20_low-cycle fatigue of turbocharger compressor wheels online prediction and lifetime extension

7/29/2019 20_Low-Cycle Fatigue of Turbocharger Compressor Wheels Online Prediction and Lifetime Extension

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Low-cycle fatigue of turbo chargercompressor wheels online prediction and

lifetime extension

R. Christmann1, F. Lngler2, M. Habermehl3, P.-M. Fonts4, L. Fontvieille5,P. Moulin6

1)-3) Borg Warner Turbo Systems Engineering GmbH, Germany4)-5) Renault SA, France

6) Institut francais du ptrole, France

ABSTRACT:

Compressor wheels on turbochargers in passenger vehicles and commercial vehiclesbelong to the category of highly stressed components which are exposed inparticular to mechanical (or thermo mechanical) cyclic loading during operation,besides all ambient conditions which motor vehicles typically have to cope with.Frequent causes of failure on the compressor wheel are fatigue fractures, wherebya distinction can be made between Low-Cycle Fatigue (LCF) und High-Cycle Fatigue(HCF) as regards the tolerable number of cycles and the damage effects occurring.The LCF range is characterized by the dominant occurrence of plastic strain.This article is intended to present a method allowing the damage to the compressorwheel during vehicle operation to be calculated online and, as a result,

appropriate measures to be taken with respect to charging pressure control toprolong the lifetime or increase the tolerable number of load cycles of the wheel.

Keywords: Turbocharger, Low-Cycle Fatigue (LCF), Compressor Wheel. OnlineLifetime Estimation

NOMENCLATURE

CPU Central Processing Unitd, D Damagedx Partial Distanced2 Compressor wheel outer

diameterE StrainE Strain width rangeFEM Finite Element MethodLife Lifetime in kilometres or hoursn, N Number of cyclesn' Cyclic solidification exponentPOS Probability of survivalp2max Maximum boost pressureR Stress ratioRm Mechanical strengthrpm Revolutions per minuteRp0.2 Yield strength Stress

Ratio of damage and distancet Timeu Turbocharger tip speedu Controller output

x, X Distance

() Delta or Difference()a Amplitude()est Estimated()i Cycle i()max Maximum()mean Mean()min Minimum()sp Setpoint()sum Summarized

(

)tot Total


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1 INDRODUCTIONThe reliability of vehicles in general has gained more and more importance in thecar industry. The very greatest efforts are made to continuously monitor andimprove the quality of the components from their origins to their integration in the

vehicle. All required tests and calculations are conducted in order to ensure theindividual components can endure the stresses the vehicles are typically required tocope with and so guarantee the reliability.Among those, lifetime calculations are performed on critical components in order toestimate the survivability in the run-up. Turbocharger compressor wheels inpassenger vehicles and commercial vehicles belong to this category. Turbochargercompressor wheels are highly stressed components exposed in particular tomechanical alternating stress during operation which can cause LCF fractures. Themechanical stress-strain behaviour is caused by centrifugal-force loading atcircumferential speeds which leads to an exceeding of the yield point and causesplastic deformation of the material.The first section gives an overview of the calculation of the LCF lifetime in order to

allow the reader to better understand the usually performed procedure. It explainsthe required data and the corresponding steps in the procedure for forecasting thelifetime.In the second part of the paper two strategies to extend the lifetime of thecompressor impeller are explained. Both methods for calculating the damage to thecompressor wheel are based on the measured turbocharger speed during vehicleoperation. The problems implementing an online lifetime estimation algorithm isdescribed. A comparison to the offline calculation is presented as well.Moreover, it discusses suitable measures that may prolong the lifetime of thecompressor wheel during operation. The simplifications of the algorithms toimplement them in the vehicle and the resultant compromises are explained, too.The article concludes with a summary and an outlook.

2 LCF OFFLINE LIFETIME CALCULATIONThe lifetime calculation used here is a combination of local and nominal stressconcept for arithmetically verifying the operational strength [1], [2], [3]. Allinfluences on the fatigue behavior are recorded by (stress-controlled) componentWhler curves. Instead of taking recourse to across-the-board nominal stresses infailure-critical cross-sections, the calculated stresses are corrected locally in respectof the plastification occurring and the resultant inherent stresses when subject toelastic-plastic alternating-deformation loading. The procedure is validated on thebasis of numerous field tests and overspeed tests. Figure1 outlines the procedureschematically.

