We analyze a general multiposition comparator measurement procedure that leads to partial removal of artifact error for a class of problems including roundness metrology, measurement of radial error motions of precision spindles, and figure error metrology of high-accuracy optical components. Using spindle radial error motion as an explicit example, we present a detailed analysis of a complete test with N orientation of a test ball with respect to the spindle. In particular, we show that (1) all components of the ball roundness error average to zero except those with frequencies of kN cycles/revolution, where k is a positive integer; and (2) the combined standard uncertainty of the measurement is proportional to 1/sqrt(N). We then show how a complete set of measurements for an N-position test can be synthesized from only two measurements, and we derive a general expression for the combined standard uncertainty as a function of the number of positions n (2 < n < N) actually measured in an N-position test. This uncertainty can serve as a useful guide to measurement design, involving trade-offs between multiple setup cost and complexity and required levels of angular harmonic resolution and combined standard measurement uncertainty.
Citation: Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology
Pub Type: Journals
difference techniques, dimensional metrology, error separation, multistep methods, optical figure metrology, roundness, spindle errors