Bolted Joints are convenient to assemble and disassemble parts but sometimes loosening problems have happened spontaneously and it might cause major accidents. It is important to prevent loosening issues when mechanical engineers design bolted joints, but it becomes increasingly difficult because optimized machine design using cutting-edge material is getting complicated. Recently loosening mechanisms could be obvious gradually by using FEM, but still there is not enough study how much bolted joints loosen like estimated spontaneous loosening torque.
Takenaka et al. (Wed,) studied this question.