Fatigue and fracture mechanical behaviour of a wind turbine rotor … · 2017. 1. 25. ·...

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ScienceDirect Structural Integrity Procedia 00 (2016) 000–000

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2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal

Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine

P. Brandãoa, V. Infanteb, A.M. Deusc* aDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal bIDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal cCeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal

Abstract

During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +351 218419991.

E-mail address: [email protected]

Procedia Structural Integrity 2 (2016) 2951–2958

Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer review under responsibility of the Scientific Committee of ECF21.10.1016/j.prostr.2016.06.369

10.1016/j.prostr.2016.06.369




2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Fatigue and fracture mechanical behaviour of a wind turbine rotor shaft made of cast iron and forged steel

Jenni Herrmanna*, Thes Rauerta, Peter Dalhoffa and Manuela Sanderb aInstitute of Renewable Energy and Energy-efficient Systems, Hamburg University of Applied Sciences, Berliner Tor 21, 20099 Hamburg,

Germany bInstitute of Structural Mechanics, University of Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany

Abstract

To reduce uncertainties associated with the fatigue behaviour of the highly safety relevant wind turbine rotor shaft and also to review today’s design practice the fatigue life time is tested on a full scale test rig. Further investigations of weight saving potentials contribute to suggestions for the usage of other materials. Therefore, a comprehensive comparison regarding the fatigue and the fracture mechanical behaviour of the rotor shaft made of different materials is done. For the loading situation it is distinguished between test conditions and a realistic cumulative frequency distribution of loads in a wind turbine. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: rotor shaft; wind turbine component test; cast iron; forged steel; fatigue test rig; remaining life

1. Introduction

Because of various wind and environmental conditions, wind turbines have to withstand enormous loads over a life of 20 years. Consequently, in terms of growth in wind turbine size, not just the height of the system and the rotor diameter increase, all drive train components have to be scaled up regarding the new conditions. For economic reasons it should be figured out, if there are possibilities for optimization with respect to component weight. If the weight of a drive train component decreases, the material usage of the structure below could also be reduced and hence the costs.

* Corresponding author. Tel.: +49-40-42875-8661.





2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Fatigue and fracture mechanical behaviour of a wind turbine rotor shaft made of cast iron and forged steel

Jenni Herrmanna*, Thes Rauerta, Peter Dalhoffa and Manuela Sanderb aInstitute of Renewable Energy and Energy-efficient Systems, Hamburg University of Applied Sciences, Berliner Tor 21, 20099 Hamburg,

Germany bInstitute of Structural Mechanics, University of Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany

Abstract

To reduce uncertainties associated with the fatigue behaviour of the highly safety relevant wind turbine rotor shaft and also to review today’s design practice the fatigue life time is tested on a full scale test rig. Further investigations of weight saving potentials contribute to suggestions for the usage of other materials. Therefore, a comprehensive comparison regarding the fatigue and the fracture mechanical behaviour of the rotor shaft made of different materials is done. For the loading situation it is distinguished between test conditions and a realistic cumulative frequency distribution of loads in a wind turbine. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: rotor shaft; wind turbine component test; cast iron; forged steel; fatigue test rig; remaining life

1. Introduction

Because of various wind and environmental conditions, wind turbines have to withstand enormous loads over a life of 20 years. Consequently, in terms of growth in wind turbine size, not just the height of the system and the rotor diameter increase, all drive train components have to be scaled up regarding the new conditions. For economic reasons it should be figured out, if there are possibilities for optimization with respect to component weight. If the weight of a drive train component decreases, the material usage of the structure below could also be reduced and hence the costs.

* Corresponding author. Tel.: +49-40-42875-8661.


Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the Scientific Committee of ECF21.

http://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/http://crossmark.crossref.org/dialog/?doi=10.1016/j.prostr.2016.06.369&domain=pdf

2952 Jenni Herrmann et al. / Procedia Structural Integrity 2 (2016) 2951–2958 Jenni Herrmann et al./ Structural Integrity Procedia 00 (2016) 000–000 3

stress. The damage relevant operational load of the rotor shaft is dominated by the cyclic bending load, which results from a correlation of the stochastically distributed wind loads and the gravitational load of the rotor (see Fig. 1).

Fig. 1. Rotor shaft – (a) assembly situation , (b) loading time series of the bending moment at the main bearing, (c) cumulative frequency dis-tribution of bending stresses

Fig. 2 presents the full scale fatigue test rig. The rotor shaft of a 2.1 MW-turbine that is mounted on the test rig, has a weight of 8 tonnes, a length of around 2.6 m and a diameter of more than 0.7 m at the main bearing seat (Fig. 2 c)). On the left hand side, the hydraulic system is shown, which induces the load by a cable pulley at the end of a cast load lever. The rotor shaft is connected to the load lever by a flange joint and supported by a locating/floating bearing arrangement. For the locating bearing, close to the notch root of the shaft (hotspot), the real main bearing of the turbine drive train is used. In the considered wind turbine the rear part of the shaft is normally connected to the gearbox, which is supported and connected to the main frame by a torque support. Because the gearbox is not a part of the test rig, the degree of freedom of tilting of this connection is reproduced at the test rig. To minimize constraining forces a cardan joint connects the rear part with the engine, which rotates the shaft.

