• Title/Summary/Keyword: cylindrical coordinates

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Method of Numerical Simulation by Using the Local Harmonic Functions in the Cylindrical Coordinates (국소적 조화함수를 사용한 원통좌표계에서의 유동 해석)

  • Suh, Yong-Kweon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.31 no.3 s.258
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    • pp.300-305
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    • 2007
  • Many practical flow problems are defined with the circular boundary. Fluid flows within a circular boundary are however susceptible to a singularity problem when the cylindrical coordinates are employed. To remove this singularity a method has been developed in this study which uses the local harmonic functions in discretization of derivatives as well as interpolation. This paper describes the basic reason for introducing the harmonic functions and the overall numerical methods. The numerical methods are evaluated in terms of the accuracy and the stability. The Lamb-dipole flow is selected as a test flow. We will see that the harmonic-function method indeed gives more accurate solutions than the conventional methods in which the polynomial functions are utilized.

Study On Manufacturing of General Cam Using Coordinate Mapping in Multi CNC Machining Center (좌표계 맵핑을 이용한 다축 CNC 머시닝센터에서의 캠 가공에 관한 연구)

  • 박세환;신중호;장세원;강동우
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2002.10a
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    • pp.999-1002
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    • 2002
  • Cylindrical Cam Mechanism is widely used in the fields of industries, such as machine tool exchangers, textile machinery. This paper proposes a method for manufacturing of cylindrical cam in Multi CNC machining center. Multi CNC machining center has two different types depending on the tilting axis. For the manufacturing procedures. in this paper the location and the orientation of cutter path are defined from shape design data of cam. The integral NC code fur the both types of multi-axis CNC machining center can be created using the coordinates mapping between design coordinates and work coordinates. Finally, CAD/CAM program is developed on $C^{++}$ language. This program can display manufacturing and kinematics simulation, which can make integral NC code for multi-axis CNC machining center of two types.

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A Fast Poisson Solver of Second-Order Accuracy for Isolated Systems in Three-Dimensional Cartesian and Cylindrical Coordinates

  • Moon, Sanghyuk;Kim, Woong-Tae;Ostriker, Eve C.
    • The Bulletin of The Korean Astronomical Society
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    • v.44 no.1
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    • pp.46.1-46.1
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    • 2019
  • We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

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Adaptive Control of a Nonholonomic Mobile Robot with Parametric Uncertainty (불확실한 파라미터를 갖는 비홀로노믹 이동로봇의 적응제어)

  • Baik, Jong-Ik;Yun, Tae-Ung
    • Proceedings of the KIEE Conference
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    • 2003.11b
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    • pp.15-18
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    • 2003
  • This paper presents an adaptive control scheme for parking or regulating a nonholonomic mobile robot of an unicycle type with parameter uncertainty. The kinematics can be described with Brockett's nonholonomic integrator. The control law is designed in cylindrical coordinates together with the estimation law for the uncertain parameters such that the controlled signals converge to zero while guaranteeing the boundedness of the estimation errors. The effectiveness of the proposed scheme is demonstrated using simulations.

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Development of Zonal-Embedded-Grid Method for a Polar Coordinate System and Application to the Spin-up Flow within a Semi-Circular Cylinder

  • SUH Yong Kweon;YEO Chang-Ho
    • 한국가시화정보학회:학술대회논문집
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    • 2004.12a
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    • pp.81-90
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    • 2004
  • A zonal embedded grid technique has been developed for computation of the two-dimensional Navier-Stokes equations with cylindrical coordinates. The fundamental idea of the zonal embedded grid technique is that the number of azimuthal grids can be made small near the origin of the coordinates so that the grid size is more uniformly distributed over the domain than with the conventional regular-grid system. The code developed using this technique combined with the explicit, finite-volume method was then applied to calculation of the spin-up flows within a semi-circular cylinder. It was shown that the numerical results were in good agreement with the experimental results both qualitatively and quantitatively.

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Radiative transfer In General grid: RIG

  • Lee, Seok-Ho;Park, Young-Sun;Lee, Jeong-Eun
    • The Bulletin of The Korean Astronomical Society
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    • v.36 no.1
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    • pp.82.1-82.1
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    • 2011
  • We present a new code for solving non-LTE radiative transfer problems in a general grid (RIG). RIG develops from RATRAN code (Hogerheijde & van der Tak 2000) using the Accelerated Monte-Carlo method, and it can cope with line overlap effect among multiple molecular and atomic species. In this algorithm we make grids in arbitrary coordinates adequate to the problem, but, on the other hand, photons propagate in the Cartesian coordinates. For spherical, cylindrical and other well defined coordinate, the problem of tracing photon's path reduces to solving simple quadratic equations. For example, the outflow in the star formation have high dynamic range in scales from a few AU to ~ 0.1 pc and have also cylindrical symmetry. So, we have used (r, ${\alpha}$) coordinate system, where r is the distance from the origin and ${\alpha}$ is z/ R2 in the cylindrical coordinate of (R,z). The (r, ${\alpha}$) coordinate realizes the density - power function of r - and temperature distributions of the problems with smaller numbers of grid than the cylindrical coordinate does, and the former consumes less time to solve the problems than the latter.

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Dynamic Stability of Cylindrical Shells Subjected to Follower Forces (종동력을 받는 원통형 쉘의 동적 안정성에 관한 연구)

  • 김현순;김지환
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1997.10a
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    • pp.396-401
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    • 1997
  • Dynamic stability of cylindrical shells subjected to follower forces is analyzed in this paper. Motion of shells is formulated in curvilinear coordinates that is consistent with assumptions made in the Timoshenko beam and the Mindlin plate. Using the finite element method, the induced equations are reduced to an equation with finite degrees of freedom. The 9-node Lagrangian element is used, and reduced integration is used to avoid shear and membrane locking. The effects of thickness ratio on the dynamic stability of cylindrical shells are studied.

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