Experimental and theoretical investigations of the lateral vibrations of an unbalanced Jeffcott rotor
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RESEARCH ARTICLE
Experimental and theoretical investigations of the lateral vibrations of an unbalanced Jeffcott rotor Ali ALSALEHa, Hamid M. SEDIGHIb,c, Hassen M. OUAKADd* a
Saudi Arabian Oil Company (ARAMCO), Dhahran 31311, Saudi Arabia Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran c Drilling Center of Excellence and Research, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran d Mechanical and Industrial Engineering Department, Sultan Qaboos University, Al-Khoudh Muscat, Oman b
*
Corresponding author. E-mail: [email protected]
© Higher Education Press 2020
ABSTRACT The current work experimentally explores and then theoretically examines the lateral vibrations of an unbalanced Jeffcott rotor-system working at several unbalance conditions. To this end, three conditions of eccentric masses are considered by using a Bently Nevada RK-4 rotor kit. Measurements of the steady-state as well as the startup data at rigid and flexible rotor states are captured by conducting a setup that mimics the vibration monitoring industrial practices. The linear governing equation of the considered rotor is extracted by adopting the Lagrange method on the basis of rigid rotor assumptions to theoretically predict the lateral vibrations. The dynamic features of the rotor system such as the linearized bearing induced stiffness are exclusively acquired from startup data. It is demonstrated that, with an error of less than 5%, the proposed two-degrees-of-freedom model can predict the flexural vibrations at rigid condition. While at flexible condition, it fails to accurately predict the dynamic response. In contrast to the other works where nonlinear mathematical models with some complexities are proposed to mathematically model the real systems, the present study illustrates the applicability of employing simple models to predict the dynamic response of a real rotor-system with an acceptable accuracy. KEYWORDS rotor-dynamics, Jeffcott rotor, lateral vibrations, Lagrange method, system-equivalent stiffness, sleeve bearings, oil film induced stiffness
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Introduction
The literature presents good efforts on mathematically simulating the unbalance response of rotor systems with high accuracy. Krodkiewski et al. [1] presented a nonlinear mathematical model to simulate the unbalance response of a rotor considering the nonlinear effect of its support system. Sanches and Pederiva [2] worked on identifying the unbalance response in a rotor using correlation matrices and modal order reduction method. Pjadatare and Pratiher [3] used the strain energy and the kinetic energy equations to study the effect of nonlinear geometric coupling on the dynamics of an unbalanced rotor. Gunter [4] illustrated the use of the single mass flexible model to industrial machines based on the simple Jeffcott rotor dynamics and by Article history: Received Aug 17, 2019; Accepted Sep 14, 2019
employing some eigenvalue analyses [5]. Taplak et al. [6] designed a neural network predictor [7]
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