Novel Formulation of the Tightening and Breakaway Torque Components in Threaded Fasteners

New formulas are developed for the torque-tension relationship, various torque components, and breakaway torque values in threaded fastener applications. The three-dimensional aspects of the lead helix and thread profile angles and the kinetic and static friction coefficients are all taken into account. Two scenarios of the contact pressure between threads and under the turning fastener head are considered, namely, uniformly distributed and linearly distributed contact pressure scenarios. The effect of thread pitch, lead helix and thread profile angles, friction coefficients, and fastener geometry is discussed. Results from the new formulas are compared with the approximate torque-tension relationship provided in the literature. A percentage difference analysis indicates that the new formulas provide a significant improvement that would enhance the reliability and safety of bolted connections, especially in critical applications.