• Honam Mathematical Journal
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• v.45 no.4
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• pp.585-597
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• 2023

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼⁵. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼⁵.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.521-522
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• 2010

• Journal of Drive and Control
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• v.13 no.4
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• pp.59-67
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• 2016

This paper proposes a model-prediction-based collision-avoidance algorithm for excavators for which the recursive-least-squares (RLS) estimation of the excavator's rotational inertia is used. To estimate the rotational inertia of the excavator, the RLS estimation with multiple forgetting and two updating rules for the nominal parameter and the forgetting factors was conducted based on the excavator-swing dynamics. The average value of the estimated rotational inertia that is for the minimizing effects of the estimation error was computed using the recursive-average method with forgetting. Based on the swing dynamics, the computed average of the rotational inertia, the damping coefficient for braking, and the excavator's braking angle were predicted, and the predicted braking angle was compared with the detected-object angle for a safety evaluation. The safety level defined in this study consists of the three levels safe, warning, and emergency braking. The analytical rotational-inertia-based performance evaluation of the designed estimation algorithm was conducted using a typical working scenario. The results of the safety evaluation show that the predictive safety-evaluation algorithm of the proposed model can evaluate the safety level of the excavator during its operation.

• Journal of the Korean Ceramic Society
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• v.55 no.3
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• pp.275-284
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• 2018

In the ball milling process of ceramic powders, according to economic considerations for industrial applications, it is very important to quickly determine the optimum process condition with the maximum grinding efficiency. However, it is still difficult to determine the optimum condition for a ball mill with respect to the various process parameters, such as the rotational speed and the milling time. Ball milling was carried out at the same starting conditions with given amounts of alumina powders, balls and water, and was conducted slower or faster or a critical rotational speed was just determined by observing the angular position of the slurry in a semi-translucent polyethylene laboratory container. With respect to the different rotational speeds, which were slower or faster than the critical rotational speed, the particle size distribution of the grained powders and the acoustic intensity caused by cascading of the balls led to various behaviors. From the results of the particle size distribution and the acoustic signal analysis in the ball milling, there was one rotational speed that made the finest milled powder with maximum acoustic intensity. As a result, there was a correlation between the ground particle size and the acoustic intensity, which yields the interpretation that it can be possible in-situ to determine the optimum condition of ball milling by acoustic signal without repeated measurement efforts.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.1
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• pp.1-6
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• 2017

This paper presents development of the nine-node co-rotational(CR) planar element applicable for elastoplastic and contact analysis. The CR formulation is one of the efficient geometrically nonlinear formulations. It is based on the assumptions of small strain and large displacement. Further, it is extended to both elastoplastic analysis and contact analysis in this paper. For accurate plastic analysis, nine-node quadrilateral element, which can provide accurate stress prediction, is chosen. Bi-linear hardening rule based on Newton- Raphson return-mapping is employed. Also, Lagrange multiplier is used in order for constraints regarding the contact analysis. The present development is validated via the time transient problems. The present results are compared with those obtained by the other existing software.

• Archives of Plastic Surgery
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• v.38 no.3
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• pp.279-286
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• 2011

Purpose: Chin is located in a prominent position, and is important to balance and harmony of the face. Genioplasty is widely performed with patients' high satisfaction, yet being relatively simple procedure. Recently in analysis of dentofacial trait, three rotational variables of yaw, pith, and roll are considered with three translational variables (forward/backward, up/down, right/left). And we could correct chin deformity effectively by applying the three rotational variables with three translational variables in genioplasty. Methods: Twenty-eight patients who have chin deformity underwent osseous genioplasty. Preoperative photography, facial three dimensional computed tomography, and cephalography were taken while chin deformities were accessed. The chin deformity was classified into four categories; macrogenia, microgenia, asymmetric chin deformity, and combined chin deformity groups. According to the nature of chin deformities and the patients' desire, preoperative plans were formulated, in consideration of three rotational variables and translational variables. Through intraoral approach, anterior mandible was exposed in the subperiosteal plane between the mental foramens and beneath the mental foramens. In the anterior mandible, vertical and horizontal grid lines with 5 mm intervals were marked to confirm the spatial location of osteomized bone segment after osteotomy. Chin repositioning was done in consideration of axial rotation and planar translation. Results: Most of the patients had achieved satisfactory results with few complications. By considering the three rotational variables, it was possible to make the chin repositioning effectively. One of the patients complained about insufficient chin correction. In other case, persistent sensory impairment around chin was observed. Conclusion: In conclusion, it is worthwhile to apply preoperative analysis and operative procedures in consideration of a three rotational variables with three translational variables in genioplasty.

