Four-point error separation technique for cylindricity

A four-point error separation technique integrating three-point roundness and two-point straightness error separations is proposed to measure and reconstruct a cylindrical profile for the accurate evaluation of cylindricity. Four probes mounted onto two sections in the probe carriage target the surface of the cylinder to detect the differential vector of the least-squares centers in two adjacent cross-sectional profiles of the cylinder. The vector of the least-squares center in each cross-sectional profile is extracted by accumulation. The spatial curved median line of the cylinder is determined by fitting the extracted least-squares centers. Theoretical analysis and numerical validation prove that radial error motions of the spindle and straightness error motions of the slider are eliminated during reconstruction of the cylindrical profile. The influence of tilt error motions of the spindle on the accuracy of error separation can be weakened by reducing the distance between the two sections in which the four probes are located. The spatial median line profile of the cylinder is accurately determined even if the error motions of the spindle are not repeatable in each revolution. An experimental system was constructed to perform comparison experiments. The results validate the fact that the technique has higher precision in reconstructing cylindrical profiles owing to its robust anti-interference ability. The technique is suitable for in situ measurement of cylindricity under unrepeatable radial error motions of the spindle and indeterminate straightness error motions of the slider.