Form Defects Tolerancing by Natural Modes Analysis

The form defects quality needs methods to express allowable deviations. We propose a new language for form defects expression. This one is based on natural mode shapes of a discretized feature. The finite element method is used in order to compute those modes. Then a basis of defects is built with the natural modes. A defect is projected in this basis and thus the coordinates (modal coefficient) represent it. Hence, tolerancing is possible, by limiting those coordinates. The methods proposed in the literature can be applied on elementary geometries or there is a need to express the set of possible features (explicit geometry). Our method is versatile because it is based on the discretization of the feature (implicit geometry). The modal tolerancing method proposes two ways to express specifications of form defects: (1) The spectral tolerancing shows the modal coordinates and their limits in a bar chart graph by drawing the limits. In this method, we can see the decomposition of the measured feature and express tolerancing on each coordinate. (2) When a specification needs to link coordinates, we propose the modal domain method. An inclusion test of the feature coordinates gives the result of the metrology. Those methods are presented in an example.