Applied Load on Blade Bearing in Horizontal Axis Wind Turbine Generator

Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

Applied Load on Blade Bearing in Horizontal Axis Wind Turbine Generator 1

Chen L.1, a, Xia X. T. 1,2, Qiu M. 1 1 – College of Mechatronics Engineering, Henan University of Science & Technology, Luoyang, China 2 – Collaborative Innovation Centre of Machinery Equipment advanced Manufacturing of Henan Province, China a – haustchenlong@163.com DOI 10.2412/mmse.3.51.716 provided by Seo4U.link

Keywords: applied load, blade bearing, horizontal axis, slewing ring, wind turbine.

ABSTRACT. Rolling bearing life is typically calculated on the basis of its load ratings relative to the applied loads and the requirements regarding bearing life and reliability. Variation of applied load influences the load distribution in blade bearing directly and the load on maximum-loaded ball fluctuates with the applied load. Life of blade bearing is influenced by these variations eventually. Analysis and calculation method of applied load on blade bearing is illustrated by the case of a horizontal axis wind turbine.

Introduction. Wind turbine generator (WTG) is the equipment, which translates wind power to electrical energy, it can be divided into horizontal axis and vertical axis wind turbine. WTG can also be classified by the types of control modes. They are fixed speed stall regulated, fixed speed pitch regulated, variable speed stall regulated and variable speed pitch regulated, respectively. Horizontal axis wind turbine generator (HAWT) by variable speed pitch regulated is rapid developed in recent years and there are four kinds of bearings in the turbine. Structural rigidity is an important characteristic of WTG, and many investigators published relative results. For example, Jianhong et al. [12] analysed Dynamic Behaviour of Wind Turbine by a Mixed Flexible-Rigid Multi-Body Model.

Blade is the component which gaining energy from the wind. Hence, the relationship between blade shape and velocity attracted more attention, for instance, Yukimaru [11] investigated the flow around blade tip of a HAWT. As for rolling bearings being used in HAWT, it mainly includes yaw bearing, blade bearing, mainshaft bearing and gearbox bearing, as illustrated in Fig. 1. There are various structures of rolling bearing. Many researchers developed special researches on determining appropriate structure of rolling bearing for HAWT. Chen et al. [3] discussed better choice of rolling bearings mounted on different positions in HAWT. Nobuyuki and Souich [6] illustrated technical trends of wind turbine bearings.

1

© 2017 The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

Mainshaft bearing Gearbox bearing

Blade bearing Yaw bearing

Fig. 1. Bearings in wind turbine generator.

Slewing ring is usually adopted as yaw bearing and blade bearing. Slewing is defined as the rotation of an object about an axis. Thus a slewing ring is a bearing used in slewing applications for transferring or supporting axial, radial, and moment loads, singularly or in combination, consisting of rings mounted with threaded fasteners, and usually having a gear integral with one of the rings. In the last decades, a lot of research efforts have been devoted to study application characteristics of slewing ring. Prebil et al. [10] established calculation model of load distribution onto rolling elements in a rotational connection. Zupan et al. [7] validated the theory analysis by experiment. With the deepening of research on slewing ring, many researchers developed special researches on relations between inner geometry structure and performance of slewing ring. Zupan et al. [8] established relation between carrying angel and carrying capacity of four-point-contact slewing bearing. Chen et al. [3] presented influence of groove shape on clearance in four-point-contact slewing bearing.

Blade bearing, as can be seen in Fig. 2 (a), is mounted between adjustable blades and hub. A pitchregulated wind turbine has individual pitch actuators for each blades, the possibility arises to send different pitch angle demands to each blade. In order to guarantee proper functioning of wind turbine, pitch system (as shown in Fig. 2 (b) drives blade rotating around its own axis under different wind velocity. Four-contact-point slewing ring is widely used as blade bearing in current application. The detail of blade bearing mounted in WTG is shown in Fig. 2 (c). Both double-row and single-row fourcontact-point slewing rings are adopted according to different power level of wind turbine. Working conditions of blade bearing is more complex than yaw bearing in HAWT. Hence, some special investigations on blade bearing were developed in recent years. Chen et al., 2010 introduced contact stress and deformation of blade bearing in HAWT. Rolling bearing life is typically calculated on the basis of its load ratings relative to applied load and the requirements regarding bearing life and reliability. Load rating of the bearing is only one kind of key factor, which influences bearing life and applied load is the other key factor, which impacts it.

