Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Perturbation Analysis of the Bulk-Flow Theory (Influence of Whirling Amplitude in the Case With Concentric Circular Whirl)

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Atsushi Ikemoto ◽  
Tsuyoshi Inoue ◽  
Kazukiyo Sakamoto ◽  
Masaharu Uchiumi
Keyword(s):  
Perturbation Analysis ◽  
Large Amplitude ◽  
Flow Analysis ◽  
Flow Theory ◽  
Bulk Flow ◽  
Rotating Shaft ◽  
Fluid Force ◽  
Fluid Forces ◽  
Shaft System ◽  
Large Amplitude Vibration

The bulk-flow theory for the rotordynamic (RD) fluid force has been investigated for many years. These conventional bulk-flow analyses were performed under the assumption and restriction that the whirl amplitude was very small compared to the seal clearance while actual turbomachinery often causes the large amplitude vibration, and these conventional analyses may not estimate its RD fluid force accurately. In this paper, the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in the case of concentric circular whirl with relatively large amplitude. A set of perturbation solutions through third-order perturbations are derived explicitly. It relaxes the restriction of conventional bulk flow analysis, and it enables to investigate the RD fluid force for the whirl amplitude up to about a half of the clearance. Using derived equations, the nonlinear analytical solutions of the flow rates and pressure are deduced, and the characteristics of the RD fluid force are investigated in both radial and tangential directions. The influence of the whirl amplitude on the RD fluid force is explained and validated by comparing with computational fluid dynamics (CFD) analysis. These results are useful for the analysis and prediction of frequency response of the vibration of the rotating shaft system considering the RD fluid forces.

Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Koya Yamada ◽  
Atsushi Ikemoto ◽  
Tsuyoshi Inoue ◽  
Masaharu Uchiumi
Keyword(s):  
Perturbation Analysis ◽  
Flow Analysis ◽  
Flow Theory ◽  
Bulk Flow ◽  
Design Stage ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Static Eccentricity ◽  
Harmonic Components

Rotor-dynamic fluid force (RD fluid force) of turbomachinery is one of the causes of the shaft vibration problem. Bulk flow theory is the method for analyzing this RD fluid force, and it has been widely used in the design stage of machine. The conventional bulk flow theory has been carried out under the assumption of concentric circular shaft's orbit with a small amplitude. However, actual rotating machinery's operating condition often does not hold this assumption, for example, existence of static load on the machinery causes static eccentricity. In particular, when such a static eccentricity is significant, the nonlinearity of RD fluid force may increase and become non-negligible. Therefore, conventional bulk flow theory is not applicable for the analysis of the RD fluid force in such a situation. In this paper, the RD fluid force of the annular plain seal in the case of circular whirling orbit with static eccentricity is investigated. The case with both the significant static eccentricity and the moderate whirling amplitude is considered, and the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in such cases. In this analysis, the assumption of the perturbation solution is extended to both static terms and whirling terms up to the third order. Then, the additional terms are caused by the coupling of these terms through nonlinearity, and these three kinds of terms are considered in the extended perturbation analysis of the bulk flow theory. As a result, a set of nonlinear analytical equations of the extended perturbation analysis of the bulk flow theory, for the case with both the significant static eccentricity and the moderate whirling amplitude, is deduced. The RD fluid force for such cases is analyzed, and the occurrence of constant component, backward synchronous component, and super-harmonic components in the RD fluid force is observed in addition to the forward synchronous component. The representation of RD fluid force coefficients (RD coefficients) are modified for the case with significant static eccentricity, and the variation of RD fluid force coefficients for the magnitude of static eccentricity is analyzed. These analytical results of RD fluid force and its RD coefficients are compared with the numerical results using finite difference analysis and experimental results. As a result, the validity of the extended perturbation analysis of the bulk-flow theory for the case with both the significant static eccentricity and the moderate whirling amplitude is confirmed.

Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude

2018 ◽  
Author(s):  
K. Yamada ◽  
A. Ikemoto ◽  
M. Uchiumi ◽  
T. Inoue
Keyword(s):  
Perturbation Analysis ◽  
Flow Analysis ◽  
Flow Theory ◽  
Bulk Flow ◽  
Design Stage ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Static Eccentricity ◽  
Harmonic Components

Rotor-dynamic fluid force (RD fluid force) of turbo-machinery is one of the causes of the shaft vibration problem. Bulk flow theory is the method for analyzing this RD fluid force, and it has been widely used in the design stage of machine. Conventional bulk flow theory has been carried out under the assumption of concentric circular shaft’s orbit with small amplitude. However, actual rotating machinery’s operating condition often does not hold this assumption, for example, existence of static load on the machinery causes static eccentricity. In particular, when such a static eccentricity is significant, the nonlinearity of RD fluid force may increase and become non-negligible. Therefore, conventional bulk flow theory is not applicable for the analysis of RD fluid force in such situation. In this paper, RD fluid force of the annular plain seal in the case of circular whirling orbit with static eccentricity is investigated. The case with both the significant static eccentricity and the moderate whirling amplitude is considered, and the perturbation analysis of the bulk-flow theory is extended to investigate RD fluid force in such cases. In this analysis, the assumption of the perturbation solution is extended to both static terms and whirling terms up to the third order. Then, the additional terms are caused by the coupling of these terms through nonlinearity, and these three kinds of terms are considered in the extended perturbation analysis of the bulk flow theory. As a result, a set of nonlinear analytical equations of the extended perturbation analysis of the bulk flow theory, for the case with both the significant static eccentricity and the moderate whirling amplitude, is deduced. RD fluid force for such cases are analyzed, and the occurrence of constant component, backward synchronous component and super-harmonic components in RD fluid force is observed in addition to the forward synchronous component. The representation of RD fluid force coefficients (RD coefficients) are modified for the case with significant static eccentricity, and the variation of RD fluid force coefficients for the magnitude of static eccentricity is analyzed. These analytical results of RD fluid force and its RD coefficients are compared with the numerical results using finite difference analysis and experimental results. As a result, the validity of the extended perturbation analysis of the bulk-flow theory for the case with both the significant static eccentricity and the moderate whirling amplitude is confirmed.

