Multi-Excitation Fatigue Testing for Large Full-Scale Wind Turbine Blade

PAN ZujinWU JianzhongZHANG Zhenguo

1 School of Mechanical Engineering,Tongji University,Shanghai 200092,China 2 Shanghai Electric Wind Power Co.,Ltd.,Shanghai 200235,China

Abstract：In order to solve the problem of insufficient exciting force of equipment for large full-scale wind turbine blade fatigue testing,the influence of gravity on the performance of excitation equipment and fatigue damage evaluation of the different positions of wind turbine blades are analyzed. With the multi-excitation loading in the horizontal direction,the actuator force of the excitation equipment does not need to overcome the gravity of the dynamic mass,which directly outputs the exciting force of the system vibration. The excitation efficiency of the equipment is 77% higher than that of the vertical load. The gravity moment of the horizontal loading mode is perpendicular to the loading direction. That is,the mean load in the flapwise direction is zero. The weight of excitation equipment could replace the tuning mass on the condition that the self-weight of equipment is reduced by the multi-excitation mode,which helps the excitation equipment play the comprehensive function of excitation equipment and tuning mass. At the same time,the gravity moment in the edgewise direction will be decreased by 17.0%-22.5% under the multi-excitation horizontal loading mode. In the vertical loading mode,the gravity moment is the mean load,which only increases fatigue damage accumulation by 15.6%. By comparing the role of gravity in the excitation equipment and fatigue damage evaluation,the multi-excitation horizontal loading mode has more advantage to performance the exciting force than the contribution of gravity to the fatigue damage accumulation in the vertical loading mode. Through the fatigue testing of multi-excitation horizontal loading,the potential of excitation equipment is explored,and the problem of insufficient exciting force in large full-scale wind turbine blade fatigue testing will be solved.

Key words:wind turbine blade;fatigue testing;multi-excitation；exciting force;equivalent fatigue damage accumulation

Introduction

Fatigue testing of full-scale wind turbine blades as a mandatory procedure for blade certification is required by international standards and guidelines[1-3].With the development of wind turbine blades towards large scale,the technology of fatigue testing for large full-scale wind turbine blades becomes a key bottleneck[4].Researchers[5-7]implemented the fatigue testing of 48.3 m and 56.0 m blades by using a linear hydraulic exciter,and then analyzed the fatigue damage of the blade.White[8]developed the dual-axis fatigue testing,which was more in line with the actual operation of wind turbine blades.Researchers[9-10]studied the fatigue testing specification optimization method for resonance-type fatigue testing of full-scale wind turbine blades.Ederetal.[11]proposed a method by simultaneously exciting the blade with a combination of two or more eigenfrequencies in order to shorten the duration of fatigue testing.Lee and Lee[12]performed a measurement theory of test bending moments to deal with biaxial test bending moment that occurred during single-axial fatigue testing,which helped in reducing the deviations of the measured results.Researchers[13-14]analyzed the control strategy of excitation equipment for fatigue testing.Lee and Lee[15]presented the damping mechanism model based on the concept that fluid inertia damping was caused by a delayed response of flow development,and measured the modal damping ratios of wind turbine blades for the fatigue testing.Baietal.[16]introduced the analytic hierarchy process and the fuzzy (AHP-Fuzzy) decision method to the health assessment of wind turbine blades after fatigue testing.Large blades mentioned below were rotor blades with a diameter of more than 160 m.

