Ultra-precision grinding is widely used in fields such as precision instrumentation, military industry, and aerospace. Focusing on a grinding system based on hydrostatic support, this paper investigates the formation mechanism and variation patterns of roundness error during grinding. The dynamic equations are derived based on the structural characteristics of a vertical grinding system. The uncut chip thickness is formulated, enabling the prediction of grinding forces through mathematical expressions. The dynamic equations are solved using a fully discrete algorithm to obtain the surface profile of the workpiece after machining, and roundness error is extracted using the least squares method. As the speed ratio of the grinding wheel to the workpiece increases, the grinding accuracy improves, and the roundness error can be controlled within 0.2 μm. The farther the grinding force application point is from the center of the slider, the greater the roundness error. Under the condition of meeting the processing range, a shorter grinding wheel contact rod should be selected.
Li et al. (2026) studied this question.