• 제목/요약/키워드: Approximate Equation

검색결과 487건 처리시간 0.023초

압연해석을 위한 슬래브-유한요소법에 대한 연구 (An Investigation of Slab-FEM for Rolling Analysis)

  • 송정훈;박종진
    • 대한기계학회논문집A
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    • 제20권11호
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    • pp.3454-3462
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    • 1996
  • Compared to a full three dimensional FEM, the Slab-FEM hybrid method reduces the required computation time distinctly and it can be applied to the analysis of a shape rolling process. However, the method is somewhat approximate and predictions by the method contain certain inaccuracies. In the present investigation a parameter called T-factor was introduced to compensate the inaccuracies of the method and proper values of the parameter were estimated for different widths of bars and reduction ratios. Then, the method was applied to analyze cold and hot rollings of rectangular bars and predicted results were compared to those of experiments. Nonuniform distributions of temperature in the bars were predicted by utilizing the temperature equation obtained for a semi-infinite solid under radiation and convection boundary conditions. It was found out that accuracies of spread and roll separating force predictions could be enhanced by using proper values of the T-factor.

원료불출기의 역기구학: 여유자유도와 구속조건을 이용한 닫힌 형태의 해 (Inverse kinematics of a Reclaimer: Redundancy and a Closed- Form Solution by Exploiting Geometric Constraints)

  • Hong, K.S.;Kim, Y.M.;Shin, K.T.
    • 한국정밀공학회지
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    • 제14권7호
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    • pp.144-153
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    • 1997
  • The inverse kinematics problem of a reclaimer which excavates and transports raw materials in a raw yard is investigated. Because of the geometric feature of the equipment in which scooping buckets are attached around the rotating disk, kinematic redundancy occurs in determining joint variable. Link coordinates are introduced following the Denavit-Hartenbery representation. For a given excavation point the forward kinematics yields 3 equations, however the number of involved joint variables in the equations is four. It is shown that the rotating disk at the end of the boom provides an extra passive degree of freedom. Two approaches are investigated in obtaining inverse kinematics solutions. The first method pre-assigns the height of excavation point which can be determined through path planning. A closed form solution is obtained for the first approach. The second method exploits the orthogonality between the normal vector at the excavation point and the z axis of the end-effector coordinate system. The geometry near the reclaiming point has been approximated as a plane, and the plane equation has been obtained by the least square method considering 8 adjacent points near the point. A closed form solution is not found for the second approach, however a linear approximate solution is provided.

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불균일계 액-액 접촉 계면을 통한 ester의 알카리 가수분해 반응 (Alkaline Hydrolysis of Esters across the Heterogeneous Liquid-Liquid Interface)

  • 박상욱;문진복;고명숙;김건우
    • 공업화학
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    • 제3권1호
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    • pp.119-129
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    • 1992
  • Ethyl acetate와 n-butyl acetate의 $25^{\circ}C$에서 알카리 가수분해 반응을 개량된 Lewis cell에서 행하여 화학반응을 수반한 물질전달 속도를 측정하였다. 측정한 물질전달 속도는 교반조의 교반속도에 무관하였고 이온강도 증가에 따라 감소하였으나 화학반응촉진 계수는 일정하였다. 측정한 화학반응 촉진계수를 경막설로부터 얻은 용질의 확산방정식의 근사해로부터 해석하여 ester의 알카리 가수분해반응의 2차 비가역 반응속도 정수를 얻을 수 있었으며, 그 값은 ethyl acetate의 경우 $0.041m^3/kgmol{\cdot}s$, n-butyl acetate의 경우 $0.338m^3/kgmol{\cdot}s$이었다.

