# Application of a hybrid method to the bifurcation analysis of a relative short gas journal bearing system with herringbone grooves

Application of a hybrid method to the bifurcation analysis of a relative short gas journal... Purpose – This paper employs a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM) to study the bifurcation and nonlinear behavior of a rigid rotor supported by a relative short gas lubricated journal bearing system with herringbone grooves. The analysis reveals a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. The dynamic behavior of the bearing system varies with changes in the rotor mass and bearing number. The current analytical results are found to be in good agreement with those of other numerical methods. This paper discusses these issues. Design/methodology/approach – In this paper, DT is used to deal Reynolds equation and is also one of the most widely used techniques for solving differential equations due to its rapid convergence rate and minimal calculation error. A further advantage of this method over the integral transformation approach is its ability to solve nonlinear differential equations. In solving the Reynolds equation for the current gas bearing system, DTM is used for taking transformation with respect to the time domain τ , and then the FDM is adopted to discretize with respect to the directions of coordinates. Findings – From the Poincaré maps of the rotor center as calculated by the DTM&FDM method with different values of the time step, it can be seen that the rotor center orbits are in agreement to approximately four decimal places for the different time steps. The numerical studies also compare the results obtained by the SOR&FDM and DTM&FDM methods for the orbits of the rotor center. It is observed that the results calculated by DTM&FDM are more accurately than SOR&FDM. Therefore, the DTM&FDM method suits this gas bearing system and provides better convergence than SOR&FDM method. Originality/value – This study utilizes a hybrid numerical scheme comprising the DTM and the FDM to analyze nonlinear dynamic behavior of a relative short gas lubricated journal bearing system with herringbone grooves. The system state trajectory, phase portraits, the Poincaré maps, the power spectra, and the bifurcation diagrams reveal the presence of a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short gas lubricated journal bearing systems with herringbone grooves. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Industrial Lubrication and Tribology Emerald Publishing

# Application of a hybrid method to the bifurcation analysis of a relative short gas journal bearing system with herringbone grooves

, Volume 63 (5): 13 – Aug 16, 2011
13 pages

/lp/emerald-publishing/application-of-a-hybrid-method-to-the-bifurcation-analysis-of-a-0CJk8SY303

# References (19)

Publisher
Emerald Publishing
ISSN
0036-8792
DOI
10.1108/00368791111154922
Publisher site
See Article on Publisher Site

### Abstract

Purpose – This paper employs a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM) to study the bifurcation and nonlinear behavior of a rigid rotor supported by a relative short gas lubricated journal bearing system with herringbone grooves. The analysis reveals a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. The dynamic behavior of the bearing system varies with changes in the rotor mass and bearing number. The current analytical results are found to be in good agreement with those of other numerical methods. This paper discusses these issues. Design/methodology/approach – In this paper, DT is used to deal Reynolds equation and is also one of the most widely used techniques for solving differential equations due to its rapid convergence rate and minimal calculation error. A further advantage of this method over the integral transformation approach is its ability to solve nonlinear differential equations. In solving the Reynolds equation for the current gas bearing system, DTM is used for taking transformation with respect to the time domain τ , and then the FDM is adopted to discretize with respect to the directions of coordinates. Findings – From the Poincaré maps of the rotor center as calculated by the DTM&FDM method with different values of the time step, it can be seen that the rotor center orbits are in agreement to approximately four decimal places for the different time steps. The numerical studies also compare the results obtained by the SOR&FDM and DTM&FDM methods for the orbits of the rotor center. It is observed that the results calculated by DTM&FDM are more accurately than SOR&FDM. Therefore, the DTM&FDM method suits this gas bearing system and provides better convergence than SOR&FDM method. Originality/value – This study utilizes a hybrid numerical scheme comprising the DTM and the FDM to analyze nonlinear dynamic behavior of a relative short gas lubricated journal bearing system with herringbone grooves. The system state trajectory, phase portraits, the Poincaré maps, the power spectra, and the bifurcation diagrams reveal the presence of a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short gas lubricated journal bearing systems with herringbone grooves.

### Journal

Industrial Lubrication and TribologyEmerald Publishing

Published: Aug 16, 2011

Keywords: Bifurcation; Differential transformation method; Herringbone grooves; Bearings; Gas flow; Computer discs