The finishing machine is for inner wedge groove surfaces and has a holding device for a workpiece (W) with inner wedge groove surfaces. It has a grinding stone (42) with several tooth sections for simultaneous grinding of the inner wedge groove surfaces of a workpiece. A pivot device is provided for pivoting the grinding stone at high speed in the axial direction of the workpiece.A widening device is incorporated for widening the tooth sections of the grinding stone in their radial direction outwards. A rotary device is provided for rotating the grinding stone with a rotary force and a braking device brakes the workpiece with a brake force. A pressure unit presses the workpiece onto the grinding stone.
