Dynamic Self-balancing Mechanism of Double Balls Solved by Variation Amplitude Method

doi:10.12068/j.issn.1005-3026.2025.20230251

Abstract

Abstract:

The dynamic self-balancing mechanism of a dual-ball automatic balancing device based on a single-disc rotor model is investigated using the variation amplitude method. The system control equations are established through Lagrange equations， and the amplitude-frequency characteristic equations under four working conditions are derived. The Jacobian matrix is directly constructed based on the solution form of the variable amplitude method， avoiding the case-by-case discussion of steady-state equations in the traditional methods， and the system stability conditions are obtained using the Routh-Hurwitz criterion. Numerical analysis reveals that： system vibration intensifies in the lower resonance region； in the upper resonance region， zero-amplitude motion occurs only when parameters satisfy the complete balancing condition， at which point the balls jump to the opposite side of the mass center， achieving complete or partial balance. The research results are validated through time-domain simulations， providing a theoretical basis for the design and optimization of ball-type automatic balancing devices.

Key words: variation amplitude method, rotor, ball, stability, resonance

CLC Number:

TH 113.1

Xiao-zhe CHEN, Shan ZHONG, Bai-tong ZHOU, Wei-ye SHI. Dynamic Self-balancing Mechanism of Double Balls Solved by Variation Amplitude Method[J]. Journal of Northeastern University(Natural Science), 2025, 46(5): 46-53.

Figures/Tables 10

Fig.1 Dynamic model

Table 1 Four ball motion states associated with the steady-state analytical solution

$A ≠ 0$	$A ≠ 0$	$A ≠ 0$	$A = 0$
(a)	(b)	(c)	(d)

Table 1 Four ball motion states associated with the steady-state analytical solution

$A ≠ 0$	$A ≠ 0$	$A ≠ 0$	$A = 0$
(a)	(b)	(c)	(d)

Table 2 Parameters of the vibration system

参数	单位	数值
圆盘质量m₁	g	300
滚珠质量m₀	g	0.4/0.08
圆盘刚度k	N/m	1 700
偏心距e	mm	0.01
滚槽半径a	mm	16.5
圆盘运动阻尼c	Ns/m	0.084
滚珠阻尼c_b	Ns/m	0.001

Fig.2 Amplitude-frequency curves and stability judgment of case (a)

Fig.3 Amplitude-frequency curves and stability judgment of case （b）

Fig.4 Amplitude-frequency curves and stability judgment of case (c)

Fig.5 System vibration amplitude with ball motion states

Fig.6 Time domain response with case one

Fig.7 Time domain response with case two

Fig.8 Stable position of balls

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