Distributions of tension and torsion in a threaded connection

Threaded connection is a common structure in engineering applications, and its load distribution plays a critical role on the static and dynamic performances of the system. Although Sopwith (1948) studied the tension distribution along a thread helix, a model that includes the tension and torsion distributions in threaded connections is still missing. In this paper, we establish a comprehensive model which takes tension-torsion coupling into consideration for thread connection for the first time. In the proposed model, the bolt and nut are considered as two linearly elastic bodies with a tension-torsion coupling deformation, and deformation of the thread is calculated by the modified theory of the trapezoidal cantilever beam model. Based on the compatibility condition of these deformations, tension-torsion coupling equilibrium equations for the threaded connection can be built up. Our theoretical analysis shows that the proposed model agrees with the Sopwith's theory when the lead angle of the threaded connections is sufficiently small. However, the torque neglected by the Sopwith's theory must be taken into account in the cases of threaded connections with large lead angles. In addition, we perform a three-dimensional finite element analysis to demonstrate the validity of the proposed model. Finally, influence of geometrical and material parameters on load distribution is investigated. The finding of this work may provide a new insight into the fastening and anti-loosening design for threaded connections.