• The Optical Journal
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• s.150
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• pp.31-41
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• 2014

현재까지 많은 업체에서 사용되는 비구면 표현식의 단점을 해결하여 직관적이며 예측가능한 면을 표현할 수 있는 새로운 비구면 표현식, 일명 Q Polynomials (또는 Forbes Polynomials, Q-type Polynomials)을 소개한다. Q Polynomials은 기존 quadratic polynomial을 이용한 표현식과 달리 서로 영향을 미치지 않는 유일한 함수 Qm를 기본으로 하는 다항식으로 구성되어 있기 때문에 각 계수는 하나의 비구면에 대해 유일한 계수다. 각 항의 함수의 모양이 이미 정해져 있기 때문에 계수들의 크기를 살펴보면 비구면도, 측정 가능성, 가공 및 생산 가능성에 대한 예측이 가능하다. 따라서 비구면 설계 시점에서부터 시험/검사, 생산이 실질적으로 가능한 비구면 광학요소인지가 판정되므로 설계시부터 설계자, 시험/검사자, 생산자 사이의 합의가 이루어지는 것과 같다. 따라서 생산성과 간섭계 측정을 이용한 초정밀 비구면를 제조할 수 있는 결과에 이르게 된다. 이미 도입한 여러 업체에서 긍정적인 결과를 얻고 있다. Q polynomials은 기존에 현업에서 사용되고 있는 광학 설계 프로그램에도 적용되어 사용 가능하다.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1539-1550
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• 2019

We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.409-430
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• 2010

The present paper will be concerned to the investigation of the stress-strain field around the cavity that is loaded or partially loaded at the inner surface by the rotationally symmetric loading. The cavity of the spherical, cylindrical or elliptical shape is situated in a stressed elastic continuum, subjected to the gravitation field. As the contribution to the similar investigations, the paper introduces the new function of loading in the form of the infinite sine series. Besides, in this paper the solution of stresses around an oblong ellipsoid cavity, has been obtained using appropriate curvilinear elliptical coordinates. This analytical approach avoids the solutions of the same problem that lead to expressions that contain rather complex integrations. Thus the presented solutions provide the applicable and explicit expressions for stresses and strains developed in infinite series with easily determinable coefficients by the use of contemporary mathematical packages. The numerical examples are also included to confirm the convergence of the obtained solutions.

• Korean Journal of Optics and Photonics
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• v.3 no.3
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• pp.155-160
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• 1992

1)iscussed in this paper are the effects of phase modulation on the line spread functions (LSF) and MTFs of ;I binocular objective system. The binocular objective lens is made in Korea. It has rotationally symmetric aberrations. The LSFs and MTFs are measured experimentally. The phase modulation is carried out by applying phase retardation n on the aperture. The area where the phase is not retarded presents a double annular type. The OTF curves of phase modulated aperture are compared with that of unmodulated aperture. The comparison shows that there is the aberration compensation effect in aberration loaded system. Therefore the performance of many optical system can be improved without any loss of light energy by properly modulating the phase on the aperture.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.26 no.1
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• pp.66-73
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• 2017

This study attempted to design lights with Type II distribution suitable for LED street lights based on the regulations of street light distribution developed by the Illuminating Engineering Society of North America (IESNA). The shape of an asymmetric lens, different from that of a rotationally symmetric lens, cannot be generated using a simple mathematical formula. In the first trial, the outline of the lens was fixed and simulated to confirm the distribution type. Following ISENA regulations, some problems that occurred during simulations and repeating was be modified that process is how we detected errors. Through optical research and simulations, a lens conforming to the regulations of Type II very short, Type II short, and Type II medium distributions was developed. A prototype was developed using simulation data and it was subjected to distribution tests. The results show that it can compare with property of Type II distribution.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.847-852
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• 2007

This paper investigates the characteristics of cogging torque and magnetic force of a brushless DC (BLDC) motor due to imperfect magnetization of permanent magnet (PM) numerically and experimentally which results in the magnetically induced vibration. A predicted magnetization pattern of the PM of the BLDC motor, which is derived from the measured surface magnetic flux density along the PM, is applied to the finite element analysis in order to calculate the cogging torque and the unbalanced magnetic force. This research also develops the experimental setup to measure the unbalanced magnetic force as well as the cogging torque. It shows numerically and experimentally that the imperfect magnetization of permanent magnet generates the driving frequencies of cogging torque with integer multiple of slot number in addition to the least common multiple of pole and slot. It also shows that the driving frequencies of unbalanced magnetic force are integer multiple of slot number ${\pm}1$ due to imperfect magnetization of PM even in the rotationally symmetric design.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.585-604
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• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.10a
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• pp.132-135
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• 2000

A process design expert system for rotationally symmetric deep drawing products has been developed The application of the expert system to non-axisymmetric components, however, has not been reported yet. Thus, in this present study, the expert system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first one is a recognition of shape module to recognize non-axisymmetric products. The second one is three dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third one is a blank design module to create an oval-shaped blank with the identical surface area. The forth one is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing with field engineers.

• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.255-262
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• 2000

A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. The application for non-axisymmetric components, however, has not been reported yet. Therefore, this study investigates process sequence design in deep drawing process and constructs an expert system of process planning for non-axisymmetric motor frame products with elliptical shape. The system developed consists of four modules. The first one is recognition of shape module to recognize the products. The second one is a 3-D modeling module to calculate surface area for non-axisymmetric products. The third one is a blank design module that creates an oval-shaped blank with the identical surface area. The forth one is a process planning module based on production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing with field engineers. The constructed system using AutoLISP language under the AutoCAD environment is baled on the knowledge base system which is involved a lot of expert's technology. Results of this system will be provide effective aids to the designer and engineer in this field.