At present,the excitation equipment shows the problem of insufficient exciting force in the fatigue testing of large full-scale wind turbine blades.In order to reach the target bending moment of the vibration system,it is often necessary to increase the power of the exciter,add the dynamic mass block,strengthen the fixture and so on.As shown in Fig.1,these measures lead the weight of the excitation to equipment increase and cause a series of other problems.Firstly,the tunning mass is introduced to the position where the exciter is located，which leads to the deviation between the local bending moment and the target value increases.Secondly,because the weight of the excitation equipment belongs to the additional mass of the blade,the resonance frequency of the whole vibration system is pulled down.The excitation efficiency of the excitation equipment is directly proportional to the resonance frequency’s square.The decrease of the resonance frequency of the system will greatly reduce the excitation efficiency of the equipment.Thirdly,the decrease of the excitation frequency results in the prolongation of the test period.When the same number of the target cycle is reached,the test period is inversely proportional to the resonance frequency.Finally,in order to reduce the influence of the excitation equipment’s weight on the frequency,the position of exciters is often arranged near the blade root.The amplitude of the first shape mode near the root is small,and the amplitude near the tip is large.When the same excitation energy output is achieved,the smaller the amplitude of the installation position of the exciter is,the larger the exciting force is required.

Fig.1 Shortcomings of the present test method for large blade

The fatigue testing of wind turbine blades includes vibration in the flapwise direction and the edgewise direction.Moreover,the demand of exciting force in the flapwise direction is higher than that in the edgewise direction.Therefore,the problem of the insufficient exciting force in the flapwise direction is mainly discussed.In the traditional blade fatigue testing,the vertical loading mode is used in the flapwise direction.The main reason for adopting this loading mode is that the gravity moment produced by the weight of excitation equipment and the tuning mass on the blade is relatively large.The structure of the blade determines that it has anisotropy to bear the load.The bending moment that the blade can withstand in the flapwise direction is larger than that in the edgewise direction.The traditional method of blade fatigue testing in the flapwise direction is loading in the vertical direction,the pressure side of the blade is upward,the suction side is downward,and the chord length direction is parallel to the ground.The moment of gravity is supported by the blade in the flapwise direction.If the horizontal loading is used in the flapwise direction of fatigue testing,the trailing edge of the blade is upward and the chord of blade is perpendicular to the ground.The gravity moment is withstood by the blade in the edgewise direction.The ratio of the gravity moment to the ultimate moment of the blade in the edgewise direction is too high,so there is high risk of damage in the edgewise direction during fatigue testing.In summary,these measures to improve the capacity of the excitation equipment increase the additional weight.The gravity moment generated by these additional weight is imposed on the blade.Moreover,the resonance frequency of the system is reduced,which leads to that the exciting force of excitation equipment is still not developed.In order to improve the exciting force,the design of excitation equipment has to increase mass,which might result in the decrease of the resonance frequency of the system.Therefore,the excitation efficiency could not be fully developed.The design of excitation equipment for fatigue testing of large wind turbine blades falls in a vicious cycle.

Based on the problem of insufficient exciting force of large full-scale blade fatigue testing in the flapwise direction,the excitation efficiency of the equipment should be developed by changing the mode of fatigue testing.This paper proposes the multi-excitation horizontal loading mode to solve the problem in the fatigue testing.The loading orientation of fatigue testing is transformed from single-excitation in the vertical direction to multi-excitation in the horizontal direction.The method of multi-excitation is used to solve bottleneck of fatigue testing for large full-scale blades.In order to fit the target bending moment,it is necessary to add tuning mass at different positions of the blade and adjust the dynamic mass of excitation equipment during the fatigue testing.The excitation points are arranged according to the optimized tuning mass position of fatigue testing specification.This specification will greatly reduce the gravity moment generated by the excitation equipment and tuning mass,so that the blade can withstand it in the edgewise direction too.Therefore,the multi-excitation horizontal loading mode could be realized in the flapwise direction of fatigue testing.

1 Structure and Performance Analysis of Excitation Equipment

1.1 Structure of excitation

The excitation equipment of wind turbine blade fatigue testing includes servo motor,power transmission chain,support equipment,signal communication,safety limited control,etc.As shown in Fig.2,the power transmission chain includes linear actuator,linear guided rail,guided rail bracket,and dynamic mass block.The exciting force in the fatigue testing comes from the reciprocating inertia force of the dynamic mass block driven by the servo motor,which can also be considered as the reaction force of the dynamic mass block on the blade.The blade and the exciter are fixed together by the support rod.The servo motor controls the dynamic mass block to perform sinusoidal harmonic vibration,by which the inertia force generated drives the blade to move together.Therefore,this produces the exciting force driving the harmonic vibration on the blade.

