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Description
Geometrical tolerances define allowable manufacturing variations in the features of mechanical parts. For a given feature (planar face, cylindrical hole) the variations may be modeled with a T-Map, a hyper solid in 6D small displacement coordinate space. A general method for constructing T-Maps is to decompose a feature into points, identify the variational limits to these points allowed by the feature tolerance zone, represent these limits using linear halfspaces, transform these to the central local reference frame and intersect these to form the T-Map for the entire feature. The method is explained and validated for existing T-Map models. The method is further used to model manufacturing variations for the positions of axes in patterns of cylindrical features.
When parts are assembled together, feature level manufacturing variations accumulate (stack up) to cause variations in one or more critical dimensions, e.g. one or more clearances. When the T-Maps model is applied to complex assemblies it is possible to obtain as many as six dimensional stack up relation, instead of the one or two typical of 1D or 2D charts. The sensitivity of the critical assembly dimension to the manufacturing variations at each feature can be evaluated by fitting a functional T-Map over a kinematically transformed T-Map of the feature. By considering individual features and the tolerance specifications, one by one, the sensitivity of each tolerance on variations of a critical assembly level dimension can be evaluated. The sum of products of tolerance values and respective sensitivities gives value of worst case functional variation. The same sensitivity equation can be used for statistical tolerance analysis by fitting a Gaussian normal distribution function to each tolerance range and forming an equation of variances from all the contributors. The method for evaluating sensitivities and variances for each contributing feature is explained with engineering examples.
The overall objective of this research is to develop method for automation friendly and efficient T-Map generation and statistical tolerance analysis.
When parts are assembled together, feature level manufacturing variations accumulate (stack up) to cause variations in one or more critical dimensions, e.g. one or more clearances. When the T-Maps model is applied to complex assemblies it is possible to obtain as many as six dimensional stack up relation, instead of the one or two typical of 1D or 2D charts. The sensitivity of the critical assembly dimension to the manufacturing variations at each feature can be evaluated by fitting a functional T-Map over a kinematically transformed T-Map of the feature. By considering individual features and the tolerance specifications, one by one, the sensitivity of each tolerance on variations of a critical assembly level dimension can be evaluated. The sum of products of tolerance values and respective sensitivities gives value of worst case functional variation. The same sensitivity equation can be used for statistical tolerance analysis by fitting a Gaussian normal distribution function to each tolerance range and forming an equation of variances from all the contributors. The method for evaluating sensitivities and variances for each contributing feature is explained with engineering examples.
The overall objective of this research is to develop method for automation friendly and efficient T-Map generation and statistical tolerance analysis.
ContributorsChitale, Aniket (Author) / Davidson, Joseph (Thesis advisor) / Sugar, Thomas (Thesis advisor) / Shah, Jami (Committee member) / Arizona State University (Publisher)
Created2018
Description
Conformance of a manufactured feature to the applied geometric tolerances is done by analyzing the point cloud that is measured on the feature. To that end, a geometric feature is fitted to the point cloud and the results are assessed to see whether the fitted feature lies within the specified tolerance limits or not. Coordinate Measuring Machines (CMMs) use feature fitting algorithms that incorporate least square estimates as a basis for obtaining minimum, maximum, and zone fits. However, a comprehensive set of algorithms addressing the fitting procedure (all datums, targets) for every tolerance class is not available. Therefore, a Library of algorithms is developed to aid the process of feature fitting, and tolerance verification. This paper addresses linear, planar, circular, and cylindrical features only. This set of algorithms described conforms to the international Standards for GD&T.; In order to reduce the number of points to be analyzed, and to identify the possible candidate points for linear, circular and planar features, 2D and 3D convex hulls are used. For minimum, maximum, and Chebyshev cylinders, geometric search algorithms are used. Algorithms are divided into three major categories: least square, unconstrained, and constrained fits. Primary datums require one sided unconstrained fits for their verification. Secondary datums require one sided constrained fits for their verification. For size and other tolerance verifications, we require both unconstrained and constrained fits
ContributorsMohan, Prashant (Author) / Shah, Jami (Thesis advisor) / Davidson, Joseph K. (Committee member) / Farin, Gerald (Committee member) / Arizona State University (Publisher)
Created2014
Description
Almost all mechanical and electro-mechanical products are assemblies of multiple parts, either because of requirements for relative motion, or use of different materials, shape/size differences. Thus, assembly design is the very crux of engineering design. In addition to nominal design of an assembly, there is also tolerance design to determine allowable manufacturing variations to ensure proper functioning and assemblability. Most of the flexible assemblies are made by stamping sheet metal. Sheet metal stamping process involves plastically deforming sheet metals using dies. Sub-assemblies of two or more components are made with either spot-welding or riveting operations. Various sub-assemblies are finally joined, using spot-welds or rivets, to create the desired assembly. When two components are brought together for assembly, they do not align exactly; this causes gaps and irregularities in assemblies. As multiple parts are stacked, errors accumulate further. Stamping leads to variable deformations due to residual stresses and elastic recovery from plastic strain of metals; this is called as the ‘spring-back’ effect. When multiple components are stacked or assembled using spot welds, input parameters variations, such as sheet metal thickness, number and order of spot welds, cause variations in the exact shape of the final assembly in its free state. It is essential to understand the influence of these input parameters on the geometric variations of both the individual components and the assembly created using these components. Design of Experiment is used to generate principal effect study which evaluates the influence of input parameters on output parameters. The scope of this study is to quantify the geometric variations for a flexible assembly and evaluate their dependence on specific input variables. The 3 input variables considered are the thickness of the sheet material, the number of spot welds used and the spot-welding order to create the assembly. To quantify the geometric variations, sprung-back nodal points along lines, circular arcs, a combination of these, and a specific profile are reduced to metrologically simulated features.
ContributorsJoshi, Abhishek (Author) / Ren, Yi (Thesis advisor) / Davidson, Joseph (Committee member) / Shah, Jami (Committee member) / Arizona State University (Publisher)
Created2020