Fuzzy Analysis of Geometric Tolerances Using Interval Method

Abstract

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.