Tolerance analysis and synthesis by interval constraint networks

v V variable (corresponding to entity, attribute, and functional requirement) v interval assigned for V vup upper limit of V viow lower limit of V VnOm nominal value of the variable V any value in V 1. Introduct ion Tolerance design plays an important a role in the relationship between performance and the manufacturing cost of a product. Decreasing the tolerance range will improve performance but will also increase manufacturing costs. It is desirable to optimize the tolerance range under such constraints of product design as the relationship between the dimensions of entities of a component and the functional requirement of the design. In this paper, we develop a constraint-based reasoning mechanism to analyze a given set of design tolerances and synthesize a new set of tolerances to satisfy the functional requirements of a product. For a given design of a mechanical part, a relationship can be derived for the functional requirement in terms of the entities. This relationship can be expressed as: Y = f(Xl,X;z, ..., X,) where Y is the functional requirement and Xi is the im entity. n is the number of entities that are related by the equation to the corresponding functional requirement. In tolerance analysis, the entity tolerances, X1.X2, ..., Xn, are given. The goal is to ensure that the functional requlrement tolerance, Y, is met. The tolerances Xi and Y, are the range of acceptable values for, Xi and Y, respectively. If the assigned functional requirement tolerances are not met, the tolerances for the entities need to be reassigned by tolerance synthesis in order to achieve the functional requirements. In tolerance synthesis, the functional requirement tolerance, Y, is given. The goal is to determine a set of feasible entity tolerances, X1,X2, ..., Xn, to fulfill the functional requirement. The task of tolerance synthesis is more difficult because n entity tolerances are determined based on one functional requirement tolerance. I n contrast, in tolerance analysis, one functional requirement tolerance is determined based on n entity tolerances. Figure 1 gives the concept and relationship of tolerance analysis and synthesis.