On the Fatigue Life of Wind Turbine Structural Components

© Germanischer Lloyd Industrial Services GmbH, Business Segment Wind Energy Page 1 of 4

On the Fatigue Life of Wind Turbine Structural Components

Axel Dombrowski, Milan Ristow, Shanmuga Priyan Subramanian Germanischer Lloyd Industrial Services GmbH, Business Segment Wind Energy (GL Wind)

Steinhoeft 9, 20 459 Hamburg, Germany Phone: + 49 40 – 36 149 – 7141

Fax: + 49 40 – 36 149 – 1720 [email protected]

Abstract: Modern wind turbines are characterised by high, complex loads and by relatively light weight, optimised structures. The load bearing structural components in wind turbines are mostly made of large, elaborately shaped iron castings and steel fabrications. Complex, varying loads call for analysis methods to consider the different phase relationships between the loads acting on the components. These cause variations in stress directions, usually termed as multiaxiality. One problem is that the limitation of brittle materials, such as cast iron, to withstand multi-axial stresses is a little known problem outside the research centres. This paper intends to focus on the effect of high fatigue stresses and multiaxiality on wind turbine components and discusses the results of recent collaborative research work carried out at GL Wind.

1 Introduction

Fatigue failures of structural components under cyclical loading occur in distinct phases – the crack initiation phase, followed by the crack growth phase and then rupture.

The crack initiation phase is the life of the component up to the formation of a surface crack under fatigue loading, the size of this crack being defined by the engineering crack criterion. The crack-propagation phase is the remaining part of the life till the crack length reaches the critical length. The later part belongs to the science of fracture mechanics where material properties and micro-structure (grain size, imperfections, etc.) play a major role. The former, the crack initiation life is predicted using methods of damage accumulation which include hysteresis properties of the material involved and stress or strain histories at highly stressed locations.

2 Fatigue in wind turbine machinery

Modern wind turbines are characterised by high, complex loads and by relatively light weight, optimised structures. The load bearing structural components in wind turbines are mostly made of large, complexly shaped spheroidal graphite iron castings and steel fabrications. Also because of remote operations, conservative safety requirements and long life expectancy, a long crack initiation phase is necessary. The unpredictability of loads also makes determination of remaining life during crack propagation phase very difficult. Hence, the prediction of life up to the crack initiation is more relevant to these heavily loaded structural components. Based on this assumption, suitable fatigue analysis procedures could be applied on the components to be investigated, to determine the crack initiation life.

A stress based analysis can be divided to two parts: the determination of stresses under fatigue loading and the determination of representative fatigue property of the material under consideration.

Figure 1: Fatigue Analysis Procedure

Stress Hypothesis

Stress Time Histories

Material Data

SN Curves

Cycle counting, Mean Stress Corrections, Knock Down Factors, etc.

Safety Concept

Damage Accumulation: Life, Strength Reserves,

Degree of Utilisation

FE Analysis Stress Response

Characteristic Fatigue Loads


The diagram shows a typical fatigue analysis using the two above mentioned parts. The life of a component is a function of these two parts. The stresses on the component are calculated using appropriate stress hypothesis and then cycle counted to enable a comparison with applicable material data such as Stress-Life curves (SN curves). Different safety and knock down factors are considered in these calculations before damage accumulation is carried out to determine the component life and the degree of utilisation.

Stress

Prob

abilit

y De

nsity

50%

PÜ

97.

5% P

Ü

50%

5 %

Safety Factors

Component Stress due to Loading

Component Material Strength

Figure 2: Safety Concept in Fatigue Calculations (based on FKM Guidelines, [2])

Based on FKM Guidelines [2], the concept of safety for fatigue is accordingly represented in the above diagram. It vividly tells that even component stress due to loading (with a low probability of occurrence), needs to be below a material strength value with high probability of survival, after consideration of all applicable knock down and correction factors. The difference between these stress values is the safety margin and should at least cover the fatigue safety factor requirements determined by the consequences of failure and the probability of its occurrence.

3 Determination of material properties

Complexly varying loads call for fatigue analysis methods to consider the different phase relationships between the loads acting on the components. These can cause variations in stress directions, usually termed as multiaxiality. The problem is that the limitations of brittle materials, such as cast iron, to withstand multi-axial stresses are a little known problem outside the research centres.

Fatigue strength of materials, such as SN curves for spheroidal graphite cast iron, is experimentally determined on specially prepared laboratory test specimens and usually defined only for uniaxial stress states. The uncertainties involved in quantifying this property are covered using statistical parameters such as probability of failure, scatter, slope & knee of SN curve, level of confidence and the number of tests. Influence of surface roughness, technical defects, wall thickness, mean stress and residual stress, notch effects are also appropriately considered as knock down factors to determine the component material strength under fatigue loads for uniaxial stress states. These factors cover all related known risks and a careful combination of these factors is necessary to theoretically optimise load carrying capacity of the component.

This is the generally accepted procedure to derive component SN curves since it has been financially unviable to conduct accelerated tests on full size components to gain the necessary material data.

4 Determination of component stresses

Because of the increased complexity of the component geometry and varying load scenarios, the local stress approach in combination with detailed FE models and load time histories is the most widely used method in this industry.

The finite element calculations are based on CAD models of component geometries with linear, isotropic material properties and multiple loading points. The load histories for the components are extracted from multi-body simulations of a wind turbine model for various fatigue loading scenarios. Linear superposition of the load-coefficients (unit load stresses or transfer functions) determined from FE computations are multiplied with load histories to get local stress tensor histories at critical locations. This is the generally accepted procedure for linear calculations but if non-linear boundary conditions are to be observed, for e.g. contact surfaces of bearings etc., then modified approaches are necessary.

