Matching Items (2)
Filtering by
- All Subjects: Mathematics
Description
Mostly, manufacturing tolerance charts are used these days for manufacturing tolerance transfer but these have the limitation of being one dimensional only. Some research has been undertaken for the three dimensional geometric tolerances but it is too theoretical and yet to be ready for operator level usage. In this research, a new three dimensional model for tolerance transfer in manufacturing process planning is presented that is user friendly in the sense that it is built upon the Coordinate Measuring Machine (CMM) readings that are readily available in any decent manufacturing facility. This model can take care of datum reference change between non orthogonal datums (squeezed datums), non-linearly oriented datums (twisted datums) etc. Graph theoretic approach based upon ACIS, C++ and MFC is laid out to facilitate its implementation for automation of the model. A totally new approach to determining dimensions and tolerances for the manufacturing process plan is also presented. Secondly, a new statistical model for the statistical tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables is presented. 4-D probability Maps have been developed in which the probability value of a point in space is represented by the size of the marker and the associated color. Points inside the part map represent the pass percentage for parts manufactured. The effect of refinement with form and orientation tolerance is highlighted by calculating the change in pass percentage with the pass percentage for size tolerance only. Delaunay triangulation and ray tracing algorithms have been used to automate the process of identifying the points inside and outside the part map. Proof of concept software has been implemented to demonstrate this model and to determine pass percentages for various cases. The model is further extended to assemblies by employing convolution algorithms on two trivariate statistical distributions to arrive at the statistical distribution of the assembly. Map generated by using Minkowski Sum techniques on the individual part maps is superimposed on the probability point cloud resulting from convolution. Delaunay triangulation and ray tracing algorithms are employed to determine the assembleability percentages for the assembly.
ContributorsKhan, M Nadeem Shafi (Author) / Phelan, Patrick E (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Farin, Gerald (Committee member) / Roberts, Chell (Committee member) / Henderson, Mark (Committee member) / Arizona State University (Publisher)
Created2011
Description
Current trends in the Computer Aided Engineering (CAE) involve the integration of legacy mesh-based finite element software with newer solid-modeling kernels or full CAD systems in order to simplify laborious or highly specialized tasks in engineering analysis. In particular, mesh generation is becoming increasingly automated. In addition, emphasis is increasingly placed on full assembly (multi-part) models, which in turn necessitates an automated approach to contact analysis. This task is challenging due to increases in algebraic system size, as well as increases in the number of distorted elements - both of which necessitate manual intervention to maintain accuracy and conserve computer resources. In this investigation, it is demonstrated that the use of a mesh-free B-Spline finite element basis for structural contact problems results in significantly smaller algebraic systems than mesh-based approaches for similar grid spacings. The relative error in calculated contact pressure is evaluated for simple two dimensional smooth domains at discrete points within the contact zone and compared to the analytical Hertz solution, as well as traditional mesh-based finite element solutions for similar grid spacings. For smooth curved domains, the relative error in contact pressure is shown to be less than for bi-quadratic Serendipity elements. The finite element formulation draws on some recent innovations, in which the domain to be analyzed is integrated with the use of transformed Gauss points within the domain, and boundary conditions are applied via distance functions (R-functions). However, the basis is stabilized through a novel selective normalization procedure. In addition, a novel contact algorithm is presented in which the B-Spline support grid is re-used for contact detection. The algorithm is demonstrated for two simple 2-dimensional assemblies. Finally, a modified Penalty Method is demonstrated for connecting elements with incompatible bases.
ContributorsGrishin, Alexander (Author) / Shah, Jami J. (Thesis advisor) / Davidson, Joe (Committee member) / Hjelmstad, Keith (Committee member) / Huebner, Ken (Committee member) / Farin, Gerald (Committee member) / Peralta, Pedro (Committee member) / Arizona State University (Publisher)
Created2010