Fatigue Strength and Modal Analysis of Bogie Frame for DMUs Exported to Tunisia

The equivalent stress at key positions of Bogie Frame for DMUs Exported to Tunisia is obtained by using simulation analysis. The evaluation of static strength and fatigue strength is checked referring to UIC specification and Goodman sketch for welding materials. In addition, the modal analysis of the frame is made, and the vibrational modal of frame in given frequency domain is predetermined to evaluate the dynamical behavior of the frame in order to meet the dynamical design requirements. The results show that the key points of the calculated frame of the equivalent stress are less than allowable stress, and thus it could provide a theoretical foundation for the optimized design of frame structure and safety of industrial production.


Introduction
The bogie frame is the main load bearing components and power transmission components of the vehicle, when the vehicle is in motion the process, not only to the bogie frame to withstand loads, but also need to pass a variety of forces between the body and the wheel.Due to the fatigue test costs are expensive, the fatigue strength assessment of key components in the bogie frame using finite element model can find out the fatigue strength of the weak parts, can reduce the risk of fatigue testing prototypes, shorten development cycles, reduce trial costs.In addition, the current domestic commonly uses Electric Multiple Units [1], lacks of bogie products of Diesel Multiple Units; Diesel Multiple Units still have a large market in many countries such as Tunisia for its poor line conditions and economic factors.Therefore, strength analysis and dynamic assessment for the bogie frame of Diesel Multiple Units is of great significance.
This paper is to understand the export Tunisia DMUs bogie basic components, infrastructure characteristics, determined the type of bogie frame load sources and calculated in accordance with the relevant specifications to determine the load; then to use the Hyper mesh software architecture network entities meshing, to re-use the ANSYS finite element analysis software for finite element analysis of the bogie frame.The evaluation of static strength and fatigue strength is checked referring to UIC specification and Goodman sketch for welding materials.In addition, the modal analysis of the frame is made [2].

Bogie Frame Structure
The bogie Frame for DMUs Exported to Tunisia is adopted by welded structure, Figure 1 demonstrates that the main framework architecture is H-shaped in the horizontal plane, which is composed of two box-shaped side sills, the overall composition of the box beam welding, by the central concave belly of the fish box structure composed of a spring seat side beam welding, basic brake mounts, anti-roll torsion bar seat, etc., the cavity has a thickness of 10 mm stiffener plate [3].Box beam structure for the central opening, the transverse beam welding has ended with stopper seat, traction rod seat, motor bracket, gearbox bracket and secondary lateral damper seat and so on.

FEM Model of Bogie Frame
Considering calculating workload, precision and the actual situation in structure of the entire bogie frame, this research selects 10-node solid element of solid 92.Based on the model, the entire bogie frame is discrete with the software Hyper mesh and analyzed with the large generally used finite element software ANSYS [4].In order to simulate the real boundary conditions of the bogie frame, axle box spring in the bogie frame mount simulated by a series of axle box spring unit Combine14 spring means, consistent with the axle box spring stiffness of the spring element stiffness.In the end, the finite element discrete nodes of 110,368, the number of units to 341,334, finite element discrete model shown in Figure 2.

Evaluating Standard of Bogie Frame Strength
In the fatigue strength of welded bogie frame has now formed the international standard UIC 615-4 [5] as the representative of the design, evaluation system.Bogie frame structure strength assessment generally includes three aspects, namely, the role of analysis to determine the load, static strength analysis and assessment, analysis and evaluation of the fatigue strength.According to the UIC 615-4 regulations, we can calculate the appropriate supernormal load, simulated operational load and special operational load.Supernormal load when the maximum load operations may occur; simulate actual operating load refers to the load operations occur frequently; special operational load refers to the load frame by a special device caused.In the practical constraints are consistent with the principles of the frame, and the constraints of the axial knuckle arm spring constraints loads.Then, referring to the UIC 615-4 regulations on load conditions are combined to get the final five groups exceptional load cases, four groups of special load cases and 13 groups of operational load cases.Tables 1-3 lists the typical cases of supernormal loads and operating loads.

