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Nonlinear dynamic analysis of a rotor-bearing system with porous tilting pad bearing support

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Abstract

Porous tilting pad bearings (PTPBs) show a potential for using in high-speed, high precision rotating machinery that requires high bearing stiffness and good stability. In this study, the nonlinear characteristics of a rotor supported on PTPBs are investigated. The Darcy equations and the modified Reynolds equations are adopted to establish the gas flow model in porous materials and gas film region, respectively. The pad motions and rotor motions are also included in the numerical nonlinear model. The advantages of PTPBs over tilting pad journal bearings are discussed. PTPBs with externally pressurized gas can avoid friction during startup and shutdown, improve the load capacity at low rotational speeds, and effectively suppress subsynchronous vibrations at high rotational speeds. The nonlinear characteristics of the rotor-bearing system with various bearing parameters, such as supply pressure ratio, nominal bearing clearance, pad tilting and radial stiffness, are analyzed. Poincaré maps, predicted rotor orbit and bifurcation diagrams are used. High supply pressure ratio and small nominal bearing clearance can significantly decrease the orbit size and increase the critical speed. Low tilting and high radial stiffness can improve system stability. This study reveals the complex nonlinear characteristics of the system and provides guidance for designing PTPBs for using in high-speed rotating machinery.

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Abbreviations

W :

Pad width (m)

L :

Pad axial length (m)

\(r_0 ,\;r_d \) :

Pad radius and rotor diameter (m)

\(\Theta _p \) :

Pad arc angle (rad)

\(\theta _s ,\;\theta _e \) :

Pad leading edge and pad trailing edge (rad)

\(\;\theta _p \) :

Angular position of pivot (rad)

\(\delta ,\;\xi \) :

Pad radial displacement (m) and pad tilting angle (rad)

\(m_p ,\;I_p \) :

Pad mass (kg) and moment of inertia of pad (kg m\(^{2})\)

\(p_a ,\;p_s \) :

Ambient and supply pressures (pa)

p :

Pressure (pa)

P :

Dimensionless pressure \((p/p_a)\)

\(r,\;\theta ,\;z\) :

Coordinates in the r, \(\theta \), and z directions

\(R,\;Z\) :

Dimensionless coordinates in the r and z directions

C :

Nominal clearance (m)

\(h,\;H\) :

Film thickness (m) and dimensionless film thickness (h / C)

\(e_x ,\;e_y \) :

Components of rotor eccentricity

\(\omega \) :

Angular velocity of shaft (rad/s)

\(m_\theta ,\;m_r ,\;m_z \) :

Mass flow rates in the \(\theta ,\;r\) and z directions

\(\Delta m_t \) :

Varied amount of mass flow rates per unit time

\(x,\;y\) :

x and y axes

\(F_x ,\;F_y \) :

Forces acting on shaft along the x and y axes caused by gas pressure (N)

\(F_{p\delta } ,\;M_{p\xi } \) :

Radial force (N) and tilting moment (N m)

\(K_\delta \) :

Radial stiffness of the straight beam (N/m)

\(K_\xi \) :

Tilting stiffness of the pivot (N m/rad)

\(\eta \) :

Porosity of porous materials

k :

Permeability of porous materials (m\(^{2})\)

\(\mu ,\;\rho \) :

Gas viscosity (Pa s) and density (kg/m\(^{3})\)

\(\mathfrak {R}\) :

Air gas constant (J/kg K)

T :

Temperature of the supply gas (K)

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Acknowledgements

The authors acknowledge the financial support from the National Natural Science Foundation of China (No. 51575170), The Joint Advance Research Program of equipment, Ministry of Education of China (6141A02033503). Research program supported by Science and Technology Commission of Shanghai Municipality (17DZ1201000), Supported by the fund of the State Key Laboratory of Digital Manufacturing Equipment & Technology in HUST (DMETKF2017012).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Yihua Wu, Kai Feng, Yun Zhang, Wanhui Liu & Wenjun Li

  2. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China

    Kai Feng

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  1. Yihua Wu
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  2. Kai Feng
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  4. Wanhui Liu
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Correspondence to Kai Feng.

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Wu, Y., Feng, K., Zhang, Y. et al. Nonlinear dynamic analysis of a rotor-bearing system with porous tilting pad bearing support. Nonlinear Dyn 94, 1391–1408 (2018). https://doi.org/10.1007/s11071-018-4431-7

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  • DOI: https://doi.org/10.1007/s11071-018-4431-7

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