Error correction in hydrostatic spindles by optimal bearing tuning

In this paper a high precision grinding wheel is considered as a rigid rotor mounted on two hydrostatic bearings. The equations for small perturbations of the wheel on the bearings are derived in the form of a multi-input, multi-output transfer function matrix, enabling the frequency response function of the wheel to be determined. Thereafter an optimisation algorithm is proposed which considers speed, load and dimensions of the spindle, and computes optimal stiffness and damping of the bearings. The dynamic characteristics of the bearings, tuned for minimum radial displacement of the spindle, is achieved maximising thereby the accuracy of the grinding process. Simulation results show that by stiffness coarse adjustment, and fine adjustment of the damping in the bearings, a spindle with 35 μm manufacturing error, can produce components with 3 μm accuracy.