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Office of Energy Efficiency & Renewable Energy

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Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Fatigue Test Design: Scenarios 

for Biaxial Fatigue Testing of a 

60-Meter Wind Turbine Blade

Nathan Post

National Renewable Energy Laboratory

Technical Report

NREL/TP-5000-65227

July 2016
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Fatigue Test Design: Scenarios 

for Biaxial Fatigue Testing of a 

60-Meter Wind Turbine Blade

Nathan Post

National Renewable Energy Laboratory

Prepared under Task No. WE15.1G01

Technical Report

NREL/TP-5000-65227

July 2016
NOTICE

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Abstract

Current practice in commercial certification of wind turbine blades is to perform separate flap 

and lead-lag fatigue tests. The National Renewable Energy Laboratory (NREL) has been 

researching and evaluating biaxial fatigue testing techniques and demonstrating various options,

typically on smaller-scale test articles at the National Wind Technology Center (NWTC). This 

report evaluates some of these biaxial fatigue options in the context of application to a 

multimegawatt blade certification test program at the Wind Technology Testing Center (WTTC)

in Charlestown, Massachusetts. To perform this evaluation, a fictional 60-meter (m) blade test 

specification is generated by extrapolating data from recent test programs to provide a realistic 

problem statement for evaluating biaxial fatigue test designs. A simple simulation technique 

including the addition of virtual mass is introduced that enables tuning of the frequency and 

moment curve in one direction independent of the other direction. This virtual mass tuning has 

been demonstrated at a smaller scale by installing mass on a slide table connected to the blade by 

a pushrod as in the Hybrid test program at the NWTC. Alternatively, virtual mass may be 

added—or in theory removed—using a hydraulic actuator with a force function that is in phase 

with the displacement. This has been shown to be possible using a Ground-based Resonance 

EXciter (GREX)–type approach at the WTTC where the bending moment distribution of a blade 

can be significantly altered by changing the test frequency. Several testing scenarios are 

generated and compared, including a quantum biaxial fatigue test and two phase-locked 

scenarios with 1:1 and 1:2 ratios between the flap and lead-lag frequencies. Each method offers 

some advantages and disadvantages when compared to the other approaches. Future work toward 

implementation of these phase-locked test techniques will require development of hardware 

capable of implementing virtual masses near the tip of blades where there are large deflection 

amplitudes to achieve target moment curves during biaxial testing of megawatt-scale blades.
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Acknowledgments

This project was possible through the collaboration between NREL and the Massachusetts Clean 

Energy Center’s WTTC. Experience and test data gained through this partnership have been key 

to making the observations, analysis, and conclusions of this report possible. The test designs 

considered are based on concepts that have been prototyped at a small scale at NREL’s NWTC 

with the goal of applying these to large wind turbine blades at the WTTC. This would not have 

been possible without detailed knowledge of the available hardware and test technology at the 

WTTC. The author would like to acknowledge WTTC Executive Director Rahul Yarala for 

supporting these collaborative efforts that are mutually beneficial to both laboratories and the 

industry at large.

Research projects conducted at the NWTC were integral in developing and prototyping the 

concepts that are employed in the blade test simulations presented in this paper. Key NREL staff 

working on these projects include Michael Desmond, David Snowberg, Ryan Beach, Bill Gauge, 

Michael Jenks, and Scott Hughes. 

Special thanks also go to Eric Harvey at Massachusetts Clean Energy Center and David 

Snowberg at NREL for their detailed review of this report.

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-

08GO28308 with the National Renewable Energy Laboratory. Funding for the work was 

provided by the DOE Office of Energy Efficiency and Renewable Energy, Wind and Water 

Power Technologies Office.
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List of Acronyms

BREX Blade Resonance EXciter

GREX Ground-based Resonance EXciter

Hz hertz

IREX Inertial Resonance EXciter (formerly UREX or 

Universal Resonance EXciter)

kg kilogram

kN kilonewton

m meter

MTS MTS Systems Corporation

MW megawatt

NREL National Renewable Energy Laboratory

NWTC National Wind Technology Center

PHLEX PHase Locked EXcitation 

R-ratio load ratio for a fatigue cycle (minimum 

load/maximum load)

Sandia Sandia National Laboratories

WTTC Wind Technology Testing Center
vi

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Mathematical Symbols

Symbol Description Typical units

Beam stiffness where E is the elastic modulus and I 

is the second moment of area

kN-m2

[ ] Mass matrix

Displacement vector

[ ] Stiffness matrix

Force vector

i Index for indicating the node {0,1, ..., n} or element 

{1,2,..., n} along the blade span

Displacement at node i m

Rotation at node i rad

Mass per unit length of element i kg/m

Length of element i m

, Mass of saddle applied at node i kg

, Rotational moment of inertia of saddle at node i kg-m

[ ]( ) Subset of mass matrix corresponding to the 

contribution from element i and point mass at node i

with individual matrix elements indicated as ( )

where j is the row and k is the column in the 4x4 

submatrix 

[ ]( ) Subset of the stiffness matrix corresponding to the 

contribution for each element with individual matrix 

elements indicated as ( ) where j is the row and k is 

the column in the 4x4 submatrix

Internal reaction moment at node i kNm

Internal shear reaction at node i kN

( ) Beam bending stiffness for element i kN-m2

Target moment at node i kNm

Mass kg

Force N

Frequency (typically resonance frequency) Hz.

Time s

Undamped natural frequency Hz.

Damping ratio

Displacement m

Damping coefficient kg/s

Spring constant kg/s2

Critical damping coefficient kg/s

Log decrement damping

q Index referring to a specific cycle

Energy J

Energy (potential and kinetic) during cycle q J
vii

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Symbol Description Typical units

, Maximum velocity of node i m/s

, Maximum rotational velocity of node i rad/s

Density, specifically density of air 1.2 kg/m3

Cross section height of element m

Coefficient of drag

Displacement of the blade at the exciter location m

Displacement amplitude of the blade at the exciter 

location

m

Acceleration of IREX moving mass relative to the 

blade

m/s2

Displacement of IREX moving mass m

Displacement amplitude of IREX moving mass m

Mass of portion of IREX that moves relative to the 

blade

kg

Acceleration of the blade at exciter location m/s2

Force amplitude applied by a GREX kN

Gravitational acceleration constant 9.80665 m/s2

{xg, yg, zg} Global coordinate system in the laboratory with 

gravity acting in the negative zg direction

m

di Local displacement of a node i m

, Mass of blade element i kg

Axial force in an element acting at a node kN

Angle of applied force at a node rad
viii

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Executive Summary

Structural testing of new wind turbine blade designs is conducted as part of third-party 

certification to help ensure the reliability and durability of these large complex structures over 

their lifetime. The goal is to apply mechanical loads in the laboratory that approximate the 

maximum loads and fatigue loads the blade will see over its lifetime on the turbine. Current 

industry practice for utility-scale wind turbines is to apply fatigue loads separately in the flap and 

lead-lag directions in the laboratory using resonance testing techniques where the structure is 

oscillated at its first natural frequency in the respective direction. Although simpler to 

implement, a significant disadvantage of running two separate fatigue tests is that this approach 

may miss defects or damage development in the blade due to combined loading present on the 

turbine. In addition, certification testing imposes economic costs on the turbine development 

cycle, and the development of methods to reduce the total testing time is advantageous. By 

applying the flap and lead-lag test loads simultaneously, it may be possible to reduce the total 

testing time compared to running separate fatigue tests sequentially. Therefore, significant 

research effort over the last decade has been focused on developing techniques for biaxial fatigue 

testing of these large structures. Most of these research techniques have only been demonstrated 

on relatively small stiff blades in comparison to modern 50+ meter blade designs. A challenge in 

these research efforts has been adequately demonstrating how the techniques can be scaled up to 

a multimegawatt turbine blade certification test. This report provides data and insights that help 

to bridge that gap with the goal of encouraging the evaluation of biaxial fatigue options in 

commercial test programs carried out at the WTTC and other laboratories worldwide.

This report develops a fictional 60-m blade test specification based on extrapolating data from 

recent test programs to provide a realistic problem statement for evaluating biaxial fatigue test 

designs. Available test excitation equipment is assumed to be the Inertial Resonance EXciter 

(IREX) system and Ground-based Resonance EXcitation (GREX) servo hydraulic systems 

supplied by MTS Systems Corporation. A simple simulation technique, including the addition of 

virtual mass, is introduced that enables tuning of the frequency and moment curve in one 

direction independently of the other direction. This virtual mass tuning has been demonstrated at 

a smaller scale by installing mass on a slide table connected to the blade by a pushrod as in the 

Hybrid test program at the NWTC. Alternatively, virtual mass may be added—or in theory 

removed—using a hydraulic actuator with a force function that is in phase with the displacement. 

This has been demonstrated through alteration in the bending moment distribution applied to a 

blade at resonance by changing the test frequency. In practice, there are limits to the range of 

virtual mass that can be applied with this method because increasing the frequency very much

beyond resonance tends to lead to control system instabilities. However, this method does work 

well for increasing the virtual mass and reducing the test frequency within the capacity of the 

available actuator.

Several testing scenarios are generated and compared to evaluate the new concepts against more 

traditional approaches. Single-axis tests in the lead-lag and flap direction are compared with a 

quantum test design where the frequencies in the flap and lead-lag directions are independent. 

The results show that some compromises are required in the accuracy of the bending moment 

curve for a quantum biaxial fatigue test, particularly if virtual mass is not used. Snowberg et al.

(2014) previously demonstrated that there are drawbacks to quantum biaxial fatigue testing in 

practice because the moment amplitude in the lead-lag direction will not be constant amplitude, 
ix

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which could result in extending the duration of the fatigue testing to achieve the required damage 

equivalent loads. These observations along with the goal of matching the phase angle between 

the lead-lag and flap loading directions to those typically experienced by a blade on a turbine in 

operation motivates the consideration of phase-locked testing (D. White 2004). Options for 

phase-locked testing are currently under investigation at the NWTC, including a scaled prototype 

“Hybrid” test setup currently being conducted on a 12-m blade. Two scenarios are considered in 

this report for phase-locked testing of a 60-m blade with a flap to lead-lag frequency ratio of 1:1 

and a frequency ratio of 1:2. The 1:1 frequency offers the greatest opportunity to control the 

phase angle in fatigue testing and thus best represent the real loading on the turbine if phase 

information is available. However, this test scenario extends the total biaxial testing to last 

roughly as long as for separate single-axis tests and the large virtual masses make achieving the 

lead-lag target bending moment distribution a challenge. A 1:2 frequency ratio has an advantage 

of not requiring nearly as much virtual mass, and the total testing time is reduced to just the time 

of a traditional lead-lag test. The phase relationship between the loading directions is not 

necessarily representative of the loads seen on a turbine; however, some combined loading is 

achieved and the phase angles can in theory be adjusted to represent certain operating states of 

the turbine. For a 1:2 frequency ratio test, virtual masses are often required near the tip of the 

blade in the flap direction, which experiences large deflections (a range as much as 10 m) and 

may be difficult to implement, particularly without adding mass in the lead-lag direction, which 

is undesirable as it reduces the lead-lag frequency. Future work in this area to develop and 

prototype systems capable of applying these virtual masses is recommended.
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Table of Contents

Executive Summary................................................................................................................................. viii

1 Introduction........................................................................................................................................... 1

2 Blade Test Specification...................................................................................................................... 8

2.1 Normalized Data and Parameters.................................................................................................. 8

2.2 Fictional 60-m Blade Specification............................................................................................. 20

3 Excitation and Control Equipment.................................................................................................... 28

3.1 Static Calibration......................................................................................................................... 28

3.2 Added Masses ............................................................................................................................. 28

3.3 IREX Actuator for Lead-Lag Fatigue ......................................................................................... 29

3.4 GREX Actuator for Flap Fatigue ................................................................................................ 29

3.5 PHLEX Concept.......................................................................................................................... 30

3.6 Hybrid Test Research Project...................................................................................................... 30

3.7 Virtual Mass................................................................................................................................ 32

4 Resonance Fatigue Test Simulation................................................................................................. 34

4.1 Dynamic Model........................................................................................................................... 34

4.2 Energy Balance ........................................................................................................................... 39

4.2.1 Structural Damping ........................................................................................................ 40

4.2.2 Aerodynamic Energy Loss............................................................................................. 43

4.2.3 Evaluating Damping Parameters.................................................................................... 45

4.2.4 Energy Input Calculations.............................................................................................. 45

4.2.5 Energy balance ............................................................................................................... 48

4.3 Gravitational Loading and Deformed Shape............................................................................... 50

4.4 Model Implementation ................................................................................................................ 55

5 Traditional Single-Axis Test Design ................................................................................................. 56

5.1 Flap Fatigue Test......................................................................................................................... 56

5.2 Lead-Lag Fatigue Test ................................................................................................................ 59

6 Biaxial Fatigue Test Design............................................................................................................... 62

6.1 Quantum Test (Random Phase)................................................................................................... 62

6.2 Phase Locked 1:1 ........................................................................................................................ 65

6.3 Phase Locked 1:2 ........................................................................................................................ 69

6.4 Total Test Time Comparison....................................................................................................... 72

7 Conclusion .......................................................................................................................................... 74

References................................................................................................................................................. 76
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List of Figures

Figure 1. A biaxial force-displacement fatigue test on a wind turbine blade using two actuators and a bell 

crank conducted at NREL in 2002........................................................................................... 2

Figure 2. A prototype resonance fatigue shaker mounted on a 37-m blade at NREL. The blue mass is 

moved up and down relative to the blade using a hydraulic actuator mounted on top of the 

device. ...................................................................................................................................... 3

Figure 3. BREX fatigue test system combining a linear flap fatigue resonance shaker and a forcedisplacement lead-lag fatigue test. ........................................................................................... 4

Figure 4. Prototype linear initial resonance excitation system in both the flap and lead-lag directions 

mounted on a 9-m blade........................................................................................................... 5

Figure 5. MTS IREXs installed on a turbine blade (viewed from root to tip) for conduction of a biaxial 

resonance fatigue test............................................................................................................... 5

Figure 6. GREX 50 in operation on a flap fatigue test at the Wind Technology Testing Center. ................ 6

Figure 7. Normalized prebend based on maximum prebend ...................................................................... 11

Figure 8. Normalized chord based on the maximum chord........................................................................ 11

Figure 9. Normalized thickness based on maximum (root) thickness........................................................ 12

Figure 10. Normalized twist based on twist at 30% span ........................................................................... 12

Figure 11. Normalized mass per unit length based on mass per until length at 30% span ......................... 13

Figure 12. Normalized flap direction stiffness (EI) based on EI at 30% span............................................ 13

Figure 13. Normalized edge stiffness (EI) based on EI at 30% span.......................................................... 14

Figure 14. Normalized maximum flap static test target moment distribution ............................................ 14

Figure 15. Normalized minimum flap static test target moment distribution ............................................. 15

Figure 16. Normalized maximum edge static test target moment distribution ........................................... 15

Figure 17. Normalized minimum edge static test target moment distribution............................................ 16

Figure 18. Normalized lead-lag fatigue target moment range distribution................................................. 16

Figure 19. Normalized flap fatigue target moment range distribution........................................................ 17

Figure 20. Single actuator with fixed mass (black) and minimum moving mass (yellow)......................... 29

Figure 21. Hybrid concept for applying mass to the blade in the lead-lag direction but leaving the mass in 

the flap direction unchanged. In this case, the IREX is mounted off the blade as part of the 

virtual mass in the lead-lag direction. .................................................................................... 31

Figure 22. Hybrid configuration using IREX and GREX excitation systems attached to the same saddle.31

Figure 23. Addition of two sine wave force functions showing the result as a sine wave with shifted 

phase. Phase shifting is accomplished with a GREX-type device by modifying the excitation 

frequency, and a target phase can be set to include virtual mass in the forcing function for 

the test. ................................................................................................................................... 33

Figure 24. Modification of the bending moment by operating a GREX located at 43% span at different 

frequencies, effectively adding a virtual mass to this location as the frequency was decreased 

from 0.78 Hz to 0.75 Hz. The force amplitude was adjusted to achieve the same strain 

amplitude at the first set of strain gauges at each frequency.................................................. 33

Figure 25. Finite element concept for dynamic analysis............................................................................. 34

Figure 26. Deflection of element 1 ............................................................................................................. 38

Figure 27. Example global coordinate system description referencing the test rig .................................... 50

Figure 28. Deformation of element i under shear and bending................................................................... 51

Figure 29. Geometry definition for calculation of updated position Xg and Zg .......................................... 53

Figure 30. Free-body diagram of an element in deformed position............................................................ 54

Figure 31. Bare blade moment distribution at resonance in flap direction. Natural frequency is 0.56 Hz. 57

Figure 32. Flap fatigue test moment range achieved relative to target moment ......................................... 58

Figure 33. Bending moment extrema during flap fatigue test compared to static test target loads............ 58

Figure 34. R-ratio (minimum moment/maximum moment) distribution for proposed flap fatigue test..... 59
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Figure 35. Bare blade moment distribution at resonance in lead-lag direction. Natural frequency is 1.01 

Hz........................................................................................................................................... 59

Figure 36. Lead-lag fatigue test moment range achieved relative to target moment.................................. 60

Figure 37. Lead-lag fatigue moment relative to maximum and minimum edge static test target moment. 61

Figure 38. Quantum biaxial fatigue test flap direction moment distribution.............................................. 64

Figure 39. Quantum biaxial fatigue test lead-lag direction moment distribution ....................................... 64

Figure 40. Motion pattern representing 30 seconds of test operation for quantum biaxial fatigue test...... 65

Figure 41. Flap bending moment distribution achieved with 1:1 frequency ratio test setup ...................... 67

Figure 42. Lead-lag bending moment achieved with 1:1 frequency ratio test setup .................................. 68

Figure 43. Displacement representation for 1:1 frequency ratio with phase angle of 90 deg (left), 45 deg 

(center) and 0 deg (right). The mirror image of these is also possible.................................. 68

Figure 44. Flap bending moment distribution achieved with 1:2 frequency ratio test setup ...................... 70