Fig. 2. Rotor shaft fatigue test rig – (a), (b) pictures of the assembly (Fraunhofer (2016)), (c) CAD model (Kyling (2014))

Six single S-N fatigue tests will be conducted on the test rig. For the block load tests a combination of the methods of discrete load steps and fixed horizon is pursued, to get an information about the inclination of the S-N curve in the

0

20

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1E+00 1E+02 1E+04 1E+06

stres

s am

plitu

de σ

a[M

Pa]

load cycles (divided by 144) N/144 [-]

periodical load out of rotor weight

-2000

0

2000

0 200 400 600

MB

[kN

m]

time [sec]

Wind turbine drive train (Hau (2008))

a)

b)

c)

Cable pulley Hydraulic system

Rotor shaft Main bearing Load lever

a)

c)

b)

2 Jenni Herrmann et al./ Structural Integrity Procedia 00 (2016) 000–000

Recently full scale test benches were developed to investigate the overall performance of wind turbines less to analyse the fatigue behaviour of single components. But, especially for the constructive design of the main components the fatigue strength over the whole wind turbine service life is decisive. Thus, a gap in systematic testing is evident in between common material investigations and entire turbine system tests. Separate main component test rigs for fatigue strength and behaviour only exist for a few components, like rotor blades and gear boxes.

On this account a research project called BeBen XXL – accelerated fatigue testing of wind turbine large components using the example of the main shaft was started. The aim of this joint project, with the cooperation partners Suzlon Energy Ltd., Fraunhofer IWES and Hamburg University of Applied Sciences, is to reduce the material usage for rotor shafts while not changing the turbine integrity. Therefore, six S-N fatigue tests of full size forged shafts are performed.

In addition to the investigation of weight saving potentials by reviewing today’s design practice, alternative rotor shaft materials are of great interest. It is examined, if alternative materials to forged steel are able to withstand the requirements of a wind turbine main component, like high reliability, simple and cost-effective manufacturing and resistance against high payload at low self-weight.

2. Materials in wind turbines

Almost all structural components at the top of a wind turbine (AWEA (2011)), like main frames, rotor hubs, blade root and tower top adapters, torque supports, planet carriers of the gearbox, brake disks as well as rotor axles and stator elements in direct-drive turbines are made of normal strength spheroidal graphite cast iron. The bearing and gearbox housing are usually made of lamellar graphite cast iron. Nowadays, higher strength ductile iron is only used for the planet carrier and rarely for the rotor hub. One of the exceptions among the main components inside the nacelle is the rotor shaft, which is made of normal strength ductile iron only in rare cases. Predominantly, rotor shafts are manufactured out of forged steel. Next to forged steel, for the following comparison different cast iron variants are considered for the rotor shaft (see Table 1).

Table 1. Considered materials for possible rotor shaft application

Material Tensile strength Rm (t < 30 mm)

Application in a wind turbine

42CrMo4s 1100 MPa Rotor shaft mostly made of forged steel.

EN GJS-400-18-LT 400 MPa Normal strength ductile iron often used for wind turbine components (Shirani et al. (2011)).

EN GJS-600-3, EN GJS-700-2

600 MPa, 700 MPa Higher strength ductile iron, rarely used in wind turbines, so far almost exclusive for the planet carrier (Pollicino (2006)).

EN GJS-800-8, EN GJS-1000-5

800 MPa, 1000 MPa Austempered ductile iron, no application for wind turbine main components so far (Her-furth (2003)).

GJSF-SiNi30-5 410 MPa*

*(60 < t < 200 mm)

Si-solid solution strengthened ductile iron especially developed for wind turbine application (Mikoleizik et al. (2014)).

3. Fatigue behavior of wind turbine rotor shafts made different materials

To examine the efficiency of materials for main wind turbine parts, especially for the rotor shaft, the fatigue strength plays a crucial role. In this section the rotor shaft on a full scale fatigue test rig is investigated.

3.1. Rotor shaft fatigue testing

Initially, the test rig, which is developed and built in the scope of this research project, is considered more closely. Thereby the setup, the testing strategy and the validation of the simulation model is presented. In addition, the calcu-lative assumption of the fatigue life of the rotor shaft, made of different materials, is described. In this fatigue life estimation the testing conditions with a constant load amplitude and also the realistic conditions in a wind turbine are considered. During the turbine operation the rotor shaft suffers a circumferential bending stress, besides the torsional

Jenni Herrmann et al. / Procedia Structural Integrity 2 (2016) 2951–2958 2953 Jenni Herrmann et al./ Structural Integrity Procedia 00 (2016) 000–000 3

stress. The damage relevant operational load of the rotor shaft is dominated by the cyclic bending load, which results from a correlation of the stochastically distributed wind loads and the gravitational load of the rotor (see Fig. 1).

Fig. 1. Rotor shaft – (a) assembly situation , (b) loading time series of the bending moment at the main bearing, (c) cumulative frequency dis-tribution of bending stresses

Fig. 2 presents the full scale fatigue test rig. The rotor shaft of a 2.1 MW-turbine that is mounted on the test rig, has a weight of 8 tonnes, a length of around 2.6 m and a diameter of more than 0.7 m at the main bearing seat (Fig. 2 c)). On the left hand side, the hydraulic system is shown, which induces the load by a cable pulley at the end of a cast load lever. The rotor shaft is connected to the load lever by a flange joint and supported by a locating/floating bearing arrangement. For the locating bearing, close to the notch root of the shaft (hotspot), the real main bearing of the turbine drive train is used. In the considered wind turbine the rear part of the shaft is normally connected to the gearbox, which is supported and connected to the main frame by a torque support. Because the gearbox is not a part of the test rig, the degree of freedom of tilting of this connection is reproduced at the test rig. To minimize constraining forces a cardan joint connects the rear part with the engine, which rotates the shaft.

