According to a large amount of the test data, the mid and high frequency vibrations of high-speed bogies are very notable, especially in the 565~616 Hz range, which are just the passing frequencies corresponding to the 22nd to 24th polygonal wear of the wheel. In order to investigate the main cause of wheel higher-order polygon formation, a 3D flexible model of a Chinese high-speed train bogie is developed using the explicit finite element method. The results show that the couple vibration of bogie and wheelset may lead to the high-order wears of wheel. In order to reduce the coupled resonance of the wheelset and the bogie frame, the effects of the stiffness and damping of the primary suspensions, wheelset axle radius, and bogie frame strength on the vibration transmissibility are discussed carefully. The numerical results show that the resonance peaks in high frequency range can be reduced by reducing the stiffness of axle box rotary arm joint, reducing the wheelset axle radius or strengthening the bogie frame location. The related results may provide a reference for structure improvement of the existing bogies and structure design of the new high-speed bogies.
Nowadays more and more people consider high-speed trains to be a comfortable, safe, low, and clean energy consumption transportation tool. However, increasing the operation speed and mileage accelerated the polygonal wear of high-speed train wheels, which leads to the fierce vibration of the vehicle-track system in a wide frequency range. According to site tests and experiences of the authors, the high-order polygonal wear of wheel and the mid and high frequency vibrations of high-speed bogies are very notable [
The multibody modeling and dynamic behavior of the railway vehicles are well understood in the low frequency range, and the wheelset can be modeled well in the frequency range up to several thousand Hertz [
In order to reduce the vibrations of the high-speed bogie in in mid and high frequency, a 3D flexible model of a Chinese high-speed train bogie is developed using the explicit finite element (FE) method. Based on the bogie FE model, the vertical vibration responses of the axle boxes and the bogie frame are obtained in frequency domains. The reasons which cause the high-order wear of wheel are analyzed, and the effects of the parameters of the primary suspensions, wheelset axle radius, and stiffened thin plates in bogie frame on the vibration transmissibility are discussed carefully. It is noted that the numerical methods and the results would be helpful in understanding the mid and high frequency vibration characteristics and the vibration transmissibility of the high-speed train bogie.
Both wheel polygon and vehicle vibration of the trailer bogie were tested. Wheel polygon measurements before and after reprofiling were completed while the bogies were standing on the rail. Vibrations of the axle box and the bogie frame before reprofiling were monitored while the train was running at the speed of 250 km/h.
The wheel polygon can cause a series of vibration and noise problems of high-speed train according to a lot of previous test data. Therefore, the wheel roughness of the wheel circumference was tested firstly. Test of wheel polygon was carried out by OSD-RRM01 [
The wheel roughness is defined with logarithmic form
The polygon order distributions before and after reprofiling are compared in Figure
Wheel polygon order.
Figure
Test photo of accelerations installed on the bogie frame and axle box.
Figure
Vibrations of bogie frame and axle box.
When wheel rotates a circle, the rotating frequency
The passing frequency of the wheel polygon
Figure
FEM of the whole bogie system.
Figure
Values of stiffness and damping involved in this study.
Stiffness (N/mm) | Damping (N⋅s/mm) | |||||
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Vertical | Horizontal | Longitudinal | Vertical | Horizontal | Longitudinal | |
Primary suspension | ||||||
Rubber bearings | 4000 | 400 | 4000 | 0.02 | 0.02 | 0.24 |
Primary dampers | - - | - - | - - | - - | 33 | - - |
Damper rubber joints | 70000 | 7500 | 70000 | 1.66 | 0.18 | 1.66 |
Rotary arm rubber joints | 160000 | 18000 | 76000 | 9 | 0.43 | 3.79 |
Secondary suspension | 1150 | 174 | 174 | 37 | 29.4 | 245 |
3D geometry and FEM of the primary suspension.
Coil spring and the rubber bearing
Primary damper and the rubber joint
Rotary arm rubber joints
To improve the calculating efficiency, some 1D and 2D elements are applied to the model. For example, beam elements are used to simulate bogie frame horizontal beams and axles, mass elements are used to simulate the brake disc seat on the bogie frame, and shell elements are used to simulate bogie side frames. The total element and node numbers are 234165 and 184209, respectively.
