LAUSR

Abstract Error separation (ES) techniques can eliminate the systematic error caused by the rotary table, and thus, overcome the accuracy limit of state-of-the-art roundness instruments. However, up to now, no rigorous and effective approaches are available for evaluating the measurement uncertainty in ES techniques. To achieve the highest precision of ES techniques, this paper investigates the uncertainty in the two-step roundness measurements, including modeling, quantification, and mitigation of the uncertainty propagation. First, the law of propagation of angle uncertainty is analytically derived by calculating the partial derivative of the Laplace transform of roundness function with respect to the angle. Based on the uncertainty propagation law, the measurement uncertainty can be evaluated quantitatively. Moreover, for inhibiting the uncertainty propagation, approaches are proposed, which not only eliminate the suppressed harmonics completely but also reduce the measurement uncertainty substantially. Finally, Monte Carlo simulations and test measurements are both performed for verification.