FATIGUE ANALYSIS OF CAST COMPONENTS IN WIND TURBINESLOCAL NOTCH STRAIN APPROACH VERSUS NOMINAL STRESS APPROACH

P. Dalhoff*, A. Dombrowski*, H. Idelberger**, M. Morr*** Germanischer Lloyd Windenergie GmbH, e-mail: dal@germanlloyd.org

** University of Siegen, Institute for Mechanical Design, e-mail: idelberger@ik.mb.uni-siegen.de

ABSTRACT: Determination of wind turbine loads, especially fatigue loads has become more and more extensive overthe past years. Whereas fatigue load spectra were derived from mean load values of single load cases years ago, it iscommon practice nowadays to perform complete numerical simulations considering aero-elastic structures and three-dimensional turbulent wind fields.The so derived fatigue loads are the basis for the fatigue analysis of all dynamically-cyclic loaded wind turbine structures.It is still common practice to reduce the data amount of fatigue loads before starting the fatigue analysis. The result of thisare rainflow counted load spectra where essential information about load phase relations, mean values, frequency, etc. arelost. Assumptions are necessary to account for this.A local notch strain approach will be presented using the load time series. This will be compared with the nominal stressapproach and application of load spectra. Physical influence and consideration of practical aspects related to castcomponents like cast quality grade, surface roughness, size effect, etc. will be discussed.

Keywords: Certification, Fatigue, Large machines, Loads, Materials

1..INTRODUCTION

Cast Components have become more and morepopular for the design of wind turbine machinerycomponents over the past years. Nowadays not onlyrotor hubs or tubular adapters are cast, but also mainframes, axles and other structures. Casting allowscomplex geometries and smooth transitions and can becost effective in case of large production numbers incomparison to welded structures.

The most widely used cast material is spheroidalgraphite cast iron EN-GJS-400-18U-LT, formerdesignation GGG40.3. This material is comparable witha structural steel in its static strength. The fatiguebehaviour of this material is tolerable against fatiguedamage due to the spheroidal shape of the enclosedgraphite and the ferrite texture.

Fatigue strength verification of the components design isa complex task. The complex geometry can beconsidered by using Finite Element Models. This is stateof the art. The special characteristics of cast componentslike cast quality, size effects, surface roughness etc. areto be considered also. The cast quality is a generic termfor the amount of faults like shrink holes, dross, chunkygraphite and texture degradation. A lot of these factorsdo influence the fatigue strength of the cast components.The Regulations of Germanischer Lloyd (GL) [4] giveclear advise how to achieve the fatigue strength bycalculation of synthetic S/N- curves using the“Leitfaden für eine Betriebsfestigkeitsrechnung” [2] orcomparable. In [3] and [6] further fatigue life approachesincluding synthetic S/N-curves are given.

In the following the methods of nominal stress approachand local strain approach are briefly described.

2 NOMINAL STRESS APPROACH

In the nominal stress approach the stresses respectivelystress spectra are calculated for a nominal section, i.e. across section where no stress concentration occurs. Sincethe notch effects are not included in these stresses theyhave to be included on the strength side. The fatiguestrength, i.e. the nominal S/N-curve can be eithersynthetic or measured. Within calculation of a syntheticS/N-curve notch effects will be considered using therelevant notch geometry (notch radius and diameter orthickness of the component).

This definition of a nominal stress of course requires thata cross section exists in the structure that is to beinvestigated. In case this is existing one has a simplemethod to calculate fatigue life, since calculation ofnominal stresses is in general easier than the calculationof local notch stresses. Looking into reality, e.g. on arotor hub one will find a complex geometry but not anominal cross section. Since then application of thenominal stress approach in its original form is notpossible the following modification is applied:

Instead of the nominal stresses the local notch stresses inthe structure are calculated. The synthetic S/N-curve isthen calculated with the assumption that there is nostress concentration, i.e. the notch radius is assumed tobe infinite. This is done since the stress concentration isalready considered in the stresses.

3 STRAIN LIFE APPROACH

In the strain life approach the stresses (time series) arecalculated by application of load time series on thestructure. The stress analysis is performed by

considering linear elastic material behaviour. Localplastification will be considered using Neuber`s rule [2].

After this step strain time series for all relevant fatigueload cases do exist. A rainflow count of these strain timeseries results in a strain rainflow matrix which may alsobe transformed into a mean value and range matrix(Markov-Matrix). Weighting the different load cases onthe basis of their number or time of occurrence allowsadding the single rainflow matrices into an overallrainflow matrix.

To account for the mean strain a damage parameter isintroduced. Smith, Watson and Topper introduced thePSWT damage parameter, further description can befound in [2]. Instead of a stress life curve a strain lifecurve will be used. The strain life curve is built bycombining the plastic and the elastic life curves, seefigure 1. Sonsino measured a strain controlled S/N-curvefor spheroidal graphite cast iron GGG40 and respectivecyclic stress-strain-curve [7].

