Tolerance analysis and synthesis by means of clearance and deviation spaces

Abstract

A mathematical representation of tolerance zones is used to analyse toleranced mechanisms. This method permits to choose optimal geometric tolerances, in many cases. A mechanism is considered as constituted of solid bodies and joints. The set of displacements allowed by a joint is called clearance space. It takes into account the degrees of freedom of the joint but also the clearance between the two bodies linked by this joint. For each functional and toleranced surface, the set of displacements of the actual surface with regard to its nominal location and according to the tolerance zone, is called deviation space. For a simple closed loop mechanism, topological operations are made on the clearance spaces, and on the deviation spaces. In the case of a mechanism with a complex structure, the analysis is more complex but can be computed thanks to a few topological operations on the clearance and deviation spaces. This method allows to compare different tolerancings for each part. Consequently, it is possible to define optimal geometrical tolerances in many cases.