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진공환경에서 수평 웨이퍼 표면으로의 입자침착 해석 (Analysis on Particle Deposition onto a Horizontal Semiconductor Wafer at Vacuum Environment)

  • 유경훈
    • 대한기계학회논문집B
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    • 제26권12호
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    • pp.1715-1721
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    • 2002
  • Numerical analysis was conducted to characterize the gas flow field and particle deposition on a horizontal freestanding semiconductor wafer under the laminar flow field at vacuum environment. In order to calculate the properties of gas, the gas was assumed to obey the ideal gas law. The particle transport mechanisms considered were convection, Brownian diffusion and gravitational settling. The averaged particle deposition velocities and their radial distributions fnr the upper surface of the wafer were calculated from the particle concentration equation in an Eulerian frame of reference for system pressures of 1 mbar~1 atm and particle sizes of 2nm~10$^4$ nm(10 ${\mu}{\textrm}{m}$). It was observed that as the system pressure decreases, the boundary layer of gas flow becomes thicker and the deposition velocities are increased over the whole range of particle size. One thing to be noted here is that the deposition velocities are increased in the diffusion dominant particle size range with decreasing system pressure, whereas the thickness of the boundary layer is larger. This contradiction is attributed to the increase of particle mechanical mobility and the consequent increase of Brownian diffusion with decreasing the system pressure. The present numerical results showed good agreement with the results of the approximate model and the available experimental data.

수지상가지의 조대화를 고려한 이원합금의 응고과정동안 용질 재분배 해석 (Analysis on the solute redistribution in coarsening dendrite arms during solidification of binary metal alloys)

  • 유호선
    • 대한기계학회논문집B
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    • 제20권4호
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    • pp.1437-1448
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    • 1996
  • This paper presents a simplified model for approximate analysis of the solute redistribution in coarsening dendrite arms during solidification of binary metal alloys. By introducing a quadratic concentration profile with a time-dependent coefficient, the integral equation for diffusion in the solid phase is reduced to a simple differential relation between the coefficient and the solid-liquid interface position. The solid fraction corresponding to the system temperature is readily determined from the relation, phase equilibrium and the overall solute balance in which the liquid phase is assumed to be completely mixed. In order to validate the developed model, calculations are performed for the directional solidification of Al-4.9 mass Cu alloy. The predicted eutectic fractions for a wide range of the cooling rate reasonably agree with data from the well-known experiment as well as sophisticated numerical analyses. Also, the results for the back diffusion limits are consistent with available references. Additional calculations show that the characteristic parameters such as the coarsening, density variation and nonlinarity in the phase diagram significantly affect the microsegregation. Owing to the simplicity, efficiency and compatibility, the present model may be suitable for the micro-macroscopic solidification model as a microscopic component.

수직하방 분사된 주의 비선형 거동에 관한 연구 (A Study on the Nonlinear Motion of a Vertical Liquid Jet)

  • 석지권;정환문;문수연;이충원
    • 대한기계학회논문집B
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    • 제26권1호
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    • pp.45-54
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    • 2002
  • The breakup phenomena of a vertical laminar jet issuing from capillary tubes in a quiescent ambient air are investigated using a forced vibration analysis of the surface wave. Using a linear approach to the transient jet velocity, an approximate solution fur the longitudinal motion of a vertical liquid jet is theoretically derived, thus performing an instability analysis by a vibration method. The damping term of this equation is nonlinear as it depends on dimensionless parameters, a Weber number, and an Ohnesorge number. The instability condition is determined based on whether the coefficient of the damping term is less than zero or not. Uniform drop formation is dependent on the vibration frequency fur the forced vibration case.

