Готові списки джерел за темами / Rotor Dynamic Eccentricity

Добірка наукової літератури з теми "Rotor Dynamic Eccentricity"

Автор: Grafiati

Опубліковано: 14 березня 2023

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Статті в журналах з теми "Rotor Dynamic Eccentricity"

Li, M., and L. He. "The dynamics of a parallel-misaligned and unbalanced rotor system under the action of non-linear oil film forces." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 9 (September 1, 2010): 1875–89. http://dx.doi.org/10.1243/09544062jmes1916.

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Анотація:

A mathematical model of a parallel-misaligned rotor system with mass eccentricity that is supported on journal bearings is discussed and its dynamic behaviours are analysed under the action of non-linear oil forces in the present work. First, some assumptions are introduced, such as the long bearing model, small parallel misalignment between rotors and tiny eccentricity of discs, the misaligned displacement constraint between two rotors is taken into account, and the motion equations are deduced by the Lagrange method of undetermined multiplier. Then, the rotor orbits, Poincaré maps, and bifurcation diagrams of the system are studied by a numerical method; the results show that there exists some unrevealed motions and phenomena in the parallel-misaligned and unbalanced rotor system such as period 2, 3, 6, and 7 motions besides chaotic oscillations and so on.

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Muszynska, A. "Improvements in Lightly Loaded Rotor/Bearing and Rotor/Seal Models." Journal of Vibration and Acoustics 110, no. 2 (April 1, 1988): 129–36. http://dx.doi.org/10.1115/1.3269489.

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A model for lightly loaded steadily rotating shaft/bearing/seal systems is proposed in this paper. The model is based on modal characteristics for the rotor, and rotational characteristics for the fluid dynamic forces generated in bearings and/or seals. The fluid average circumferential velocity ratio as a nonlinear function of shaft eccentricity represents a key factor in the model. The model is extremely useful for rotor stability analysis. The model adequacy was proved for one and two lateral mode models of rotors.

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Chen, Guoda, Yijie Chen, Qi Lu, Quanhui Wu, and Minghuan Wang. "Multi-Physics Fields Based Nonlinear Dynamic Behavior Analysis of Air Bearing Motorized Spindle." Micromachines 11, no. 8 (July 25, 2020): 723. http://dx.doi.org/10.3390/mi11080723.

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The air bearing motorized spindle (ABMS) is the key component of the ultra-precision machine tool, which plays an important role in the ultra-precision machining process and directly influences machining accuracy. The influence of unbalanced magnetic force (UMF) on the nonlinear dynamic behavior of the ABMS is not understood clearly. To reveal the potential influence of the UMF, a mathematical model of the ABMS considering multiphysics fields is established. The variation trend of the UMF is simulated, and the nonlinear dynamic behavior of the ABMS is analyzed which emphasizes on the stability of the rotating shaft. It is shown that the UMF varies linearly at large rotor eccentricity which meets well with previous research, but it is noteworthy the UMF varies nearly to a quadratic function at small rotor eccentricity. The result of rotor dynamics shows that the UMF can change the converge position of the rotor center and the converge speed. Moreover, when at certain rotor mass and external load, the UMF can enlarge the stability boundary of the rotor. This research provides an example of analyzing the nonlinear dynamic behavior of the ABMS considering multiphysics fields which may help to the further investigation.

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WERNER, ULRICH. "THEORETICAL VIBRATION ANALYSIS OF SOFT MOUNTED TWO-POLE INDUCTION MOTORS WITH STATIC ROTOR ECCENTRICITY." International Journal of Applied Mechanics 03, no. 01 (March 2011): 131–59. http://dx.doi.org/10.1142/s1758825111000919.

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Анотація:

The paper shows a mathematical model for vibration analysis of soft mounted two-pole induction motors regarding electromagnetic excitation due to static rotor eccentricity. A static rotor eccentricity causes an electromagnetic force, acting on the rotor and on the stator and oscillating with the double supply frequency. This magnetic force is implemented into a simplified analytical machine dynamic model and the correlations between the rotor dynamics, electromagnetic, oil film characteristics of the sleeve bearings, and the stiffness and damping of a soft foundation are mathematically described. The derived results are clarified using an example that shows the influence of the rotor speed and the direction of the magnetic force on the vibration behavior. On one hand the aim of the paper is to show the mathematical correlations, based on a simplified model. On the other hand, the aim is to derive a method for calculating the forced vibrations — as a worst case — caused by a static rotor eccentricity. Therefore, the paper shall prepare the basis for implementing this method in more detailed numerical programs, e.g., finite element programs.