Applied load on blade bearing is a dynamic variable value and it must be analysed and calculated strictly to ensure service life of blade bearing. This paper draws its attention on analysis & calculation of applied loads on blade bearing.

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

a)

Bolts

Blade

Blade bearing

Drive gear

Motor c)

b)

Fig. 2. a) The photo of the blade bearing, b) Electric pitch control system, c) Hydraulic pitch control system.

Applied load types. Energy resource of HAWT is the natural wind and, gusts and turbulence are inevitable. Variation of instantaneous wind speed causes enormous impulsive load on HAWT. Several other factors, such as wind shear, varying wind direction and tower shadow effect, bring aerodynamic loading on blades. In addition, controlling action processes, i.e. braking, yawing and pitching, produce variation of loads on HAWT components. All these loads mentioned above are applying on blade bearing and influence bearing service life.

Applied loads on HAWT can be divided as dynamic load, random load and static load according to different working stages. Aerodynamic force on blades, gravitational force of blades, centrifugal force and gyroscopic torque due to yawing are main loads on blade bearing.

Coordinates and velocity vector. In accordance with the characteristics of movement and structure of HAWT, four appropriate coordinates are established which is shown in Fig. 3. They are tower coordinate (T), cabin coordinate (B), hub coordinate (R) and blade coordinate (S), respectively. The tower coordinate system is established on the tower as an inertial coordinate system and the cabin coordinate system is on the cabin. The hub coordinate system is established on the main shaft and the blade coordinate system is established on one blade. All these coordinates interact with each other and they are dynamic in working and adjusting process. For the sake of simplifying calculation, tower is considered as installing on a stationary base and then the tower coordinate is fixed. Some special application cases, for example offshore HAWT, are not considered in following analysis.

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954 XS Mx-s Fx-s Φ

ZS Mz-s

YS My-s

Fy-s

Fz-s

Yb

Xb Mx-b Zb Zr

Fz-r Fz-t My-t

My-b

Fx-b

Fy-b

Fz-b

Mz-r

Zt Mz-t

Mz-b

Fy-t

en er

ek

δ

Yt Fx-r Fy-r Yr My-r

Mx-r

Fx-t Mx-t

Xr

Xt

Fig. 3. Coordinates in a horizontal axis wind turbine.

Coordinates transformation. Relation between coordinates of T and B is the yaw rotation movement.

There are two adjusting movements in yaw rotation process. One is the rotation on xt-axis for tracking wind direction and the other is on yt-axis for aiming wind angle. Conversion relation between can be given by 0 0  1 0 0  cos tilt 0 sin tilt  1  aTB   0 1 0  0 cos  yaw sin  yaw  0 1 0  sin tilt 0 cos tilt  0 sin  yaw cos  yaw  0 0 1  

(1)

Where ϴtilt – is the angle between wind direction and horizontal plane of coordinate T; ϴyaw – is the elevation of the cabin.

The difference between coordinates of B and R is only that zr-axis on coordinate R is rotating in working process of WTG. Then the relation of these two coordinates may be written as

aBR

 cos  wing    sin  wing  0 

sin  wing cos  wing 0

0 0  1

(2)

Where ϴwing is the rotational angle of the hub around zr-axis.

The blades are rotating with the hub together in working process. The difference between coordinates of R and S is only that zs-axis on coordinate S is rotating in pitching process. Then the relation of these two coordinates can be expressed as MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

aRS

cos  cone  0   sin  cone

0  sin  cone   1 0  0 cos  cone 

(3)

Where ϴcons is the pitching angle of the hub around zs-axis.

