Dynamic Support Characteristics of a Conical Hydrostatic Bearing Spindle and Their Effects on Surface Formation in Precision Grinding

The dynamic support characteristics of hydrostatic spindles have an important influence on precision grinding stability and surface quality. However, existing grinding surface-generation models usually prescribe spindle motion as a known input and rarely establish a direct transfer relationship from hydrostatic-bearing dynamics to spindle vibration and subsequent surface formation. To address this issue, a sequential analysis framework is developed for a precision grinding spindle supported by conical hydrostatic bearings. The complete three-dimensional stiffness and damping matrices of the conical bearings are obtained from the oil-film force responses to small displacement and velocity perturbations and are assembled into a spatial rotor dynamic model to calculate the grinding-wheel-end vibration response. The calculated normal vibration displacement is then introduced into the abrasive grain trajectory model to predict the generated surface topography and roughness. The results show that the bearing dynamic support characteristics significantly affect the spindle response. In particular, increasing the average oil-film thickness from 30 μm to 40 μm increases the RMS grinding-wheel-end normal displacement by 79.82%, whereas the effects of eccentricity ratio and cone half-angle are comparatively smaller within the investigated ranges. Incorporating the calculated spindle-vibration response also improves the agreement between predicted and measured surface roughness. Single-crystal silicon grinding experiments show that the mean relative errors of Ra and Rq decrease from 28.40% and 33.45% to 23.61% and 28.54%, respectively. Although the model still tends to underestimate the measured roughness, it reproduces the overall variation tendency under different grinding conditions and clarifies the sequential transfer relationship from hydrostatic-bearing dynamics to spindle vibration and grinding surface formation.