The required input variables for calculation are as follows:Representative driving cycles in the form of turbocharger speed profiles as a loadspectrum with adequately long recording time and adequately high sampling rate.The cyclic flow curve for describing the material behaviour andThe stress-controlled Whler curve of the compressor wheel for mapping the fatigueinfluences.


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Figure 1: Schematic representation of the lifecycle calculation ofcompressor wheels

2.1 Rainflow analysisThe first step is to filter out a damage-equivalent load spectrum in respect of speedcycles from representative data taken from turbocharger speed curves as a functionof time, featuring different characteristics in respect of speed peaks and speedgradients as a function of the travel distance (see Figure 2).Using the statistical Rainflow counting method [4], the speed profiles are dissectedinto discrete damaging events by means of two parameters. The result comprisespairs of local maxima and minima that identify a loading cycle and exert adamaging influence. The filtered load spectrums are combined to simulate theentire assumed vehicle life in order to calculate the lifetime. Information on theorder of loading cycles is lost as the result of data reduction. This is justified inparticular if the driving cycle input contains all characteristic load features.

Figure 2: Example speed-time data of a turbocharger for various travelroutes: a) Country road, b) Highway.

Cyclic load

Cyclic flow curve FEM Simulation

Neuber rule

Stress-strain path

Whler curve HAIGH diagram

Damageaccumulation


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2.2 Determining the linear stressesAfter Rainflow counting, the maxima and minima of the individual turbochargerrevolution speed cycles (rpmi) are converted to corresponding circumferentialspeeds (ui) over the outer diameter (d2) of the compressor wheel and then relatedstress values (i) are computed in linear-elastic fashion as the result of purecentrifugal-force loading with i ~ ui

2.

This stress computation also requires a reference stress that occurs at a specificspeed of rotation (or circumferential speed). This reference is assessed through ananalysis of the particular compressor wheel or on a compressor wheel that isgeometrically similar with respect to the typical defect symptoms (see Figure 3).These (local) reference values are determined and validated a priori by FEMcalculations.

Figure 3: Characteristic LCF damages of a compressor wheel

2.3 Stresses in the cyclic stress-strain curve Neuber ruleApplication of the NEUBER rule [5] allows pre-calculated, ideal, fictitious, elasticoverstresses and understresses to be projected onto the cyclic stress-strain curve(also referred to as flow curve) of the stabilized material state in the RAMBERG-OSGOOD formulation [6]:

n

.pR

.

E

E

+

=

1

202

0020

22

(1)

so that one obtains corrected stresses for elastic-plastic material behavior. The flowcurve is described by the yield strength Rp0.2 and the cyclic solidification exponentn'. A further stress correction is allowed for over-elastic tensile stress. For thispurpose, the cycle with maximum stress amplitude and, thus, with maximumdamage is taken from the temporary load spectrum, and the resultant inherentcompressive stress is calculated following the NEUBER correction and completelinear-elastic relief [7]. In order to describe the strength-increasing influence, thisinherent compressive stress is superimposed additively on the stresses derivedfrom the remaining load cycles.The cyclic stress-strain curve can be determined both by LCF tests on materialsamples or by hub expansion tests as the result of differing centrifugal-forceloading on the compressor wheel itself, which may also be dependent on thecharacteristic defect symptoms of the compressor wheel used.

2.4 Critical stress amplitude a (R = 0) for the same lifetime NThe next step is to transform the corrected minimum and maximum stresses of theload cycles to equivalent amplitudes a and mean stresses mean:

2

minmaxa

= (2)

2

minmaxmean

+= (3)


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The individual cycles are identified by the different R values, the ratio of minimumand maximum stresses, in order to take in account that the average stressinfluence (cycle-dependent) is not a constant:

max

minR

= (4)

Consequently, it is necessary to project the numbers extracted from the loadspectrum, given by (a, mean), along a line of equal lifetime or damage effect in theHAIGH diagram onto the state of the given component Whler curve with knownaverage stress influence. In general, the Whler curve is determined in the case ofpure threshold loading, i.e. R = 0, so that one obtains (a, mean)|R=0. The curve ofconstant damage effect is defined in the HAIGH diagram on the abscissa by thefracture stress (model of equal damage effect analogous to GOODMANN linear slopefor brittle material).

