Bolt loosening evaluation method based on normalized screw root equivalent stress and loosening life curve

Bolts are subject to complex loads and prone to loosening failure in transverse random service environments. To establish a loosening life evaluation method applicable to different types of bolts, numerous bolt clamping-force recession curves were obtained by bolt-loosening tests, and the relationship between the transverse displacement external load and loosening life (D-N curve) was established. Subsequently, an equivalent model of the bolt external load and screw load was established based on Castigliano's theorem, and an equivalent model of the screw load and screw-tooth root stress was established based on the deformation coordination equation of elastic mechanics. Based on the above bolt-load equivalent models, the screw-tooth root stresses were equivalently characterized by the transverse displacement of the bolted connection, and then the screw-tooth root equivalent stress-loosening life curve (S_u-N curve) was established to normalize the D-N curves with different bolt diameters. Finally, a bolt-loosening bench test of an antenna bracket under transverse random vibration was performed, and the loosening life of the bolts was evaluated using the S_u-N curve. The maximum relative error between the test and theoretically predicted lives was only 6.26%, which verified the accuracy of the bolt-loosening life evaluation method based on the bolt-load equivalence and provided a certain reference for the bolt-loosening life evaluation and anti-loosening design in a random vibration environment.