Effects of wheel spindle error motion on surface generation in grinding

In ultra-precision grinding, error motions of the aerostatic bearing wheel spindle lead to unexpected variations in the actual depth of cut, thereby directly affecting machining accuracy. However, few studies have focused on dynamic characteristics of the wheel spindle error motion and its effects on surface generation. In this paper, the ground surface generation mechanism under the wheel spindle error motion is explored by establishing a grinding kinematics-based surface topography model integrated with a wheel spindle dynamics model considering the wheel topography and the overlapping effect. Grinding experiments are performed to identify the theoretical results through spindle vibration signals and machined surface topographies. The results show that the spindle error motions include the drift of the axis average line which produces the surface form error, and the spindle vibration relative to the axis average line that contributes to the waviness circumferentially. It is also found that the increasing wheel speed leads to the decreasing waviness amplitude at a small radial distance of the workpiece while the trend of the waviness amplitude with the wheel speed is the same as that of the spindle vibration amplitude at a large radial distance. Furthermore, based on the ground surface simulation, the grinding mark pattern formation mechanism is found to include three types, identified by the machined surfaces. A novel and convenient method, where the ratio of the grinding contact width to the cross feed distance per workpiece revolution and the reduced fraction of rotational speed ratio are used, is proposed to predict the grinding mark patterns and spatial frequencies, and validated by the ground surface simulation and experimental results.