GapSpace multi-dimensional assembly analysis

Assembly tolerance analysis is a process to determine the effect that tolerances specified on individually manufactured parts have on an assembly of these parts. Tolerance specifications form an important link between the product design, the manufacturing process and the assembly process. Mechanical engineers use tolerances to define allowable/possible manufactured uncertainties to insure interchangeable assemblies with proper functionalities. This paper proposes a revised GapSpace assembly analysis (RGSA) model to analyze the assembleability of the design under various tolerance specifications, such as worst-case tolerance specifications, statistical tolerance specifications and assembly tolerance specifications. The distinct property of this method is that it uses an inter-element gap (the clearance between different mechanical parts) as the basic functional unit for performing various assembly analyses.;A prominent characteristic of the GapSpace assembly analysis model is that the assembly success for a group of parts is exclusively determined by intrinsic geometric properties of manufactured parts. The model is composed of three main elements: gaps, constraining simplices and fitting conditions. A gap describes the relationship between a pair of features on two different parts; A constraining simplex represents a basic dimensional unit of a part; A fitting condition is a necessary and sufficient condition for assembly-level checking of the design. The set of independent fitting conditions is treated as the key element for performing various GapSpace assembly analyses. Each fitting condition has two equivalent representations: a gap representation and a geometric representation. Through properly analyzing the two representations, four types of assembly analyses are supported by the model: assembleability analysis, sensitivity analysis, assembly quality analysis (free play, e.g.) and tolerance synthesis. Developed from the GapSpace model (Zou 2002), the revised model (RGSA model) integrates various dimension and tolerance schemes (including both limit tolerances and geometric tolerances) into the calculation of constraining simplices, and uses various numerical methods, including Monte Carlo simulations, to evaluate the multivariate distributions of linear or non-linear fitting conditions. The application of the RGSA model is shown for some practical engineering examples and the results are compared with traditional tolerance analysis methods. The RGSA model is thus proven to be a reasonable and effective tolerance analysis technique.