Analytical Prediction and Experimental Validation of Bolt Self-Loosening under Vibration

The self-loosening of bolted joints under vibrational loading remains a persistent challenge in many engineering applications, especially in the automotive industry, where safety and reliability are of paramount importance. Predicting self-loosening behavior is challenging because numerous parameters influence joint performance, as well as the limitations of conventional experimental testing. This study presents a novel analytical model for predicting bolt and nut loosening behavior under transverse vibration. The model extends existing approaches by incorporating additional parameters such as displacement, clamping force, and under-head friction torque. To enhance usability, the model was implemented in an MS Excel–based calculator with macro functions, enabling engineers to perform loosening analyses under varying conditions. The model adapts and extends existing approaches from the literature by incorporating an energy equilibrium approach, which calculates bolt rotation by balancing the torsional strain energy accumulated during vibration with the kinetic energy released once the applied torque exceeds the critical threshold. The analytical predictions were validated through Junker vibration tests, showing strong agreement with experimental data. The proposed model and tool provide a practical and accessible method for predicting loosening, thereby enabling the design of safer and more reliable fasteners while strengthening industrial competitiveness.