2.5 Damage accumulation at 50 % probability of survival (POS)These transformed stress amplitudes allow the related load changes to be takenfrom the (given) component Whler curve with damage-equivalent stress

amplitudes. The multi-stage load spectrum is converted to a damage-equivalentsingle-stage spectrum with the linear damage accumulation hypothesis afterPalmgren [8] and Miner [9]. Each oscillation or closed hysteresis supplies a damagecontribution that is accumulated in linear fashion. The linear hypothesis assumesthat, in the case of multi-stage loading, each stress amplitude i/2 that occurs nitimes causes a damage share in failure. The damage share is determined for eachspeed cycle i found:

)i(N

)i(n)i(d = (5)

whereby N(i) corresponds to the maximum number of load changes that thecomponent endures at an amplitude ofi/2.The damage shares for the individual cycles are summed in linear fashion. The sumis the result for i cycles of a spectrum

==

=

ki

isum )i(dD

1

(6)

A failure of the compressor wheel is assumed in the case of overall damage D = 1.It is necessary to know the distance for the spectrum in kilometers or hours inorder to state for instance lifetime in operating hours or kilometers. Thus,ultimately, one obtains the maximum travel distance for a 50 % POS in kilometersfor example:

sumD

cetanDis%)POS(Life == 50 (7)

2.6 Lifetime for the required POS on the basis of the Weibulldistribution

The lifetime for another POS is calculated on the basis of the lifetime for a POS of50 %. The lifetime for a POS of 90 %, 95 % and 98 % is determined by default. Inorder to forecast the distance traveled for other failure probabilities, it is possible touse a WEIBULL diagram with known failure slope, determined by overspeed tests.The lifetime for a required POS can be determined as follows:

b

.ln

POSln%)POS(Life)POS(Life

1

5050

== (8)

where b is the slope of the straight Weibull function in the Weibull diagram asresults from experimental testing.


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3 ONLINE LCFFollowing the analysis described above, we now want to design an online damageestimation, in order to control this damage to a desired value. It is thereforenecessary to make various simplification assumptions.The degree of damage is all the higher when the difference between the turbo

speed reached at the end of the transient and the initial turbo speed is high, andthe mean turbo speed during the transient is high. Other operating conditions alsohave an influence (temperature, for example), but to a lesser extent.This phenomenon is explained by the fact that the compressor wheel is subjected toa succession of cyclic stresses leading to plastic micro-deformations and, therefore,component damage. Component damage can be estimated by a linear accumulationof the damage incurred on each cycle (Miner damage) and the application of Whlercurves which gives the damage corresponding to cyclic stresses at constantamplitude, characterized by testing.A simple algorithm detects extrema values of the turbocharger speed and selects atransient or half-cycle when the difference between a minimum and a maximumvalue exceeds a calibrated threshold. The online damage calculation is then applied

to this transient. Overall component damage corresponds to the sum of thissuccessive damage.On a given transient, the extreme and mean stress values on these transients canbe determined. The stress incurred by the component during the transient iscomposed of a term proportional to the amplitude of the transient (differencebetween maximum and minimum turbocharger speed), corrected as a function ofmean stress on the transient (mean between maximum and minimum turbochargerspeeds), according to the GOODMANN principle. The following formula is applied:

m

mean

minmax

R

=

1

(9)

where max

, min

and mean

are the maximum, minimum and mean material stressvalues which, in our case, correspond to compressor speed during the transient,and Rm the mechanical strength of the compressor wheel material.This formula may be corrected to take account of more complex dependencies. Thetemperature of the compressor wheel could therefore be considered as an influencefactor. The temperature can be estimated from the boost pressure gastemperature, calculated using the diabatic temperature increase.

