Abstract
An improved hydraulic yaw damper model with series in-service clearance and comprehensive stiffness was proposed by Wang et al. (Nonlinear Dyn 65(1–2):13–34 2011). In order to study how in-service parameter variations to the hydraulic yaw damper affect the dynamics of a Chinese \(\hbox {SS}_{9}\) locomotive, this study continued that research by establishing a multibody system (MBS) model of the \(\hbox {SS}_{9}\) locomotive–rail coupling system, and then validating the MBS model using field test data from the \(\hbox {SS}_{9}\). Extensive simulations were performed, and the results demonstrated that both the effective stiffness and the small clearance accumulated between two ends of the damper due to wear and lack of maintenance had remarkable impacts on the locomotive’s critical speed and on its normal operation. The results also influenced the locomotive’s ride comfort, but the effect of the small clearance was more remarkable than that of the effective stiffness in this regard, and these parameters had little to no influence on the locomotive’s curve-negotiation performance. The small clearance and effective stiffness are usually omitted or simplified in engineering, and so it was important to apply the proposed in-service nonlinear damper model with series clearance and stiffness to a vehicle dynamics study and improve the accuracy of vehicle design. The study was also useful for setting pertinent vehicle maintenance standards in engineering to control the influence of such in-service parameter variations.
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References
Wang, W.L., Huang, Y., Yang, X.J., Xu, G.X.: Nonlinear parametric modeling of a high-speed rail hydraulic yaw damper with series clearance and stiffness. Nonlinear Dyn. 65(1–2), 13–34 (2011)
Wickens, A.: Fundamentals of rail vehicle dynamics: guidance and stability. Swets & Zeitlinger Publishers, Lisse (2003)
Zhai, W.M.: Vehicle-track coupling dynamics. Science Press, Beijing (2007). (in Chinese)
Lee, S.Y., Cheng, Y.C.: Hunting stability analysis of high-speed railway vehicle trucks on tangent tracks. J. Sound Vib. 282, 881–898 (2005)
Cheng, Y.C., Lee, S.Y.: Hunting stability analysis of a new high-speed railway vehicle model moving on curved tracks. In: ASME International Mechanical Engineering Congress and Exposition, pp. 1615–1624, Seattle, WA, USA (2007)
Zboinski, K., Dusza, M.: Self-exciting vibrations and Hopf’s bifurcation in non-linear stability analysis of rail vehicles in a curved track. Eur. J. Mech. A 29(2), 190–203 (2010)
Mohan, A., Ahmadian, M.: Nonlinear investigation of the effect of suspension parameters on the hunting stability of a railway truck. In: Proceedings of the IEEE/ASME Joint Rail Conference, pp. 327–336, Atlanta, GA, USA (2006)
Sayyaadi, H., Shokouhi, N.: A new model in rail-vehicles dynamics considering nonlinear suspension components behavior. Int. J. Mech. Sci. 51(3), 222–232 (2009)
Suarez, B., Felez, J., Maroto, J., Rodriguez, P.: Sensitivity analysis to assess the influence of the inertial properties of railway vehicle bodies on the vehicle’s dynamic behavior. Veh. Syst. Dyn. 51(2), 251–279 (2013)
Fujimoto, H., Miyamoto, M.: Lateral vibration and its decreasing measure of a Shinkansen train. Veh. Syst. Dyn. 25(suppl), 188–199 (1996)
