Nonlinear Tolerance Allocation for Assembly Components

As one of many design variables, the role of dimension tolerances is to restrict the amount of size variation in a manufactured feature while ensuring functionality. In this study, a nonlinear integer model has been modeled to allocate the optimal tolerance to each individual feature at a minimum manufacturing cost. While a normal distribution determines statistically worst tolerances with its symmetrical property in many previous tolerance allocation studies, a asymmetrical distribution is more realistic because its mean is not always coincident with a process center. A nonlinear integer model is modeled to allocate the optimal tolerance to a feature based on a beta distribution at a minimum total cost. The total cost as a function of tolerances is defined by machining cost and quality loss. After the convexity of manufacturing cost is checked by the Hessian matrix, the model is solved by the Complex Method. Finally, a numerical example is presented demonstrating successful model implementation for a nonlinear design case.

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