• Title/Summary/Keyword: Closed-form equation

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A Study on the Prediction of Teeth Deformation of the Automobile Transmission Part(Shaft/Gear) in Warm Shrink Fitting Process (온간압입공정에서 자동차 변속기 단품(축/기어) 치형 변화 예측에 관한 연구)

  • Kim, Ho-Yoon;Choi, Chang-Jin;Bae, Won-Byong;Kim, Chul
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.9 s.186
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    • pp.54-60
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    • 2006
  • Fitting process carried out in automobile transmission assembly line is classified into three classes; heat fitting, press fitting, and their combined fitting. Heat fitting is a method that heats gear to a suitable range under the tempering temperature and squeezes it toward the outer diameter of shaft. Its stress depends on the yield strength of gear. Press fitting is a method that generally squeezes gear toward that of shaft at room temperature by press. Another method heats warmly gear and safely squeezes it toward that of shaft. Warm shrink fitting process for automobile transmission part is now gradually increased, but the parts (shaft/gear) assembled by this process produced dimensional changes of gear profile in both radial and circumferential directions. So that it may cause noise and vibration between gears. In order to solve these problems, we need an analysis of warm shrink fitting process, in which design parameters are involved; contact pressure according to fitting interference between outer diameter of shaft and inner diameter of gear, fitting temperature, and profile tolerance of gear. In this study, an closed form equation to predict contact pressure and fitting load was proposed in order to develop optimization technique of warm shrink fitting process and verified its reliability through the experimental results measured in the field and FEM, that is, thermal-structural coupled field analysis. Actual loads measured in the field have a good agreement with the results obtained by theoretical and finite element analysis and also the expanded amounts of the gear profile in both radial and circumferential directions are within the limit tolerances used in the field.

A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate

  • Belabed, Zakaria;Bousahla, Abdelmoumen Anis;Houari, Mohammed Sid Ahmed;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Earthquakes and Structures
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    • v.14 no.2
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    • pp.103-115
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    • 2018
  • In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

Development of Optimization Technique of Warm Shrink Fitting Process for Automobile Transmission Part(Shaft/Gear) (자동차 변속기 단품(축/기어)용 온간압입공정 최적화 기법 개발)

  • Kim Ho-Yoon;Bae Won-Byong;Kim Chul
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.5 s.182
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    • pp.37-43
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    • 2006
  • Fitting process carried out in automobile transmission assembly line is classified into three classes; heat fitting, press fitting, and their combined fitting. Heat fitting is a method that heats gear to a suitable range under the tempering temperature and squeezes it toward the outer diameter of shaft. Its stress depends on the yield strength of gear. Press fitting is a method that generally squeezes gear toward that of shaft at room temperature by press. Another method heats warmly gear and safely squeezes it toward that of shaft. Warm shrink fitting process for automobile transmission part is now gradually increased, but the parts (shaft/gear) assembled by this process produced dimensional change in both outer diameter and profile of the gear. So that it may cause noise and vibration between gears. In order to solve these problems, we need an analysis of warm shrink fitting process, in which design parameters are involved; contact pressure according to fitting interference between outer diameter of shaft and inner diameter of gear, fitting temperature, and profile tolerance of gear. In this study, an closed form equation to predict contact pressure and fitting load was proposed in order to develop optimization technique of warm shrink fitting process and verified its reliability through the experimental results measured in the field and FEM, that is, thermal-structural coupled field analysis. Actual loads measured in the field have a good agreement with the results obtained by theoretical and finite element analysis and also the expanded amounts of the outer diameters of the gears have a good agreement with results.