Figure 45. Lead-lag bending moment achieved with 1:2 frequency ratio test setup .................................. 71

Figure 46. Displacement representation for 1:2 frequency ratio with phase angle of 90 deg (left), 45 deg 

(center) and 0 deg (right). The mirror images of these are also possible............................... 71

Figure 47. Comparison of test time between different test methods........................................................... 73

List of Tables

Table 1. Blade Parameters and Normalization Parameters........................................................................... 9

Table 2. Normalized Mean Property Distribution ...................................................................................... 17

Table 3. Scaled 60-m Blade Geometry and Beam Element Properties....................................................... 21

Table 4. Scaled 60-m Test Target Loads Including All Design and Test Factors ...................................... 24

Table 5. IREX Actuator Specifications....................................................................................................... 29

Table 6. GREX Specifications.................................................................................................................... 30

Table 7. Proposed Uniaxial Flap Fatigue Test Configuration and Dynamics at Each Saddle .................... 57

Table 8. Proposed Uniaxial Lead-Lag Fatigue Test Configuration and Dynamics at Each Saddle............ 60

Table 9. Mass Distribution for Quantum Biaxial Fatigue Test................................................................... 63

Table 10. Saddle Amplitudes and Forces from Quantum Biaxial Fatigue Test Simulation ....................... 63

Table 11. Mass Configuration for Phase-Locked Biaxial Test with 1:1 Frequency Ratio Using an IREX in 

the Lead-Lag Direction and a GREX in the Flap Direction to Excite the Blade ................... 66

Table 12. Displacement, Acceleration, and Forces for Phase-Locked Biaxial Test with 1:1 Frequency 

Ratio....................................................................................................................................... 67

Table 13. Mass Configuration for Phase-Locked Biaxial Test with 1:2 Frequency Ratio ......................... 69

Table 14. Displacement, Acceleration, and Forces for Phase Locked Biaxial Test with 1:2 Frequency 

Ratio....................................................................................................................................... 70
1

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1 Introduction

This report presents a study of a biaxial fatigue test simulation for a fictional 60-meter (m) blade 

to better assess the future needs and potential for implementation of these techniques in 

certification and research and development testing of large wind turbine blades. The primary 

goal of structural testing of wind turbine blades is to demonstrate the performance of the 

structure under the anticipated lifetime loads. Advantages to biaxial testing include the potential 

for a reduction in total test time and possibly to apply test loads that are closer to the loading the 

blade will experience in operation on the turbine and thus are more realistic when compared with 

separate, single-axis fatigue tests. Reduced test time reduces the costs both of the testing itself 

and of the business uncertainty associated with having a production line ready to go prior to the 

completion of the test program. More realistic structural testing can better identify weaknesses in 

a design that could lead to failures once the turbine is deployed, therefore improving the turbine 

blade reliability. In both cases, these benefits can lead to reductions in the cost of wind energy. 

However, achieving these advantages in large-scale commercial certification testing has proven 

elusive due to a combination of technical challenges and industry momentum to continue with 

the current accepted practice rather than risk applying a potentially more severe biaxial loading 

condition. This report explores several concepts for biaxial testing to evaluate the design space of 

a multimegawatt biaxial fatigue test by defining the forces and displacements required for a 

typical certification test program under the IEC 61400-23 Standard (2014). These results also 

provide a design space scope for biaxial test systems with the goal of encouraging test labs and 

blade original equipment manufacturers to explore implementation of biaxial test techniques 

when planning a certification test.

Early structural tests of wind turbine blades were primarily performed in the flap direction. For 

relatively small blades, the flap fatigue loads are higher than the lead-lag loads, and these singleaxis tests thus represented the primary load the blades seen on the turbine. Fatigue loading was 

conducted using actuator(s) operating in a force-displacement mode with frequencies well below 

the first resonance frequency of the structure. A force-displacement mode test is defined as a test 

run well below the system resonance frequency where the applied force is in phase with the 

resulting displacement. This test method is similar to approaches used in other large-scale 

structural testing applications, for example, in aviation. Force-displacement enabled good control 

of the bending moment and load ratio (sometimes called the R-ratio) applied. As blades grew 

longer in the 1990s, the lead-lag direction fatigue loads became more significant due to the 

weight of the blades as the turbine rotor spins. Separate force-displacement lead-lag and flap 

tests were sometimes conducted, but it was recognized that these separate tests did not accurately 

represent the phase angle of the combined loading on the turbine. In 1999, the National 

Renewable Energy Laboratory (NREL) introduced a method for biaxial loading of a wind 

turbine blade using actuators and a bellcrank to simultaneously load the flap and lead-lag 

directions (Hughes, Musial and Stensland 1999). A photo depicting this type of fatigue test is 

shown in Figure 1. Because of the relatively large deflections seen in the blade test, an algorithm 

was developed for controlling the motion and thus the applied moment combinations and phase 

angle given the nonlinearity due to the test set-up geometry.
2

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Figure 1. A biaxial force-displacement fatigue test on a wind turbine blade using two actuators 

and a bell crank conducted at NREL in 2002. 

Photo by NREL 14825

However, as wind turbine blade size increased in the 2000s, traditional force-displacement test 

techniques became expensive to implement and time consuming due to the large strokes and 

slow test speeds required to achieve the desired moments. Resonance fatigue testing was 

developed by several different laboratories, including NREL, to accelerate testing speeds and 

achieve more accurate bending moment distributions on the blade while using less energy to 

conduct the test. At NREL, early resonance fatigue testing involved a custom servo-hydraulic 

linear shaker with a mass attached to the end of an actuator mounted on the blade (Figure 2). The 

actuator would be operated in displacement control applying a sinusoidal motion to the mass. At 

the resonance frequency of the test system (turbine blade plus added the added test equipment), 

this will excite the blade. The exciter amplitude is increased until the target load level is 

achieved. A balance between the energy input and the energy loss due to structural and 

aerodynamic damping per cycle is maintained. A combination technique utilizing a forcedisplacement test in the lead-lag direction and a resonance fatigue test in the flap direction was 

developed by White et al. (2004) and is referred to as the Blade Resonance Excitation (BREX) 
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system. This approach enabled control of the phase angle and has the advantages of resonance 

testing in the flap direction. The BREX was implemented successfully for the test of a 37-m 

wind turbine blade shown in Figure 3 (D. White 2004). However, the energy requirements and 

point loading for the lead-lag direction were substantial and achieving the desired bending 

moment curve in the lead-lag direction would likely require multiple loading points along the 

span. This further increases the energy requirement and becomes technically challenging on 

large blades ( i.e., blades longer than 50 m) that can have flap-fatigue tip displacement ranges 

greater than 10 m. An additional drawback of this approach is that typically modern fatigue tests 

are designed with more cycles in the lead-lag direction than in the flap direction to avoid nearing 

the static strength of the blade during the accelerated fatigue test. Because the BREX requires 

testing the lead-lag frequency at the flap resonance frequency, the test time to achieve the leadlag damage equivalent loads may be significantly extended.

Figure 2. A prototype resonance fatigue shaker mounted on a 37-m blade at NREL. The blue mass 

is moved up and down relative to the blade using a hydraulic actuator mounted on top of the 

device.

Photo by Warren Gretz, NREL 12890
4

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Figure 3. BREX fatigue test system combining a linear flap fatigue resonance shaker and a forcedisplacement lead-lag fatigue test.

Photo by Warren Gretz, NREL 12893

Following the development of the BREX, efforts were undertaken to design and demonstrate a 

system for biaxial resonance fatigue testing where the blade would be excited in both the flap 

and lead-lag directions at resonance. A smaller scale prototype system mounted on a 9-m blade is 

shown in Figure 4. This research resulted in an excitation technology (Hughes, Musial and White 

2014) that has been licensed for manufacturing by MTS Systems Corporation (MTS) which 

created the Inertial Resonance Exciter (IREX) product—initially called the Universal Resonance 

Exciter (UREX)—to meet the requirements for this type of biaxial fatigue testing. The IREX 

technology was used to perform uniaxial fatigue tests on blades up to 50 m in length (Snowberg 

and Hughes 2013). In addition, a biaxial “quantum” fatigue test using IREX actuators in both the 

flap and lead-lag directions was successfully conducted and the required controls to maintain the 

desired test amplitude were demonstrated (Snowberg, et al. 2014). The hardware configuration 

for this test is shown in Figure 5.
5

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Figure 4. Prototype linear initial resonance excitation system in both the flap and lead-lag 

directions mounted on a 9-m blade.

Photo by Mike Jenks, NREL 17641

Figure 5. MTS IREXs installed on a turbine blade (viewed from root to tip) for conduction of a 

biaxial resonance fatigue test.

Photo by David Snowberg, NREL 28708

In 2008, the U.S. Department of Energy sought to expand the large-scale blade testing capability 

in the United States. The Massachusetts Clean Energy Center was selected to own and operate a 

new laboratory located in Boston, Massachusetts. This new laboratory, named the Wind 

Technology Testing Center (WTTC), was constructed to meet the growing need for commercial 

testing of large wind turbine blades. The WTTC opened in 2011. MTS IREX units were 

purchased as part of the initial test equipment and technology at the WTTC and are currently in 

use for lead-lag fatigue testing of multimegawatt-scale blades at the laboratory. However, 

limitations were identified in the MTS IREX to provide sufficient energy input in the flap 

direction to overcome the aerodynamic damping of flexible 50+ m blades. The problem was that 

to increase the energy input, more mass must be added to the blade, in turn decreasing the test 
6

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frequency. A reduced test frequency reduces the energy input per cycle from an inertial massbased exciter, preventing the target flap moment range from being achieved with this hardware. 

While an IREX-like device with greater stroke will improve the possible energy input, all other 

things being equal, it would still be a challenge to design flap fatigue tests that meet the target 

bending moment distribution on a large blade using this type of exciter. A collaboration between 

NREL, MTS, and the WTTC to address these challenges in designing flap fatigue tests with 

existing hardware resulted in the development of the Ground-based Resonance Exciter (GREX) 

system, which was first implemented in 2013. In this approach to resonance fatigue testing, an 

actuator is connected between the blade and the ground and applies a forcing function to excite 

the structure at or near its fundamental resonance frequency. The GREX (Figure 6) enables 

significant greater energy input to a blade without requiring adding significant mass to the test 

system. This in turn results in typically achieving higher test frequencies compared with an 

IREX excitation system depending on the required additional mass to meet the target bending 

moment distribution. The GREX is operated at the first flap resonance frequency of the test 

system such that it applies an approximately sinusoidal forcing function to the blade that leads 

the displacement by a phase angle of roughly 90 degrees. In addition, the GREX technology 

enables adding or removing virtual mass, a concept that will be discussed in more detail later in 

this report, by running slightly off resonance so that part of the forcing function is in phase with 

displacement and part is out of phase.

Figure 6. GREX 50 in operation on a flap fatigue test at the Wind Technology Testing Center.

Photo by Nathan Post, NREL 34756

This report considers the options for biaxial fatigue testing of a 60-m wind turbine blade at the 

WTTC using the IREX and GREX technology as well as estimating what additional hardware or 

technology might be required. Insight into the use of these test systems is gained through 
7

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experience at the WTTC testing blades in the 50+ m length along with results from recent 

research undertaken at the National Wind Technology Center (NWTC) at NREL to prototype 

potential systems using smaller-scale test articles. In particular, this report will evaluate potential 

test systems that combine resonance loading with virtual masses—masses mounted to slide 

tables or other mechanical linkages so that they only act in one direction or forcing functions 

from hydraulic actuators—to enable phase-locked resonance or quasi-resonance testing. These 

research projects include the phase-locked excitation (PHLEX) approach (Beckwith, White and 

Barsotti 2013) where the concept is to increase the flap fatigue test frequency to match the leadlag resonance frequency and more recently the “Hybrid” test project that adds mass in one test 

direction without impacting the other test direction.

Unfortunately, the mechanical properties and test load levels for most commercial blades are 

considered company proprietary information and cannot be used in this type of public research 

study. Past blade scaling studies and research blade designs, such as the Sandia 61.5-megawatt 

(MW) blade model developed for the NREL 5-MW reference turbine (Resor 2013) are 

considerably stiffer and heavier in comparison with similar size commercial blades produced 

recently. This may be attributed to different design criteria: the Sandia 61.5 blade was designed 

for IEC class IB wind conditions while most of the blades currently tested in the US are designed 

for lower power output turbines in IEC wind class II and III conditions and therefore are 

subjected to lower wind speeds within their design envelope. Differences in mass and stiffness 

are critical in the design of a fatigue test where the larger deflections significantly increase the 

energy input requirements and change the natural frequencies and mode shapes. To provide as 

representative a test article as possible, the data from 17 different commercial turbine blades has 

been normalized and averaged to generate a single scalable blade used to provide the 

specifications for the 60-m test article considered in this report.

To estimate the loading applied to a turbine blade, a simple fatigue modeling approach is 

presented that has been fit and verified against existing test data and provides good estimates of 

the required energy and force inputs during resonance fatigue testing. This model is similar to 

approaches taken by White (2004) and Desmond (2009), but separates the aerodynamic and 

structural damping to enable more accurate representation of the energy requirements as blades 

become larger and aerodynamic damping in fatigue testing dominates the total damping.

In addition to the phase-locked testing concept where the flap and lead-lag frequencies have a 

1:1 ratio, this report also introduces the idea of using other simple Lissajous figures where a 

specific phase angle is maintained between the flap and lead-lag frequencies. This report 

specifically considers the ratio of 1:2 because many blades in the 50–60 m range have test 

frequencies that fall close to this ratio.
8

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2 Blade Test Specification

To provide a realistic assessment of a possible biaxial test configuration and the hardware 

required to excite and control that test, an accurate blade model is required. Several scaling 

studies in the past have developed reference wind turbine blade models that are publicly 

available and have been used for turbine simulation and cost studies. One example is the Sandia 

National Laboratories (Sandia) 61.5-m reference blade created by Sandia for the NREL offshore 

5-MW baseline wind turbine (Resor 2013). Unfortunately, these fictional blades have proven to 

be insufficient for modeling structural test requirements due to significantly overpredicting the 

stiffness and mass of the blades in comparison to the present day commercial blade designs. 

Several factors for this include the continuous improvement in blade design, materials, and 

manufacturing technology as well as an industry trend to design larger rotors optimized for lower 

wind speed conditions. Most utility-scale wind turbine blades currently under certification testing 

in the United States have lengths in the 50- to 60-m range and are designed for 1.6- to about 3-

MW turbines. These blades are typically designed for wind class II or III turbines although this 

information is not available for all of the blades included in this study. As longer blades have 

been designed for smaller-capacity turbines and lower wind conditions, the corresponding 

stiffness and mass of the blade have not increased as much as might have been predicted from 

scaling earlier designs.

Rather than attempt the design of a blade, this study relies on curve fitting and extrapolating the 

geometry, mass, stiffness, and applied test loads based on data from commercial blade tests 

conducted over the past 4 years. This enables us to provide a realistic example blade without 

compromising proprietary information. The blade test article specifications and target loads from 

17 different test articles in the 44-m to 57-m length range have been normalized, combined, and 

slightly extrapolated to generate a realistic fictional test article whose properties can be released 

in the public domain. The process used for normalizing the data is described here along with the 

final results; however, to keep the source data confidential, the precursor data cannot be 

provided. Reasonable extrapolation of these data to a fictional blade exceeding the length of any 

of the blades studied was made possible by considering each normalizing parameter as a function 

of blade length. Although there is always some risk of nonlinearities impacting the accuracy 

when extrapolating a data set, the small extrapolation from a 57-m length to a 60-m length limits 

the risk of a gross error in the predicted blade properties. A 60-m blade length was selected 

because it is desirable to consider how proposed test methods will apply to larger blades.

2.1 Normalized Data and Parameters

The fatigue test simulation to be conducted for this study requires the data necessary to assemble 

a beam element model of the blade. The parameters that are included in this scaling study are 

listed in Table 1. The undeformed geometry, global stiffness parameters, and applied target 

loading are considered. The fatigue test design for the blades used as input in this study varied 

from 1 million to 9 million cycles. In each case, the test target was scaled to 2 million cycles for 

lead-lag fatigue and 1 million cycles for flap fatigue using the S-N curve inverse slope parameter 

provided by the customer, if available, or assumed to be an inverse slope of 9 if not available. 

Not all information was available for all blades. In some cases, multiple blades used in the study 

had the same external geometry, so to develop a representation of each parameter only the subset 

of blades with unique information is used. To define the final curve fit blade, several parameters 

must be arbitrarily selected, including the blade length, maximum chord, and prebend.
9

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

The following process was performed to normalize and combine the data. First, the respective 

data for each blade were interpolated for 101 equally spaced nodes between the blade root and 

the blade tip from data provided by the blade manufacturer or turbine original equipment 

manufacturer to the test laboratory. Then, the resulting values were normalized based on the 

values at a specific normalization location, as indicated in Table 1. For target loading, it was 

reasonable to use the root moments. However, different blade designers and blade designs state 

widely varying unit mass and stiffness properties near the root of the blade, so a point farther out 

where results were more consistent was selected for normalization, in this case, using the values 

at 30% span. Likewise, the twist reported for the root of a blade where it is round varies widely;

again, the twist at 30% span was used for normalization of the data. Geometric data were 

normalized by the maximum value of the chord, thickness, and prebend regardless of where they

occurred.

