• Title/Summary/Keyword: Surface of revolution

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ON LORENTZ GCR SURFACES IN MINKOWSKI 3-SPACE

  • Fu, Yu;Yang, Dan
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.227-245
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    • 2016
  • A generalized constant ratio surface (GCR surface) is defined by the property that the tangential component of the position vector is a principal direction at each point on the surface, see [8] for details. In this paper, by solving some differential equations, a complete classification of Lorentz GCR surfaces in the three-dimensional Minkowski space is presented. Moreover, it turns out that a flat Lorentz GCR surface is an open part of a cylinder, apart from a plane and a CMC Lorentz GCR surface is a surface of revolution.

Electromagnetic Scattering from arbitrarily shaped dielectric Bodies of Revolution (임의의 모양을 갖는 회전형 유전체의 전자파 산란 현상)

  • Shin, Yong-Jae;Kim, Jung-Ki
    • Proceedings of the KIEE Conference
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    • 1987.07a
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    • pp.18-21
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    • 1987
  • The problem of electromagnetic scattering from arbitrarily shaped lossy dielectric bodies of revolution is studied. Two coupled vector integral equations are formulated from the potential formulas, the equivalence principle and boundary condition. The unknown surface currents (both electric and magnetic) can be found by the moment method, Galerkins's procedure. After the surface currents are determined, the scattering pattern can be evaluated.

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SURFACES OF REVOLUTION SATISFYING ΔIIG = f(G + C)

  • Baba-Hamed, Chahrazede;Bekkar, Mohammed
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1061-1067
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    • 2013
  • In this paper, we study surfaces of revolution without parabolic points in 3-Euclidean space $\mathbb{R}^3$, satisfying the condition ${\Delta}^{II}G=f(G+C)$, where ${\Delta}^{II}$ is the Laplace operator with respect to the second fundamental form, $f$ is a smooth function on the surface and C is a constant vector. Our main results state that surfaces of revolution without parabolic points in $\mathbb{R}^3$ which satisfy the condition ${\Delta}^{II}G=fG$, coincide with surfaces of revolution with non-zero constant Gaussian curvature.

Effects of Machining Conditions for Improvement of Surface Roughness on Micro End-Milling (마이크로 엔드밀 가공시 가공인자가 표면거칠기 향상에 미치는 영향)

  • Cho, Byoung-Moo;Kim, Sang-Jin;Park, Hee-Sang;Bae, Myung-Il
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.17 no.2
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    • pp.71-76
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    • 2008
  • Micro end-milling is one of effective technology that is able to do ultra-precision machining while increasing the productivity and has wide application field. But selection of machining condition is very difficult because of complicated machining mechanism. Therefore this study was carried out to select working factors to get the optimum surface roughness. Machining condition are depth of cut, feed rate and spindle revolution. The result of this study showed that Surface roughness was affected, in the other of depth of cut, spindle revolution, feed rate. And this study provided an regression equation relating surface roughness to working factors through Regression Analysis and determination coefficient of regression equation had a satisfactory reliability of 79%.

A Study on the High-Speed Machining of Die/Mold Material Using a Spindle-Speeder (주축증속기를 이용한 금형강의 고속절삭에 관한 연구)

  • 이용철;강명창;이득우;김정석
    • Journal of the Korean Society for Precision Engineering
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    • v.15 no.8
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    • pp.81-87
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    • 1998
  • High-speed machining is one of the most effective technologies to improve productivity. Because of the high speed and high feedrate, high-speed machining can give great advantages for the machining of dies and molds. In this paper, high-speed machining for HP-4 die material was carried out with a coated tungsten carbide ball endmill. In the high-speed machining, the cutting force and surface roughness of workpiece show various characteristics in different cutting conditions. Especially, the surface roughness of the workpiece depends largely on pick feed and feed-per-revolution of the ball endmill. In the condition where pick feed and feed-per-revolution are equal, better surface roughness is measured. By obtaining good surface roughness at high speed, efficiency of machining can be increased.

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ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

  • Kim, Young-Ho;Lee, Chul-Woo;Yoon, Dae-Won
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1141-1149
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    • 2009
  • In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map G satisfies the condition ${\Delta}^hG\;=\;AG,A\;{\in}\;Mat(3,{\mathbb{R}}),\;where\;{\Delta}^h$ denotes the Laplace operator of the second fundamental form h of the surface and Mat(3,$\mathbb{R}$) the set of 3${\times}$3-real matrices, and also obtain the complete classification theorem for those. In particular, we have a characterization of an ordinary sphere in terms of it.

