RESEARCH ARTICLE

Optimization design of spar cap layup for wind turbineblade

Jie ZHUa,*, Xin CAIa,b, Pan PANa, Rongrong GUa

a College of Mechanics and Materials, Hohai University, Nanjing 210098, Chinab College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China*Corresponding author. E-mail: zhukejie2222@163.com

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2012

ABSTRACT Based on the aerodynamic shape and structural form of the blade are fixed, a mathematical model ofoptimization design for wind turbine blade is established. The model is pursued with respect to minimum the blade massto reduce the cost of wind turbine production. The material layup numbers of the spar cap are chosen as the designvariables; while the demands of strength, stiffness and stability of the blade are employed as the constraint conditions. Theoptimization design for a 1.5 MWwind turbine blade is carried out by combing above objective and constraint conditionsat the action of ultimate flapwise loads with the finite element software ANSYS. Compared with the original design, theoptimization design result achieves a reduction of 7.2% of the blade mass, the stress and strain distribution of the blade ismore reasonable, and there is no occurrence of resonance, therefore its effectiveness is verified.

KEYWORDS wind turbine blade, spar cap layup, optimization design, blade mass

1 Introduction

As one of the most important parts of wind turbines, theblade is required to have a reasonable structural form,advanced materials and a scientific production technologyto endure the bending moments and tension caused bydifferent loads such as wind force, blade weight andcentrifugal force [1]. Therefore, the design and manufac-turing process have a decisive influence on the structuralperformance of the blade.Because of the light-weight, high-strength, good corro-

sion resistance and designable characteristics, compositematerials are broadly used in virtually every area of ourlife, from aerospace to medicine applications, and also inwind turbine industry [2]. The large-scale turbine bladesmade by composite materials have the advantages of highbearing capacity and reliable structural performance.

However, these blades are high cost and the structuraldesign analysis is very complex. Decreasing the use of thematerials and minimizing the blade mass by optimizing theblade structure is one of the effective ways to reduce thecost, which means to improve the structural design andfinally reach the economy and rationality of the bladestructure by adjusting the layer numbers, layer shape,stacking sequence and layer orientations of the materials[3,4].The spar cap is the chief structure to endure the force and

bending moment in a blade, its size has a significant impacton the blade mass and the stiffness of the blade [3]. Toensure the security and stability of the blade under differentload cases, the spar cap layup is generally thicker, thus theblade could not make full use of the materials. Hence, thematerial layup numbers of the spar cap can be properlydecreased to reduce the cost of production. Based on theaerodynamic shape and structural form of the blade arefixed, the material layup numbers of the spar cap arechosen as the design variables and the minimum of theblade mass is selected as the objective function, theoptimization design for a 1.5 MW wind turbine blade iscarried out at the action of ultimate flapwise loads with thefinite element software ANSYS.

Article history: Received January 9, 2012; Accepted February 9,2012

Front. Struct. Civ. Eng. 2012, 6(1): 53–56DOI 10.1007/s11709-012-0147-9

2 Structure parameters of the blade

The blade is made of composite materials with a length of37 m and a mass of 6543.6 kg. It comprises an imbeddedstud root structure, a thickened spar cap, and two shearwebs. The materials consist of a surface gel coat,reinforcing materials and UD-tapes for the skin and thespar cap. Balsa and PVC core materials are also used in theleading edge, the trailing edge and the shear webs. Figure 1shows the blade planform and a typical structural crosssection.

3 Mathematical model of optimizationdesign

3.1 General expression of optimization design

The mathematical model for design variable X ¼x1,x2, � � � ,xn½ �T can be expressed as follows:Objective function minFðX Þ

s:t: hjðX Þ ¼ 0 j ¼ 1,2, � � � ,k;GiðX Þ£0 i ¼ 1,2, � � � ,m;X³0,

(1)

where hjðX Þ is the non-upper and non-lower limit equalityconstraint, k is the number of equality constraints, GiðX Þ isthe non-upper and non-lower limit inequality constraint, mis the number of inequality constraints.

3.2 Design variables

The blade mass changes with the change of the thickness ofthe spar cap. Therefore, the material layup numbers of thespar cap are chosen as the design variables. Due to thematerial layup numbers of the spar cap close to the root andin the middle areas of the blade are much more than thatclose to the tip, only the areas from 3.8 to 26.7 m of thespar cap along the span wise are selected to be optimized.For the sake of simplicity, the spar cap layup on two sidesare defined the same. The selected areas are divided into 15sections, each as a variable, so there are 15 designvariables.

3.3 Objective function

Considering the cost, the minimum blade mass is selectedas the optimization objection function. It is given asfollows:

FðX Þ ¼X

i

�i � Vi, (2)

where �i is the material density, Vi is the volume of thematerial.