Table 1. Blade Parameters and Normalization Parameters

Property Normalization 

location

Parameter slope

linear fit of 

normalization value 

vs. span (m)

Parameter offset

linear fit of 

normalization value 

vs. span (m)

Geometry

Prebend Tip (max prebend)

Chord Max Chord

Thickness Max Thickness

Twist 30% span 0.1583 deg/m 0.5212 deg

FEA beam properties

Mass/unit length 30% span 4.298 (kg/m)/m -6.443 kg/m

Stiffness EI–Flap 30% span 32,118 kN-m2/m -1,061,000 kN-m2

Stiffness EI–Lead-lag 30% span 125,886 kN-m2/m -4,449,000 kN-m2

Test target moment including all test factors

Static Max Flap Root 484.4 kNm/m -15,780 kNm

Static Max Edge Root 269.0 kNm/m -8,689 kNm

Static Min Flap Root 458.3 kNm/m -16,630 kNm

Static Min Edge Root 266.9 kNm/m -9,221 kNm

Fatigue lead-lag bending 

moment range for 2 million 

cycles

Root

409.7 kNm/m -13,970 kNm

Fatigue flap bending moment 

range for 1 million cycles Root 252.2 kNm/m -6,394 kNm

The normalized blade properties along with ±2 standard deviations are presented in Figure 7

through Figure 13 to demonstrate the range of variability observed in each parameter. Prebend 

shape is relatively inconsistent between different blades; however, as this has limited impact on 
10 

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the fatigue tests, the exact shape of the prebend is not critical. The mean distribution of the 

normalized prebend provides a smooth curve and is considered acceptable for this study. 

Normalized chord and thickness distributions are relatively consistent among the blades

surveyed. As previously mentioned, twist shows wide variability near the root but is reasonably 

consistent past 30% span and again will have no impact on the fatigue simulations undertaken in 

this study. Mass per unit length, flap, and lead-lag stiffness all vary widely in the root portion of 

the blade but are reasonably consistent and provide a smooth curve past the 30% span 

normalization point. Results are consistent across the blades surveyed for the shape of the 

normalized target test loads as shown in Figure 14 through Figure 19, so the test specification 

developed for the fictional blade will be fairly representative of the typical target load 

distribution required. 

Once the results are normalized, the mean, median, and standard deviation of these normalized 

values can be found as a function of percent span. The mean values reported in Table 2 are used 

to calculate the distribution of the reference blade. For most properties, the normalizing 

parameter is approximately linear as a function of blade span. The slope and offset for this 

normalizing parameter as a function of blade span in meters are presented in Table 1. Thus, once 

the blade length, prebend, and maximum chord are selected, the rest of the test specification 

information can be generated as follows:

1. Determine normalizing parameter

A. Chord normalization is maximum chord, prebend normalization is the prebend. 

B. Thickness normalization is the root chord from chord distribution to provide a 

round root. 

C. All others–select length of blade to be generated, then:

= +

(1)

2. Multiply normalized distribution (Table 2) by normalizing parameter.

3. Multiply span fraction by selected blade length.
11

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Figure 7. Normalized prebend based on maximum prebend

Figure 8. Normalized chord based on the maximum chord.

Note, because the data for each blade as normalized is based on that blade’s maximum 

chord and the maximum chord occurs at different fractional spans for different blades, the 

mean and median values do not quite reach 1.0.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized prebend

Fraction span

Mean

Median

2 SD+

2 SD0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized chord 

Fractopm span

Mean

Median

2 SD+

2 SD-
12

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Figure 9. Normalized thickness based on maximum (root) thickness

Figure 10. Normalized twist based on twist at 30% span

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized thickness

Fraction span

Mean

Median

2 SD+

2 SD-

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized twist

Fraction span

Mean

Median

2 SD+

2 SD-
13

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Figure 11. Normalized mass per unit length based on mass per until length at 30% span

Figure 12. Normalized flap direction stiffness (EI) based on EI at 30% span

0.01

0.1

1

10

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized mass per unit length - Log scale

Fraction span

Mean

Median

2 SD+

2 SD0.0001

0.001

0.01

0.1

1

10

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized flap stiffness - Log scale

Fraction span

Mean

Median

2 SD+

2 SD-
14

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Figure 13. Normalized edge stiffness (EI) based on EI at 30% span

Figure 14. Normalized maximum flap static test target moment distribution

0.0001

0.001

0.01

0.1

1

10

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized edge stiffness - Log scale

Fraction span

Mean

Median

2 SD+

2 SD0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized maximum flap static load

Fraction span

Mean

Median

2 SD+

2 SD-
15

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Figure 15. Normalized minimum flap static test target moment distribution

Figure 16. Normalized maximum edge static test target moment distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized min flap static load

Fraction span

Mean

Median

2 SD+

2 SD0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized max edge static load

Fraction span

Mean

Median

2 SD+

2 SD-
16

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Figure 17. Normalized minimum edge static test target moment distribution

Figure 18. Normalized lead-lag fatigue target moment range distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized min edge static load

Fraction span

Mean

Median

2 SD+

2 SD0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized lead-lag fatigue target moment

Fraction span

Mean

Median

2 SD+

2 SD-
17

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Figure 19. Normalized flap fatigue target moment range distribution

Table 2. Normalized Mean Property Distribution

Span fractionPrebendChordThicknes

s

TwistMass per unit lengthFlap stiffnessEdge stiffnessStatic max flapStatic max edgeStatic min flapStatic min edgeDynamic flapDynamic lead-lag

0.00 0.000 0.633 1.000 1.247 9.245 16.160 5.593 1.000 1.000 1.000 1.000 1.000 1.000

0.01 0.000 0.634 0.996 1.247 4.920 12.633 4.283 0.981 0.980 0.979 0.979 0.982 0.978

0.02 0.000 0.635 0.990 1.247 2.791 9.540 3.147 0.963 0.959 0.959 0.958 0.968 0.957

0.03 0.001 0.642 0.981 1.271 2.094 7.903 2.555 0.945 0.940 0.939 0.938 0.954 0.936

0.04 0.001 0.655 0.970 1.319 1.857 6.903 2.202 0.927 0.922 0.919 0.918 0.934 0.916

0.05 0.001 0.671 0.955 1.393 1.717 6.112 1.937 0.909 0.904 0.898 0.899 0.917 0.896

0.06 0.001 0.691 0.938 1.483 1.599 5.495 1.733 0.891 0.886 0.878 0.881 0.900 0.875

0.07 0.001 0.715 0.917 1.573 1.521 5.125 1.654 0.873 0.868 0.858 0.863 0.884 0.855

0.08 0.001 0.742 0.895 1.647 1.461 4.802 1.607 0.855 0.850 0.838 0.846 0.869 0.835

0.09 0.001 0.770 0.872 1.701 1.410 4.511 1.582 0.837 0.832 0.818 0.828 0.852 0.815

0.10 0.002 0.799 0.848 1.716 1.378 4.250 1.582 0.819 0.814 0.799 0.810 0.834 0.796

0.11 0.002 0.827 0.824 1.730 1.359 3.975 1.590 0.801 0.795 0.780 0.793 0.818 0.775

0.12 0.002 0.853 0.799 1.718 1.346 3.734 1.612 0.783 0.777 0.761 0.775 0.802 0.754

0.13 0.003 0.877 0.775 1.708 1.340 3.495 1.639 0.765 0.759 0.743 0.757 0.787 0.733

0.14 0.004 0.899 0.750 1.683 1.329 3.261 1.663 0.748 0.741 0.725 0.739 0.770 0.715

0.15 0.004 0.918 0.725 1.655 1.325 3.046 1.676 0.731 0.723 0.707 0.721 0.753 0.697

0.16 0.005 0.934 0.700 1.625 1.305 2.819 1.674 0.714 0.706 0.689 0.704 0.737 0.679

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized flap fatigue moment range

Fraction span

Mean

Median

2 SD+

2 SD-
18

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Span fraction Prebend Chord Thicknes

s

TwistMass per unit lengthFlap stiffnessEdge stiffnessStatic max flapStatic max edgeStatic min flapStatic min edgeDynamic flapDynamic lead-lag

0.17 0.006 0.949 0.676 1.594 1.293 2.615 1.681 0.697 0.688 0.671 0.686 0.721 0.662

0.18 0.007 0.961 0.652 1.556 1.278 2.430 1.677 0.681 0.670 0.653 0.669 0.705 0.644

0.19 0.008 0.969 0.629 1.513 1.249 2.251 1.614 0.664 0.653 0.636 0.652 0.689 0.627

0.20 0.009 0.975 0.607 1.469 1.228 2.074 1.543 0.648 0.636 0.619 0.636 0.673 0.609

0.21 0.011 0.977 0.586 1.420 1.202 1.913 1.475 0.631 0.619 0.602 0.619 0.657 0.592

0.22 0.012 0.978 0.565 1.370 1.177 1.776 1.392 0.615 0.602 0.585 0.604 0.641 0.575

0.23 0.014 0.977 0.545 1.319 1.148 1.643 1.335 0.600 0.586 0.569 0.588 0.626 0.559

0.24 0.016 0.973 0.527 1.268 1.122 1.530 1.265 0.584 0.569 0.553 0.572 0.611 0.543

0.25 0.019 0.968 0.509 1.220 1.093 1.422 1.215 0.568 0.553 0.538 0.557 0.596 0.527

0.26 0.021 0.961 0.492 1.171 1.068 1.321 1.163 0.552 0.538 0.522 0.542 0.581 0.510

0.27 0.024 0.954 0.475 1.122 1.047 1.231 1.120 0.537 0.522 0.507 0.526 0.565 0.494

0.28 0.027 0.945 0.459 1.080 1.030 1.150 1.081 0.521 0.506 0.492 0.511 0.550 0.478

0.29 0.030 0.932 0.444 1.039 1.014 1.071 1.041 0.506 0.491 0.477 0.497 0.535 0.463

0.30 0.034 0.919 0.430 1.000 1.000 1.000 1.000 0.492 0.476 0.463 0.482 0.520 0.448

0.31 0.038 0.905 0.416 0.960 0.988 0.933 0.960 0.477 0.461 0.449 0.468 0.505 0.433

0.32 0.042 0.890 0.403 0.922 0.978 0.871 0.922 0.463 0.447 0.435 0.454 0.491 0.418

0.33 0.046 0.876 0.391 0.885 0.966 0.812 0.883 0.449 0.432 0.421 0.439 0.477 0.404

0.34 0.050 0.860 0.379 0.849 0.952 0.756 0.843 0.434 0.418 0.407 0.425 0.463 0.389

0.35 0.055 0.845 0.367 0.814 0.936 0.704 0.803 0.421 0.405 0.394 0.411 0.448 0.375

0.36 0.060 0.829 0.356 0.779 0.927 0.658 0.769 0.408 0.392 0.382 0.398 0.435 0.361

0.37 0.065 0.814 0.345 0.746 0.914 0.614 0.731 0.395 0.379 0.369 0.385 0.421 0.347

0.38 0.070 0.798 0.335 0.715 0.901 0.572 0.691 0.382 0.366 0.356 0.372 0.407 0.334

0.39 0.076 0.783 0.325 0.684 0.888 0.533 0.655 0.369 0.354 0.344 0.359 0.394 0.321

0.40 0.081 0.767 0.315 0.654 0.876 0.499 0.622 0.357 0.341 0.332 0.346 0.380 0.308

0.41 0.087 0.752 0.306 0.625 0.858 0.465 0.586 0.344 0.329 0.320 0.333 0.367 0.296

0.42 0.093 0.736 0.297 0.597 0.846 0.434 0.554 0.332 0.317 0.308 0.321 0.355 0.284

0.43 0.100 0.721 0.288 0.570 0.834 0.404 0.521 0.320 0.305 0.297 0.309 0.342 0.272

0.44 0.106 0.707 0.281 0.543 0.822 0.378 0.493 0.309 0.294 0.286 0.298 0.330 0.261

0.45 0.113 0.692 0.273 0.517 0.808 0.353 0.465 0.297 0.283 0.275 0.287 0.319 0.249

0.46 0.120 0.679 0.267 0.495 0.795 0.330 0.436 0.286 0.272 0.265 0.276 0.307 0.238

0.47 0.128 0.666 0.260 0.475 0.780 0.308 0.409 0.275 0.261 0.255 0.265 0.295 0.227

0.48 0.135 0.654 0.254 0.455 0.763 0.288 0.385 0.265 0.250 0.244 0.255 0.284 0.217

0.49 0.143 0.642 0.248 0.438 0.751 0.270 0.361 0.254 0.240 0.235 0.245 0.272 0.207

0.50 0.150 0.631 0.243 0.421 0.739 0.253 0.338 0.244 0.230 0.226 0.234 0.261 0.197

0.51 0.157 0.620 0.238 0.405 0.728 0.237 0.317 0.234 0.220 0.217 0.224 0.250 0.188

0.52 0.164 0.609 0.233 0.389 0.717 0.223 0.296 0.224 0.210 0.208 0.214 0.240 0.179
19

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s

TwistMass per unit lengthFlap stiffnessEdge stiffnessStatic max flapStatic max edgeStatic min flapStatic min edgeDynamic flapDynamic lead-lag

0.53 0.173 0.598 0.228 0.374 0.708 0.209 0.278 0.214 0.201 0.199 0.205 0.230 0.170

0.54 0.182 0.587 0.224 0.359 0.698 0.197 0.261 0.204 0.192 0.190 0.195 0.220 0.162

0.55 0.191 0.577 0.219 0.344 0.686 0.184 0.245 0.195 0.182 0.181 0.186 0.210 0.154

0.56 0.201 0.567 0.215 0.329 0.674 0.173 0.231 0.186 0.174 0.172 0.178 0.200 0.146

0.57 0.211 0.557 0.211 0.315 0.663 0.162 0.218 0.178 0.166 0.164 0.169 0.191 0.139

0.58 0.222 0.548 0.206 0.303 0.649 0.152 0.205 0.169 0.158 0.157 0.161 0.182 0.131

0.59 0.232 0.539 0.202 0.291 0.636 0.142 0.193 0.161 0.150 0.149 0.153 0.173 0.124

0.60 0.243 0.530 0.197 0.278 0.625 0.133 0.182 0.153 0.142 0.142 0.145 0.165 0.117

0.61 0.255 0.521 0.192 0.266 0.613 0.125 0.173 0.146 0.135 0.135 0.137 0.156 0.111

0.62 0.266 0.511 0.187 0.253 0.599 0.117 0.161 0.138 0.128 0.128 0.130 0.148 0.104

0.63 0.277 0.502 0.183 0.237 0.598 0.107 0.149 0.131 0.121 0.121 0.122 0.140 0.098

0.64 0.288 0.492 0.178 0.221 0.572 0.099 0.138 0.123 0.114 0.114 0.115 0.133 0.092

0.65 0.299 0.482 0.174 0.206 0.558 0.091 0.128 0.116 0.107 0.108 0.109 0.125 0.086

0.66 0.311 0.473 0.170 0.191 0.542 0.083 0.118 0.110 0.101 0.102 0.102 0.118 0.081

0.67 0.322 0.464 0.165 0.176 0.527 0.076 0.108 0.103 0.095 0.095 0.096 0.111 0.076

0.68 0.334 0.454 0.161 0.162 0.514 0.070 0.099 0.096 0.088 0.089 0.090 0.104 0.070

0.69 0.347 0.445 0.157 0.147 0.502 0.064 0.090 0.090 0.082 0.083 0.083 0.097 0.065

0.70 0.360 0.437 0.153 0.133 0.488 0.059 0.083 0.084 0.076 0.078 0.078 0.090 0.060

0.71 0.374 0.428 0.149 0.120 0.471 0.054 0.078 0.077 0.071 0.072 0.072 0.084 0.056

0.72 0.388 0.420 0.146 0.107 0.454 0.049 0.073 0.071 0.065 0.067 0.066 0.077 0.052

0.73 0.402 0.412 0.142 0.094 0.438 0.045 0.068 0.065 0.059 0.061 0.061 0.071 0.047

0.74 0.417 0.404 0.138 0.082 0.424 0.041 0.063 0.059 0.054 0.056 0.055 0.065 0.043

0.75 0.433 0.396 0.134 0.068 0.411 0.037 0.058 0.054 0.049 0.051 0.050 0.060 0.040

0.76 0.449 0.388 0.131 0.056 0.396 0.034 0.053 0.049 0.044 0.046 0.045 0.055 0.036

0.77 0.466 0.381 0.128 0.044 0.382 0.030 0.048 0.044 0.040 0.042 0.041 0.050 0.033

0.78 0.483 0.374 0.124 0.032 0.368 0.027 0.044 0.040 0.036 0.038 0.037 0.045 0.030

0.79 0.501 0.366 0.121 0.021 0.354 0.025 0.040 0.036 0.032 0.034 0.033 0.041 0.027

0.80 0.519 0.359 0.118 0.010 0.342 0.022 0.037 0.032 0.029 0.031 0.029 0.037 0.024

0.81 0.538 0.352 0.115 -0.001 0.328 0.020 0.034 0.028 0.025 0.027 0.026 0.033 0.021

0.82 0.557 0.345 0.112 -0.012 0.314 0.018 0.031 0.025 0.022 0.024 0.023 0.029 0.019

0.83 0.577 0.338 0.109 -0.023 0.298 0.016 0.028 0.021 0.019 0.021 0.020 0.026 0.017

0.84 0.598 0.331 0.106 -0.033 0.283 0.014 0.025 0.018 0.016 0.017 0.017 0.023 0.014

0.85 0.618 0.324 0.102 -0.043 0.270 0.013 0.023 0.015 0.014 0.015 0.014 0.020 0.013

0.86 0.638 0.316 0.099 -0.052 0.257 0.011 0.021 0.013 0.011 0.012 0.012 0.017 0.011

0.87 0.659 0.308 0.096 -0.060 0.246 0.010 0.019 0.010 0.009 0.010 0.009 0.015 0.009

0.88 0.680 0.299 0.093 -0.067 0.235 0.008 0.017 0.008 0.007 0.008 0.007 0.012 0.008
20

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Span fraction Prebend Chord Thicknes

s

TwistMass per unit lengthFlap stiffnessEdge stiffnessStatic max flapStatic max edgeStatic min flapStatic min edgeDynamic flapDynamic lead-lag

0.89 0.702 0.290 0.089 -0.071 0.224 0.007 0.016 0.006 0.005 0.006 0.006 0.010 0.006

0.90 0.724 0.280 0.086 -0.075 0.212 0.006 0.014 0.004 0.004 0.005 0.004 0.008 0.005

0.91 0.747 0.271 0.082 -0.077 0.198 0.005 0.013 0.003 0.003 0.004 0.003 0.007 0.004

0.92 0.772 0.260 0.078 -0.076 0.182 0.004 0.011 0.002 0.002 0.003 0.003 0.005 0.003

0.93 0.797 0.249 0.074 -0.071 0.167 0.003 0.009 0.002 0.002 0.002 0.002 0.004 0.003

0.94 0.823 0.237 0.070 -0.065 0.156 0.003 0.008 0.001 0.001 0.002 0.002 0.003 0.002

0.95 0.850 0.225 0.065 -0.056 0.142 0.002 0.006 0.001 0.001 0.001 0.001 0.002 0.001

0.96 0.878 0.208 0.059 -0.013 0.125 0.001 0.005 0.001 0.001 0.001 0.001 0.001 0.001

0.97 0.906 0.186 0.051 0.056 0.106 0.001 0.004 0.000 0.000 0.000 0.000 0.001 0.001

0.98 0.936 0.160 0.044 0.142 0.087 0.000 0.002 0.000 0.000 0.000 0.000 0.001 0.000

0.99 0.966 0.121 0.035 0.270 0.079 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000

1.00 1.000 0.022 0.005 0.452 0.065 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

2.2 Fictional 60-m Blade Specification

Using the normalized average blade and scaling parameters, a fictional 60-m test article 

specification was defined. The length of the blade was selected because it represents the upper 

end of blades that are typically manufactured in the United States at present and does not overly 

extrapolate the data set it is based on. The maximum chord selected is 3.8 m, and the prebend is 

3.5 m. These parameters are similar to those for blades in the 50–60 m span and are typically 

constrained by transportation restrictions for truck transit. The resulting blade has a root diameter 

of 2.406 m, a total mass of 13,117 kg, and a center of gravity at a span of 18.3 m, all of which 

are within line of typical blades of this size. The resulting distribution of blade properties is 

provided in Table 3. 

