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PARAMETRIC STUDY OF SANDWICH PANEL BUCKLING IN COMPOSITE WIND TURBINE BLADESShicong Miao, Steven Donaldson, and Elias Toubia

Parametric Study of Sandwich Panel Buckling in Composite Wind Turbine BladesShicong Miao, Steven Donaldson * , and Elias Toubia

*Corresponding author: [email protected]

Department of Civil and Environmental Engineering, University of Dayton, Dayton, OH 45469. USA

ABSTRACT: A parametric study of the buckling performance of composite wind turbine blade regions with thin symmetric laminated sandwichrectangular panels, subjected to uniform axial shell edge compression loads is presented. The research focused on the critical buckling load and strainlevels with core material parameters, such as transverse core shear modulus and core thickness, for rectangular sandwich strips with long aspect ratios.Both flat and curved-section models were considered. The buckling design plots generated provide an insight into optimal core solutions for efficientdesigns.

NOMENCLATUREa = length of the panel, mb = width of the panel, mc = core thickness, mk = panel curvature ratio, % (arc height divided by the panel width)l = curve length, mr = radius, mt = facing thickness on one surface, mh = overall thickness of sandwichC0 = normalized core thickness (core thickness divided by total facingsheet thickness)1, 2, 3 = general coordinates. (1:longitudinal direction; 2: widthdirection; 3: direction normal to the panel planform)r, t, z = cylindrical coordinates. (r: radial direction normal to panel; t:curve angle direction; z: longitudinal direction)

U1,

U2, U

3= displacement in 1, 2, 3 direction

Ur, Uz, U t = displacement in r, z, t directionPcr= critical buckling end load (=eigenvalue), N/mεcr = critical buckling end strain, %E1, E 2, E 3 = Moduli of elasticityG13 = Core transverse shear modulus in 1-3 plane, PaG23 = Core transverse shear modulus in 2-3 plane, Pa

ν12 , ν21, ν23 = Poisson's ratiosN1 = Uniform compressive end load, N/m

INTRODUCTION

Renewable energy sources continue to increase as a percentage of global energy production. This trend is dominated by wind energy andis the result of both an increase in the number of turbines installed, aswell as the increasing diameter of turbine rotors with the correspondingenergy output per turbine (Roczek, 2010). As a consequence of thisdesign strategy, the blade structures are becoming increasingly thin-walled, such that buckling problems in the blade panels must beaddressed (Lund, Johansen, 2008).

In general, the wind turbine blade works in much the same way as thesteel I-beam, except that there are shells around the outside that form

the aerodynamic shape and resist buckling and torsional loads (WEHandbook- 3- Structural Design). Utility-scale wind turbine blades useextensive sandwich construction, in both the aerodynamic shells andshear webs. To meet stiffness constraints such as deflection limits, thefiber composite materials in the broad unsupported spans of shell andshear web laminates are stiffened through the use of sandwichconstruction to prevent local deformation and buckling. In bladestructures, the largest single role of the sandwich core is to assureadequate stability of the large panel regions against buckling. As such,the most significant attributes of the core materials are the transverse

shear modulus and the core thickness. Since core materials aregenerally available in a wide range of weights, mechanical properties,and cost, a study focused on the shell core is appropriate.

Several related and valuable plate buckling studies and wind turbineblade preliminary design studied have been done in this area. Generalwind turbine blade optimization methods are discussed and presented in(Roczek, 2010, Lund, Johansen, 2008 and Lund, 2005). Structuralreliability and mechanical behavior predictions for blade materials arereported in reference (Mishnaevsky et al., 2011). A preliminary designstudy of an advanced 50 m blade for utility wind turbines is presentedin reference (Jackson et al., 2005) Closed form, exact solutions for thebuckling of simply supported, rectangular, orthotropic plates under

different load conditions are given in (Narita, Leissa, 1990, Leissa,1985). Many nondimensional buckling parameters were generated byNemeth and Weaver (Nemeth, 1995, Nemeth 2004, Weaver, Nemeth,2007) for long or infinitely long symmetrically laminated anisotropicrectangular plates subjected to various combined load conditions.Theoretical prediction of buckling loads for cyclic sandwich shellsunder axial compression with laminated facings and foam core ispresented in (Morovvati, 2011). Although many researchers haveinvestigated the buckling of simply supported laminated compositeplates, the early buckling analysis works focused on anisotropic plate

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excluding sandwich plates or shells. Therefore, it is useful to perform aparametric study of both flat and curved section strips representingdifferent characteristic regions of sandwich laminates in blades.

