• Journal of the Korean Society for Precision Engineering
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• v.32 no.3
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• pp.243-251
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• 2015

In order to develop an automatic system for welding thin steel plates with curvature such as the corrugated membranes of an LNG storage tank, a rotating mechanism should be firstly designed for the torch to easily follow the weld seam with a constant distance and angle. In this study, a torch rotating mechanism consisting of three circular links, two square-type links and a torch link was proposed for automation of the welding process. A weld-seam tracking system with two axis slides and the proposed rotating mechanism was successfully simulated with a dynamic simulation software. A prototype tracking system was manufactured and a tracking test with the system was then carried out. The test results with tracking system showed that the rotating mechanism could be implemented and it was feasible to be used in automatic tracking of weld seam with curvature.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.107-114
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• 2007

In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1998.03a
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• pp.250-253
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• 1998

The kinematically admissible velocity field is developed for the shapes of dead metal zone and the curving velocity distribution in the eccentric plane dies extrusion. The shape of dead metal zone is defined as the boundary surface with the maximum friction constant between the deformable zone and the rigid zone. The curving phenomenon in the eccentric plane dies is caused by the eccentricity of plane dies. The axial velocity distribution in the plane dies is divided in to the uniform velocity and the deviated velocity. The deviated velocity is linearly changed with the distance from the center of cross-section of the workpiece. The results show that the curvature of products and the shapes of the dead metal zone are determined by the minimization of the plastic work and that the curvature of the extruded products increases with the eccentricity.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.49-52
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• 1997

The kinematically admissible velocity field is developed for the analysis of the curving of an eccentric extrusion. The curving of product in extrusion is caused by the difference of the linearly distributed longitudinal velocity on the cross-section of the workpiece at the dies exit. The result of the analysis show that the curvature of product increases with the increase in eccentricity of gravity center of the cross-section of the workpiece at the die entrance from that of the cross-section at the die exit. It also increase with the die land dimension. By the DEFORMTM-3D analysis, the curving of T-shaped product in extrusion is changed by the eccentricity, die land length and the friction constant. The result of the analysis by DEFORMTM-3D software shows that the curvature of circular shaped product increases with the eccentricity. The two analysis and one experiment show the curving phenomenon in eccentric extrusion process.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.5 s.170
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• pp.55-62
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• 2005

This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.471-479
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• 2015

In this paper, we prove that any stable f-harmonic map ${\psi}$ from ${\mathbb{S}}^2$ to N is a holomorphic or anti-holomorphic map, where N is a $K{\ddot{a}}hlerian$ manifold with non-positive holomorphic bisectional curvature and f is a smooth positive function on the sphere ${\mathbb{S}}^2$with Hess $f{\leq}0$. We also prove that any stable f-harmonic map ${\psi}$ from sphere ${\mathbb{S}}^n$ (n > 2) to Riemannian manifold N is constant.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1407-1419
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• 2021

The Iwasawa decomposition NAK of the Lie group G = SO₀(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.163-174
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• 2019

The object of this paper is to classify paracontact metric ($k,{\mu}$)-spaces satisfying certain curvature conditions. We show that a paracontact metric ($k,{\mu}$)-space is Ricci semisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric ($k,{\mu}$)-space is ${\phi}$-Ricci symmetric if and only if the metric is Einstein, provided $k{\neq}0$, -1. Moreover, we show that in a paracontact metric ($k,{\mu}$)-space with k < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.237-248
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• 2024

In this manuscript, the hypersurfaces of non-flat Riemannian 4-space forms are considered. A hypersurface of a 4-dimensional Riemannian space form defined by an isometric immersion 𝐱 : M³ → 𝕄⁴(c) is said to be biconservative if it satisfies the equation (∆²𝐱 )^⊤ = 0, where ∆ is the Laplace operator on M³ and ⊤ stands for the tangent component of vectors. We study an extended version of biconservativity condition on the hypersurfaces of the Riemannian standard 4-space forms. The C-biconservativity condition is obtained by substituting the Cheng-Yau operator C instead of ∆. We prove that C-biconservative hypersurfaces of Riemannian 4-space forms (with some additional conditions) have constant scalar curvature.

• Journal of the Korean Chemical Society
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• v.16 no.6
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• pp.341-348
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• 1972

The significance of the curvature dependency correction of surface tension is studied in calculating the pore volume distribution of porous adsorbent from nitrogen adsorption isotherm. That is, Kelvin radii are calculated with curvature dependent surface tension values calculated by Chang et al, and then with these Kelvin radii, pore volume distributions of three porous adsorbents, silica alumina (steam deactivated), silica gel (Davidson 59), and silica gel (Mallinc-krodt Standard Luminescent), are calculated. The results are compared with those obtained by the previous method in which surface tension is taken as constant and also with the others. obtained by the modelless method proposed by Brunauer et al. The maximum point of the distribution curve shift to the larger pore radius, when the curvature dependency is considered. Furthermore, the relative pressure at which capillary condensation commences is by far the lower than that accepted previously. This effect becomes significant as the pore radius approaches to the micropore range.