Determination of the position of handtight engagement plane of a tapered inch thread based on the cloud of points from coordinate measuring machine

Traditionally, control of manufactured threaded surfaces is carried out using gauges. However, in single-piece or small-scale production of parts with non-standard threads, the production of expensive special gauges becomes unprofitable. The trend of recent decades, associated with a reduction in serial production, has led to the increasingly widespread use of universal measuring equipment and, above all, coordinate measuring machines (CMM). To control metric or buttress cylindrical threads, the accuracy of which, according to the standard, is determined using the virtual pitch thread diameter, a number of methods have being developed to calculate this diameter using point clouds from CMMs. In the case of tapered threads, their accuracy must be determined by the position of their planes of handtight engagement. This position, namely: the distance from this plane to the end plane of the threaded part has to be within the limits specified by the tolerance. To calculate that distance, the presented paper proposes to use two contiuous ideal helical surfaces adjacent to the point cloud obtained from the CMM. These two surfaces together, like a ring gauge with a given virtual pitch thread diameter, define the desired plane. The calculations of the point cloud for the case of an inch tapered thread, performed using the proposed method, showed that the distance of the axial position of the plane corresponds to the values specified in the standard. At the same time, the has established that the accuracy of calculations significantly depends on the accuracy of determining the coordinates of the thread points. An acceptable accuracy calculation (0.2%) was obtained when determining the thread points coordinates with an accuracy of 5 µm, which is achievable using some of optical CMMs. The proposed approach can also be applied for the case of screwing an external tapered threads with an internal cylindrical thread. Thus, the research results presented in this article have prospects and require further improvement, for example, in order to determine the axis of ideal screw surfaces adjacent to the point cloud of real threads