Abstract
Generalized models have been built of one-, two-, and three-mass vibration machines with a rectilinear translational motion of platforms and a vibration exciter in the form of a ball, a roller, or a pendulum auto-balancer. In the generalized model of a single-mass vibration machine, the platform relies on an elastic-viscous support with the guides enabling the platform’s rectilinear translational motion. A passive auto-balancer is installed on the platform. In the generalized models of two- and three-mass vibration machines, each platform relies on a fixed external elastic-viscous support with the platforms coupled in pairs by elastic-viscous inner supports. The guides allow the platforms to move rectilinearly translationally. A passive auto-balancer is installed on one of the platforms. We have derived differential equations of the motion of vibration machines. The equations are reduced to the form that is independent of the type of an auto-balancer. The models of particular one-, two- and three-mass vibration machines can be obtained from the generalized models by selecting a specific type of the auto-balancer. The models of particular two-mass vibration machines can also be obtained from the corresponding generalized model by rejecting one of the external elastic-viscous supports. The models of particular three-mass vibration machines can also be derived from the corresponding generalized model by rejecting: – one or two external elastic-viscous supports; – one of the three inner elastic-viscous supports; – one or two external elastic-viscous supports and one of the three inner elastic-viscous supports. The constructed models are applicable both for analytical studies into dynamics of the relevant vibration machines and for performing computational experiments. When employed in analytical studies, the models are designed to search for the established modes of a vibration machine motion, to determine conditions for their existence and stability
Highlights
That is why it is a relevant task to create vibration machines that combine the benefits of multi-frequency and resonant vibration machines [3]
The simplest and most reliable ways to excite the resonance oscillations of platforms and rotors are based on the Sommerfeld effect [4,5,6,7,8,9,10,11,12,13,14,15,16]
One of these techniques is based on using a ball, a roller, or a pendulum auto-balancer in the form of a vibration exciter [8, 11, 12]
Summary
Among such types of vibration machines as screens, vib ration tables, vibration conveyors, vibration mills, etc., the promising ones are multi-frequency and resonant machines. A special mode of the pendulums’ motion is exploited for this purpose [9], or of the balls or rollers [10], which occurs at small resistance forces to the motion of loads relative to the autobalancer housing Under this mode, the loads get together, cannot catch up with the shaft on which the auto-balancer is mounted, and get stuck on the resonance frequency of the platform oscillations. The above review demonstrates that it is a relevant task to theoretically investigate the workability of the technique for exciting the two-frequency vibrations by a ball, a roller, or a pendulum auto-balancer For this purpose, it is necessary to build generalized models and derive differential equations of motion of one-, two-, and three-mass vibration machines with translational motion of vibration platforms and a vibration exciter in the form of a passive auto-balancer. The scope of application of the generalized models and differential equations of motion: conducting theoretical research and computational experiments
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