Searching for the twofrequency motion modes of a three-mass vibratory machine with a vibration exciter in the form of a passive auto-balancer

Abstract

The dynamics of a three-mass vibratory machine with the rectilinear translational motion of platforms and a vibration exciter in the form of a ball, roller, or pendulum auto-balancer have been analytically investigated. The existence of steady state motion modes of a vibratory machine that are close to two-frequency regimes has been established. At these motions, the loads in an auto-balancer create constant imbalance, cannot catch up with the rotor, and get stuck at a certain frequency. These loads work as the first vibration exciter, thereby exciting vibrations in resonance with the frequency at which loads get stuck. The second vibration exciter is formed by an unbalanced mass on the body of the auto-balancer. The mass rotates at the rotor's rotation frequency and excites faster vibrations with this frequency. The auto-balancer excites almost ideal two-frequency vibrations. Deviations from the two-frequency law are proportional to the ratio of the mass of the loads to the mass of the platform, which hosts the auto-balancer, and do not exceed 5 %. A three-mass vibratory machine has three resonant (natural) oscillation frequencies, q1, q2, q3 (q1<q2<q3), and three corresponding shapes of platform oscillations. Loads can only get stuck at speeds close to the resonance (natural) oscillation frequencies of the vibratory machine; and to the rotor rotation frequency. A vibratory machine always has only one frequency of load jam, slightly less than the rotor speed. For the case of small viscous resistance forces in the supports of a vibratory machine, an increase in the rotor speed leads to that the new frequencies of load jam: - emerge in pairs in the vicinity of each natural frequency of the vibratory machine oscillations; - one of the frequencies is slightly smaller, and the other is somewhat larger than the natural frequency of the vibratory machine oscillations. Arbitrary viscous resistance forces in the supports can prevent the occurrence of new frequencies at which loads get stuck. Therefore, in the most general case, the number of such frequencies can be 1, 3, 5, or 7, depending on the rotor speed and the magnitudes of the viscous resistance forces in the supports. The results obtained are applicable when designing new vibratory machines and for the numerical modeling of their dynamics. © 2020, V. Yatsun, G. Filimonikhin, A. Haleeva, L. Krivoblotsky, Yu. Machok, M. Mezitis, N. Podoprygora, M. Sadovyi, G. Strautmanis.