Development and implementation of computer-based methods for tolerancing of mechanical parts

Computer-aided tolerancing is a key issue of integrated CAD/CAM. Tolerances specify restrictions on dimensional and geometric deviations of components since excessive deviations hinder assembling without interference and impair assembly performance. This research describes new methods to address each of the three activities that comprise tolerancing: Geometric analysis, tolerance analysis, and tolerance design. Geometric analysis converts design requirements into algebraic inequality form.;This module transforms assembly critical dimensions into algebraic expressions relating component dimensions and deviations. Components are represented by a generic surface feature based scheme, and assemblies are represented by a mating of relatively located components. Geometric analysis is performed in two stages. A vectorial contribution is obtained through vector loop analysis after identifying functional dimensions. A small-deviation contribution is then superposed calculated using an orthogonal matrix chain representing small translational and rotational deviations between components. A geometric reasoning based prototype implemented in prolog was tested on an example. Statistical tolerance analysis estimates the percentage of assemblies simultaneously satisfying all design requirements given known statistical distributions. The new method supports multiple, non-linear design requirements, and virtually all distribution types. The method is based on the second moment reliability method with Chen-Lind modification. Non-convergence problem in finding the design point was addressed. Effectiveness of the method in handling deviations from normal distribution, termed distributional non-linearity, was verified through a series of experiments. Common situations with functional non-linearity involving product-form were identified from Bjorke's method. Bjorke's application of equivalent beta distribution was incorporated to address functional non-linearity. The new method was compared with other analytical methods under a wide range of conditions and was found to give the best results in all cases; the results are very close to the exact results in most cases.;Tolerance design determines optimal design tolerances which are related to parameters of corresponding statistical distributions. The problem is formulated as a constrained non-linear optimization model, with a flexible cost-based objective function, and yield or tolerance based constraints. Zoutendijk's feasible directions method and the tolerance analysis method described earlier forms the basis of this module. The accuracy and the efficiency of the method was demonstrated through three examples.