Evaluation of the Fatigue Life of Aluminum Bogie Structures for the Urban Maglev

1 Nam-Jin Lee, 2Hyung-Suk Han, 3Sung-Wook Han, 3Peter J. Gaede, Hyundai Rotem company, Uiwang-City, Korea1; KIMM, Daejeon-City2, Korea;

Hyundai Rotem company, Uiwang-City, Korea3;

Abstract

A modular assembly carries the electromagnets which provide levitation and guidance of the vehicles; moreover, the linear motors used for traction are integrated into the same mechanical structure. These modular bogies for Maglev vehicles are made of aluminum, which helps to reduce the overall vehicle weight. The weight of an urban Maglev vehicle is a critical issue. When minimizing the weight of the bogie structure, life cycle requirements have to be taken into consideration at the same time. It is required to know the operating load history to be an input to fatigue analysis. This paper describes a dynamic simulation which includes the characteristics of the track, of the levitation and guidance system, and of a flexible bogie structure. The secondary suspension and the carbody are modeled in the simulation as well. The simulation can predict the load histories of the bogie structure. The results of the fatigue analysis will be presented, which in a first approach turned out to comply with a life time requirement of 25 years.

1. Introduction

Maglev is considered as an environmentally friendly future transportation system because of its non-contact levitation/guidance and linear motor propulsion system. A commercial Maglev project for urban application has been under development in Korea since 2006, targeting to start commercial service by 2012. The Maglev vehicle’s concept used in this project is based upon electromagnetic suspension (EMS), which employs attraction force of magnets for levitation and guidance.[1] The levitation system of EMS requires an active control system to keep the appropriate clearance between electromagnet and guideway. In general Maglev is operated on elevated-beam guideways supported by piers as shown in Figure 1.

Figure 1 Prototype Urban Maglev running over an elevated guideway

The modular bogie structures applied for Maglev vehicles are made of aluminum. Compared to conventional rolling stock, the type of load input affecting the bogie structure is not a discrete, localized interaction between the track and the bogies (wheel-set). In case of Maglev vehicles the loads are distributed along the bogie due to the continuous support of the magnets. This

characteristic allows the use of aluminum as a structural material. Furthermore, as weight of Urban MAGLEV vehicles is a critical issue; the relative lighter aluminum bogie structures help to reduce the overall vehicle weight. When minimizing the structure weight, the bogie life span has to be taken into account at the same time. In order to achieve these aims, the following method will be applied. Based upon a vehicle given load specification, a conceptual design of the vehicle including its secondary suspension is established first which is then used to derive a load specification for the bogie sub-system itself. This sub-system specification will be derived from dynamic simulations taking into account the characteristics of the electromagnetic suspension. The track parameters will also be used as important inputs for these simulations. The proposed procedure is organized as follows:[2,3]

- Establishment of a vehicle model including its electromagnetic suspension system - Definition of “guide way” parameters (track geometry, elasticity, irregularities etc…) - Preparation of an FEM model for the bogie structure. - Establishment of simulation program for the dynamic performance - Extraction of load spectra from simulations - Fatigue analysis for bogie structural stresses

The target of this approach is to derive realistic load spectra as a guideline for the design of Urban MAGLEV bogies and to achieve an optimized bogie structure.

2. Maglev vehicle system

2.1 Bogie and vehicle system

The configuration of a bogie is in Figure 2. Eight electromagnets and two Linear motors are attached to one bogie; the secondary suspension system connecting the bogies to the car body consists of an air-spring with leveling valve, two dampers and a traction rod per side module of bogie. The schematic of Figure 3 explains the vehicle model used for the simulation. It includes the electromagnetic forces calculated by a user-defined subroutine; other components such as secondary suspension are modeled with elements provided in ‘Virtual. Lab Motion’ as a dynamic analysis program[4,5], and the flexible body structures are covered by FE modeling using Nastran FE software.