Fig. 2. Rotor shaft fatigue test rig – (a), (b) pictures of the assembly (Fraunhofer (2016)), (c) CAD model (Kyling (2014))

Six single S-N fatigue tests will be conducted on the test rig. For the block load tests a combination of the methods of discrete load steps and fixed horizon is pursued, to get an information about the inclination of the S-N curve in the

0

20

40

60

80

100

120

140

1E+00 1E+02 1E+04 1E+06

stres

s am

plitu

de σ

a[M

Pa]

load cycles (divided by 144) N/144 [-]

periodical load out of rotor weight

-2000

0

2000

0 200 400 600

MB

[kN

m]

time [sec]

Wind turbine drive train (Hau (2008))

a)

b)

c)

Cable pulley Hydraulic system

Rotor shaft Main bearing Load lever

a)

c)

b)


Recently full scale test benches were developed to investigate the overall performance of wind turbines less to analyse the fatigue behaviour of single components. But, especially for the constructive design of the main components the fatigue strength over the whole wind turbine service life is decisive. Thus, a gap in systematic testing is evident in between common material investigations and entire turbine system tests. Separate main component test rigs for fatigue strength and behaviour only exist for a few components, like rotor blades and gear boxes.

On this account a research project called BeBen XXL – accelerated fatigue testing of wind turbine large components using the example of the main shaft was started. The aim of this joint project, with the cooperation partners Suzlon Energy Ltd., Fraunhofer IWES and Hamburg University of Applied Sciences, is to reduce the material usage for rotor shafts while not changing the turbine integrity. Therefore, six S-N fatigue tests of full size forged shafts are performed.

In addition to the investigation of weight saving potentials by reviewing today’s design practice, alternative rotor shaft materials are of great interest. It is examined, if alternative materials to forged steel are able to withstand the requirements of a wind turbine main component, like high reliability, simple and cost-effective manufacturing and resistance against high payload at low self-weight.

2. Materials in wind turbines

Almost all structural components at the top of a wind turbine (AWEA (2011)), like main frames, rotor hubs, blade root and tower top adapters, torque supports, planet carriers of the gearbox, brake disks as well as rotor axles and stator elements in direct-drive turbines are made of normal strength spheroidal graphite cast iron. The bearing and gearbox housing are usually made of lamellar graphite cast iron. Nowadays, higher strength ductile iron is only used for the planet carrier and rarely for the rotor hub. One of the exceptions among the main components inside the nacelle is the rotor shaft, which is made of normal strength ductile iron only in rare cases. Predominantly, rotor shafts are manufactured out of forged steel. Next to forged steel, for the following comparison different cast iron variants are considered for the rotor shaft (see Table 1).

Table 1. Considered materials for possible rotor shaft application

Material Tensile strength Rm (t < 30 mm)

Application in a wind turbine

42CrMo4s 1100 MPa Rotor shaft mostly made of forged steel.

EN GJS-400-18-LT 400 MPa Normal strength ductile iron often used for wind turbine components (Shirani et al. (2011)).

EN GJS-600-3, EN GJS-700-2

600 MPa, 700 MPa Higher strength ductile iron, rarely used in wind turbines, so far almost exclusive for the planet carrier (Pollicino (2006)).

EN GJS-800-8, EN GJS-1000-5

800 MPa, 1000 MPa Austempered ductile iron, no application for wind turbine main components so far (Her-furth (2003)).

GJSF-SiNi30-5 410 MPa*

*(60 < t < 200 mm)

Si-solid solution strengthened ductile iron especially developed for wind turbine application (Mikoleizik et al. (2014)).

3. Fatigue behavior of wind turbine rotor shafts made different materials

To examine the efficiency of materials for main wind turbine parts, especially for the rotor shaft, the fatigue strength plays a crucial role. In this section the rotor shaft on a full scale fatigue test rig is investigated.

3.1. Rotor shaft fatigue testing

Initially, the test rig, which is developed and built in the scope of this research project, is considered more closely. Thereby the setup, the testing strategy and the validation of the simulation model is presented. In addition, the calcu-lative assumption of the fatigue life of the rotor shaft, made of different materials, is described. In this fatigue life estimation the testing conditions with a constant load amplitude and also the realistic conditions in a wind turbine are considered. During the turbine operation the rotor shaft suffers a circumferential bending stress, besides the torsional


Table 2. Calculated fatigue life of a bending loaded rotor shaft with R=-0.94

Material GJS-1000-5 GJS-800-10 GJS-700-2 GJS-600-3 42CrMo4 GJSF-SiNi30-5 GJS-400-18-LT

Load cycles 1.88E+07 2.48E+06 1.32E+06 5.76E+05 3.72E+05 1.63E+05 1.08E+05

Days 217.6 28.7 15.3 6.7 4.3 1.9 1.3

The synthetic component S-N curves for the considered materials are presented in Fig. 5. It is shown that at room

temperature austempered ductile iron (EN-GJS-800-10 and EN-GJS-1000-5) has the highest fatigue strength. Whether the higher-strength cast iron materials are better suited for this component than forged steel depends on the cumulative frequency distribution. Only in the low-cycle fatigue regime forged steel is more resistant to fatigue loading, because of higher static properties. The normal-strength cast shaft (EN-GJS-400-18-LT) shows the lowest fatigue strength closely followed by GJSF-SiNi30-5.

