General Geometric Model for the Cutting Edge in Thread Turning

Modern requirements for highly critical threads, such as drilling tool-joint threads or trapezoidal threads of heavy machine tools, impose requirements for high accuracy and at the same time wear resistance of thread cutters. Conventional thread cutters available on the global market have a profile that coincides with the thread profile. Their rake angle and the angle of inclination of the cutting edge are typically zero. However, to ensure long tool life and high cutting performance, such tools should have optimal values of the geometric parameters of the cutting part, particularly the rake angle and the inclination angle of the cutting edge. Non-zero values of these angles distort the thread profile, and there are currently no established algorithms for profiling such cutters. This analytical study aims to develop an algorithm that enables the straightforward manufacture of high-performance and at high-precision thread cutters with interpolated straight sides profile flanks for producing trapezoidal, triangular and buttress threads, including those made of difficult-to-machine materials. The obtained analytical expressions accurately describe the cutting edge of such cutters as a hyperbola, functionally dependent on geometric parameters such as pitch, diameter and thread profile angle, as well as on the rake angle and the inclination angle of the cutting edge. To simplify manufacturing, methods of rectilinear approximation of the curvilinear profile are proposed. The validity of such a replacement has been theoretically confirmed, as the maximum deviation of the hyperbolic profile from the linear approximation does not exceed 2 micrometers. The results indicate no significant deviations in the profile angle of the cutters with relatively large rake and inclination angles (γ = 10° and λ = 7°). Deviations from the nominal profile angle of the trapezoidal thread profile angle of 15° do not exceed 0.1°, while for tool-joint threads (30°), they range from 0.01° to 0.09°. However, significant deviations in the profile (up to 0.49°) occur in the case of machining buttress threads with a profile of 7°/45°. Experimental verification on a lathe confirms the theoretical results.