70

75

80

85

90

95

100

105

110

10 100 1000 10000 100000

Number of cycles

Stressamplitude

[%

Figure 4: Whler curve for the compressor for a certain temperature


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In the context of estimating damage, it can be assumed that the wheel temperatureis equal to the temperature of the gas at the compressor outlet, while ignoring thedynamic aspects.For this study, the choice was made to keep to a simple formula and not to takeaccount of temperature in estimating wheel damage. Consideration of morecomplex (but static) phenomena does not affect the estimation and limitation

principles described below.The calculated stress is then projected onto a Whler curve to estimate damage.In the case of the compressor wheel, we can therefore plot in this baseline themaximum number of cycles corresponding to a given stress as shown on Figure 4.The damage suffered for a cycle is therefore the inverse of this maximum numberof cycles.In the case in question, the Whler curve can be inverted by the followingcalculation:

=

b

ai i

e

d1

(10)

where di is the damage occurring during transient i and i is the stress level duringtransient i, calculated using the formula indicated above. Constants a and b arecalibration parameters, i is calculated through an extrema detection software thatwas optimized for limited CPU memory consumption and compatibility withtransient frequency.Finally, the single damages for each transient are summarized to achieve thedamage estimation.The validation process adopted consists of comparing the damage estimated by thesimple calculations described in this section and a more accurate assessmentconducted in the offline LCF estimation. In the case studied, this comparison isillustrated in Figure 5. There is a direct linear relationship between the twoestimations. The damage estimate proposed in this section has been validated inrelation to the results provided by the offline lifetime calculation obtained from thesame data considered as a reference.

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

0.00016

0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 3.50E-06 4.00E-06

Offline damage estimation

Onlin

edamageestimation

Figure 5: Comparison between the estimate of compressor damagecomputed offline and the simplified criterion computed online for various

drive cycles


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The proposed method is optimized in terms of computation time and memory use,with the developments being designed to be implemented in an ECU. Theimplementation of the damage criterion is the crucial point in the strategiesdeveloped. The online damage estimation gets a good correlation with the offlinedamage estimation, only a slope adjustment has to be tuned during some drivingcycles.

4 MEANS TO IMPROVE THE LIFETIME4.1 Corrective actions: analysis/validationFollowing the above analysis, it is possible to act on damage in two ways:

by reducing the amplitude of the transients by reducing the average compressor speed value during this cycle.

We cannot influence the number of cycles as this depends solely on the driver.It may be noted that time derivative parameters do not have a direct influence onthe damage estimate which is derived from static factors only. However, a changein the time derivative parameters can have an indirect effect on damage during a

transient: if the duration of the transient is too short for the system to be stable atthe end

the maximum value attained by the state of the system depends on its inthe time derivative parameters.

To reduce the damage, the following corrective actions were considered: reducing the maximum boost pressure setpoint allowed by the engine

control, called p2max-method calculating a maximum compressor speed on each transient by reversing

the damage rate estimation calculations described above and computingthe corresponding maximum pressure setpoint by the inversion of thecompressor map. This method is called d-method

300 320 340 360 380 400 420 440 460 480 5000

0.5

1

1.5

2x 10

5

Time [s]Turbochargerspeed[rpm]

0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6x 10

-5

Time [s]

TotalDamage[-

]

no limitationP2,max

limitation

d

limitation

Figure 6: Turbocharger speeds without limitation (solid line), with a p2maxlimitation (green/dot and dash line) and with a d-limitation (red/dash

line), and corresponding damage estimation (arbitrary driving cycle)


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The difference between the two methods comes from the fact that the maximumboost pressure setpoint is the same for all the transients in the first method, butdepends on the transient with the second strategy. The difference is illustrated bythe results shown below.In order to validate the selected corrective actions, tests were performed bysimulation with an arbitrary reduction value. By applying the damage estimation

described above, the positive impact of the action in question can be ascertained.The data resulting from these tests were also validated by applying the complexdamage estimate calculation. The comparison between online calculation and theoffline calculation is shown in the points in Figure 5.Figure 6 shows the difference in damage estimation, with and without theapplication of a limit for the two adopted solutions. The effect on the system andthe resulting damage reduction can be observed. For each test, the limitationcorresponds to an arbitrary constant value.

4.2 Damage limitation strategiesAfter constructing an estimate of compressor wheel damage and selecting acorrective action, the loop can be closed by designing a controller to limit this

damage. The proposed structure is illustrated in the schematic below.

