Tolerance Analysis by Polytopes: Application to Assembly Interferences Diagnosis

One way to perform tolerance analysis on over-constrained mechanical systems is to manipulate sets of constraints. During the 25 last years, several models (domains by Giordano et al., polytopes by Teissandier et al. or T-Maps by Davidson et al.), have been developed to control the assembly of parts without contact interferences. In general, if the intersection between sets of contact constraints is non empty, it is possible to perform an assembly made up of two parts without interference. Then, several works have been realized to qualify the clearance of the assembly. On the other hand, if the intersection is an empty set, it is not possible to perform the assembly between two parts without interference (i.e. without induced strains by the assembly process). This paper will focus on the diagnosis of such empty sets.Operations on n-polytopes (1≤ n ≤6)can be used to predict if an assembly made up of two parts can be performed without interferences. When parts cannot be assembled, the objective of engineers is also to determine the corrections that should be applied to them in order to achieve an assembly. The main objective of this paper is to present a method to determine these corrections. A protocol to find the origins of the interferences and to investigate about the possible modifications to suppress the interference contact between the fabricated parts is described. Finally, a diagnosis is performed and can be used to correct real parts or in some cases to correct manufacturing processes. An example will illustrate the proposed method.