Form Defects Consideration in Polytope Based Tolerance Analysis

The polytope-based tolerance analysis in design process uses a finite set of constraints to represent specifications and propagates these constraints to any objective point in the Euclidean space. The operations of Minkowski sum and intersection on polytopes are well suited to serial and parallel assemblies. The polytope model has been applied to complex assemblies which contain a large number of joints and geometrical tolerances. However, the previous studies on this model consider toleranced features as surfaces of perfect form. The ignorance of form defects in tolerance analysis would result in a significant loss in accuracy and reliability. In this paper, an extension of the polytope model for tolerance analysis considering form defects is described in which the skin model shape representing the physical shape of the product is adopted to simulate the actual toleranced feature in place of the substitute one used conventionally. The combination of polytope model and skin model shape is expected to inherit many of the advantages of each model, combining easy-to-use tolerance propagation and form defects representation with accuracy guarantees. To demonstrate the method and its respective application, a case study of an assembly is illustrated in detail. The proposed method further enhances the capability of the polytope model in handling form defects and provides more realistic assembly results that approximate the actual assembly conditions for design evaluation.