The target test loads are given in Table 4. These loads are defined by the selected blade length 

and the corresponding normalization parameter slope and offset in Table 1. The resulting 

normalization parameters calculated in this way represent the root target moments for each test 

type and loading direction. Thus, the loads specified for this fictional blade test represent a 

typical or average target load based on the test specifications for the blades studied extrapolated 

for a 60-m blade.
21

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Table 3. Scaled 60-m Blade Geometry and Beam Element Properties

Span Prebend Chord Thickness Twist Unit Mass

EI 

Flapwise

EI

Lead-Lag

(m) (m) (m) (m) (deg) (kg/m) (Nm2) (Nm2)

0.00 0.000 2.406 2.406 12.50 2325.1 1.40E+10 1.74E+10

0.60 -0.001 2.408 2.395 12.50 1237.4 1.09E+10 1.33E+10

1.20 -0.002 2.411 2.381 12.50 701.9 8.26E+09 9.77E+09

1.80 -0.002 2.441 2.362 12.74 526.7 6.84E+09 7.93E+09

2.40 -0.002 2.488 2.333 13.22 467.1 5.98E+09 6.84E+09

3.00 -0.002 2.548 2.299 13.95 431.8 5.29E+09 6.01E+09

3.60 -0.002 2.627 2.256 14.86 402.2 4.76E+09 5.38E+09

4.20 -0.003 2.718 2.206 15.76 382.5 4.44E+09 5.14E+09

4.80 -0.003 2.818 2.154 16.51 367.3 4.16E+09 4.99E+09

5.40 -0.004 2.926 2.099 17.05 354.6 3.91E+09 4.91E+09

6.00 -0.006 3.036 2.041 17.19 346.6 3.68E+09 4.91E+09

6.60 -0.007 3.141 1.982 17.33 341.8 3.44E+09 4.94E+09

7.20 -0.009 3.242 1.923 17.21 338.4 3.23E+09 5.00E+09

7.80 -0.011 3.331 1.864 17.11 336.9 3.03E+09 5.09E+09

8.40 -0.013 3.415 1.804 16.86 334.2 2.82E+09 5.16E+09

9.00 -0.015 3.488 1.744 16.58 333.2 2.64E+09 5.20E+09

9.60 -0.017 3.551 1.684 16.29 328.1 2.44E+09 5.20E+09

10.20 -0.020 3.605 1.626 15.97 325.3 2.26E+09 5.22E+09

10.80 -0.024 3.650 1.569 15.59 321.5 2.10E+09 5.20E+09

11.40 -0.028 3.681 1.514 15.16 314.2 1.95E+09 5.01E+09

12.00 -0.032 3.704 1.460 14.72 308.8 1.80E+09 4.79E+09

12.60 -0.037 3.714 1.410 14.23 302.4 1.66E+09 4.58E+09

13.20 -0.043 3.716 1.361 13.72 296.1 1.54E+09 4.32E+09

13.80 -0.050 3.712 1.313 13.22 288.7 1.42E+09 4.14E+09

14.40 -0.057 3.699 1.268 12.71 282.3 1.32E+09 3.93E+09

15.00 -0.065 3.677 1.225 12.22 274.8 1.23E+09 3.77E+09

15.60 -0.074 3.653 1.183 11.73 268.6 1.14E+09 3.61E+09

16.20 -0.083 3.624 1.143 11.24 263.4 1.07E+09 3.48E+09

16.80 -0.094 3.590 1.105 10.82 259.1 9.95E+08 3.35E+09

17.40 -0.106 3.543 1.069 10.41 255.0 9.27E+08 3.23E+09

18.00 -0.118 3.492 1.035 10.02 251.5 8.66E+08 3.10E+09

18.60 -0.132 3.439 1.002 9.62 248.4 8.08E+08 2.98E+09

19.20 -0.146 3.384 0.971 9.24 246.0 7.54E+08 2.86E+09

19.80 -0.161 3.327 0.941 8.86 243.0 7.03E+08 2.74E+09

20.40 -0.177 3.269 0.912 8.51 239.4 6.54E+08 2.62E+09

21.00 -0.193 3.210 0.884 8.15 235.4 6.10E+08 2.49E+09
22

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Span Prebend Chord Thickness Twist Unit Mass

EI 

Flapwise

EI

Lead-Lag

(m) (m) (m) (m) (deg) (kg/m) (Nm2) (Nm2)

21.60 -0.210 3.151 0.856 7.81 233.1 5.70E+08 2.39E+09

22.20 -0.227 3.092 0.830 7.47 229.9 5.31E+08 2.27E+09

22.80 -0.246 3.033 0.806 7.16 226.5 4.95E+08 2.15E+09

23.40 -0.265 2.974 0.782 6.86 223.3 4.62E+08 2.03E+09

24.00 -0.285 2.915 0.758 6.55 220.2 4.32E+08 1.93E+09

24.60 -0.305 2.856 0.735 6.26 215.7 4.03E+08 1.82E+09

25.20 -0.326 2.799 0.714 5.98 212.7 3.76E+08 1.72E+09

25.80 -0.348 2.741 0.694 5.71 209.8 3.50E+08 1.62E+09

26.40 -0.372 2.685 0.676 5.44 206.8 3.28E+08 1.53E+09

27.00 -0.396 2.630 0.658 5.18 203.3 3.06E+08 1.44E+09

27.60 -0.421 2.580 0.642 4.96 199.9 2.86E+08 1.35E+09

28.20 -0.447 2.532 0.626 4.75 196.2 2.67E+08 1.27E+09

28.80 -0.473 2.486 0.611 4.56 192.0 2.49E+08 1.19E+09

29.40 -0.500 2.441 0.597 4.39 188.8 2.34E+08 1.12E+09

30.00 -0.526 2.397 0.584 4.22 185.8 2.19E+08 1.05E+09

30.60 -0.549 2.354 0.572 4.05 183.1 2.05E+08 9.83E+08

31.20 -0.573 2.313 0.560 3.90 180.4 1.93E+08 9.18E+08

31.80 -0.605 2.272 0.549 3.75 178.0 1.81E+08 8.63E+08

32.40 -0.638 2.232 0.538 3.59 175.6 1.70E+08 8.11E+08

33.00 -0.670 2.192 0.527 3.44 172.5 1.59E+08 7.60E+08

33.60 -0.702 2.154 0.517 3.30 169.4 1.49E+08 7.17E+08

34.20 -0.738 2.118 0.507 3.16 166.6 1.40E+08 6.77E+08

34.80 -0.775 2.083 0.496 3.03 163.2 1.32E+08 6.35E+08

35.40 -0.813 2.049 0.485 2.91 159.9 1.23E+08 5.98E+08

36.00 -0.852 2.014 0.474 2.79 157.1 1.16E+08 5.66E+08

36.60 -0.892 1.979 0.462 2.66 154.2 1.08E+08 5.36E+08

37.20 -0.932 1.943 0.451 2.53 150.7 1.01E+08 5.00E+08

37.80 -0.969 1.906 0.440 2.37 150.4 9.30E+07 4.61E+08

38.40 -1.007 1.870 0.429 2.22 143.9 8.55E+07 4.27E+08

39.00 -1.046 1.833 0.418 2.06 140.3 7.87E+07 3.97E+08

39.60 -1.087 1.797 0.408 1.91 136.3 7.22E+07 3.66E+08

40.20 -1.128 1.762 0.398 1.77 132.7 6.61E+07 3.35E+08

40.80 -1.171 1.727 0.388 1.62 129.2 6.06E+07 3.06E+08

41.40 -1.215 1.693 0.378 1.48 126.1 5.53E+07 2.80E+08

42.00 -1.262 1.660 0.369 1.34 122.8 5.07E+07 2.59E+08

42.60 -1.309 1.627 0.359 1.20 118.5 4.66E+07 2.42E+08

43.20 -1.357 1.596 0.350 1.07 114.3 4.25E+07 2.26E+08
23

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Span Prebend Chord Thickness Twist Unit Mass

EI 

Flapwise

EI

Lead-Lag

(m) (m) (m) (m) (deg) (kg/m) (Nm2) (Nm2)

43.80 -1.406 1.564 0.341 0.94 110.3 3.87E+07 2.10E+08

44.40 -1.460 1.534 0.332 0.82 106.7 3.53E+07 1.94E+08

45.00 -1.514 1.504 0.323 0.69 103.3 3.22E+07 1.79E+08

45.60 -1.571 1.475 0.315 0.56 99.6 2.91E+07 1.64E+08

46.20 -1.630 1.447 0.307 0.44 96.0 2.63E+07 1.50E+08

46.80 -1.691 1.420 0.299 0.33 92.6 2.37E+07 1.38E+08

47.40 -1.754 1.392 0.291 0.21 89.1 2.15E+07 1.26E+08

48.00 -1.818 1.365 0.284 0.10 85.9 1.93E+07 1.15E+08

48.60 -1.883 1.338 0.276 -0.01 82.6 1.74E+07 1.05E+08

49.20 -1.949 1.311 0.269 -0.12 79.0 1.55E+07 9.57E+07

49.80 -2.021 1.284 0.261 -0.23 75.0 1.39E+07 8.66E+07

50.40 -2.093 1.257 0.254 -0.33 71.2 1.23E+07 7.76E+07

51.00 -2.164 1.230 0.247 -0.43 67.9 1.09E+07 7.05E+07

51.60 -2.234 1.200 0.239 -0.52 64.6 9.49E+06 6.39E+07

52.20 -2.307 1.169 0.231 -0.60 61.8 8.24E+06 5.85E+07

52.80 -2.381 1.136 0.223 -0.67 59.2 7.13E+06 5.35E+07

53.40 -2.458 1.101 0.214 -0.71 56.2 6.11E+06 4.85E+07

54.00 -2.534 1.066 0.206 -0.76 53.4 5.19E+06 4.39E+07

54.60 -2.615 1.029 0.198 -0.77 49.8 4.31E+06 3.90E+07

55.20 -2.702 0.989 0.188 -0.76 45.8 3.52E+06 3.38E+07

55.80 -2.790 0.945 0.178 -0.71 42.1 2.81E+06 2.87E+07

56.40 -2.882 0.900 0.168 -0.66 39.4 2.17E+06 2.43E+07

57.00 -2.975 0.854 0.157 -0.56 35.7 1.60E+06 2.01E+07

57.60 -3.071 0.790 0.142 -0.13 31.5 1.13E+06 1.58E+07

58.20 -3.172 0.707 0.123 0.56 26.8 7.16E+05 1.11E+07

58.80 -3.275 0.608 0.107 1.42 22.0 3.77E+05 6.79E+06

59.40 -3.381 0.460 0.084 2.70 20.0 1.08E+05 2.60E+06

60.00 -3.500 0.083 0.011 4.53 16.3 8.52E+03 5.51E+04
24

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Table 4. Scaled 60-m Test Target Loads Including All Design and Test Factors

Span 

Static 

Max Flap

Static

Max Edge

Static 

Min Flap

Static

Min Edge

Fatigue

Flap 

Range

Fatigue

Lead-lag 

Range

(m) (kNm) (kNm) (kNm) (kNm) (kNm) (kNm)

0.00 13,032 7,297 10,642 6,652 8,741 10,500

0.60 12,784 7,146 10,419 6,509 8,582 10,272

1.20 12,545 7,004 10,200 6,372 8,462 10,047

1.80 12,306 6,865 9,981 6,235 8,337 9,831

2.40 12,067 6,730 9,761 6,107 8,165 9,616

3.00 11,829 6,598 9,538 5,987 8,016 9,410

3.60 11,592 6,466 9,320 5,868 7,868 9,191

4.20 11,351 6,332 9,102 5,747 7,728 8,982

4.80 11,112 6,198 8,887 5,627 7,600 8,767

5.40 10,872 6,061 8,680 5,507 7,443 8,556

6.00 10,633 5,925 8,474 5,387 7,291 8,353

6.60 10,396 5,788 8,271 5,265 7,152 8,133

7.20 10,165 5,655 8,071 5,143 7,013 7,914

7.80 9,936 5,521 7,873 5,022 6,878 7,699

8.40 9,709 5,388 7,677 4,902 6,732 7,506

9.00 9,483 5,255 7,481 4,782 6,586 7,317

9.60 9,259 5,124 7,289 4,664 6,440 7,129

10.20 9,038 4,994 7,099 4,548 6,301 6,946

10.80 8,820 4,865 6,910 4,434 6,163 6,765

11.40 8,603 4,735 6,722 4,320 6,026 6,584

12.00 8,386 4,609 6,537 4,209 5,884 6,398

12.60 8,174 4,485 6,362 4,102 5,742 6,216

13.20 7,962 4,363 6,187 3,997 5,602 6,036

13.80 7,751 4,242 6,014 3,890 5,470 5,865

14.40 7,541 4,123 5,843 3,786 5,340 5,696

15.00 7,332 4,004 5,674 3,681 5,210 5,529

15.60 7,126 3,887 5,507 3,577 5,076 5,360

16.20 6,921 3,770 5,343 3,474 4,941 5,191

16.80 6,724 3,658 5,185 3,375 4,806 5,024

17.40 6,528 3,546 5,030 3,277 4,672 4,858

18.00 6,336 3,436 4,877 3,181 4,543 4,699

18.60 6,145 3,328 4,726 3,083 4,416 4,544
25

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Span 

Static 

Max Flap

Static

Max Edge

Static 

Min Flap

Static

Min Edge

Fatigue

Flap 

Range

Fatigue

Lead-lag 

Range

(m) (kNm) (kNm) (kNm) (kNm) (kNm) (kNm)

19.20 5,957 3,222 4,576 2,985 4,291 4,392

19.80 5,769 3,116 4,427 2,888 4,167 4,242

20.40 5,593 3,017 4,286 2,796 4,043 4,088

21.00 5,417 2,919 4,146 2,705 3,920 3,937

21.60 5,242 2,823 4,007 2,615 3,798 3,788

22.20 5,072 2,727 3,872 2,526 3,677 3,642

22.80 4,904 2,633 3,738 2,437 3,558 3,504

23.40 4,736 2,540 3,606 2,350 3,440 3,371

24.00 4,571 2,449 3,475 2,265 3,323 3,238

24.60 4,408 2,358 3,347 2,181 3,208 3,108

25.20 4,253 2,273 3,227 2,102 3,099 2,982

25.80 4,100 2,189 3,109 2,025 2,993 2,859

26.40 3,949 2,106 2,993 1,950 2,888 2,738

27.00 3,802 2,025 2,878 1,876 2,784 2,619

27.60 3,657 1,944 2,766 1,804 2,682 2,502

28.20 3,514 1,864 2,654 1,732 2,580 2,388

28.80 3,376 1,788 2,554 1,662 2,480 2,279

29.40 3,239 1,712 2,455 1,592 2,381 2,174

30.00 3,105 1,637 2,358 1,524 2,285 2,073

30.60 2,973 1,565 2,263 1,457 2,189 1,973

31.20 2,843 1,496 2,161 1,392 2,096 1,875

31.80 2,714 1,426 2,060 1,328 2,007 1,787

32.40 2,590 1,359 1,964 1,267 1,920 1,701

33.00 2,469 1,294 1,871 1,207 1,833 1,616

33.60 2,358 1,234 1,787 1,151 1,750 1,534

34.20 2,248 1,175 1,703 1,095 1,668 1,455

34.80 2,141 1,117 1,621 1,039 1,588 1,379

35.40 2,036 1,061 1,541 985 1,513 1,304

36.00 1,934 1,006 1,463 932 1,438 1,231

36.60 1,832 951 1,386 880 1,366 1,162

37.20 1,734 899 1,312 832 1,295 1,095

37.80 1,639 848 1,240 785 1,227 1,031

38.40 1,547 799 1,172 740 1,160 969
26

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Span 

Static 

Max Flap

Static

Max Edge

Static 

Min Flap

Static

Min Edge

Fatigue

Flap 

Range

Fatigue

Lead-lag 

Range

(m) (kNm) (kNm) (kNm) (kNm) (kNm) (kNm)

39.00 1,456 751 1,103 695 1,095 908

39.60 1,367 704 1,036 652 1,031 850

40.20 1,279 657 970 609 969 793

40.80 1,193 612 906 567 907 739

41.40 1,109 568 844 527 846 685

42.00 1,027 525 783 488 787 635

42.60 946 483 723 449 730 587

43.20 866 442 664 411 675 542

43.80 789 402 608 375 621 497

44.40 719 366 555 342 570 456

45.00 649 330 503 308 522 417

45.60 588 297 456 278 477 380

46.20 528 266 411 250 434 344

46.80 476 239 371 225 394 311

47.40 425 213 332 200 357 280

48.00 377 188 295 177 321 250

48.60 329 164 258 154 288 223

49.20 284 141 224 134 258 197

49.80 239 119 189 113 229 173

50.40 203 101 162 96 201 151

51.00 166 83 134 79 176 132

51.60 134 68 110 64 152 113

52.20 103 53 87 50 129 96

52.80 79 41 68 39 109 80

53.40 54 29 49 28 90 66

54.00 42 22 39 22 73 54

54.60 33 17 30 18 58 43

55.20 25 13 23 14 46 34

55.80 18 9 17 10 36 26

56.40 11 6 11 7 28 20

57.00 7 4 7 5 18 14

57.60 4 2 4 3 12 9

58.20 2 1 2 2 8 6
27

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Span 

Static 

Max Flap

Static

Max Edge

Static 

Min Flap

Static

Min Edge

Fatigue

Flap 

Range

Fatigue

Lead-lag 

Range

(m) (kNm) (kNm) (kNm) (kNm) (kNm) (kNm)

58.80 1 0 1 1 5 4

59.40 0 0 0 0 3 2

60.00 0 0 0 0 2 1
28

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3 Excitation and Control Equipment

The test configuration and excitation systems considered in this study are based on equipment 

and standard certification test practices in use at the WTTC laboratory. Typically, for a 

resonance fatigue test the blade will be mounted on the test stand in a high pressure up 

configuration with the zero pitch line horizontal. Flap fatigue tests are excited using a GREX;

whereas edge tests are excited using an IREX. The proposed biaxial test design will use a 

combination of a GREX in the flap direction and either an IREX or a GREX type device 

(possibly including a bell crank) in the lead-lag direction.