Speed variation in coordinates Generally, wind speed is defined as a value relative to a fixed-coordinate system. The speed relative to the blade is really caring about in this paper. Supposed the speed in a coordinated system is v0, wind speed on the blades v1 is

v1  aTB  aBR  aRS  v0

(4)

The real relative speed of the blade consists of the portions caused by wind speed (v1), blade rotating speed (vrot), induced velocity (W) owing to blade shape and yawing speed (vyaw) due to yawing, as can be seen in Fig.4. Then the real relative speed can be expressed by a vector expression as

vrel  v1  vrot  W  v yaw

(5)

Fig. 4. Speed triangle in wind turbine blade.

Calculation of applied load. With regard to blade bearing load analysis, loads on blades are the most critical factor. As discussed previously, aerodynamic force, gravity and inertia force are main loads on blade bearing. They will be analysed one on as following.

Aerodynamic force. There are several theories, such as blade element-momentum theory, Computational Fluid Dynamics (CFD) etc., for calculating aerodynamic force. Blade elementmomentum theory has simple forms, less calculation for convenient application. It is applied to calculate aerodynamic force in the following.

The blade is supposed to be consisted of many tiny sections, namely the blade elements, and there is no interference between each section in the theory. Momentum theory can be used to calculate the force and momentum in each element, the force and momentum of the whole blade can be obtained by integration as

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

 dF  4 rV12a1 (1  a1 )dr ,  3 2 d M  4  r  V (1  a ) a  d r  1 1 2

(6)

where a1 – is a normal inducible factor; a2 – is a tangential inducible factor; ω – is the blade rotating angular velocity; ρ – is the air density; V1 – is the wind speed; r – is the length from blade root to hub centre.

Load applied to the blade can be decomposed into a tangential force and horizontal pressure force, as shown in Fig. 5 (a). The tangential force drives the blade to rotate for electric power generation and there is no benefit of the other force of power generation. Thereupon, the relative velocity can be divided into two directions, as can be seen in Fig. 5 (b), and they can be expressed as

(1  a1 )V  ]   arctan[ (1  a2 )r       

(7)

Based on aerodynamics theory, lift and drag force can be calculated as

1  2 dFL  2  vrel cLcdr  dFD  1  vrel 2cD cdr  2

(8)

 



Fa

FL

V (1  a1 )

 o

FD

Fr

  r (1  a2 )

a)

b)

Fig. 5. a) Applied load on blades, b) Inflow angle and velocity resolution.

Where FL – is the lift force in blade element due to aerodynamic pressure; MMSE Journal. Open Access www.mmse.xyz

Vrel

Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

FD – is the drag force in blade element due to dynamic pressure; c – is the blade element chord; v – is the relative velocity; cL – is a lift force coefficient; cD – is a drag force coefficient.

For the sake of more intuitive axial load, radial load and overturning moment applied to the blade bearings, the lift force and drag force can be divided into axial and radial directions in a hub coordinate which is shown in the following:  dFa  dFL sin  wing  dFD cos  wing   dFr  dFL cos  wing  dFD sin  wing

(9)

Gravity and inertia force calculation Flexure moment in the shimmy direction of blades produced by its gravity presents a periodic variation law with its varying direction angles, as shown in Fig. 6 (a). Because of its gravity, each blade element has a lumped mass mi, so the total gravitational torque in a whole blade can be obtained as M j    mi grdr  sin  wing  0  R

(10)

Where g – is the gravitational acceleration; R – is turning radius of the blade.

Inertial loads on the blade include centrifugal force and gyro force. The centrifugal force caused by the wind wheel rotating directs outside. It has an effect to reduce the deflection as flexible blades deviating from the rotation plane of the wind wheel, and it is known as centrifugal stiffening effect.

Inertia force on the blade section depends on the rotational velocity, the radial location and the blade element mass. It can be expressed as n

Fc   mi 2 ri

(11)

i 1

Where mi – is the mass of the ith element of the blade; ri – is distance between gyration centre and the ith element of the blade; ω – is the angular velocity of the blade around main-shaft.

