• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.95-98
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• 1999

In this study, a method to find the optimal intermediate die geometry for the multi-stage drawing process for the rectangular rod from a round bar is proposed and a program using the proposed method is developed. On the stage of the design of the intermediate die geometry, the virtual die was constructed using the initial billet as a inlet of the drawing die and the final product as a exit of that and the virtual die was divided by the number of pass. Divided die was transformed into the rectangular one which is the intermediate die geometry for the multi-stage rectangular drawing process. In order to verify the application of the proposed method on the real industrial product, the drawing of the rectangular rod from a round which composed two stage has been performed and simulated by the three dimensional rigid plastic finite element method.

• The Journal of the Acoustical Society of Korea
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• v.14 no.1
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• pp.115-122
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• 1995

It is practical to taper the element (e.g., antenna or sensor) spacing with uniform weight rather than to taper the weights with uniform spacing. In a rectangular array, a triangular grid geometry of elements is more economical than a rectangular grid geometry in terms of reducing the number of elements. A space-tapering approach is proposed to improve the performance of a rectangular phased array with a triangular grid geometry of elements above a ground plane. The effects of space tapering on the main beam width and sidelobe level are discussed. It is shown that the proposed approach improves the sidelobe performance while the main beam width becomes a little broader.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.37-51
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• 2012

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

• Journal of Mechanical Science and Technology
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• v.18 no.1
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• pp.92-105
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• 2004

A new algorithm for planning a collision-free path based on algebraic curve is developed and the concept of collision-free Path Space (PS) is introduced. This paper presents a Geometry Mapping (GM) based on two straight curves in which the intermediate connection point is organized in elliptic locus ($\delta$, $\theta$). The GM produces two-dimensional PS that is used to create the shortest collision-free path. The elliptic locus of intermediate connection point has a special property in that the total distance between the focus points through a point on ellipse is the same regardless of the location of the intermediate connection point on the ellipse. Since the radial distance, a, represents the total length of the path, the collision-free path can be found as the GM proceeds from $\delta$=0 (the direct path) to $\delta$=$\delta$$\_$max/(the longest path) resulting in the minimum time search. The GM of elliptic workspace (EWS) requires calculation of interference in circumferential direction only. The procedure for GM includes categorization of obstacles to .educe necessary calculation. A GM based on rectangular workspace (RWS) using Cartesian coordinate is also considered to show yet another possible GM. The transformations of PS among Circular Workspace Geometry Mapping (CWS GM) , Elliptic Workspace Geometry Mapping (EWS GM) , and Rectangular Workspace Geometry Mapping (RWS GM), are also considered. The simulations for the EWS GM on various computer systems are carried out to measure performance of algorithm and the results are presented.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.699-702
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• 2001

The increasing demand in industry to produce rectangular cans at the reduction by the rectangular backward extrusion process involves better understanding of this process. In 2-D die deflection and dimensional variation of the component during extrusion, punch retraction, component injection and cooling was conducted using a coupled thermal-mechanical approach for the forward extrusion of aluminum alloy and low-carbon steel in tools of steel. Backward extrusion FE simulation and experimental simulation by physical modeling using wax as a model material have been performed. These simulations gave good results concerning the prediction of th flow modes and the corresponding surface expansions of the material occuring at the contact surface between the can and the punch. There prediction are the limits of the can height, depending on the reduction, the punch geometry, the workpiece material and the friction factor, in order to avoid the risk of damage caused by sticking of the workpiece material to the punch face. The influence of these different parameter on the distribution of the surface expansion along the inner can wall and bottom is already determined. This paper deals with the influence of the geometry changes of the forming tool and the work material in the rectangular backward using the 3-D finite element method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.911-912
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• 2010

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.4
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• pp.313-319
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• 2007

The effect of capillary cross-section geometry on evaporation is investigated in terms of the meniscus shape, evaporation rate and evaporation-induced flow for circular, square and rectangular cross-sectional capillaries. The shapes of water and ethanol menisci are not much different from each other in square and rectangular capillaries even though the surface tension of water is much larger than that of ethanol. On the other hand, the shapes of water and ethanol menisci are very different from each other in circular capillary. The averaged evaporation fluxes in circular and rectangular capillaries are measured by tracking the meniscus position. At a given position, the averaged evaporation flux in rectangular capillaries is much larger than that in circular capillary with comparable hydraulic diameter. The flow near the evaporating meniscus is also measured using micro-PIV, so that the rotating vortex motion is observed near the evaporating ethanol and methanol menisci except for the case of methanol meniscus in rectangular capillary. This difference is considered to be due to the existence of corner menisci at the four comers.

• Transactions of Materials Processing
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• v.20 no.6
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• pp.450-455
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• 2011

This paper presents an inverse design methodology for the cross section geometry of mold spring with a rectangular cross section as the starting material for a coiling process. The cross-sections of mold springs are universally rectangular, as the parallel sides minimize the possibility of failure under high service loads. Pre-coiled wires are initially designed to have a trapezoidal cross section, which becomes a rectangle by the coiling process. This study demonstrates a numerical exercise to predict changes in the sectional geometry in spring manufacture and to obtain the initial cross section which becomes the exact rectangle desired from the manufacturing process. Finite element analysis was carried out to calculate the sectional changes for various mold springs. Geometrical parameters were the widths at inner and outer radii, the inner and the outer corner radii, and the height. A partial least square regression analysis was carried out to find the main contributing factors for deciding initial design values. The height and the width mainly affected various initial parameters. The initial width at the inner radius was mostly affected by various specification parameters.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.663-677
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• 2022

This present paper extends some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Kannan type mappings. Non-trivial examples are further provided to support the hypotheses of our results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.3
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• pp.304-314
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• 2004

An experimental study has been conducted to measure the temperature fields and the local film cooling effectiveness for two and three staggered rows of the rectangular shaped-holes with various blowing rates. The hydraulic diameter of rectangular-shaped hole is 10mm. To compare with the film cooling performance of rectangular-shaped hole, two kinds of circular holes are tested. One has the same hydraulic diameter as the rectangular hole and the other has the same cross sectional area. Also, rectangular holes with expanded exit with same inlet area as rectangular ones are tested. Temperature fields are measured using a thermocouple rake attached on three-axis traversing system. Adiabatic film cooling effectiveness on the surface are obtained based on experimental results of thermochromic liquid crystals. The film cooling effectiveness is measured for various blowing rates and compared with the results for the cylindrical holes. In case of 2 rows, the rectangular holes has better performance than circular holes due to its slot-like geometry. In case of 3 rows, the effecta of hole shape is not clear.