• Title/Summary/Keyword: Slip equation

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Analysis of Temperature Distribution and slip in Rapid Thermal Processing (급속 열처리시 실리콘 웨이퍼의 온도분포와 슬립 현상의 해석)

  • Lee, Hyouk;Yoo, Young-Don;Earmme, Youn-Young;Shin, Hyun-Dong;Kim, Choong-Ki
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.4
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    • pp.609-620
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    • 1992
  • A numerical solution of temperature and thermally induced stress in a wafer during rapid thermal processing (R.T.P) is obtained, and an analysis of onset and propagation of slip is performed and compared with experiment. In order to calculate temperature distribution of a wafer in R.T.P system, heat conduction equation that incorporated with radiative and convective heat transfer model is solved, and the solution of the equation is calculated numerically using alternating direction implicit (A.D.I) method. In dealing with radiative heat transfer, a partially transparent body that absorbs the radiation energy is assumed and this transparent body undergoes multiple internal reflections and absorptions. Two dimensional (assuming plane stress) thermoelastic constitutive equation is used to calculate thermal stress induced in a wafer and finite element method is employed to solve the equation numerically. The stress resolved in the slip directions on the slip planes of silicon is compared with the yield stress of silicon in order to predict the slip. The result of the analysis shows that the wafer temperature at which slip occurs is affected by the heating rate of the R.T.P system. It is observed that once slip occurs in the wafer, the slip grows.

Numerical Study on Blockage and Slip Characteristics of Centrifugal Compressor Impellers (원심압축기 임펠러의 Blockage와 Slip 특성에 관한 수치연구)

  • Oh, Jongsik
    • 유체기계공업학회:학술대회논문집
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    • 2000.12a
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    • pp.236-244
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    • 2000
  • As the second part of the author's study, the aerodynamic blockage and the slip factor of 8 centrifugal compressor impellers are investigated, when the flow rate is changed from numerical stall to choke, using three-dimensional Navier-Stokes analysis results. Based on all the exit blockage distributions, an improved model equation with two adjusting coefficients is developed for the use in design processes with the agile engineering purpose. A popular expression of constant slip factors, the Wiesner's equation, cannot be applied in design processes when more accurate prediction is strongly required at design and off-design points. Slip factor variation is found to be also influenced by the blade loadings at midspan. When the flow rate is changed, a pattern of the slip factor variations is assumed to be a simple form which can be explained using midspan blade loading distributions.

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Analysis of slope stability based on evaluation of force balance

  • Razdolsky, A.G.;Yankelevsky, D.Z.;Karinski, Y.S.
    • Structural Engineering and Mechanics
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    • v.20 no.3
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    • pp.313-334
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    • 2005
  • The paper presents a new approach for the analysis of slope stability that is based on the numerical solution of a differential equation, which describes the thrust force distribution within the potential sliding mass. It is based on the evaluation of the thrust force value at the endpoint of the slip line. A coupled approximation of the slip and thrust lines is applied. The model is based on subdivision of the sliding mass into slices that are normal to the slip line and the equilibrium differential equation is obtained as the slice width approaches zero. Opposed to common iterative limit equilibrium procedures the present method is straightforward and gives an estimate of slope stability at the value of the safety factor prescribed in advance by standard requirements. Considering the location of the thrust line within the soil mass above the trial slip line eliminates the possible development of a tensile thrust force in the stable and critical states of the slope. The location of the upper boundary point of the thrust line is determined by the equilibrium of the upper triangular slice. The method can be applied to any smooth shape of a slip line, i.e., to a slip line without break points. An approximation of the slip and thrust lines by quadratic parabolas is used in the numerical examples for a series of slopes.

Solutions of the Navier-Stokes equation in slip flow region (Slip flow 영역에서 Navier Stokes 방정식의 해석 연구)

  • Park, W.H.;Kim, T.K.
    • Proceedings of the KSME Conference
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    • 2000.11b
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    • pp.597-602
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    • 2000
  • In a MEMS(micro-electro mechanical system), the fluid may slip near the surface of a solid and have a discontinuous temperature profile. A numerical prediction in this slip flow region can provide a reasonable guide for the design and fabrication of micro devices. The compressible Navier-Stokes equation with Maxwell/smoluchowski boundary condition is solved for two simple systems; couette flow and pressure driven flow in a long channel. We found that the couette flow could be regarded as an incompressible system in low speed regions. For the pressure driven flow system, we observed nonlinear distribution of pressure in the long channel and numerical results showed a good agreement with the experimental results.