Propagation and Crosstalk Characteristic Analysis of Pulse Shaped Signals on the Coupled Microstrip Lines (결합 마이크로스트립 선로상의 펄스형태 신호의 전파 및 누화 특성 해석)

  • Park, Sun-Keun;Kim, Nam;Rhee, Sung-Yup;Jang, Woo-Hyun
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.8 no.5
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    • pp.516-524
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    • 1997
  • The propagation properties of various pulse signal types(square pulse, Gaussian pulse, trapezoid pulse, RF pulse) on coupled microstrip lines are investigated. Numerical integration technique which has its accuracy and is easily simulated, is used to obtain the time domain response of pulse signals. Frequency-dependent characteristics of coupled microstrip line is obtained using Jansen's approximate equation. The propagation properties of pulse signal on coupled microstrip lines is analyzed regarding to its geometric structure (relative permittivity ${varepsilon}_r$ substrate height h, strip width w of the microstrip line) and pulse width ${\tau}$ of signal pulse. The simulation results show that space between two lines is very significant parameter in pulse distortion in comparison of any other parameters. The results of this paper are compatible to the trade-off determination of relative permittivity, substrate height, strip width and pulse width of signal pulse when a design of MIC and MMIC is necessary.

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Free Surface Flow in a Trench Channel Using 3-D Finite Volume Method

  • Lee, Kil-Seong;Park, Ki-Doo;Oh, Jin-Ho
    • Journal of Korea Water Resources Association
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    • v.44 no.6
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    • pp.429-438
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    • 2011
  • In order to simulate a free surface flow in a trench channel, a three-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes (RANS) equations are closed with the ${\kappa}-{\epsilon}$ model. The artificial compressibility (AC) method is used. Because the pressure fields can be coupled directly with the velocity fields, the incompressible Navier-Stokes (INS) equations can be solved for the unknown variables such as velocity components and pressure. The governing equations are discretized in a conservation form using a second order accurate finite volume method on non-staggered grids. In order to prevent the oscillatory behavior of computed solutions known as odd-even decoupling, an artificial dissipation using the flux-difference splitting upwind scheme is applied. To enhance the efficiency and robustness of the numerical algorithm, the implicit method of the Beam and Warming method is employed. The treatment of the free surface, so-called interface-tracking method, is proposed using the free surface evolution equation and the kinematic free surface boundary conditions at the free surface instead of the dynamic free surface boundary condition. AC method in this paper can be applied only to the hydrodynamic pressure using the decomposition into hydrostatic pressure and hydrodynamic pressure components. In this study, the boundary-fitted grids are used and advanced each time the free surface moved. The accuracy of our RANS solver is compared with the laboratory experimental and numerical data for a fully turbulent shallow-water trench flow. The algorithm yields practically identical velocity profiles that are in good overall agreement with the laboratory experimental measurement for the turbulent flow.

A Model for Assessing Maximum Overtime Rate in Labor Subcontracting Practices

  • Nassar, Khaled;Hosny, Ossama
    • Journal of Construction Engineering and Project Management
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    • v.2 no.2
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    • pp.18-27
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    • 2012
  • Despite the rapid development in the construction industry due to the changing new technologies, many projects still fail to meet target deadlines. Shortage in manpower and skilled laborers is one of the main reasons for such delays. Markets with high economic growth and economic expansion (such as Gulf Countries in the Middle East) may have pronounced labor the shortages. Labor subcontracting practices are used sometimes to increase production rates and meet project deadlines. This paper explains and analyses labor subcontracting practices currently being used in many places around the world (and especially in the Gulf Countries) and in particular defines a maximum overtime rate for laborers in the laborer-subcontracting method ensuring that the contractor gains both the time saved during overtime and also reduces the cost per unit produced. The mathematical model used formalizes a closed-form equation for overtime pay in similar situations and as such can be applicable worldwide. Data was collected from representative projects that employed such practices from various trades. Validation of the model and formula has been tested successfully by analyzing historic data. The results prove that contractors often do not reach the optimum use of their practices resulting in a higher cost per unit. The presented model and the analysis should be of interest to many contractors currently involved in the practice or considering its use and to those who wish to find new methods that would help in eliminating as much wastes as possible by allocating their resources in the most efficient way.

