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Masaharu Uchiumi - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude
Journal of Engineering for Gas Turbines and Power, 2018Co-Authors: Koya Yamada, Atsushi Ikemoto, Tsuyoshi Inoue, Masaharu UchiumiAbstract: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.
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NONLINEAR ANALYSIS OF ROTORDYNAMIC Fluid ForceS IN THE ANNULAR PLAIN SEAL BY USING EXTENDED BULK-FLOW ANALYSIS (INFLUENCE OF STATIC ECCENTRICITY AND WHIRLING AMPLITUDE)
Volume 7B: Structures and Dynamics, 2018Co-Authors: Koya Yamada, Masaharu Uchiumi, Atsushi Ikemoto, Tsuyoshi InoueAbstract: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.
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Coupled Analysis of the Rotor-Dynamic Fluid Forces in the Annular Plain Seal and the Shaft Vibration
Volume 7A: Structures and Dynamics, 2018Co-Authors: Kenjiro Miyake, Masaharu Uchiumi, Atsushi Ikemoto, Tsuyoshi InoueAbstract:In recent years, along with demands for higher rotational speed and higher efficiency in the rotating machinery, shaft vibration has been a serious problem. One of the causes of this shaft vibration problem is the rotor-dynamic Fluid Force (RD Fluid Force) generated by working Fluid at turbo machinery parts. It is important in the design stage of rotating machines to estimate the RD Fluid Force and predict the stability of the rotor system accurately. Therefore, many researches have been conducted to clarify the characteristics of RD Fluid Force. One of the traditional methods for analyzing the RD Fluid Force is the bulk flow theory. However, in conventional bulk flow analysis, it is assumed that the amplitude of the shaft displacement is sufficiently smaller than the clearance. Therefore, influence of nonlinearity in the large amplitude whirl may not be included in this analysis. Accordingly, this paper focuses on constructing a coupled analysis of the Fluid Force and the shaft vibration that describes each behavior of Fluid and shaft at the same time. By using this coupled analysis, the interaction between Fluid and shaft systems can be taken into consideration more accurately. Regarding the Fluid region, finite difference method is used for bulk flow continuity and momentum transport equations. Incompressible Fluid is assumed, and the pressure field is calculated by solving the Poisson equation of pressure. In solving the Poisson equation of pressure, a specific problem for this coupled analysis relating unknown shaft acceleration arises. In this paper, this problem is solved by obtaining the approximated acceleration based on Newmark-beta technique. This coupled analysis is conducted for a simple flexible rotor system with annular plain seal, and the frequency response is obtained. First, the case with isotropic support stiffness and with no gravitational Force is considered. Then, the case with the constant load and the case with anisotropic support stiffness are analyzed. These analytical results show that both the constant load and structural anisotropy may affect the stability of the rotor system. As a result, the usefulness of the proposed coupled analysis procedure of the Fluid Force and the shaft vibration is validated.
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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)
Journal of Tribology, 2018Co-Authors: Atsushi Ikemoto, Tsuyoshi Inoue, Kazukiyo Sakamoto, Masaharu UchiumiAbstract: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.
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Analytical Investigation on the Rotational Speed Dependence of the Rotordynamic Fluid Force: The Case of Concentric Circular Whirl in the Annular Plain Seal
Volume 7: Fluids Engineering, 2016Co-Authors: Atsushi Ikemoto, Tsuyoshi Inoue, Kazukiyo Sakamoto, Masaharu UchiumiAbstract: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.Copyright © 2016 by ASME
Masaaki Konno - One of the best experts on this subject based on the ideXlab platform.
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Estimate of the Fluid Force related to washing mechanism 1 measurement of the drag of fine wires on a plate caused by the flow of aqueous solutions of surfactant and dilute aqueous solution of polymer
Journal of Rheology, 1994Co-Authors: Keiko Amaki, Tomiichi Hasegawa, Masaaki KonnoAbstract:The effect of Fluid Force on detergency has been experimentally investigated. More than one hundred wires of 50 μm in diameter, as a model of two dimensional soil, were set so as to adhere to a bottom flat plate of a two dimensional channel. The aqueous solution of surfactant and the dilute aqueous solution of polymer were made to flow through the channel and the pressure drop caused by the wires was measured. The drag and the drag coefficient (CD) of one wire were estimated with the pressure drop by the use of the law of momentum. The following results are obtained. For all solutions used, the drag increases and the drag coefficient decreases with an increase in the Reynolds number based on the wire diameter taken as the characteristic reference length. The solution of LAS, one of familiar anionic surfactants, gives CD values lower than the pure water, and the difference becomes marked as the concentration of the solution increases. A nonionic surfactant solution, AE 1.0%, shows a time dependent characte...
