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A Model for Geometry-Dependent Errors in Length Artifacts



Daniel S. Sawyer, Brian Parry, Christopher J. Blackburn, Balasubramanian Muralikrishnan, Steven D. Phillips


We present a detailed model of dimensional changes in long length artifacts, such as step gauges and ball bars, due to bending under gravity. The comprehensive model is based on evaluation of the gauge points relative to the neutral bending surface. It yields the well-known errors observed when the gauge points are located off the center of symmetry of a bar or rod but also reveals the under appreciated, but significant, error associated with out-of-straightness of a bar or rod even if the gauge points are on the center of symmetry. For example, one experimental result shows a length change of greater than 1.5 µm on a 1 m ball bar with an out-of-straightness of 0.4 mm. This and other results are in good agreement with the model presented in this paper
Journal of Research (NIST JRES) - 117.013
Report Number


ASME B89.1.12, ball bars, Coordinate Measuring Machine (CMM), design of length artifacts, dimensional artifacts, ISO 10360, high accuracy length standards, performance evaluation of (CMM), Step Gauges


Sawyer, D. , Parry, B. , Blackburn, C. , Muralikrishnan, B. and Phillips, S. (2012), A Model for Geometry-Dependent Errors in Length Artifacts, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 19, 2024)


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Created September 27, 2012, Updated November 10, 2018