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Fatigue Life Prediction of a Railway Bogie underDynamic Loads through SimulationSTEFAN DIETZ a b , HELMUTH NETTER b & DELF SACHAU ba Technical University Berlin, Aerospace Institute , Marchstr. 12, Berlin, 10587, Germanyb Institute of Robotics and System Dynamics , Deutsches Zentrum für Luft- und Raumfahrt(DLR), Wessling, 82234, GermanyPublished online: 27 Jul 2007.

To cite this article: STEFAN DIETZ , HELMUTH NETTER & DELF SACHAU (1998) Fatigue Life Prediction of a Railway Bogie underDynamic Loads through Simulation, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, 29:6,385-402, DOI: 10.1080/00423119808969381

To link to this article: http://dx.doi.org/10.1080/00423119808969381

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Vehicle System Dynamics. 29 ( 19981, pp. 385-402 0042-3 1 14/98/2906-385$12.00 O Swets & Zeitlinger

Fatigue Life Prediction of a Railway Bogie under

Dynamic Loads through Simulation

STEFAN DIETZ 'v2, HELMUTH NETTER and DELF SACI-IAU

SUMMARY

For dynamically loaded lightweight structures fatigue strength is an important design criteria. In this paper a new method to predict fatigue lifetime is shown. This is based on the combination of frequency domain and time domain calculations, which allows lifetime prediction with reduced computational effort. The method is implemented to work in a concurrent engineering software environment together with a computer aided design (CAD), a finite-element-method (FEM) and a multibody system (MBS) program. The benefits of the new approach are demonstrated by application to the bogie of a freight locomotive. The dynamic loads acting on the bogie are computed by multibody simulation. The bogie frame is considered as an elastic body of the MBS and the highly nonlinear wheel rail contact is modeled quasi.-elastically. For the ride on a straight track the equations of motion can be linearized and the covariance matrix of the loads is calculated. The ride through a ramp is simulated by using the nonlinear differential equations. FEM yields the stresses in the most stressed locations of the bogie depending on the loads calculated by multibody simulation. Based on these stresses the fatigue life prediction is carried out in the MBS post-processing program FATIGUE.

1. INTRODUCTION

Savings of energy and material are currently design drivers towards lightweight vehicle constructions. Such vehicles as a consequence are more likely to be faced with vibrational and fatigue life problems. The past design process, in which small steps of improvements are made with many trial and error experiments, field tests and prototyping, can not be maintained. New requests are right-first-time to drastically reduce the time-to-market avoiding long test series with protoypes, [7]. These strategies require more and more to develop and design new systems by computer using CAE (Computer Aided Engineering) software.

Within CAE computer simulation and numerical analysis play a central role. For the analysis of the dynamical behaviour of ground transportation systems multibody software packages are generally accepted.

One major advantage of MBS-software tools from their very beginning versus other kind of simulation software was their requests for various analysis features,

' Technical University Berlin, Aerospace Institute, Marchstr. 12, 10587 Berlin, Germany. 2 Institute of Robotics and System Dynamics, Deutsches Zentrum fur Luft- und Raumfahrt (DLR),

82234 Wessling, Germany

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386 STEFAN DIETZ ET AL.

Fig. I . MBS-analysis features.

see Figure 1 . Today the request for the features of MBS-software, in particular for vehicle system dynamics, is complex: Firstly, computation and evaluation of system behaviour requires detailed analysis and post-processing to determine vehicle stability, curving behaviour, comfort in presence of disturbances such as wind gusts or track irregularities and response for defined manoeuvres. Secondly, as results of MBS-simulations, principal trends are not any more sufficient nowadays. In many situations the exact correspondence with the real vehicle in Iield tests is required. Verification as well as validation of the models and the software are prerequisites for simulation to be used for system qualification and to reduce the amount of field and acceptance tests, [9].