원형 단면을 갖는 180° 굽은 곡관내 발달하는 난류유동에 관한 수치해석 (Numerical Simulation of Developing Turbulent Flow in a Circular Pipe of 180° Bend)

  • 명현국
    • 대한기계학회논문집B
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    • 제30권10호
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    • pp.966-972
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    • 2006
  • A numerical simulation is performed fur developing turbulent flow in a strongly curved 180 deg pipe and its downstream tangent by a new solution code(PowerCFD) which adopts an unstructured cell-centered method. The governing equations are discretized as the full elliptic from of the equations of motion. Three typical two-equation turbulence models of low-Reynolds-number form are used to approximate the turbulent stress field. Solutions fur both streamwise and circumferential velocity components are compared with the experimental data by Azzola et at.(1986). The ${\kappa}-{\omega}$ model by Wilcox(1988) is found to give better prediction performance than the other two. Predicted secondary velocities and streamwise velocity component contours at sequential longitudinal stations are also presented in order to enable a detailed description of the complete flow. It is also found that, in the bend both mean streamwise and secondary velocities never achieve a fully-developed state and the code is capable of producing very well the complex nature of steady flow in a strongly curved pipe.

중주파수 대역 해석을 위한 Beam-plate-beam 연성 구조물의 웨이브 모형 연구와 시험적 규명 (Wave Models and Experimental Studies of Beam-plate-beam Coupled Systems for a Mid-frequency Analysis)

  • 유지우
    • 한국소음진동공학회논문집
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    • 제17권2호
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    • pp.121-129
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    • 2007
  • There has been much effort to find suitable methods for structural analysis in the mid-frequency region where traditional low frequency methods have increasing uncertainties whilst statistical energy analysis is not strictly applicable. Systems consisting of relatively stiff beams coupled to flexible plates have a particularly broad mid-frequency region where the beams support only a few modes whilst the plate has a high modal density and modal overlap. A system of two parallel beams coupled to a plate is investigated based on the wave method, which is an approximate method. Muller's method is utilised for obtaining complex roots of a dispersion wave equation, which does not converge in the conventional wave method based on a simple iteration. The wave model is extended from a single-beam-plate system, to a plate with two identical beams which is modelled using a symmetric-antisymmetric technique. The important hypothesis that the coupled beam wavenumber is sufficiently smaller than the plate free wavenumber is experimentally verified. Finally, experimental results such as powers and energy ratios show the validity of the analytical wave models.

$Pad{\acute{e}}$ 근사에 의한 포물형 파랑 근사식 - 입사각 $80^{\circ}$까지 적용 모형 (Parabolic Wave Equations Based on $Pad{\acute{e}}$ Approximants - Model Applicable to Incidence Angle $80^{\circ}$)

  • 서승남
    • 한국해안해양공학회지
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    • 제19권4호
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    • pp.375-384
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    • 2007
  • [ $Pad{\acute{e}}$ ] 근사에 의한 포물형 근사모형들을 제시하였고 $Pad{\acute{e}}$(15, 15) 근사모형은 일정 경사의 지형에 대한 엄밀해와 비교할 때 입사각 $80^{\circ}$까지 적용 가능함을 보였다. 포물형 근사식에 대한 체계적인 유도방법을 보인 후, 본 연구에서는 15차 $Pad{\acute{e}}$ 근사모형까지 나타내었고 일정 경사지형에서의 파랑변형에 대한 수치결과들을 제시하였다.

Laser-assisted machining에서 질화규소 시편의 표면온도와 절삭특성에 관한 연구 (Investigation of the Surface Temperature and Cutting Characteristics of Silicon Nitride in Laser-Assisted Machining)

  • 임세환;이제훈;신동식;김종도;김주현
    • 한국레이저가공학회지
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    • 제12권1호
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    • pp.25-33
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    • 2009
  • In laser-assisted machining (LAM), laser beam is used to locally increase the temperature of a workpiece and thus to enhance the machinability. In order to set the temperature of the material removal area of a workpiece at an optimal value, process parameters, such as laser power, feed rate, and rotational velocity, have to be carefully controlled. In this work, the effects of laser power and feed rate on the temperature distribution of a silicon nitride rotating at a constant velocity were experimentally investigated. Using a pyrometer, temperatures at various locations of the silicon nitride were measured both in circumferential and axial directions. The measured temperatures were fitted to a quadratic equation to approximate the temperature at the cutting location. The machining results showed that cutting force and tool wear were decreased when the temperature at the cutting location was increased.

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