Abstract
Analytical-numerical methods have been applied to investigate the steady-state vibrations of a two-mass 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. A procedure for studying the modes of load jamming has been devised for the systems similar to the one under consideration. The procedure is based on the idea of parametric solution to the problem of finding the frequencies of load jamming and a bifurcation theory of motion. It has been established that a two-mass vibratory machine has two resonance frequencies of rotor rotation and two corresponding shapes of platform oscillations. The use of the procedure has shown that for the case of small resistance forces, a vibratory machine: ‒ has five possible modes of load jamming, with the first shape of resonance vibrations of platforms being excited under modes 1 and 2, the second shape ‒ 3 and 4, and, under the mode 5, the frequency of load jamming is close to the frequency of rotor rotation; ‒ demonstrates stable jamming modes under the odd (1, 3, 5) load jamming modes; ‒ shows that the jamming modes 1 and 2 are suitable to excite the resonance oscillations of platforms and for industrial application; ‒ exhibits that increasing the rotor speed monotonously increases the amplitudes of platform oscillations corresponding to a certain jamming mode; ‒ proves that the amplitude of resonance platform oscillations can be controlled by changing the rotor rotation velocity. The viscous resistance forces acting on a first platform reduce (up to the complete elimination) the first range of rotor speeds, at which the first resonance shape of platform oscillations is excited. The internal forces of viscous resistance, acting between the platforms, reduce (up to the complete elimination) the second range of rotor speeds, at which the second shape of resonance platform oscillations is excited. The viscous resistance forces acting on the loads at motion relative to an auto-balancer reduce both ranges
Highlights
The most effective and simple technique to excite resonance two-frequency vibrations is based on the use of a ball, a roller, or a pendulum auto-balancer as a vibration exciter [10]
The bifurcation theory of motion makes it possible to assess the stability of different jamming modes
The procedure is based on the idea of parametric solution to the problem of finding the frequency of load jamming (14) and a bifurcation theory of motion
Summary
Among such vibratory machines as sieves, vibratory tables, vibratory conveyors, vibratory mills, etc., the promising ones are multi-frequency-resonance machines. – the anti-resonance mode of vibratory machine operation is implemented over a wide parameter range [8], and is less dependent on the mass of a load [9], etc It is proposed in [10] to use a ball-, a roller-, or a pendulum auto-balancer to excite two-frequency resonance vibrations in vibratory machines with different kinematic motion of platforms. Paper [17] developed the generalized models of single-, two-, and three-mass vibratory machines with a translational motion of the platforms and a vibration exciter in the form of a ball-, roller-, or a pendulum auto-balancer. To investigate the steady-state vibrations of a two-mass vibratory machine, excited by a passive auto-balancer, one can apply the analytical-numerical methods developed in [19, 20] using an example of the single-mass vibratory machines. The following tasks have been set: – to devise a methodology for the analytical-numerical analysis of the steady-state vibrations of a two-mass vibratory machine; – to find, at certain ratios of smallness between the system parameters, different steady-state motions of a vibratory machine and to assess their stability; – to investigate the influence of external and internal resistance forces on these motion modes
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