Abrasive wear characteristics of high Cr cast iron hardfacing (고 Cr 주철계 육성용접부의 연삭(abrasion)마모 특성에 대한 연구)

  • 이형근
    • Journal of Welding and Joining
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    • v.15 no.4
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    • pp.154-165
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    • 1997
  • Abrasive wear characteristics of high Cr white cast iron-based hardfacing were investigated using the rubber wheel abrasion wear test method according with the ASTM G65-85. Mild steel was also tested for comparison with high Cr cast iron hardfacing. Wear experiments, where the applied force, wheel revolution rate and abrasive powder feed rate were selected as test valuables, were planned and analyzed by response surface method to evaluate wear statistically and quantitatively. Weight loss of high Cr cast iron hardfacing was mostly affected by the applied force and wheel revolution rate, and little by the powder feed rate. Weight loss of mild steel was greatly affected by the wheel revolution rate and powder feed rate, and slowly and steadily increased with the applied force. Abrasive wear mechanism of high Cr cast iron and mild steel was discussed in the light of the wear test results.

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A Study on the Machinability of High Hardness Steel in Ball End Milling (볼 엔드밀 가공에서 고경도 강재의 절삭특성에 관한 연구)

  • Won S. T.;Hur J. H.;Lee Y. J.
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 2002.02a
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    • pp.11-18
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    • 2002
  • The STD11 and KP4 are important steels and applied to the manufacturing of the die and mold. The purpose of this study is to investigate the machinability of tool steels of STD11(HRC60) and KP4(HRC32) when machining them by using ball end milling tools coated with TiAlN. Cutting forces by using a Kistler piezo-cell type tool dynamometer, surface roughness and tool wear by using tool microscope are used in the tests. The results from the cutting tests of KP4 specimens show that 85m/min. of cutting speed and 0.32mm/rev. of feed per revolution are optimum conditions for the higher productivity and 0.26mm/rev. with the same cutting speed are optimum conditions for better surface finishing. The results from machining STD11 workpiece at 30m/min. of cutting speed and 0.17m/rev. of feed per revolution show recommended for the higher productivity. The KP4 shows relatively smaller cutting forces than STD11 and STD11 shows the better surface finish than KP4.

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Abrasion Resistance and Surface Hardness of Gold Plated Carbonized Board (도금처리 탄화보드의 내마모성 및 표면경도)

  • Hwang, Sung-Wook;Park, Sang-Bum;Lee, Won-Hee
    • Journal of the Korea Furniture Society
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    • v.23 no.4
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    • pp.435-439
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    • 2012
  • This research was performed to evaluate surface performance of gold plated carbonized board. After the carbonization at $850^{\circ}C$, volume, weight, and density decreased by 65.25%, 71.35% and 17.64%, respectively. Abrasion resistance and surface hardness of non-carbonized board exhibited the highest values of 0.093 g/100 revolution and 26.43 N/$mm^2$, respectively. Gold plated carbonized board showed intermediate values, 0.587 g/100 revolution of abrasion resistance and 24.35 N/$mm^2$ of surface hardness. Carbonized board showed the lowest values, 0.863 g of abrasion resistance and 21.50 N/$mm^2$, of surface hardness. These results were thought to reflect propertional relationship between abrasion resistance and surface hardness. Abrasion resistance and surface hardness of carbonized board appeared able to be improved by surface treatment such as plating.

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Surfaces of Revolution of Type 1 in Galilean 3-Space

  • Cakmak, Ali;Es, Hasan;Karacan, Murat Kemal;Kiziltug, Sezai
    • Kyungpook Mathematical Journal
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    • v.60 no.3
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    • pp.585-597
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    • 2020
  • In this study, we classify surfaces of revolution of Type 1 in the three dimensional Galilean space 𝔾3 in terms of the position vector field, Gauss map, and Laplacian operator of the first and the second fundamental forms on the surface. Furthermore, we give a classification of surfaces of revolution of Type 1 generated by a non-isotropic curve satisfying the pointwise 1-type Gauss map equation.