Arc Extraction Analysis for Circularity Measurement of Small Cylindrical Parts by the Segmenting-stitching Method

To reduce the stitching error of circularity measurement of small cylindrical workpieces(Diameter less than 3 mm)by the segmenting-stitching method,arc contour extraction is analyzed in this paper.The coordinates of cross-sectional circle of a small cylindrical part are segmented into several equal arcs to be obtained by a two-dimensional coordinate measuring machine.The circularity contour of the small cylindrical part can be formed by stitching a series of arc contours which are calculated by the obtained arc coordinate data.Due to the different measuring pressure angles of different measuring positions,the accuracy of obtained arc coordinate points is different.The bigger the pressure angle is,the accurate the obtained arc coordinate data are.The experiments show that the accuracy of two ends of the arc data is not as good as the central part.Therefore,the two ends of the obtained arc data are appropriately to be cut off,namely,only the central part of the arc data are extracted to be used for the stitching.As a result,the mean value of the matching coefficient is enhanced by 12%,the deviation between the overlap part of the neighbouring arc contour is reduced by 26%,and the average curvature of the arc contours is improved with the extraction method.Thus,the accuracy of the stitched circularity contour can be improved by this extraction procedure in the segmenting-stitching method for the circularity measurement of the small cylindrical parts.

Improved Circularity Metrology of Small Cylindrical Workpieces by the Segmenting-stitching Technique

To address the alignment and measuring force problem in the segmenting-stitching technique for the circularity metrology of small cylindrical workpieces(diameter less than 1.5 mm and length less than 10 mm),a magnet combination jig method is proposed.A small round magnet is attached between the round magnetic jig and small cylinder,and the other end of the small cylindrical workpiece is attached to some cylindrical magnets.Thus,the smaller cylinder can be put in the V-groove and measured successfully with the magnet combination.For verifying the advantage of the magnet combination jig,four measurement quality evaluations are proposed:the circumferential deviation of neighbor arc contours,radial deviation of neighbor arc contours,angle of inclination between the V-groove and small cylinder,and curvature of the obtained arc.The results show that the matching coefficient is enhanced by 98%,the Euclidean distance of overlap parts of neighbor arc contours is reduced by 68%,the position error is reduced 27%,and the average curvature of the arc contours is improved.It can be concluded that the measuring quality can be enhanced prominently by this magnet combination method for the segmenting-stitching method.

On the construction of balanced repeated measurements designs with good circular properties

Several fields,such as biological,medical,public health,agricultural sciences,etc.,require circular balanced repeated measurement designs with fewer unequal number of repeated measure-ments than the number of treatments.Also,the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units.However,balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case.In this paper,several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed.The proposed construction of designs has high efficiency and,therefore,can save the cost of experimentations due to a fewer exper-imental subjects.Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters.A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.