Alongside the proverbial pmh precision, the newly developed pmh axial clamping chuck excels above all thanks to a compact design and a quick exchange of parts subject to wear during ongoing production. So that this case also occurs as late as possible, the axial clamping chuck has been made of particularly wear-proof steels. For individual adaptation to specific workpieces, the sound sensorics, the dressing wheel (grinding) and the balancing weights (eccentric processing) can be added. A coolant duct has also been provided. As a further option, a body of hard-coated aluminium is also possible.