Fig.2 Exploded view of excitation equipment

1.2 Exciting force

Figure 3 is the motion state schematic diagram of the vibration mass and the blade under steady-state operation.The initial state is A,the cycle is A-B-C-D,and the dotted line is the position of mass block in state C.The vibration amplitude curve of blade exciting point and dynamic mass block in cycle is shown in Fig.4.

Fig.3 Sketch of steady state motion of vibration

The dynamic mass of excitation equipment moves sinusoidally in the vertical direction.Since the mass and the blade are in the resonance state when the vibration is stable,the initial position of the blade is selected when the vertical displacement of the blade is zero.The motion equation of the blade with the ground as the reference point is

A(t)=-Asinωt.

(1)

Taking the blade as the reference point,the motion equation of the mass block is

s(t)=-Scosωt，

(2)

whereAis the blade amplitude with the ground as the reference,Sis the dynamic mass stroke with the blade exciting point as the reference,tis the time history of blade vibration,andωis the angular frequency of the system vibration.

As the dynamic mass block moves sinusoidally with respect to the exciting point of the blade,it also vibrates up and down with the blade.Therefore,the displacement equation of mass relative to ground should be the vector displacement sum of dynamic mass relative to blade exciting point and blade exciting point relative to ground.The displacement equation of dynamic mass block relative to the ground is

x(t)=s(t)+A(t)=-Scosωt-Asinωt.

(3)

The actual motion displacement curves of the dymanic mass block relative to different reference points are shown in Fig.4.By deriving the displacement equation from time,the velocity equation of the mass block to ground is obtained.

υ(t)=x′(t)=ωSsinωt-ωAcosωt.

(4)

The acceleration equation of mass to the ground is obtained by further deriving the velocity equation from the time.

a(t)=υ′(t)=ω2Scosωt+ω2Asinωt.

(5)

Therefore,the exciting force required to drive the dynamic mass block movement is

F(t)=ma(t)=mω2Scosωt+mω2Asinωt.

(6)

Fig.4 Actual motion displacement curve of dynamic mass block

The horizontal loading mode means that the actuator force of the excitation equipment is horizontal to the ground,and the vertical loading mode is vertical.The difference between the two loading methods is shown in Fig.5.

Fig.5 Horizontal and vertical loading modes of excitation equipment:(a) horizontal loading mode;(b) vertical loading mode

When the exciter is loaded vertically,the exciting force required for the motion of the dynamic mass block is the actuator force subtracts the mass gravity according to Eq.(7).

F(t)=Fs-mg.

(7)

The output actuator force of the linear actuator is

Fs=F(t)+mg=mω2Scosωt+mω2Asinωt+mg.

(8)

(9)

whereFVis the actuator force when the excitation is loading in the vertical direction.

When the exciter is loaded horizontally,the output actuator force of the linear cylinder is the exciting force.

(10)

whereFHis the actuator force when the excitation is loading in the horizontal direction.

The maximum speed of the dynamic mass block is determined by the angular frequency and stroke,as shown in Eq.(11).The maximum speed is determined by the helical pitch and the speed of the servo motor,as shown in Eq.(12).Then the relationship between the stroke and vibration frequency is deduced as shown in Fig.6.

Vmax=ωS=2πfS,

(11)

(12)

whereVmaxis the maximum speed of the dynamic mass block,his the helical pitch,nis the rotation rate,andfis the resonance frequency.