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Chen-Hui, Jia, Du Cai-Feng, and Qiu Ming. "Research on Nonlinear Dynamic Characteristics and Stability of Aerodynamic Bearings." Open Mechanical Engineering Journal 8, no. 1 (September 16, 2014): 243–50. http://dx.doi.org/10.2174/1874155x01408010243.

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In order to research the conical spiral groove aerodynamic bearings, the lubrication mathematical model of the bearings was established. The Reynolds equation of the laminar flow condition is used to calculate the partial differential equation of the perturbation pressure with the local finite difference method. Through calculating the stiffness and damping coefficient, the influence of the speed of law and eccentricity ratio on the dynamic characteristic coefficients has been gained. The mathematical model for the stability of the bearing-rotor system is established to study the influence law of speed influence of the law of speed and eccentricity ratio on the stability. The results show that the influence of the bearing's speed and eccentricity on the dynamic characteristics is significant. A reasonable choice of the bearing's speed and eccentricity contributes to improve the dynamic characteristics and the stability of the bearing-rotor system.

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Wan, Shuting, and Yuling He. "INVESTIGATION ON STATOR AND ROTOR VIBRATION CHARACTERISTICS OF TURBO-GENERATOR UNDER AIR GAP ECCENTRICITY FAULT." Transactions of the Canadian Society for Mechanical Engineering 35, no. 2 (June 2011): 161–76. http://dx.doi.org/10.1139/tcsme-2011-0010.

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This paper investigates the stator and the rotor vibration characteristics of turbo-generator under the air gap eccentricity fault. Firstly the air gap magnetic flux density of the fault is deduced, and the formula of the magnetic pull per unit area acting on the stator and the unbalanced magnetic pulls of x-axis and y-axis acting on the rotor are respectively gotten. Then the static eccentricity, the dynamic eccentricity and the mixed eccentricity are respectively studied to analyze the stator and the rotor vibration characteristics. Finally experiments are done on a SDF-9 non-salient fault simulating generator to verify the theoretical results. The investigation results of this paper will be beneficial to the air gap eccentricity fault diagnosis of turbo-generator.

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Wu, Quanhui, Yazhou Sun, Wanqun Chen, Guoda Chen, Qingshun Bai, and Qingchun Zhang. "Effect of motor rotor eccentricity on aerostatic spindle vibration in machining processes." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 7 (April 24, 2017): 1331–42. http://dx.doi.org/10.1177/0954406217705686.

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Анотація:

In ultra-precision machining field, the air motorized spindle which is composed of a motor and an air bearing, plays a major role. In air motorized spindle, the motor eccentricity between the stator and the rotor is inevitably introduced during the manufacturing process, which directly affects the machining results of workpiece surface, and this phenomenon is particularly unwanted in machining. However, little attention has been paid to the motor eccentricity of air motorized spindle. In this paper, a new integrated electromechanical coupling method for estimating unbalanced force in air motorized spindle is presented, and the effects of motor rotor eccentricity on surface topography in ultra-precision processes are analyzed. An electromagnetic-mechanical method is used to study the coupling effects between the motor rotor and the aerostatic spindle. Meanwhile, the motor rotor and the aerostatic spindle are analyzed as a whole. In order to clearly describe the electromagnetic–mechanical method, the ultra-precision spindle for potassium dihydrogen phosphate crystal machining tool is selected as the research object, and the model of air motorized spindle and motor rotor eccentricity are presented. Besides, in order to assess the impact of the radial magnetic force caused by motor rotor eccentricity on the spindle performance, a range of rotor eccentricities is calculated. Additionally, the influence of the motor rotor eccentricity on the dynamic response of spindle is further analyzed. It is found that motor rotor eccentricity has a significant influence on the spindle vibration, which dramatically reduces the processing quality. Finally, the machining experiments are carried out, and the flatness errors of the workpiece caused by the motor rotor eccentricity are obtained by the wavelet method. The experimental results are consistent with the analysis results, which verifies the reliability of this method. This study is quite meaningful for deeply understanding the influence of motor rotor eccentricity on the machined surface.

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Zhu, Youfeng, Zibo Wang, Qiang Wang, Xinhua Liu, Hongyu Zang, and Liang Wang. "Nonlinear Dynamic Analysis of Rotor Rub-Impact System." Shock and Vibration 2019 (November 29, 2019): 1–20. http://dx.doi.org/10.1155/2019/4867364.

