• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.274-280
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• 2004

This paper presents the analysis fur the radial vibration characteristics of cylindrical piezoelectric transducers. Taking into account the piezoelectric anisotropy, the differential equations of piezoelectric radial motion have been derived in terms of radial displacement and electric potential. Applying mechanical and electric boundary conditions has yielded a characteristic equation for radial vibration. Numerical analysis also has been carried out by using the finite element method. Theoretical calculations of the fundamental natural frequency have been compared with the experimental observations for transducers of several sizes. Comparison with the previous report of theoretical analysis simplifying the piezoelectric anisotropy into isotropy concludes that isotropic analysis is a reasonable process to predict the vibration characteristics of piezoelectric transducers.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.753-765
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• 2011

The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

• Proceedings of the KIEE Conference
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• 1997.07a
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• pp.171-173
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• 1997

This paper presents analysis of the radial force density in brushless DC motor of which distribution is not uniform in the axial direction. The analysis considering 3D shape of teeth and overhang is not only important but essential to calculate the radial force density that acts on the teeth of stator, because it is frequent source of vibration and changes at the end of teeth. For the analysis, a new 3D equivalent magnetic circuit network method taking into account movement of the rotor without remesh is proposed. The radial force density is calculated by Maxwell stress tensor and analyzed by discrete Fourier transform.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.11
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• pp.1990-1995
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• 2010

Main reasons for causing vibration in a permanent magnet synchronous motor (PMSM) are torque ripple and radial force harmonics, and hence, both of them are undesirable in high-precision machine tools and accurate motion-control actuators. Recent research on radial force is the prediction of major vibration frequencies and modes in terms of motor design such as different winding types and a fractional slot number per pole in the stator. Also, proper phase current has been investigated for minimizing radial force harmonics. During the previous studies, all the motors are assumed to be ideally built up in terms of mechanical dimensions, but it is impossible due to dimensional variation within or outside tolerance in production. Therefore, in this paper, the effect of several key factors on radial force is examined and compared regarding manufacturing imperfection.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.5
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• pp.949-954
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• 2011

This paper presents a comparative study on motor characteristics with specific consideration of radial vibration force in interior permanent magnet synchronous motors (IPMSM) according to pole/slot combinations. Three IPMSM models, 16-pole/15-slot design, 16-pole/18-slot design and 16-pole/24-slot design are built, in which 16-pole/15-slot and 16-pole/18-slot designs provide high winding factor and 16-pole/24-slot design is known as a general pole/slot combination. By coupling finite element analysis (FEA) with equivalent circuit method, motor characteristics, back electro-motive force (Back-EMF), inductances, cogging torque, etc. as well as machine output performances are analyzed and compared. The radial vibration force (RVF) distribution in air gap causing stator vibration and noise is interested. It is expected that this study help with appropriate choice of pole/slot combination in IPMSM design.

• Journal of Electrical Engineering and Technology
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• v.5 no.3
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• pp.462-467
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• 2010

This paper presents the rotor shape optimization of an interior type permanent magnet (IPM) motor for a reduction of vibration and Electromagnetic Interference (EMI). The vibration and EMI in permanent magnet motors is generated by cogging torque ripple, radial force and commutation torque ripple. Consequently, in order to improve vibration and EMI, the optimal notches are put on the rotor pole with an arc shape proposed. The variation of vibration frequency due to the cogging torque and radial force of each model is computed by the finite element method (FEM). From the analysis result and experiment, we confirmed the proposed model has remarkably improved the vibration and EMI.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.12
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• pp.1986-1991
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• 2016

The vibration soucre of motor has a electromagnetic and mechanical causes. The most widely known, electromagnetic reasons are cogging torque and RMF(Radial magnetic force). Recently, analysis of the cogging torque has been made actively. but analysis of the RMF was not filled. So, in this paper, analyzed RMF. the vibration test were performed for the basic and reduced model of cogging torque and RMF. And it analyzed for the effect of each factor on the vibration. Finally, the vibration was formulated for stator's weight and RMF. To this end, natural, cogging torque and RMF of frequency were analyzed and these relationships were considered.

• Journal of Biosystems Engineering
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• v.12 no.4
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• pp.9-15
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• 1987

The vibrational characteristics of a radial-ply (155SR13 4PR) and a biased-ply tire (6.15-134PR) were investigated for examining the effects of tires with different structure on the ride characteristics of the vehicle. The natural frequencies at the tread band, mode shapes, and damping factors of two tires at the state of plane vibration were determined experimentally. The test work was performed at four levels of the inflation pressure, ranging from 171.7 kPa to 245.2 kPa, and three levels of the vertical load, deviating by 10% from the standard load designated by the Department of Transportation of the United States of America. The following results were drawn by the analysis of the test results: 1. The first-order natural frequencies of the radial-ply and the biased-ply tires at the tread band were 112 Hz and 159 Hz, respectively, at the state o f the free vibration when the inflation pressure of 196.2 kPa was applied. It was known that the biased-ply tire has higher resonant frequency than the radial-ply tire and the natural frequencies of the both tires move to the high frequency range as t he inflation pressure is increased. 2. The vibration modes of both tires were quite different. No big difference in mode shapes was examined as the inflation pressure was increased. But the natural frequencies of two tires were changed. For the radial-ply tire, no difference in mode shape was found whether the vertical load was applied or not. But a significant difference in mode shape was examined for the biased-ply tire. 3. Any difference was not found in damping factor as the different inflation pressures were applied. 4. When no vertical load was applied, damping factors of the radial-ply and biased-ply tire at the state of the natural vibration ranged from 2.6 to 5.9%, and from 4.1 to 7.8%, respectively. It was estimated that the radial-ply tire would have better cushioning than the biased-ply tire since the vertical spring rate of the radial-ply tire was much less than that of the biased-ply tire, even though the damping effect of the radial-ply tire was smaller than that of the biased-ply tire.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.380.2-380
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• 2002

SRM(Switched Reluctance Motor) 내부의 Radial Force는 소음ㆍ진동의 주원인이 되는 가진력으로 작용하는 것으로 알려져 있다. 따라서 본 논문에서는 Radial Force의 주 요인인 Motor 내부의 Air Gap 편심에 따른 반경방향의 전자기 가진력을 전자장 수치해석을 통하여 해석하고 소음ㆍ진동에 미치는 영향을 분석하였다. Air Gap 편심량을 변화시켜 가면서 Stator, Rotor의 Local Force와 Gloval Force인 Torque Fluctuation을 해석하고 이를 실험 결과와 비교함으로서 해석결과의 타당성을 입증하였다.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.2
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• pp.208-216
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• 2009

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.