Fig.6 Stroke and vibration frequency of dynamic mass

1.3 Comparison of exciting force in vertical and horizontal direction

According to Eq.(9),the actuator force under different dynamic masses of vertical loading is calculated.The distribution of actuator force and frequency under different dynamic masses of horizontal loading is shown in Figs.7-8.We can see from Fig.9,when the blade is loaded in the horizontal direction,the actuator force ratio of the horizontal direction to the vertical direction is 10%-23% in the frequency range of 0.3-0.5 Hz.That is,the actuator force of the exciter can be reduced by at least 77%.

When the fatigue testing in the flapwise direction is loaded in multi-excitation horizontal direction,the actuator force of the excitation equipment output is mostly the exciting force,which does not need to overcome the huge gravity of dynamic mass.It is not necessary to select extra-large power motor,electric driver and other related parts for excitation equipment,which is beneficial to the lightweight of the excitation equipment.

Fig.7 Actuator force distribution of excitation equipment in horizontal loading direction

Fig.8 Actuator force distribution of excitation equipment in vertical loading direction

Fig.9 Actuator force ratio distribution of excitation equipment in horizontal and vertical loading directions

2 Fatigue Equivalent Damage Accumulation

2.1 Mean and amplitude

The gravity moment generated by the dead weight of blade,the weight of excitation equipment and tuning mass is the mean value of the vibration loading on blade.

(13)

whereMiis the bending moment of blade sectioni,Mi+1is the bending moment of blade sectioni+1,ρi+1is the linear density of blade sectioni+1,Δli+1is the span of blade sectioni+1,mT(i+1)is the tuning mass of blade sectioni+1,gis the acceleration constant of gravity,and Δliis the span of blade sectioni.

According to Eq.(14) and the boundary condition of the wind turbine blade,the first natural frequency and mode shape will be solved by multiple iterations[17].

(14)

(15)

whereTis the force distribution along the blade,ziis the distance from the root,MTiis the vibration bending moment of blade sectioni,MT(i+1)is the vibration bending moment of blade sectioni+1,mi+1is the mass of blade sectioni+1,ωis the angular frequency,Ai+1is the amplitude of blade sectioni+1,and Δliis the span of blade sectioni.

2.2 Goodman diagram and fatigue damage accumulation

The gravity moment is generated by the dead weight of blade,tuning mass and excitation equipment on the blade.When the blade is excited in the vertical direction,the loading direction of the gravity moment is the same as that of the vibration moment.Therefore,the gravity moment is the mean value of the vibration moment.The gravity moment is as the mean value of the vibration moment to participate in the statistics of fatigue damage accumulation.As shown in Fig.10,the spar cap of pressure side (PS) is always under tension-tension fatigue loads,and the spar cap of suction side (SS) is always under compression-compression fatigue load.However,the required target fatigue load of PS and SS spar caps is in the state of tension-compression fatigue load.Therefore,there is a great difference between the target and the measurement in evaluating the fatigue damage accumulation of the spar cap.When the blade is excited in horizontal direction,the loading direction of the gravity moment and the vibration moment is perpendicular to each other.Then the gravity moment is not involved in the count of fatigue damage accumulation.That is,the mean value of the load is zero.

Fig.10 Time history of spar cap strain

The fatigue damage analysis is based on the Goodman diagram,which is drawn based on the strain-number (S-N) characteristic curve of the corresponding laminate.Goodman curve is drawn according to the S-N characteristic curve of unidirectional fiberglass laminates fatigue testing,in which theRvalues are 0.1,-1.0 and 10.0,respectively.The design allowable cycles corresponding to the mean value and amplitude value of each cyclic loading are shown in Fig.11.

Fig.11 Goodman curve of unidirectional fiberglass laminates

MoreR-values could be used by adding extra coordinates if required.Given a strain cycle range and mean value,it is possible to plot itsR-value using simple trigonometry,and then decide which sector it lies in based on the angle that it makes with thex-axis.Goodman diagram is piecewise linear,S-N curve changes with the cycleR-value,so there is no unified statistical formula of fatigue damage.After theR-value is determined,the S-N curve based on the value can be restored,as shown in Fig.12.

