Axis determination for calculation of virtual pitch diameter of a thread given by point cloud from CMM

Abstract

Measurement of thread surfaces accuracy is a subject of this investigation. The standard complex indicator of thread accuracy – the virtual pitch thread diameter (VPTD) is considered. The author previously developed and published the method of calculation of VPTD. This method is based on data, which are obtained from coordinate measuring machines (CMM). However, using this method the preliminary determination of the thread axis position is assumed. Actually this case does not always occur in practice. This disadvantage limited the possibility of CMM application for the assessment of the thread accuracy significantly.
Taking it into account, the additional method for the thread axis determination for the cases where the axis is located arbitrarily is offered in this article. This method includes two stages. One of them is based on the determination of average values of point cloud coordinates received from CMM. The second one is based on minimization (maximization) of objective function. The objective function, in turn, includes such parameters as parameters of thread location in CMM coordinate system. VPTD is used as the minimized (maximized) value. The concerned method is confirmed by computer calculations, which show sufficient reliability and «robust» algorithm of the accepted approach.
Calculations were done with point cloud calculated theoretically by using other computer program, and also with points that were received from CMM in real measurement. This investigation determined sufficient minimum number of points to obtain the reliable result at the first most effective stage of the method. Thus, the research showed that for VPTD assessment the earlier offered method and the additional new method gives a possibility to use CMM instead of using gauges.