Development of Experimental Active Magnetic Bearing Device for Measurement of Mechanical Seal Reaction Force Acting on Rotor

2018 ◽  
Author(s):  
Hiroki Manabe ◽  
Shota Yabui ◽  
Hideyuki Inoue ◽  
Tsuyoshi Inoue
Keyword(s):  
Force Measurement ◽  
Reaction Force ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Mechanical Seal ◽  
Rotating Shaft ◽  
Fluid Force ◽  
Fluid Forces ◽  
Whirling Motion ◽  
Measurement And Evaluation

In turbomachinery, seals are used to prevent fluid leakage. At seal part, rotordynamic fluid force (RD fluid force), which causes whirling motion of rotor, is generated. Under certain conditions, the RD fluid force may contribute to instability of the machine. There are several cases that the whirling is accompanied by eccentricity due to the influence of gravity, or the whirling orbit becomes elliptical due to the influence of the bearing support anisotropy. In these cases, mathematical modeling of the RD fluid forces becomes increasingly complex. As a result, the RD fluid force measurement is more preferable. To improve the measurement and evaluation technology of the RD fluid force, a method to arbitrarily control whirling of the orbit is required. In this paper, RD fluid force measurement by controlling the shape of the orbit using an active magnetic bearing (AMB) is proposed. A contact type mechanical seal is used as a test specimen. When the rotating shaft is whirling, the RD fluid force due to hydrodynamics lubrication and the frictional force due to contact occur on the sliding surface. The resultant force of these forces is taken as the reaction force of mechanical seal and the measurement is performed. The measured reaction force of the mechanical seal is compared with simulation results and the validity of the proposed measurement method is confirmed.

scholarly journals Flow-Induced Vibration of Tubes in Cross-Flow

1996 ◽  
Vol 118 (4) ◽  
pp. 253-258 ◽  
Author(s):  
S. S. Chen ◽  
Y. Cai ◽  
S. Zhu
Keyword(s):  
Unsteady Flow ◽  
Mathematical Models ◽  
Cross Flow ◽  
Flow Theory ◽  
General Description ◽  
Flow Induced Vibration ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces

This paper presents an unsteady-flow theory for flow-induced vibration of tubes in cross-flow. It includes a general description of motion-dependent fluid forces, characteristics of fluid-force coefficients, and mathematical models. Detailed results are presented for the constrained mode in the lift direction for various tube arrangements.

Analytical Investigation on the Rotational Speed Dependence of the Rotordynamic Fluid Force: The Case of Concentric Circular Whirl in the Annular Plain Seal

2016 ◽  
Author(s):  
Atsushi Ikemoto ◽  
Kazukiyo Sakamoto ◽  
Tsuyoshi Inoue ◽  
Masaharu Uchiumi
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
Quadratic Function ◽  
Analytical Investigation ◽  
Experimental Unit ◽  
Rotating Shaft ◽  
Fluid Force ◽  
Force Coefficients ◽  
Fluid Forces ◽  
Speed Dependence

Rotordynamic (RD) fluid forces of various kinds of seals has been investigated and reported by Childs [1], Iwatsusbo [2][3] and so on, because it has significant influence on the stability of rotating machinery. Those studies were carried out at lower speeds than the actual machines because of various restrictions such as the limitations of the experimental unit. Then, extrapolation approximations using the obtained results were used to predict the RD fluid force of the actual machines. However, when the rotor vibration is analyzed for the high speed rotating shaft such as a rocket turbopump, a more accurate evaluation of the rotational speed dependence of the derived RD fluid force is desired. In this study, the rotational speed dependence of RD fluid forces in the case of the concentric circular whirl in the annular plain seal is investigated. As a result, the characteristics of these fluid forces vary with the rotational speed significantly. In addition, the strong dependencies of RD fluid force coefficients calculated from these fluid forces on the rotational speed are observed. It is revealed that the changes of the RD fluid force coefficients to rotational speed were modeled by using the quadratic function.

Analysis of the rub-impact forces between a controlled nonlinear rotating shaft system and the electromagnet pole legs

2021 ◽  
Vol 93 ◽  
pp. 792-810
Author(s):  
N.A. Saeed ◽  
Emad Mahrous Awwad ◽  
Mohammed A. EL-meligy ◽  
Emad Abouel Nasr
Keyword(s):  
Rotating Shaft ◽  
Shaft System ◽  
Impact Forces
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