Quantitative evaluation of residual torque of a loose bolt based on wave energy dissipation and vibro-acoustic modulation: A comparative study

A wave energy dissipation (WED)-based linear acoustic approach and a vibro-acoustic modulation (VM)-based nonlinear method were developed comparatively, for detecting bolt loosening in bolted joints and subsequently evaluating the residual torque of the loose bolt. For WED-based, an analytical model residing on the Hertzian contact theory was established, whereby WED was linked to the residual torque of a loose bolt, contributing to a linear index. For VM-based, contact acoustic nonlinearity (CAN) engendered at the joining interface, when a pumping vibration perturbs a probing wave, was interrogated, and the nonlinear contact stiffness was described in terms of a Taylor series, on which basis a nonlinear index was constructed to associate spectral features with the residual torque. Based respectively on a linear and a nonlinear premise, the two indices were validated experimentally, and the results well coincided with theoretical predication. Quantitative comparison of the two indices surmises that the VM-based nonlinear method outperforms the WED-based linear approach in terms of sensitivity and accuracy, and particularly when the bolt loosening is in its embryo stage. In addition, the detectability of the nonlinear index is not restricted by the type of the joint, against a high dependence of its linear counterpart on the joint type.