The total damage sum of a rotor shaft under a realistic wind turbine cumulative frequency distribution of the loads of 20 years of service life (Fig. 1 c)) is calculated corresponding to the linear damage accumulation in accordance with the Palmgren-Miner rule modified by Haibach and is shown in Fig. 6. Because the maximum stresses are almost completely below the endurance limit, the resulting damages of the austempered and higher strength ductile iron are far lower than the damage of the forged shaft.

Fig. 5. Synthetic component S-N curves according to Gudehus (2007) Fig. 6. Damage sum from realistic variable wind turbine bending moment according to Fig. 1 c)

4. Fracture mechanical assessment of different materials for the rotor shaft

Additionally to the strength and fatigue strength assessment, especially for the higher strength cast iron variants, fracture mechanical examinations are necessary. Fracture mechanical concepts can be used to evaluate a higher ten-dency to crack initiation and propagation to minimize the risk of total failure. In accordance to the wind turbine design guideline from Germanischer Lloyd (2010) for components made of brittle materials an additional fracture mechanical evidence of safety is required. If the fracture elongation exhibits a value less than 12.5 %, the material cannot be used for a structure that is involved in the flow of forces, like the rotor hub, the gearbox, the bearing housing or the main frame, without extensive assessments.

These analytical investigations are based on Forman/Mettu-parameters (Fig. 7) according to Henkel (2008) and Sander (2008). In conformity with ASTM E 647 (2013), if the stress ratio has a negative algebraic sign, only the maximum stress intensity value is considered for the stress intensity range.

First, different factors are considered, which can influence the crack growth of a potential crack. In Fig. 8 the influence on crack growth is shown by varying the magnitude of these parameters. The direction of each influencing parameter is similarly correct for cast and forged shafts. However, the magnitude of the effect is different. Obviously the initial crack length has a strong influence on the remaining life. The lowest crack propagation rate is calculated in the 42CrMo4 shaft, followed by growth rate in the GJS-800-10 shaft. At an initial crack depth of 4 mm, following the propagation rate in these two materials, the next lowest rate is estimated in GJS-1000-5. However, if the potential

0

200

400

600

800

1000

1200

1.E+01 1.E+03 1.E+05 1.E+07

stres

s am

plitu

de σ

a[M

Pa]

load cycles N [-]

42CrMo4GJS-1000-5GJS-800-10GJS-700-2GJS-600-3GJSF-SiNi30-5GJS-400-18-LT

0.00

43

0.00

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finite life regime and about the variance of its position. At the test rig, only the bending moment will be applied to the shaft. All six specimen have the same rotor shaft design.

Due to the increased loading and rotational speed, a synthetically determined testing time for each load horizon between about 45 h and 140 h is predicted (with a probability of failure of 50 %). The first test run stops when noticing a drop in the measured strain and when detecting a fist initial crack. Afterwards a couple of load cycles will be passed through to get some information about the crack propagation, but thereby unstable crack growth necessarily should be avoided.

3.2. FE-Model

Fig. 3 shows the finite element model of the experimental setup. On the right side the boundary conditions are listed. Furthermore, it is referred to the hotspot at the shaft shoulder, which is closely located to the main bearing.

Fig. 3. FE-model of the test rig

The cyclic strain of the strain gauges at the shaft close to the notch of the first specimen is pictured in Fig. 4 (grey line). For a validation the simulation results are plotted as a black dotted curve. The maximum deviation between the measured strain amplitude and the FE-results is smaller than the largest deviation of the measured results of the 20 strain gauges among each other.

Fig. 4. Comparison of strain gauge results and simulated data at different load levels

3.3. Fatigue life estimation

For a fatigue strength determination of different materials an imperfection-free rotor shaft is assumed. The fatigue life values in Table 2 result from a constant amplitude loading with a bending moment of 2.2 MNm and a reduced notch radius for the test. The fatigue life is determined in accordance with the calculation method for synthetic com-ponent S-N curves in Gudehus (2007). The hotspot stress amplitude is determined by an FE-simulation of the rotor shaft in the experimental setup. The press-fit between the shaft and the main bearing close to the notch area leads to a tension stress in the notch. This influence of the R-ratio is strongly affected by the tolerances of the structures. On this account the R-ratio of the stress range slightly deviates from -1. Standard values are used for the material properties at the considered structural thickness.

-1.20-0.80-0.400.000.400.801.20

0 90 180 270 360

strai

n ε

[mm

/m]

normalized angle [°]-1.2-0.8-0.4

00.40.81.2

0 90 180 270 360

strai

n ε

[mm

/m]


00.40.81.2

0 90 180 270 360

strai

n ε

[mm

/m]

normalized angle [°]

Hotspot

A B C D, E

A

B

C

D

E

Fixed Support

Cylindrical Support

Earth Gravity

Force

Point Mass

strain gauge results FE results


Table 2. Calculated fatigue life of a bending loaded rotor shaft with R=-0.94

Material GJS-1000-5 GJS-800-10 GJS-700-2 GJS-600-3 42CrMo4 GJSF-SiNi30-5 GJS-400-18-LT

Load cycles 1.88E+07 2.48E+06 1.32E+06 5.76E+05 3.72E+05 1.63E+05 1.08E+05

Days 217.6 28.7 15.3 6.7 4.3 1.9 1.3

The synthetic component S-N curves for the considered materials are presented in Fig. 5. It is shown that at room

temperature austempered ductile iron (EN-GJS-800-10 and EN-GJS-1000-5) has the highest fatigue strength. Whether the higher-strength cast iron materials are better suited for this component than forged steel depends on the cumulative frequency distribution. Only in the low-cycle fatigue regime forged steel is more resistant to fatigue loading, because of higher static properties. The normal-strength cast shaft (EN-GJS-400-18-LT) shows the lowest fatigue strength closely followed by GJSF-SiNi30-5.

