• 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.

• 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.

• 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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.1
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• pp.175-181
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• 2012

This paper presents a novel dynamic vibration absorber (DVA) to suppress the unbalance response of flexible rotor-bearing systems. The DVA unit consists of two DVAs, an adapter to place the DVAs and an adapter frame to locate the adapter. The essential feature of the proposed DVA unit is to place itself on any desirable location of the shaft without disassembling the rotor-bearing system under consideration. A simulation with a 3D element based commercial rotor dynamic software is made to test the possibility of the proposed DVA on the suppression of unbalance response in rotor-bearing systems. Experiments are performed to validate the proposed DVA unit. The simulation and experiments show that the proposed DVA unit is very effective to suppress the unbalance response in rotor-bearing system at designated rotational speeds of interest.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.8
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• pp.598-604
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• 2003

In this paper a general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system, whose shafts rotate at their different speeds from each other. Particularly, are proposed analytical solutions of the maximum and minimum radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system having a bull-pinion speed increasing gear. Bumps in the unbalance response of the driven high speed compressor rotor system have been observed at the first torsional natural frequency due to the coupling effect of lateral and torsional dynamics. Further, the proposed analytical solutions have agreed well with those obtained by a full numerical approach. The proposed analytical solutions can be generally applied to obtain the maximum and minimum radii of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.811-812
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• 2009

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.1056-1061
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• 2004

The vibration of rotor systems is caused by various factors, such as misalignment, unbalance, gear meshing, error of assembly, etc. Modal test and TDA/ODS analysis were done. The dynamic analysis of the armature was done with SAMCEF which is a commercial software for finite element and kinematic analysis. The transient response of the armature is calculated by the SAMCEF with the consideration of magnetic force and bearing stiffness, which are the essential elements for the design of high speed cutter. Main frequency of the vibration is due to the unbalance of the armature. The FEM analysis model considering unbalance and the high speed cutter have same vibration properties. The vibration sources of the high speed cutter is proved to be unbalance.

• 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.

• 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.

• 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.