A parametric study of the buckling performance of core materials onthe basis of transverse shear modulus and thickness, within a given

design domain (a fixed set of laminate designs and critical bucklingloads) is presented. This will provide insight into optimal coresolutions . This study considers both flat and curved-section rectangularsandwich strip models with long aspect ratios, which provide closeapproximations to the buckling loads and mode shapes (wavelengths)expected in the sandwich panel regions of the blades. Considering thedesign process and the characteristic strains in axial compressionconditions, the buckling trends are on the basis of both critical bucklingload and strain.

A complete parametric study using practical design properties does notappear to exist in the literature, and was therefore the goal of this study.The results of the present work in practical design optimization studieswould then involve assessing the cost and weight of various coreproducts as an indication of optimal thickness values, then comparingthe cost and weight of the various solutions.

ANALYSIS AND DESCRIPTION

Finite Element Analysis

In setting up the model, two panel models (flat and curved-section)were considered to represent different regions of the blade shell. It was

assumed that all layers of the panel were perfectly bonded together andthus the displacements were continuous throughout the thickness.

The model of the panel strips were built in ABAQUS 6.10 withelements of S4R ( ABAQUS User’s Manuals, Version 6.10 ). For theflat-section model, there were a total of 1111 nodes and 1000 elements

used. The curved section model used 1313 nodes and 1200 elements.This mesh density was established in a prior convengence study byToubia (Toubia, 2008).

The general boundary condidtions of the sandwich panel models areshown in Figure 1. In the flat-section model, on the loaded edge, U 2

U3 = 0. The long edges have U 2 = U 3 = 0, and the far end has U 1 = U 2

U3 = 0. In the curved-section model, on the loaded edge, U t = U r = 0In this initial study, the load profile was assumed to be uniform acrossthe ends (later studies to examine non-uniform loading are appropriate).The long edges have U t = U r = 0, and the far end has U t = U r = U z = 0The analyzed material data and panel model information can be foundin Table 1 and Table 2. The facing material used in this study is E_TLX5500 (E_TLX5500, 15 December 2011.) which is [0/45/-45] E-glassmaterial commonly used as composite reinforcement in wind turbineblade shell regions. Four representative core materials (M1 to M4) areselected to cover the prevalent material shear modulus range. Thecritical buckling eigenvalues were found by buckling analysis usingABAQUS, and then applied in the linear analysis approach to obtainthe critical buckling strains. Sample dominant buckling mode shapesare shown in Figure 2 and Figure 3.

Figure 1. General bounduary conditions of the infinitely long strip of the panel (1, 2, 3) and shell (r, t, z)





Figure 2. ABAQUS buckling wavelength result for flat-section sandwich panel model





Figure 3. ABAQUS result for high aspect ratio curved-section sandwich panel model a) with no rigid ends and b) rigid ends included

The core transverse shear moduli, G 13 and G 23, are studied because theyare the core properties that have the most significant effect on panelbuckling (Toubia, 2008). As shown in Figure 4, for a core with hightransverse shear modulus G 13, the FEA result and analytical solutionsconverge. When the core shear modulus is too low, the local skin

buckling wrinkling mode is dominant. As shown in Table 1, the lowestshear modulus studied has a value of G 13 of 20 MPa (less than a 5%deviation from the closed form solution), while the highest had a valueof 250 (essentially no deviation).

The flat-section model result was validated by the closed form solutionsprovided by Allen (Allen, 1969) for orthotropic sandwich panels (validfor flat plates only). The infinitely long curved plate solution forisotropic plates was found in Gambhir (Gambhir, 2004).Since the S4R element in ABAQUS is a soft shell element, rigid endswere required in the sandwich panel models to get more accuratebuckling eigenvalues. The validated results can be seen in Figure 4.

Closed Form Solution Validation

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Figure 4. Flat model FEA result compare with the closed form solution

RESULTS AND DISCUSSIONThe local buckling phenomenon, such as core shear crimping and skinwrinkling, are discussed in references (Eringen, 1952, Vinson, 1999).The core thickness and shear modulus must be adequate to prevent thepanel from buckling or failing under end compression loads. Thecompressive modulus of the facing skin and the core compressionstrength must both be high enough to prevent a skin wrinkling failure.Since the anayzed skin material is sufficently stiff, local skin failurewas not taken into consideration herein (Toubia, 2008). Each of thecurves in the subsequent plots were created from five or six individualcalculation points. Since no dramatic shape variations were observedin the results, for clarity the individual data points are not shown, butsmoothed lines are presented.