Due to the tendency towards lightweight structures, the elastic deformations of the bodies in the MBS can no longer be neglected. Small deformations can be takcn into consideration by using results from finite element programs. The pre-processor FEMBS, [16], calculates the volume integrals for the equations of motion of flexible bodies to be used in the multibody simulation program SIMPACK [8], see Figure 2.

'The finite element method is a valuable tool for vibration and stress analysis of structures. A weakness of the approach lies in the assumptions made for the boundary conditions. Reliable information is generally available for static situa- tions, but many mechanical systems are loaded dynamically. In such cases the determination of time varying boundary and load conditions can be determined by multibody simulation. MBS-simulation delivers realistic toads for the analysis of stresses and life cycle calculations. The dynamical behaviour of the vehicle, the excitation by the track, the vehicle velocity and other data, defining operational conditions influence these loads, see [6].

An important task is the identification of the most stressed or critical locations. For that, the loads and accelerations for some time steps can be transformed into a FE-load vector by the MBS-postprocessor FEMBS-'. Subsequently a FEM calcu- lation is performed for the component under consideration and the visualisation of

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FATIQUE LlFE PREDICTION

. / . . . . . . . . .:.:.:.:.,.:<.:;*. . . . . . .. < > ,: .. ??,% ...+< :.??$.? 1; -2. ;?;;M B:S-prep[ocesso&g% Ma K <?&.,

. . . ,-,. ... : -A <:.;:.::..:.. . . .-. ........... ;-. I : : ..... SID

ANSYS

FEMBS

FATIGUE

.....................

Fig. 2. FE-MBS interfacing scheme.

the stresses indicates the critical locations. For fatigue life predictions the stress history for the most stressed and therefore critical locations of the components is important. In order to obtain realistic results one has to consider the whole operation of the vehicle. In order to consume less computer time wedecompose the whole operation into operational conditions, asriding on a straight track or passing a ramp for instance.

The ride on a straight track causes only small dynamic toads and movements, therefore the force laws and the wheel-rail-contact of the MBS-model can be assumed as linear relations. In this case the MBS- calculation can be treated as a covariance analysis, by which the whole operational condition is simulated in one solution step. As MBS input data, the spectral densities of the track irregularities are required. Loads acting on the bogie are obtained as covariance matrix. In contrast to the operational condition mentioned above, riding through a ramp for example produces large dynamic loads. For such single irregu- larities the force laws and the wheel-rail-contact must be considered nonlinear. The MBS calculation is performed as a time integration and results in forces and accelerations for each time step.

The distinction between linear and nonlinear operational conditions is useful to avoid large MBS-simulation times, because there is no need for simulations over long distances. MBS-simulations are performed for all operational conditions separately. Information about the length of the straight track, the number of switches and the frequency of other possible situations are given subsequently , inside the MBS-postprocessor FATIGUE. In FATIGUE the magnitude of damage for the critical locations is determined for all operational conditions separately and they can be superimposed to the total damage value in a final step. As the

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STEFAN DIETZ ET AL.

Fig. 3. Flexible body; 3rd eigenmode: vertical bending at 52 Hz.

calculation of damage values from the MBS-results takes only a few minutes, the investigation of a multitude of situations is feasible.

2. FE-MBS COUPLING

2.1. Flexible Bodies in Multibody Sytems Thc coordinate systems shown in Figure 3 will be used to describe the body's motion. There are two systems, the inertial frame and the body fixed reference frame. In general all vectors will be resolved in the reference frame. The motion of a representative material point P with respect to inertial space is described as

In this representation the body motion is given in terms of the reference or rigid body motion as described by r ( t ) and c and in terms of small dispIacements u(c,t). A Ritz-approximation of the deformation variables u(c,t), is used

with the unknown modal coordinates q(t). Here eigen modes and static modes calculated by the finite element code ANSYST" are used as interpolation functions @(c>