The bending moment curve is adjusted to best fit the target load by placing masses along the 

blade as needed. As little mass as possible is used to reduce the mean bending moment in the 

flap direction and keep the test frequency as high as possible as is typically requested by the 

manufacturer or turbine OEM. The required input energy is calculated based on estimates of the 

structural and aerodynamic damping. Additionally, “virtual” mass may be conceptually added in 

one direction, but not in the other by either using a physical mass connected to the blade via a 

pushrod or by adjusting the frequency so that the GREX type actuator applies a force that is in 

phase with the blade movement.

Fatigue tests are controlled by an MTS FlexTest 200 controller using amplitude control to 

maintain the desired strain level corresponding to the desired bending moment by adjusting the 

amount of input energy (IREX stroke or GREX force). This results in a nearly constant 

amplitude test even as temperature and other environmental effects change. In addition, to keep 

the blade at resonance as the ambient temperature changes, the controller is typically configured 

to use a resonance tracking algorithm. This software enables the controller to continuously 

measure the phase angle between the excitation command and the response of the blade and 

adjust the test frequency to keep the test at a constant phase angle at or near the resonance 

frequency.

3.1 Static Calibration

Static calibrations are conducted in either the horizontal (lead-lag) or vertical (flapwise) direction 

pulling on the blade to a nominal load at an outboard saddle and measuring the strain response. 

Unlike for a static test, the loading cable is configured to be approximately perpendicular to the 

span axis of the blade during the static calibration test. Then, the bending moment at each strain 

gauge is simply the product of the difference in span between that gauge and the loaded saddle 

and the force applied (neglecting geometric nonlinearity due to blade deformation). For a biaxial 

fatigue test, cross talk matrix compensation will be required and is typically applied in a similar 

way to the method described in the IEC 61400-13 technical specification for wind turbine 

measurements (IEC_61400-13 2001). 

3.2 Added Masses

The bending moment curve may be adjusted by adding masses to the blade to better match the 

target test load distribution along the blade span. The acceleration of the mass as the blade moves 

creates a point load that is in phase with the displacement and increases the applied bending 

moment amplitude linearly between the mass and the root of the blade. The applied masses also 

modify the mean bending moment in the flap direction. Large masses on the order of 1,000–
29

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3,000 kg are sometimes required between 20% and 50% of the span to increase the root bending 

moment. Smaller masses may also be required outboard on the blade. Typically, either a saddle 

or parts of a saddle are used if the mass required is between 100 and 400 kg. If a small tip mass 

is required, then small steel plates may be attached directly to the blade tip using straps and 

adhesively bonded aluminum angles.

3.3 IREX Actuator for Lead-Lag Fatigue

The primary method of lead-lag fatigue excitation for a WTTC fatigue test is the IREX system 

with specifications shown in Table 5. In general, for a lead-lag fatigue test, a single IREX 

actuator (Figure 5) is placed on a saddle at approximately mid-span of the blade. The moving 

mass oscillates linearly with a sinusoidal displacement command. The MTS controller tracks the 

resonance frequency of the blade to keep the system operating at optimum efficiency and 

simultaneously adjusts the displacement amplitude to achieve the target fatigue strain amplitude.

Table 5. IREX Actuator Specifications

Maximum Stroke Rangea 0.300 m

Moving Mass 160–1,525 kg

Fixed Massb 320 kg

a Maximum stroke range is further limited for test frequencies 

exceeding 0.8 Hz.

b The fixed mass does not include the weight of the saddle and 

mounting equipment.

Figure 20. Single actuator with fixed mass (black) and minimum moving mass (yellow).

NREL 17637

3.4 GREX Actuator for Flap Fatigue

The GREX actuator is designed to connect to a saddle on the blade, and the applied force is 

reacted by a base plate mass on the laboratory floor. During normal operation, the MTS 

controller is configured to excite the blade at resonance using a sinusoidal force command. 

Maximum forces that can be applied by the actuator are limited by two sets of valves, one 

electronic and one mechanical. The electronic valves are designed to open on an interlock or 

other sudden stop event allowing the blade to keep moving and the motion to damp out gradually 
30

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without damaging the test article or actuator. The mechanical valves will relieve pressure in the 

actuator if the force exceeds a preset value. In combination, these valves provide redundant 

protection to ensure that the actuator and test article are not damaged due to the high energy 

stored in the test article during excitation. During demonstration testing, it was found that during 

a normal interlock the maximum force applied to the blade never exceeded the target force 

amplitude.

Two versions of the GREX are available at the WTTC: GREX 50 and GREX 100. The 

capabilities of each actuator are listed in Table 6.

Table 6. GREX Specifications

Specification GREX 50 GREX 100

Max static force rating 50 kN 100 kN

Max dynamic force ~30 kN ~60 kN

Max stroke amplitude 875 mm 875 mm

Max velocity 2.5 m/s 2.5 m/s

Max horizontal acceleration at 

top pivot 1.0 g 1.0 g

Max angle of actuator from 

vertical 12 degrees 12 degrees

Minimum mean stroke length 5,692 mm 5,795 mm

Maximum mean stroke length 

with extension tube 8,687 mm 8,790 mm

Length adjustment increment 75 mm 75 mm

Base height (typical) 600 mm 215 mm

3.5 PHLEX Concept

The PHLEX is a concept for increasing the flap frequency until it equals the lead-lag frequency 

by providing real or virtual (hydraulic actuator) springs in the flap direction. If successfully 

implemented, this concept has the advantage that the test can be run relatively quickly at the 

higher lead-lag frequency. Experiments were conducted to implement this on a 9-m blade using a 

hydraulic actuator mounted at 7 m, relatively close to the blade tip. See White et al. (2011) and 

Beckwith et al. (2013) for more details on these test simulations and experiments. 

3.6 Hybrid Test Research Project

The hybrid test research project is an ongoing set of experiments to evaluate methods for 

elliptical phase-locked testing using different energy input approaches. Experiments are 

conducted using inertial mass excitation (IREX), direct forcing (GREX) and base excitation 

where the plate where the blade is mounted is moved by actuators. Different geometry and 

linkage mechanisms are also considered. One incarnation of this experimental program achieves 

a phase-locked resonance testing using a mass mounted on a slide table to reduce the lead-lag 

frequency to match that of the flap frequency. This concept is shown in Figure 21 and may be 

combined with a GREX-type flap exciter as shown in Figure 22. At the present time, 
31

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experiments have demonstrated successful excitation of the blade at matching flap and lead-lag 

frequencies using this test configuration installed on a 12-m blade. Further results of this project 

will be published after its conclusion.

Figure 21. Hybrid concept for applying mass to the blade in the lead-lag direction but leaving the 

mass in the flap direction unchanged. In this case, the IREX is mounted off the blade as part of the 

virtual mass in the lead-lag direction. 

Image credit: Scott Hughes, NREL

Figure 22. Hybrid configuration using IREX and GREX excitation systems attached to the same 

saddle.

Image credit: Scott Hughes, NREL
32

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3.7 Virtual Mass

This study uses the term virtual mass to refer to a force applied to the blade that behaves like a 

mass acting in just one direction from a numerical standpoint. Virtual mass may be implemented 

as real mass that is connected through some type of mechanical linkage such that it only acts in 

one of the primary directions of motion—lead-lag or flap—as demonstrated in the hybrid test 

research project. 

Alternatively, a virtual mass may be implemented using a servo hydraulic actuator to apply a 

sinusoidal force in phase with the displacement that is the equivalent to the virtual mass times the 

blade acceleration in that direction. The same actuator could be used to simultaneously apply the 

excitation for resonance. The sum of the two applied sine waves is simply another sine wave 

with a shifted phase (Figure 23). In essence, the virtual mass is created by modifying the phase 

angle between the force and displacement, which in turn modifies the resonance frequency of the 

system. This concept has successfully been demonstrated using a GREX actuator to both excite a 

blade in the flap direction and by modifying the command frequency, and thus the phase angle 

between the force and displacement, the bending moment distribution was changed (Figure 24).

The bending moment curve will be modified just as if a mass was added to the blade at the 

exciter saddle. However, the mean load and the resonance mode shape in the other direction 

(lead-lag vs. flap) will remain unchanged.

By increasing the excitation test frequency above resonance, it is also possible to apply “negative 

virtual mass.” In this case the actuator is applying a force that is 180 degrees out of phase with 

the displacement. Essentially, the actuator is carrying some of the saddle and blade rather than 

relying on the blade to accelerate that mass. Small amounts of negative virtual mass are possible; 

however, experimentally control instabilities tend to occur if the test frequency with a GREX is 

increased very far above the system resonance frequency. Numerically the simulation 

eigenvector analysis described in the next section also becomes unstable if more mass is 

removed than is present at that saddle location. Other models that include actual dynamic timeseries approaches may be required to accurately simulate this type of test. This is a topic area for 

further investigation in the future.

The required force amplitude for a virtual mass is estimated by multiplying the virtual mass 

required in kilograms by the acceleration in meters per seconds squared at a given saddle 

location. Farther out on a blade where the acceleration is relatively high, large forces may be 

generated with relatively small masses. However, in the middle of the blade and closer to the 

root, a large mass of several thousand kilograms may be replaced with a reasonable force for an 

actuator in the 10–40 kN range, and the strokes and velocities required are reasonable for a 

hydraulic actuator. Therefore, it is reasonable to consider actuators be used for virtual mass in 

about the first 50% of a blade span and a system with actual masses attached to the blade through 

mechanical linkage be developed for outboard stations.
33

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Figure 23. Addition of two sine wave force functions showing the result as a sine wave with 

shifted phase. Phase shifting is accomplished with a GREX-type device by modifying the 

excitation frequency, and a target phase can be set to include virtual mass in the forcing function 

for the test.

Figure 24. Modification of the bending moment by operating a GREX located at 43% span at 

different frequencies, effectively adding a virtual mass to this location as the frequency was 

decreased from 0.78 Hz to 0.75 Hz. The force amplitude was adjusted to achieve the same strain 

amplitude at the first set of strain gauges at each frequency.

-40

-30

-20

-10

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Amplitude (GREX force)

Time

Sine 1 phase = 0

Sine 2 phase = 90 deg

Sine 1 + Sine 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fraction target bending moment

Fraction span (m)

0.780 Hz. HP

0.762 Hz. HP

0.750 Hz. HP

0.780 Hz. LP

0.762 Hz. LP

0.750 Hz. LP
34 

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4 Resonance Fatigue Test Simulation

A simplified two degree-of-freedom beam element model is used to predict the blade behavior 

during the simulated resonance tests. For biaxial test simulation, the model is run twice, once for 

the flapwise direction and once for the lead-lag direction. The two solutions are then 

superimposed on each other. The implementation is in Microsoft Excel using the add-in “Eigs()” 

function from PopTools (Hood n.d.) to compute the eigenvalues and eigenfrequencies. The 

model makes the key assumption that the total damping is relatively low, only a few percent of 

critical; thus, the operational mode shapes can be predicted adequately using undamped analysis. 

Also, because the system is operated at steady state with energy input equal to the damping, the 

maximum potential “spring” energy stored at maximum displacement is assumed to be equal to 

the maximum kinetic energy achieved at maximum velocity.

4.1 Dynamic Model

For the dynamic analysis to determine mode shapes and frequencies of resonance, a two degreeof-freedom beam element model is constructed by spitting the blade into short beam segments. 

Each node has two degrees of freedom, a displacement, and a rotation as shown in Figure 25.

Figure 25. Finite element concept for dynamic analysis

The general equation for free oscillation of an undamped system is shown in equation 2:

[ ] + [ ] = = 0 (2)

where [ ] is the mass matrix, [ ] is the stiffness matrix, is the displacement vector, and is 

the applied forcing function, which is neglected for the mode shape analysis as the system is 

highly underdamped so the forcing does not have a significant role in the overall mode shape. 

For this two degree-of-freedom system, the displacement vector is made up of the displacements 

and rotations of each node as follows in Eq. 3:

Node 

0

Node 

1

Node 

2

Node 

i

Node 

i+1

ui

ui+1

Element

1

Element

i

i

i+1

Element

2
35 

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= (3)

Note that and are taken to be 0, corresponding to the fixed boundary condition at the root 

of the blade where it is mounted on the test stand. To generate the mass and stiffness matrices 

corresponding to the blade, an approach of building and then combining submatrices 

representing the properties at each node as described in chapter 10 of (Shames and Dym 1996) is 

followed. 

Euler-Bernoulli beam elements are used for the stiffness matrix while a lumped mass approach is 

used to approximate all of the mass of the elements and saddles at each node, resulting in a 

diagonal mass matrix and a simpler solution. Half of the mass of each element is approximated 

to reside at each node at either end of that element. Likewise, half of the rotational moment of 

inertia of each element is applied to each node. Each saddle or added point mass is taken to be 

located at a node, and the entire mass and rotation of inertia of that saddle, if provided, is applied 

to that node. Thus, the mass and moment of inertia of each element i are divided up between the 

i

th node and the previous node (i-1). This is done by assembling the mass matrix using a set of 

submatrices in Eq. 4 as follows. 

[ ]( ) =

2

24

 

2 + ,

24 + ,

(4)

where is the mass per unit length, is the length of the beam element i and , , and , are 

the mass and rotational moment of inertia of the saddle at node i. Then, the mass matrix for the 

nodes is formed using a combination of the properties of the element before and after that node 

by adding the elements ( ) as follows in Eq. 5. The first two rows and columns are removed 

corresponding to the boundary conditions where the displacement and rotation of node 0 is 0. 
36 

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[ ] =

( ) + ( )

( ) + ( )

( ) + ( )

( ) + ( )

( )

( )

(5)

Likewise, the subset of the stiffness matrix is formed for each element by combinations of the 

matrix for each element before and after the node so that the internal reactions of each element 

are accounted for in the motion of that node (Eq. 6):

[ ]( ) = ( )

12 6

 6 4 12 66 2

12 6

6 2

12 6

 6 4

(6)

Thus, after removing the first two rows and columns corresponding to the boundary conditions at 

node 0 the submatrices are combined to form the complete stiffness matrix (Eq. 7):
37 

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[ ] =

( ) + ( ) ( ) + ( )

( ) + ( ) ( ) + ( )

( )

 ( )

( )

 ( )

( ) ( )

( ) ( )

( ) + ( ) ( ) + ( )

( ) + ( ) ( ) + ( )

( )

 ( )

( )

 ( )

( ) ( )

( ) ( )

( ) + ( ) ( ) + ( )

( ) + ( ) ( ) + ( )

( ) ( )

( ) ( )

(7)

The solutions to the system of linear differential equations represented in Eq. 2 are given by the 

eigenvectors and eigenvalues of the matrix in Eq. 8:

[ ] [ ]

(8)

The eigenvalues are the resonance frequencies in radians per second corresponding to each mode 

shape given by the eigenvectors. We are primarily interested in the first mode, although it is 

useful to consider the resonance frequencies for the second and third modes in both the flap and 

lead-lag directions to ensure that they are not a harmonic of the base excitation frequencies that 

will be used. 

The final step in determining the deformed shape of the blade and corresponding applied loading 

is to scale the eigenvector to the appropriate test amplitude. To do this, we consider the moment 

and shear that must be applied at node 1 to achieve the deflection and rotation of this node given 

that node 0 is fixed. For a simple Euler beam, as shown in Figure 26, the deflection and rotation 

calculated for the superimposed moment M and shear V at the end of the beam element (at 

node 1) are given in Eq. 9 and 10. 
38 

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Figure 26. Deflection of element 1

= 2( ) + 3( )

(9)

= ( ) + 2( )

(10)

Solving these simultaneous equations for M and V produces Eq. 11 and 12:

= ( ) 6 12

(11)

= ( )

2

(12)

Equations 11 and 12 are used to determine the moment and shear at node 1. Then the moment at 

the root of the blade, node zero is estimated as (Eq. 13):

= +

(13)

V1

M1

u1

1

l

1

M0

Node 0 Node 1
39 

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The above calculations are performed using the first two elements of the unscaled eigenvector 

corresponding to the lowest (first mode) resonance frequency. Then because V and M are linear 

functions of u Eq. 11 and 12, the eigenvector can be scaled linearly to achieve 

the target root moment (Eq. 14):

=

(14)

where is the target root moment amplitude. From here on only the scaled displacement 

vector will be used without specifically noting that and are the scaled values. The moment 

and shear at each node can be calculated using the scaled eigenvector values for and and 

considering the relative deflection and rotation of each element (Eq. 15 and 16). 

