A method for analyzing and evaluating form errors of cylindrical parts is investigated. The profile of a cylindrical test piece is measured at several sections along the axis under the same setting on the rotating table of a roundness measuring machine which has an accurate vertical feed of the detector. An orthogonal function consisting of Fourier series and orthogonal polynomials is fitted to the observed data in cylindrical coordinates sampled at every 7.5 degrees for each section of the test piece. Geometrical meanings of individual terms of the orthogonal function are disclosed. By dissolving the total sum of squares of the observations into parts corresponding to individual terms and testing their significances against the residual variance, the form erorrs of the test piece as well as the errors in measurement are assessed independently of the setting conditions. The method is applied for measuring form errors in a few plug gauges and cylindrical machine parts.
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