• Title/Summary/Keyword: Theoretical Equation

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Performance Analysis of Air Foil Bearings with Bump Friction (범프마찰을 고려한 공기포일베어링의 성능해석)

  • Kim, Young-Cheol;Kim, Dong-Hyun;Kim, Kyun-Woong
    • The KSFM Journal of Fluid Machinery
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    • v.9 no.1 s.34
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    • pp.47-55
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    • 2006
  • This paper presents the theoretical model to investigate the effect of Coulomb damping in the sub-structure of a foil bearing. Foil deflection is restricted by friction of bumps. Equivalent viscous damping of the bump foils is derived from the Coulomb friction. Dynamic equation of the bumps is constituted by stiffness and damping terms. This point give the difference from Heshmat's frictionless and simple compliance bump model. The fluid is modeled with the compressible Reynolds equation. A perturbation approach is used to determine the static and dynamic performance of the bearing from the coupled fluid-structural model. The analysis result shows that the static and dynamic performance is enhanced by bump friction. This analysis technique would be extended to development of a high performance bearing.

Study on Controller Design for an Active Magnetic Bearing Milling Spindle Using Chatter Stability Analysis (채터 안정성 해석을 이용한 자기베어링 밀링 주축의 제어기 설계 연구)

  • 경진호;박종권;노승국
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2002.10a
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    • pp.440-445
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    • 2002
  • The characteristic equation for regenerative chatter loop including a delay element replaced by a rational function is presented by a linear differential-difference equation, accounting for the dynamics of the AMB controllers, the uncut chip thickness equation and the cutting process as well as the rigid spindle dynamics itself. The chatter stability analysis of a rigid milling spindle suspended by 5-axes active magnetic bearings(AMBs) is also performed to investigate the influences of the damping and stiffness coefficients of AMBs on the chatter free cutting conditions, as they are allowed to vary within the stable region formed by the AMB control gains. Several cutting tests varying the derivative gains of the AMB were performed to investigate the regenerative chatter vibrations, and it was concluded that the theoretical analysis results are in good consistency with the test results.

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Activity Coefficients of Uni-univalent Electrolytes in Anhydrous Ethylenediamine (에틸렌디아민 非水溶液中에서의 1:1 염의 活性係數)

  • Joon Yong Kim
    • Journal of the Korean Chemical Society
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    • v.17 no.4
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    • pp.229-234
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    • 1973
  • The dependence of ionic activity and electrode potential upon electrolyte concentration in ethylenediamine includes the effects of ion-pair formation involving all possible combinations of cations and anions represent in the solution and includes the ion-atmosphere effects of dissociated ions. For calculating activity coefficients, Debye-Huckel limiting law, extended Debye-Huckel,equation, and Marshall Grunwald equation were used in comparison of experimental and calculated plots of the electromotive force of the cell versus the logarithum of concentration. The fit of the experimental points to the theoretical curves was improved in case of the Marshall-Grunwald equation.

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Pullout capacity of vertical plate anchors in cohesion-less soil

  • Kame, G.S.;Dewaikar, D.M.;Choudhury, Deepankar
    • Geomechanics and Engineering
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    • v.4 no.2
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    • pp.105-120
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    • 2012
  • In this paper, the ultimate pullout capacity of a vertical plate strip anchors in cohesion-less soil is analyzed with the consideration of active and passive state of equilibrium in the soil. K$\ddot{o}$tter's equation is used to compute the active and passive thrusts (along with their point of application) which are subsequently used in the analysis in which, all the equation of equilibrium are properly interpreted. A comparison of the results with the experimental results vis-$\grave{a}$-vis available theoretical/empirical solutions shows that, the proposed analysis provides a better estimate of the pullout capacity.

Theoretical Prediction of AC Characteristics of Low Pressure Lamps (저압 방전등 교류 접등 특성의 이론적 예측)

  • 지철근;장우진;여인선;이진우
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.38 no.6
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    • pp.470-476
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    • 1989
  • In order to develop a mathematical model which can predict the operating voltage and current of a discharge lamp, the properties and the physical phenomena of a low pressure gas discharge are investigated. Fluorescent lamp which uses a low pressure mercury-argon gas discharge is used in the model development. In a low pressure mercur-argon gas discharge, the continuity equation for each excited atom and electron, and the electron energy balance equation can predict the physical quantities of discharge. By coupling these equations and the circuit equation, the electrical characteristics of the discharge lamp can be predicted. To verify the validity of the suggested model, we calculated the voltage and current of a fluorescent lamp operating with inductor ballast for source frequency of 5KHz, 8KHz, 10KHz, and 13KHz. The results show good agreements in wave forms between the measured voltage and current, and the difference between the measured and calculated one is less than 5%.