= ( ) 6( ) 12 ( + )

(15)

= ( ) ( )

2

(16)

The fraction target moment achieved is determined by comparing the dynamic range achieved to 

the test target moment at each node (Eq. 17):

=

(17)

4.2 Energy Balance

To maintain resonance oscillation at the target amplitude, the excitation system must add energy 

to the system at the same rate that it is removed from the mechanical blade system due to 

damping. Two types of damping are considered, structural damping and aerodynamic drag as the 

blade moves back and forth through the air. The energy removed from the blade is calculated 

separately for structural and aerodynamic damping and then added together. Two energy input 

devices are also considered, an idealized IREX type device moving a mass relative the blade in a 

sinusoidal displacement, or an idealized GREX type device that applies a sinusoidal forcing 

function to the blade. The objective of the following calculations are to estimate the energy input 

required for the simulated test at the target excitation amplitude and then to calculate the 

necessary IREX displacement amplitude or GREX force amplitude to keep the test at a constant 

amplitude. 
40 

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4.2.1 Structural Damping

Structural damping is a result of the materials in a blade not being entirely elastic. Some of the 

strain energy introduced to the material is converted to heat through viscoelastic behavior and is 

not recovered as the displacement is reversed. We assume the structural damping may be 

modeled as an equivalent linear-viscous damper. The damping may be expressed in the form of a 

damping ratio, , typically represented as a percentage corresponding to the fraction of damping 

relative to a critically damped system. 

Let us consider the blade to be a single degree-of-freedom oscillator subjected to linear-viscous 

damping. The equation of motion is defined in Eq. 18 as:

+ + = ( )

(18)

where f is the excitation frequency in hertz and F is the amplitude of the applied forcing function. 

The undamped natural frequency for this one degree-of-freedom system is shown in Eq. 19:

= 1

2

(19)

And the damping ratio is defined as (Eq. 20):

= = 2 (2 ) = 2

(20)

If we consider an unforced system with = 0 starting with an initial amplitude during cycle q of 

, the amplitude will decrease with each cycle. The log decrement damping is defined as the 

natural log of the change in amplitude from one cycle to the next (Eq. 21):

=

(21)

where is the amplitude of a cycle q, and is the amplitude of the next successive cycle. 

The log decrement damping can also be related mathematically to the damping ratio as shown in 

Eq. 22:

= 2

1 + 1
41 

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(22)

The maximum energy stored in the spring during cycle q is equal to the maximum potential 

energy, which occurs when the velocity is zero (Eq. 23):

= 1

2 ,

(23)

Solving for x in Eq. 24:

, = 2

(24)

Thus, the log decrement can be related to the stored maximum potential energy for two 

successive cycles as shown in Eq. 25:

=

2

2 = = 1

2

(25)

The total strain energy for a simple beam with an applied moment can be calculated as shown in 

Eq. 26:

= 2 = 2( )

(26)

where the summation is performed to account for the stored energy in each element. However, 

the blade as a cantilever beam is also subjected to shear. Calculating the strain energy due to 

shear is more complicated and requires knowledge of the cross section, shear distribution 

through the material, and the material shear modulus. As these properties are not typically 

available to this model, it is not possible to calculate the maximum shear strain energy. However, 

it is relatively easy to determine the maximum total kinetic energy by evaluating the system 

when the velocity is maximum and the strain energy is zero. We make the assumption that the 

system is highly underdamped ( << 1) so the loss in energy per cycle is small compared to the 

energy stored and thus the kinetic energy at maximum velocity is equal to the potential energy at 

maximum displacement (Eq. 27):
42 

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= 1

2 ( ) +

1

2

(27)

The maximum velocity, , at node i is a function of the displacement, which is assumed to be 

sinusoidal. The displacement amplitude is defined by the scaled displacement from equation 14, 

and the frequency is defined by the first eigenvalue (Eq. 28).

, = = sin(2 ) = 2

(28)

where is the resonance frequency of the first mode of the blade in hertz. Likewise, the 

maximum rotational velocity at node i is:

, = = sin(2 ) = 2 (29)

Thus, taking the conservative estimate (higher energy) using the displacement and rotation of the 

node at the outboard end of the element (Eq. 30):

= 1

2 + , ( 2 ) +

1

2 12 + , ( 2 )

(30)

This estimate of the total energy will typically be a few percent different compared to the energy 

estimated using the applied moment in equation 26. For the purpose of calculating the structural 

energy loss, either result can be used. The dynamic analysis in Eq. 30 has been selected for 

implementation.

Now that we know the total energy in the system, the loss in energy per cycle, = , 

and from Eq. 25 the log decrement damping is given in Eq. 31:

= 1

2 = 12

(31)
43 

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where

=

(32)

Solving for and evaluating in terms of the structural damping ratio as shown in Eq. 32 yields

the total energy absorbed through structural damping per cycle (Eq. 33):

= 1 = 1 = 1

(33)

In Eq. 33, the log decrement damping, , and damping ratio, , are taken as only representing the 

structural or equivalent linear damping of the system. The energy loss due to aerodynamic drag 

is considered separately. It should be noted that the structural energy loss is proportional to 

dynamic energy stored in the system and thus is proportional to the square of the test amplitude. 

4.2.2 Aerodynamic Energy Loss

The aerodynamic energy loss per cycle is estimated by considering the effective drag force on 

each element of the blade. In general, drag force (F. M. White 1999) as a function of time is 

given as

( ) = 1

2 ( )

(34)

where is the air density, typically taken as 1.2 kg/m3, v(t) is the velocity, h is the height, and l

the length, so hl is the cross sectional area and is the coefficient of drag. Because the damping 

force is proportional the velocity squared, this type of damping is sometimes referred to as 

velocity squared damping. For the blade in the lead-lag direction, hl is taken as the thickness of 

the blade times the element length, whereas in the flap direction, hl is the chord times the 

element length. For a given element:

( ) = = sin(2 ) = 2 (2 )

(35)

The energy used over a cycle of time, = , is the integral of the force times the displacement.
44 

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= =

(36)

Because the drag is a nonconservative force, we evaluate the energy for one-quarter of a cycle 

and multiply the result by four. This calculation assumes a symmetric drag coefficient for the 

blade moving in either direction and neglects effects of turbulence.

= 4

1

2 ( 2 (2 )) ( 2 (2 ))

= 2 (2 ) (2 )

(37)

= 2 (2 )

3

4(2 )

sin(2 ) +

1

12(2 )

sin(3(2 ) )

= 2 (2 )

3

42 sin 2 +

1

12(2 )

sin 3 2 0

= 2 (2 )

3

4(2 )

1

12(2 )

(38)

or

= 4

3 (2 )

(39)

The total energy absorbed per cycle due to aerodynamic drag is found by summing the result of 

Eq. 39 for all elements. The conservative (higher energy) result is found by using the 

displacement at the outboard end of the element.

= 4

3 (2 )

(40)

Note that the aerodynamic energy loss is proportional to the cube of the displacement amplitude. 
45 

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4.2.3 Evaluating Damping Parameters

There is no wind tunnel data available for what the coefficient of drag should be for an airfoil 

oscillating at relatively low frequencies, such as in a fatigue test. However, the coefficient of 

drag has been measured for symmetric airfoils at a wide range of angles of attack for the 

application of vertical-axis wind turbines. For a symmetric airfoil at low Reynolds numbers and 

0 angle of attack, the coefficient of drag may be very low, around 0.03, while the coefficient of 

drag for an airfoil at 90 degrees angle of attack has been measured to be around 1.8 (Sheldahl 

and Kilmas 1981). B. Montgomerie (1996) cites coefficient of drag data for airfoils at 90 degrees 

to be in the range of 1.45 to 2.06 depending on the shape. Because blades undergoing a structural 

fatigue test move back and forth in a sinusoidal fashion passing through their own wake and 

operate in an enclosed volume inside a laboratory, relatively close to the laboratory walls and 

floor, the effective coefficient of drag has been found to be higher than these numbers. A 

numerical simulation of a blade oscillating perpendicular to the chord with a displacement range 

of 1 m or 2 m in an enclosed volume has predicted equivalent effective drag coefficients of 5.3 

and 4.45 respectively (Greaves 2013). Unfortunately, drag coefficients for higher amplitudes 

were not computed but it would be anticipated that they would continue to decrease and 

approach the steady state flow values as the test amplitude is increased.

The structural damping of the first mode of a large wind turbine blade measured during a modal 

impact experiment is typically in the range of 0.1% to 0.3% critical. However, losses in the 

excitation system either due to damping in the attachment between the system and the blade or 

due to not having a sinusoidal force function or not being exactly on resonance will result in 

more energy input being required than theoretically needed. It is difficult to separate the 

structural damping from these excitation system inefficiencies, so instead they are considered a 

combined total “structural” damping.

As the structural damping energy transfer is proportional to the amplitude squared and the 

aerodynamic damping energy transfer to the amplitude cubed, it is possible to curve fit the two 

values simultaneously to data collected while operating at steady state at a selection of different 

test amplitudes and measuring the energy input required to maintain steady state. Previous 

experience in curve fitting experimental data to match the measured energy input and test 

amplitude yielded the following results. A structural damping of about 0.7% critical works well 

for both flap and lead-lag fatigue tests for the size blade considered in this study regardless of the 

excitation technology used. For aerodynamic damping, coefficient of drag of about 2.1 fits 

experimental data for flap direction tests while a CD of 0.15 works for lead-lag direction tests.

4.2.4 Energy Input Calculations

The energy added per cycle from the excitation equipment is evaluated in two different ways 

depending on whether inertial mass excitation (IREX) or direct forcing excitation (GREX) is 

used. In either case, the energy input is calculated by integrating the force times the distance over 

the cycle as shown in Eq. 41:

= =

(41)
46 

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The blade is assumed to move in a sinusoidal fashion with the local blade displacement 

amplitude, , determined from the result of Eq. 14 for the node where the exciter is located. The 

equation of motion of the blade at the exciter location is then (Eq. 42):

( ) = sin(2 )

(42)

The velocity of the blade at the exciter location is calculated by Eq. 43:

= sin(2 ) = 2 (2 )

(43)

For an IREX, the force on the blade is equal but opposite to the force applied to move the shaker

mass (moving part of the IREX), which is the moving mass times the total acceleration (Eq. 44):

( ) = ( ) = ( ( ) + ( ))

(44)

where ( ) is the acceleration of the exciter mass relative to the blade. The acceleration of the 

node of the blade at the exciter location is shown in Eq. 45:

( ) = = sin(2 ) = (2 ) (2 )

(45)

The actuator displacement relative to the blade, , is assumed to be 90 degrees out of phase 

(optimum resonance) ahead of the blade motion, so the equation of motion for the actuator 

relative to the blade is calculated by Eq. 46:

( ) = sin 2 + 2 = cos(2 )

(46)

where is the displacement amplitude of the IREX actuator. The acceleration of the moving 

mass relative to the blade is calculated by Eq. 47:

( ) = = cos(2 ) = (2 ) (2 )

(47)

Thus, from Eq. 41:
47 

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= ( ( ) + ( ))

= ( (2 ) cos(2 ) + (2 ) sin(2 )) 2 (2 )

= (2 ) cos (2 ) + sin(2 ) (2 )

(48)

and integrating results in:

= (2 ) 2

1

2 2 +

1

4 sin(4 ) + 2

1

2 sin (2 )

= (2 )

1

2 2

(49)

= 4

(50)

Thus, for the inertial mass type exciter, the energy input per cycle is proportional to the 

displacement of the mass, the displacement of the blade and the frequency squared.

For a GREX, the excitation force is applied directly by the actuator and leads the blade 

displacement by 90 degrees. Thus:

( ) = sin 2 + 2 = cos(2 )

(51)

where is the amplitude of the force applied by the actuator to the blade. The energy input 

from a GREX per cycle period is: 

= ( ) = ( cos(2 )) 2 (2 )
48 

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= 2 cos (2 ) = 2

1

2

1

2 2 +

1

4 sin(4 )

(52)

The result of this computation for the energy input per cycle from a GREX type device is:

=

(53)

Unlike an IREX-type device, the energy input per cycle does not depend on the frequency and is 

only dependent on the applied force amplitude and the displacement of the blade at the excitation 

location. This is a significant advantage when operating tests on larger blades where the lowresonance frequency results in relatively little energy input from an inertial mass device and 

increasing the moving mass further reduces the test frequency and therefore does not necessarily 

increase the total energy input. However, the energy removed from the system due to structural 

and aerodynamic damping is a function of the test frequency and therefore the exciter amplitude 

( ) required to maintain the test level will be dependent on the test frequency. In addition, 

imperfections in the real system operation, for example, deviations from a perfectly sinusoidal 

input function or not running at exactly the system resonance frequency will decrease the 

effective energy input. For the present model, these imperfections are included in the empirically 

determined equivalent structural damping coefficient as previously discussed rather than 

attempting to evaluate them in the energy input equations. 

4.2.5 Energy balance

To determine the exciter amplitude required to achieve the target moment distribution for a given 

test setup the energy input per cycle is equated to the energy output per cycle (Eq. 54):

= +

= 1

1

2 + , ( 2 ) +

1

2 12 + , ( 2 )

+

4

3 (2 )

(54)

For a single IREX type device from Eq. 50 we can solve for the required displacement amplitude 

to obtain equilibrium and maintaine the test amplitude (Eq. 55):
49 

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= 4

= 1

4

1

1

2 + , ( 2 )

+

1

2 12 + , ( 2 ) +

4

3 (2 )

= 11

1

2 + , ( )

+

1

2 12 + , ( ) +

4

3

(55)

Thus the displacement amplitude required is a function of the blade mode shape and amplitude, 

and an inverse function of the moving mass and blade amplitude at the exciter location.

Likewise for a single GREX type device from Eq. 53 we can solve for the required force 

amplitude to obtain equilibrium and maintain the test amplitude (Eq. 56):

= = 11

1

2 + , ( 2 )

+

1

2 12 + , ( 2 ) +

4

3 (2 )

(56)

Thus the force amplitude required is a function of the overall blade mode shape and amplitude, 

and an inverse function of and blade amplitude at the exciter location. In addition, the applied 

GREX force required is a function of the frequency squared.
50 

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4.3 Gravitational Loading and Deformed Shape

To determine the neutral position of the blade in the laboratory under gravity and the total 

moments and displacements including gravity, a separate finite element calculation is performed. 

Calculations are again performed using a two degree-of-freedom finite beam element model in 

Excel. However, rather than using stiffness and mass matrix calculations, the model 

implementation is iterative, computing the loads for a given position, then computing the 

displacements for those loads before recalculating the loads based on the new displacements.

The same elements and nodes in the span direction along the zb axis are used from the dynamic 

analysis. The gravitational constant, g, is taken to be 9.80665 m/s2. Several other assumptions are 

made to simplify the analysis. In particular, the blade elements are taken to be axially rigid; thus, 

the length of each element and the total length of the blade do not change. Also, it is assumed 

that the original shape of the blade is a smooth curve and that a sufficient number of elements are

used so that the change in angle from one element to the next is small.

The first step in the calculations is to transform the undeformed blade coordinates of each node 

to global coordinates. Until now, calculations have been performed in rotor coordinates as 

defined by the IEC 61400-23 standard (IEC_61400-23 2014). To include gravitational effects, 

we will first transform the problem to global coordinates that reference the laboratory mounting 

scenario such that gravity acts in the negative zg direction. An example is shown in Figure 27. To 

avoid confusion, the subscript g will be used for the position vector in the global coordinate 

system {xg, yg, zg}. The transformation to global coordinates takes into account the pitch angle of 

the blade and the angle of the test stand as well as the offset of the root of the blade from the test 

stand due to the adapter plate, spacers, and so on. 

Figure 27. Example global coordinate system description referencing the test rig

Each element i of the blade is taken to be a uniform beam of length li with mass , = and 

stiffness EIi in the vertical gravitationally loaded direction. The stiffness of the element is taken 

Test 

stand 

angle

yg

zg

xg

zg

Origin is directly below 

center of test stand 

face plate

Test lab floor

Reaction 

footing

0 0

View from side View from front
51 

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as the average of the stiffness at node i-1 and node i. The undeformed element length is 

calculated by Eq. 57 as:

= , , + , , + , ,

(57)

Thus, each element is taken to be a straight line segment connecting the node positions 

determined by the prebend and sweep geometry of the blade. Blade deformation due to gravity is 

assumed to be entirely in the vertical plane. This simplification means that torsion effects due to 

pre-bend, sweep, and flap/lead-lag coupling are not included in the analysis. However, any 

existing displacement of the blade in the yg direction will be maintained throughout the analysis 

and reflected in predicted position of the test article in the laboratory. The following analysis is 

performed in the two dimensional xg-zg plane. The original (in zero gravity) angle of the blade at 

each node is estimated based on the location of the previous node.

, = atan , ,

, ,

(58)

The deflection at each node is calculated using cantilever beam tables superimposing the results 

from the internal moment and perpendicular shear force at that node. The local deflection, di, of 

each element in the direction perpendicular to that element is small, and therefore linear Euler 

beam theory applies to the element. This is shown graphically in Figure 28.

Figure 28. Deformation of element i under shear and bending

Vi

Mi

Node i-1 di

i

i-1

i

li

xgi

zgi

Node i
52 

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The change in the angle of node i is given by Eq. 59:

= ( ) 2( )

(59)

and is negative because positive rotation about yg is upwards in the global coordinate system

while the reaction moments and forces are taken to be positive as shown. The Euler beam 

deflection is given by Eq. 60:

= 2( ) + 3( )

(60)

The angle at each node is given by the angle of the undeformed blade at that node plus the sum 

of the change in angles at each node up until that point starting at the root of the blade (Eq. 61):

, = , +

(61)

Making the assumption that the blade does not stretch axially and thus the length of each element 

remains constant, the new global position of node i is calculated in Eq. 62 and 63 in terms of the 

position and angle of the previous node i-1 and the deformation di calculated in Eq. 60 with 

reference to Figure 29. 