The starting point for the development of the O(N)-formalism in SIMPACK is a set of equations of motion for the flexible bodies. Introducing the Ritz-approxima- tion into Hamilton's principle and using the fundamental theorem of variational calculus, the equations of motion result as follows

Matrix M contains inertia terms, K stiffness terms, k gyroscopic terms, and h the applied forces. They depend on the acceleration a, the angular velocity w , the

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FATIQUE LIFE PREDICTION

Fig. 4. Dynamically loaded elastic body; f', to j4 secondary suspension forces 1; to primary suspension forces; 1st eigenmode: torsion at 42 Hz.

angular acceleration h and the orientation A of the bogie frame. The flexible body data required to generate the MBS-equations are those, which are needed to compute the elements of the mass matrix, the gyroscopic t cms and the stiffness terms. To compute such data the pre-processor FEMBS has been developed, [16]. The data are stored in the standard-input-data (SID) file, [17]. The relative orientation matrix A j j ( q ) is developed up to linear terms i n the displacement coordinates, [16]. While reading the SID file SIMPACK automatically assigns the MBS-marker to the corresponding FE-nodes.

2.2. Possibilities for Stress Calculation

2.2. I . MBS-postprocessor FEMBS - ' The time history of all forces and torques acting on the flexible body are calculated during the MBS simulation. In the postprocessor FEMBS-' the mark- crs on the body are checked and the forces resulting from joints, force laws or constraints at each marker are collected and transformed in the body coordinate system at each time step, [ I ] . The post-processor FEMBS-' generates files to be used in:

a ANSYST": Some time steps are selected by the user for which the FEM load vector is generated ready to be used in quasistatic finite element calculations. The FEM-calculation delivers the stress distribution for the whole body under consideration. From these results critical locations with maximal stresses in the body can be found.

a FATIGUE: The time histories of loads and body accelerations as calcu- lated by the MBS-code are written to a file, to be used for life prediction. The MBS-loads are transformed into stresses at some critical locations.

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390 STEFAN DlETZ ET AL.

For linear systems the covariance matrix of the forces can be calculated directly by SIMPACK.

2.2.2. MBS-postprocessor FATIG WE Because of the large number of degrees of freedom, approximately 100000 for a bogie frame, stress calculations in the FE-code are not practicable within each time step. Another method is implemented in FATIGUE, which takes advantage of the linearity of the FE-model. Loads and accelerations, acting on the bogie, can be defined in SIMPACK as MBS output vector y and the stresses a depends on them, via the stress load matrix B

u ( c , t ) BG) The stress load matrix is calculated for those locations, for which the FEMBS-'- ANSYST" post-processing indicates high stresses. It contains column by column pre-calculated stresses for unit loads, unit accelerations and eigenmodes. The elements of the MBS-output vector are time dependent weighting factors for them. In [2] one possibility for pre-calculating stresses is described.

For linear operational conditions the MBS-output is given by the covariance matrix

The time independent stress load matrix allows the transformation of P ( y ) into a stress covariance matrix

3. FATIQUE LIFE PREDICTION

The majority of information about the stresses has to be reduced, because one is only interested in the most stressed locations of the bogie frame and the magnitude of damage for these locations. Therefore, a procedure proposed by [ I 31 is used in FATIGUE, see also [14].

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FATlQUE LIFE PREDICTION

3.1. Stress Evaluation in the Time Domain For the whole time history of stresses the range between the maximum and the minimum values of stresses is divided into equidistant intervals or classes n,, see Figure 5a. Considering a nonlinear stress strain relationship E = f ( a ) , the classi- fied time history of stress can be mapped into the stress strain plane. Figure 5b shows 3 closed stress strain hysteresis loops which are mainly responsible for the fatigue of the material and therefore counted by the rainflow method, see [3]. The total number of hysteresis loops or cycles N,, the start of the cycle n,, and its reversal point n, is stored in a Markov matrix R , i n which each element

