**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32451

##### Damping and Stability Evaluation for the Dynamical Hunting Motion of the Bullet Train Wheel Axle Equipped with Cylindrical Wheel Treads

**Authors:**
Barenten Suciu

**Abstract:**

Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.

**Keywords:**
Bullet train,
dynamical hunting,
cylindrical wheels,
damping,
stability,
creep,
vibration analysis.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1474317

**References:**

[1] S. Iwnicki, Handbook of Railway Vehicle Dynamics. New York: CRC Press, Taylor & Francis, 2006, pp. 21–38.

[2] A. H. Wickens, Fundamentals of Rail Vehicle Dynamics. New York: Swets & Zeitlinger Publishers, 2003, pp. 101–123.

[3] A.H. Wickens, “The Dynamic Stability of Railway Vehicle Wheelsets and Bogies having Profiled Wheels,” International Journal of Solids and Structures, 1(3), pp. 319–341, 1965.

[4] B. Suciu, “Clarifications on the Damping Mechanism Related to the Hunting Motion of the Wheel Axle of a High-Speed Railway Vehicle,” International Journal of Aerospace and Mechanical Engineering, 12(1), pp. 1–8, 2018.

[5] U. Olofsson, and R. Lewis, Tribology of the Wheel-Rail Contact. New York: Taylor & Francis, 2012, pp. 121–141.

[6] A. Kapoor, D. I. Fletcher, F. Schmid, K. J. Sawley, and M. Ishida, Tribology of Rail Transport. New York: CRC Press, 2001, pp. 161–202.

[7] D. J. Inman, and R.J. Singh, Engineering Vibration. New York: Prentice Hall, 2001.

[8] H. Benaroya, and M. L. Nagurka, Mechanical Vibration: Analysis, Uncertainties, and Control. London: CRC Press, 3rd ed., 2010.

[9] T. Makino, and H. Sakai, “Fatigue Property of Railway Axles for Shinkansen Vehicles,” Technical Report, 395, pp. 56–63, 2013 (in Japanese).

[10] D. Yamamoto, “Study on the Running Vibration Characteristics of Railway Vehicle. 1st Report: Estimation of Creep Coefficient between Actual Wheel and Rail,” Journal of System Design and Dynamics, 4(6), pp. 823–836, 2010.

[11] H. Sakai, “A Consideration to Hunting of Wheel Set,” Proceedings of JSME TRANSLOG, 1101, pp. 1–10, 2016 (in Japanese).

[12] F. W. Carter, “On the Action of a Locomotive Driving Wheel,” Proceeding of the Royal Society London, A112, pp. 151–157, 1926.

[13] J. J. Kalker, “Wheel-Rail Rolling Contact Theory,” Wear, 144, pp. 243–261, 1991.

[14] H. Sakamoto, and M. Yamamoto, “Effect on Nonlinear Creep Force on Railway Truck Dynamics,” Transactions of JSME, 52(473), pp. 302–309, 1986 (in Japanese).

[15] K. Yokose, M. Igarashi, and J. Takayanagi, “Basic Investigation on the Hunting Motion of the Railway Truck by Considering the Nonlinear Characteristics of the Creep Force,” Transactions of JSME, 51(466), pp. 1198–1208, 1985 (in Japanese).

[16] T. Matsudaira, N. Matsui, S. Arai, and K. Yokose, “Problems on Hunting of Railway Vehicle on Test Stand,” Journal of Engineering for Industry, 91(3), pp. 879–885, 1969.

[17] M. Smith, “Train Suspension System,” Patent No. US 9403543, pp. 1–13, 2016.

[18] B. Suciu, and R. Kinoshita, “Investigation on the Bogie Pseudo-Hunting Motion of a Reduced-Scale Model Railway Vehicle Running on Double- Curved Rails,” International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 11(1), pp. 39–46, 2017.

[19] E. J. Routh, A Treatise on the Stability of a Given State of Motion: Particularly Steady Motion. London: MacMillan, 1877, pp. 51–62.

[20] R.C. Dorf, and R.H. Bishop, Modern Control Systems. New York: Prentice Hall, 2001, pp. 41–74.

[21] D. E. Newland, Mechanical Vibration Analysis and Computation. London: Longman Scientific and Technical, 1989, pp. 125–144.

[22] C. Hoen, “An Engineering Interpretation of the Complex Eigen-Solution of Linear Dynamic Systems,” Proceedings of IMAC XXIII, pp. 1–6, 2005.