Figure 7: Schematic of the calculation

In Figure 7 dsp and dest are the setpoint and estimated damage rate, C is a PI-typecontroller, and u the selected corrective action. Only negative errors areconsidered, if a transient damage is lower than the setpoint, no action is made onthe system and the controller is inactive. This is represented by the block Min(u,0).The damage rate is calculated by the ratio between the damage (dest) measuredover a distance travelled by the vehicle (dx), and this distance:

dx

destdest = (11)

This strategy is difficult to implement as the selected corrective action will have animpact on vehicle operation. It must therefore be accompanied by saturations of

the controller output corresponding to extreme cases not to be exceeded; these areto be determined on fine-tuning the engine or vehicle.The damage setpoint is calculated to enable the vehicle to achieve a certainmileage. This calculation can be done at any time, by taking account of the distancetravelled and the total damage incurred. The following formula is proposed:

totmax

totmaxdsp

tot

esttot

XX

DD

dxX

dD

=

=

=

(12)

where Dtot is the total damage, Xtot the total distance travelled, and Dmax the totaldamage allowed corresponding to a target distance of Xmax.

The selected state variable is distance as it corresponds to the baseline in which thetarget maximum damage is expressed. The estimated damage rate is obtained by

Min(u,0)

spd

dest

+

-

Cu

Xtot

Dtot


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filtering the damage rate per transient (ratio between the damage occurring duringthe transient and the distance travelled during this transient).This strategy is difficult to implement as the selected corrective action will have animpact on the vehicle operation. It must therefore be completed by saturations ofthe controller output corresponding to extreme cases that must not be exceeded;these are to be determined during fine-tuning of the engine or vehicle.

For the strategy based on limiting the maximum boost pressure setpoint, thecontroller output (u on Figure 7) corresponds directly to the maximum pressure(p2max setpoint).For the maximum turbo speed limitation strategy, the calculations are morecomplex as they require that the damage estimation formulae be inverted. Thecontroller output dPI is applied as an input for the inversion calculations in (14) and(15), thus giving:

dPIdspd += (13)

where d is the damage rate used for the inversion calculations, and dPI the setpointcorrection provided by the controller (u on Figure 7).A maximum speed setpoint is calculated continuously by considering that the

minimum speed at the beginning of the transient is equal to the final value of thelast detected minimum (min). The distance travelled since this minimum is recordedas x. The accepted damage for the transient i considered (di) is equal to the productdx. To avoid this value being too low just after detecting the beginning of atransient, value x is limited by a minimum value (it is assumed that the distancecovered during the transient will be greater than a minimum). The damageestimation calculations are then inverted:

=

xlnba

di

1 (14)

and

m

i

imimin

max

R

R

21

21

+

+

= (15)

The maximum speed allowed on the transient i considered is thus obtained.Figure 8 shows a comparison of the results for the cumulated damage obtained withthe two methods. In this case, contrary to Figure 6, the two controllers force theevolution of the total damage to the same value. This is the reason why the twodamages increase almost at the same rate.

0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6x 10

-5

Time [s]

TotalDamage[-]

no limitationP

2,maxcontrol

d

control

Figure 8: Comparison of the two methods of limitation on the turbo speedand damage (OEM specific cycle)


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0 0.5 1 1.5 2 2.5 3

x 105

0

0.5

1

1.5x 10

-5

Distance [km]

d

[1/km]

setpoint

P2,max

control

d

control

0 0.5 1 1.5 2 2.5 3

x 105

-0.5

0

0.5

1

Distance [km]

TotalDamage[-]

P2,max

control

d

control

0 0.5 1 1.5 2 2.5 3

x 105

1500

2000

2500

3000

Distance [km]

P2,maxsetpoint[hPa]

0 0.5 1 1.5 2 2.5 3

x 105

0

2

4

6x 10

-5

dsetpoint[1/km]

Figure 9: Simplified model with damage rate control on a test conductedfor 100 000 km of urban driving, followed by 100 000 km of highway

driving and a return to urban driving

Simulations representative of a vehicle lifetime have been performed to validate thedeveloped methods. Damage is controlled to obtain a maximum total damage valueof 1 after 300 000 km, which guarantees correct compressor operation whiledegrading its performance levels as little as possible. The Figure 9 shows thebehaviour of the controllers (p2maxmethod in green/dot and dash line, and d-method in red/dash line) for changes in the drivers behaviour.The two strategies exhibit similar performances. In both cases, limitation can beobserved up to 100 000 km for driving causing significant damage. Then, over the