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A dynamic model of a double-disk rub-impact rotor-bearing system with rubbing fault is established. The dynamic differential equation of the system is solved by combining the numerical integration method with MATLAB. And the influence of rotor speed, disc eccentricity, and stator stiffness on the response of the rotor-bearing system is analyzed. In the rotor system, the time history diagram, the axis locus diagram, the phase diagram, and the Poincaré section diagram in different rotational speeds are drawn. The characteristics of the periodic motion, quasiperiodic motion, and chaotic motion of the system in a given speed range are described in detail. The ways of the system entering and leaving chaos are revealed. The transformation and evolution process of the periodic motion, quasiperiodic motion, and chaotic motion are also analyzed. It shows that the rotor system enters chaos by the way of the period-doubling bifurcation. With the increase of the eccentricity, the quasi-periodicity evolution is chaotic. The quasiperiodic motion evolves into the periodic three motion phenomenon. And the increase of the stator stiffness will reduce the chaotic motion period.

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Zhao, Jianhua, Weidong Yan, Ziqi Wang, Dianrong Gao, and Guojun Du. "Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing." Processes 8, no. 8 (August 12, 2020): 973. http://dx.doi.org/10.3390/pr8080973.

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Анотація:

As a new type of suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting. Its bearing capacity and stiffness can be greatly improved. Because of the small liquid film thickness (it is smaller 10 times than air gap), the eccentricity, crack, bending of the rotor, and the assembly error, it is easy to cause a clearance-rubbing fault between the rotor and stator. The coating can be worn and peeled, the operating stability can be reduced, and then it is one of the key problems of restricting the development and application of MLDSB. Therefore, the clearance-rubbing dynamic equation of 2-DOF system of MLDSB is established and converted into Taylor Series form and the nonlinear components are retained. Dimensionless treatment is carried out by dimensional normalization method. Finally, the rotor displacement response under different rotor eccentricity ratio and rotating speeds is numerically simulated. The studies show that the trajectory of the rotor is periodic elliptic without clearance-rubbing phenomenon when the eccentricity ratio is less than 0.2, while the rotor is greatly affected by the rotation speed and a variety of motions, such as single-period, quasi-period, double-period and chaos, are presented when greater than 0.3. Within the largest range of rotating speed and eccentricity ratio, the rotor presents the single-period trajectory, and then the number of Poincare mapping point is 1, without a clearance-rubbing fault. When the rotational speed is in the scope of (9, 13) krpm and the eccentricity ratio is in the scope of (0.27, 0.4), the number of Poincare mapping point is more than one, the maximum dimensionless rubbing force is −5.7, and then clearance-rubbing fault occurs. The research can provide a theoretical basis for the safe and stable operation of MLDSB.

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Dai, Bing, Guang Bin Yu, Jun Peng Shao, and Long Huang. "Eccentricity and Rotational Speed Effect on the Rotor-Bearing." Applied Mechanics and Materials 274 (January 2013): 237–40. http://dx.doi.org/10.4028/www.scientific.net/amm.274.237.

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Bearing dimensionless nonlinear oil film force model is deduced based on Capone theory of cylindrical bearings in this paper. Jeffcot rigid rotor-bearing system dynamic equations are built based on nonlinear dynamics, bifurcation, chaos theory. Eccentricity increases with the speed of the system by writing MATLAB codes. It appears the periodic motion, times of periodic motion and a series of non-linear kinetics. The system eccentricity increases with a series of emergence of non-linear dynamics when speed conditions is fixed, which is the actual system design’s basis. The finite element model of gas turbine rotor-bearing system is built by ANSYS software platform in this paper. The radial bearing deformation relationship are obtained by deformation theory of centrifugal force at high speed bearing radial deformation.

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Більше джерел

Дисертації з теми "Rotor Dynamic Eccentricity"

BELMONTE, DARIO. "MODEL BASED CORRELATION METHODS FOR FAULTS DETECTION AND IDENTIFICATION ALGORITHMS ON ELECTROMECHANICAL ACTUATORS USED IN PRIMARY FLIGHT CONTROL SYSTEMSMODEL BASED CORRELATION METHODS FOR FAULTS DETECTION AND IDENTIFICATION ALGORITHMS ON ELECTROMECHANICAL ACTUATORS USED IN PRIMARY FLIGHT CONTROL SYSTEMS." Doctoral thesis, Politecnico di Torino, 2019. http://hdl.handle.net/11583/2746072.

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Частини книг з теми "Rotor Dynamic Eccentricity"

Bontinck, Zeger, Oliver Lass, Herbert De Gersem, and Sebastian Schöps. "Uncertainty Quantification for a Permanent Magnet Synchronous Machine with Dynamic Rotor Eccentricity." In Progress in Industrial Mathematics at ECMI 2016, 493–99. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63082-3_77.

