Research on Bolt Loosening Detection Based on Fractional Fourier Transform and Vibro-Acoustic Modulation Method

By applying nonlinear vibration-to-sound modulation technology to bolt loosening detection, this paper proposes a new experimental setup and signal-processing method. A linear swept-frequency signal is used to excite low-frequency vibrations, while a fixed-frequency sine wave is used for high-frequency ultrasonic excitation. First, a fractional Fourier transform is applied to the vibration-acoustic modulation signal to transform it into the optimal fractional domain where the energy of the swept-frequency signal is concentrated; next, the swept-frequency signal undergoes a masking filter, and the filtered signal is transformed back to the time domain; finally, the time-domain signal is transformed back to the frequency domain, and the amplitudes of the sum and difference frequency components of the high-frequency signal are extracted as damage parameters. The effectiveness of this method in bolt loosening detection was verified through bolt connection tests, with the applied tightening torque ranging from 10 to 30 N·m. This method is simple to operate and highly robust, making it a reliable approach for detecting the degree of loosening in bolt connections.