The final step is to achieve the damage or life by thedamage accumulation method. The same methods asused for the stress-life approach are used, e.g. Palmgren-Miner. A further explanation of the strain life approachfor wind turbine components can be found in [1].

Fig. 1: Strain life curve including elastic and plasticstrains.

4 DETERMINATION OF S/N-CURVES

The determination of the fatigue life depends on onehand largely on the correct shape of the S/N-curve buton the other hand it may be assumed that the highestuncertainties in the fatigue life estimation arise fromuncertainties in the S/N-curve.

One reason for this is that fatigue life of structuralcomponents or test specimen shows a generally broadscatter in fatigue life time even when comparing anumber of identical test specimen.

For wind turbine cast components there is a secondreason that no measured component S/N-curves exist.Whereas in the automotive industry full scale componentfatigue tests are state of the art, fatigue tests for windturbine cast components have hardly been carried out.From this point of view there is a lack of knowledge forwind turbine cast component designs. In wind energy itmay be hardly impossible to perform full scale fatiguetests for a rotor hub or a main frame of a large windturbine, since the high load cycle numbers and loadamplitudes would exceed the abilities of actuators andlaboratory equipment to apply the loads.

Fig. 2: Cast failure: Shrink holes, from Kaufmann [5]

Test cases currently available are the turbines running.They proved that cast components up to now haveworked very satisfactorily and fatigue problems arealmost unknown. But from this „real life experience“ noquantitative evaluation or calibration of methods can bederived, it gives qualitative statements only.

A first step forward could be the measurement of S/N-curves for small test specimen taken from castcomponents’ surfaces. These specimen would includesome characteristics of the large component. Reducinginfluences to be considered are:

1. Mean Stress: The mean stress / mean strain can beconsidered by the damage parameter, e.g.Smith/Watson/Topper or Morrow [2]

2. Component Size: The size effect may be or may atleast partly be included in the test specimen in casethis is taken from the large component’s surface.

3. Technological parameters: The cast quality gradeshould include uncertainties like shrink holes,dross, chunky graphite and quality of the texture[5]. These effects will probably not be included inthe specimen S/N curve and thus additionalreduction factors are to be considered.

4. Surface Roughness: Surface roughness is difficultto specify for a cast surface which is not machined.The surface influence is not covered by thespecimen S/N-curve.

5. Survival probability: S/N-curves are often specifiedfor a survival probability PS of 50%. Since the GLRegulations require a survival probability of at least97.7% [4], reduction factors are to be consideredfor smaller values of PS.

6. Multiaxial stress states: Hypotheses for equivalentstresses / strains are mainly based on non varyingprincipal stress directions. Further investigationsare needed to evaluate whether multiaxial stressstates do occur in the hot spot zone. For most windturbine components the hot spots are on the surfacethus at least a plane stress state exists. VerifiedMethods for fatigue life estimation in case ofmultiaxial stress states do currently not exist.Sonsino [7] states that the principal stresshypothesis is applicable for GGG 40 for uniaxial aswell as for multiaxial stress states.

5 MAIN FRAME OF A 2.5 MW WIND TURBINE

A cast main frame of a 2.5 MW wind turbine has beenanalysed using the strain life approach. The entire set ofload time series from the aero-elastic simulation of thewind turbine behaviour is the input for the fatigue lifeassessment. The structural response on unit loads isderived by Finite Element Analysis, see figures 3 and 4.

Fig. 3: FEM-model of a cast main frame of a 2.5 MWwind turbine.

Fig. 4: Stress distribution (von Mises equivalent stress)for unit load case tilt moment.

Fig. 5: Damage distribution.

The fatigue calculations were performed with theprogram FALANCS. Fig. 5 shows the damagedistribution for the structure analysed. Several hot spotscan be identified. The advantage of this method is thatno simplifications for phase relations, shape of loadspectra or pre-selection of hot spots were necessary. Adisadvantage is the amount of data and the calculationtime needed.

6 CONCLUSION

In the design and certification process of large windturbines it is nowadays standard to generate load timeseries for all relevant loading conditions byconsideration of the aero-elastic turbine behaviour. Thispaper presents a local notch strain approach for fatiguelife analysis under consideration of the entire set of loadtime series. For this a huge data amount is to be handledhowever the correct phase relations of load componentsand the correct mean stresses are automatically achieved.A pre-selection of hot spots is not necessary since theentire structure is assessed for its fatigue life. A damagedistribution plotted on the components surface revealsthe fatigue critical sections.

A problem is the choice of the correct S/N-curve for thecast material or component since fatigue life experimentswere not performed yet. Current practice is the use ofsynthetic S/N-curves. A first step forward could beperformance of strain life measurements on testspecimen taken from the surface of such wind turbinecast components.

ACKNOWLEDGEMENT

The investigations described in this paper are part of theresearch project ELA „Enhanced Life Time Analysis ofWind Turbine Structures“ supported by the FederalGerman Ministry for Economy and Technology BMWi.

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