In this paper, radial displacement error of a high precision spindle grinding caused by unbalance force was studied. The spindle shaft is considered as a flexible rotor supported by two pairs of angular contact ball bearing. The finite element method (FEM) have been adopted for obtaining the spindle equation motion. In this study, firstly, natural frequencies, critical frequencies and amplitude of unbalance response caused by residual unbalance are determined in order to investigate the spindle behaviors. Further more, an optimization design technique is conducted to minimize radial displacement of the spindle which considers shaft diameters, dynamic characteristics of the bearings, critical frequencies and amplitude of the unbalance response, and computes optimum spindle diameter and stiffness and damping of the bearings. Numerical simulation results show that by optimizing the shaft diameters, and stiffness and damping in the bearings, radial displacement of the spindle can be reduced. A spindle about 4 µm radial displacement error, can be compensated with 2 µm accuracy
