A Spline Algorithm for Modeling Cutting Errors on Turning Centers

Published

October 1, 2002

Author(s)

David E. Gilsinn, Herbert T. Bandy, Alice V. Ling

Abstract

Turned parts on turning centers are made up of features with profiles defined by arcs and lines. An error model for turned parts must take into account not only individual feature errors but also how errors carry over from one feature to another. In the case where there is a requirement of tangency between two features, such as a line tangent to an arc or two tangent arcs, any error model on one of the features must also satisfy a condition of tangency at a boundary point between the two features. Splines, or piecewise polynomials with differentiability conditions at intermediate or knot points, adequately model errors on features and provide the necessary degrees of freedom to match constraint conditions at boundary points. The problem of modeling errors on features becomes one of least squares fitting of splines to the measured feature errors subject to certain linear constraints at the boundaries. The solution of this problem can be formulated uniquely using the generalized or pseudo inverse of a matrix. This is defined and the algorithm for modeling errors on turned parts is formulated in terms of splines with specified boundary constraints.

Citation

Journal of Intelligent Manufacturing

Volume

13

Issue

No. 5

Pub Type

Journals

Keywords

error modeling, generalized inverse, least squares, machine tool, pseudo inverse, spline

Citation

Gilsinn, D. , Bandy, H. and Ling, A. (2002), A Spline Algorithm for Modeling Cutting Errors on Turning Centers, Journal of Intelligent Manufacturing (Accessed May 9, 2025)