Containing geometrical tolerances in concurrent optimal allocation of design and process tolerances

Abstract

Geometrical tolerances are used to limit the variations of the actual measured features of a part relative to its ideal features or datum features in form, profile, orientation, location, and run-out. Although the geometrical feature variations can also contribute significantly to the manufacturing cost as well as the quality of a product, the current studies on concurrent tolerancing mainly focus on the concurrent optimal allocation of dimensional tolerances, with little consideration of geometrical tolerances. The purpose of this paper is to extend the concurrent tolerance allocation model to take the geometrical tolerance requirements into account for multi-process machining parts. Firstly, the function relationship between the quality loss and the process tolerances of a product with multiple relevant assembly dimensions is studied, and the geometrical tolerance is attached to the contact point of the corresponding feature surface of the part as a zero-length dimension parameter with tolerance. Then, the functional assembly tolerances are assigned to process dimensional and geometrical tolerances based on the given part process planning, during which geometrical tolerances are treated as the equivalent dimensional tolerances or the additional tolerance constraints according to their own characteristics. An extended model for concurrently allocating dimensional and geometrical tolerances is established by using total cost minimization as the criteria, the product function constraints, geometrical tolerance constraints, and economical process tolerance bounds as constraint conditions, and the nonlinear programming technique is used to solve the extended model to obtain the optimized design tolerances and process tolerances. Finally, an example of concurrent tolerance allocation of bevel gear assembly is given to validate the effectiveness of the proposed method.