distance on dynamic stability and rotational accuracy are studied. In the second part, a dynamics model for the wheel spindle is proposed considering the radial and tilting motions to analyze its vibration characteristics. A surface profile model is established considering the spindle vibration and wheel topography. A series of grinding experiments were conducted in which the measured spindle vibration signals and machined surfaces were analyzed to study the surface profile formation mechanism under the spindle vibration. The theoretical and experimental analysis shows that the spindle vibration contains a low-frequency drift of the axis average line that produces surface form error, and a synchronous vibration around the axis average line that contributes to surface waviness. It was also found that the grinding process can remove the effect of high-order harmonics on surface generation. Besides, the non-uniform wheel topography produces surface waviness and is the primary origin of waviness for a coarse wheel, but the spindle vibration dominates waviness formation for a fine wheel. In the third part, a theoretical and experimental study of the surface generation mechanism in ultra-precision grinding is presented. A three-dimensional surface topography model is established for the parallel grinding mode, taking the wheel spindle vibration, wheel topography, and overlapping effect into account. Grinding experiments were conducted using different rotational speed ratios (RSRs) to observe the variation of the machined surfaces. Based on the simulated and experimental results, the formation mechanism of surface patterns is divided into three types, depending on the RSR. A prediction approach based on the reduced fraction of the RSR and the ratio of grinding contact width to the feed distance per workpiece revolution is proposed for the surface patterns and spatial frequencies. The overlapping effect that occurs at non-integer RSRs greatly influences surface roughness and waviness. The thesis studies the dynamics of aerostatic bearing wheel spindle and surface generation in ultra-precision grinding. It contributes to (i) a comprehensive understanding of the dynamics of aerostatic bearings, which can be useful for guiding the design of aerostatic bearing spindles to achieve the required running accuracy and avoid instability; (ii) a deeper understanding of surface generation mechanism under the spindle vibration, which can be helpful for optimizing grinding conditions; (iii) modeling approaches, which can be transferred to the analysis of other machining processes.