• Title/Summary/Keyword: Unbalance Response Analysis

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An Improved Substructure Synthesis Method for Unbalance Response Analysis of Rotor Bearing Systems (회전체 베어링계의 불균형 응답 해석을 위한 개선된 부분 구조 합성법)

  • 홍성욱;박종혁
    • Journal of KSNVE
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    • v.6 no.1
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    • pp.71-82
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    • 1996
  • The finite element analysis for rotor bearing systems has been an essential tool for design, identification, and diagnosis of rotating machinery. Among others, the unbalance response analysis is fundamental in the vibration analysis of rotor bearing systems because rotating unbalance is recognized as a common sourve of vibration in rotating machinery. However there still remains a problem in the aspect of computational efficiency for unbalance response analysis of large rotor bearing systems. Gyroscopic terms and local bearing parameters in rotor bearing systems often make matters worse in unbalance response computation due to the complicated dynamic properties such as rotational speed dependency and/or anisotropy. The present paper proposes an efficient method for unbalance responses of multi-span rotor bearing systems. An improved substructure synthesis scheme is introduced which makes it possible to compute unbalance responses of the system by coupling unbalance responses of substructures that are of self adjoint problem with small order matrices. The present paper also suggests a scheme to easily deal with gyroscopic tems and local, coupling or bearing parameters. The proposed method causes no errors even though the computational effort is reduced drastically. The present method is demonstrated through three test examples.

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Unbalance Response Analysis of Induction Motor Rotor Considering Unbalanced Electromagnetic Forces (불평형 전자기력을 고려한 유도전동기 회전자의 불평형 응답해석)

  • 손병구
    • Journal of Advanced Marine Engineering and Technology
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    • v.23 no.2
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    • pp.201-209
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    • 1999
  • This paper presents a general analytical method for analyzing mechanical unbalance response of unbalanced electromagnetic forces produced in induction motors with an eccentric rotor and a phase unbalance. The equations to be solved are a set of second order differential equations which give matrices with periodic coefficients that are a function of time due to the unbalanced electro-magnetic force. Unbalance response is processed by Newmark $\beta$ method. Two examples are given including an industrial application. The results show that the method proposed is satisfactory.

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An efficient method for computation of unbalance responses of rotor-bearing systems (회전체 베어링계의 불균형 응답을 위한 효율적인 계산 방법)

  • Hong, Seong-Wook;Park, Jong-Heuck
    • Journal of the Korean Society for Precision Engineering
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    • v.12 no.9
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    • pp.137-147
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    • 1995
  • The unbalance response analysis is one of the essential area in the forced vibration analysis of rotor-bearing systems. Local bearing parameters in rotor-bearing systems are the major sources which give rise to a difficulty in unbalance response computation due to the complicated dynamic properties such as rotational speed dependency and anisotropy. In the present paper, an efficient method for unbalance responses is proposed so as to easily take into account bearing parameters in computation. An exact matrix condensation procedure is proposed which enables the present method to compute unbalance responses by dealing with condensed, small matrices. The proposed method causes no errors even though the computation procedure is based on the small matrices condensed from the full matrices. The present method is illustrated through a numerical example and compared with the conventional method.

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Estimation of the Unmeasured Unbalance Responses and Identification of Bearing Parameters in Flexible Rotor-Bearing Systems (회전체 베어링계의 불균형응답 간접추정과 베어링 매개변수 규명)

  • 홍성욱;이종원
    • Journal of KSNVE
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    • v.2 no.3
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    • pp.193-202
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    • 1992
  • The unbalance response analysis is one of the essential area in the forced vibration analysis of rotor bearing systems because of it usefulness in balancing and diagnosis as well as identification of parameters involved in rotor bearing systems. However some unbalance responses are not measurable due to the fact that rotor bearing systems are often encapsulated by fixtures or safety protectors. In the present paper, an efficent estimation scheme for unmeasured unbalance responses in rotor bearing systems is developed. The fundamental fearture of the proposed method is characterized by the linear formulae to estimate the unbalance responses from the measured unbalance responses and the finite element auxilliary model equation which is constructed to be identical to the prototype excluding the uncertain parameters such as bearing coefficients. The identification formulae for bearing parameters are also derived by using the unbalance response and the finite elements auxiliary model. Simulation is provided to verify the effectiveness of the proposed method.

