Abstract
This study introduces an improved numerical algorithm that is capable of analyzing nonlinear vibrations and bifurcations of general, finite, large-order rotordynamic systems supported on nonlinear bearings. An industrial rotor generally consists of several sections and stages, but numerical shooting/continuation method has been applied to a simple Jeffcott type rotor instead of complex models due to the computational burden of the numerical procedure; it becomes significant when the rotor combined with nonlinear finite bearing models. Here, some mathematical/computational techniques such as a deflation algorithm and the parallel computing are suggested for acceleration along with the conventional treatment of model reduction scheme. An eight-stage compressor rotor supported by two identical five-pad tilting pad journal bearings (TPJB) is selected as a mechanical model to test the numerical incorporation of the algorithms. The rotor beam is modelled with 35 nodes, 140 DOF based on Euler beam theory, and the fluid reaction forces from the two TPJB are calculated using simplex, triangular type finite meshes on the pads. In the numerical procedure, the shooting/continuation combined with the acceleration schemes identifies the solution curves of periodic responses and determines their stability. The orbital motions of coexistent responses are obtained from the solution manifolds.
Highlights
Most of the rotating machineries in industry are not simple as a “Jeffcott” rotor but are consisted of multiple shafts and multiple discs; the structural vibrations and gyroscopic effects should be taken into consideration for the motions of the machines
In a series of research from [2,3,4], Component mode synthesis (CMS) had been proven as an accurate dimension reduction method for transient, nonlinear rotordynamics
The objective of this paper is to extend the solubility of the improved numerical algorithms, i.e. shooting/continuation with deflation and the parallel computing, to industrial turbomachinery applications such as a steam turbine compressor
Summary
Most of the rotating machineries in industry are not simple as a “Jeffcott” rotor but are consisted of multiple shafts and multiple discs; the structural vibrations and gyroscopic effects should be taken into consideration for the motions of the machines. A six-node shaft beam model supported on plain journal bearings was used as a mechanical model; the model has 24 DOF, and the fluid film pressures on the supports are obtained using the short bearing approximation They obtained the unbalance response amplitude with respect to spin speeds using continuation and determined the local stability based on Floquet theory. If a finite element-based tilting pad journal bearing (TPJB) is employed to the numerical procedure, it can significantly delay the execution speed In this present study, mathematical and computational acceleration techniques such as a deflation algorithm and the parallel computing strategy are imported to speed up the conventional shooting/continuation-CMS algorithm. The objective of this paper is to extend the solubility of the improved numerical algorithms, i.e. shooting/continuation with deflation and the parallel computing, to industrial turbomachinery applications such as a steam turbine compressor
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