Search for the dual­frequency motion modes of a dual­mass vibratory machine with a vibration exciter in the form of passive auto­balancer

We analytically investigated dynamics of the vibratory machine with rectilinear translational motion of platforms and a vibration exciter in the form of a ball, a roller, or a pendulum auto-balancer. The existence of steady-state motion modes of the vibratory machine was established, which are close to the dual-frequency regimes. Under these motions, loads in the auto-balancer create constant imbalance, cannot catch up with the rotor, and get stuck at a certain frequency. In this way, loads serve as the first vibration exciter, inducing vibrations with the frequency at which loads get stuck. The second vibration exciter is formed by the unbalanced mass on the casing of the auto-balancer. The mass rotates at rotor speed and excites faster vibrations of this frequency. The auto-balancer excites almost perfect dual-frequency vibrations. Deviations from the dual-frequency law are proportional to the ratio of loads’ mass to the mass of the entire machine, and do not exceed 2 %. A dual-frequency vibratory machine has two oscillation eigenfrequencies. Loads can get stuck only at speeds close to the eigenfrequencies of vibratory machine's oscillations, or to the rotor rotation frequency. The vibratory machine has always one, and only one, frequency at which loads get stuck, which is slightly lower than the rotor speed. At low rotor speeds, there is only one frequency at which loads get stuck. In the case of small viscous resistance forces in the supports, at an increase in the rotor speed, the quantity of frequencies at which loads get stuck in a vibratory machine increases, first, to 3, then to 5. In this case, new frequencies at which loads get stuck: – occur in pairs in the vicinity of each eigenfrequency of the vibratory machine's oscillations; – one of the frequencies is slightly lower, while the other is slightly higher, than the eigenfrequency of vibratory machine's oscillations. Arbitrary viscous resistance forces in the supports may interfere with the emergence of new frequencies at which loads get stuck. That is why, in the most general case, the quantity of such frequencies can be 1, 3, or 5, depending on the rotor speed and the magnitudes of viscous resistance forces in supports.