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Basitleştirilmiş Tekerlek/Ray Temas Modelinin ve Kalker Doğrusal Teorisinin Demiryolu Taşıtı Sinüs Hareketi Kararlılığı Açısından Değerlendirilmesi

Yıl 2021, Sayı: 14, 87 - 98, 31.07.2021
https://doi.org/10.47072/demiryolu.860789

Öz

Bu makalede, demiryolu taşıtlarının dinamik analizinde kullanılabilecek basitleştirilmiş bir tekerlek/ray temas modelinin performansı incelenmiştir. Bu amaçla, makalenin kapsamı iki tekerlek takımına sahip bir boji sistemi ile sınırlı tutulmuştur ve problem demiryolu taşıtının sinüs hareketi kararsızlığı açısından incelenmiştir. Buna göre, elastik olarak birbirine bağlı olan iki tekerlek takımına sahip bir bojinin matematiksel modeli geliştirilmiştir ve önerilen dört serbestlik dereceli matematiksel modelin hareket denklemleri elde edilmiştir. Bu denklemler ilk olarak tekerlek/ray temas arayüzündeki temas kuvvetlerinin basitleştirilmiş bir yaklaşım kullanılarak hesaplanması ile analitik olarak çözülmüştür. Daha sonra, temas kuvvetleri Kalker doğrusal teorisi kullanılarak hesaplanmıştır ve doğrusal olmayan hareket denklemleri sayısal olarak çözülmüştür. Analitik ve sayısal olarak elde edilen sonuçlar karşılaştırıldığında çözümlerin iyi bir şekilde eşleştiği görülmüştür. Bu nedenle, basitleştirilmiş tekerlek/ray temas modelleme yaklaşımının, özellikle sistemin sinüs hareketi davranışı açısından kararlı bir durumda olması halinde, sistemin dinamiğini başarılı bir şekilde temsil edebileceği sonucuna varılmıştır. Daha sonra, doğrusal hareket denklemlerinden elde edilen özdeğer problemi ile sistemin karmaşık özdeğerleri, bojinin operasyonel hız aralığı üzerinde hesaplanmıştır. Sistemin doğal frekanslarının hıza bağlı olduğu ve tekerlek takımlarından birinin veya her ikisinin belirli parametre setlerinde dinamik olarak kararsız hale gelebileceği gözlenmiştir. Son olarak, farklı parametreler için kararlılık haritaları üretilmiştir ve sistem parametrelerinin iki tekerlek takımına sahip bojinin dinamik kararlılığı üzerindeki etkileri daha iyi anlaşılmıştır.