Remington [
The wheel and rail can each then represented by an
Or the upper matrix can be translated to other forms:
Note the negative signs for the wheel, since here the force acts in the opposite direction to that of the displacement. Hence, from equation (
Equation (
Framework of theoretical model of wheel-rail force.
The local deformations of two bodies in contact act as nonlinear stiffness between them. However, for small displacement, linearized Hertzian contact stiffness,
The contact patch wavenumber filter is presented by Remington, which is given by
Prestress and wheel/rail contact forces are applied to the points on the four wheel treads (Figure
Wheel/rail contact force in frequency domain.
Based on the above FE model, the vibrations of the axle box and the bogie frame, both in time domain and frequency domain, are calculated by ANSYS. The FE model takes wheel/track force in time domain as input; the vibrations of the axle box and the bogie frame are calculated by transient dynamic analysis method. Figure
Vibration comparison of testing and simulation (in time domain).
Vibration comparison of testing and simulation (in frequency domain).
Axle box
Bogie frame
Harmonic response analysis is used to calculate the steady vibration responses of bogie key components under the swept frequency excitation. Then the vibration peaks from the frequency response function are counted out. In these peak frequencies, vibration displacement color clouds of the whole bogie are invested. The car body’s 6 DOFs are all constrained. The harmonic forces are applied to the points on the four wheel treads. The magnitude of the force is 50 N, and the analysis frequency band is from 0 Hz to 1000 Hz, and the frequency resolution is 4 Hz. The calculated progress is as follows: First of all, the modal parameters and extended models are calculated. Based on the modal results, the vibrations of axle box and bogie frame are extracted by the full arithmetic. The vibration results in one-third octave of four bogie key part compartments, which are bogie over the primary damper, bogie over the spring, rotary arm support, and axle box respective, are shown as Figure
Vibration in one-third octave.
Furthermore, the FFT vibrations of these four component parts in the frequency band of 400~800 Hz are calculated. Results are shown as Figure
Vibration in FFT.
From Figure
Displacement color clouds of bogie frame in 520~560 Hz.
The displacement color clouds of bogie frame in 528 Hz
The displacement color clouds of bogie frame in 544 Hz
The vibrations at three points on the bogie frame, near the vertical damper, coil spring, and the rotary arm rubber joint, are calculated. The responses of the axle box are obtained. All of them are used to evaluate the vibration isolation characteristics from the axle box to the bogie.
The stiffness and damping of the primary suspension have important influence on the vibration isolation, so three parameters are investigated; they are, respectively, stiffness of the rubber bearing under coil spring, the rotary arm rubber joint, and the damping of the vehicle damper. Beyond that, the radius of wheelset axle and the number of bogie stiffened plates are also considered. Tables
The overall vibration isolation (changing parameters of the primary suspension).
Stiffness of rubber bearing |
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Stiffness of rotary arm rubber joint |
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Damping of vertical damper |
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The overall vibration isolation (changing geometries of the bogie).
Radius |
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Stiffened plates |
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Original |
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Add 10 mm |
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Add 20 mm |
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Sub 10 mm |
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Compared to the stiffness of the rubber bearing, the stiffness of the rotary arm rubber joint is higher. Therefore, it has an obvious effect on the overall vibration isolation performance as shown in Table
Figure
Different stiffness of the rotary arm rubber joint.
Vibration isolation of the primary suspension (0~800 Hz)
Vibration of bogie frame and axle box (400~800 Hz)
Figure
The rubber bearing under coil spring is an important vibration absorbing element, which connects the coil spring and the axle box. Its stiffness is lower than other rubber materials of the primary suspension. From Table
Figure
Different stiffness of the rubber bearing under coil spring.
