• Journal of the Korean Society for Railway
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• v.13 no.5
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• pp.509-515
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• 2010

Primary function of a transition curve is to accomplish gradual transition from the straight to circular curve, so that curvature changes from zero to a finite value. The transition curve enhances the running safety and ride comfort of the vehicle in curve. There are a couple of transition curve such as clothoid, cubic parabola and cosinusoidal curve, etc. In this study, running behaviors of cubic parabola and cosinusoidal curve were investigated and compared by numerical analysis result using VAMPIRE program. Ride comforts for an individual transition curve were evaluated for each transition curve and running behavior and safety were also evaluated to compare the capacity of transition curves.

• Journal of Korean Ophthalmic Optics Society
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• v.12 no.4
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• pp.83-86
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• 2007

In this study, a program has been developed to enable a simulation of spherical aberration - originated from a spherical surface and an aspheric surface - via ray tracing and calculation of the degree of spherical aberration. This process has been verified for the variation of spherical aberration generated from ray tracing for aspheric surfaces such as an oval, a parabola, and a hyperbola. By comparing it with the spherical surface, the principle and necessity of the aspheric surface lens design have been understood. In addition, it allows confirming the accuracy of the simulation by developing a ray tracing program in relation to the mirror plane of a parabola.

• Computers and Concrete
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• v.31 no.2
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• pp.163-171
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• 2023

Face gear transmission is widely used in aerospace shunt-confluence transmission system. Tooth wear is one of the main factors affecting its bearing transmission performance. Furthermore, the installation errors of face gear are inevitable. In order to study the wear mechanism of face gear tooth surface with installation errors, based on tooth contact analysis numerical method and Archard wear theory, the UMESHMOTION subroutine in ABAQUS is developed.Combining with Arbitrary Lagrangian-Eulerian adaptive mesh technology, the finite element mesh wear model of abraded face gear pair is established.The preprocessing conditions are set to generate the inp files.Then,the inp files for each corner are imported and batch processed in ABAQUS.The loading tooth contact problem at each rotation angle is solved and the load distribution coefficient among gear tooth, tooth root bending stress, tooth surface contact stress and loaded transmission error are obtained. Results show that the tooth root wear is the most serious and the wear at the pitch cone is close to 0.The wear law of tooth surface along tooth width direction is convex parabola and the wear law along tooth height direction is concave parabola.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.483-495
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• 2023

In his book "Exercitationum Mathematicalarum," a 17th-century mathematician van Schooten proposed linkages for drawing parabola, ellipse, and hyperbola. The linkages proposed by van Schooten can be used in action-based mathematics education and as a material for using mathematical history in school mathematics. In particular, students are not provided with the opportunity to learn by manipulating the quadratic curves in the high school curriculum, so van Schooten's linkages can be used for school mathematics. To this end, a method of implementing van Schooten's linkage in a dynamic geometry environment was presented, and proved that the traces of the figure drawn using van Schooten's linkage were parabola, ellipse, and hyperbola.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.10
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• pp.1259-1268
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• 1995

This note presents the robust root clustering problem of interval systems whose characteristic equation might be given as either a family of interval polynomials or a family of polytopes. Corresponding to damping ratio and robustness margin approximately, we consider a certain class of D-region such as parabola, left-hyperbola, and ellipse in complex plane. Then a simpler D-stability criteria using rational function mapping is presented and prove. Without .lambda. or .omega. sweeping calculation, the absolute criteria for robust D-stability can be determined.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.12
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• pp.36-47
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• 1995

The main purpose of this paper is to determine a new focal point and field distribution due to the shape deformation of reflector antenna by numerical method such as geometrical optics and the aperture field method. It is shown the 4 types deformations to be added into original shape of parabola antenna and offset antenna: linear, quadratic, cubic and hybrid distortion. These results can be applied to deformed reflector antenna in order to fit a focal point and radiation pattern.

• Journal of the Korean Statistical Society
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• v.15 no.1
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• pp.71-78
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• 1986

In this paper, multivariate discrete distribution is dealt with, where a set of r distinct counts are misreported as another set of r counts. First, the variance for the one variable marginal case is expressed in the form of an inverted parabola. Next, for the multivariate negative binomial case, elements of the covariance matrix are evaluated with reference to asymptotic distributions. Finally, for the same case of multivariate negative binomial, Bayesian estimates of the parameters and of the modification rates are provided.

• Journal of the Korea Concrete Institute
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• v.24 no.1
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• pp.15-23
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• 2012

This paper is about proposal of a calculation method and development of an analytical program for predicting crack width and deflection in structural concrete members. The proposed method numerically calculate stresses in steel rebar using a parabola-rectangle stress-strain curve and a modified tension stiffening factor considering the effect of the cover thickness. Based on the study results, a calculation method to predict crack width and deflection in reinforced concrete flexural members is proposed utilizing effective tension area and idealized tension chord as well as effective moment-curvature relationship considering tension stiffening effect. The calculation method was applied to the test specimens available in literatures. The study results showed that the crack width and deflections predicted by the proposed method were closed to the experimentally measured data compared the current design code provisions.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.3
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• pp.279-288
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• 2012

The material removal mechanism in machining is significantly affected by the cutting edge geometry. Its effect becomes even more substantial when the depth of cut is relatively small as compared to the characteristic length which represents the shape and size of the cutting edge. Conventionally, radius or focal length has been employed as the characteristic length with the assumption that the shape of cutting edge is round or parabolic. However, in reality, there could be various ways to determine the radius or focal length even for the same tool edge profile, depending on the region to be considered as cutting edge in the measured profile and the constraints to be set in constructing the best fitted circle or parabola. In this regard, the present study proposes various models to determine the characteristic length in terms of radius or focal length. Their physical compatibility are validated by carrying out 2D orthogonal cutting experiments using inserts with a wide range of characteristic length ($30{\sim}180\;{\mu}m$ in terms of radius) and then by investigating the correlation between the characteristic length and the cutting forces. Such validation is based on the common belief that the larger the characteristic length is, the blunter the cutting edge is and the higher the cutting forces are. Interestingly, the results showed that the correlation is higher for the radius or focal length obtained with a constraint that the center of best fitted circle or the focus of the best fitted parabola should be on the bisectional line of the wedge angle of tool.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.11A
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• pp.1078-1084
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• 2010

The tracking performance of a big parabola tracking antenna system for tracking and receiving of the signal from the vehicle is impacted by many factors of the internal and the external of the system. In this paper, we analyze the tracking error due to the radio refraction in the application of the tracking and positioning of the vehicle by using radio frequency. The real measurement data are used for the analysis which had been acquired by using GPS and the tracking systems of C- and S-band frequencies in NARO Space centre. To verify the correlation between the tracking errors measured and the radio refraction, we review the error factors and the accuracies of the tracking systems, and the characteristics of the refractivity. The analysis shows that there are angular errors which are due to the radio refraction and not to be neglected, compared to the accuracies of the tracking systems, in case of low elevation angle less than 10 degrees. Also, the tracking errors depend on the target altitude as well as the elevation angle for the case of the target in the troposphere. It is recommended to correct the tracking angle considering the target altitude and elevation angle for the precise target positioning.