Kaynakça

  • [1] G. Stephenson, “Observations on edge and tram railways,” 1821.
  • [2] A. H. Wickens, “The dynamics of railway vehicles on straight track: Fundamental considerations of lateral stability,” Proc. Inst. Mech. Eng., vol. 180, no. 6, pp. 29-44, 1965.
  • [3] A. H. Wickens, “The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels,” Int. J. Solids Struct., vol. 1, no. 3, pp. 319-341, 1965.
  • [4] S. Y. Lee and Y. C. Cheng, “Hunting stability analysis of high-speed railway vehicle trucks on tangent tracks,” J. Sound Vib., vol. 282, no. 3, pp. 881-898, 2005.
  • [5] S. Y. Lee and Y. C. Cheng, “A new dynamic model of high-speed railway vehicle moving on curved tracks,” J. Vib. Acoust., vol. 130, no. 1, 2008.
  • [6] Y. C. Cheng, S. Y. Lee and H. H. Chen, “Modeling and nonlinear hunting stability analysis of high-speed railway vehicle moving on curved tracks,” J. Sound. Vib., vol. 324, no. 1-2, pp. 139-160, 2009.
  • [7] A. A. Shabana, M. Tobaa and K. E. Zaazaa, “Effect of the wheel geometric design on the nonlinear dynamics of railroad vehicles,” J. Mech. Des., vol. 128, no. 5, pp. 1130-1140, 2006.
  • [8] P. Kim, J. Jung and J. Seok, “A parametric dynamic study on hunting stability of full dual-bogie railway vehicle,” Int. J. Precis. Eng. Manuf., vol. 12, no. 3, pp. 505-519, 2011.
  • [9] M. Taheri and M. Ahmedian, “Investigation of parameters influencing hunting performance of a railway vehicle with three-piece trucks,” in 2015 Joint Rail Conference, San Jose, California, USA, 2015.
  • [10] J. H. Park, H. I. Koh and N. P. Kim, “Parametric study of lateral stability for a railway vehicle,” J. Mech. Sci. Technol., vol. 25, no. 7, pp. 1657-1666, 2011.
  • [11] Y. Nath and K. Jayadev, “Influence of yaw stiffness on the nonlinear dynamics of railway wheelset,” Commun. Nonlinear Sci. Numer. Simul., vol. 10, no. 2, pp. 179-190, 2005.
  • [12] S. Z. Meymand, A. Keylin, M. Ahmadian, “A survey of wheel–rail contact models for rail vehicles,” Vehicle System Dynamics, vol. 54, no. 3, pp. 386-428, 2016.
  • [13] J. J. Kalker, “Wheel-rail rolling contact theory,” Wear, vol. 144, no. 1-2, pp. 243-261, 1991.
  • [14] J. J. Kalker, Rolling Contact Phenomena. Vienna: Springer, 2000.
  • [15] J. J. Kalker, “Simplified theory of rolling contact,” Delft Progress Rep., Delft Univ. Press, pp. 1- 10, 1973.
  • [16] J. J. Kalker, Three-dimensional elastic bodies in rolling contact. Kluwer Academic Publishers, Dordrech, 1990.
  • [17] H. Hertz, “Über die Berührung fester elastischer Körper,” Journal für die Reine und Angewandte Mathematik, vol. 92, pp. 156-171, 1882.
  • [18] A. A. Shabana, M. Berzeri and J. R. Sany, “Numerical procedure for the simulation of wheel/rail contact dynamics,” J. Dyn. Syst. Meas. Contr., vol. 123, no. 2, pp. 168-178, 2001.
  • [19] J. Klingel, “Über den Lauf der Eisenbahnwagen auf gerader Bahn,” Organ für die Fortschritte des Eisenbahnwessens, vol. 20, no. 4, pp.113-123, 1883.
  • [20] A. M. Whitman, “On the lateral stability of a flexible truck,” J. Dyn. Syst. Meas. Contr., vol. 105, no. 2, pp. 120-125, 1983.

Assessment of a Simplified Wheel/Rail Contact Model and Kalker’s Linear Theory from the Perspective of Hunting Instability

Yıl 2021, Sayı: 14, 87 - 98, 31.07.2021
https://doi.org/10.47072/demiryolu.860789

Öz

This paper investigates the performance of a simplified wheel/rail contact modeling approach that can be implemented to dynamics analysis of railway vehicles. The scope is limited to a two-axle bogie system and the problem is investigated from the hunting instability perspective. Accordingly, a mathematical model of a two-axle bogie with elastically connected wheelsets is developed. The governing equations of the proposed four degree of freedom mathematical model are obtained. These equations are then first solved analytically by considering a simplified approach for the interfacial forces at the wheel/rail contact interface. Second, the contact forces are calculated by using Kalker’s linear theory, and the corresponding nonlinear governing equations are solved numerically. Based on the results, it is observed that the analytical and numerical solutions show a good match. Hence, it is concluded that the simplified wheel/rail contact modeling approach can represent the dynamics of the system successfully, especially when the system is in a stable state for hunting behavior. Third, the corresponding eigenvalue problem is formulated from the linear equations, and complex eigenvalues are calculated over the operational speed range of the bogie. It is observed that the natural frequencies of the system are speed-dependent, and either one or both of the wheelsets may become unstable at certain parameter sets. Finally, stability maps are generated for several parameters, and a better understanding of the effects of system parameters on the stability of two-axle bogie is obtained.