, = , , = cos( ) sin arcsin 2

(62)

, = , , = sin( ) cos arcsin 2

(63)

The deformed blade position is calculated iteratively along the blade from node 0 to node 200 (in 

the positive span direction). 
53 

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Figure 29. Geometry definition for calculation of updated position Xg and Zg

The bending moment M and shear force V are functions of the deformed position. The free-body 

diagram for an element is shown in Figure 30. As we are only interested in the blade under 

gravity, the applied force F is zero. mb,i+1 is the mass of the blade element. ms,i+1 is the saddle 

mass applied at a particular node i+1 and is zero for most nodes except where a saddle is located. 

Likewise, the applied force is zero except at nodes located where a saddle is present. The applied 

force at a saddle, F i+1 i+1 relative to vertical. However, 

i+1 i+1. In the 

case of the blade under gravity alone, F = 0.

Vi

Node i-1

i-1

xgi

zgi

Node i

Mid-point line segment di

Angle of line segment of 

length is 
54 

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Figure 30. Free-body diagram of an element in deformed position

There is zero force at the tip of the blade, so calculations are performed working from the tip

back toward the root. In each case, the forces and moments at the i+1 node are known, and the 

forces and moments at the i

th node can be calculated. The final equations are:

= cos( ) 1000 , + , sin( ) sin( )

sin( )

(64)

= cos( ) + 1000 , + , cos( ) + sin( )

+ cos( )

(65)

= + 1000

,

2 + , cos( ) + cos( )

+ sin( ) + cos( )

(66)

Because the deformation depends on the moments and forces and the moments and forces 

depend on the deformation, the solution is iterative, first calculating deflection under a given 

load case, then calculating the moments and forces based on that deflection and repeating using 

the new moments and forces to calculate new deflections. For the case of dead weight loading 

Node i

Node i+1

g
55

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only, the initial configuration is taken to be the undeformed blade. Three iterations were found to 

converge to at least four significant digits for the tip deflection and the root bending moment. 

Once the mean moment and shear loading in the flap direction are determined, the maximum and 

minimum moments and shear during fatigue are calculated by superimposing the results of the 

dynamic and static analyses.

4.4 Model Implementation

The Excel implementation of the above analysis involves first defining the node locations along 

the blade span (zb) and then interpolating the blade properties at each node. The element 

properties are taken as the average of the properties at the nodes starting and ending each 

element. The nodes are selected to be evenly distributed along the blade span dimension with the 

exception of the nodes located closest to each saddle. To increase the accuracy for the relatively 

large point masses at saddle locations, the finite elements at the node closest to each saddle 

location is placed exactly at that saddle span location with corresponding longer and shorter 

elements on either side of it. Dynamic analysis ignores the prebend or sweep of the blade as well 

as any influence of the blade deformed shape under gravity. This two-DOF model is also unable 

to consider any torsion or out-of-plane coupling due to prebend and sweep. However, this 

geometry information and gravitational loading is taken into account later when the deformed 

position of the blade is calculated.

The analysis is performed twice, once in the flap direction and once in the lead-lag direction. For 

a biaxial fatigue test, it is assumed that these may be superimposed on each other without 

influencing one another. It is known that there will be some cross energy transfer as well as bend 

twist coupling due to the geometry of the blade between the two loading directions; however, for 

simplicity of the model and because torsional properties are rarely provided by blade 

manufacturers, this is neglected. The model should still be capable of providing reasonable 

estimates of the load distribution and energy input required in each direction sufficient to 

evaluate various test design scenarios.

Real saddle mass and virtual mass are added together at each node corresponding to a saddle 

location. Virtual mass is mass that only acts in one direction without influencing the other 

direction and could be physically implemented by locating mass off the blade on a slider table. 

Alternatively, positive or negative virtual mass can be used to simulate the influence of a GREX 

type actuator run slightly off resonance to introduce a force that is in phase or 180 degrees out of 

phase relative to the displacement of the blade. Virtual mass is included in the dynamic model of 

the blade for the corresponding loading direction but is not included when evaluating the 

deformation of the blade under gravity.

Experimentation has shown reasonable convergence with 100–150 nodes for typical blades. A 

total of 201 nodes are used in the analyses presented in this paper as this provides reasonable 

assurance of sufficient convergence while maintaining a numerically efficient model.
56

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5 Traditional Single-Axis Test Design

To contrast the loading that can be achieved with a biaxial fatigue test with traditional separate 

flap and lead-lag fatigue tests, optimized test designs are considered for each of these load cases. 

The obvious advantage to separating the two tests is that they can each be optimized to achieve 

the best target moment distribution for that loading direction. The number and location of saddle

locations are often constrained by the blade manufacturer or certifier to avoid constraining 

specific critical sections of the test article. Also, to avoid putting excessive shear loads into a 

single saddle, masses will sometimes be distributed over two or more saddle locations that are 

placed close together, often within a meter or two of each other. In the case of these fictional 

tests, no such constraints are given. However, an effort is made to keep the test design and total 

mass on each saddle within the range of options typically selected for a certification test. The 

amount of allowable load overshoot along the span relative to the target is also a critical 

parameter. In general, more added mass is required to more accurately achieve the target moment 

distribution. This slows the test down by reducing the natural frequency, changes the R-ratio, and 

can impose very large mean flap loads on the blade that may not be called for by the 

manufacturer. Therefore, a compromise is typically selected that does not overload the blade 

more than a specified amount. Depending on the manufacturer, something in the range of a 10%

to 20% overload is typically accepted at some point along the span. Typically at least the first 

70% of the blade span from the root toward the tip must be subjected to a moment range equal or 

greater than the target. Some manufacturers prefer to see as much as 90% of the blade span 

loaded to target.

5.1 Flap Fatigue Test

The bare blade oscillated in the flap direction results in the moment distribution shown in Figure 

31. Significant damping mass will be required in the middle of the blade to achieve the target 

root moment without excessively overloading the middle and outer portions of the blade.
57

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Figure 31. Bare blade moment distribution at resonance in flap direction. Natural frequency is

0.56 Hz.

To increase the moment at the root relative to the outer portion of the blade, significant damping 

masses are required. Masses are added to achieve approximately the target flap moment over 

most of the blade span. The results are summarized in Table 7. The test frequency is calculated 

to be 0.53 Hz, and a GREX input force amplitude at 30.0 m span of 25.9 kN is required to 

overcome the estimated 58.8 kJ of energy absorbed due to damping and aerodynamic drag each 

cycle. This GREX location is selected to minimize the force input required while staying within 

the stroke and velocity limits for the GREX.

Table 7. Proposed Uniaxial Flap Fatigue Test Configuration and Dynamics at Each Saddle

Saddle 

location

Saddle 

mass

Fixed 

added 

mass

GREX 

added 

mass

GREX 

force 

amplitude

Total 

flap 

mass

Dynamic 

Saddle 

amplitude

Max Flap 

Acceleration

Max 

Flap 

Velocity

Max 

Flap 

Saddle 

force

(m) (kg) (kg) (kg) (kN) (kg) (m) (g) (m/s) (kN)

18.0 1,000 1,000 2,000 0.17 0.19 0.56 1.11

24.0 800 1,000 1,800 0.37 0.42 1.25 2.24

30.0 600 1,000 200 25.9 1,800 0.72 0.82 2.41 4.34

58.0 20 20 5.53 6.27 18.44 0.37

60.0 6.09 6.91 20.31 0.00

The saddle masses are approximately representative of typical saddles employed at the WTTC. 

The achieved flap fatigue moment distribution is plotted in Figure 32. To ensure that the blade is 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Dynamic range

achieved (kNm)

Test target

(minimum)

moment range

flapwise (kNm)

Fraction target

range achieved
58

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not overloaded, the maximum and minimum fatigue moment distributions are compared to the 

maximum flap and minimum flap static test target moment distributions in Figure 33, and the 

resulting R-ratio is plotted in Figure 34. As a target mean load is not typically provided by a test 

customer, no effort was made to achieve a specific mean load beyond keeping the total dead 

mass on the blade reasonable—in this case, 5,620 kg of mass will be added to the blade.

Figure 32. Flap fatigue test moment range achieved relative to target moment

Figure 33. Bending moment extrema during flap fatigue test compared to static test target loads

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 70

Bending applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Flap fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum)

moment range

flapwise (kNm)

Fraction target

range achieved

-15000

-10000

-5000

0

5000

10000

15000

0 10 20 30 40 50 60 70

Bending moment (kNm)

Span Zb (m)

Flap fatigue moment relative to static test

Total Postive Bending moment (kNm)

Mean bending moment (kNm)

Total Negative Bending moment (kNm)

Max Flap Static Test Target (kNm)

Min Flap Static Test Target (kNm)
59

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Figure 34. R-ratio (minimum moment/maximum moment) distribution for proposed flap fatigue test

5.2 Lead-Lag Fatigue Test

The bare blade oscillated in the lead-lag direction achieves the moment distribution shown in 

Figure 35. Significant damping mass will be required in the middle of the blade to achieve the 

target root moment without excessively overloading the middle and outer portions of the blade.

Figure 35. Bare blade moment distribution at resonance in lead-lag direction. Natural frequency is 

1.01 Hz.

Masses are added to achieve approximately the target flap moment over most of the blade span. 

The results are summarized in Table 8. The test frequency is calculated to be 0.90 Hz. With the 

IREX placed at 28.0 m span, an input displacement amplitude of 120 mm is required to 

overcome the estimated 3.62 kJ of energy loss due to damping and aerodynamic drag each cycle.

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 5 10 15 20 25 30 35 40 45 50

R-ratio

Span Zb (m)

R-ratio based on moment - flap

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Lead-lag fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum) moment

range lead-lag (kNm)

Fraction target range

achieved
60

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Table 8. Proposed Uniaxial Lead-Lag Fatigue Test Configuration and Dynamics at Each Saddle

Saddle 

location

Saddle 

mass

Fixed 

added 

mass

IREX 

nonmoving 

mass

IREX 

exciter 

moving 

mass

IREX 

displacement 

amplitude

Total 

lead-lag 

mass

Dynamic 

saddle 

amplitude

Acceleration

in g

Lead-lag

saddle 

force 

amplitude

(m) (kg) (kg) (kg) (kg) (mm) (kg) (m) (g) (kN)

20.0 1,000 1,500 2,500 0.15 0.48 11.88

24.0 800 500 1,300 0.22 0.71 9.02

28.0 600 400 1,000 120 2,000 0.30 0.98 19.22

36.0 400 400 800 0.51 1.69 13.25

58.0 20 20 1.50 4.92 0.97

The achieved lead-lag fatigue moment distribution is plotted in Figure 36. To ensure that the 

blade is not overloaded, the maximum and minimum fatigue moment distributions are compared 

to the maximum flap and minimum flap static test target moment distributions in Figure 37. The 

R-ratio is -1 because the test is run horizontally. This closely resembles the loading the blade will 

see in the lead-lag direction when spinning on the turbine. In this case, 6,620 kg of mass will be 

added to the blade to keep within 10% overshoot of the target moment distribution.

Figure 36. Lead-lag fatigue test moment range achieved relative to target moment

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Lead-lag fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum) moment

range lead-lag (kNm)

Fraction target range

achieved
61

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Figure 37. Lead-lag fatigue moment relative to maximum and minimum edge static test target 

moment

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

0 10 20 30 40 50 60 70

Bending moment range (kNm)

Span Zb (m)

Lead-lag fatigue moment relative to static test

Total Postive Bending moment (kNm)

Mean bending moment (kNm)

Total Negative Bending moment (kNm)

Min Edge Static Test Target KNm

Max Edge Static Test Target kNm
62

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6 Biaxial Fatigue Test Design

When considering a biaxial fatigue test design, both the flap and lead-lag moment distributions 

must be optimized together. Added mass at a given location will impact the mode shape in both 

the flap and lead-lag directions simultaneously. Virtual mass is an additional tool that can be 

used to influence one test direction without significantly impacting the other. This can be 

accomplished in a real test setup either with mass located off the blade or using a hydraulic 

actuator to apply a force in phase with the displacement. In the simulation, virtual mass is 

implemented by including those masses only in the mass matrix for one test direction and not in 

the other for the mode shape analysis. Virtual masses are not included in the static mean load 

calculations.

The other consideration is the relationship between the two test frequencies. If each direction is 

allowed to run at its own resonance frequency, then the phase angle between the flap and leadlag moments will change continuously. This result is sometimes referred to as a quantum biaxial 

fatigue test. An example of this type of test implemented on a 50-m turbine blade is described by 

Snowberg et al. (2014). Although relatively easy to configure, a quantum biaxial test has several 

drawbacks, including unavoidable variation in the energy transfer between the test directions 

resulting in a variable amplitude loading. The variable amplitude loads will be most obvious in 

the lead-lag direction due to the relatively low damping and thus greater sensitivity to changes in 

energy input. If there are fixed limits on the maximum load that can be applied the result under 

variable amplitude loading is that more cycles will be required to achieve the target damage 

equivalent load. The other drawback of a quantum biaxial resonance test is that at some points 

the blade will be loaded at the maximum flap and lead-lag loads simultaneously. This loading 

condition may significantly overload some of the panels and other components of the blade and 

could result in premature failure during the test due to load combinations that are not 

representative of those experienced on the turbine.

Using real and virtual mass it may be possible to achieve a simple ratio between the flap and 

lead-lag frequencies. When this is achieved, a fixed phase angle between the lead-lag and flap 

moments can be selected for operation of the test. This could enable more accurate loading of the 

blade where the phase angle is matched to experimental turbine data and should also result in the 

ability to maintain constant amplitude in both test directions. The resulting motion will follow a 

repeating Lissajous figure. The two frequency ratios of interest are 1:1, which results in an 

elliptical blade motion with an equal number of flap and lead-lag cycles and can in theory be 

adjusted to achieve the desired phase angle, and 1:2, which results in a figure eight pattern with 

twice as many lead-lag cycles as flap cycles. An additional challenge is to avoid exciting higher 

modes so care must be taken to ensure that the higher-order frequencies are not equal to a 

harmonic of the first flap and lead-lag mode frequencies.

6.1 Quantum Test (Random Phase)

For a quantum biaxial fatigue test, the goal is to optimize both the flap and lead-lag moments 

simultaneously. The goal is to achieve or exceed the target moment range over at least the first 

70% of the span from the root toward the tip and ideally up to 90% of the blade should be loaded 

to the target level. From the uniaxial cases above, we can observe that significantly more added 

masses were required for the lead-lag fatigue test than the flap fatigue test to increase the root 

moment to the required level relative to the middle of the blade. For a quantum test, excluding 
63

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the use of virtual mass, it is apparent that either the outer portion of the blade will be underloaded in the flap direction or overloaded in lead-lag. The compromise presented below achieves 

or nearly achieves the flap target moment over the entire tested span while overloading the blade 

in the lead-lag direction by 10% out to 35 m and up to 20% beyond that. While these overloads 

will significantly increase the damage equivalent load achieved on the outer portion of the blade, 

they are not uncommon for lead-lag fatigue tests where it can be particularly challenging to 

achieve the root target moment without exceeding the target on much of the blade. For this 

example, the lead-lag frequency is 0.89 Hz and the flap frequency is 0.51 Hz. The mass 

distribution proposed is summarized in Table 9 along with the required excitation to maintain 

test amplitude. The predicted saddle amplitude, acceleration, and forces are given in Table 10. 

The resulting moment distribution is shown in Figure 38 and Figure 39 and the motion of the 

blade tip is shown in Figure 40. 

Table 9. Mass Distribution for Quantum Biaxial Fatigue Test

Saddle 

location

Saddle 

mass

Fixed 

added 

mass

IREX 

nonmoving 

mass

IREX 

Exciter 

moving 

mass

IREX 

displacement 

amplitude

GREX 

added 

mass

GREX 

force 

amplitude

Total 

real 

saddle 

mass

(m) (kg) (kg) (kg) (kg) (mm) (kg) (kN) (kg)

20.0 1,000 1,500 2,500

24.0 800 800 1,600

28.0 600 400 1,000 125 200 28.72 2,200

36.0 400 200 600

56.0 70 70

60.0

Table 10. Saddle Amplitudes and Forces from Quantum Biaxial Fatigue Test Simulation

Flap Lead-lag

Saddle 

location

Dynamic 

saddle 

amplitude

Acceleration 

in g

Max 

flap 

velocity 

Flap 

saddle 

force

Dynamic 

saddle 

amplitude

Acceleration in 

g

Lead-lag 

saddle 

force 

amplitude

(m) (m) (g) (m/s) (kN) (m) (g) (kN)

20.0 0.22 0.23 0.71 1.77 0.15 0.47 11.57

24.0 0.37 0.39 1.19 1.90 0.22 0.69 10.83

28.0 0.58 0.61 1.86 29.01 0.30 0.96 20.61

36.0 1.25 1.30 4.00 2.40 0.52 1.65 9.70

56.0 4.93 5.11 15.71 1.10 1.42 4.53 3.11

60.0 6.01 6.23 19.16 0.00 1.64 5.25 0.00
64

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Figure 38. Quantum biaxial fatigue test flap direction moment distribution

Figure 39. Quantum biaxial fatigue test lead-lag direction moment distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Flap fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum)

moment range

flapwise (kNm)

Fraction target

range achieved

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Lead-lag fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum) moment

range lead-lag (kNm)

Fraction target range

achieved
65

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 40. Motion pattern representing 30 seconds of test operation for quantum biaxial fatigue 

test

Because the lead-lag test direction only achieves 1.756 cycles for every flap fatigue cycle, it will 

only reach 1.756 million lead-lag cycles in the time it takes the flap fatigue test to reach 1 million 

cycles. The remaining 0.244 million lead-lag cycles could be run after that or alternatively, either 

the lead-lag fatigue load level could be increased or the flap loading decreased so that both test 

directions achieve the target damage equivalent load at the same time.