Fig.12 S-N curve of unidirectional fiberglass laminates

The allowable number of load cyclesNcan be determined by[3]

N=

(16)

3 Comparison of Two Loading modes

3.1 Vertical and horizontal loading modes

The 83.4 m blade fatigue testing specification is taken as an example,and the effects of two loading modes on the deviation in verification,damage assessment and the period of fatigue testing are compared.Figure 13 is single-excitation in the vertical loading mode[18].Figure 14 is the multi-excitation in the horizontal loading mode.As shown in Fig.15,when the blade is loaded in the vertical direction,the contribution of the mean value of the vibration moment generated by the gravity on the equivalent fatigue damage accumulation is 15.6%.Figure 16 shows the ratio of the mean load in the single-excitation to the static ultimate load of blade in the flapwise and edgewise directions,respectively.As shown in Fig.16,the mean value generated by the gravity accounts for 27.4% of the static ultimate load in the flapwise direction and 56.9% of that in the edgewise direction,respectively.The ratio of the mean load has been at a high level in the blade dangerous area which is 0-20 m away from the blade root.According to the traditional specification of single-excitation and tuning mass distribution for the horizontal excitation fatigue testing,this mean load generated by the gravity needs to be withstood by the edgewise direction of the blade.During the fatigue testing in the flapwise direction,the edgewise direction of the blade is easy to be damaged because the gravity moment is too large.Therefore,the fatigue testing specification should be optimized if the horizontal excitation fatigue testing is used.It is not possible to realize multi-excitation horizontal loading until the tuning mass is replaced by the self-weight of the excitation equipment,which could help to reduce the gravity moment of the fatigue testing system.

Fig.13 Single-excitation vertical loading mode

Fig.14 Multi-excitation horizontal loading mode

Fig.15 Effect of mean load generated by gravity moment on fatigue damage

Fig.16 Ratio of mean load generated by gravity moment to the ultimate load in flapwise and edgewise directions,respectively

3.2 Single and multiple excitation

Table 1 shows the specification of single-excitation vertical loading mode.The fatigue testing specification is optimized,which the self-weight of the excitation equipment is used to replace the tuning mass.Table 2 shows the specification of the multi-excitation horizontal loading mode,and the eigenfrequency of the fatigue testing system (including the self-weight of blades,excitation equipment and tuning mass) is 0.479 Hz.The eigenfrequency of the system is 0.512 Hz,saving 7.93% of the time in the whole test period compared with the single-excitation specification.

Table 1 Single-excitation vertical loading mode

Table 2 Multi-excitation horizontal loading mode

3.3 Comparisons

As shown in Fig.17,the deviation of multi-excitation between vibration moment and target moment is 3% lower than that of single-excitation specification from 0 to 20 m distance away from blade root.This area is the maximum chord length of blades,which is also complex area where the aerofoil shape and the structure of blades change dramatically.Therefore,the load deviation in this area has a great influence on the assessment of the fatigue reliability of the blade structure.The load deviation in this area is relatively smooth using the multi-excitation test specification,which is helpful to improve the fitting accuracy of the fatigue target load.

Fig.17 Multi-excitation vibration moment distribution

When the single-excitation is applied in the vertical direction,the ratio of the gravity moment of the fatigue testing system to the ultimate load in the edgewise direction is too large.Therefore,in order to improve the safety of the blade in the edgewise direction,it is necessary to reduce the gravity moment of the fatigue testing system when the horizontal loading mode is used.As shown in Fig.18,through the optimization of the fatigue testing specification,the gravity moment of the multi-excitation fatigue testing system is about 17.0%-22.5% lower than that of the single-excitation,and the ratio of the gravity moment of the fatigue testing system to the ultimate load in the edgewise direction could be accepted by the horizontal multi-excitation specification.The multi-excitation specification is beneficial to reduce the gravity moment of the fatigue testing system and avoid the danger of damage in the edgewise direction during the fatigue testing.