• Tribology and Lubricants
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• v.33 no.5
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• pp.220-227
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• 2017

In this work, carbon nanotube and nano-size alumina particle are exploited as additive for lubrication experiment. We used pin-on-disk type tribometer to investigate the tribological characteristics of lubricants with respect to additives and rotational speed. We conducted more than 15 trials of tribotests for two hours for each specimen to obtain stable and accurate frictional force and to create measurable wear track on the substrate. We conducted tests at the boundary/mixed lubrication regime to evaluate the influence of additives on the tribological characteristics. We found that the friction coefficient decreased as the rotational speed increased and as additives were added. In particular, the reduction of friction by adding additives was more significant at low rotational speed than at high rotational speed. We speculate that the additives helped to separate and protect the two contacting surfaces at low speed, while the influence of additives was not significant at high speed since sufficiently thick lubricant film was formed. The wear of the substrate was also reduced by adding additives to the lubricant. However, in contrast to friction, the amount of wear at high rotational speed was less when alumina particles were added to the lubricant than the amount of wear at low speed. We speculate that the increased wear at low rotational speed is as a result of the intermittent abrasive wear caused by alumina particles with uneven shape, while the reduced wear at high speed is as a result of sufficient film thickness which prevented the abrasive wear.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.1
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• pp.69-75
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• 2016

In this paper, we propose a inverse synthetic aperture radar(ISAR) rotational motion compensation(RMC) method to remove residual blurring caused by non-uniform rotational motion of a target. First, a range bin having an isolated scatterer is selected. Next, polynomial phase signal in the selected range bin is estimated by using both Fourier transform(FT) and polynomial-phase transform(PPT). Finally, a new slow time variable that uniformly samples radar signal along the aspect angle directions is defined by using the estimated phase signal, and we interpolate radar signal in terms of the new time variable. As a result, rotational motion to blurr ISAR images is removed, and focused ISAR images are obtained. Simulation results using battleship model validate the robustness and effectiveness of our proposed RMC method.

• Publications of The Korean Astronomical Society
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• v.4 no.1
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• pp.31-52
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• 1989

The rotational properties of late-type main sequence stars in the solar neighborhood have been investigated. So rotation periods and stellar radii are determined for 104 field stars, 8 Ursa Major Group stars, and 20 Hyades cluster stars. Most of the rotation periods are derived using the Noyes et al. (1984)'s relation between chromospheric activity and rotation period. Stellar radii are calculated by the Stefan law for the nearby stars within 25 pc from the sun. Rotational velocities at equator are determined by the above rotation periods and stellar radii. Their distribution along the (B-V) color shows an upper boundary and an abrupt drop for the stars in the range of 0.4<(B-V)<0.8, as found from the apparent rotational velocity data. Furthermore, it is apparent that there is an lower boundary of rotational velocity. The inclination of rotation axis to line-of-sight is obtained by comparing the rotational velocity at equator with the apparent rotational velocity given by the analysis of the line profiles. For the field stars, it is found that the inclination has no correlation with the galactic lattitude and follows random distribution.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.477-483
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• 2015

In this paper, Euler-Bernoulli beam theories(EB-beam) are used, and Fast Fourier Transformation(FFT) analysis is then employed to extract their natural frequencies using both analytical approach and Co-rotational plane beam(CR-beam) EDISON program. EB-beam is used to analyze a spring-mass system with a single degree of freedom. Sinusoidal force with various frequencies and constant magnitude are applied to tip of each beam. After the oscillatory tip response is observed in EB-beam, it decreases and finally converges to the so-called 'steady-state.' The decreasing rate of the tip deflection with respect to time is reduced when the forcing frequency is increased. Although the tip deflection is found to be independent of the excitation frequency, it turns out that time to reach the steady state response is dependent on the forcing frequency.