The invention concerns vehicle wheel service machines, in particular automatic tire changers, having a wheel or rim mounting device (2) which is mounted rotatably about an axis (11) and to which a wheel (1) is to be fixed. The vehicle wheel service machine comprises first and second detectors (6, 7) and a controller to detect the rotational speeds of the rim mounting device (2) and the wheel (1) respectively. Furthermore, a method for controlling the rotational speed of the rim mounting device (2) is provided. If the detected rotational speeds are different, slipping is determined and eliminated by approximating the rotational speed of the rim mounting device (2) to that of the wheel (1). A rim mounting device (2) can comprise a rim mounting plate (23) having a rim support surface (24) with a high-friction lining adapted to increase friction between the rim mounting plate (23) and the wheel (1).