3.4 Constraint conditions

The blade optimization design is a multi-criteria con-strained optimization problem [5,6]. In this paper, thedemands of strength, stiffness and stability of the blade aretaken into account.The strength constraints: the stress and strain generated

in the blade cannot exceed allowable value [7]. It isexpressed as follows:

�£�max;

ε£εmax,

((3)

where � is the blade stress, �max is the maximumallowable stress, ε is the blade strain, εmax is the maximumallowable strain.The stiffness constraints: in order to avoid the risk of the

blade and tower collisions, the maximum tip deflectionshould be less than the set value [8]. It is expressed asfollows:

d£dmax, (4)

where d is the tip deflection, dmax is the maximumallowable tip deflection.The stability constraints: to prevent the occurrence

of resonance, the first natural frequency of the bladeshould be separated from the harmonic vibration asso-ciated with rotor rotation [6]. It is expressed in theinequality form:

Fblade –Frotorj j³Δ, (5)

where Fblade is the first natural frequency of the blade, Frotoris the frequency of the rotor rotation and Δ is the associatedallowable tolerance.Considering the manufacturing maneuverability and the

continuity of the materials layup, the design variablesshould be satisfied with the following inequality form:

xLi £xi£xUi , i ¼ 1,2, � � � ,15;xj – xjþ1£0, j ¼ 1,2, � � � ,7;xkþ1 – xk£0, k ¼ 8,9, � � � ,14,

8><

>:(6)

where xL is the lower bound variables, xU is the upperbound variables.

Fig. 1 Blade planform and a typical structural cross section

54 Front. Struct. Civ. Eng. 2012, 6(1): 53–56

The detail range values of the constraint conditions arein Table 1.

4 The analysis and calculation model of theblade

According to the geometrical parameters, the airfoil dataand the actual layup design, the finite element model of theblade is created using SHELL91 element and SHELL99element in ANSYS. SHELL91 element is a layeredcomposite shell element with shear deformation and linearcapability, while SHELL99 element is a layered compositeshell element with shear deformation and nonlinearcapability. The created model consists of 27453 elements,80687 nodes, as shown in Fig. 2.The blade is treated as a cantilever beam [9], and the

calculated 4429.3 kN$m ultimate flapwise loads arereduced to several concentrated loads. Figure 3 showsthe distribution of the loads.

5 Results and analysis

The optimization design is carried out by combing aboveobjective and constraint conditions with the APDLlanguage and the First-Order optimization method inANSYS. The process converges in 20 steps.Figure 4 shows the changing process of material layup

numbers of the spar cap, which all decrease afteroptimization. The material layup numbers decreaseobviously from 11 to 20 m and from 22 to 23.5 m alongspan wise, while the numbers decrease slightly at the otherareas between the final optimization design and theoriginal design. As the design variables are not constrainedto change linearly, the shapes of the optimized spar caplayup are irregular.Table 2 lists the structural performance of the blade

before and after optimization. The mass of the blade finallyreduces 473.4 kg (or 7.2%) after optimization. The max-imum stress, strain and tip deflection all increases, and themaximum strain reaches the allowable value, but they still

Table 1 Range values of the constraint conditions

layup numbers stress/MPa strain/μ tip deflection/m first natural frequency/Hz

lower bound 20 – – – £0.94 or≥0.96

upper bound 65 520 5 000 5.5

Fig. 2 Finite element model of the blade

Fig. 3 Distribution of the loads

Fig. 4 Comparison of the material layup numbers between theoriginal design and the optimization design

Jie ZHU et al. Optimization design of spar cap layup for wind turbine blade 55

satisfy the constraint conditions set in the procedure. Thestress and strain distribution of the blade is more reason-able after optimization, which means the optimizationdesign result has a better use of the materials. Both of thestructural stiffness of the blade and the blade mass reduceswith the decrease of the material layup numbers of the sparcap. Meanwhile, the reduced ratio of the stiffness is greaterthan that of the blade mass. Therefore, the first naturalfrequency decreases, but there is no occurrence ofresonance. In general, the blade mass reduces and thestructural performance improves after optimization, theresult achieves the purpose of the optimization design.

6 Conclusions

First, the result to reduce the blade mass is obtained afteroptimization. The reduction of the blade mass cannot onlydecrease the brake torque and the periodic vibrationbending moment of the blade, but also reduce the use ofmaterials and the cost of the whole wind turbine system.Secondly, compared with the original design, the

optimization result has obvious advantages. It verifies therationality and effectiveness of the optimization designmodel and can be a reference for the engineering design ofthe wind turbine blade.

References

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Table 2 Structural performance of the blade before and after optimization

schemeblade mass

/kgmaximum stress

/MPamaximum strain

/μmaximum tip deflection

/mthe first natural frequency

/Hz

the original design 6543.6 90.0 4519.6 4.5 1.01

the 8th optimization design 6348.6 93.3 4719.7 4.9 0.99

the 12th optimization design 6283.3 94.8 4866.4 5.0 0.99

the final optimization design 6070.2 99.7 5000.0 5.2 0.98

56 Front. Struct. Civ. Eng. 2012, 6(1): 53–56