Mechanism of high-speed train carbody shaking due to degradation of wheel-rail contact geometry

Figures & data

Table

Abbreviation
CSP	Carbody shaking phenomenon
HST	High-speed train
DM	Diamond mode
FEM	Finite element method
DAQ	Data acquisition system
GPS	Global positioning system
CWT	Continuous wavelet transform
WWP	Worn wheel profile
SWP	Standard wheel profile
BGRP	Before grinding rail profile
AGRP	After grinding rail profile
SRP	Standard rail profile
MAC	Modal assurance criterion
CBMSM	Craig-Bampton modal synthesis method
MBD	Multibody dynamics

Figure 1. Field test: (a) Measuring points arrangement; (b) Accelerometer on axle box above wheelset; (c) Accelerometers on carbody floor; (d) DAQ equipment.

Figure 2. Statistics of CSPs location.

Figure 3. (a) Sperling index of front, middle and rear position of floor; (b) CWT of vertical acceleration in middle floor.

Figure 4. Test results for the vehicle: (a) Vertical acceleration of middle floor; (b) Partial enlargement of Figure (a); (c) Lateral acceleration of bogie frame; (d) Partial enlargement of Figure (c); (e) PSD comparison of middle floor, frame and axle box; (f) Identified carbody DM in modal testing.

Figure 5. Bogie frame acceleration in turnout section: (a) Time domain; (b) Partial enlargement.

Figure 6. Carbody FE model under service environment: (a) Overall view; (b) Bolster and secondary suspension; (c) Equipment hanging connection.

Figure 7. FE model updating flow chart.

Table 1. Comparison of experimental and simulated modal results.

Mode	Mode of vibration	FEM (Hz)	Test (Hz)	Difference (%)	MAC
1	First-order diamond	8.92	8.73	2.18	0.913
2	First-order respiratory	10.23	9.96	2.71	0.901
3	First-order vertical bending	13.07	12.91	1.24	0.935
4	Second-order diamond	15.25	15.86	3.66	0.883
5	First-order torsion and first order lateral bending	18.36	17.79	3.20	0.895
6	Second-order torsion and second-order lateral bending	18.71	19.04	1.73	0.929

Figure 8. (a) Schematic view of vehicle-track coupled dynamics model; (b) Floating reference frame for carbody; (c) Schematic diagram of co-simulation of vehicle system and track system.

Table 2. Degrees of freedom of vehicle system.

Component	Type of motion
	Longitudinal	Lateral	Vertical	Roll	Pitch	Yaw
Bolster (i = 1–2)	Xci	Yci	Zci	ϕci	βci	ψci
Vehicle-mounted equipment (i = 1–5)	Xtri	Ytri	Ztri	ϕtri	βtri	ψtri
Frame (i = 1–2)	Xti	Yti	Zti	ϕti	βti	ψti
Wheelset (i = 1–4)	Xwi	Ywi	Zwi	ϕwi	βwi	ψwi
Axle box (i = 1–4)	–	–	–	–	βmi	–

Figure 9. Schematic diagram of turnout near high-speed railway station.

Figure 10. (a) Key sections of switch rail; (b) Schematic diagram of key sections fitting method.

Figure 11. Measured wheel and rail profiles: (a) Wheel profiles; (b) Rail profiles

Figure 12. Wheel-rail contact pairs: (a) SWP-CHN60; (b) SWP-BGRP; (c) SWP-AGRP; (d) WWP-CHN60; (e) WWP-BGRP; (f) WWP-AGRP.

Figure 13. Geometric analysis of wheel-rail contact: (a) Equivalent conicity of SWP; (b) Equivalent conicity of WWP; (c) Rail coordinate position of SWP; (d) Rail coordinate position of WWP.

Table 3. Cause classification of hunting motion frequency of bogie.

No.	Wheel-rail matching type	Equivalent conicity (3 mm position)	Rigid positioned bogie	Elastic positioned bogie
1	SWP-SRP	0.15	5.24	5.83
2	SWP-BGRP	0.10	4.28	4.88
3	SWP-AGRP	0.16	5.41	6.22
4	WWP-SRP	0.28	7.16	7.72
5	WWP-BGRP	0.33	7.78	8.31
6	WWP-AGRP	0.22	6.35	6.97

Figure 14. Simulation results of wheel-rail force: (a) Time domain; (b) PSD of wheel-rail vertical force; (c) PSD of wheel-rail lateral force.

Figure 15. Simulation results of middle floor: (a) Time domain of vertical acceleration; (b) Time domain of lateral acceleration; (c) CWT of vertical acceleration; (d) CWT of lateral acceleration.

Figure 16. Distribution comparison diagram of carbody middle floor acceleration: (a) Vertical; (b) Lateral.

Figure 17. Bogie frame lateral acceleration: (a) Time-domain; (b) PSD.

Figure 18. Time-domain of carbody underframe side beam accelerations: (a) Operation modal test; (b) Vertical acceleration; (c) Lateral acceleration; (d) Partial enlargement of Figure (a); (e) Partial enlargement of Figure (c).

Figure 19. Comparison diagrams of middle floor accelerations before and after rail grinding: (a) Time-domain; (b) PSD.

Figure 20. (a) SWP-Switch rail with top width of 35 mm; (b) WWP-Switch rail with top width of 35 mm; (c) Rail coordinate position of WWP-Switch rail.

Figure 21. Type of turnout layout and middle floor acceleration: (a) Type A; (b) Type B; (c) Vertical; (d) Lateral.

Figure 22. Middle floor acceleration: (a) PSD of vertical acceleration; (b) PSD of lateral acceleration; (c) CWT of vertical acceleration under SWP and WWP condition.

Figure 23. Bogie frame lateral acceleration: (a) Time-domain; (b) PSD.