Vibration Analysis of a Self-Excited Vibration in a Rotor System Caused by a Ball Balancer

Abstract

The ball balancer has been used as a vibration suppression device in rotor systems. It has a superior characteristic that the vibration amplitude is reduced to zero theoretically at a rotational speed range higher than the critical speed. However, the ball balancer causes a self-excited vibration near the critical speed when the balls rotate in the balancer. This self-excited vibration may occur in the wide rotational speed range with a large amplitude vibration, and in such a case, escaping from it becomes difficult. In this paper, the occurrence region and the vibration characteristics of the self-excited vibration caused by the ball balancer are investigated. The nonlinear theoretical analysis is performed and a set of the fundamental equations governing the self-excited vibration is obtained. The influences of the parameters of the ball balancer, such as, the damping of the ball’s motion, the ball’s mass, and radius of the balls’ path, are explained and they are also validated experimentally.

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

“…Ozan [19] proposed a new flap based mass distribution control system adjusting the orientations of the flaps and moving the COG of the balancers to an appropriate location to compensate the imbalance vibration. Furthermore, Inoue, T., Ishida [20] also validated the limit cycle analysis of planar ABD-rotor with the experimental results. 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.…”

“…Consequently, the AB/rotor unit dynamically interacts with the flexible foundation; thus this system is quite in accordance with two-spring and two-mass coupled oscillator in the vertical direction. Compared to the previous works [20][21][22][23] focusing on a single unit of AB-rotor-bearing system, the eccentricity of this study is that the AB-rotor-bearing unit has been connected with an additional component, flexible foundation, in coupled oscillating manner. Here, the two fixed inertial frames, { 1 , 2 , 3 } with the origin 1 and { 1 , 2 , 3 } with the origin 2 , are devised to describe the proposed system.…”

“…As long as the two balls of AB are fitted in an identical racing track of AB, it is well known from [13,[20][21][22][23] and extensive numerical investigations that the two balls of AB are merged together, continuously rotated around the rotor in nonsynchronous manner, resulting in a large whirling of system. And the whirling speed of merged balls is approximated as a constant frequency such as ∈ R. In other words, ( ) = 1 ( ) = 2 ( ) = ⋅ , where is a time.…”

“…(2) Using the harmonic like balancing approach, the synchronous response Y can be obtained from the coefficients of cos[Ω⋅ ] and sin[Ω⋅ ] in (15a) through (15c), which is independent of nonsynchronous response X. [20,21]. Also, although the coefficients 4 (X) for = 5, 6, are described as a function of X, these are insignificant.…”

“…Also, although the coefficients 4 (X) for = 5, 6, are described as a function of X, these are insignificant. This is because the limit cycle response appears with the first harmonic + Ω [20,21].…”