Analytical Expression of Cross Sectional Geometry of Various Screw Threads and Finite Element Analysis of the Mechanical Behavior of Multiple-Thread Screws

Abstract

Distinctive mechanical behavior of bolted joints is caused by the helical shape of thread geometry. Mathematical expression of the helical thread geometry of a single-thread screw has successfully been derived in the previous study. Using the derived equations, finite element models were constructed by taking account of the effect of the helix, and it is clarified how the stress distributes along the thread root and where the maximum stress occurs. Meanwhile, there are various thread forms other than a single-thread triangular screw. In this study, mathematical expressions of the helical thread geometry and the cross sectional area of multiple-thread screws, trapezoidal thread and pipe thread are derived in the same manner as in the case of a single-thread screw. Using the equations thus obtained, finite element models with multiple-thread screws are constructed, and its tightening process by torque method is analyzed. Numerical results show that the stress distribution patterns are basically identical along all helixes for each multiple-thread screw. It is also found that the maximum Mises stress occurs at the first bolt thread root and it increases as the lead of multiple-thread screw increases.