Numerical modelling and robust parametric estimation of surfaces useful for representation of tooth flanks
Abstract
This paper concerns modelling of surfaces resulting from measurements or from digital simulation of surfaces e.g., tooth flanks, based on the theory of gearing, with intentionally introduced modification usually defined in discrete form. Computational methods of modelling of curves and surfaces are briefly reviewed. Problems of stability of geometric modelling and related problems of parametric estimation of mathematical models, representing curves and surfaces are discussed. An analysis of multicollinearity of the measurement matrix is performed. A method of regularization of matrix, containing coordinates of nodes from considered surface, is proposed. This method allows to improve the robustness of parametric estimation and is specially helpful for on-line parametric estimation of surface models utilized during measurements.
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References
[1] ADINA Theory and Modeling Guide. ADINA R&D, Inc., Watertown, MA, 1997.[2] B.D.O. Anderson, J.B. Moore. Optimal Filtering. Prentice Hall, Inc., Englewood Cliffs, NJ, 1979.
[3] K.J. Bathe. Finite Element Procedures. Prentice Hall, Inc., Englewood Cliffs, NJ, 1996.
[4] M.L. Baxter. Basic geometry and tooth contact of hypoid gears. Industrial Mathematics, 2: 1- 28, 1961.
[5] M.S. Casale, E.L. Stanton. An overview of analytic solid modeling. IEEE Computer Graphics and Applications 5: 45- 56, 1985.
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