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A Study on Dynamic Characteristics of Synchronously Controlled Hydrodynamic Journal Bearing (동기 제어되는 동압 베어링의 동특성에 관한 연구)

  • Rho, Byoung-Hoo;Kim, Kyung-Woong
    • Proceedings of the KSME Conference
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    • 2001.06c
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    • pp.311-315
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    • 2001
  • In this paper synchronous whirl of bearing is employed as control algorithm of actively controlled hydrodynamic journal bearing to suppress the whirl instability and unbalance response of a rotor-bearing system. Also, the cavitation algorithm implementing the Jakobsson-Floberg-Olsson boundary condition is adopted to predict cavitation regions in the fluid film more accurately than conventional analysis which uses the Reynolds condition. The stability and unbalance responses of a rotor-bearing system are investigated for various control gain and phase difference between the bearing and journal motion. It is shown that the unbalance response of a rotor-bearing system can be greatly improved by synchronous whirl of the bearing, and there is an optimum phase difference, which gives the minimum unbalance response of the system, at given operating condition. It is also found that the speed at onset of instability can be greatly increased by synchronous whirl of the bearing.

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Finite Element Analysis of Unbalance Response of a High Speed Flexible Polygon Mirror Scanner Motor with Asymmetric Finite Element Equations (비대칭 유한 요소 방정식으로 표현되는 고속 유연 폴리곤 미러 스캐너 모터의 유한 요소 불평형 응답 해석)

  • Seo, Chan-Hee;Jung, Kyung-Moon;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.1022-1027
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    • 2007
  • This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered metal bearing and flexible structures by using the finite element method and the mode superposition method considering the asymmetry of the gyroscopic effect and sintered metal bearing. The eigenvalues and eigenvectors are calculated by solving the eigenvalue problem and the adjoint eigenvalue problem by using the restarted Arnoldi iteration method. The decoupled equations of motion can be obtained from global finite element motion equations by using the orthogonal relation between the right eigenvectors and left eigenvectors. The decoupled equations of motion are used to analyze the unbalance response of a high speed polygon mirror scanner motor. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results.

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효율적인 회전기계 불균형 응답 계산 방법

  • 박종혁;홍성욱
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1995.04a
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    • pp.615-619
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    • 1995
  • The unbalance response analysis is one of the essential area in the forced vibration analysis of rotor-bearing systems. Local bearing parameters in ortor-bearing systems are the major sources which give rise to a difficulty in unbalance response computation due to the complicated dynamic properties such as rotational speed dependency and anisotropy. In the present paper, an exact condensation procedure is introduced to easily take into account bearing parameters in computation of unbalance responses for rotor bearing systems. The present method is illustrated through a numerical example and compared with the conventional method.

Unbalance Response Analysis of Copper Die Casting High Speed Induction Motor (동 다이캐스팅 고속 유도전동기의 불평형 응답 해석)

  • Hong, Do-Kwan;Jung, Seung-Wook;Woo, Byung-Chul;Koo, Dae-Hyun;Ahn, Chan-Woo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.7
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    • pp.642-649
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    • 2012
  • This paper deals with a copper die casting induction motor which has several advantages of motor performance. The developed motor is used as spindle motor in machining center. The dynamic characteristic analysis of rotor is dealt with for precision machining. The critical speed of rotor considering rotation and gyroscopic effect should be above operating speed, 18,000 rpm, and have a 201 % sufficient separation margin. Also, the 3-D unbalance vibration response analysis is performed and enabled the prediction of the expected vibration amplitude by unbalance in high speed. The unbalance vibration responses of each position on the rotor are satisfied with allowable vibration displacement of API 611 standard according to balancing G grade(G 0.4, G 2.5, G 6.3). Copper die casting high speed induction motor is successfully developed and verified by experiment.

Finite Element Analysis of Unbalance Response of a High Speed Flexible Polygon Mirror Scanner Motor Considering the Flexibility of Supporting Structure (지지구조의 유연성을 고려한 고속 유연 폴리곤 미러 스캐너 모터의 유한 요소 불평형 응답 해석)

  • Jung, Kyung-Moon;Seo, Chan-Hee;Kim, Myung-Gyu;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.05a
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    • pp.859-865
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    • 2007
  • This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

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Dynamic Behavior Analysis of Rotor-Bearing System Under External Forces in Swash Plate Compressor (외부 가진력을 고려한 사판식 압축기 회전축-베어링계의 동적 거동 해석)

  • 김태종
    • Tribology and Lubricants
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    • v.17 no.1
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    • pp.56-63
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    • 2001
  • The dynamic behavior of rotor-bearing system used in swash plate compressor has been investigated using the combined methodologies of finite elements and transfer matrices. The finite element is formulated including the field element for a shaft section and the point element for swash plate, disk pulley and bearings. The Houbolt method is used to consider the time march for the integration of the system equations. The transient whirl response of rotating shaft supported on roller bearings is obtained, considering compression forces and unbalance forces at swash plate and driving pulley. And, the steady state displacements of the rotor are compared with a variation in unbalance mass. Results show that the loci of rotating shaft considering unbalance forces and external compression forces are more severe in flutter motion than with only unbalance forces.