As is shown in Fig.6b, centrifugal force is consisted of tangential force (Fc sinϴ cone) and normal force (Fccosϴ cone). Gyroscopic moment (Mo) applied normally to its rotating plan will turn up when rotating and yawing and can be expressed as

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954 n

M o  2k  mi ri

(12)

i 1

Where ωk – is angular velocity of yawing.

Composition of applied load. On account of the different loads applied to the blade, the axial load and the radial load were combined together, respectively.

 Ftot a  Fa  Fca  mg  sin  wing   Ftot r  Fr  Fcr  mg  cos  wing

(13)

Where Ftot-a – is the total axial force; Fa – is the axial component of dynamic force; Fc-a – is the axial component of centrifugal force; Ftot-r – is the total radial force; Fr – is the radial component of dynamic force; Fc-r – is the radial component of centrifugal.

Applying mode shape symmetry, bending moment arising from the axial component is neglected and it is not from the radial component. The bending moment can be decomposed into x-direction and ydirection as  M tot  x  0R ridFx r  M c  x r  M j  x r  M o x    M  R ridFy r  M c  y r  M j  y r  M o y   tot  y  0

Where Mtot-x – is the total flexural moment in x-direction; Fx-r – is the radial component force in x-direction; Mc-x-r – is the radial component of centrifugal force in x-direction; Mj-x-r – is the inertial moment component in x-direction; Mo-x – is the yawing moment component in x-direction; Mtot-y – is the total flexural moment in y-direction; Fy-r – is the radial component force in y-direction; Mc-y-r – is the radial component of centrifugal force in y-direction; Mj-y-r – is the inertial moment component in y-direction; Mo-y – is the yawing moment component in y-direction.

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(14)

Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954 n

dFc   rmdr

Fc   mi  2 ri

dr

i 1

Fc sin  cone

M

Fc cos  cone r

v0

v0

 cone

a)

b)

Fig. 6. a) Additional load caused by velocity variation, b) variation of centrifugal force.

Blade bearing loading model. As is shown in Fig.7, a single-row-four-contact-point slewing ring is adopted to connect the hub and the blade. The blade bearing under study has the outer ring fixed to a rigid hub and the blade is supposed as rigid. The mass of the blade is equivalent to a mass-block located at centroid position. Then blade-bearing loading model can be regarded as a simple beam model.

Single row ball bearing. For a pitch control system adopting single-row-four-contact-point slewing ring as blade bearing, suppose that the distance between the equivalent action point of aerodynamic force and the contact point close to the blade of the bearing is r1, and suppose that the distance between mass-block and the contact point mentioned-above is r2. Generally, the clearance in blade bearing is a negative value. Namely, the bearing is pre-loaded before it is mounted on the WTG. Then the bearing load consists of pre-load and applied load. As for the calculation method of the pre-load, it has been introduced completely in reference named “Load Distribution for Blade Bearing”, and there is no more repeat here. hub 叶

Fy1

Fx1



R 0

ridFyr



R 0

ridFxr

Moy

M jyr

M cyr M cxr

M jxr

Mox 叶 blade

2 Rw 2

Fig. 7. Loads acting on a blade bearing.

The bending moment can be expressed as   M tot  x  Fx   M  Fy   tot  y

2  Dw 2 2  Dw 2

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(15)

Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

Double rows ball bearing. To a high-power wind turbine generator, a double-row-four-contact-point slewing ring is a better choice for blade bearing. It takes the same analytical procedure to obtain the radial force Fx and Fy. Noted that the contact position is changed. Suppose that the distance between two rows is h, the distance between two contact points in load zone is

L  h-

2 D 2 w

(16)

Case study. A 850 kW horizontal axis WTG is taken as an example for case study. According to the guidelines of wind turbine design published by Harris et al. [1] the fundamental structure of WTG can be determined. It consists of three blades and every blade is regulated by individual variablespeed-pitch system. The diameter of wind wheel is 56.3 m, the swept area is 2490 m2, the cut-in wind speed is 3 m/s, the rated wind speed is 12 m/s, the cut-out wind speed is 20 m/s, the extreme wind speed is 52.5 m/s, the blade top speed ratio is smaller than 7 and the tip speed under rated speed is 70.7 m/s.