Menglan Duan - One of the best experts on this subject based on the ideXlab platform.
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Integral transform solution for Fluid Force investigation of a flexible circular cylinder subject to vortex-induced vibrations
Journal of Marine Science and Technology, 2016Co-Authors: Menglan DuanAbstract:In the present paper, Fluid Force distribution of a long flexible cylinder subject to vortex-induced vibrations is investigated by Generalized Integral Transform Technique (GITT). This method is using experimental response data as input, and then implementing GITT to transfer the governing differential equations to ordinary differential equations. Therefore, the selection of truncation order could be analyzed to avoid the error induced by the high-mode response. Once each mode contribution of Fluid Force is obtained, the analytical inversion transfer recovers the Fluid Force. An experiment was carried out in a towing tank and the experimental response was accurately measured and used as input, then GITT was performed to calculate the Fluid Force distribution of the long flexible cylinder. The comparison between the numerical results from GITT and the experimental results from load cell verified the capability and availability of the proposed method. If one can use this method for lower modes, then one certainly can extend the method for higher modes. Two experimental cases from the literature were evaluated and good agreement was obtained based on the spatio-temporal evolutions of the lift coefficient and the mode numbers. Since this method is easy to implement, it could be an alternative method to investigate Fluid Force of such slender structures.
Atsushi Ikemoto - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude
Journal of Engineering for Gas Turbines and Power, 2018Co-Authors: Koya Yamada, Atsushi Ikemoto, Tsuyoshi Inoue, Masaharu UchiumiAbstract: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.
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NONLINEAR ANALYSIS OF ROTORDYNAMIC Fluid ForceS IN THE ANNULAR PLAIN SEAL BY USING EXTENDED BULK-FLOW ANALYSIS (INFLUENCE OF STATIC ECCENTRICITY AND WHIRLING AMPLITUDE)
Volume 7B: Structures and Dynamics, 2018Co-Authors: Koya Yamada, Masaharu Uchiumi, Atsushi Ikemoto, Tsuyoshi InoueAbstract: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.
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Coupled Analysis of the Rotor-Dynamic Fluid Forces in the Annular Plain Seal and the Shaft Vibration
Volume 7A: Structures and Dynamics, 2018Co-Authors: Kenjiro Miyake, Masaharu Uchiumi, Atsushi Ikemoto, Tsuyoshi InoueAbstract:In recent years, along with demands for higher rotational speed and higher efficiency in the rotating machinery, shaft vibration has been a serious problem. One of the causes of this shaft vibration problem is the rotor-dynamic Fluid Force (RD Fluid Force) generated by working Fluid at turbo machinery parts. It is important in the design stage of rotating machines to estimate the RD Fluid Force and predict the stability of the rotor system accurately. Therefore, many researches have been conducted to clarify the characteristics of RD Fluid Force. One of the traditional methods for analyzing the RD Fluid Force is the bulk flow theory. However, in conventional bulk flow analysis, it is assumed that the amplitude of the shaft displacement is sufficiently smaller than the clearance. Therefore, influence of nonlinearity in the large amplitude whirl may not be included in this analysis. Accordingly, this paper focuses on constructing a coupled analysis of the Fluid Force and the shaft vibration that describes each behavior of Fluid and shaft at the same time. By using this coupled analysis, the interaction between Fluid and shaft systems can be taken into consideration more accurately. Regarding the Fluid region, finite difference method is used for bulk flow continuity and momentum transport equations. Incompressible Fluid is assumed, and the pressure field is calculated by solving the Poisson equation of pressure. In solving the Poisson equation of pressure, a specific problem for this coupled analysis relating unknown shaft acceleration arises. In this paper, this problem is solved by obtaining the approximated acceleration based on Newmark-beta technique. This coupled analysis is conducted for a simple flexible rotor system with annular plain seal, and the frequency response is obtained. First, the case with isotropic support stiffness and with no gravitational Force is considered. Then, the case with the constant load and the case with anisotropic support stiffness are analyzed. These analytical results show that both the constant load and structural anisotropy may affect the stability of the rotor system. As a result, the usefulness of the proposed coupled analysis procedure of the Fluid Force and the shaft vibration is validated.
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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)
Journal of Tribology, 2018Co-Authors: Atsushi Ikemoto, Tsuyoshi Inoue, Kazukiyo Sakamoto, Masaharu UchiumiAbstract: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.
