Ultrasonic measurement method for axial stress in bolts based on the multi-frequency weighted energy attenuation coefficient

In response to the low measurement accuracy of traditional single-wave and dual-wave methods for bolt axial stress based on the acoustic elasticity effect, this paper proposes a method for measuring bolt axial stress based on the ultrasonic multi-frequency band weighted energy decay coefficient. Firstly, a functional relationship between the energy decay coefficient and the bolt axial stress is established based on the theory of polycrystalline ultrasonic scattering. Secondly, to improve the calibration accuracy of model parameters and bolt stress measurement, the particle swarm optimization algorithm is combined to determine the optimal normalization weight coefficient of the decay coefficient in each frequency band, establishing a multi-frequency band weighted energy decay coefficient model. Finally, hardware and software systems for measuring bolt axial stress are established. The multi-frequency band weighted energy decay coefficient method proposed in this paper, as well as the traditional single-wave and dual-wave methods based on the acoustic elasticity effect, are used to calibrate parameters and measure stresses on different strength bolt specimens. This validates the accuracy and stability of the method proposed in this paper. This method provides higher measurement accuracy for high-strength short bolts, with an average relative error of only 3.09%.