Based on specified wind speed conditions in planed region for mounting of WTG, the values of force and torque applied to blades are calculated by rain-flow algorithm, and it is shown in Fig. 8. Ultimate load is calculated by the methods provided by Peter et al. [2]. According to Fig. 8, the minimum value of radial blade load is -24 kN, the maximum value is 224 kN and the mean value in operating time is 98.7 kN. The minimum value of turning force is -40 kN, the maximum value is 60 kN and the mean value is 4.7 kN. The minimum value of waved force is -48 kN, the maximum value is 92 kN and the mean value is 30.5 kN. The minimum value of pitching moment is -13 kN·m, the maximum value is 6 kN·m and the mean value is -3 kN·m. The minimum value of waved moment is -1472 kN·m, the maximum value is 896 kN·m and the mean value is -460.8 kN·m. The minimum value of waved moment is -480 kN·m, the maximum value is 704 kN·m and the mean value is 69.8 kN·m.

Using safety coefficient from IEC61400-1 and substituting above loads into Eqs. (13) ÷ (16), applied load is obtained as list in Tab. 1.

Table 1. Loads and torques in one 850KW wind turbine blade bearings.

Design Load Condition

Fa (kN)

Fr (kN)

Mk (kN·m)

Ma (kN·m)

Applied gust wind

3599

725

939.3

-73

Extreme turbulence fatigue model

1764

1418

2150.4

-145

Extreme wind speed model

-252

999

1194

509

Extreme wind shear model

2053

1418

2204.4

-166

According to required load ratings in the Tab. 1, blade bearing for the WTG is designed as shown in Fig. 9. It is a double rows four point contact slewing bearing with inner gear. The inner gear module is 12, the number of teeth is 108 and the modification coefficient is +0.5. The diameter of gyration centre is 1500 mm for meeting the requirement of the hub.

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954 1. 80E+05

1. 80E+05

1. 60E+05

1. 60E+05

1. 40E+05

1. 40E+05 1. 20E+05

1. 20E+05 1. 00E+05

1. 00E+05

Hour s Hour s( akk)

8. 00E+04 6. 00E+04

6. 00E+04

4. 00E+04

4. 00E+04

2. 00E+04

2. 00E+04

0. 00E+00

Hour s Hour s( akk)

8. 00E+04

0. 00E+00

-8

24

8

40

56

72

4 10

88

0 12

6 13

2 15

8 16

4 18

0 20

6 21

0 -4

2 -3

4 -2

6 -1

-8

0

a)

24

32

40

48

56

b)

1. 80E+05

1. 80E+05

1. 60E+05

1. 60E+05

1. 40E+05

1. 40E+05

1. 20E+05

1. 20E+05

1. 00E+05

Hour s Hour s( akk)

8. 00E+04

1. 00E+05

Hour s Hour s( akk)

8. 00E+04

6. 00E+04

6. 00E+04

4. 00E+04

4. 00E+04

2. 00E+04

2. 00E+04 0. 00E+00

0. 00E+00

2 0 8 47 28 08 -1 -1 -1

96 704 -8 -

12 -5

20 128 -3 -

64

6 25

8 44

0 64

80 16 52 88 24 60 96 - 32 -4 -4 -3 -2 -2 -1 -

2 83

c)

32

96 160 224 288 352 416 480 544 608 672

d)

1. 80E+05

1. 80E+05

1. 60E+05

1. 60E+05

1. 40E+05

1. 40E+05 1. 20E+05

1. 20E+05 1. 00E+05

Hour s Hour s( akk)

8. 00E+04

1. 00E+05

Hour s Hour s( akk)

8. 00E+04

6. 00E+04

6. 00E+04

4. 00E+04

4. 00E+04

2. 00E+04

2. 00E+04

36

44

52

60

68

76

84

92

e)

4

28

6

20

0

12

2

4

-2

-4

-6

2 -1

-8

0 -2

-1 0

8 -2

-1 4

6 -3

-1 2

0. 00E+00

0. 00E+00

4 -4

16

8

-4

4 -2

f)

Fig. 8. a) radial force and working hours, b) turning force and working hours, c) waved force and working hours, d) pitching moment and working hours, e) waved moment and working hours, f) turning moment and working hours.

