passage through the resonance
S.E. Kvashnin, A.A. Maximov
We consider the passage through the resonance at a constant rate of change of frequency of the harmonic excitation of the ultrasonic langevin transducer of longitudinal vibrations with waveguides during idling and under load. The values of the amplitudes of vibrations at the frequency of the dynamic resonance in relation to the amplitude at the resonance frequency in the steady state, as well as the displacement of the dynamic resonance frequency relative to the frequency resonance in the steady state were determined from the mathematical modeling of unsteady vibrations for different values of the friction coefficient and the different rates of change of frequency of the exciting action. Experimental studies of passage through resonance, confirming receipt of the mathematical modeling results, were conducted.
The results obtained from the estimated experiments and mathematical modeling show that, even in the slow passage through resonance (parameter q0 from 106 to 107) for the high-Q ultrasonic vibration systems must take into account the fact that even at not too high speeds of frequency scanning the dynamic resonance frequency shift relative to the resonance frequency of stationary vibrations can reach 30 Hz. With that, the bandwidth of the amplitude frequency response of the ultrasonic vibration system at stationary vibrations at the level of 0.7 of the maximum amplitude is in the range (5–40) Hz. Therefore we can say that in the range n[16–128] s–1, which for the considered ultrasonic system corresponds to the switching range (600–5000), the use in the automatic frequency control system scanning speeds of more than 100 Hz/s makes it impossible to accurately tune to the resonance frequency. However, the search for a preliminary review of the resonance frequency of the ultrasonic system can be scanned with high speeds (up to 300–500 Hz/s), but the accuracy of the determination of the resonance frequency in this case is approximately 10–40 Hz and will require obligatory slow scan near the resonance.