Figure 2 Configuration of Bogie for Maglev

Figure 3 Schematic of Vehicle modeling

2.2 Modal model of Bogie structure

In dynamic simulation the flexibility of bogie structure affects the interaction between track and electromagnet. So to improve the accuracy of the simulation results, the modal model of bogie structure is applied for dynamic simulation. The MNF (modal neutral file) is generated by Nastran and it is introduced into the dynamic model. Figure 4 shows the results of the modal model of bogie structure. [2,3]

Figure 4. Modal Analysis of Bogie Structure

2.2 Irregularity and deflection of guideway

It is assumed that the deflection ratio of the guideway would be L/2000 with 25m span length and a vehicle would run at 110km/h as maximum operating speed on a straight track. Under these conditions, the levitation force of the manget excites the guideway with less than 1.3Hz when passing a girder. Because the excitation frequency caused by the running vehicle is sufficiently lower than the natural frequency of a guideway girder, the effect of the flexibility of the guideway on the bogie structure is negligible. Therefore the bending effect of girders is considered as a static problem, so the deformation is treated as a kind of vertical irregularity. The irregularity of guideway is derived from measured ones originating from the test track located at KIMM in Deajeon-city, Korea. In addition, the sawtooth wave is added representing the rail profile to emphasize the step irregularity of the discrete arrangement of 5m length guiderail units. Figure 5 shows the applied guideway profile.

0 50 100 150 200 250 300 350 400 450 500-15-10-50

Z pr

ofile

R [mm

]

0 50 100 150 200 250 300 350 400 450 500-15-10-50

Z pr

ofile

L [mm

]

0 50 100 150 200 250 300 350 400 450 500-5

0

5

Y p

rofil

e R [mm

]

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0

5

Y p

rofil

e L [mm

]

distance [m] Figure 5 Irregularities of guideway

2.3 Levitation/guidance System

Levitation/guidance system consists of electromagnets, the voltage suppliers (choppers), controllers and sensors as shown in Figure 6. The input signals from sensors are acceleration signal of bogie frame and airgap signal as distance between magnet and guideway. The control algorithm calculates magnet voltage, which secures stable levitation of vehicle. The applied control algorithm consists of two steps; firstly state observer estimates 5 states, then state-feedback controller calculates required voltage with state-control gains. The control output is to be sent to the chopper as PWM signal, finally the chopper provides voltage and thus magnet currents. The state-feedback law is used as equation (1) and excitation current for magnet is controlled by equation (2).[5]

uutu

gkgkzkzkzku ffpppp

Δ+=

++++=Δ

0

54321

)( (1)

In the above equations, fpppp gzzz ,,, , and fg are states estimated by state observer,

5~1k are control gains. )(tu is the control voltage for the electromagnet, and 0u is required magnet voltage for equilibrium status.[1]

[ ]

))(,,(

)())(,,()()()(

)())(,,()()(

tiggL

titiggLdtdtiRtu

dttdi

titiggLdtdtiRtu

lv

lv

lv

⋅−⋅−=

⋅+⋅= (2)

Here, R is the ohmic resistance of the magnet coils, ))(,,( tiggL lv represents the inductance

of a magnet, )(ti is the magnet current.

Carbody

Bogie

Figure 6 Schematics of Levitation/Guidance system

The electromagnetic force characteristics as well as the inductances are non-linear functions of air gaps, and magnet currents. The electromagnet model is established on the base of the performance characteristics derived from static ones as shown by Fig. 7.

a) FE model (b) flux density

020

4060 5

10

15-40

-30

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-10

0

vertical gap[mm]current [A]

Forc

e [k

N]

lateral gap: 15[mm]lateral gap: 12[mm]lateral gap: 9[mm]lateral gap: 6[mm]lateral gap: 3[mm]lateral gap: 0[mm]

0 10 20 30 40 50 60 5

10

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-8

-6

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vertical gap[mm]

current [A]

