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Naval Report 1994
Home : Tolerancing Bibliography : Naval Report 1994
Robust Geometric Calculations with Applications to Tolerancing


Table of Contents:

  1. Principal Investigator.
  2. Productivity Measures.
  3. Summary of Objectives and Approach.
  4. Detailed Summary of Technical Progress.
  5. Transitions and DOD Interactions.
  6. Software and Hardware Prototypes.
  7. List of Publications.
  8. Invited and Contributed Presentations.
  9. Honors, Prizes or Awards Received.
  10. Project personnel promotions obtained.
  11. Project Staff.
  12. Misc Hypermedia URL.
  13. Keywords.


Principal Investigator.


Productivity Measures.


Summary of Objectives and Approach.

  1. Click here to see the project summary.


Detailed Summary of Technical Progress.

  • 3-D Vector Assembly Tolerance Modeling. We have investigated a classic problem which appeared in the literature. It is an analysis of the effects of geometric variation on an assembly of a pin inserted into a hole. The two mating surfaces are cylinders of finite length which can make contact in a variety of ways. It is a significant problem because it has been used to formulate a consistent theory of assembly tolerance analysis.

    The original solution consisted of a complex algebraic derivation, suitable only for simple geometries. Alternative closed form solutions have been derived, based on a statistical solution, for both the position and orientation tolerance of the pin/hole assembly. The new solutions are simpler than the previously published solutions and are more intuitive due to the use of vector loops to define the problem.

  • Free-form Deformation. This work has been extended to show how these solutions can be applied if the hole is non-circular. A free-form deformation is used to change the hole shape. The vector loop is also transformed via this same deformation and tolerance sensitivities are extracted for the new arbitrary shape.

  • Tolerance Bibliography. We currently have a large bibliography on tolerance analysis. This bibliography is available on the network and has been distributed to other researchers. It is being converted into HTML format with abstracts available. Click here for more information on this topic.

  • 3-D Surface Modeling. This year saw the completion of two PhD dissertations by Alan Zundel and Mel Spencer. Alan's dissertation presents a significant improvement in loop detection for surface intersections; Mel addressed the fundamental problem of real root finding for polynomials in Bernstein form. The resulting algorithms are much faster than current library routines, plus they are more numerically stable due to the Bernstein polynomial basis.


    Transitions and DOD Interactions.

  • We are currently working with Boeing Corporation and Hercules Aerospace to determine methods of performing tolerance analysis of large composite panel sections. Large composite panels warp during the curing process and this warpage can severely affect the assembly process. It is believed that the proper allocation of tolerances can be used to minimize assembly problems. For a detailed description of this effort click here


    Software and Hardware Prototypes.

    1. Software for finding all real zeros of polynomials in Bernstein form.
    2. Loop detection for surface patch intersections.
    3. Kinematic Analysis of pin/hole problem using free-form deformations.


    List of Publications.

    1. Jinsong Gao, "Nonlinear Tolerance Analysis of Mechanical Assemblies", Ph.D. dissertation, August 1993, Brigham Young University.
    2. K. W. Chase, Jinsong Gao, S.P. Magleby, "General 2-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments", ADCATS Report No. 94-1, April 1994, Brigham Young University.
      Now Available on the Web: HTML | ACROBAT 3.0
    3. Jinsong Gao, K.W. Chase, S.P. Magleby, "General 3-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments", ADCATS Report No. 94-2, July 1994, Brigham Young University.
    4. K.W. Chase, Jinsong Gao, S.P. Magleby, and C. D. Sorenson, "Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies", ADCATS Report No. 94-3, Aug. 1994, Brigham Young University.
      Now Available on the Web: HTML | ACROBAT 3.0
    5. Jinsong Gao, K.W. Chase, S.P. Magleby, "A Generalized Monte Carlo Simulation Method for Assembly Tolerance Analysis" ADCATS Report No. 94-1, Brigham Young University.
    6. S.E. Benzley, K.G. Merkley, T.D. Blacker, L. Schoof, "Pre- and Post-Processing for the Finite Element Method" Finite Elements in Analysis and Design, (to be published).
    7. Charles David Carr, "A Comprehensive Method for Specifying Tolerance Requirements for Assemblies", M.S. thesis, April, 1993, Brigham Young University.
    8. Douglas Cheney, "A User Interface Specification for CAD/CAM Application Development", M.S. Thesis, Aug. 1994, Brigham Young University.
    9. T. W. Sederberg and G. Wang, "A simple verification of the implicitization formulae for rational Bezier curves," Computer Aided Geometric Design, 11, 225--228, 1994.
    10. Thomas W. Sederberg and Melvin R. Spencer, "Polynomial Real Root Finder in Bernstein Form",
    11. G. Chang and T. W. Sederberg, "Nonnegative quadratic Bezier triangular patches," Computer Aided Geometric Design, 11, 1, 1994.
    12. A. Zundel, T. Saito, S. Owen, T. W. Sederberg, and H. N. Christiansen, "Gas flow visualization for combustion analysis," Energy and Fuels, 1993.
    13. B. Stander, T. W. Sederberg, R. P. Burton, and G. Wang, "Hybrid surfaces," Computer Aided Design, Drafting, and Manufacturing, Vol. 3, No. 2, 1993, 1--7.
    14. T. W. Sederberg and G. Z. Chang, "Isolating the real roots of polynomials using isolator polynomials,'' Algebraic Geometry and Applications, Special Issue of Symposium on the occasion of Shreeram Abhyankar's 60th Birthday edited by C. Bajaj, Springer Verlag, (1993).
    15. Thomas W. Sederberg, Takafumi Saito, Guojin Wang, "Hodographs and normals of rational curves and surfaces", BYU Engineering Computer Graphics Lab Tech Report, 1993."
    16. Thomas W. Sederberg, "Point and tangent computation of tensor product rational Bezier surfaces", BYU Engineering Computer Graphics Lab Tech Report, 1993."
    17. Thomas W. Sederberg and Takafumi Saito, "Rational Ruled Surfaces: Implicitization and Section Curves" BYU Engineering Computer Graphics Lab Tech Report, 1993."
    18. Alan Keith Zundel, "Surface-Surface Intersection: Loop Destruction Using Bezier Clipping and Pyramidal Bounds", Ph.D. Dissertation, Brigham Young University.


    Invited and Contributed Presentations.

    1. 9 June 1994, "Tolerance Analysis - A Quantitative Tool for Concurrent Engineering", Investigating Parametric Design, Chicago, IL.
    2. Nov 1993, "Loop detection in Surface Patch Intersections, "SIAM conference on geometric modeling, Tempe AZ.
    3. 16 Nov 1993, NTT, Tokyo, "B-splines made simple".
    4. 17 Nov 1993, Invited speaker at the NICOGRAPH conference, "A quarter century of computer graphics at BYU"
    5. 19 Nov 1993, Fukuyama University, "B-splines made simple."
    6. 22 Nov 1993, Hiroshima University, "Computer Graphics at BYU."
    7. 16 June 94 International conference on CAGD, Ulvik, Norway, "Shape blending of piecewise curves."


    Honors, Prizes or Awards Received.


    Project Personnel Promotions Obtained.


    Project Staff.


    Misc Hypermedia.

    1. The document , Tolerance Bibliography, is being converted into an HTML document that will include abstracts.


    Keywords.

    1. Tolerance Analysis.
    2. Surface-surface intersection.

     

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