Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Liu, Wanhui; Bättig, Philipp; Wagner, Paweł; Schiffmann, Jürg

doi:10.1016/j.ymssp.2020.106983

Cited by 37 publications

(18 citation statements)

References 49 publications

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“…The forces acting on the rotor are its weight, the total aerodynamic force, and an eventual imbalance force if the axis of inertia of the rotor is shifted from the axis of rotation (static imbalance). Using the non‐dimensional parameters defined in Reference 45, the governing equations of the rotor dynamics in the (fixed) reference frame of the bearing bushing are given by:

{\overline{m}}_r\frac{{\mathrm{d}}^2{\epsilon}_x}{\mathrm{d}{\tau}^2}\kern0.5em ={\overline{m}}_r\overline{g}+{\overline{F}}_x+{\bar{U}}_{im}\cos \left(2\tau \right)

{\overline{m}}_r\frac{{\mathrm{d}}^2{\epsilon}_y}{\mathrm{d}{\tau}^2}\kern0.5em ={\overline{F}}_y+{\bar{U}}_{im}\sin \left(2\tau \right)

where

\tau =\omega t/2

, with

\omega

the rotation speed of the rotor, and where

{\overline{F}}_x

and

$$ {...

…”

Section: Parametric Reduced Order Model Of a Gas Bearings Supported T...mentioning

confidence: 99%

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

Goutaudier

Nobile

Schiffmann

2023

Numerical Meth Engineering

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SummaryThe proper orthogonal decomposition (POD) is successfully employed in a variety of projection‐based methods for parametric model order reduction (pMOR) of large dynamical systems. It extracts the most energetic modes describing the dynamics of a system from time snapshots of the solution. In practice, these snapshots are computed at user‐defined parameters of the system with a high fidelity model. Then either all the snapshots are concatenated to extract a global POD basis, or a different POD basis is extracted for each parameter value. In the latter case, for unseen target parameters, the POD bases need to be adapted with a dedicated technique. An established method addressing this task is the interpolation on the tangent space to the Grassmann manifold (ITSGM). It interpolates the linear subspaces spanned by the known POD bases, discarding by construction the knowledge on the modes ordering by energy levels. In this paper, we formalize an ordered reduced basis interpolation (ORBI) technique which preserves such ordering. This approach improves the adaptation accuracy of the resulting POD basis as more information is taken into account in the construction of the interpolation operator. Numerical investigations are conducted on the parametric reduced order model of a dynamical system representing a small‐scale gas‐bearings supported rotor. Results show that the proposed method is more accurate than the ITSGM method at a similar computation cost. Trained at only three points of the parameters space, the developed hyper reduced order model (h‐ROM) performs to faster simulations with satisfactory accuracy, even far from the training points.

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{\overline{m}}_r\frac{{\mathrm{d}}^2{\epsilon}_x}{\mathrm{d}{\tau}^2}\kern0.5em ={\overline{m}}_r\overline{g}+{\overline{F}}_x+{\bar{U}}_{im}\cos \left(2\tau \right)

{\overline{m}}_r\frac{{\mathrm{d}}^2{\epsilon}_y}{\mathrm{d}{\tau}^2}\kern0.5em ={\overline{F}}_y+{\bar{U}}_{im}\sin \left(2\tau \right)

where

\tau =\omega t/2

, with

\omega

the rotation speed of the rotor, and where

{\overline{F}}_x

and

$$ {...

…”

Section: Parametric Reduced Order Model Of a Gas Bearings Supported T...mentioning

confidence: 99%

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

Goutaudier

Nobile

Schiffmann

2023

Numerical Meth Engineering

Self Cite

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“…Then the expression of the partial derivative of pressure with respect to the coordinate axis direction in the Reynolds equation can be obtained: (12) Substitute Formula (12) into the Reynolds equation in the Cartesian coordinate system and organize the static Reynolds equation in the oblique coordinate system as:…”

Section: Static Reynolds Equationmentioning

confidence: 99%

“…The research on herringbone grooved journal bearings mainly focuses on the optimization of the performance of the herringbone grooves and their structural parameters [10][11][12]. Eliott et al used herringbone grooves to improve bearing performance [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Structural Design and Optimization of Herringbone Grooved Journal Bearings Considering Turbulent

Liu

Chen

2022

Applied Sciences

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In order to improve the performance of the traditional constant-width herringbone grooved journal bearing in a computed tomography tube under a high-temperature environment, the present study designed a convergent herringbone grooved journal bearing (HGJB) structure lubricated by liquid metal. The bearing oil film thickness and the Reynolds equation considering the influence of turbulence are established and solved by using the finite difference method in the oblique coordinate system. The performance of the two bearings was compared, and the static and dynamic performance change trends of the two bearing structures under different eccentricities were systematically studied. The results show that the convergent herringbone grooved journal bearings are superior to the constant-width herringbone grooved journal bearings in terms of bearing capacity and stiffness coefficient. At the same time, the influence of structural parameters, such as the number of grooves, helix angle, groove to ridge ratio, groove depth on the performance of the constant-width herringbone grooved journal bearings, and the convergent herringbone grooved journal bearings was studied. Finally, we conclude that the performance of the convergent herringbone grooved journal bearings is optimal when the number of grooves is 15–20, the helix angle is 30–45°, the ratio of the groove to ridge is 1, and the groove depth is 0.02 mm −0.024 mm. This research has provided the thinking and reference basis for the design of liquid metal bearings for high-performance CT equipment.

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“…The effects of the parameters of the grooves in the bearing pad surfaces on the load performance of the three-pad aerodynamic bearing were investigated. By two-dimensional narrow groove theory, a model of a rigid rotor with herringbone-grooved journal gas bearing support was established by Liu et al 18 The onset speed of the sub-synchronous vibration of the rotor system was predicted by the theoretical model and experimental data. In order to reduce the gas film vortex and oscillation and improve the operation stability of rotor system supported in spherical spiral groove hybrid gas bearing, Jia et al 19 investigated the dynamic change of the gas film stiffness and damping coefficients under different motion conditions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic response and bifurcation of asymmetric rotor system supported in axial-grooved gas-lubricated bearings

Sha

Lü

Zhang

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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Dynamic characteristics of the asymmetric rotor system supported in axial-grooved gas-lubricated bearings are studied. In order to solve nonlinear dynamic response of rotor system effectively, a hybrid numerical model is established by coupling the motion equation of rotor with the rational function model of the gas film forces. The rational function model of the gas film forces of gas-lubricated bearing is established based on vector fitting theory. By using the hybrid numerical model, the repeated calculations of the unsteady Reynolds equation and gas film forces are avoided; the continuous rotor trajectory and the dynamic gas film forces can be calculated simultaneously; and for the rotor system supported in the same bearings, the computing cost can be saved effectively. The nonlinear dynamic responses of asymmetric rotor system supported in axial-grooved gas-lubricated bearings are investigated by trajectory diagrams, frequency spectrum, Poincaré maps, and time series. The bifurcations are analyzed by the bifurcation diagrams with different rotating speeds and mass eccentricities. The dynamic behaviors of the asymmetric rotor system appear complex nonlinear dynamic phenomenon and specific bifurcation characteristics.

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Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Cited by 37 publications

References 49 publications

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

Structural Design and Optimization of Herringbone Grooved Journal Bearings Considering Turbulent

Nonlinear dynamic response and bifurcation of asymmetric rotor system supported in axial-grooved gas-lubricated bearings

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