Nonsynchronous Vibration of Planar Autobalancer/Rotor System With Asymmetric Bearing Support

Abstract

Due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, nonsynchronous limit-cycle vibration exists. In such undesirable situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. However, a comprehensive study into this nonlinear behavior of an imbalanced planar-rigid rotor/autobalancing device (ABD) system mounted on a general bearing holding asymmetric damping and stiffness forces including nonconservative effects cross-coupling ones has not been fully conducted. Therefore, this research primarily focuses on the unstable nonsynchronous limit-cycle behavior and the synchronous balancing condition of system under the influence of the general bearing support. Here, solutions for rotor limit-cycle amplitudes and the corresponding whirl speeds are obtained via a harmonic balance approach. Furthermore, the limit-cycle stability is assessed via perturbation and Floquet analysis, and all the possible responses including undesirable coexistence for the bearing parameters and operating speeds have been thoroughly studied. It is found that, due to asymmetric behavior of bearing support, the multiple limit cycles are encountered in the range of supercritical speeds and more complicate coexistences are invited into the ABD–rotor system compared to the case with idealized symmetric bearing supports. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in more practical rotor systems mounted on a asymmetric general bearing support.

Supercritical Coexistence Behavior of Coupled Oscillating Planar Eccentric Rotor/Autobalancer System

“…As shown in (24), the natural frequencies are the function of vertically coupled two masses (i.e., AB/rotor unit and foundation) and the associated stiffness. Fundamentally, Ω cr.2 represent the natural frequency associated with the mode of rotor in horizontal direction.…”

“…Furthermore, [21] showed three different types of limit cycle behavior of the planar dual-ball automatic balancer: a pure-rotary periodic motion, a pure oscillatory periodic motion, and a compoundrotary periodic motion. Recently, Jung and DeSmidt [22][23][24] presented the analytical approach for merged synchronous responses and unstable nonsynchronous supercritical limit cycle of single-plane ABD/rotor system based on harmonic like balancing approach. Although such nonlinear and automatic balancing behavior of ideally configured single unit AB/rotor with symmetric supports (or bearings) has been widely studied and is generally understood, an investigation about the coupled behavior of AB/rotor system with other oscillating subsystems has not been fully conducted.…”

Studying the load jam modes within the framework of a flat model of the rotor with an auto­balancer

“…-a rotor on anisotropic supports that executes flat motion and is statically balanced with a two-ball auto-balancer [12]; -a rotor mounted on isotropic supports atop a platform that moves in a straight-line direction, with the rotor balanced with a two-ball auto-balancer.…”

“…Passive auto-balancers, ball (roller), pendulum, etc. [1][2][3][4][5][6][7][8][9][10][11][12][13], are used for balancing high-rotational rotors at operation. The same devices with a single or more loads can be used in vibration machines in order to excite vibrations [14][15][16][17][18].…”

“…-load jams (caused by the Sommerfeld effect) [5][6][7][8][9][10][11][12][13][14][15][16]; -parametric and other oscillations of loads [17,18].…”