following 100 000 km, an increase in the setpoint rate is due to driving causinglittle damage. The system is safe and does not require any modification. Thestrategy has therefore no action on the system because positive errors are notconsidered (see Figure 7). Over the final 100 000 km, the return to urban drivingcausing significant damage leads to limitation being reapplied after a short transientperiod. It may be noted that the system is less stressed at the end of the simulationthan at the beginning, whereas the driving cycle is identical. This is due to theintermediate period during which the distance covered was high but the damageincurred remained low. A higher damage rate at the end of the vehicle life is thusaccepted. If the return to damaging conditions was made later, the system couldend up at a final damage value of less than or equal to 1 even with normalcompressor working conditions. The limitation strategy would automatically bedeactivated by increasing its command to ineffective values.


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5 CONCLUSION AND OUTLOOKTo derive good offline LCF estimations there is a lot of input data required.Characteristic turbo charger speed profiles, geometric, material data and spinningtests which do result in Whler curves are needed. A high effort is needed to deriveall the required input data, but they are essential to give a good LCF estimate.

Calculation methods today at BorgWarner are very precise due to long experiencein this field and a lot of correlations of the offline calculations with the real world inthe past did lead to an improvement in the estimations algorithms used. Differencesof offline estimations and real world failures do mainly occur due to imperfections ofthe casted compressor wheels, or because of turbocharger speed profiles which donot represent the application in reality.Compared to the very complex offline LCF calculation a simplified online LCFcalculation method is described. Limitations of calculation time and memory in anECU cause the algorithms used to be less complex. Two methods to extend thelifetime of a compressor wheel during operation are presented. Both strategiesimpact the drivability of the vehicle in a different way and usually extend thecompressor wheels lifetime in a different way, too. But the d-limitation method

minimizes this impact thanks to a boost pressure reduction to the most damagingtransients only.In addition a control algorithm is presented which leads to a similar damage rate forboth strategies presented.The speed sensor commonly used to limit overspeed gets here some new functions:

a) extending the reliability of some severe applicationsb) applying preventive service possibilitiesc) reducing the occurrence of failures during the regular operation of an engine

Instead of applying online LCF calculation and limitation strategies in the vehiclesthe use of milled compressor wheels made of aluminium instead of cast aluminiumwheels may be advisable as the basis of these results. The service life of suchmilled compressor wheels made of aluminium is longer than that of the aluminiumcast materials used.

For even more critical vehicle applications, BorgWarner also offers compressorwheels made of titanium primarily for the commercial vehicle sector.

Authors 2010

6 REFERENCE LIST[1] Buxbaum, O.: Betriebsfestigkeit, 2. erw. Auflage, Stahleisen Verlag, 1992[2] Hnel, B. et al.: Rechnerischer Festigkeitsnachweis fr Maschinenbauteile, 3.

Auflage, Forschungskuratorium Maschinenbau, 1998[3] Haibach, E.: Betriebsfestigkeit - Verfahren und Daten zur Bauteilberechnung,

VDI-Verlag, 1989

[4] ASTM E 1049-85 (Reapproved 1997): Standard practices for cycle countingin fatigue analysis, in: Annual Book of ASTM Standards, Vol. 03.01,Philadelphia 1999, pp. 710-718

[5] Neuber, H.: Theory of stress concentration for shear-strained prismaticalbodies with arbitrary nonlinear stress-strain-law, Journal of AppliedMechanics, Volume 26(4), pp. 544-550, 1961

[6] Ramberg, W. and W. R. Osgood: Description of stress-strain curves by threeparameters, Technical Report No. 902, NACA, 1943

[7] Issler, L. Ruo, H. und P. Hfele: Festigkeitslehre Grundlagen, 2. Auflage.Berlin, Heidelberg, New York: Springer-Verlag, 1997

[8] Palmgren, A.: Die Lebensdauer von Kugellagern, Zeitschrift des VereinsDeutscher Ingenieure, Band 68, Nr. 14, 1924, pp. 339-341

[9] Miner, M. A.: Cumulative Damage in Fatigue, Journal of Applied Mechanics,Vol. 12, No. 3, 1945, pp. 159-164.

20_low-cycle fatigue of turbocharger compressor wheels online prediction and lifetime extension

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