6.2 Phase Locked 1:1

There are several concepts used to achieve a 1:1 flap to lead-lag frequency ratio resulting in an 

elliptical blade motion. In general, either the flap frequency would need to be increased as 

proposed in the PHLEX project (Beckwith, White and Barsotti 2013) or the lead-lag frequency 

decreased as demonstrated in recent experiments in the Hybrid testing program previously 

described. Although both methods have been demonstrated at a smaller scale in research 

programs, neither has been attempted by NREL on a 50+ m utility-scale blade. Some biaxial 

tests using this approach have been conducted on larger blades at WMC although very limited 

information is available publically regarding these experiments (Westphal 2014). It is possible to 

use hydraulic actuators to increase the flap frequency by applying virtual mass in the flap 

direction This has been done at the WTTC for some uniaxial fatigue tests to modify the bending 

moment curve. However, maintaining stable control for an increase in frequency of more than 

about 0.05 Hz has not been possible on a megawatt-scale blade. In addition, in a PHLEX test, as 

the resonance frequency is forced higher, the outer portion of the blade will be overloaded 

relative to the root. Physical limits on the stroke of the GREX actuator prevent it from being 

applied farther outboard on the blade and the forces required to nearly double the flap frequency 

would be very high. Therefore, we will focus on the Hybrid test scenario, applying mass that 

only acts in the lead-lag direction to reduce the lead-lag frequency to equal the flap frequency.

The resulting test concept has an operational frequency of 0.511 Hz. The proposed mass 

distribution is shown in Table 11, and the resulting displacements, acceleration, and force at each 

saddle are given in Table 12. Very large virtual masses—over 24 tons—are required to reduce 

-8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m)
66

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the lead-lag test frequency. While impractical to implement this entirely using mass directly, the forces required are of a scope that 

implementation using a hydraulic actuator similar to a GREX but set up for horizontal loading should be considered. A force of 70 kN 

would be required at the 28-m saddle with a displacement range of 0.6 m. This could be accomplished using an actuator and bellcrank 

or other mechanical setup and would also eliminate the need for an IREX. Alternatively, a real mass could be used in combination 

with a mechanical system to multiply the effective inertial mass by increasing the displacement of the mass relative to the 

displacement of the blade. Farther out, damping masses connected to the blade using linkages to only act in the lead-lag direction 

would likely be more practical. However, accommodating the large flap deflections would make implementing this virtual damping 

masses difficult and potentially require expensive hardware components.

Table 11. Mass Configuration for Phase-Locked Biaxial Test with 1:1 Frequency Ratio Using an IREX in the Lead-Lag Direction and a 

GREX in the Flap Direction to Excite the Blade

Saddle 

location

Saddle 

mass

Fixed 

added 

mass

IREX 

nonmoving 

mass

IREX 

exciter 

moving 

mass

IREX 

displacement 

amplitude

GREX added 

mass

GREX force 

amplitude

Total real 

saddle 

mass

Virtual 

mass flap 

dir only

Virtual 

mass 

lead-lag 

dir only

(m) (kg) (kg) (kg) (kg) (mm) (kg) (kN) (kg) (kg) (kg)

20.0 1,000 1,000 2,000

24.0 800 1,000 1,800

28.0 600 400 1,000 119 200 31.38 2,200 -500 20,550

45.0 250 250 3,500

58.0 30 30 500

60.0
67

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Table 12. Displacement, Acceleration, and Forces for Phase-Locked Biaxial Test with 1:1 

Frequency Ratio

Flap Lead-lag

Saddle 

location

Dynamic 

Saddle 

amplitude Acceleration

max 

flap 

velocity 

Flap 

Saddle 

force

Dynamic 

Saddle 

amplitude Acceleration

Lead-lag

Saddle 

force 

amplitude

(m) (m) (g) (m/s) (kN) (m) (g) (kN)

20.0 0.22 0.24 0.72 1.44 0.15 0.16 3.06

24.0 0.38 0.40 1.21 2.17 0.22 0.23 4.02

28.0 0.59 0.62 1.90 31.54 0.30 0.31 70.26

45.0 2.58 2.72 8.29 2.07 0.84 0.89 32.59

58.0 5.63 5.93 18.09 0.54 1.48 1.56 8.09

60.0 6.20 6.53 19.92 0.00 1.59 1.67 0.00

Overall the loading distribution achieved in the flap direction is relatively good (Figure 41). 

However, in the lead-lag direction, shown in Figure 42, the blade ends up underloaded at the 

saddles where the virtual masses are applied and overloaded between them. This curve could be 

smoothed out by adding more saddles with more smaller virtual masses, but this would greatly 

increase the complexity of the test, especially outboard where the deflections are high.

Figure 41. Flap bending moment distribution achieved with 1:1 frequency ratio test setup

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Flap fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum)

moment range

flapwise (kNm)

Fraction target

range achieved
68

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Figure 42. Lead-lag bending moment achieved with 1:1 frequency ratio test setup

In theory, any phase relationship could be maintained between the flap and lead-lag moments. 

The resulting test motion will range between an ellipse and a straight line as shown in Figure 43. 

Preliminary experiments with the hybrid test have shown that it may be difficult to obtain the 

desired phase relationship using an IREX because of energy transfer between the flap and leadlag directions. This would also suggest a possible preference for a direct actuation system like 

the GREX in the lead-lag direction to gain more control of the phase angle. However, 

sophisticated control algorithms may be required to account for the changing geometry and load 

application angles as the blade moves. Other variations on the mechanical configuration may 

enable better separation of the lead-lag and flap excitation but there is likely always going to be 

some level of coupling due to the twisted structure of the blade.

Figure 43. Displacement representation for 1:1 frequency ratio with phase angle of 90 deg (left), 45 

deg (center) and 0 deg (right). The mirror image of these is also possible.

One disadvantage of the 1:1 frequency is that the lead-lag direction will be tested at the flap 

frequency. Due to the relatively high fatigue loads in the lead-lag direction compared to static 

strength for large turbine blades (see Figure 37 for example), it is desirable not to accelerate the 

fatigue test as much as is common in the flap direction. Two million cycles or more are often 

required for lead-lag tests as is the case for this proposed fictional blade. As a result, to complete 

the damage equivalent load at the same time, the flap loading would need to be rescaled for 2 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Lead-lag fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum) moment

range lead-lag (kNm)

Fraction target range

achieved

-8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m) -8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m) -8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m)
69

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million cycles. The total testing time will be significantly longer than for a quantum test. In this 

case, 2 million cycles at 0.51 Hz. will take 45 days–much longer than the 26 day quantum fatigue 

test and nearly as long as the single axis flap and lead-lag fatigue tests combined. While there 

may be advantages in terms of achieving more realistic load combinations during the fatigue test, 

reducing testing time is not likely to be a significant benefit for this type of test.

6.3 Phase Locked 1:2

A phase locked test with a ratio of 1:2 is also considered. This is potentially advantageous 

because the natural frequencies of the blade are closer to this ratio to begin with and typically 

lead-lag fatigue tests are designed with more cycles than flap fatigue tests to limit the peak loads. 

Again it would be very difficult to significantly increase the lead-lag fatigue test frequency so 

instead, we reduce the flap frequency by adding virtual mass in that direction. Starting with the 

optimized lead-lag fatigue test scenario we seek to achieve a flap frequency of half of the leadlag frequency or about 0.45 Hz. To maintain a reasonable target moment distribution virtual 

masses that act in the flap direction must be attached near the tip of the blade which may be 

difficult to do mechanically. If a test article has natural frequencies that are closer to 1:2 to begin 

with, this approach may be more feasible.

The example developed below also compromises on the lead-lag load distribution to place 

saddles where they are needed to obtain the desired flap frequency and distribution. However, 

the overall result is relatively good from a load distribution standpoint.

The resulting test concept has an operational frequency of 0.4507 Hz. in the flap direction and 

0.9014 Hz. in the lead-lag direction. The proposed mass distribution is shown in Table 13 and 

the resulting displacements, acceleration and force at each saddle is given in Table 14. The 

outboard virtual masses are reasonable with relatively small forces imposed on the saddles 

although a mechanism to handle the large displacement amplitudes of 2.5 and 5 m, respectively,

will be required. A mechanism capable of applying a virtual mass through a displacement range 

of 10 m without undue influence in the lead-lag direction could pose a significant design 

challenge. However, farther inboard, the 11 kN in phase force required to achieve the virtual 

mass at the 28-m saddle can be easily accomplished with the GREX in combination with the 

23.5 kN excitation. 

Table 13. Mass Configuration for Phase-Locked Biaxial Test with 1:2 Frequency Ratio

Saddle 

location

Saddle 

mass

Fixed 

added 

mass

IREX 

nonmoving 

mass

IREX 

exciter 

moving 

mass

IREX 

displacement 

amplitude

GREX 

added 

mass

GREX 

force 

amplitude

Total 

real 

saddle 

mass

Virtual 

mass 

flap 

dir 

only

(m) (kg) (kg) (kg) (kg) (mm) (kg) (kN) (kg) (kg)

20.0 1,000 1,500 2,500

24.0 800 500 1,300

28.0 600 400 1,000 126 200 23.46 2,200 2,400

45.0 220 220 450

56.0 45 45 105

60.0
70

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Table 14. Displacement, Acceleration, and Forces for Phase Locked Biaxial Test with 1:2 

Frequency Ratio

Flap Lead-lag

Saddle 

location

Dynamic 

saddle 

amplitude Acceleration 

Max 

flap 

velocity 

Flap 

saddle 

force

Dynamic 

saddle 

amplitude Acceleration

Lead-lag 

saddle 

force 

amplitude

(m) (m) (g) (m/s) (kN) (m) (g) (kN)

20.0 0.22 0.18 0.63 1.58 0.15 0.48 11.88

24.0 0.37 0.31 1.06 1.38 0.22 0.71 9.04

28.0 0.59 0.48 1.67 24.68 0.30 0.98 21.22

45.0 2.55 2.08 7.22 4.83 0.87 2.86 6.16

56.0 5.00 4.09 14.16 2.12 1.45 4.74 2.09

60.0 6.08 4.97 17.22 0.00 1.68 5.50 0.00

Overall the loading distribution achieved in the flap direction is relatively good (Figure 44). The 

lead-lag direction, shown in Figure 45, ends up slightly overloaded because of the need for 

saddles on the outer portion of the blade. 

Figure 44. Flap bending moment distribution achieved with 1:2 frequency ratio test setup

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Flap fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum)

moment range

flapwise (kNm)

Fraction target

range achieved
71

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 45. Lead-lag bending moment achieved with 1:2 frequency ratio test setup

Although the phase angles will not be constant, there will be two dominant phase relationships 

that could be used to test critical regions of the blade not fully tested in a uniaxial test. A range of 

phase relationships are possible (Figure 46), but most likely phase angles close to 0 and 180 

degrees producing a figure eight would be preferable.

Figure 46. Displacement representation for 1:2 frequency ratio with phase angle of 90 deg (left), 45 

deg (center) and 0 deg (right). The mirror images of these are also possible.

The primary advantage of the 1:2 frequency ratio tests is that it is possible to complete the flap 

fatigue test simultaneously with the lead-lag test without a significant increase in the lead-lag

fatigue test time. The ratio of the frequencies in this case is the same as the ratio of the target 

cycles to achieve damage equivalent load. Thus, in theory the damage equivalent load is 

achieved at the same time without modifying the test load level. However, the modeling 

approach incorporated here fails to evaluate the influence of blade twist, which will result in 

some coupling of the flap and lead-lag moments. Thus, actual results may still show variable

amplitude loading, particularly in the lead-lag direction similar to those experienced by the blade 

during a quantum fatigue test. More complex time-dependent modeling or real experiments will 

be required to evaluate how significant this effect is. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70

Fraction applied moment range to target moment 

range

Bending moment range (kNm)

Span Zb (m)

Lead-lag fatigue moment

Dynamic range

achieved (kNm)

Test target

(minimum) moment

range lead-lag (kNm)

Fraction target range

achieved

-8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m) -8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m) -8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8 Vertical displacement (m)

Horizontal displacement (m)
72

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6.4 Total Test Time Comparison

One of the primary motivations for conducting biaxial testing is to more thoroughly test the 

blade structure under loading representative of the loads seen on the turbine. However, due to 

commercial pressures in the industry, reducing test time is a secondary goal and a significant 

reduction in test time will help to promote a new test technology. Therefore, it is relevant to the 

industry to evaluate the possible changes in test time depending on the test method selected. It is 

noted in the previous discussion that not all biaxial test configurations lead to a substantial 

reduction in test time. This can be due to the reduction in test frequencies required to achieve the 

target moment or due to resulting load amplitude modulation as was seen by Snowberg et al.

(2014) in the quantum biaxial test demonstration. It is hard to estimate the extent of the variable 

amplitude in the lead-lag direction based on the simplified test analysis performed in this study 

so this effect is not included in the analysis below. Future analysis or experiments will be 

required to evaluate how much error in these estimates results from this simplification.

In this analysis, only the operational test time at amplitude is calculated. Test setup, down time 

for inspections and equipment maintenance, and so on, is not included. Experience has shown a 

factor of between 1.2 and 1.5 times the operational test time is typical for actual blade tests; thus, 

the differences in operational test time will have less impact on the total program time than is

represented here. However, for fatigue test with more cycles than assumed in this report, 

reducing operational test time can result in greater reduction in the overall test campaign time. 

Assuming that a minimum of 1 million flap fatigue cycles and 2 million lead-lag fatigue cycles is 

required, the resulting total test time is shown in Figure 47. The phase-locked test with a 

frequency ratio of 1:2 provides the least total test operational time of 25.7 days for this example 

blade and set of target load cycles. Next is the quantum biaxial test at 26.0 days with the caveat 

that in both of these cases, some higher maximum load amplitude cycles must be accepted due to 

the expected load modulation or the total number of test cycles must be extended to achieve the 

required damage equivalent load. A phase-locked 1:1 test results in the longest total test time of 

45.4 days although the result is negligibly different from the traditional sequential test approach 

of 43.6 days, particularly when considering the additional test setup time required to switch from 

flap to lead-lag tests.
73

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* Quantum biaxial test time and 1:2 phase locked time are possibly underestimated due to likely load amplitude 

modulation requiring more than the target number of cycles to achieve the desired damage equivalent load.

Figure 47. Comparison of test time between different test methods

0

5

10

15

20

25

30

35

40

45

50

Traditional singleaxis sequential tests

Quantum biaxial

fatigue *

1:1 phase locked 1:2 phase locked *

Test time (days)

Flap

Lead-lag

Total
74

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7 Conclusion

This report examined several potential biaxial fatigue test scenarios for a fictional 60-m blade. 

Normalized properties of a number of real blades were combined to produce a fictional test 

article specification that is similar to current blades in production. Current test hardware 

available at the WTTC was considered for use in a test program along with several new 

concepts, including those employed by the Hybrid test research project where virtual mass is 

located off the blade and connected with a push rod such that it only impacts the test in one 

direction—either the lead-lag or flap but not both. In addition, a GREX or GREX-type hydraulic 

actuator device may be employed to both excite the blade with a force function at 90 degrees 

phase relative to the displacement and provide or remove virtual mass by applying a force inphase or 180 degrees out of phase with the displacement. This is accomplished by modifying the 

excitation frequency and resulting target phase angle for the actuator. The results in terms of 

bending moment distribution on the blade are the same regardless of whether real mass or an 

actuator is used to create a virtual mass so the virtual mass concept is useful for modeling these 

types of tests setups and for determining the appropriate hardware.

Four test configurations were considered. The traditional sequential test program where lead-lag 

and flap direction fatigue is performed separately is used as a baseline both to evaluate the 

possible accuracy of meeting the ideal target bending moment distribution as well as the total 

operational test time. Three alternative approaches for configuring a biaxial fatigue test were 

considered: a quantum biaxial fatigue test where the flap and lead-lag directions are excited at 

separate resonance frequencies resulting in a variable and nominally random phase angle 

between the two test directions; a phase-locked test with frequency ratio of 1:1 where the leadlag frequency is reduced to the flap frequency by adding virtual mass at multiple stations; and a 

phase-locked test with a frequency ratio of 1:2 where the flap frequency is reduced slightly using 

virtual masses to run at exactly one-half of the lead-lag frequency. In each case, attention was 

given to achieving the target bending moment distributions as accurately as possible; however, 

compromises were invariably required and individual analysis would be required to determine if 

the final load distribution is acceptable for a given blade. While each potential biaxial fatigue test 

configuration is possible to implement, the large virtual masses required for a 1:1 flap to lead-lag

may be difficult to accomplish with current test equipment. More reasonable virtual masses are 

required for the 1:2 phase-locked test, although the large tip displacements will require the 

development of new hardware to implement them.

Although the quantum test system has been successfully implemented on a multimegawatt-scale 

blade in the past, the disadvantages of widely varying phase angles and modulating amplitude 

have so far precluded adoption of this method in most commercial certification test programs. 

Achieving a 1:1 phase-locked test has the advantage that the phase angle can be actively 

controlled to best match the phase angle experienced by the blade on the turbine. However, the 

drastic change in frequency required means that very large virtual masses or applied forces are 

required in the lead-lag direction, and it is difficult to achieve the target bending moment 

distribution along the whole blade accurately without the use of many virtual mass loading 

stations. Also, the test time may be extended beyond that of a traditional sequential test due to 

the typically higher lead-lag cycle count being executed at the flap frequency. 
75

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Given the possible reduction in test time, the ability to achieve moment distributions relatively 

close to the target and the relatively small virtual masses required for the 1:2 phase-locked test 

approach appear to have a good chance of success in a commercial test program. Further 

research needs to be conducted regarding the impact of applying the lead-lag cycles with a 

combination of two different phase angles for every half flap cycle on the blade and whether this 

is an improvement in accuracy for a blade test compared to two sequential tests. An additional 

consideration is the design of small virtual masses to use at the tip of the blade where the flap 

direction deflection amplitude can be 5 m or more. Such a device will be required to enable this 

type of testing to proceed on most multimegawatt-scale wind turbine blades.
76

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

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