Scaled boundary finite element method for hydrodynamic bearings in rotordynamic simulations

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

doi:10.1016/j.ijmecsci.2021.106427

Cited by 16 publications

(22 citation statements)

References 45 publications

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“…The SBFEM solution, in which this simplification is mandatory, provides an even more efficient alternative for this case, as it requires only 0.16 to 0.73 times the numerical effort of the FEM solution with a symmetric BC. It should be noted that no oil supply BCs are considered in the study at hand, allowing to conduct the SBFEM solution with a single superelement [1]. For a model with a geometrically accurate oil supply groove, two superelements are required, increasing the numerical effort of the SBFEM [1].…”

Section: Discussionmentioning

confidence: 99%

“…To this end, the computational time per solution of the Reynolds equation is analyzed, while the node number and the polynomial degree of the shape functions are varied. Since the SBFEM solution requires a negligence of the shaft tilting [1], all simulations in this study are conducted without this effect. In numerical solutions, such as the FEM, this assumption is not mandatory, but in cases where this simplification is tolerated, the node number can be reduced.…”

Section: Comparison Of the Sbfem To An Fem Solution Regarding Numerical Efficiencymentioning

confidence: 99%

“…In [1], a semi-analytical solution of the Reynolds equation by means of the Scaled Boundary Finite Element Method (SBFEM) [2] is developed and compared to the FEM. It is observed that the relative efficiency of the two methods depends on the slenderness ratio of the bearing (length l divided by diameter d) and whether the oil supply groove is neglected, simplified, or accurately modeled.…”

Section: Introductionmentioning

confidence: 99%

“…It is observed that the relative efficiency of the two methods depends on the slenderness ratio of the bearing (length l divided by diameter d) and whether the oil supply groove is neglected, simplified, or accurately modeled. However, the investigation in [1] is limited to linear shape functions, and the computational time is only measured for the eigenvalue problems and linear equation systems. The study at hand, in contrast, includes higher-order shape functions and considers the total computational time, which still depends substantially on the eigenvalue problems and linear equation systems, but also on the integration of the element matrices and the assembly.…”

Section: Introductionmentioning

confidence: 99%

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High‐order SBFEM solution of the Reynolds equation

Pfeil

Gravenkamp

Duvigneau

et al. 2021

Proc Appl Math & Mech

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A semi-analytical solution of the Reynolds equation for hydrodynamic bearings in rotordynamic simulations is investigated, which is based on the Scaled Boundary Finite Element Method (SBFEM). The numerical efficiency of this approach is compared to the Finite Element Method (FEM), considering linear as well as higher-order shape functions. It is observed that the SBFEM requires significantly less computational time than the FEM, especially with respect to high-order formulations.

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Section: Discussionmentioning

confidence: 99%

Section: Comparison Of the Sbfem To An Fem Solution Regarding Numerical Efficiencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High‐order SBFEM solution of the Reynolds equation

Pfeil

Gravenkamp

Duvigneau

et al. 2021

Proc Appl Math & Mech

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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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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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Scaled boundary finite element method for hydrodynamic bearings in rotordynamic simulations

Cited by 16 publications

References 45 publications

High‐order SBFEM solution of the Reynolds equation

High‐order SBFEM solution of the Reynolds equation

Nonlinear vibration phenomena in hydrodynamically supported rotor systems

SBFEM with reduced modal basis for hydrodynamic bearings

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