Forc

e [k

N]

lateral gap: 3[mm]lateral gap: 6[mm]lateral gap: 9[mm]lateral gap: 12[mm]lateral gap: 15[mm] 0

20

40

605

10

15

0.8

0.9

1

1.1

1.2

1.3

1.4

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vertical gap[mm]current [A]

Indu

ctan

ce [H

]

lateral gap: 3[mm]lateral gap: 6[mm]lateral gap: 9[mm]lateral gap: 12[mm]lateral gap: 15[mm]

(c) Levitation force (d) Guidance force (e) Inductance

Figure 7 Magnetostatic analysis and its results vs. both gaps and current

3. Modeling and Dynamic/Fatigue analysis

3.1 Dynamic Simulation

In the previous chapter all components of a Maglev vehicle system had been introduced. The completed model is shown by Figure 8 in Virtual Lab Motion. As indicated by Figure 8, a flexible bogie structure had been taken into account for the front bogie only to reduce calculation time.

Figure 8 Vehicle model with flexible body on Virtual Lab Motion

The dynamic simulation finally provided the load histories affecting all of interfaces through which external forces are transferred to the bogie structure via its components such as two air springs, four dampers, and eight electromagnets. Figure 9 shows the load history of a magnet and an air spring, for example.

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4-1

0

1

forc

e x [kN

]

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4-0.2

0

0.2

forc

e y [kN

]

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time[sec]

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e x [kN

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e y [kN

]

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4-23

-22

-21

-20

forc

e z [kN

]

time[sec] (a) forces for a electromagnet (b) forces for a air-spring

Figure 9 Load histories of bogie structure

3.3 Fatigue analysis

The evaluation of the fatigue life of aluminum bogie structure for urban Maglev, is based upon quasi static fatigue analysis. Firstly, the static analysis caused by unit force on hard points as shown in Figure 10, was performed and the load histories obtained by the dynamic analysis were converted to load profiles to be applied on the hard points. Then fatigue analysis evaluated life time of the bogie structure with the accumulated damages caused by the load profile.

Figure 10 Joint points for load histories Figure 11 Result of Fatigue Analysis

As the results of the fatigue analysis, the point for minimum life time was detected at the weld for the tie beam mounting bracket as shown on Figure 11. Its life time is calculated as 322,000 hours, which complies with a life time requirement of 25 years.

4. Conclusion

To evaluate the fatigue life of the bogie structure of a Maglev vehicle, a simulation model was established including its electromagnetic suspension, track disturbance, and flexible structure. Load histories of each component interface of bogie the structure were extracted from dynamic simulations. Fatigue analysis was performed with the obtained load histories. Finally, these sequential processes show the bogie structure meets the requirement of 25 years life time. This paper was focused on the design process of the bogie structure. As a next step, loads resulting from curve negotiation, from traction/braking forces and from loads resulting from dropping of the bogies on its landing wheels will be implemented. At the end, evaluated life cycles will be proved by fatigue tests according to a well defined test specification.

Acknowledgements

This research was supported by a grant from the Maglev Realization Program, funded by the Ministry of Construction & Transportation of the Korean government.

References

[1] Sinha, P. K. 1986. Electromagnetic suspension dynamics & controls. Peter Perefrinus. [2] Yoo, W.S. and Haug, E.J. 1986. Dynamics of articulated structures:Part I. Theory. J. Struct. Mech. Vo 14, No.1, 105-126. [3] Yoo, W.S. and Haug, E.J. 1986. Dynamics of articulated structures:Part II. Computer implementation and applications. J. Struct. Mech. Vo 14, No.2, 177-189. [4] LMS Virtual.Lab Motion Users Manual. LMS International. [5] Hyungsuk Han, Jongmin Lee, Byunghyun Kim, Hokyung Sung and Kookjin Kim, “Dynamic modeling of a magnetically-levitated vehicle running over a flexible guideway”, MULTIBODY DYNAMICS 2007 ECCOMAS Thematic Conference (2007)