( r n ,,,. ntr2 ) equals to n , , see Figure 6a. For harmonic processes it is known that the

stress amplitude limit lim a, is decreasing for increasing steady state stress om. The gradient of this linear relationship can be calculated for instance from a Smith' fatigue strength diagram, shown in Figure 6b. Assuming this relationship also for stochastic processes V depends on the material and the stress evaluation method. For stochastic loaded steel constructions and the rainflow stress evalua- tion, a *-value of 0.3 is recommended in [13], see also [5]. The present stress amplitude a,, and the steady state stress can be calculated from the Markov matrix by equation

Each cycle of the process stored in the Markov matrix will be transformed by

into a cycle, in which the steady state stress is zero and the stress amplitude is magnified. By the magnification of stress amplitudes the damaging effect of the steady state stress components is taken into account. Cumulative frequency distributions which describe an equivalent stochastic process whithout steady state stresses are the result of the transformation given by Equation (10).

Fig. 5. Stress evaluation with the rainflow method: Time history of stress (a) divided into 5 classes n,; time history mapped into the stress strain plane (b) with 3 closed hysteresis loops counted by the rain flow met hod.

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392 STEFAN DIETZ ET AL

Fig. 6. Calculating the data for amptilude transfornution, see equation (8) to (10): (a) From the Markov matrix, which results from the process shown in Figure 5 and (b) from Smith fatigue strength diagmm.

3.2. Stress Evaluation in the Frequency Domain Although the stress covariance matrix contains the mean square values of the stresses, i t is possible to calculate the number of stress cycles. Therefore a probability distribution function describing the random process is assumed. Its parameters can be calculated from the stress covariance matrix, see below. The Rayleigh distribution f R ( a , ) and the Gaussian distribution fc(n,,,) were combined multiplicative by [lo] and [I21 to describe the distribution of the steady state stresses and the stress amplitudes. The integration over the product f , fc yields the number of cycles

Therefore the range of steady stresses and a~nplitude stresses range is divided into classes r r , , , and , I , , again. In Figure 7 thc integration is taken over the dark grey area. This yields the number of cycles 11, for the class n,,, = 2 and n,", = 9. The integration for each class results in a matrix in which the number of cycles is

Fig. 7. Probability distribution for Ihe steady state stresses and the stress amplitudes.

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FATIQUE LIFE PREDICTION 393

stored for each class. This matrix also can be mapped to a cumulative frequency distribution by equation (10) where (1, is set to 0.7 [13]. The parameters of Equation (1 1) will be derived subsequently from the statistical characteristic values

If the first and second derivatives of the forces are included in the MBS-output vector so, s2 and s4 can be taken from the main diagonal of the stress covariance matrix

The frequency of stress peaks N, and increasing zero passages No results in the irregularity value i and the width of the frequency band v, which are parameters of the distribution functions f, and f,.

3.3. Calculation of Damage Values The calculations described above are performed for all critical locations of the bogie frame and all components of the stress tensor. The rainflow method as well as the Kowalewski method combined with the amplitude transformation (10) are resulting in cumulative frequency distributions. As the FE-Model of the bogie frame consists of shell elements only the cumulative frequency distributions of the normal stresses q, and uv and the shear stress rxY are considered subsequently. In usual fatigue strength-diagrams, see figure 6b, the stress limit lim u is derived from fatigue tests which are based on harmonic processes. Therefore all these distributions will be mapped to an equivalent harmonic process which causes the same damage to the critical locations as the equivalent stochastic process, see Figure 8 and

1 a, = U; .

