High‐order SBFEM solution of the Reynolds equation

Pfeil, Simon; Gravenkamp, Hauke; Duvigneau, Fabian; Woschke, Elmar

doi:10.1002/pamm.202100028

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…However, the latest works on this topic deal with the so called SBFEM (scaled boundary finite element method) method, which is a combination of analytic solution in axial direction with a numerical solution in circumferential direction [54,55]. Thereby, the number of unknowns in the arising system of equations is decreased drastically.…”

Section: Numerical Modelsmentioning

confidence: 99%

Nonlinear vibration phenomena in hydrodynamically supported rotor systems

2023

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It is a well‐known fact, that hydrodynamically supported systems are prone to nonlinear vibrations. Their exact simulative prediction with respect to frequency and amplitude is complicated by the fact that different system properties interact. The paper at hand outlines an approach that takes all relevant influences like rigid body motions, elastic deformations, nonlinear relation between fluid film pressure and bearing kinematics as well as temperature increase due to power loss or adjacent heat sources into account as detailed as necessary. Both journal and thrust bearings are considered as they contribute to the system's stiffness and damping capabilities. The approach is applied to self‐excited pad vibrations of tilting pad thrust bearings as well as the run‐up simulation of a turbocharger rotor under different axial loads. Both models are validated against measurements.

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Section: Numerical Modelsmentioning

confidence: 99%

Nonlinear vibration phenomena in hydrodynamically supported rotor systems

2023

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“…Its efficiency also depends on whether oil supply BCs are present and how they are modeled [21]. High-order (A) (B) formulations are considered in [23], and a combination of the SBFEM algorithm with a cavitation model 1 is achieved in [24].…”

Section: Introductionmentioning

confidence: 99%

SBFEM with reduced modal basis for hydrodynamic bearings

Pfeil,

Song,

Woschke

2023

Proc Appl Math and Mech

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The numerical effort of transient rotordynamic simulations is often dominated by the computation of nonlinear hydrodynamic bearing forces. These forces are described by the Reynolds equation and need to be computed at every time step. Usually, numerical models, analytical approximations, or look‐up table techniques are employed, depending on the desired tradeoff between accuracy and computational cost. In recent studies, a semi‐analytical approach based on the scaled boundary finite element method (SBFEM) has been developed as an efficient alternative to these methods. The partial differential equation is transformed into a system of ordinary differential equations, leading to an eigenvalue problem. Here, the numerical effort can be further decreased by means of a modal reduction, which is investigated in this study. The shaft eccentricity determines the smoothness of the hydrodynamic pressure field and is identified as an adequate indicator as to what subset of eigenvalues and eigenvectors should be considered in the solution.

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SBFEM with perturbation method for solving the Reynolds equation

Pfeil,

Song,

Woschke

2024

Proc Appl Math and Mech

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Rotordynamic simulations with nonlinear hydrodynamic bearing forces require a solution of the Reynolds equation at every time step. As a computationally efficient alternative to the standard numerical methods, a semi‐analytical solution based on the scaled boundary finite element method (SBFEM) was developed recently. Through a discretization of the hydrodynamic pressure (dependent variable) along the circumferential but not the axial coordinate, the partial differential equation is transformed into a system of ordinary differential equations. This system of differential equations is referred to as SBFEM equation and can be solved exactly if the influence of shaft tilting is neglected. In common numerical models, this influence can be taken into account without difficulties, but as far as this semi‐analytical approach is concerned, shaft tilting complicates the equations substantially. Therefore, previous studies on the SBFEM solution of the Reynolds equation were conducted without consideration of this effect. The formulation presented in the work at hand no longer requires this simplification. The terms representing the influence of shaft tilting in the SBFEM equation are handled by the perturbation method. The pressure field is expressed by a series expansion, where the solution of order correlates to the power of a perturbation parameter chosen proportional to the tilting angle. The differential equation governing the solution contains lower‐order solutions on its right‐hand side, implying a recursive computation of the series from lowest to highest order. A universal expression for the general solution is formulated, where only the coefficients and the maximum power of the axial coordinate differ for every . This allows the implementation of a general algorithm with no inherent limitation regarding the maximum order of perturbation. For verification, the pressure fields computed by the proposed method are compared to a numerical reference solution, showing that the series converges to the correct result for the investigated set of parameters.

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High‐order SBFEM solution of the Reynolds equation

Cited by 3 publications

References 4 publications

Nonlinear vibration phenomena in hydrodynamically supported rotor systems

Nonlinear vibration phenomena in hydrodynamically supported rotor systems

SBFEM with reduced modal basis for hydrodynamic bearings

SBFEM with perturbation method for solving the Reynolds equation

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