Calculation and Analysis of Static Strength
The conditions of supernormal loads are used to verify that there is no permanent deformation when the bogie frame experiences supernormal loads, which can be used to evaluate static strength of the bogie frame.In the   supernormal main loads conditions, the maximum stress occurs at the welded joint of Cross-side beam connections under lateral beam support beams in the cover plate and cover plate in condition 5, and the maximum value is 295.2MPa; In the supernormal special loads conditions, the maximum stress occurs at the welded joint of Cross-side beam connections under lateral beam support beams in the cover plate and cover plate when the bogie derails, and the value is 256.5 MPa.All these stress analyzed above is less than the yield stress of P355NL1 steel (355 MPa), which satisfies the UIC standards static strength requirements [6].

Calculation and Analysis of Fatigue Strength
According to the framework structure and analysis of static strength, fatigue crack tends to happen on 13 major parts that endure larger stress.Finite element analysis is carried out on these 13 major parts in different conditions, as shown in Table 3. Corresponding maximum stress σ max and minimum stress σ min is found.The mean stress σ m can be found with the standards of UIC: Table 4 shows the calculation results of mean stress and dynamic stress amplitude in strong stress areas.Selective analysis is carried out on critical points, which are selected according to the framework structure.Figure 3/Figure 4 show the overall architecture , and the high stress amplitude of dynamic stress nephogram when the fatigue strength is of the greatest effect conditions, the maximum stress is found at the welded joint of Longitudinal beams and beams, and the value is 79.5 MPa.

Evaluation of Fatigue Strength
Fatigue strength is evaluated with Goodman line.Import the mean stress and dynamic stress amplitude in strong stress areas into the fatigue limit diagram of frame materials (Figure 5), we can find that all these representative and dangerous points are located inside of the Goodman line, which means that all these mean stress and dynamic stress amplitude are less than the fatigue limit of P355NL1 steel.Therefore, the bogie frame meets the design requirements of the fatigue strength.

Modal Analysis
In consideration of the influence of practical operation constrains on the modal, we apply horizontal constraint and vertical constraint on locating seat of axle box rotary arm, and we also apply vertical elastic constraint on the bottom of the axle box.In order to determine whether there is resonance or other vibration mode that against the operating of vehicles, we used the subspace iteration method provided by the ANSYS software to carry out the modal analysis on the frame.In general, there is no high-frequency vibration during the operation of trains,   Base metal so when to analyze framework of free mode, only to take the first six modal characteristics.Table 5 shows the inherent frequency and vibration shape for each modal.
From Table 5 we can find that the first-order characteristics is two side beams nod reversing, which means that the torsional stiffness of the bogie frame is small; this helps trains to overcome the vertical irregularity of lines.The six-order characteristic is that beams in the vertical plane of the first bending with a larger frequency, which means that the stiffness of the beam is pretty big; this helps the beam to bear load and keep connection to other parts.As a conclusion, the vertical stiffness and transverse stiffness of the bogie frame is ideal.Both of them meet the design requirements and the smooth running of vehicles.

Conclusions
According to the UIC615-4 specification, this research analyzes the static strength and fatigue strength of bogie frame for DMUs exported to Tunisia.The result shows that all the stress amplitudes are less than fatigue limit, which means that the bogie frame meets the requirements of fatigue strength.
ANSYS software is used to calculate the inherent frequency and vibration shape of bogie frame, and the results reveal that the torsional stiffness of the bogie frame is small.Trains benefits from the low torsional stiffness to come over lines with vertical irregularity, and bogie frame can avoid other excitation frequency.
With the help of CAD/CAE, people can do the simulation and analysis on bogie frame of high speed train effectively, which contributes a lot to shorten the development cycle, reduce cost and raise efficiency.
This research was financially supported by the National Natural Science Foundation of China (NO.51205017)

Figure 2 .
Figure 2. The FEM model of the bogie frame.

Figure 4 .
Figure 4. Partial cloud dynamic amplitude stress in large stress parts.

Figure 5 .
Figure 5. Fatigue limit diagram for base metal/welded joint of steel P355NL1.

Table 1 .
Main extraordinary load case combinations table.KN Note : K is a safety factor.

Table 2 .
Extraordinary special load case combinations table.KN

Table 3 .
Typical operating conditions load combination table.KN Note : α is roll coefficient is taken as 0.1; β coefficient for the ups and downs , taken as 0.2; m motor quality ; g is the gravitational acceleration.

Table 4 .
Synthesis of the results mean stress/dynamic stress amplitude on the frame big stress area.MPa

Table 5 .
Frame modal analysis results.Two side beams in the same direction in the horizontal plane of second-bending 6 103.2 Beams in the vertical plane of the first bending