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).
Highlights
Among such vibratory machines as sieves, vibratory tables, vibratory conveyors, vibratory mills, the promising ones are the multi-frequency, resonance, and multi-frequencyresonance machines.Multi-frequency vibratory machines demonstrate greater performance [1], resonance vibratory machines are the Eastern-European Journal of Enterprise Technologies ISSN 1729-37744/7 ( 106 ) 2020 most energy-efficient [2], and multi-frequency resonance vibratory machines combine the advantages of both multi-frequency and resonance vibratory machines [3]
The most effective and easy way to excite resonance two-frequency oscillations is based on the use of a ball, a roller, or a pendulum auto-balancer as a vibration exciter [4]
The aim of this study is to find possible two-frequency modes of motion of the vibratory platforms of a three-mass vibratory machine with the rectilinear translational motion of the platforms, excited by a passive auto-balancer
Summary
Among such vibratory machines as sieves, vibratory tables, vibratory conveyors, vibratory mills, the promising ones are the multi-frequency, resonance, and multi-frequencyresonance machines. The most effective and easy way to excite resonance two-frequency oscillations is based on the use of a ball, a roller, or a pendulum auto-balancer as a vibration exciter [4]. In this regard, there is a general issue related to substantiating the operability of the proposed technique for different vibratory machines. The proposed technique employs a Sommerfeld effect [5,6,7,8,9] The feasibility of this technique for exciting two-frequency vibrations for three-mass vibratory machines has not been theoretically investigated up to now. Our previous findings [19,20,21,22] have been applied to resolve this issue
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