The total damage sum of a rotor shaft under a realistic wind turbine cumulative frequency distribution of the loads of 20 years of service life (Fig. 1 c)) is calculated corresponding to the linear damage accumulation in accordance with the Palmgren-Miner rule modified by Haibach and is shown in Fig. 6. Because the maximum stresses are almost completely below the endurance limit, the resulting damages of the austempered and higher strength ductile iron are far lower than the damage of the forged shaft.

Fig. 5. Synthetic component S-N curves according to Gudehus (2007) Fig. 6. Damage sum from realistic variable wind turbine bending moment according to Fig. 1 c)

4. Fracture mechanical assessment of different materials for the rotor shaft

Additionally to the strength and fatigue strength assessment, especially for the higher strength cast iron variants, fracture mechanical examinations are necessary. Fracture mechanical concepts can be used to evaluate a higher ten-dency to crack initiation and propagation to minimize the risk of total failure. In accordance to the wind turbine design guideline from Germanischer Lloyd (2010) for components made of brittle materials an additional fracture mechanical evidence of safety is required. If the fracture elongation exhibits a value less than 12.5 %, the material cannot be used for a structure that is involved in the flow of forces, like the rotor hub, the gearbox, the bearing housing or the main frame, without extensive assessments.

These analytical investigations are based on Forman/Mettu-parameters (Fig. 7) according to Henkel (2008) and Sander (2008). In conformity with ASTM E 647 (2013), if the stress ratio has a negative algebraic sign, only the maximum stress intensity value is considered for the stress intensity range.

First, different factors are considered, which can influence the crack growth of a potential crack. In Fig. 8 the influence on crack growth is shown by varying the magnitude of these parameters. The direction of each influencing parameter is similarly correct for cast and forged shafts. However, the magnitude of the effect is different. Obviously the initial crack length has a strong influence on the remaining life. The lowest crack propagation rate is calculated in the 42CrMo4 shaft, followed by growth rate in the GJS-800-10 shaft. At an initial crack depth of 4 mm, following the propagation rate in these two materials, the next lowest rate is estimated in GJS-1000-5. However, if the potential

0

200

400

600

800

1000

1200

1.E+01 1.E+03 1.E+05 1.E+07

stres

s am

plitu

de σ

a[M

Pa]

load cycles N [-]

42CrMo4GJS-1000-5GJS-800-10GJS-700-2GJS-600-3GJSF-SiNi30-5GJS-400-18-LT

0.00

43

0.00

28

0.00

059

0.00

018

0.00

0024

0

0.002

0.004

0.006

0.008

0.01

0.06

8

0.03

1


finite life regime and about the variance of its position. At the test rig, only the bending moment will be applied to the shaft. All six specimen have the same rotor shaft design.

Due to the increased loading and rotational speed, a synthetically determined testing time for each load horizon between about 45 h and 140 h is predicted (with a probability of failure of 50 %). The first test run stops when noticing a drop in the measured strain and when detecting a fist initial crack. Afterwards a couple of load cycles will be passed through to get some information about the crack propagation, but thereby unstable crack growth necessarily should be avoided.

3.2. FE-Model

Fig. 3 shows the finite element model of the experimental setup. On the right side the boundary conditions are listed. Furthermore, it is referred to the hotspot at the shaft shoulder, which is closely located to the main bearing.

Fig. 3. FE-model of the test rig

The cyclic strain of the strain gauges at the shaft close to the notch of the first specimen is pictured in Fig. 4 (grey line). For a validation the simulation results are plotted as a black dotted curve. The maximum deviation between the measured strain amplitude and the FE-results is smaller than the largest deviation of the measured results of the 20 strain gauges among each other.

Fig. 4. Comparison of strain gauge results and simulated data at different load levels

3.3. Fatigue life estimation

For a fatigue strength determination of different materials an imperfection-free rotor shaft is assumed. The fatigue life values in Table 2 result from a constant amplitude loading with a bending moment of 2.2 MNm and a reduced notch radius for the test. The fatigue life is determined in accordance with the calculation method for synthetic com-ponent S-N curves in Gudehus (2007). The hotspot stress amplitude is determined by an FE-simulation of the rotor shaft in the experimental setup. The press-fit between the shaft and the main bearing close to the notch area leads to a tension stress in the notch. This influence of the R-ratio is strongly affected by the tolerances of the structures. On this account the R-ratio of the stress range slightly deviates from -1. Standard values are used for the material properties at the considered structural thickness.

-1.20-0.80-0.400.000.400.801.20

0 90 180 270 360

strai

n ε

[mm

/m]


00.40.81.2

0 90 180 270 360

strai

n ε

[mm

/m]


00.40.81.2

0 90 180 270 360

strai

n ε

[mm

/m]

normalized angle [°]

Hotspot

A B C D, E

A

B

C

D

E

Fixed Support

Cylindrical Support

Earth Gravity

Force

Point Mass

strain gauge results FE results


at a lower load level, it is just the opposite. The fatigue crack growth in the normal strength ductile iron is slower than in GJS-800-10 and in GJS-1000-5 (Fig. 11 a)). At this loading, till approximately 4E+05 load cycles, also the brittle higher strength cast iron shaft (GJS-600-3) is more insensitive to fatigue cracking than the GJS-1000-5-shaft. Espe-cially GJSF-SINI30-5 is suitable at external stresses beneath the endurance limit. But, with the increasing number of load cycles, the crack propagation rate in normal and higher strength ductile iron shafts rises and unstable crack growth starts at a lower cycle numbers than in the GJS-800-10 shaft.

