International Journal of Vehicle Structures and Systems

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Rail Vehicle Modelling and Simulation using Lagrangian Method


Affiliations
1 Mech. Engg. Dept., Maharishi Markandeshwar (Deemed to be University), Mullana, Haryana, India
2 Dept. of Mech. Engg, Amity School of Engg. and Tech., Amity University, Uttar Pradesh, Noida, India
3 Mech. Engg. Dept., AITAM, Tekkali, Andra Pradesh, India
 

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Formulation of vehicle dynamics problem is dealt either with Newton’s method or Lagrange’s method. This paper provides a broad understanding of Lagrange’s method applied to railway vehicle system. The Lagrange’s method of analytical dynamics provides a complete set of equations through differentiations of a function called Lagrangian function which includes kinetic and potential energy with respect to independent generalised coordinates assigned to the system. This paper also discusses rigid body rotational dynamics along with the concept of generalised coordinates (constrained and un-constrained) and generalised forces in detail.

Keywords

Lagrangian Function, Euler’s Angle, Newton’s Method, Generalized Forces, Generalized Coordinates, Body Fixed Axes.
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  • R.C. Sharma and K.K. Goyal. 2017. Improved suspension design of Indian railway general sleeper ICF coach for optimum ride comfort, J. Vibration Engineering & Technologies, 5(6), 547-556.

  • R.C. Sharma. 2011. Ride analysis of an Indian railway coach using Lagrangian dynamics, Int. J. Vehicle Structures & Systems, 3(4), 219-224. http://dx.doi.org/10.4273/ijvss.3.4.02.

  • R.C. Sharma. 2013. Stability and eigenvalue analysis of an Indian railway general sleeper coach using Lagrangian dynamics, Int. J. Vehicle Structures & Systems, 5(1), 9-14. http://dx.doi.org/10.4273/ijvss.5.1.02.

  • R.C. Sharma. 2017. Ride, eigenvalue and stability analysis of three-wheel vehicle using Lagrangian dynamics, Int. J. Vehicle Noise & Vibration, 13(1), 13-25. https://doi.org/10.1504/IJVNV.2017.086021.

  • R.C. Sharma and S. Palli. 2016, Analysis of creep force and its sensitivity on stability and vertical-lateral ride for railway vehicle, Int. J. Vehicle Noise and Vibration, 12(1), 60-76. https://doi.org/10.1504/IJVNV.2016.077474.

  • R.C. Sharma. 2012. Recent advances in railway vehicle dynamics, Int. J. Vehicle Structures & Systems, 4(2), 52-63. http://dx.doi.org/10.4273/ijvss.4.2.04.

  • J.H. Ginsberg 1988, Advanced Engineering Dynamics, Harper and Row, New York.

  • H. Baruh. 1999, Analytical Dynamics, McGraw Hill, New York.

  • C.O. Chang, C.S. Chou, and S.Z. Wang. 1991. Design of a Viscous ring Nutation Damper for a Freely Precessing Body, J. Guid. Control Dyn., 14, 1136–1144.https://doi.org/10.2514/3.20768.

  • W.T. Thompson. 1961. Introduction to Space Dynamics, John Wiley and Sons, New York.

  • Goldstein, Herbert, 1965, Classical Mechanics, Addison-Wesley Publishing Company, New York.

  • D.C. Rapaport. 1985. Molecular dynamics simulation using Quaternions, J. Comput. Phys., 41, 306-314. https://doi.org/10.1016/0021-9991(85)90009-9.

  • Greenwood and T. Donald. 1988, Principles of Dynamics, Prentice Hall, Englewood Cliffs, New Jersey.

  • M. Nitschke and E.H. Knickmeyer. 2000. Rotation parameters-a survey of techniques, J. Surv. Eng., 126, 83-105. https://doi.org/10.1061/(ASCE)0733-9453(2000)126:3(83).

  • M.D. Shuster. 1993. A survey of attitude representations, J. Astronautically Sci., 41, 531-543.

  • K.W. Spring. 1986. Euler parameters and the use of quaternion algebra in the manipulation of finite rotations: A review, Mechanism and Machine Theory, 21, 365-373. https://doi.org/10.1016/0094-114X(86)90084-4.

