Motion equations of the single­mass vibratory machine with a rotary­oscillatory motion of the platform and a vibration exciter in the form of a passive auto­balancer

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.150339

Keywords:

inertial vibration exciter, dual frequency vibrations, resonance vibratory machine, auto-balancer, inertial vibratory machine

Abstract

This paper describes a mechanical model of the single-mass vibratory machine with a rotary-oscillatory motion of the platform and a vibration exciter in the form of a passive auto-balancer. The platform can oscillate around a fixed axis. The platform holds a multi-ball, a multi-roller, or a multi-pendulum auto-balancer. The auto-balancer's axis of rotation is parallel to the turning axis of the platform. The auto-balancer rotates relative to the platform at a constant angular velocity. The auto-balancer's casing hosts an unbalanced mass in order to excite rapid oscillations of the platform at rotation speed of the auto-balancer. It was assumed that the balls or rollers roll over rolling tracks inside the auto-balancer's casing without detachment or slip. The relative motion of loads is impeded by the Newtonian forces of viscous resistance. Under a normally operating auto-balancer, the loads (pendulums, balls, rollers) cannot catch up with the casing and get stuck at the resonance frequency of the platform's oscillations. This induces the slow resonant oscillations of the platform. Thus, the auto-balancer is applied to excite the dual-frequency vibrations.

Employing the Lagrangian equations of the second kind, we have derived differential motion equations of the vibratory machine. It was established that for the case of a ball-type and a roller-type auto-balancer the differential motion equations of the vibratory machine are similar (with accuracy to signs) and for the case of a pendulum-type vibratory machine, they differ in their form.

Differential equations of the vibratory machine motion are recorded for the case of identical loads.

The models constructed are applicable both in order to study the dynamics of the respective vibratory machines analytically and in order to perform computational experiments.

In analytical research, the models are designed to search for the steady-state motion modes of the vibratory machine, to determine the condition for their existence and stability

Author Biographies

Volodymyr Yatsun, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

PhD, Associate Professor

Department of Road Cars and Building

Irina Filimonikhina, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

PhD, Associate Professor

Department of Mathematics and Physics

Nataliia Podoprygora, Volodymyr Vynnychenko Central Ukrainian State Pedagogical University Shevchenka str., 1, Kropyvnytskyi, Ukraine, 25006

Doctor of Pedagogical Sciences, Associate Professor

Department of Natural Sciences and their Teaching Methods

Oleksandra Hurievska, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropyvnytskyi, Ukraine, 25006

PhD, Associate Professor

Department of Mathematics and Physics

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Published

2018-12-10

How to Cite

Yatsun, V., Filimonikhina, I., Podoprygora, N., & Hurievska, O. (2018). Motion equations of the single­mass vibratory machine with a rotary­oscillatory motion of the platform and a vibration exciter in the form of a passive auto­balancer. Eastern-European Journal of Enterprise Technologies, 6(7 (96), 58–67. https://doi.org/10.15587/1729-4061.2018.150339

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Section

Applied mechanics