Fig. 10 shows the total life as a sum of fatigue life till crack initiation and remaining life (at initial thumbnail crack with a depth of 2 mm) till component failure, when the hotspot stress amplitude is 240 MPa. Here again the high discrepancy of the resistance with regard to fatigue and to fatigue crack growth is obvious.

Fig. 11. Crack propagation at cyclic-single-stage stress amplitude - a) 160 MPa, b) 300 MPa

4.2. Fracture mechanical investigation at real variable loading in a wind turbine

Furthermore, besides the assessment of remaining life after a fatigue crack initiation, the potential risk of an unde-tected imperfection in the rotor shaft has to be investigated. On this account, initially a conservative assumption for surface defects with different depths in the hotspot region of the rotor shaft from the beginning of the operation are done. The crack length increases as a function of load cycles at a realistic frequency distribution of the wind turbine bending moment as pictured in Fig. 12. The maximum value of the cumulative frequency distribution of stresses at the real notch geometry of the considered shaft is below the endurance limit (approximately 70 %). Furthermore, the high proportion of cycles with far smaller amplitudes leads to a much lower crack propagation rate in the wind turbine than at the test rig. For the crack growth calculation the cumulative frequency distribution of stress of the whole wind turbine life is divided by the cycle number of the least occurring class, sorted in descending order and then successively repeated till the whole cycles of lifetime (6E+08 cycles correspond to 20 years of service life) are passed through.

Fig. 12. Crack growth at real variable loading out of Fig. 1 c)

020406080

100120140160180

1.E+00 1.E+02 1.E+04 1.E+06

crac

k de

pth

a [m

m]

load cycles N [-]

42CrMo4GJS-400-18-LTGJSF-SiNi30-5GJS-600-3GJS-800-10GJS-1000-5

0

5

10

15

20

25

30

1E+00 4E+05

160 MPa

0

5

10

15

20

25

30

0E+00 5E+04 1E+05

300 MPa

10

60

110

160

0

50

100

1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08 1E+09

crac

k de

pth

a [m

m]

stres

s am

plitu

de σ

[MPa

]

load cycles N [-]

a0 = 20 mm

stress spectrum 42CrMo4 GJS-1000-5GJS-800-10 GJS-600-3 GJSF-SiNi30-5GJS-400-18-LT

a) b)


initial crack has a depth of 2 mm the propagation is less fast in the GJS-600-3 and the GJSF-SiNI30-5 rotor shaft. But at approximately 1E+05 load cycles the propagation rate increases, thus the crack depth exceeds the depth in the GJS-1000-5 shaft. From the beginning the crack in a shaft made of GJS-400-18-LT grows the fastest.

Fig. 7. Forman/Mettu curves of different materials Fig. 8. Influence of different parameters on crack growth – with a0 as the initial crack depth, α as the stress concentration factor and R

as the stress ratio

In this consideration a semi-elliptical crack in the shaft hotspot is assumed. Though, in sharp notched or hardened rotating bending loaded shafts, a circumferential crack is also possible. In the present case this assumption is very unlikely, but still has to be investigated. A closer look on a selection of the considered materials shows a much lower number of load cycles at the same initial crack depth than for a semi-elliptical crack geometry (see Fig. 9). Despite equal external stress and equal initial crack depth, the deciding reason for the higher stress intensity factor for a cir-cumferential crack, is the higher value of the geometry function, due to the higher cross section reduction. However, a material specific difference is not apparent.

Fig. 9. Assumption of semi-elliptical and circumferential crack Fig. 10. Total life of a rotor shaft made of different materials

4.1. Remaining life estimation at one-stage loading on the test rig

Subsequently the remaining life of the rotor shaft made of the considered materials is examined for the test environ-ment at different constant load amplitude (Fig. 11). Therefore, two different load stages are simulated. In the following investigation a 2 mm initial crack depth is assumed. The crack in the forged shaft has the lowest propagation rate independent of the loading level. The crack growth in cast shafts is considered more differentiated. At high load levels the austempered ductile iron is the most resistant material, in contrast to GJS-400-18-LT, where sudden, unstable crack growth occurs (see Fig. 11 c)). In the beginning,

1E-07

1E-05

1E-03

4 40

crac

k pr

opag

atio

n ra

te d

a/dN

stress intensity range ΔK [MPam0.5]

42CrMo4GJS-400-18-LTGJS-600-3GJS-800-10GJSF-SiNi30-5GJS-1000-5

crac

k de

pth

a

load cycles N

a

2c

a/c- +

a0+ -

a0+

-α+ -

0

5

10

15

20

25

1.E+03 1.E+04 1.E+05

crac

k de

pth

a [m

m]

load cycles N [-]

GJS-400-18-LT (semi-ellip.)GJSF-SiNi30-5 (semi-ellip.)GJS-600-3 (semi-ellip.)GJS-400-18-LT (circum.)GJSF-SiNi30-5 (circum.)GJS-600-3 (circum.)

