Base on Coulomb friction model, the workpieces with different geometry rotating in free annular polishing are simulated. From simulation, the following conclusions are drawn. The angular velocity of workpiece is higher than that of polishing pad if the ring rotates uncontrolled in free annular polishing. The circular workpiece can synchronize with polishing pad through controlling the rotation of ring, which depends on the radii of ring and workpiece, the friction coefficients of polishing pad-workpiece and ring-workpiece, and the angular velocity of polishing pad. The workpiece with sharp corner cannot contact with the ring contiguously, which causes the contact state changing and the angular velocity of workpiece fluctuating ceaselessly, and this type of workpiece should be controlled with clamp to rotate synchronistically with the polishing pad. Base on Coulomb friction model, the workpieces with different geometry rotating in free annular polishing are simulated. From simulation, the following formulas are drawn. The angular velocity of the workpiece is higher than that of polishing pad if the ring handles uncontrolled in free annular polishing. The circular workpiece can with synchronizing with polishing pad through controlling the rotation of ring, which depends on the radii of ring and workpiece, the friction coefficients of polishing pad-workpiece and ring-workpiece, and the angular velocity of polishing pad. corner can not contact with the ring contiguously, which causes the contact state changing and the angular velocity of workpiece fluctuating ceaselessly, and this type of workpiece should be controlled with clamp to rotate synchronistically with the polishing pad.