PURPOSE: To obtain an optimum engagement by providing a means which stops the feeding of a 2nd toothed wheel with the detection of the state thereof by a distortion gage, when the 1st and 2nd toothed wheels arranged on the same axis are meshed in a backrush zero state.

CONSTITUTION: A cylinder 25 for actuation is driven when a work W as for a 1st toothed wheel is fed between both centers 23, 24 and the work W is freely rotatably supported by both centers 23, 24. A grindstone G as for a 2nd toothed wheel is then fed by a feeding motor M2, the work W and grindstone G are engaged to some extent. Thereafter, the grindstone G is rotated by the motor for grindstone and also fed by the motor M2. When the work W and grindstone G become in the position of backrush zero, the distortion gage 31 sticked to the center 24 detects the above stated backrush zero state and transmits a detection signal to a control part 27. The feeding movement of the grindstone G is then stopped and the finishing grinding of the work W is performed under this optimum engagement.