An optimal frequency selection method for online torque monitoring of bolted joints based on ultrasonic guided wave

The reliability of bolted joints is crucial in aerospace, mechanical manufacturing, and civil engineering. However, online monitoring of bolt torque based on ultrasonic guided waves often suffers from suboptimal frequency selection, leading to poor detection sensitivity, while environmental noise interference further reduces measurement accuracy. To overcome these challenges, this study proposes an innovative theoretical framework for optimal frequency selection grounded in the guided wave transmission energy (TE) spectrum. A two-dimensional frequency-domain finite element model (FDFEM) is established, and a TE spectrum calculation method is derived from the principle of energy conservation, quantitatively linking guided wave TE to excitation center frequency (ECF). Different from conventional empirical approaches, the proposed method uses the global extremum of the TE spectrum as the optimization criterion, achieving maximum TE at 230 kHz. The experimental results validate that at the optimal ECF of 230 kHz, the sensitivity of TE to torque changes reaches its peak, with a nearly perfect linear correlation (R² = 0.985), demonstrating excellent detection stability. In contrast, the commonly used 150 kHz ECF exhibits significant drawbacks, with the TE at this frequency being only 1/12 of that at 230 kHz, leading to a substantial decrease in detection reliability (R² = 0.638). The comparative results fully highlight the value and significance of optimal frequency selection. The systematic method proposed in this study, from theoretical modeling and energy spectrum calculation to frequency optimization, effectively fills the critical gap in the theory of guided wave frequency selection for bolt loosening detection.