INVESTIGATING THE NONLINEAR BEHAVIOR AND STABILITY ANALYSIS OF THE AUTOMATIC BALL BALANCER BY THE MULTIPLE SCALES METHOD

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REZAEE MOUSA; GHORBANPOUR LEILA

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Journal: Modares Mechanical Engineering Year:2017 | Volume:17 | Issue:4 Page(s): 188-198

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Title

INVESTIGATING THE NONLINEAR BEHAVIOR AND STABILITY ANALYSIS OF THE AUTOMATIC BALL BALANCER BY THE MULTIPLE SCALES METHOD

Author(s)

REZAEE MOUSA | GHORBANPOUR LEILA | Issue Writer Certificate

Keywords

AUTOMATIC BALL BALANCERQ2

DYNAMIC RESPONSEQ2

STABILITYQ2

MULTIPLE SCALE METHODQ2

Abstract

Unbalance in rotating machines causes malfunction of the system operation and may lead to its failure.Therefore, the sources for imbalance should be investigated, identified, and measured to solve the mentioned challenges. Rotating unbalance appears when the geometric and the inertia axes of the rotor do not coincide, and as a result this causes self- excited vibrations. One of the methods to control and reduce the unbalances is utilizing AUTOMATIC BALL BALANCER (ABB). In previous studies, the STABILITY and the dynamic behavior of ABB have been mostly investigated using numerical methods, and the perturbation methods are applied only for STABILITY analysis. Because of the advantages of the analytical methods in studying the dynamics of the systems, in the present study, for the first time the dynamic behavior as well as the STABILITY of a rotor equipped with an ABB is analyzed by the multiple scales method. To this end, nonlinear equations of the systems are derived using the Lagrange’s equations and, firstly, the multiple scales method is applied to investigate the STABILITY of system and then the response of the system is achieved considering one and two terms of approximation. The results demonstrate that the STABILITY analysis using the multiple scales method and the first method of Lyapunov lead to the same results. Moreover, the responses obtained by the multiple scales method and the mostly used numerical method, Runge-Kutta technique, are in a good agreement.

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APA: Copy

REZAEE, MOUSA, & GHORBANPOUR, LEILA. (2017). INVESTIGATING THE NONLINEAR BEHAVIOR AND STABILITY ANALYSIS OF THE AUTOMATIC BALL BALANCER BY THE MULTIPLE SCALES METHOD. MODARES MECHANICAL ENGINEERING, 17(4 ), 188-198. SID. https://sid.ir/paper/178888/en

Vancouver: Copy

REZAEE MOUSA, GHORBANPOUR LEILA. INVESTIGATING THE NONLINEAR BEHAVIOR AND STABILITY ANALYSIS OF THE AUTOMATIC BALL BALANCER BY THE MULTIPLE SCALES METHOD. MODARES MECHANICAL ENGINEERING[Internet]. 2017;17(4 ):188-198. Available from: https://sid.ir/paper/178888/en

IEEE: Copy

MOUSA REZAEE, and LEILA GHORBANPOUR, “INVESTIGATING THE NONLINEAR BEHAVIOR AND STABILITY ANALYSIS OF THE AUTOMATIC BALL BALANCER BY THE MULTIPLE SCALES METHOD,” MODARES MECHANICAL ENGINEERING, vol. 17, no. 4 , pp. 188–198, 2017, [Online]. Available: https://sid.ir/paper/178888/en

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