Demiryolları için güncel geçiş eğrileri

Abstract

Günümüz teknolojisinin çok hızlı bir şekilde gelişmesi, ulaştırma sistemleri arasındaki rekabeti oldukça kızıştırmıştır. Artan ticaret hacmine paralel olarak, insanların ve ticari malların dünyanın herhangi bir köşesine en kısa sürede ulaştırılma isteği, seyahat hızlarının artmasına ve dolayısıyla geçki elemanlarından biri olan geçiş eğrileri üzerine araştırmaların yoğunlaşmasına neden olmuştur. Bu çalışmada öncelikle ulaştırma yapılarında yol dinamiği konusunda bilgi verildikten sonra yanal sademe kavramı anlatılmıştır. 3. bölümde geçiş eğrisi olarak Klotoid, Bikuadratik Parabol, Bloss, Cosinüsoid ve Sinusoid ayrıntılı olarak incelenmiştir. İncelemeler aşağıdaki kriterlere göre yapılmıştır. - Bitim noktasının ordinatı - Kurbun yana kayma miktarı - Dever değişimi - Rampa eğimi - Enine ivmenin değişimi - Birleştirme eğrisinin uzunluğu 4. bölümde, yukarıda bahsedilen eğrilerin birbirleri ile karşılaştırmaları yapılıp, üstün ve zayıf yönleri ortaya konmuştur. Sonuç ve öneriler kısmında ise en uygun eğri seçilmiştir.The transition curves are placed in between the route elements with different curvature, to provide a continuous and jerkless passing. The aim of these curves is to decrease the deformations which are formed both on vehicle and on the route structure, and also providing a monoton and jerkless transition which increases the travel confort. The lateral jerk is defined as the change of the resultant acceleration by time along the normal of the curve which is formed by unbalanced forces acting on a mass which moves with sudden speed v along the curved orbit. da _ Y dT (p = Lateral jerk [m/sn3] a = Resultant acceleration formed by unbalanced forces [m/sn2] T = Time [sec] n = Unit vector on the curve normal As the speed increases in the transportation systems, the effect of the lateral forces also increases, and this gives importance on the change of the lateral acceleration by time (lateral jerk) in evaluating the different transition curves. In this research, five of the most known transition curves (i.e. Clothoid, Biquadratic parabol, Bloss, Cosinusoid, Sinusoid) are examined on 6 topics which are as follows: vm - The ordinate of the end point of the curve, - The displacement of the original curve due to the transition curve, - Change of superelevation, - Gradient of the superelevation ramp, - Lateral jerk, - The length of the transition curve. 1- The ordinate of the end point of the curve The ordinates of the end point of the curves are as follows: V6 Clothoid yL = 430. 9R3 Biquadratic Parabol yL - V6 492. 5R3 Bloss yi = V6 478. SR3 Cosinusoid yL 482İ?3 Sinusoid yL = 509. 4R3 As seen in the above formulae, the ordinate of the end point of curve increases with the 6th power of the speed. The value should be minimum in rehabilitation of the existing railways to higher speed, when passing through rough surfaces and where the minimum distance should be kept with existing structures. Among the examined curves, the Sinusoid is the best on this topic. IX 2- The displacement of the original curve due to the transition curve The formulae for the displacement of the original curve due to the transition curve are as follows: Clothoid AR V6 1723. 6R* Biquadratic Parabol AR 3447. 3R3 Bloss M = 2872. 8 R3 Cosinusoid AR = 3033i?3 Sinusoid AR = 4396. li?3 The displacement of the original curve also increases with the 6th power of the speed. This is also important when increasing the speed of the existing railways where there maybe trouble with the existing structures. Considering the formulas above, it is obvious that the Sinusoid gives the best performance. 3- Gradient of the superelevation ramp The gradient of the superelevation ramp is an important topic which has a limitation property at designing stage. Clothoid m 84. 75RL 1 V2 Biquadratic Parabol - = Bloss Cosinusoid Sinusoid m 42. 37 RL 1 V2 m 56.50RL 1 m 53. 95 RL 1 V2 m 42.37 RL Clothoid gives the best perpormance on this topic. 4- Length of the transition curve 4.1- According to the gradient of superelevation ramp From the experiences, The maximum gradient of superelevation is limited with the value l/m= 1/400. By using this value, the required minimum curve lengths are as follows: V2 Clothoid L > 4. 72 - R V2 Biquadratic Parabol L > 9.44 - V2 Bloss £>7.08 - R V2 Cosinusoid L > 7.41 - R V2 Sinusoid L>9A4 - R XI This is important when the length of the curve has to be decreased in some special points, such as entrances and exits to stations or when passing through rough surfaces. As it is seen from the above formulae, the Clothoid is the best among others. 4.2- According to the lateral jerk We must concentrate on two points in evaluating the lateral jerk. The first one is the continuity and the second is the amplitude of the lateral jerk function. As a continuity, the sinusoid forms very smooth curve in lateral jerk function and is the best among the others. According to the amplitude, Clothoid seems to be the curve with the least values, but it has jump points at the beginning and the end point of the curve. So it has to be taken out of consideration. The Bloss and the Cosinusoid shows very similar performances in amplitude, but they are not smooth at the beginning and the end point of the curve. As a conclusion, The Sinusoid is the best in continuity and the Bloss is the best in amplitude of the lateral jerk function.