• 통합자연과학논문집
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• 제7권2호
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• pp.124-129
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• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• 한국정밀공학회지
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• 제12권5호
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• pp.46-56
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• 1995

As demands on the precision bevel gears are increased in the related industry, the exact kinematical investigations of a pair of spherical involute bevel gears are required for the computer aided design. The exact angular velocity ratio based on the characteristics of the spherical involute tooth is derived and verified from the relationship between rotational angles. Elementary kinematics of the gearsets is investigated by applying the transformation of the coordinate systems. The tooth contact lines based on logarithmic tooth-wise curve are examines in three dimentional space. Contact ratio is formulated and simulated according to the system parameters such as shaft angles, pressure angle, and spiral angles. The condition of teeth interference is dervied and the critical numbers of gear teeth are calculated. The whole surface geometry of a spiral bevel gearsets are discretized and visualized by a computer graphic tool.

• 산업기술연구
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• 제1권
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• pp.39-45
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• 1981

The typical characteristic shape of the Koryo inlaid celadon Maebyong was reviewed and the symmetry of S curve was analyzed by the method of geometric basis. The contours of Maebyongs sampled were drawn and divided with geometric rectangular proportion. The analytical results showed the static and dynamic symmetric of the vase and the ratios of height and base of the rectangles established for the analysis of their shapes were almost 1:1, 1:${\sqrt{2}}$ and 3:5(known as the Golden Ratio). The excellent beauty of the curve was principally caused by the balanced and harmonius division of the proportional rectangles. The contour line was developed along with the logarithmic spiral modified and introduced lately into the shape of Yi dynasty's liquor bottle.

• 한국전산유체공학회지
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• 제20권3호
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• pp.35-40
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• 2015

Centrifugal pumps consume considerable amounts of energy in various industrial applications. Therefore, improving the efficiency of pumps machine is a crucial challenge in industrial world. This paper presents numerical investigation of flow characteristics in volutes of centrifugal pumps in order to compare the energy consumption. A wide range of volumetric flow rate has been investigated for each case. The standard k-${\varepsilon}$ is adopted as the turbulence model. The impeller rotation is simulated employing the Multi Reference Frames(MRF) method. First, two different conventional design methods, i.e., the constant angular momentum(CAM) and the constant mean velocity (CMV) are studied and compared to a baseline volute model. The CAM volute profile is a logarithmic spiral. The CMV volute profile shape is an Archimedes spiral curve. The modified volute models show lower head value than baseline volute model, but in case of efficiency graph, CAM curve has higher values than others. Finally for this part, CAM curve is selected to be used in the simulation of different cross-section shape. Two different types of cross-section are generated. One is a simple rectangular shape, and the other one is fan shape. In terms of different cross-section shape, simple rectangular geometry generated higher head and efficiency. Overall, simulation results showed that the volute designed using constant angular momentum(CAM) method has higher characteristic performances than one by CMV volute.

• 한국유체기계학회 논문집
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• 제13권2호
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• pp.59-64
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• 2010

A design method of Sirocco fan is developed for constructing 3-D impeller and scroll geometries, and for predicting both the aerodynamic performance and the noise characteristics of the designed fan. The aerodynamic blading design of fan is conducted by blade angle, camber line determinations and airfoil thickness distribution, and then the scroll geometry of fan is designed by using logarithmic spiral. The aerodynamic performance of designed fan is predicted by the meanline analysis with flow blockage, slip and pressure loss correlations. Based on the predicted performance data, fan noise is predicted by two models for cutoff frequency and broadband noise sources. The present predictions for the performance and the noise level of actual fans are well agreed with measurement results.

• 한국지반공학회지:지반
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• 제10권2호
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• pp.121-140
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• 1994

본 연구에서 경계가 불규칙하고 여러 토층으로 이루어진 자연과 인공 사면에 대한, 토층의 경계에서 굴절하는 대수나선곡선을 파괴면으로 가정한 신뢰도해석 모델을 개발하였다. 이 모델에서, 사면파괴토괴는 양 끝단이 수직평면으로 된 일정한 폭을 가진 Cylindroid로 가정하여 절편법을 적용하였고, 강도정수의 공간적인 변화, 불충분한 시료의 수에 의한 오차 그리고 실험실과 현장조건의 차이에서 오는 모델오차를 고려하여, FOSM 그리고 SOSM의 방법으로 신뢰도 지수를 구하여 파괴확률을 구하는 프로그램을 개발하였다. 이러한 연구를 기초로 다음의 결과를 얻었다: (1) 내부마찰각의 변동계수가 점착력의 변동계 수보다 민감하게 영향을 미침을 보여주었다. 따라서 대수나선파괴면의 사면안정해석에서 내부마 찰각의 불확실성이 사면안정에 더 큰 영향을 주므로 내부마찰각의 추정에 더 큰 주의를 기울여야할 것으로 사료된다. (2) 지진이 없을 경우에는, 사면폭이 증가함에 따라 전체 3차원파괴확률과 한계파괴폭은 증가하였으며, 지진이 있을 경우에는 전체 3차원파괴확률은 증가하였으나 한계 파괴폭은 전체 사면폭이 비교적 클 때, 진도가 커짐에 따라 급격히 감소하였다. (3) 지하수위는 높을수록, 전단강도와 수정계수는 작을수록 사면의 한계폭을 감소시키는 효과가 있다.