Analytical Model of Tapered Thread Made by Turning from Different Machinability Workpieces

High-precision tapered threads are widely used in hard-loaded mechanical joints, especially in the aggressive environment of the drilling of oil and gas wells. Therefore, they must be made of workable materials often difficult to machine. This requires the use of high-performance cutting tools, which means the application of non-zero geometric parameters: rake and edge inclination angles. This study is based on analytical geometry methodology and describes the theoretical function of the thread profile as convoluted surfaces dependent on the tool’s geometric angles. The experiments were conducted using a visual algorithm grounded on the obtained function and prove the practical use of the scientific result. They predict the required accuracy of thread made using a lathe tool with a rake angle of up to 12°.