Peculiarities of calculating the diameter of the hole for setting the thread-forming part
Authors: Danylova Liudmyla , Lapkovskyi Serhii , Prykhodko Vasyl 
Published: December 2022

The effectiveness of technologies is determined by the total technical effect obtained from their implementation. One of the ways to improve technology efficiency indicators is the introduction of assembly-thread-forming processes based on the use of thread-forming fasteners in product designs.
Thread-forming screws, pins, bushings are screwed into smooth holes and form a threaded profile by cutting or deformation. The reduction in labor intensity is achieved by eliminating the operation of preliminary threading, and the resulting connections have high operational and technical indicators. In the production of electronic equipment and devices, where, according to technical requirements, the formation of chips is undesirable, thread-extruding screws are used. Despite the advantages of self-tapping screws, their widespread use is restrained by several disadvantages: the strength of the connection using screws is lower than in the connection using a stud or bolt, screws with an increased pitch have unsatisfactory locking performance, with a diameter of more than 10 mm torque instability and thread profile deformation are observed. Improving the quality of threaded joints by ensuring the optimal size of the hole for threading is the topic of this publication. The calculation of the setting diameter for thread-forming parts with a large step has its own characteristics and must be decided taking into account friction, strength and tolerance.
The main causes of surface defects in the installation of thread-forming fasteners are those related to geometry - rolling in a filled contour, which leads to an axial displacement of the surface layers of the metal. Determining the optimal value of the diameter of the hole for screwing the thread-forming part, on the one hand, as large as possible, but not more than the permissible value, is the purpose of this work. The nomenclature of thread-forming fastening elements is constantly expanding, while the ratio of the height of the profile to the step is a variable value even within the limits of one standard. Therefore, the calculation method should be universal, taking into account the conditions of friction, strength, tolerances.
Thread forming processes are described as plane deformation processes. Physically, the mechanism of plastic deformation of metals is presented in the form of shifts in planes where the tangential stresses have reached their maximum value. For plane deformation, the trajectories of maximum tangential stresses in two orthogonal directions are described by slip lines, or characteristics.
The slip line method allows you to calculate contact stresses and deforming forces, fully determine the fields of stresses and velocities in the sections of deformable metal, and also analyze local phenomena, which are usually fundamental in solving technological problems. The characteristics of plane plastic deformation allow you to find a solution using a graphical method. The use of this method allows you to determine the appearance of the slip line field, or its geometric characteristics, which establish the relationship between the maximum tangential stress and normal hydrostatic pressure, i.e., the deforming force, as well as determine the appearance and geometric parameters of the formed profile, the height of which is limited by the permissible amount of overflow of the profile.
Analyzing the geometric parameters of the deformation zone of the threaded turn of the part, the diameter of the hole for the thread-forming fastening part was theoretically justified. The methodology of this calculation is implemented in the form of software and mathematics. These recommendations are related to the geometric parameters of the end part of the self-tapping screw. The results of the work will improve the quality of the connection with the thread-forming fastening part due to the optimization of the diameter of the hole of the part.
On the basis of solving the problem of the plasticity theory about the immersion of the indenter into the rigid-plastic region and the analysis of the plastic zone in the region of the largest deformations, the geometric parameters and the appearance of the formed profile are established. The method of using sliding lines allows you to calculate and analyze the geometry visually, to observe the change in the shape of the deformable profile from the ratio of the height of the profile to the pitch of the thread, the material and the coefficient of sliding. This visualization allows you to choose a value of filling the profile even greater than one, when a sufficiently large size of the “crater” of the thread does not allow the profile to overflow. This makes it possible to increase the height of the thread profile and the contact area, as well as to expand the tolerance for the hole in the part. As a result, we have an increase in the strength of the connection and the reliability of the assembly process.