The present disclosure relates to a grinding machine. More particularly, the present disclosure relates to a centerless grinding machine comprising a damping device. The present disclosure also relates to a spindle for a grinding machine, and to a damping device for a spindle of a grinding machine, particularly for a grinding spindle or regulator spindle of a centerless grinding machine, wherein the damping device comprises at least one damping unit including an auxiliary mass section, an elastic section and a damping section, which are integrated in the spindle, and which jointly define a damped vibratory system for increasing the dynamic stiffness of the spindle.

Workpieces are machined in an apparatus having a central grinding station, first and second finishing stations and first and second spindles movable. First one of the workpieces is ground in a coarse-grinding station with the first spindle while rotating and finishing another of the workpieces with the second spindle in the second finishing station and then, while continuing to rotate and coarse grind the one workpiece in the coarse-grinding station, switching the other finished workpiece for an unmachined workpiece with the second spindle. Then the unmachined workpiece is ground in the coarse-grinding station with the second spindle while rotating and finishing the coarse-ground workpiece with the first spindle in the first finishing station and then, while continuing to rotate and coarse grind the unmachined workpiece in the coarse-grinding station, switching the finished workpiece for an unmachined workpiece with the first spindle.