• Title/Summary/Keyword: Infinite Series

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Stability Analysis of a Herringbone Grooved Journal Bearing with Rotating Grooves (홈이 회전하는 빗살무늬 저널 베어링의 안정성 해석)

  • 윤진욱;장건희
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.4
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    • pp.247-257
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    • 2003
  • This paper presents an analytical method to Investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic Journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill's infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

Calculation of Interaction Parameters in Mixed Layer Minerals and their Application (층상형 혼합광물의 상호작용계수의 계산 및 응용)

  • 이성근;김수진
    • Journal of the Mineralogical Society of Korea
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    • v.10 no.2
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    • pp.97-104
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    • 1997
  • Based on the method of determination for relative stability of each phase from the difference among the interaction parameters of the phases consisting the mixed layer, the types of interactions between layers were specified and interaction parameter between layers in ordered domain was analytically derived as a function parameter between layers in ordered domain was analytically derived as a function of not only temperature and mole fraction of layers but also ordering parameter. Interaction parameter between the different layers in ordered phase, L is as follows:{{{{ {L }_{1 } (X,Q,T)= { C} over { Q} -4(1-2Q) { L}^{2 } - { RT} over {2} ln { 1} over {2 } - { 2RT} over { { X}_{ s} } ln { { 4QX}`_{s } ^{2 } } over {(1- { X}_{s }- { QX}_{s })( { X}_{s }- {QX }_{s } ) } }}}}L2 is the interaction parameter between ordered and disordered phase in domain and is the mole fraction of the domain which represent the infinite length of mixed layer mineral and Q and C are the reaction progress parameter and arbitrary constant, respectively. This equation was used for the I/S mixed layer clay minerals to infer the relative stability of R1 type I/S mixed layer in the temperature range from 373K to 450K. The result of calculation suggest that, owing to the decrease in interaction parameter with increasing temperature. The interaction parameter decreases more rapidly with decreasing mole fraction of smectite in domain, which is consistent with the fact that the probability of finding the series smectite layer is lo in the domain with small mole fraction of smectite layers in natural system.

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The Design of Hybrid Cryptosystem for Smart Card (스마트카드용 Hybrid 암호시스템 설계)

  • Song, Je-Ho;Lee, Woo-Choun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.12 no.5
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    • pp.2322-2326
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    • 2011
  • General cryptosystem uses differently the data and key value for the increment of security level, processes the repetition of limited number and increases the periodic feature of LFSR similar infinite series. So, it cause the efficiency of the cryptosystem. In this thesis, proposed algorithm is composed of reformat, permutation, data cipher block and key scheduler which is applied the new function by mixed symmetric cryptography and asymmetric cryptography. We design the cryptosystem of smart card using the common Synopsys and simulate by ALTERA MAX+PLUS II at 40MHz. Consequently, we confirm the 52% increment of processing rate and the security level of 16 rounds.

Determination of Stress Intensity Factor for the Crack in Orthotropic Materials Using the Finite Element Method (유한요소법에 의한 직방성재료 내 균열의 응력확대계수 결정)

  • 조형석;강석진;이성근;임원균
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.17 no.1
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    • pp.59-65
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    • 2004
  • The stress intensity factors have been widely used in numerical studies of crack growth direction. However in many cases, omissive terms of the series expansion are quantitatively significant, so we consider the computation of such terms. For this purpose, we used the finite element method with isoparametric quadratic quarter-point elements. For examples, infinite square plate with a slant crack subjected to a uniaxial load is analyzed. The numerical analysis were performed for the wide range of crack tip element lengths and inclined angles. The numerical results obtained are compared with the theoretical solutions. Also they were accurate and efficient.

Velocity Profiles and Entrance Length of Transitional Oscillatory Flows in the Entrance Region of a Square Duct (정(正)4각(角)덕트 입구영역(入口領域)에서 천이(遷移) 진동유동(振動流動)의 입구(入口)길이와 속도분포(速度分布))

  • Choi, J.H.;Choi, B.M.;Yoo, Y.T.
    • Journal of Biosystems Engineering
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    • v.18 no.3
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    • pp.275-287
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    • 1993
  • The flow characteristics of the transitional oscillatory flows are investigated analytically and experimentally in the entrance region of a square duct. The systems of conservation equations are analytically solved by linearizing the non-linear convective terms for the developing transitional oscillatory flows in a square duct. The analytical solutions are obtained in the form of infinite series for the velocity profiles. The experimental study for the air flow in a square duct is carried out to measure the velocity profiles and waveforms by using a hot-wire anemometer with the data acquisition and processing systems. The theoretical and experimental results provide the major characteristics of the developing transitional oscillatory flows, such as velocity profiles, velocity waveforms, and entrance length. The velocity profiles in the decelerating phase are larger than those in the accelerating phase for the developing transitional oscillatory flows. The correlations of the entrance length of the transitional oscillatory flows in a square duct are found to be $Le/Dh=K{\cdot}Re_{os}/2({\omega}^+)^2$, where K is 1.23 of an experimental constant.

