Transformation between polar and rectangular coordinates of stiffness and dampness parameters in hydrodynamic journal be
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ISSN 2223-7690 CN 10-1237/TH
SHORT COMMUNICATION
Transformation between polar and rectangular coordinates of stiffness and dampness parameters in hydrodynamic journal bearings Zhuxin TIAN1, Yu HUANG1,2,* 1
School of Mechanical Engineering, Hubei University of Arts and Science, Xiangyang 441053, China
2
State Key Lab of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Received: 05 May 2019 / Revised: 26 August 2019 / Accepted: 11 September 2019
© The author(s) 2019. Abstract: The stiffness and dampness parameters of journal bearings are required in rectangular coordinates for analyzing the stability boundary and threshold speed of oil film bearings. On solving the Reynolds equation, the oil film force is always obtained in polar coordinates; thus, the stiffness and dampness parameters can be easily obtained in polar coordinates. Therefore, the transformation between the polar and rectangular coordinates of journal bearing stiffness and dampness parameters is discussed in this study. Keywords: coordinate transformation; stiffness parameters; dampness parameters; hydrodynamic journal bearings
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Introduction
In modern industry, rotating parts of engineering equipment are supported by journal bearings in the vertical direction. The machine characteristics are significantly dependent on the performances of journal bearings. Due to the oil whip effect in a rotating hydrodynamic journal bearing, self-excited vibration occurs in the oil film, which increases with an increase in the rotation speed [1–4]. As a result of the self-excited vibration, threshold speed and stability boundary exist for the rotating bearings. When the rotating speed is larger than the threshold speed, the vibration results in large orbiting amplitudes of the journal and leads to the contact between the journal and bearing, causing bearing failure. Further, the bearing is stable at the journal bearing center in the stability boundary. Khonsari and Chang [5] analyzed the nonlinear stability of journal bearings, and obtained the stability boundary by tracking the journal center trajectory. To easily derive the linear threshold speed, Huang et al. [6] chose polar * Corresponding author: Yu HUANG, E-mail: [email protected]
coordinates instead of Cartesian coordinates to signify the state vector. Lin et al. [7, 8] discussed the threshold speed and stability boundary of hydrodynamic journal bearings lubricated using non-Newtonian fluids. Kushare and Sharma [9] dealt with the threshold speed of two lobe symmetric hole entry worn hybrid journal bearing by theoretically considering the non-Newtonian behavior of the lubricants. The threshold speed and stability boundary of the hydrodynamic journal bearing are determined based on the stiffness and damping coefficients. Lund and Thomsen [10] proposed a method to study these coefficients. The Reynolds equation is derived with respect to Cartesian coordinates and stiffness and damping coeffici
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