Wrang, M.: Instability phenomena of a passenger coach, caused by internal yaw damper flexibility. Veh. Syst. Dyn. 33, 406–417 (1999)
Mellado, A.C., Gómez, E., Viñolas, J.: Advances on railway yaw damper characterisation exposed to small displacements. Int. J. Heavy Veh. Syst. 13(4), 263–280 (2006)
Piao, M.W., Kong, W.G., Liu, T., Zhao, W.Z.: Stability analysis of a high-speed bogie subject to anti-hunting damper failures. J. Dalian Jiaotong University. 32(4), 1–5 (2011) (In Chinese)
Ahmed, A.S., Jalil, R.S.: A survey of rail vehicle track simulations and flexible multi-body dynamics. Nonlinear Dyn. 26(2), 179–210 (2001)
Schupp, G.: Simulation of railway vehicles: necessities and applications. Mech. Des. Struct. 31(3), 297–314 (2003)
Pérez, J., Busturia, J.M., Mei, T.X., Vinolas, J.: Combined active steering and traction for mechatronic bogie vehicles with independently rotating wheels. Annu. Rev. Control 28, 207–217 (2004)
Zolotas, A.C., Pearson, J.T., Goodall, R.M.: Modelling requirements for the design of active stability control strategies for a high speed bogie. Multibody Syst. Dyn. 15, 51–66 (2006)
Eom, B.G., Lee, H.S.: Assessment of running safety of railway vehicles using multibody dynamics. Int. J. Precis. Eng. Man. 11(2), 315–320 (2010)
Schupp, G., Jaschinksi, A.: Virtual prototyping: the future way of designing railway vehicles. Int. J. Veh. Des. 22(1–2), 93–115 (1999)
Stribersky, A., Moser, F., Rulka, W.: Structural dynamics and ride comfort of a rail vehicle system. Adv. Eng. Softw. 33(7–10), 541–552 (2002)
Jalil R.S.: Accurate rail vehicle dynamic simulations by DynaRail. In: ASME International Mechanical Engineering Congress and Exposition, pp. 1–16, Anaheim, CA, USA (2004)
Wallrapp, O.: Review of past developments in multi-body system dynamics at DLR-from FADYNA to SIMPACK. Veh. Syst. Dyn. 41(5), 339–348 (2004)
Eichberger, A., Hofmann, G.: TMPT: multi-body package SIMPACK. Veh. Syst. Dyn. 45(suppl), 207–216 (2007)
European Standard: Railway Applications—Suspension Components—Hydraulic Dampers, CEN EN 13802 (2004)
Yu, W.B.: Shaoshan 9 electric locomotive. China Railway Publishing House, Beijing (2005). (in Chinese)
Wang, F.T., Zhou, J.S., Ren, L.H.: Analysis of track spectrum density for dynamic simulation of high-speed vehicles. J. China Railway, Society. 24(5), 21–27 (2002) (in Chinese)
Li, J.B.: Irregularity power spectrum density analysis for speed-up tracks. Master’s Degree Thesis, Tongji University, 2008 (in Chinese)
INTEC GmbH.: SIMPACK: Wheel/Rail Basic Training. INTEC GmbH, Wessling, Germany (2006)
Field Test Report: Dynamics performance field test report for \(\text{ SS }_{9}\) 0001# electric locomotive. China Academy of Railway Sciences, Beijing (1999) (in Chinese)
Yang, X.J.: Module design of installation seat for yaw damper on locomotive car-body. Electr. Locomot. & Mass Transit. Veh. 28(1), 18–20 (2005) (In Chinese)
Chinese Railway Society Standard: Evaluation methods and criteria for dynamics performance test of railway locomotives, TB/T 2360–93 (1993) (in Chinese)
Acknowledgments
Financial supports from the open foundation (Grant No. 201308) of the State Key Laboratory of Fluid Power Transmission and Control in Zhejiang University and Hunan Provincial Natural Science Foundation (Grant No. 13JJ9037) of China are gratefully acknowledged.