It is to be noted that reliable fatigue material properties exist predominantly for uniaxial stress states. Several hypotheses also exist to enable conversion of component stresses to an equivalent uniaxial stress. There also


exist separate methods such as the critical plane approach to deal with multiaxial stress states caused by non proportional loading conditions.

To help understand this, structural components of a 2 MW wind turbine are used as an example in this study. Fatigue loads in combination with FE models of the components were used to compute the stress histories at critical locations. Based on this, a local stress state analysis was performed to analyse the multi-axial behaviour of the stresses at critical locations and investigate the degree of multiaxiality (i.e. change in principal stress directions during a loading sequence).

Figure 3: Locations selected for Local Stress State Analysis

The results show that at several locations in the hub there exist multiaxial stress states. At these locations, it was observed that though the directions of principal stresses change greatly, the magnitude of the stresses remain low. The main frame on the other hand, has several locations with uniaxial stress states. Following are plots showing samples of typical uniaxiality and multiaxiality.

Figure 4: Sample results of Local Stress State Analysis

The procedure for fatigue analysis needs to consider the influence of these changing principal stress directions by applying appropriate stress hypothesis and quantify its detrimental effect on fatigue strength of the chosen material. This is critical since the used materials show an additional cyclical stress hardening effect with varying principal stress directions. Fatemi has even indicated that out of phase stresses are more damaging than equivalent in-phase stresses in the low cycle region [7]. The appropriate stress hypothesis is to be selected based on several factors:

- Uniaxial or multiaxial stress state

M

U

U

M

M

U

U: Uniaxial Stress during loading

M: Multiaxial Stress during loading


- Brittle or ductile material - Phase relationships between applied loads - Tensile, compressive or shear loading - Type of stress concentration (for e.g., fillets and small radii, seam welds, spot weld, etc.)

The following is a summary of widely used stress hypotheses. Conventional maximum stress theory (Tresca) is not a good parameter for the multiaxial fatigue life

predictions [7]. This method has not been included in the comparative-analysis and has been mentioned just as information.

Von-Mises or Equivalent stress approaches reduce the multiaxial stress or strain states to a single scalar value that can be used to calculate fatigue damage just as for a uniaxial state of stress. These approaches are exact if the state of stress is uniaxial, and are generally very good if the state of stress is proportional or nearly proportional [6]. It also correlates well with tests on ductile materials [7].

Maximum principal stress theory successfully predicts fatigue life in brittle material for in-phase loading [7]. Critical plane approach proves to be reasonably accurate in predicting fatigue life for both in-phase and out-of-

phase loading [7].To determine the critical plane, the multiaxial stress state at a particular point is estimated. Then, this multiaxial stress state is resolved to particular planes (orientations) in the material to compute the normal and shear stresses and strains acting on the plane. Fatigue damage for these resolved stress histories is computed based on a rainflow counting and an appropriate damage parameter. When all of the calculations for the planes are complete, the plane with the highest calculated damage is the critical plane, and determines the fatigue life of the structure at that location. Although there is an infinite number of planes at a particular point, candidate critical planes are commonly taken to be ten degrees apart, because it has been observed that fatigue damage does not vary much for planes less than ten degrees apart. Furthermore, if the damage is to be calculated on a free surface of a structure, the number of candidate planes can be greatly reduced [6].

Absolute Maximum Principal Stress approach does not represent the real local stress-time history at the location but the calculated damage is, according to the academicians, representative of the experimental results and this has been accepted as de facto standard, although the approach neglects or nullifies the mean stress corrections. If an SN curve specifically developed for the component under representative loading is not available, statistically determined or analytically determined uniaxial SN curves for the material are used. This is accepted but care has to be taken to convert multiaxial stresses at hot spot locations into representative uniaxial stresses (using appropriate hypotheses), before cycle counting and comparison with a SN curve. Absolute maximum principal stress approach is one such hypothesis. It gives conservative results and it covers the uncertainties involved in combining multiaxial stress states with uniaxial material properties.

5 Conclusion

The paper presented briefly the fatigue analysis procedure, the concept of safety and the generally accepted method for the determination of material properties. The main aim of this paper was to throw some light on to the determination of equivalent component stresses that are representative and valid enough, in combination with uniaxial material properties, for use in fatigue computations. Samples of uniaxial and multiaxial stresses were shown to encourage designers to investigate the local stress states thoroughly before deciding on a stress hypothesis. Interpretation of such local stress state investigations also reveal significant information that could be used for further optimising the component geometries.

6 References

[1] Germanischer Lloyd Rules and Guidelines, IV – Industrial Services, Part 1 – Guideline for the Certification of Wind Turbines, Edition 2003 with Supplement 2004

[2] FKM Guideline, Analytical Strength Assessment of Components in Mechanical Engineering, 5th, revised Edition, 2003, VDMA Verlag

[3] Haibach, E., Betriebsfestigkeit, 2nd Edition, 2002, VDI Verlag [4] Gudehus, H., Zenner, H., Leitfaden für eine Betriebsfestigkeitsberechnung, 4th Edition, 1999, Verlag

Stahleisen, Düsseldorf [5] Bishop, N.W.M., Sherratt, F., Finite Element Based Fatigue Calculations, 2000, NAFEMS Ltd. [6] LMS-FALANCS Theory Manual, LMS Durability Technologies GmbH, 2000. [7] Fatemi, A., Socie, D.F., “A Critical Plane Approach to Multiaxial Fatigue Damage including Out-Of-Phase

Loading” Fatigue Fract. Engng. Mater. Struct. Vol. 11, No. 3, pp. 149-165, 1988.

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On the Fatigue Life of Wind Turbine Structural Components