Influence of geometrical tolerances of machine tool fixtures on the accuracy of manufactured parts on the example of turning mandrels

The geometrical tolerances (tolerances of shape and location) of machine tool fixtures influence the same tolerances of machined parts. However, there are few academic papers with mathematical models describing this influence, and therefore the geometrical tolerances of machine tool fixtures are mostly assigned as some part of the component tolerance. It is proposed to link the tolerances of parts and fixtures by a dimensional chain and to perform tolerance analysis by probabilistic method. As an example, the analysis of solid and collet turning mandrels installed either directly in the tapered hole of the machine spindle or in a three-jaw chuck with bored soft jaws is considered. Analysis of calculation results shows that the influence of angular misalignments in tapered joints is comparable to the influence of parallel axis displacements (eccentricities). So the permissible runout of mandrel installed in the spindle is less than the runout of mandrel installed in well bored soft jaws (with runout not more than 0,02 mm). At the same time, the runout tolerance of the mandrel installed in the spindle can be expanded by reducing its overhang. Also the influence of workpiece’s outer surface runout on the total runout was evaluated and it was found that the runout of the workpiece can be neglected if the technological system is sufficiently rigid.
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