Vibration isolation of the primary suspension (0~800 Hz)
Vibration of bogie frame and axle box (400~800 Hz)
Figure
As shown above, the stiffness of some components has effects on the vibration isolation. Furthermore, the influences of damping of the primary suspension can be invested. The primary damper can improve the stability and comfortability of railway vehicles; furthermore in this section the effect of the damping on isolation in high frequency is studied. The damping of the primary suspension parts mainly depends on the vertical damper and the rubber material damping. As for the damping of the rubber material, it is hard to get, so this paper mainly invests the influence of the vertical damper. In Table
Figure
Different dampings of the vertical damper.
Vibration isolation of the primary suspension (0~800 Hz)
Vibration of bogie frame and axle box (400~800 Hz)
Figure
The coupled resonance of wheelset and bogie frame at 520 Hz may be the main reason which leads to the high-order wheel polygon, so the vibration in high frequency may be reduced by improving the structure of these two components.
Because of the high weigh, wheelset can generate large vibration energy once its model is excitated, which lead to the serious wheel-rail force. In the frequency band of 520~550 Hz. the model deformation of wheelset is shown as the third bend of axle, So this mode can be improved by changing the radius of the wheelset axle. From Table
Figure
Different radiuses of the wheelset axle.
Vibration isolation of the primary suspension (0~800 Hz)
Vibrations of bogie frame and axle box (400~800 Hz)
Figure
Because of the high weigh, bogie frame can generate large vibration energy once its model is excitated. Then the wheel-rail force and the vibration increase dramatically. Modal shapes of bogie frame in low orders are almost shown as the global deformations; as the modal frequencies increase, side beams’ and horizon beams’ local deformations become dominant. In the frequency range of 520~550 Hz, the modal shapes are always shown as the local movements of the end of side beams. Thus, adding stiffened thin plates in the side beams can improve the local stiffness of bogie frame and then change these modal frequencies. The stiffened thin plates are located in the middle of the upper covers, lower covers, outside covers, and inside covers, and numbers are one, three, and five, respectively. Figure
Stiffened plates of bogie.
From Table
Figure
Different numbers of the stiffened thin plates.
Vibration isolation of the primary suspension (0~800 Hz)
Vibration of bogie frame and axle box (400~800 Hz)
Figure
To reduce the vibration of the bogie in the mid and high frequency, a 3D flexible model of a whole bogie is developed using the explicit finite element (FE) method. Then the influences of material and structure parameters on bogie are analyzed carefully. Based on the obtained results, the following conclusions are drawn:
(1) The field tests show that the mid and high frequency vibrations of high-speed bogies are very notable, especially in the 560~590 Hz range, which are very close to the passing frequencies corresponding to the 22nd to 23rd polygonal wear of the wheel.
(2) Based on the roughness and receptance by site test, the wheel/rail contact forces are calculated as the FE model’s input. Then vibrations of the axle box and the bogie frame obtained by simulation are in good agreement with the measured results. Thus, the FE model and the calculated method are validated effectively.
(3) The vibration responses of the bogie FE model are calculated by the harmonic response analysis. The numerical results show that magnitudes of serious vibrations on the axle box are close to that of the bogie frame in the frequency band of 520~560 Hz. The vibration deformations of the whole bogie in the frequency band of 520~560 Hz are mainly shown as the couple vibration of bogie side beam local movements and the third bend of wheelset. The couple vibrations of bogie frame and wheelset may be the main reasons which lead to the resonance vibration in high frequency and then induce the high-order wear of wheel.
(4) The numerical results show that stiffness of the rubber bearing and damping of the primary damper have little effect on the vibrations of the bogie frame and axle box, while the resonance peaks in high frequency range can be reduced by reducing the stiffness of axle box rotary arm joint, reducing the wheelset axle radius, or strengthening the bogie frame location.
The authors declare that they have no conflicts of interest.
The present work was supported by the National Key R&D Program of China (nos. 2016YFB1200503-02, 2016YFB1200506-08, 2016YFE0205200), the National Natural Science Foundation of China (nos. U1434201, U1734201, 51475390), and the Scientific Research Foundation of State Key Laboratory of Traction Power, China (no. 2015TPL_T08).