Abstract
This paper reports a study into the dynamics of a vibratory machine composed of a viscoelastically-fixed platform that can move vertically and two identical inertial vibration exciters. The vibration exciters' bodies rotate at the same angular velocities in opposite directions. The bodies host a single load in the form of a ball, roller, or pendulum. The loads' centers of mass can move relative to the bodies in a circle with a center on the axis of rotation. The loads' relative movements are hindered by the forces of viscous resistance. It was established that a vibratory machine theoretically possesses the following: – one to three oscillatory modes of movement under which loads get stuck at almost constant angular velocity and generate total unbalanced mass in the vertical direction only; – a no-oscillation mode under which loads rotate synchronously with the bodies and generate total unbalanced mass in the horizontal direction only. At the same time, only one oscillatory mode is resonant and exists at the above-the-resonance speeds of body rotation, lower than some characteristic speed. At the bodies' rotation speeds: ‒ pre-resonant; there is a globally asymptotically stable (the only existing) mode of load jams; ‒ above-the-resonance, lower than the characteristic velocity; there are locally asymptotically stable regimes ‒ both the resonance mode of movement of a vibratory machine and a no-oscillations mode; ‒ exceeding the characteristic velocity: there is a globally asymptotically stable no-oscillations mode. Computational experiments have confirmed the results of theoretical research. At the same time, it was additionally established that it would suffice, to enter a resonant mode of movement, to slowly accelerate the bodies of vibration exciters to the above-the-resonance speed, less than the characteristic speed. The results reported here could be interesting both for the theory and practice of designing new vibratory machines
Highlights
In resonant vibratory machines, low-mass inertial vibration exciters induce the intense vibrations of platforms [1]
The results reported here could be interesting both for the theory and practice of designing new vibratory machines Keywords: resonant vibratory machine, Sommerfeld effect, inertial vibration exciter of targeted action, single-mass vibratory machine
The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect
Summary
Low-mass inertial vibration exciters induce the intense vibrations of platforms [1]. ‒ reacts to a change in the resonant frequencies of a vibratory machine caused by a change in the platform loading Due to these features, resonant vibration exciters that operate on the Sommerfeld effect do not need an automatic control system and, have the simplest design. To build resonant vibratory machines with the translational movement of platforms, it is important to design and investigate the performance of an inertial vibration exciter of targeted action, which operates on the Sommerfeld effect. Such a vibration exciter could induce perturbing forces only in the direction of platform movement, and would not. 3/7 ( 111 ) 2021 load the vibratory machine (its frame, guides, supports, etc.)
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