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Analysis of the Sound Source Field Using Spatial Transformation of the Sound Pressure in a Near-field (근거리 음압의 공간 변환에 의한 음원의 음장 분포 해석)

  • 김원호;윤종락
    • The Journal of the Acoustical Society of Korea
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    • v.22 no.8
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    • pp.660-669
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    • 2003
  • This paper describes a theory to calculate sound source field from the spatial transform of sound field and the measured cross-power spectrum of sound pressure over a hologram plane close to a sound source, Calculating method is proposed to solve sound pressures from cross-power spectrums over a hologram plane, For this, Taylor series for the nonlinear equations is expanded, and it is calculated using Newton-Raphon method, Also, a wave number filter is used to reduce errors that is occurred on the backward propagation, and is performed numerical simulation of the circular piston sound source with infinite baffle in water to verify the proposed theory.

Design of Fuzzy Controller for Firing Angle of TCSC Using Tabu Search (Tabu Search를 이용한 TCSC의 점호각 제어용 퍼지 제어기의 설계)

  • Kim, Woo-Geun;Hwang, Gi-Hyeon;Mun, Gyeong-Jun;Kim, Hyeong-Su;Park, Jun-Ho
    • Proceedings of the KIEE Conference
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    • 2000.07a
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    • pp.37-39
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    • 2000
  • This paper describes the application of Fuzzy Logic Controller (FLC) to Thyristor Controlled Series Capacitor (TCSC) which can have significant impact on Power system dynamics. The function of the FLC is to control the firing angle of the TCSC. We tuned the scaling factors of the FLC using Tabu Search. The proposed FLC is used for damping the low frequency oscillations caused by disturbances such as the sudden changes of small of large loads or the outages in the generators or transmission lines. To evaluate usefulness of the proposed FLC. we performed the computer simulation for single-machine infinite system. The response of FLC is compared with that of PD controller optimized using Tabu Search. Simulation results that the FLC shows the better control performance than PD controller.

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Coordinated Control of TCSC and SVC for System Damping Enhancement

  • So Ping Lam;Chu Yun Chung;Yu Tao
    • International Journal of Control, Automation, and Systems
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    • v.3 no.spc2
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    • pp.322-333
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    • 2005
  • This paper proposes a combination of the Thyristor Controlled Series Capacitor (TCSC) and Static Var Compensator (SVC) installation for enhancing the damping performance of a power system. The developed scheme employs a damping controller which coordinates measurement signals with control signals to control the TCSC and SVC. The coordinated control method is based on the application of projective controls. Controller performance over a range of operating conditions is investigated through simulation studies on a single-machine infinite-bus power system. The linear analysis and nonlinear simulation results show that the proposed controller can significantly improve the damping performance of the power system and hence, increase its power transfer capabilities. In this paper, a current injection model of TCSC is developed and incorporated in the transmission system model. By using equivalent injected currents at terminal buses to simulate a TCSC no modification of the bus admittance matrix is required at each iteration.

Current Distributions on the Infinite Plane Mattaric Grattings for TM Waves (TM파에 의한 무한 평면 격자상의 전류분포)

  • 김흥수;이상설
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.13 no.3
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    • pp.255-259
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    • 1988
  • The distributing current is calculated on the infinit plane mattaric grattings for the TM waves. The matrix is larger, when the moment method is applied this structure. So, the moment method of this case is required large memory and long CPU times. Those boundary condition and the scattering formura are transformed into spectal domain. Taking account of the peridic structure, this formular is changed in a series form by using the Flouquet mode. By making a suitable basis function, this equation is expreseed matrix form. So the distributing current on the mattaric strip is able to caculate by using this equation. We calculate magnitude of the distributing current for varing these spaces, widthes and an angle of incident waves.

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Dynamic Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness (I) -Vibration Analysis- (Waviness가 있는 볼베어링으로 지지된 회전계의 동특성 해석 (II)-안정성 해석 -)

  • Jeong, Seong-Weon;Jang, Gun-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.12
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    • pp.2647-2655
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    • 2002
  • This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).