Abstract: Lapping machine comprising a revolving turret (11) carrying at least several laps (13 to 17) that can be brought selectively into the machining position so that the laps can machine, in turn, one and the same cylindrical internal surface of a component. The laps comprise at least one expansion lap (17) and several progressive laps (15). The expansion lap (17) preferably has a stationary connector part (20) on its non-rotating part that can be coupled automatically to a moving connector part (21) when the expansion lap is in the machining position.