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Appendix
Appendix
Parameters and values used in the MBS model of the ${{SS}}_{9}$ locomotive--rail coupling system
Notation (unit) | Description | Value | Remarks |
|---|---|---|---|
\(M_\mathrm{c }\) (kg) | Carbody mass | 63400 | |
\(I_\mathrm{cx}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Carbody roll moment of inertia | 143500 | |
\(I_\mathrm{cy}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Carbody pitch moment of nertia | 1521000 | |
\(I_\mathrm{cz}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Carbody yaw moment of inertia | 1718000 | |
\(H_\mathrm{c}\) (m) | Vertical distance from the carbody’s centre of gravity to rail top | 2.1 | |
\(M_\mathrm{t }\) (kg) | Bogie frame mass | 20563 | Includes the suspended mass of the primary suspension and unsprung mass of the secondary suspension |
\(I_\mathrm{tx}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Bogie frame roll moment of inertia | 7370 | |
\(I_\mathrm{ty}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Bogie frame pitch moment of inertia | 73274 | |
\(I_\mathrm{tz}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Bogie frame yaw moment of inertia | 78243 | |
\(H_\mathrm{t}\) (m) | Vertical distance from the bogie’s frame centre of gravity to rail top | 0.9 | |
\(M_{w }\) (kg) | Wheelset mass | 3239 | Includes the unsprung mass of the primary suspension |
\(I_\mathrm{wx}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Wheelset roll moment of inertia | 2450 | |
\(I_\mathrm{wy}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Wheelset pitch moment of inertia | 405 | |
\(I_\mathrm{wz}\) (\(\hbox {kg}\, \hbox {m}^{2})\) | Wheelset yaw moment of inertia | 2450 | |
\(K_\mathrm{px }\) (N/m) | Longitudinal stiffness of primary suspension | 3.3E\(+\)007 | Per axle side |
\(K_\mathrm{py }\) (N/m) | Lateral stiffness of primary suspension | 4.0E\(+\)006 | Per axle side |
\(K_\mathrm{pz }\) (N/m) | Vertical stiffness of primary suspension | 2.15E\(+\)006 | Per axle side |
\(C_\mathrm{pz }\) (Ns/m) | Vertical damping of primary suspension | 80000 | Per axle side (no damping in the bogie’s centre axle) |
\(K_{\mathrm{rubber}\_-\mathrm{v1}}\) (N/m) | Attachment stiffness of the primary vertical hydraulic damper | 7.0E\(+\)006 | Per damper (under normal conditions) |
\(K_\mathrm{sx }\) (N/m) | Longitudinal stiffness of secondary suspension | 4.26E\(+\)005 (1.42E\(+\)005 for one spring) | Per bogie side |
\(K_\mathrm{sy}\) (N/m) | Lateral stiffness of secondary suspension | 4.26E\(+\)005 (1.42E\(+\)005 for one spring) | Per bogie side |
Notation (Unit) | Description | Value | Remarks |
|---|---|---|---|
\(C_\mathrm{pz }\) (Ns/m) | Vertical damping of primary suspension | 80000 | Per axle side (no damping in the bogie’s centre axle) |
\(K_{\mathrm{rubber}\_-\mathrm{v1}}\) (N/m) | Attachment stiffness of the primary vertical hydraulic damper | 7.0E\(+\)006 | Per damper (under normal conditions) |
\(K_\mathrm{sx }\)(N/m) | Longitudinal stiffness of secondary suspension | 4.26E\(+\)005 (1.42E\(+\)005 for one spring) | Per bogie side |
\(K_\mathrm{sy}\) (N/m) | Lateral stiffness of secondary suspension | 4.26E+005 (1.42E\(+\)005 for one spring) | Per bogie side |
\(K_\mathrm{sz}\)(N/m) | Vertical stiffness of secondary suspension | 1.596E\(+\)006 (5.32E\(+\)005 for one spring) | Per bogie side |
\(C_\mathrm{yaw }\)(Ns/m) | Longitudinal damping of secondary suspension | 1000000 | Per damper (one damper per bogie side) |
\(K_{\mathrm{rubber}\_\mathrm{yaw}}\) (N/m) | Attachment stiffness of the hydraulic yaw damper | 1.25E\(+\)007 | Per damper (under normal conditions) |
\(C_{sy }\) (Ns/m) | Lateral damping of secondary suspension | 90000 | Per damper (one damper per bogie side) |
