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Modeling Geometrical Deviations and Tolerance Analysis Based on NURBS and Isogeometric Method

Aghabeigi, Mostafa | 2022

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 56729 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Movahhedy, Mohammad Reza; Khodaygan, Saeed
  7. Abstract:
  8. Non-uniform rational B-spline (NURBS) curves and surfaces are one of the most powerful tools of computer-aided design, which are able to model both free-form and analytic shapes. In this dissertation, the idea of using NURBS curves as a tool for modeling geometrical deviations and tolerance analysis of mechanical assemblies is presented and evaluated. In the first step the effect of changing the defining variables of NURBS on shape of the curve is investigated. After that, by establishing a relationship between profile tolerance and random NURBS curves, two concepts of tolerance zone width and correlation function are introduced, and a method based on regression algorithms and covariance of the control polygon are used for their calculations. Consequently, a sample problem involving attachment of some elastic parts and creating a closed ring is presented and solved, in order to evaluate the application of the presented concepts in solving tolerance analysis problems. In the process of solving the problem the NURBS control polygons are utilized as vector chains and isogeometric analysis is invoked to take deformation of the parts during the assembly process into account. The numerical examples demonstrated that in the case of using sufficient number of control vertices, the outcome of the model is independent of the details of the utilized NURBS structure and the outcome converges to a unique solution. Comparison of the model results with Monte Carlo simulations and experimental evidence shows accuracy of the method. Finally, the example problem is used as a platform to study design of an assembly with the aim of reducing the effect of error propagation and existence of error-absorbing region and the optimum point within the design space is demonstrated
  9. Keywords:
  10. Non-Uniform Rational B-Splines (NURBS)Functions ; Random Process Model ; Isogeometric Method ; Computer Aided Design (CAD) ; Static Tolerance Analysis ; Profile Tolerance ; Tolerance Analysis

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