| The failure of bolted connections in mechanical systems is often difficult to prevent and extremely harmful.The main failure modes of static load bolts include plastic deformation or even fracture of the thread or screw caused by excessive axial stress,and loosening caused by insufficient axial prestress.And for dynamic load bolts,long-term monitoring of their axial stress is particularly important for early warning of fatigue fracture failure.It can be seen that it is of great significance to realize the accurate measurement and control of the bolt axial stress.Based on the actual industrial production requirements,a bolt axial stress measurement method based on the ratio of transit time of high-frequency cylindrical guided waves is proposed to nail the problems of poor versatility and cumbersome measurement procedures that exist in the current ultrasonic measurement methods of bolt axial stress.First,the Pochhammer-Chree equation including the attenuation caused by the ultrasonic scattering is derived.Then,a joint solution algorithm based on particle swarm optimization and Newton's method is proposed to solve the equation.Therefore,the high-frequency cylindrical guided wave dispersion curves of the complex wave number,the phase velocity,the group velocity and the attenuation coefficient in a typical circular bolt-like cross-section steel rod are obtained.Then,the above solution results are analyzed in depth,and the propagation characteristics of high-frequency cylindrical guided waves are summarized.Secondly,combining the acoustoelastic effect and the above results,after a series of deformations and simplifications are carried out in the neighborhood of the extreme value of the group velocity,the expression of the group velocity of the cylindrical guided wave considering the axial static load is derived.Then,combining the actual characteristics of the bolt axial stress measurement,a bolt axial stress measurement method based on the ratio of the transit time of the different modes among the high-frequency cylindrical guided wave is proposed.Thirdly,based on the propagation characteristics of high-frequency cylindrical guided waves,the signal characteristics under impulse excitation response are analyzed.Aiming at the significant modal aliasing interference problem,a guided wave modal decomposition method based on the empirical wavelet transform is proposed and its validity is proved by a comparative experiment of processing a noisy aliasing simulation signal between the well-known empirical mode decomposition.Then,in order to make the stress measurement method practical(obtain the precise transit time of the signal),a nonlinear filtering method based on the extended Kalman filter is proposed and applied to the signal of the decomposed modes.In the end,the software and hardware of the experimental system are introduced in detail.Then,the measured signal was analyzed in depth.According to the actual situation and the physical characteristics of the guided waves,the extraction and mode decomposition of certain pulses in the full-length signal is proposed.Then,the axial stress calibration and measurement experiments were carried out on M8 ordinary hexagon head half-threaded bolts.The R square coefficient of the calibration fitting curve reached 0.9773,and the average measurement error was only 5.7%.In conclusion,the method proposed in this paper can greatly simplifies the measurement procedure of bolt axial stress measurement with acceptable accuracy. |
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