Recently,Coordinate Measuring Machines(CMMs)are widely used to measure roundness errors.Roundness is calculated from a large number of points collected from the profiles of the parts.According to the Guide to the Expression of Uncertainty in Measurement(GUM),all measurement results must have a stated uncertainty associated the them.However,no CMMs give the uncertainty value of the roundness,because no suitable measurement uncertainty calculation procedure exists.In the case of roundness measurement in coordinate metrology,this paper suggests the algorithms for the calculation of the measurement uncertainty of the roundness deviation based on the two mainly used association criteria,LSC and MZC.The calculation of the sensitivity coefficients for the uncertainty calculation can be done by automatic differentiation,in order to avoid introducing additional errors by the traditional difference quotient approximations.The proposed methods are exact and need input data only as the measured coordinates of the data points and their associated uncertainties.
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