-0.787 (I 7, 2.0. 106 1'6.5 ['Jm] ( nl 1 - -

U n

From the shape u of the cumulative frequency distribution and the duration n of the operational condition a factor l/(un) reducing u ' to a is calculated. The

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394 S E F A N DlETZ ET AL.

stochastic process cf d harmonic process

Fig. 8. Mapping the equivalent stochastic process to an equivalent harmonic process using cumulative frequency distributions (cfd).

stress limit lim u can be taken from a usual fatigue strength-diagram, where lim u is given as a function of the stress amplitude 5 and the static stress star u. The present stresses and the stress limits are known yet, so the damage values can be calculated. In FATIGUE, damage values for the normal stress

stat ux + Tf = lirn ux

and the other elements of the stress tensor are calculated separately. At weldings for example, where the stress limit depends on the direction of stresses, this procedure is useful. The damage value D,, is a measure for the magnitude of damage, resulting from the normal stiess ux. Information about the correlation of ur and a, for instance, is given by the correlation coefficient ex,,

Those P , , ~ can be interpreted as average phase angles between the elements of the stress tensor and they are required to meet the equilibrium of the stress compo- nents. For a single location of the bogie the damage value

is derived from the maximum shear strain criterion [13].

4. LIFETIME CALCULATIONS FOR DIFFERENT OPERATIONAL CONDITIONS

4.1. FE-Model of the Bogie Frame The welded bogie frame of the freight locomotive is approximately 5.5 m long and 2.4 m wide and its mass is about 2200 kg. The corresponding finite element model

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(Ah'SYSf"I const?lu nf c)2m) f i n ~ l c \hell clcmcnts. \ re F l y r e 3. Cnnstr;~tnt cquatlon\ ;ire u\cd tn d ~ ~ ~ h u r c the exrental forces which , I ~ I on the h o p e The FE model h,l\ approx~rn;~lcly .50(XK) dcprees of freedom To enwre n r c n l ~ \ t ~ c dlrn~rnl- cnl m ( ~ l c l . the lirst tlircc etgcnrnorlc\ o f [tie unrcsrralnetl hoglc are con\ldcrcd tc) s c ~ u p the eclunllons of niot~on fur [he rnul~thncly s ~ m u l a r ~ o n wtth SIXIPACK [I61 Thc\c arc tho turuon u ~ t h a irt.r\uency of 42 HI. see F ~ p u r c 4, vert~cal b e n d ~ n ~ u ~ t h s frcqt~cncy o f ahc~ut 52 Hi-. ~ C C fipurc 7 and Inleral k n d ~ n e u ~ t h a lrcyucncy I I ~ 43 HI. (nnt \hrrwnl

4.2. MRS-.Vlodecl of the Freight Lwornntive and the Whect- Rnil System The freipht lnromorive has heen mdcl led with !he aid (of' SJMPACK t i h r a ~ c l c m c n ~ s like furce clcmcnrs and joints. Rie hnpie frames were dcscrihed as elastic hrdics usiny the darafrnn the SID-file as deccrihcrl nhrrve. Sevcral linear spring and dampcr clemcnrs dcscnbe theprimary and sccontinry suspension unils. The hump tops and (he vi~cous dnmprs arc rcprescntcd by nonlinear charau~cristics. Thc rnulrilwcly rnrxlel of the freight I ( s t~mnt ive consisls of nine ripid hudics (car htd?-. four wheel sets and frjur drivinp morors) and the two clnstic hndies (lhc hopic frames), see Figure 9.

The IWO h x i u fcatures nf !he rai1uri)' functinnali~y rn SIMPACK arc h l th , thc

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396 STEFAN DlETZ ET AL.

description of the track to simulate arbitrary maneuvres and the modelling of the contact between the interface of wheel and rail, [15]. Common measured track datalike curvature and superelevation can be used to obtain all necessary track quantities. A special track joint positions each wheel or wheelset along the track at an arc-length s ( t ) and also permits the simulation of acceleration and braking maneuvres in curves. The general wheel-rail contact 'element calculates the normal contact of the wheel -rail interaction as kinematical contraint of the relative vertical displacement of the wheel with respect to the rail. Multiple contacts between one wheel and rail are allowed. To investigate wheel lifts or impacts caused by short contact separations the normal wheel-rail contact can also be modelled by a one-sided spring-damper element accepting increased CPU-simula-