\(K_{\mathrm{rubber}\_\mathrm{h2}}\) (N/m) | Attachment stiffness of the secondary lateral hydraulic damper | 7.0E+006 | Per damper (under normal conditions) |
\(C_\mathrm{sz}\) (Ns/m) | Vertical damping of secondary suspension | 120000 | Per damper (two dampers per bogie side) |
\(K_{\mathrm{rubber}\_\mathrm{v2}}\) (N/m) | Attachment stiffness of the secondary vertical hydraulic damper | 8.0E+006 | Per damper (under normal conditions) |
\(K_\mathrm{seat}\) (N/m) | Hydraulic damper mounting seat stiffness | 2.8 E\(+\)007 | Refer to reference [30] |
\(D_\mathrm{w1}\) (m) | Diameter of new wheel | 1.25 | |
\(D_\mathrm{w2}\) (m) | Diameter of half-worn wheel | 1.2 | |
\(D_\mathrm{w3}\) (m) | Diameter of worn wheel | 1.15 | |
\(M_\mathrm{c0 }\) (kg) | Locomotive servicing mass | 126000 | Allowable relative error of \(-\)1 to +3 % |
\(M_\mathrm{axle}\) (kg) | Axle load | 21000 | |
\(V_\mathrm{r}\) (km/h) | Locomotive rated running speed | 99 | |
\(V_\mathrm{max1}\) (km/h) | Locomotive maximum running speed | 160 | With half-worn wheels |
\(V_\mathrm{max2}\) (km/h) | Locomotive allowable running speed | 170 | With half-worn wheels |
\(R_\mathrm{s}\) (m) | Locomotive minimum safe curving radius | 125 | Vehicle speed \(\le \)5 km/h |
\(L_\mathrm{coup}\) (m) | Centre distance between the front and rear couplers | 22.216 | |
\(H_\mathrm{coup}\) (m) | Vertical distance from coupler centre to rail top | 0.88 | |
\(L_\mathrm{total}\) (m) | Carbody length | 21.596 | |
\(L_\mathrm{frame}\) (m) | Carbody frame length | 21.3 | |
\(W_\mathrm{car}\) (m) | Carbody width | 3.105 | |
\(H_\mathrm{car}\) (m) | Locomotive height (vertical distance from pantograph mounting seat to rail top) | 4.1325 | |
\(H_\mathrm{max}\) (m) | Vertical distance from the car body’s highest point to rail top | 4.754 | |
\(H_\mathrm{panto}\) (m) | Vertical distance from the highest point of the lifted pantograph to rail top | 5.1–6.5 | |
\(L_\mathrm{axle}\) (m) | Bogie axle distance | 2.15 \(+\) 2.15 | \(\hbox {C}_{0}-\hbox {C}_{0}\) axle style |
Notation (Unit) | Description | Value | Remarks |
|---|---|---|---|
\(L_\mathrm{axle0}\) (m) | Distance from the first axle to the last axle of the locomotive | 15.87 | |
\(H_\mathrm{traction}\) (m) | Vertical distance from the traction rod centre to rail top | 0.46 | |
\(L_\mathrm{half}\) (m) | Half of the distance between the carbody’s front and rear side bearings | 5.391 | |
\(W_\mathrm{track}\) (m) | Track gauge | 1.435 | |
\(M_\mathrm{r }\)(kg/m) | Effective railroad mass | 330 | Includes the steel rails, sleepers and the vibration fraction of the roadbed |
\(I_\mathrm{rx}\) (\(\hbox {kg}\, \hbox {m}^{2}\)/m) | Effective railroad mass roll moment of inertia | 10 | |
\(K_\mathrm{ry }\)(N/m) | Effective railroad lateral stiffness | 2.0E+007 | Per rail side |
\(C_\mathrm{ry }\)(Ns/m) | Effective railroad lateral damping | 4.9E+004 | Per rail side |
\(H_\mathrm{rail}\) (m) | Vertical distance from the railroad’s lateral suspension point to rail top | 0.176 | Refer to Fig. 2c |
\(K_\mathrm{rz }\)(N/m) | Effective railroad vertical stiffness | 7.5E+007 | Per rail side |
\(C_\mathrm{rz }\)(Ns/m) | Effective railroad vertical damping | 9.4E+004 | Per rail side |
\(L_\mathrm{rail}\) (m) | Distance between the two railroad vertical suspension points | 1.508 | Refer to Fig. 2c |
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Wang, W.L., Yu, D.S., Huang, Y. et al. A locomotive’s dynamic response to in-service parameter variations of its hydraulic yaw damper. Nonlinear Dyn 77, 1485–1502 (2014). https://doi.org/10.1007/s11071-014-1393-2
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DOI: https://doi.org/10.1007/s11071-014-1393-2