• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1331-1343
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• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

• The KSFM Journal of Fluid Machinery
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• v.11 no.2
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• pp.38-45
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• 2008

This study presents a numerical procedure to optimize the compressor design to increase the surge margin of compressor with response surface method (RSM). The Box-Behnken design method is used to reduce the number of calculation for fitting the second-order response surface. In order to consider the increase of surge margin during numerical optimization without any calculation at the surge point, the slope of compressor characteristic curve at the design point is suggested as an objective function in the present optimization problem. Mean line performance analysis method is used to get the design and off-design characteristic curves of centrifugal compressor. The impeller exit angle, impeller exit height and impeller radius are chosen as design variables. The optimum shapes show the increase of surge margin for the surge margin optimization and increase of efficiency for the efficiency optimization in comparison with an initial shape.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.8
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• pp.1037-1045
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• 2001

The effect of hysteresis in saturated pool boiling of water from stainless-steel surfaces has been investigated experimentally. Several sets of test sections of different surface conditions, geometries, orientations, diameters, lengths, and water types were tested at atmospheric pressure. The experimental results show that hysteresis effects in pool boiling heat transfer are not significant, but some appreciable trends are observed in accordance with parameters change. At higher heat flux regions, the curve for heat flux decrease is shifted to the left side of the curve for heat flux increase. To clarify hysteresis in pool boiling and to give some improvement on published correlations, four empirical correlations are obtained in terms of tube diameter, surface roughness, and tube wall superheat.

• Journal of KSNVE
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• v.7 no.2
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• pp.215-222
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• 1997

The flow and acoustic fields due to a vortex ring interaction with a rigid sphere are simulated numerically. The flow field is regarded as three-dimensional inviscid and incompressible. The vorticity is assumed to be concentrated inside the finite core of vortex filament. The vortex filament curve, described by parabolic blending curve function, is used to effectively solve the modified Biot-Savart equation. The interaction between a vortex ring and a rigid sphere using the parabolic blending curve is calculated. The trajectory of the vortex ring is obtained with several different initial positions between the ring and the sphere. The force variations acting on the sphere are calculated by using the boundary integral method. Finally, we can also obtain the acoustic signals at the far field observation positions from the force variations acting on the rigid surface. We can find that the dipole axis of the directivity patterns are rotated during the interacting phenomena.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.1
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• pp.28-35
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• 1983

Quantitative analysis have been carried out on the micro-cracks on the surface and into the depth of unnotched smooth mild steel specimen under cyclic stains by rotating bending fatigue tests. Some of the results are; (1) Cracks initiate at the early stage of fatigue life N$_{I}$/ N$_{f}$=10 to 20%, and propagate during the rest of fatigue life. (2) Coalescence of highly crowded small fatigue cracks of random distribution seems to induce the final fracture at higher stress level. (3) The curves of crack initiation and the equal crack length on the graph of stress versus number of cycles are parallel to the S-N curve. (3) The curves of crack initiation and the equal crack length on the graph of stress versus number of cycles are parallel to the S-N curve. (4) The distributions of micro-surface crack length and depth show the composite Weibull distributions which are approximated to two straight lines separated by the value of transient region between stage I and stage II crack.k.k.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.509-531
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• 2022

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.3
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• pp.448-457
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• 2002

Heat treatment such as quenching of a high-temperature cylinder is being used on steel to produce high strength levels. Especially, the mist cooling with the high and uniform surface heat flux rate s expected to contribute for better products. The experimental mist cooling curve is produced for better understanding, and two distinct heat transfer regions are recognized from the cooling curve produced. It is shown that the liquid film evaporation dominated region follows the film boiling-dominated region as decreasing the temperature of test cylinder by mist flow. Based on the intuitive view from some previous investigations, a simplified model with some assumptions is introduced to explain the mist cooling curve, and it is shown that the estimation agrees well with our experimental data. In the meanwhile, it is known that the wetting temperature, at which surface heat flux rate is a maximum, increases with mass flow rate ratio of water to air ($\varkappa$ < 10). However, based on our experimental data, it is explained that there exists a critical mass flow rate ratio, at which the wetting temperature is maximum, in the range of 3 < $\varkappa$ < 130. Also, it is described that despite of the same value of $\varkappa$, the wetting temperature may increase with mist velocity.

• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.269-279
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• 2002

Geometric shape morphing is an interesting geometric operation that interpolates two geometric shapes to generate in-betweens. It is well known that Minkowski operations can be used to test and build collision-free motion paths and to modify shapes in digital image processing. In this paper, we present a new geometric modeling technique to control the morphing on geometric shapes based on Minkowski sum. The basic idea develops from the linear interpolation on two geometric shapes where the traditional algebraic sum is replaced by Minkowski sum. We extend this scheme into a Bezier-like control structure with multiple control shapes, which enables the interactive control over the intermediate shapes during the morphing sequence as in the traditional CAGD curve/surface editing. Moreover, we apply the theory of blossoming to our control structure, whereby our control structure becomes even more flexible and general. In this paper, we present mathematical models of control structure, their properties, and computational issues with examples.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1145-1150
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• 2005

The aim of this paper is to investigate the effect of surface texturing on metal surface and to understand the potential of friction reduction through micro-scale dimple to fabricate by photolithography on pin-on-disk test using flat-on-flat contact geometry. It was verify that the friction property with respect to the same pitch has been influence on the size of dimple under lubricated sliding contact. Also, we can recognize from Stribeck curve that the friction property has a connection with the size of dimple. It can explain a relationship between the friction coefficient and a dimensionless parameter for lubrication condition. The friction property has been an effect on the size of surface texture on reduction friction, not only because the density of dimple, but also because the ratio of diameter/pitch. This ratio of approximately 0.5 is recommend under the tested friction condition. It suggested that the ratio of d/p is an important parameter for surface texture design.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.325-330
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• 2004

Recently, the request for the high strength of material is more and more increased in the area of industrial environment and machinery. To accomplish the high strength of materials, carbonizing treatment, nitrifying treatment, shot-peening method are representatively applied, however, shot-peening method is generally used among the surface processes. Shot peening is a cold working process used to impact Compressive residual stressed in the exposed surface layers. Benefits due to shot peening are increase in resistance to fatigue, stress corrosion cracking, fretting, galling, erosion and closing of pores. In this study, the influence of shot peening on the corrosion was investigated on spring steel immersed in 3.5% NaCl. The immersion test as performed on the two kinds of specimens. Corrsion potential, polarization curve, residual stress and etc, were investigated from experiment results. From test result the effect of shot peening on the corrosion was evaluated. The important results of the experimental study on the effects of shot peened on the environment corrosion of spring steels are as follows; In case of corrosion potential, shot peened specimen shows more activated negative direction as compared with parent mental. Surface of specimen, which is treated with the shot peened is placed as more activated state against inner base metal. It can cause t도 anti-corrosion effect on the base metal.