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Bauer, Christian, and Ulrich Werner. "Rotordyamic Analysis of a 2-Pole Induction Motor Considering Magnetic Excitation Due to Dynamic Rotor Eccentricity During Startup." In Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, 661–76. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-06590-8_54.

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Iglesias, M., A. Fernández, A. de Juan, A. Díez, P. García, and F. Viadero. "Planet Eccentricity Error on a Planetary Gear Transmission: Influence on Load Sharing." In Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, 1381–90. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-06590-8_113.

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He, Yu-Ling, Fa-Lin Wang, Meng-Qiang Ke, and Gui-Ji Tang. "Rotor Vibration Difference Among the Single and the Combined Faults Composed by Static Air-Gap Eccentricity and Rotor Interturn Short Circuit." In Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, 637–48. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-06590-8_52.

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Тези доповідей конференцій з теми "Rotor Dynamic Eccentricity"

Sobra, Jan, Toomas Vaimann, and Anouar Belahcen. "Mechanical vibration analysis of induction machine under dynamic rotor eccentricity." In 2016 17th International Scientific Conference on Electric Power Engineering (EPE). IEEE, 2016. http://dx.doi.org/10.1109/epe.2016.7521732.

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Xue, Shiming, Junyi Cao, and Yangquan Chen. "Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47415.

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Fatigue cracking of the rotor shaft is an important fault observed in rotating machinery of key industry, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The four-th order Runge-Kutta method and ten-th order CFE-Euler (Continued Fraction Expansion-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction and mass eccentricity on the system dynamics are demonstrated by using bifurcation diagram, Poincare map and rotor trajectory diagram. The results show that the rotor system displays chaotic, quasi-periodic and periodic motions as the fractional order increases. It is also found that the imbalance eccentricity level, crack depth, rotational speed, fractional damping and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system.

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Liu, Yuqing, Zaigang Chen, Xia Hua, and Wei Li. "Dynamic Investigation of Traction Motor Bearings Considering Rotor Eccentricity in a Locomotive." In 2021 7th International Conference on Condition Monitoring of Machinery in Non-Stationary Operations (CMMNO). IEEE, 2021. http://dx.doi.org/10.1109/cmmno53328.2021.9467524.

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Liu, Heng, Yi Liu, Xuebin Song, Jun Yi, Minqing Jing, Weimin Wang, Shiquan Zhao, and Xiaobing Qi. "Nonlinear Dynamic Effect of Thrust Bearing on a Flexible Rotor Bearing System." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68487.

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This article is concerned with the effect of nonlinearities on the stability and bifurcation of a flexible rotor system subjected to the influences of thrust bearing and mass eccentricity. The shaft is modeled by using the finite element method and then the model is reduced by a component mode synthesis method which can account for nonlinear forces and moment of the bearing. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The numerical results indicate that thrust bearing and mass eccentricity have great influence on stability and bifurcation of the motion of system. Thrust bearing can postpone the bifurcation of the periodic motion of system, heighten the critical speed and the stability threshold speed, and lower the resonant amplitude of the rotor.

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Hong, Jie, Qi Yan, Bo Sun, and YanHong Ma. "Vibration Failure Analysis of Multi-Disk High-Speed Rotor Based on Rotary Inertia Load Model." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-83174.

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Abstract The fan rotor of an advanced low-bypass turbofan engine is usually composed of multistage blisk, a typical multi-disk highspeed rotor working in the postcritical range. A fan rotor test rig had been well balanced, but the phenomenon of excessive vibration occurred several times. This phenomenon showed that the traditional balance theory based on mass eccentricity control has limitations for multi-disk high-speed rotors. Therefore, an analysis model was established in this paper that described the rotor’s mass distribution and the rotary inertia load by two kinds of parameters: the eccentricity and the skew angle of the principal axis of inertia. Then the dynamic response properties of the rotor were simulated and analyzed. The model and simulation results showed that if the principal axis of inertia of the rotor skewed, the amplitude of bearing dynamic load continues to increase with speed, which agrees with the experimental data. Therefore, for the multi-disk rotor, it is necessary to control its eccentricity and the skew angle of the principal axis of inertia at the same time to effectively reduce its dynamic response at high speed.

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Enemark, Søren, and Ilmar F. Santos. "Dynamic Interaction Between Rotor and Axially-Magnetized Passive Magnetic Bearing Considering Magnetic Eccentricity." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38032.

