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The Calculation of CMM Measurement Uncertainty via The Method of Simulation by Constraints



Steven D. Phillips, Bruce R. Borchardt, Daniel S. Sawyer, William T. Estler, David E. Ward, K Eberhardt, M. Levenson, Marjorie A. McClain, B Melvin, Ted Hopp, Y Shen


The calculation of task specific measurement uncertainty when using coordinate measuring machines is an important and challenging task. Current methods to address this issue use simulation techniques (e.g., the virtual CMM) where the propagation of known parametric errors (angular and translational errors of each axis) is computed using the kinematic equations for the CMM structure. These methods require the assessment of the individual parametric errors of the CMM - information that is usually not immediately available and is not included in National or International Standards regarding CMM performance specifications. We have developed a simulation technique which generalizes this simulation concept to allow the calculation of task specific measurement uncertainty based on standardized performance data, e.g., ANSI B89.4.1 CMM performance specifications. The method treats the performance specifications as mathematical constraints on the (infinite number) of possible virtual CMM states (each defined by specific parametric errors) that are permitted by the performance data. These constraints, together with reasonable assumptions, such as the parametric errors are smoothly varying functions, greatly limit the number of permissible states that the CMM may occupy. (This can be considered as placing limits on the allowed regions of CMM parametric error phase space.) For example, the ANSI B89.4.1 Standard''s volumetric performance test includes the measurement of ball bar lengths near the extremes of the CMM workzone. This is, in effect, a boundary condition on the allowed parametric error functions. In order to be self consistent, the constrained parametric errors, i.e. the permissible virtual CMM states, must faithfully reproduce the original performance specifications when a simulation of the performance test is computed. Surprisingly, standard specifications provide sufficient constraints to allow the reasonable calculation of task specific uncertainty. Several examples of this technique are shown, and the relationship with current simulation methods -- as highly constrained virtual states confined to a small region of phase space - is presented.
Proceedings Title
Proceedings of American Society for Precision Engineering
Conference Dates
October 5-10, 1997
Conference Location
Norfolk, VA
Conference Title
American Society for Precision Engineering


Phillips, S. , Borchardt, B. , Sawyer, D. , Estler, W. , Ward, D. , Eberhardt, K. , Levenson, M. , McClain, M. , Melvin, B. , Hopp, T. and Shen, Y. (1997), The Calculation of CMM Measurement Uncertainty via The Method of Simulation by Constraints, Proceedings of American Society for Precision Engineering, Norfolk, VA (Accessed June 22, 2024)


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Created January 1, 1997, Updated June 2, 2021