  • P.E. Nikravesh and I.S. Chung. 1982. Application of Euler parameters to the dynamic analysis of three dimensional constrained mechanical systems, J. Mech. Des., 104, 785-791. https://doi.org/10.1115/1.3256437.

  • P.E. Nikravesh, R.A. Wehage and O.K. Kwon. 1985. Euler parameters in computational kinematics and dynamics: Part 1, J. Mechanisms, Transmissions and Automation Design, 107, 358-365. https://doi.org/10.1115/1.3260722.

  • P.E. Nikravesh, O.K. Kwon, and R.A. Wehage. 1985. Euler parameters in computational kinematics and dynamics: Part 2, J. Mechanisms, Transmissions and Automation Design, 107, 366-369. https://doi.org/10.1115/1.3260723.

  • P.E. Nikravesh. 1988. Computer Aided Analysis of Mechanical Systems, Prentice Hall, Englewood Cliffs, New Jersey.

  • S.R. Vadali. 1988. On the Euler Parameter Constraint, J. Astronaut. Sci., 36, 259-265. https://doi.org/10.2514/6.1988-670.

  • Jr. Morton and S. Harold. 1993. Hamiltonian and Lagrangian formulations of rigid body rotational dynamics based on Euler parameters, J. Astronaut. Sci., 41, 561-5991.

  • R.C. Sharma. 2010. Coupled vertical-lateral dynamics of railway vehicle. PhD dissertation Thesis, MIED, IIT Roorkee.

  • R.C. Sharma. 2016. Evaluation of passenger ride comfort of Indian rail and road vehicles with ISO 2631-1 standards: Part 1 - Mathematical modeling, Int. J. Vehicle Structures & Systems, 8(1), 1-6. https://doi.org/10.4273/ijvss.8.1.01.

  • R.C. Sharma. 2016. Evaluation of passenger ride comfort of Indian rail and road vehicles with ISO 2631-1 standards: Part 2 - Simulation, Int. J. Vehicle Structures and Systems, 8(1), 7-10. https://doi.org/10.4273/ijvss.8.1.02.

  • S.K. Sharma and A. Kumar. 2017. Impact of electric locomotive traction of the passenger vehicle ride quality in longitudinal train dynamics in the context of Indian railways, Mechanics & Industry, 18(2), 222. https://doi.org/10.1051/meca/ 2016047.

  • S.K. Sharma and A. Kumar. 2017. Ride performance of a high speed rail vehicle using controlled semi active suspension system, Smart Materials and Structures, 26(5), 55026.

  • S.K. Sharma and A. Kumar. 2017. Ride comfort of a higher speed rail vehicle using a magnetorheological suspension system, Proc. IMechE, Part K: J. Multi-body Dynamics, 232(1), 32-48. https://doi.org/10.1177/1464419317706873

  • S. K. Sharma, R.C. Sharma, A. Kumar and S. Palli, 2015. Challenges in rail vehicle-track modelling and simulation. Int. J. Vehicle Structures and Systems, 7(1), 1-9. http://dx.doi.org/10.4273/ijvss.7.1.01.


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  • Rail Vehicle Modelling and Simulation using Lagrangian Method

Abstract Views: 460  |  PDF Views: 189

Authors

Rakesh Chandmal Sharma
Mech. Engg. Dept., Maharishi Markandeshwar (Deemed to be University), Mullana, Haryana, India
Sunil Kumar Sharma
Dept. of Mech. Engg, Amity School of Engg. and Tech., Amity University, Uttar Pradesh, Noida, India
Srihari Palli
Mech. Engg. Dept., AITAM, Tekkali, Andra Pradesh, India

Abstract


Formulation of vehicle dynamics problem is dealt either with Newton’s method or Lagrange’s method. This paper provides a broad understanding of Lagrange’s method applied to railway vehicle system. The Lagrange’s method of analytical dynamics provides a complete set of equations through differentiations of a function called Lagrangian function which includes kinetic and potential energy with respect to independent generalised coordinates assigned to the system. This paper also discusses rigid body rotational dynamics along with the concept of generalised coordinates (constrained and un-constrained) and generalised forces in detail.

Keywords


Lagrangian Function, Euler’s Angle, Newton’s Method, Generalized Forces, Generalized Coordinates, Body Fixed Axes.

References





DOI: https://doi.org/10.4273/ijvss.10.3.07