Relationship between strain distributions and shape deviations of rings caused in clamping

In 2010 Frerichs et al. proposed a comparatively simple equation describing the relationship between shape deviations and the internal strain state of a ring. It can also be applied to predict shape deviations of rings on the basis of one analyzed clamping case. In this paper the validity of the equation is shown for elastic and elastic-plastic deformations of rings fixed in k clamping jaws (k = 2, 3, 4, 6) in analytical and 3D Finite Element Analyses, respectively. The theoretical results are in very good agreement with Frerichs' formula for both cases. However, in the elastic case constant strain energy for different numbers of clamping jaws seems to be the necessary and sufficient prerequisite to use Frerichs' approach for predicting amplitudes of order k based on the knowledge of a certain amplitude an?k. For a given ring geometry this is fulfilled in the elastic case, if clamping forces are proportional to k21.