- - - -- -

I 1

~ Q ~ ~ ~ L B V ~ U O I Y nurcuvot on s ~raau, Railway Standard Track: ) ~ o BtBn Chrnge o f frmak Curvaturn

Bttslpht S ~ s r a l b v r t i r m Ramp

i Tap view bf t rack Rotatlon about Inner Rall

= 3.83666371)+02

I i 1

1 3.16478840+02 / 5.530516ib+Oi

i

! -7.00009060-02

s 1.0888BB8D-01 I

I = .WWWOWOO j

3.81243400-Oi

vl.1 = .OOWWOD+00 ._..-._I._II._I._..-.-...-..-. ! -

I

Y ! . . .

.000OOOOO+~O

= 7.1200000(3+02

u = 1.0000000D-01

. __ -----.- - .- ----- ...... -. i Fig. 10. Top view of the curved track and progression of superelevation of the track and associated

parameters.

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FATIQUE LIFE PREDICTION 397

tion time compared to the constrained formulation because of a high value of contact stiffness. The calculation of the creep forces is based on Hertzian contact properties and uses Kalkers code FASTSIM (1983) or any other creep law defined by the user. 'The elasticity of the track is taken into account by a rigid sleeper below each wheelset with three degrees of freedom with respect to the track interconnection to inertial system by linear spring and damper elements.

As a total the complete wheel-rail system model includes 64 joint states with 8 of these states restricted by constraints, 6 states describing the elastic deformation,

Lateral Deviation of Wheelsets 1 Laadlng h d u t : Bogie Front 2 TmUlngWh.da.t: 8-1. Front 3 Lsadlng Wheelrst: Bogla Rear I TmlllngWhnlaat: Bogk Fmnt

.OO 5.00 10.00 1b.W 20.00 25.00

time [s]

Primary Suepenrrion Bogie Front: Lateral Forces 1 Leadlng Wheala.1: Rlght 2 Leadlng Whulmd L.R ................ ............. """ * ...........................

time [s]

Primary Suspension Bogie Front: Vertical Forces 2 Ludtng WheeL.1: Rlpht 2 Leadlng Whrolrot LOR

-IOD.O I .OO 5.00 10.00 15.00 20.00 25.00

time [s]

Fig. I I . MBS-simulation results from SIMPACK: Freight locomotive passing a curve; V = 140km/h; track gauge 1435 mm; 1:40; FASTSIM; p = 0.4; R = 712 m; Rail Profile: UIC-60.

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SEFAN DIETZ ET AL.

Fig. 12. MBS-postprocessing with FEMBS-' and ANSYST": Stress distribution for the whole bogie frame at t , = 5.87 sec; Locations marked as 1 and 2 were investigated with FATIGUE.

4 states describing dynamical force elements and 8 algebraic states representing the constraint forces of the constrained wheel-rail contacts.

4.3. Simulation Results

4.3.1. Passing a curve Passing a curve is a critical loading condition for the bogies, because of their torsional weakness. Investigation of this typical manoeuvre is only possible with nonlinear time simulation. The total length of the curve is 480 m the radius is 712

stress at location 1 A,/. 4 u

1

stress at 1ocation 2 / 0 5 10 15 20 25

Fig. 13. MBS-postprocessing with FATIGUE: Time historys for the normalized stresses uis2 at the locations 1, 2, see figure 12.

