Exploring Benefits of Using Blending Splines as Transition Curves

Brustad, Tanita Fossli; Dalmo, Rune

doi:10.3390/app10124226

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…Based on this law, the coordinates of the points of the simulated curve are calculated. This is the difference between the proposed approach and those approaches reported in [1][2][3][4][5][6][7][8][9][10][11][12][13][14] that consider the construction of a railroad track's curvilinear sections. In those papers, a curve is constructed, and then the distribution of the curvature and its derivative are determined.…”

Section: Discussion Of Results Of Studying the Geometric Modeling Of ...mentioning

confidence: 99%

“…It should be noted that the author of the cited work adheres to the traditional approach to form a curvilinear section of the track. To simulate transition curves, work [12] employs the smoothing B-splines, which have certain advantages, in terms of smoothness, at the final points of the curvilinear sections of the track over the clothoid curves. However, in the cited work, B-splines are adapted to a smooth transition between two circular curves of an actual section of the railroad track.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

Borisenko

Ustenko

2022

EEJET

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This paper proposes an approach to arranging curvilinear sections of the railroad track, which involves the replacement of two transitional ones and a circular curve with one curvilinear section. Modeling this section implies the construction of a curve in the plan and profile, the joint consideration of which forms the spatial appearance of the curve, which ensures a smooth transition between the rectilinear rails. The need for such transitions is due to the terrain, the need to bypass settlements, and the presence of geological, geographical, and other obstacles that occur when laying railroads. A curvilinear section is modeled in the plan using a curve that is represented in natural parameterization under the law of curvature distribution in the form of a fifth-power polynomial. At the same time, at the start and end points of the section, the curvature and its derivative accept zero values. The outer rail elevation retraction (modeling in the profile) is performed using the curve built, whose sections are also represented in natural parameterization with the dependences of the curvature distribution on the arc length in the form of fourth-power polynomials. At the docking point of the sections, the third order of smoothness is ensured, which implies the equality of values of the functions, their derivatives, the curvature, and a derivative of the curvature from the length of its natural arc. Measures have been proposed to ensure the predefined track gauge retraction. The application of the proposed approach to model a railroad track along the curvilinear section with a variable-radius curve could make it possible to achieve a favorable curvature distribution, a smooth elevation retraction of the outer rail and the track gauge. That would consequently improve the safety of rolling stock running along the curvilinear section of the track, reduce the lateral and vertical efforts that predetermine the wear of rails and wheelsets.

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Section: Discussion Of Results Of Studying the Geometric Modeling Of ...mentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

Borisenko

Ustenko

2022

EEJET

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“…However, a linear curvature is not a sufficient parameter to provide all the requirements of high-speed train traffic. The main results presented in the article [4] are related to the use of new types of transition curves, which turned out to be smoother than clothoide. The proposed method allows to improve the geometry of the existing railways without the need to introduce significant changes in the restructuring of the railway track.…”

Section: Introductionmentioning

confidence: 99%

Determination of the type and the length for the transition curves on the directions of high-speed train operation

Kurhan

Hmelevska

2022

Acta Tech. Jaurinensis

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In many countries around the world, a cubic parabola is used as transition curves in a simplified form. Today, the properties of many mathematical curves are well studied, which can be used as transition curves. The object of research is the process of restructuring transition curves when organizing high-speed trains operation. The use of modern means of mathematical modelling allows to add a number of dynamic characteristics for evaluation parameters of motion in the curved sections of the tracks. Thus, with an increase in speed for transition curves, both the values of unbalanced acceleration and its change in time, and also the velocity attenuation of oscillations of rolling stock when moving from a transition curve to a circular curve or to a direct section. On the basis of the conducted research, it has been found that when increasing the speed of the vehicle movement in the range from 120 to 200 km/h, the length of the stabilization section increases at the output of the curvature by an average of 20 m for every 40 km/h. The analysis showed that with correctly set parameters of transition curves, which correspond to the maximum speed of movement and radius of a circular curve, the strength and reliability of the bearing elements in the structure of the permanent way and the travel comfort are fully ensured.

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Simpson kuralının farklı geçiş eğrilerinde kullanılması

2022

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Modern karayolu ve demiryolu ulaştırma yapılarında geçiş eğrileri, doğru ve daire kadar önemli olan güzergâh öğeleridir. Merkezkaç kuvvetinin aniden değişmesini önlemek için, hareketin keskin bir eğri üzerindeki etkisinden dolayı geçiş eğrisi uygulanması gerekmektedir. Yıllar içinde, geçiş eğrisi olarak klotoid uygulanması dünyanın birçok ülkesinde yaygınlaşmıştır. Ancak klotoid uygulamasının yüksek hızlarda yolun güvenliğinde ve konforunda sorunlara sebep olması nedeniyle farklı geçiş eğrilerine ihtiyaç duyulmuştur. Bu kapsamda; yüksek hızdaki araçlar için klotoidin oluşturduğu yol dinamikleri ile ilgili sorunları gidermek amacıyla sinüsoid ve dördüncü dereceden parabol geçiş eğrileri kullanılmıştır. Klotoidin basit matematiksel çözümlemesine karşılık, sinüsoid ve dördüncü dereceden parabol geçiş eğrilerinin koordinatlarının hesaplanması, karmaşık matematiksel çözümler içermektedir. Bu çalışmada klotoid, sinüsoid ve dördüncü dereceden parabolün temel matematiksel özellikleri sunularak, herhangi bir bilgisayar yazılımı kullanmaksızın, Simpson kuralı kullanılarak ile sinüsoid ve dördüncü dereceden parabol geçiş eğrilerinin koordinatlarının sayısal integrasyon ile sinüsoid ve dördüncü dereceden parabol geçiş eğrilerinin koordinatlarının proje amacına uygun hassasiyet ile hesaplandığı gösterilmiştir.

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Exploring Benefits of Using Blending Splines as Transition Curves

Cited by 3 publications

References 21 publications

Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

Determination of the type and the length for the transition curves on the directions of high-speed train operation

Simpson kuralının farklı geçiş eğrilerinde kullanılması

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