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Passive magnetic bearings are known due to the excellent characteristics in terms of friction and no requirement of additional energy sources to work. However, passive magnetic bearings do not provide damping, are not stable and, depending on their design, may also introduce magnetic eccentricity. Such magnetic eccentricities are generated by discrepancies in magnet fabrication. In this framework the main focus of the work is the theoretical as well as experimental investigation of the non-linear dynamics of a rotor-bearing system with strong emphasis on the magnetic eccentricities and non-linear stiffness. In this investigation passive magnetic bearings using axially-aligned neodymium cylinder magnets are investigated. The cylinder magnets are axially magnetised for rotor as well as bearings. Compared to bearings with radial magnetisation, the magnetic stiffness of axially-aligned bearings is considerably lower, nevertheless they allow for asymmetric stiffness mounting, and it could be beneficial for rotor stabilization. A theoretical model is proposed to describe the non-linear rotor-bearing dynamics. It takes into account non-linear behaviour of the magnetic forces and their interaction with a multi-body system composed of rigid rotor and flexible foundation. The magnetic eccentricities of the shaft magnets are modelled using the distances (amplitudes) and directions (phase angles) between the shaft axis and the centre of the magnetic fields generated. A perturbation method, i.e. harmonic balancing, is used in order to evaluate the frequency response of the non-linear system. The experimental validation of the model is carried out using a dedicated rotor-bearing system set-up. The test set-up consists of a vertical rigid shaft and disc supported by two passive magnetic bearings using axially-aligned neodymium cylinder magnets. The magnetic bearing housings are flexibly supported, allowing horizontal motions. The housings are connected to each other by means of elastic beams. The shaft is free in one end and coupled to a DC motor on the other by means of a flexible coupling. On the free end a disc is attached where imbalances and gyroscopic effect can be generated. Comparison between theory and experiment shows high level of resemblance, which validates the theoretical model and the explanations for the quasi-static and dynamic responses. The magnetic eccentricities and mass imbalance effects are clearly detected and distinguished.

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McKinnon, D. J. "Three-dimensional rotor parameter modelling for dynamic performance analysis and rotor eccentricity identification in three-phase induction machines." In Second IEE International Conference on Power Electronics, Machines and Drives. IEE, 2004. http://dx.doi.org/10.1049/cp:20040389.

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Zhang, X. Z., and B. G. Liu. "Nonlinear Dynamics in the Estimation of Rotor-Bearing Dynamic Properties in Large Hydro-Units*." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8046.

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Abstract This paper describes a method with which the nonlinear dynamic response and the natural features of rotor-bearing systems in large hydro-units can be estimated on a personal computer. The key step of this process is to estimate the dynamic eccentricity of the journal center in every guide bearing when the system is subjected to dynamic loads. As an example, the nonlinear dynamic responses, the natural frequencies and the critical speeds of the rotor-bearing system of a 240MW hydro-unit are calculated. The calculated dynamic responses agree well with the ones measured in the field.

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Liu, Heng, Chen Li, Weimin Wang, Xiaobin Qi, and Minqing Jing. "Nonlinear Dynamic Analysis of a Flexible Rod Fastening Rotor Bearing System." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23368.

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Анотація:

This paper is concerned the stability and bifurcation of a flexible rod-fastening rotor bearing system (FRRBS). Here the shaft is considered as an integral or continuous structure and be modeled by using Timoshenko beam-shaft element which can take the effects of axial load into consideration. And using Hamilton’s principle, model tie rods distributed along the circumference as a constant stiffness matrix and an add-moment which caused by unbalanced pre-tightening forces. Then the model is reduced by a component mode synthesis method, which can conveniently account for nonlinear oil film forces of the bearing. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the FRRBS subjected to the influence of mass eccentricity. The periodic motions and their stability margin are obtained by shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The results indicate that mass eccentricity and unbalanced pre-tightening forces of tie rods have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion.

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Shiau, T. N., E. K. Lee, Y. C. Chen, and T. H. Young. "Dynamic Response of a Geared Rotor-Bearing System Under Residual Shaft Bow Effect." In ASME Turbo Expo 2006: Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90435.

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The paper presents the dynamic behaviors of a geared rotor-bearing system under the effects of the residual shaft bow, the gear eccentricity and excitation of gear’s transmission error. The coupling effect of lateral and torsional motions is considered in the dynamic analysis of the geared rotor-bearing system. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The dynamic characteristics including system natural frequencies, mode shapes and steady-state response are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between gear eccentricity and residual shaft bow will significantly affect system natural frequencies and steady-state response. When the spin speed closes to the second critical speed, the system steady state response will be dramatically increased by the residual shaft bow for the in-phase case. Moreover the zero response can be obtained when the system is set on special conditions.

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