Fig.18 Comparison of multi-excitation and single-excitation vibration moment distribution

The results of the 83.4 m blade are taken as an example.When the same exciting force is achieved,the excitation efficiency of the equipment in horizontal loading mode will increase by 77% at least than that of the equipment in the vertical loading mode.When the fatigue testing system is loaded in the vertical direction,the contribution of gravity moment to fatigue damage accumulation statistics is only 15.6%.Multi-excitation can reduce the gravity moment of the fatigue testing system by 17.0%-22.5%.Considering these factors,the fatigue testing specification with multi-excitation is better than that with single-excitation.

It has various significances to solve the bottleneck technology of large full-scale blade fatigue testing by the multi-excitation horizontal loading mode.First of all,if the multi-excitation horizontal loading mode is applied in the flapwise direction of fatigue testing,the gravity moment generated by the dead weight of the blade and excitation equipment is perpendicular to the vibration amplitude.Therefore,the mean load in the flapwise direction is zero.When the fatigue damage accumulation of the blade is counted,the amplitude of the vibration blade is used for statistics.The influence of gravity moment on the fatigue damage accumulation is eliminated.This fatigue testing method is more consistent with the actual operating conditions of wind turbine blades.Secondly,the excitation potential of the equipment is fully exploited by horizontal loading.When the same target amplitude is achieved,the power required for the excitation equipment is lower,which is benefit for the lightweight of the equipment.Thirdly,the lightweight of the excitation equipment is conducive to increase the design filedity of the fatigue testing specification,and the key indicators in the specification are optimized,such as the moment deviation in the verification area of the blade,fatigue damage accumulation and test period.Finally,the multi-excitation horizontal loading fatigue testing method is expected to solve the problem of insufficient exciting force in the fatigue testing for large full-scale blades.The fatigue testing technology of large offshore full-scale wind turbine blades will be conquered.

4 Conclusions

This paper focuses on solving the problem of insufficient capacity of excitation equipment in the fatigue testing of large wind turbine blades.The excitation efficiency of the equipment is improved to meet the fatigue testing of large blades by improving the test method of blades with the operation mechanism of the excitation equipment.The bending moment deviation in the verification area,fatigue damage accumulation and resonance frequency of the blade test system are optimized by arranging the position of the excitation equipment reasonably to improve the adjustment filedity of the fatigue testing specification.

(1) When the blade is excited in the vertical direction,the gravity moment of the fatigue testing system has an effect on the statists of fatigue damage accumulation.The gravity moment generated by the dead weight of the blade,the excitation equipment and the tuning mass,which will reduce the target vibration moment amplitude by 15.6%.

(2) When the blade reaches the same target moment,the multi-excitation horizontal loading mode is beneficial to reduce the actuator force of the excitation equipment.The excitation equipment does not need to overcome the gravity of dynamic mass.The actuator force of the excitation equipment in the vibration system is reduced by 77% at least,which has the advantage to the lightweight of excitation equipment,reduce the additional weight of the fatigue testing,and shorten the test period by 7.93%.

(3) When the blade is excited by the multi-excitation horizontal loading mode in the flapwise direction,the gravity moment generated by the dead weight of blade,excitation equipment and tuning mass has decreased by 17.0%-22.5%,which could be withstood by the blade in the edgewise direction.The gravity moment of the system is perpendicular to the blade in the flapwise direction,which is not related to the fatigue damage accumulation in the flapwise direction.That is,the mean value of fatigue vibration moment in the flapwise direction is zero.The peaks and troughs of the vibration moment on each blade section in the flapwise direction is equal,which is more in line with the target fatigue load.Compared with the traditional test method,the multi-excitation horizontal loading mode is more suitable for the time-space evolution condition of fatigue damage accumulation during the operation of wind turbine blade.