Analysis of the Warm Shrink Fitting Process for Assembling the Part(Shaft and Output Gear) (단품(축/OUTPUT 기어)조립을 위한 온간압입공정 해석)

  • Kim, Tae-Jin;Kang, Hee-Jun;Kim, Chul;Chu, Suck-Jae;Kim, Ho-Yun
    • Journal of the Korean Society for Precision Engineering
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    • v.25 no.6
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    • pp.47-54
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    • 2008
  • Fitting process carried out in the automobile transmission assembly line is classified into three classes; heat fitting, press fitting, and their combined fitting. Heat fitting is a method that heats gear to a suitable range under the tempering temperature and squeezes it toward the outer diameter of shaft. Its stress depends on the yield strength of gear. Press fitting is a method that generally squeezes gear toward that of shaft at room temperature by a press. Another method heats warmly gear and safely squeezes it toward that of shaft. Warm shrink fitting process for the automobile transmission part is now gradually increased, but the parts (shaft/gear) assembled by this process produced dimensional changes in both the outer diameter and profile of the gear. So that it may cause noise and vibration between gears. In order to solve these problems, we need an analysis of warm shrink fitting process, in which design parameters are involved; contact pressure according to fitting interference between outer diameter of shaft and inner diameter of gear, fitting temperature, and profile tolerance of gear. In this study, an closed form equation to predict contact pressure and fitting load was proposed in order to develop an optimization technique of the warm shrink fitting process and verified its reliability through the experimental results measured in the field and FEM, that is, thermal-structural coupled field analysis. Actual loads measured in the field was in good agreements with the results obtained by the theoretical and finite element analysis.

Free vibrations of a two-cable network inter-supported by cross-links extended to ground

  • Zhou, H.J.;Wu, Y.H.;Li, L.X.;Sun, L.M.;Xing, F.
    • Smart Structures and Systems
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    • v.23 no.6
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    • pp.653-667
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    • 2019
  • Using cross-ties to connect cables together when forming a cable network is regarded as an efficient method of mitigating cable vibrations. Cross-ties have been extended and fixed on bridge decks or towers in some engineering applications. However, the dynamics of this kind of system need to be further studied, and the effects of extending cross-links to bridge decks/towers on the modal response of the system should be assessed in detail. In this paper, a system of two cables connected by an inter-supported cross-link with another lower cross-link extended to the ground is proposed and analyzed. The characteristic equation of the system is derived, and some limiting solutions in closed form of the system are derived. Roots of cable system with special configurations are also discussed, attention being given to the case when the two cables are identical. A predictable mode behavior was found when the stiffness of inter-connection cross-link and the cross-link extended to the ground were the same. The vector of mode energy distribution and the degree of mode localization index are proposed so as to distinguish global and local modes. The change of mode behaviors is further discussed in the case when the two cables are not identical. Effects of cross-link stiffness, cross-link location, mass-tension ratio, cable length ratio and frequency ratio on $1^{st}$ mode frequency and mode shape are addressed.

Acceleration Technique in Particle-based Collision Detection Using Cone Area Based Dynamic Collision Regions (부채꼴 영역 기반의 동적인 충돌 영역을 이용한 입자 기반 충돌 검사의 고속화 기법)

  • Kim, Jong-Hyun
    • Journal of the Korea Computer Graphics Society
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    • v.25 no.2
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    • pp.11-18
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    • 2019
  • In this paper, we propose a framework that can perform acceleration collision detection efficiently by using a cone based collision area in a particle-based system which requires collision detection with many objects. Three conditions determine particle and cone-based collision regions: 1) If there is a cone position within the radius of the adjacent particle, 2) In the case where the position of the adjacent particle exists in the cone area, 3) When adjacent particles exist between two vectors forming a cone area. As a result, it is defined that when the above conditions are all satisfied, the particle and the region of a cone have collided. In this paper, we automatically update the area of the cone, which is the collision detection area, according to the particle movement. Determine the direction and length of the cone based on the position and velocity of the particle to calculate the dynamic change of the cone. Collision detection is performed quickly using only the particles in the finally calculated area. The acceleration method proposed in this paper is simple to implement because it is executed with a closed form equation instead of explicitly creating the tree data structure, and collision inspection performance is improved in all results.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).