Kaynakça

  • [1] G. Stephenson, “Observations on edge and tram railways,” 1821.
  • [2] A. H. Wickens, “The dynamics of railway vehicles on straight track: Fundamental considerations of lateral stability,” Proc. Inst. Mech. Eng., vol. 180, no. 6, pp. 29-44, 1965.
  • [3] A. H. Wickens, “The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels,” Int. J. Solids Struct., vol. 1, no. 3, pp. 319-341, 1965.
  • [4] S. Y. Lee and Y. C. Cheng, “Hunting stability analysis of high-speed railway vehicle trucks on tangent tracks,” J. Sound Vib., vol. 282, no. 3, pp. 881-898, 2005.
  • [5] S. Y. Lee and Y. C. Cheng, “A new dynamic model of high-speed railway vehicle moving on curved tracks,” J. Vib. Acoust., vol. 130, no. 1, 2008.
  • [6] Y. C. Cheng, S. Y. Lee and H. H. Chen, “Modeling and nonlinear hunting stability analysis of high-speed railway vehicle moving on curved tracks,” J. Sound. Vib., vol. 324, no. 1-2, pp. 139-160, 2009.
  • [7] A. A. Shabana, M. Tobaa and K. E. Zaazaa, “Effect of the wheel geometric design on the nonlinear dynamics of railroad vehicles,” J. Mech. Des., vol. 128, no. 5, pp. 1130-1140, 2006.
  • [8] P. Kim, J. Jung and J. Seok, “A parametric dynamic study on hunting stability of full dual-bogie railway vehicle,” Int. J. Precis. Eng. Manuf., vol. 12, no. 3, pp. 505-519, 2011.
  • [9] M. Taheri and M. Ahmedian, “Investigation of parameters influencing hunting performance of a railway vehicle with three-piece trucks,” in 2015 Joint Rail Conference, San Jose, California, USA, 2015.
  • [10] J. H. Park, H. I. Koh and N. P. Kim, “Parametric study of lateral stability for a railway vehicle,” J. Mech. Sci. Technol., vol. 25, no. 7, pp. 1657-1666, 2011.
  • [11] Y. Nath and K. Jayadev, “Influence of yaw stiffness on the nonlinear dynamics of railway wheelset,” Commun. Nonlinear Sci. Numer. Simul., vol. 10, no. 2, pp. 179-190, 2005.
  • [12] S. Z. Meymand, A. Keylin, M. Ahmadian, “A survey of wheel–rail contact models for rail vehicles,” Vehicle System Dynamics, vol. 54, no. 3, pp. 386-428, 2016.
  • [13] J. J. Kalker, “Wheel-rail rolling contact theory,” Wear, vol. 144, no. 1-2, pp. 243-261, 1991.
  • [14] J. J. Kalker, Rolling Contact Phenomena. Vienna: Springer, 2000.
  • [15] J. J. Kalker, “Simplified theory of rolling contact,” Delft Progress Rep., Delft Univ. Press, pp. 1- 10, 1973.
  • [16] J. J. Kalker, Three-dimensional elastic bodies in rolling contact. Kluwer Academic Publishers, Dordrech, 1990.
  • [17] H. Hertz, “Über die Berührung fester elastischer Körper,” Journal für die Reine und Angewandte Mathematik, vol. 92, pp. 156-171, 1882.
  • [18] A. A. Shabana, M. Berzeri and J. R. Sany, “Numerical procedure for the simulation of wheel/rail contact dynamics,” J. Dyn. Syst. Meas. Contr., vol. 123, no. 2, pp. 168-178, 2001.
  • [19] J. Klingel, “Über den Lauf der Eisenbahnwagen auf gerader Bahn,” Organ für die Fortschritte des Eisenbahnwessens, vol. 20, no. 4, pp.113-123, 1883.
  • [20] A. M. Whitman, “On the lateral stability of a flexible truck,” J. Dyn. Syst. Meas. Contr., vol. 105, no. 2, pp. 120-125, 1983.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Makine Mühendisliği
Bölüm Bilimsel Yayınlar (Hakemli Araştırma ve Derleme Makaleler)
Yazarlar

Osman Taha Şen 0000-0002-8604-3962

Yayımlanma Tarihi 31 Temmuz 2021
Gönderilme Tarihi 14 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Sayı: 14

Kaynak Göster

IEEE O. T. Şen, “Assessment of a Simplified Wheel/Rail Contact Model and Kalker’s Linear Theory from the Perspective of Hunting Instability”, Demiryolu Mühendisliği, sy. 14, ss. 87–98, Temmuz 2021, doi: 10.47072/demiryolu.860789.