Roundness error separation based on singularity detection and exact-stop of spindle in on-machine measurement of spindle rotation error

•A roundness error separation method based on singularity detection and exact-stop of spindle was proposed.•The method is applicable for on-machine measurement of spindle and independent of spindle encoder.•The singularities of the measured motion have significant correlation with the rotation movement of spindle.•A method was established to extract the continuous optimal WTMM ridges of the measured motion.•The method exhibited better separation accuracy of roundness error than the conventional reversal method.