27 %

44 %

45 %

76 %

89 %

99 %

73 %

56 %

55 %

24 %

11 %

1 %

1E+04 1E+06 1E+08

42CrMo4

GJS-400-…

GJSF-…

GJS-600-3

GJS-800-10

GJS-1000-5

fatigue life remaining life


at a lower load level, it is just the opposite. The fatigue crack growth in the normal strength ductile iron is slower than in GJS-800-10 and in GJS-1000-5 (Fig. 11 a)). At this loading, till approximately 4E+05 load cycles, also the brittle higher strength cast iron shaft (GJS-600-3) is more insensitive to fatigue cracking than the GJS-1000-5-shaft. Espe-cially GJSF-SINI30-5 is suitable at external stresses beneath the endurance limit. But, with the increasing number of load cycles, the crack propagation rate in normal and higher strength ductile iron shafts rises and unstable crack growth starts at a lower cycle numbers than in the GJS-800-10 shaft.

Fig. 10 shows the total life as a sum of fatigue life till crack initiation and remaining life (at initial thumbnail crack with a depth of 2 mm) till component failure, when the hotspot stress amplitude is 240 MPa. Here again the high discrepancy of the resistance with regard to fatigue and to fatigue crack growth is obvious.

Fig. 11. Crack propagation at cyclic-single-stage stress amplitude - a) 160 MPa, b) 300 MPa

4.2. Fracture mechanical investigation at real variable loading in a wind turbine

Furthermore, besides the assessment of remaining life after a fatigue crack initiation, the potential risk of an unde-tected imperfection in the rotor shaft has to be investigated. On this account, initially a conservative assumption for surface defects with different depths in the hotspot region of the rotor shaft from the beginning of the operation are done. The crack length increases as a function of load cycles at a realistic frequency distribution of the wind turbine bending moment as pictured in Fig. 12. The maximum value of the cumulative frequency distribution of stresses at the real notch geometry of the considered shaft is below the endurance limit (approximately 70 %). Furthermore, the high proportion of cycles with far smaller amplitudes leads to a much lower crack propagation rate in the wind turbine than at the test rig. For the crack growth calculation the cumulative frequency distribution of stress of the whole wind turbine life is divided by the cycle number of the least occurring class, sorted in descending order and then successively repeated till the whole cycles of lifetime (6E+08 cycles correspond to 20 years of service life) are passed through.

Fig. 12. Crack growth at real variable loading out of Fig. 1 c)

020406080

100120140160180

1.E+00 1.E+02 1.E+04 1.E+06

crac

k de

pth

a [m

m]

load cycles N [-]

42CrMo4GJS-400-18-LTGJSF-SiNi30-5GJS-600-3GJS-800-10GJS-1000-5

0

5

10

15

20

25

30

1E+00 4E+05

160 MPa

0

5

10

15

20

25

30

0E+00 5E+04 1E+05

300 MPa

10

60

110

160

0

50

100

1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08 1E+09

crac

k de

pth

a [m

m]

stres

s am

plitu

de σ

[MPa

]

load cycles N [-]

a0 = 20 mm

stress spectrum 42CrMo4 GJS-1000-5GJS-800-10 GJS-600-3 GJSF-SiNi30-5GJS-400-18-LT

a) b)


initial crack has a depth of 2 mm the propagation is less fast in the GJS-600-3 and the GJSF-SiNI30-5 rotor shaft. But at approximately 1E+05 load cycles the propagation rate increases, thus the crack depth exceeds the depth in the GJS-1000-5 shaft. From the beginning the crack in a shaft made of GJS-400-18-LT grows the fastest.

Fig. 7. Forman/Mettu curves of different materials Fig. 8. Influence of different parameters on crack growth – with a0 as the initial crack depth, α as the stress concentration factor and R

as the stress ratio

In this consideration a semi-elliptical crack in the shaft hotspot is assumed. Though, in sharp notched or hardened rotating bending loaded shafts, a circumferential crack is also possible. In the present case this assumption is very unlikely, but still has to be investigated. A closer look on a selection of the considered materials shows a much lower number of load cycles at the same initial crack depth than for a semi-elliptical crack geometry (see Fig. 9). Despite equal external stress and equal initial crack depth, the deciding reason for the higher stress intensity factor for a cir-cumferential crack, is the higher value of the geometry function, due to the higher cross section reduction. However, a material specific difference is not apparent.

Fig. 9. Assumption of semi-elliptical and circumferential crack Fig. 10. Total life of a rotor shaft made of different materials

4.1. Remaining life estimation at one-stage loading on the test rig

Subsequently the remaining life of the rotor shaft made of the considered materials is examined for the test environ-ment at different constant load amplitude (Fig. 11). Therefore, two different load stages are simulated. In the following investigation a 2 mm initial crack depth is assumed. The crack in the forged shaft has the lowest propagation rate independent of the loading level. The crack growth in cast shafts is considered more differentiated. At high load levels the austempered ductile iron is the most resistant material, in contrast to GJS-400-18-LT, where sudden, unstable crack growth occurs (see Fig. 11 c)). In the beginning,

1E-07

1E-05

1E-03

4 40

crac

k pr

opag

atio

n ra

te d

a/dN

stress intensity range ΔK [MPam0.5]

42CrMo4GJS-400-18-LTGJS-600-3GJS-800-10GJSF-SiNi30-5GJS-1000-5

crac

k de

pth

a

load cycles N

a

2c

a/c- +

a0+ -

a0+

-

α+ -

0

5

10

15

20

25

1.E+03 1.E+04 1.E+05

crac

k de

pth

a [m

m]

load cycles N [-]

GJS-400-18-LT (semi-ellip.)GJSF-SiNi30-5 (semi-ellip.)GJS-600-3 (semi-ellip.)GJS-400-18-LT (circum.)GJSF-SiNi30-5 (circum.)GJS-600-3 (circum.)