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Analytical Investigation on the Rotational Speed Dependence of the Rotordynamic Fluid Force: The Case of Concentric Circular Whirl in the Annular Plain Seal
Volume 7: Fluids Engineering, 2016Co-Authors: Atsushi Ikemoto, Tsuyoshi Inoue, Kazukiyo Sakamoto, Masaharu UchiumiAbstract: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.Copyright © 2016 by ASME
Tsuyoshi Inoue - One of the best experts on this subject based on the ideXlab platform.
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Two Way Coupled Analysis of Fluid Force in the Annular Plain Seal and Vibration of the Rotor System Using Shooting Method
Volume 8: 31st Conference on Mechanical Vibration and Noise, 2019Co-Authors: Yudai Kunori, Tsuyoshi Inoue, Kenjiro MiyakeAbstract:Abstract In turbomachinery, the rotor dynamic (RD) Fluid Force generated in a Fluid element is one of the causes of shaft vibration. RD Fluid Force is caused by the interaction between shaft vibration and Fluid Force, and its precise prediction for various rotor’s orbit is difficult. This study performs a two-way coupled analysis of the Fluid flow in the annular plain seal and shaft vibration using the shooting method. The frequency response is obtained and compared with that obtained from a direct numerical simulation of the coupled system, and the validity of the analysis is confirmed. The onset speed of instability is effectively and accurately obtained using the two-way coupled analysis with the shooting method, and the effects of the parameters on it are investigated.
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Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Bulk-Flow Analysis: Influence of Static Eccentricity and Whirling Amplitude
Journal of Engineering for Gas Turbines and Power, 2018Co-Authors: Koya Yamada, Atsushi Ikemoto, Tsuyoshi Inoue, Masaharu UchiumiAbstract: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.
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Development of Experimental Active Magnetic Bearing Device for Measurement of Mechanical Seal Reaction Force Acting on Rotor
Volume 6: 14th International Conference on Multibody Systems Nonlinear Dynamics and Control, 2018Co-Authors: Hiroki Manabe, Shota Yabui, Hideyuki Inoue, Tsuyoshi InoueAbstract: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.
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NONLINEAR ANALYSIS OF ROTORDYNAMIC Fluid ForceS IN THE ANNULAR PLAIN SEAL BY USING EXTENDED BULK-FLOW ANALYSIS (INFLUENCE OF STATIC ECCENTRICITY AND WHIRLING AMPLITUDE)
Volume 7B: Structures and Dynamics, 2018Co-Authors: Koya Yamada, Masaharu Uchiumi, Atsushi Ikemoto, Tsuyoshi InoueAbstract: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.
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Coupled Analysis of the Rotor-Dynamic Fluid Forces in the Annular Plain Seal and the Shaft Vibration
Volume 7A: Structures and Dynamics, 2018Co-Authors: Kenjiro Miyake, Masaharu Uchiumi, Atsushi Ikemoto, Tsuyoshi InoueAbstract:In recent years, along with demands for higher rotational speed and higher efficiency in the rotating machinery, shaft vibration has been a serious problem. One of the causes of this shaft vibration problem is the rotor-dynamic Fluid Force (RD Fluid Force) generated by working Fluid at turbo machinery parts. It is important in the design stage of rotating machines to estimate the RD Fluid Force and predict the stability of the rotor system accurately. Therefore, many researches have been conducted to clarify the characteristics of RD Fluid Force. One of the traditional methods for analyzing the RD Fluid Force is the bulk flow theory. However, in conventional bulk flow analysis, it is assumed that the amplitude of the shaft displacement is sufficiently smaller than the clearance. Therefore, influence of nonlinearity in the large amplitude whirl may not be included in this analysis. Accordingly, this paper focuses on constructing a coupled analysis of the Fluid Force and the shaft vibration that describes each behavior of Fluid and shaft at the same time. By using this coupled analysis, the interaction between Fluid and shaft systems can be taken into consideration more accurately. Regarding the Fluid region, finite difference method is used for bulk flow continuity and momentum transport equations. Incompressible Fluid is assumed, and the pressure field is calculated by solving the Poisson equation of pressure. In solving the Poisson equation of pressure, a specific problem for this coupled analysis relating unknown shaft acceleration arises. In this paper, this problem is solved by obtaining the approximated acceleration based on Newmark-beta technique. This coupled analysis is conducted for a simple flexible rotor system with annular plain seal, and the frequency response is obtained. First, the case with isotropic support stiffness and with no gravitational Force is considered. Then, the case with the constant load and the case with anisotropic support stiffness are analyzed. These analytical results show that both the constant load and structural anisotropy may affect the stability of the rotor system. As a result, the usefulness of the proposed coupled analysis procedure of the Fluid Force and the shaft vibration is validated.