Fig. 9. A blade bearing design in one 850 kW wind turbine generator.

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

Fig. 10. Load capacity curve in one 850 wind turbine blade bearing.

Carrying capacity curve, namely the nonlinear curve on the top of the Fig, is plotted as shown in Fig. 10. An approximately linear diagonal line on the top left of the Fig is the overturning curve. Safe zone locates at region which under both curves. The static load rating and dynamic load rating are depicted on the Fig too. Obviously, these two points are in safe zone.

Summary. Generally, load ratings of rolling bearing are provided by bearing manufactures according to raw material, roller diameter, roller number etc. However, rolling bearing life is typically calculated on the basis of its load ratings relative to the applied loads as above-mentioned. Applied load varies with different working conditions. With regard to blade bearing in WTG, different mounting location means different wind speed and eventually different load on blade bearing. Usually, applied load on blade bearing depends on load spectrum provided by supposing. In this paper, relative accurate calculating equations are derived for applied load. The numerical data through calculating equations provide evidence for designing blade bearing and the reliability of calculating life is enhanced.

Acknowledgements This project is supported by National Natural Science Foundation of China (Grant No. 51475144) and Natural Science Foundation of Henan Province of China (Grant No. 162300410065).

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[2] H. M. Peter, P. Kirk, B. Marshall. Predicting Ultimate Loads for Wind Turbine Design. USA: NREL/ DE-AC36-83CH10093, (1999).

[3] L. Chen, H.W. Du. Bearings in Wind Turbine. Bearing, 12 (2008), pp.45–50 (in Chinese).

[4] L. Chen, Z.G. Li, M. Qiu, X.T. Xia. Influence of groove shape on clearance in four-point-contact slewing bearing, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol.36, No.3(2014), pp.461-467, DOI 10.1007/s40430-013-0118-7 [5] J.H. Wang, D.T. Qin, Y. Ding. Dynamic Behavior of Wind Turbine by a Mixed Flexible-Rigid Multi-Body Model, Journal of System Design and Dynamics, Vol.3, No. 3 (2009), pp.403-419.

[6] Y. Souich and N. Nobuyuki. Technical Trends in Wind Turbine Bearings, NTN Technical Review, No.76 (2008), pp.113–120.

[7] S. Zupan and I. Prebil. Experimental Determination of Damage to Bearing Raceways in Rolling Rotational Connections. Experimental Techniques, Vol. 30, No. 2 (2006), pp. 31-36.

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Mechanics, Materials Science & Engineering, September 2017 – ISSN 2412-5954

[8] S. Zupan and I. Prebil. Carrying Angel and Carrying Capacity of a Large Single Row Ball Bearing as a Function of Geometry Parameters of the Rolling Contact and the Supporting Structure Stiffness, Mechanism and Machine Theory, Vol.36, No.10(2001), pp. 1087-1103.

[9] L. Chen, Y.P. Zhang and X.T. Xia. Contact stress and deformation of blade bearing in wind turbine, 2010 International Conference on Measuring Technology and Mechatronics Automation (2010), pp.

833-836.

[10] I. Prebil, S. Zupan and P. Luci. Load distribution onto rolling elements of a rotational connection, Proceedings of the 3rd International Congress on Air and Structure Borne Sound and Vibration (1994), pp. 1949-1956.

[11] S. Yukimaru, I. Edmond, M. Takao, K.P Yasunari. Investigation on the flow around blade tip of a HAWT equipped with MIE type tip vane by velocity measurements using LDV (effect of blade plane configuration, blade aspect ratio and number of blades), Proceedings of the 5th JSME-KSME Fluids Engineering Conference, CD-ROM, OS13-1, pp.1318-1323, 2002.

[12] J. Wang, D. Qin, Y Ding. Dynamic Behavior of Wind Turbine by a Mixed Flexible-Rigid MultiBody Model. Journal of System Design and Dynamics, Vol.3, No 3(2009), pp. 403-419.

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