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FATIQUE LIFE PREDICTION

Power Spectral Density

V = 140 kmth

i 1

DB - Lateral Hlgh

Y

---.3.--. DB - Cross Level High

Fig. 14. Spectrum of stochastic excitation.

m. On curve entry the superelevation of the track reaches its maximal value of 160 mm on a straight ramp and decreases symmetrically at the end of the curve, see figure 10. The irregularties of the track in lateral and vertical direction are negelected. The freight engine passes the curve with the operating speed of 140 km/h. As Figure 1 1 shows that the outer wheels of the leading wheelsets are flanging after transition into the curve, whereas the trailing wheelsets are almost in center position. The time history of the lateral forces acting in the primary suspension between the bogie in front and the leading wheelset indicate approxi- mately symmetric behaviour with some overshoot at the transition into the curve segment. The corresponding vertical forces reflect the dynamic influence of the sway mode of the car body directly excited by the ramp input of the supereleva- tion of the track. The distribution of the Mises stresses is shown in Figure 12. Two locations, where the stresses are comparatively high, were selected for investiga-

Table I . Riding on straight track: RMS values for dynamic loads in vertical direction.

Force (see figure 4) RMD [kN]

secondary suspension f~ 1.939 f2 2.125 13 1.950 f4 2.138

primary suspension fs 2.653 fs 2.630 f 7 2.733 f~ 2.767

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400 STEFAN DlETZ ET AL.

Table 2. FATIGUE results.

critical location D/ Dm,,, for passing ride on straight track curves (every 10 km)

I 0.79 1.00 2 0.42 0.6 1

tions with the MBS-postprocessing program FATIGUE. The time histories for the stresses were calculated for these locations using the stress load matrix and they are shown in Figure 13. Based on these stress time histories the fatigue life calculation for the operational condition passing a curve was performed.

4.3.2. Riding on straight track In order to apply linear system analysis a method based on harmonic balance is used for the quasi-linearization of the nonlinear wheel-rail-contact kinematics. The freight locomotive rides with a reference velocity of 140 km/h on the straight track. For this velocity the covariance analysis is performed. The track excitation is defined by standard power spectral density functions for the vertical, lateral and cross level track irregularities, see Figure 14. As MBS-output quantities y the vertical forces of the primary and secondary suspension are defined. From the covariance matrix P(y) RMS values are calculated and listed in Table I . The R M S values are a little smaller compared to the dynamical primary suspension forces, caused by passing the curve, see Figure 10. Nevertheless the damage values calculated from the straight track ride are greater than those calculated from passing a curve, see Table 2. This is because vibrations from the straight track ride are present permanently, whereas the curve ride occurs less frequently.

'The results shown in Table 2 depend on the frequency of operational condi- tions. We have assumed that a curve as shown in Figure 10 occurs every 10 kilometers. Changing these assumptions will also change the damage values for the investigated critical locations. Of course in the real vehicle operation we have to consider a larger number of operational conditions. They are for instance passing different types of switches, different curves, slightly or heavily disturbed tracks and others. For MBS-simulations these operational conditions and their incidence have to be tabulated as input data, see [4,1 11. Because their influence to the damage at some locations of the bogie is different, we have to distinguish between more or less important operational conditions. This distinction requires an experimental verification of the calculations described above.

CONCLUSIONS

The dynamic loads acting on a railway bogie frame are calculated from a MBS-model of a freight locomotive, at which the bogie frames are modeled as elastic bodies. The MBS-post-processor FEMBS-' transfers these loads to the

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FATIQUE LIFE PREDICTION 40 1

FE-code, in which the stress distribution for the whole bogie was calculated and high stressed locations were indicated. The stress load matrix for two of those locations were used within the MBS-post-processor FATIGUE. This enables the calculation of the time history of stresses to be performed using multibody simulation results. The advantage of the procedure proposed here, is the possibility to perfom fatigue lifetime calculations without simulating the whole time-span of vehicle life. Nevertheless all relevant operational conditions and in particular their frequency can be taken into account. The methodology described in this paper is general. So other lightweight constructions as e.g. aeroplanes or cars can be investigated with the developed tools FEMBS - ' and FATIGUE.

ACKNOWLEDGMENT

Thanks go to DUEWAG AG Main Line Rolling Stock Krefeld-Uerdingen for providing realistic FEM and MBS model data. We also would like to thank Dr.-Ing S. Stichel for preparing the basics of the fatigue calculations and inspiring discussions.

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