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Determination of shear stiffness for headed-stud shear connectors using energy balance approach

  • Ye, Huawen;Huang, Ruosen;Tang, Shiqing;Zhou, Yu;Liu, Jilin
    • Steel and Composite Structures
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    • v.42 no.4
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    • pp.477-487
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    • 2022
  • The shear stiffness of headed-stud shear connectors has no unified definition due to the nonlinear characteristics of its load-slip relationship. A unified framework was firstly adopted to develop a general expression of shear load-slip equation for headed-stud shear connectors varying in a large parameter range based on both force and energy balance. The pre- and post-yield shear stiffness were then determined through bilinear idealization of proposed shear load-slip equation. An updated and carefully selected push-out test database of 157 stud shear connectors, conducting on studs 13~30mm in diameter and on concretes 30~180 MPa in cubic compressive strength, was used for model regression and sensitivity analysis of shear stiffness. An empirical calculation model was also established for the stud shear stiffness. Compared with the previous models through statistical analysis, the proposed model demonstrates a better performance to predict the shear load-slip response and stiffness of the stud shear connectors.

The Slip-Wall Boundary Conditions Effects and the Entropy Characteristics of the Multi-Species GH Solver (다화학종 GH 방정식의 정확성 향상을 위한 벽면 경계조건 연구 및 GH 방정식의 엔트로피 특성 고찰)

  • Ahn, Jae-Wan;Kim, Chong-Am
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.37 no.10
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    • pp.947-954
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    • 2009
  • Starting from the Eu's GH(Generalized Hydrodynamic) theory, the multi-species GH numerical solver is developed in this research and its computatyional behaviors are examined for the hypersonic rarefied flow over an axisymmetric body. To improve the accuracy of the developed multi-species GH solver, various slip-wall boundary conditions are tested and the computed results are compared. Additionally, in order to validate the entropy characteristics of the GH equation, the entropy production and entropy generation rates of the GH equation are investigated in the 1-dimensional normal shock structure test at a high Knudsen number.

A Study on Heavy Metal Removal Characteristics Using Bone Char (골탄(bone char)의 중금속 제거 특성에 관한 연구)

  • Kim, Jae-Young;Kim, Hwan-Gi
    • Journal of Korean Society of Water and Wastewater
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    • v.21 no.2
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    • pp.253-258
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    • 2007
  • The adsorption capacity of bone char for lead, cadmium and zinc was studied in both single and binary multiple component systems. Equilibrium experimental studies have been performed to determine the sorption capacity of bone char for each metal ion. These have been analysed using single and multi-component equilibrum models. The results show that the sorption of metal ions for multi-component systems can be predicted reasonably well from the IAS theory with the Langmuir equation, the Freundlich and the Slip equation for metal ions.

극소공기막을 갖는 공기윤활 슬라이더 베어링의 윤활해석에 관한 연구

  • Hwang, Pyung;Yang, Seung-Han
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 1996.04b
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    • pp.94-98
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    • 1996
  • The static characteristics of air-lubricated slider bearing were performed using direct numerical method. The equations of motion of slider bearing are solved simultaneously with the Reynolds equation for three degrees of freedom. The molecular rarefaction effect is considered. The models implemented include the first-order slip, the second-order slip, and the Boltzmann equation model derived by Fukui and Kaneko(FK model)

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Study of stick-slip phenomena on spinning shaft (회전축계에서 발생하는 스틱슬립 현상 연구)

  • Kim, B;Chung, J
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2014.10a
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    • pp.250-251
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    • 2014
  • This paper investigates the stick-slip phenomena on spinning shaft. The modeling of the shaft is considered only torsional direction with nonlinear friction. The friction is adopted a negative friction-velocity slope. Based on the model, a nonlinear equation of motion is derived and analyze the stick-slip phenomena. In order to analyze the time dependent response, the nonlinear formulations are numerically solved by nonlinear Newmark method. The numerical results reveal the stick-slip phenomena on the spinning shaft system.

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Development of Calibration Equation of Portable Slip Meter(ONO·PPSM) through Comparative test of O-Y·PSM and ONO·PPSM (경사인장형 미끄럼시험기(O-Y·PSM)와의 비교실험을 통한 휴대형 미끄럼시험기(ONO·PPSM)의 교정식 작성)

  • Shin, Yoon-Ho;Choi, Soo-Kyung
    • Journal of the Korea Institute of Building Construction
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    • v.9 no.5
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    • pp.155-161
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    • 2009
  • This paper is the result of an investigation of a PORTABLE SLIP METER(ONO PPSM) by means of an experiment to determine its validity as a slip meter. ONO PPSM is a portable slip meter that was designed to address the weak points of PULL SLIP METER(O-Y PSM), which can be used to obtain an accurate measurement of slip resistance, but is very heavy and difficult to operate. To determine the stability of the measurement result of ONO PPSM, we measured the slip resistance against 4 different kind of floor materials. Our findings showed that the coefficient of variability of CSR' is less than 0.05. Furthermore, we verified the relationship between CSR' and CSR. More specifically, by performing the slip test against 7 different kinds of inorganic matter floor materials, we increased the usability of ONO PPSM as a slip meter by suggesting a method of sharing the evaluation index of slip of CSR' and C.S.R.