27 %

44 %

45 %

76 %

89 %

99 %

73 %

56 %

55 %

24 %

11 %

1 %

1E+04 1E+06 1E+08

42CrMo4

GJS-400-…

GJSF-…

GJS-600-3

GJS-800-10

GJS-1000-5

fatigue life remaining life

2958 Jenni Herrmann et al. / Procedia Structural Integrity 2 (2016) 2951–29588 Jenni Herrmann et al./ Structural Integrity Procedia 00 (2016) 000–000

Semi-elliptical surface cracks up to an initial depth of 4 mm are not growing more than 1 mm in these 20 years in any of the considered materials. Except for the GJS-1000-5-shaft, after 2E+08 cycles (around 6.7 years) an initial crack in the shaft hotspot with a depth of 10 mm is propagating less than 5 mm. And only in austempered ductile iron unstable crack growth occurs before the end of the lifetime is reached, when a 10 mm crack is located in the hotspot area since first day of operation. If the initial crack in the notch region has a depth of 20 mm, in several shafts unstable crack growth starts before completion of service life (see Fig. 12). After 1E+07 load cycles (one third of a year) no crack has grown more than 5 mm. But after 2.2E+07 load cycles (less than three quarters of a year), first of all the GJS-1000-5-rotor shaft fails, thereon the GJS-800-10-shaft (nearly 2.6E+07 load cycles), followed by the shaft made of GJS-400-18-LT (nearly 2.7E+07 load cycles) and subsequently the GJS-600-3-shaft (at 2E+08 cycles, around 7 years). In the shafts made of GJSF-SiNi30-5 and of forged steel there is no unstable crack growth till the end of turbine life. Once again, it appears that considering the realistic stress level with regard to fatigue and remaining life in the material selection process is highly important.

In this manner maintenance intervals can be deduced easily for shafts made of different materials. It should be noted, however, that these statements apply for climatically uncritical conditions. For negative temperatures a different order may arise.

5. Conclusion and outlook

In conclusion the paper contains a comprehensive comparison of the rotor shafts made of different materials under test conditions and under realistic loads in a wind turbine. It is demonstrated, why it is important to take account of other materials for the rotor shaft of a wind turbine in regard to the fatigue and the fracture mechanical behaviour. While rotor shafts made of cast iron have better qualities concerning fatigue at low loading, forged steel is superior at high load levels. Fracture mechanical investigations show a higher resistance of the forged shaft against fatigue crack propagation. Though, at stresses below the endurance limit cast iron is also persevering.

In order to realistically evaluate the risk of undetected cracks or premature initiated cracks in the rotor shaft while turbine operation, the crack propagation of different potential imperfections will be considered more closely.

Acknowledgements

The research project BeBen XXL is done in collaboration with Fraunhofer IWES and Suzlon Energy. It is funded by the German Federal Ministry for Economic Affairs and Energy (BMWi).

References

ASTM E 647-13a, 2013. Standard Test Method for Measurement of Fatigue Crack Growth Rates. ASTM International. AWEA, 2011. Wind Energy Industry Manufacturing Supplier Handbook. American Wind Energy Association. Fraunhofer, 2016. http://www.windenergie.iwes.fraunhofer.de/en/research_projects/anlagen--und-systemtechnik/beben_xxl.html, 28.03.2016. Germanischer Lloyd, 2010. Guideline for the Certification of Wind Turbines. Germanischer Lloyd WindEnergie GmbH. Gudehus, H., Zenner, H., 2007. Leitfaden für eine Betriebsfestigkeitsrechnung – Empfehlung zur Lebensdauerabschätzung von Maschinenbau-

teilen. 4th Edition, Verlag Stahleisen GmbH, Düsseldorf. Hau, E., 2008. Windkraftanlagen. 4th Edition. Springer-Verlag Berlin Heidelberg. Henkel, S., Hübner, P., Pusch, G., 2008. Zyklisches Risswachstumsverhalten von Gusseisenwerkstoffen – Analytische und statistische Aufbereitung

für die Nutzung mit dem Berechnungsprogramm ESACRACK. 40. DVM-Tagung, Arbeitskreis Bruchvorgänge. Herfurth, K., 2003. Austenitisch-ferritisches Gusseisen mit Kugelgraphit, Teil 1/ Teil 2. Giesserei-Praxis. Kyling, H., 2014. BEBEN XXL Test Bench - Final Design Review. Project-internal Document. Mikoleizik, P., Geier, G., 2014. SiWind – Werkstoffentwicklung für Offshore-Windenergieanlagen im Multimegawatt-Bereich. GIESSEREI 101. Pollicino, F., 2006. Bruchmechanische Fragestellung bei der Lebensdauerberechnung von Windenergieanlagen. Deutscher Verband für

Materialforschung und –prüfung e.V. Sander, M., 2008. Sicherheit und Betriebsfestigkeit von Maschinen und Anlagen. Springer-Verlag Berlin Heidelberg. Shirani, M., Härkegard, G., 2011. Fatigue life distribution and size effect in ductile cast iron for wind turbine components. Engineering Failure

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