Nonlinear transient analysis of rigid rotor mounted on externally pressurized double-layered porous gas journal bearings
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(2020) 42:530
TECHNICAL PAPER
Nonlinear transient analysis of rigid rotor mounted on externally pressurized double‑layered porous gas journal bearings accounting velocity slip Phani Kumar Mallisetty1,2 · P. Samanta2 · N. C. Murmu2 Received: 14 February 2020 / Accepted: 6 September 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract The present work aims at estimating the journal center trajectories of a rigid rotor mounted on a hybrid, finite gas lubricated journal bearings with double-layered porous bushing using nonlinear transient analysis. To consider velocity slip in the film at the interface between film and porous region, Reynolds equation is modified using the Beavers–Joseph boundary condition. The governing equations of flow at clearance, porous regions are discretized using finite volume method. The variable values at cell-face centers are obtained using interpolation scheme of third order. Those discretized equations coupled with equations of rigid rotor motion are solved by third-order total variation diminishing Runge–Kutta scheme. Influence of velocity slip and design parameters on critical mass parameter values were explored. The observations are presented in the form of graphs that serves as a reference during the design of such bearings. Keywords Porous gas journal bearings · Modified Reynolds equation · Nonlinear transient analysis · Double-layered porous bushing · Velocity slip List of symbols C Radial clearance D Diameter of the bearing e Bearing eccentricity F̄ r Dimensionless film force along radial direction, Fr ∕LDpa F̄ Φ Dimensionless film force along Φ direction, FΦ ∕LDpa h Local film thickness h Dimensionless film thickness (h/C) H Thickness of the porous bushing H1 , H2 Thickness of the fine and coarse layers respectively kx1 , ky1 , kz1 Fine layer permeability coefficients along x, y, z directions respectively Technical Editor: Daniel Onofre de Almeida Cruz. * P. Samanta [email protected]; [email protected] 1
Academy of Scientific and Innovation Research (AcSIR), Anusandhan Bhawan, 2 Rafi Marg, New Delhi 110001, India
Surface Engineering and Tribology Group, CSIR-Central Mechanical Engineering Research Institute, Durgapur 713209, India
2
kx2 , ky2 , kz2 Coarse layer permeability coefficients along x, y, z directions respectively K̄ x1 , K̄ z1 Dimensionless permeability coefficients, kx1 ∕ky1 , kz1 ∕ky1 respectively K̄ x2 , K̄ z2 Dimensionless permeability coefficients, kx2 ∕ky2 , kz2 ∕ky2 respectively K̄ y2 Dimensionless interlayer permeability coefficient, ky2 ∕ky1 L Length of the bearing ̄ Mass parameter, MC𝜔2 ∕(LDpa ) M ̄ c Critical mass parameter, Mc C𝜔2 ∕(LDpa ) M Ob Bearing center Oj Journal center p Film pressure p̄ Dimensionless film pressure, p∕pa pa Ambient pressure ps Supply pressure p̄ s Dimensionless supply pressure, ps ∕pa p , p0 Film pressure and steady-state film pressure respectively p̄ , p̄ 0 Dimensionless film pressure, p∕pa , p0 ∕pa p′1 Pressure at fine layer p′2 Pressure at coarse layer p
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