Jacobian-based modeling of dispersions affecting pre-defined functional requirements of mechanical assemblies

Presents a method to mathematically model 3-D tolerance chains around a desired functional requirement of a mechanical assembly. The modeling process uses the concept of virtual joints associated with the toleranced functional elements in a tolerance chain. These virtual joints simulate small possible dispersions of the toleranced functional element in terms of three general small translations and three general small rotations assuming to result from manufacturing inaccuracies. Using standard Jacobian-based computations, it becomes possible to model the effects of such small dispersions of each element in a kinematic chain around a point of interest on an assembly, in particular around the desired functional requirement. The main focus in the paper is on the important ability of the developed tolerance model to explicitly include the effects of dispersions on two types of functional element pairs in a chain around a functional requirement, namely internal pairs (pairs on the same part) and kinematic pairs (pairs on different parts in contact).