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A Simulation of the Mean energy of electrons in $SF_6$-Ar Mixtures Gas (시뮬레이션을 이용한 $SF_6$-Ar혼합기체의 전자 평균에너지)

  • Kim, Sang-Nam
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2005.07a
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    • pp.578-580
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    • 2005
  • Energy distribution function for electrons in SF6-Ar mixtures gas used by MCS-BEq algorithm has been analysed over the E/N range 30~300[Td] by a two term Boltzmann equation and by a Monte Carlo Simulation using a set of electron cross sections determined by other authors, experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6$-Ar mixtures were measured by TOF method, The results show that the deduced electron drift velocities, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients and mean energy agree reasonably well with theoretical for a rang of E/N values. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

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Dynamic Characteristics Analysis of a Rigid Rotor System Supported by Journal Air Bearings (저널 공기 베어링에 의해 지지되어진 강체 로터 계의 동특성 해석)

  • 권대규;곡순이;이성철
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.11b
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    • pp.1026-1031
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    • 2001
  • In this paper. the dynamic characteristics of a super high-speed tilting-pad air bearing(TPGB) used in a turbo expander with high expansion ratio are analyzed. The dynamic behavior and stability of a rotary system supported by two journal air bearings are investigated numerically. The transient response of the shaft is obtained by simultaneously solving the equation of motion of the shaft and the dynamic Reynolds equation. The stiffness and damping coefficients of the bearing are calculated from the loading coefficients of the bearing are calculated from the loading capacity. shaft velocity and displacement by using a curve fitting method. The natural frequencies of the 1st and 2nd rigid modes can be calculated from these coefficients. The theoretical method of a rigid rotor system is verified by experimentsut.

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Novel estimation based on a minimum distance under the progressive Type-II censoring scheme

  • Young Eun Jeon;Suk-Bok Kang;Jung-In Seo
    • Communications for Statistical Applications and Methods
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    • v.30 no.4
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    • pp.411-421
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    • 2023
  • This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

A Theoretical Analysis of the Weak Shock Waves Propagating through a Bubbly Flow (기액 이상류를 전파하는 약한 충격파에 관한 이론해석적 연구)

  • Jun, Gu-Sik;Baek, Seung-Cheol;Kim, Heuy-Dong
    • Proceedings of the KSME Conference
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    • 2004.11a
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    • pp.1617-1622
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    • 2004
  • Two-phase flow of liquid and gas through pipe lines are frequently encountered in nuclear power plant or industrial facility. Pressure waves which can be generated by a valve operation or any other cause in pipe lines propagate through the two-phase flow, often leading to severe noise and vibration problems or fatigue failure of pipe line system. It is of practical importance to predict the propagation characteristics of the pressure waves for the safety design for the pipe line. In the present study, a theoretical analysis is performed to understand the propagation characteristics of a weak shock wave in a bubbly flow. A wave equation is developed using a small perturbation method to analyze the weak shock wave through a bubbly flow with comparably low void fractions. It is known that the elasticity of pipe and void fraction significantly affect the propagation speed of shock wave, but the frequency of relaxation oscillation which is generated behind the shock wave is not strongly influenced by the elasticity of pipe. The present analytical results are in close agreement with existing experimental data.

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Estimation of Smoothing Constant of Minimum Variance and Its Application to Shipping Data with Trend Removal Method

  • Takeyasu, Kazuhiro;Nagata, Keiko;Higuchi, Yuki
    • Industrial Engineering and Management Systems
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    • v.8 no.4
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    • pp.257-263
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    • 2009
  • Focusing on the idea that the equation of exponential smoothing method (ESM) is equivalent to (1, 1) order ARMA model equation, new method of estimation of smoothing constant in exponential smoothing method is proposed before by us which satisfies minimum variance of forecasting error. Theoretical solution was derived in a simple way. Mere application of ESM does not make good forecasting accuracy for the time series which has non-linear trend and/or trend by month. A new method to cope with this issue is required. In this paper, combining the trend removal method with this method, we aim to improve forecasting accuracy. An approach to this method is executed in the following method. Trend removal by a linear function is applied to the original shipping data of consumer goods. The combination of linear and non-linear function is also introduced in trend removal. For the comparison, monthly trend is removed after that. Theoretical solution of smoothing constant of ESM is calculated for both of the monthly trend removing data and the non monthly trend removing data. Then forecasting is executed on these data. The new method shows that it is useful especially for the time series that has stable characteristics and has rather strong seasonal trend and also the case that has non-linear trend. The effectiveness of this method should be examined in various cases.