Flat Panel Core Thickness StudyFigure 5 shows the effects of increasing the core transverse shearmodulus (M1 through M4), increasing the number of facing layers (1layer facing to 5), and increasing the core thickness (C 0 is the corethickness divided by the facing thickness) on the critical buckling load,N1. Figure 5 illustrates that a higher transverse shear modulus increasescritical buckling load. It is also clear that both increasing the number of facing layers, as well as increasing the core thickness lead to increasesin the critical buckling load. Note that while increasing the thickness of the core, the critical buckling loads increase faster in the cases withhigher transverse core shear modulus. Also, for increased corethickness, a higher number of layer facing results in rapid increases incritical buckling load. Figure 6 depicts similar trends for the laminatecritical strain values: transverse shear modulus of the core, corethickness, and number of facing layers are the dominant aspects in

sandwich panel buckling resistance.Figure 5. Critical buckling load versus normalized core thickness C 0 for all five facing layers and all four core materials. Flat-section. 1m widthsandwich panel.

500600700800900

10001100

1200

0 20 40 60 80 100 120 C r i t i c a l

B u c k l i n g

L o a d

N x * 1 0 9

( N / m )

G13 (MPa)

FEA compare with closed form solution

FEA S4R

ANALYTICAL

05

1015202530354045

1 3 5 7 9 11 13 15

C r i t i c a l B u c k l i n g

L o a d

N 1

* 1 0 5 ( N / m )

Normalized core thickness C 0





Figure 6. Critical buckling strain versus core thickness for all five facing layers and all four core materials. Flat-section. 1m width sandwich panel.

Note that the strain is dependent on N cr /2t (assuming half of the load iscarried by top and bottom skin, t is the thickness of each the skin, N cr isN/m per linear width b). For a low modulus core, core shear instability(shear crimping) governs the buckling load. The shear modulus is notstiff enough to engage the top and bottom skin. So if we look at theformula: cr=G*h/(2t) (core shear instability formula for isotropiccore), and = (strain, )*E, and = (Ncr/2(bt))= (strain, )*E, thenNcr /2t decreases as strain decreases. Since N cr increases as the skin

thickness increases, N cr is divided by the number of plies, this numberdecreases for the low modulus core. As for the stiffer core, the shearmodulus is high enough that the core is coupling and engaging the skinsto effectively carry the buckling load, therefore global buckling occurs.The more the number of plies is increased, the more the structure isstraining, until an asymptotic line is reached that the buckling cannot gobeyond, until the shear modulus is increased.Figure 7 separates theresults by core type (M1-M4).

Figure 7. Critical buckling strain versus core thickness for core material M1, M2, M3, M4. Flat-section. 1m width sandwich panel

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

20 25 30 35 40 450.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 25 30 35 40 45





In Figure 8, the width of the panel was increased from 1m to 5m todepict the panel width effect. For each core thickness, the upper curveis 5 layers, the lowest is 1 layer. Note the critical buckling loads drop

faster with increasing core shear modulus. The trends level off as the

width increases to around 3m due to global flexibility. Strain is notshown because, for the flat panel, the critical buckling strain is the sameregardless of panel width.

Figure 8. Critical buckling load versus panel width for material M1, M2, M3 M4 in 20, 30, 40mm core thickness. Flat-section. 1m, 3m, 5m widthsandwich panel. For each core thickness, the upper curve is 5 layers, the lowest is 1 layer.

To gain insight into the critical buckling strain versus core transverseshear modulus relationship, additional hypothetical core materials (seeTable 3) are introduced in Figure 9. Note core material M3 is an

unbalanced core with a shear modulus G 13=108 Mpa and G 23=72 MpaAll other core materials are balanced (G 13 = G 23). Compared with corematerial Q1, M3 has an 8% increase in G 13 and 28% decrease in G 2

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 25 30 35 40 450.2

0.3

0.4

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0.6

0.70.8

0.9

1

1.1

1.2

20 25 30 35 40 45

0

2

4

6

8

10

12

1 2 3 4 50

5

10

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25

1 2 3 4 5

0

5

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25

30

1 2 3 4 5

0

5

10

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25

30

35

1 2 3 4 5





the result is approximately 9.6% maximum decrease in buckling strain.For core material Q5, the shear modulus is the same as Q4 but up to28.6% decrease in material elastic modulus. The result is onlymaximum 3.3% decreased in buckling strain. The results indicate thatin sandwich buckling resistance, the core transverse shear modulus is amajor characteristic aspect, while the material elastic modulus has

negligible effect on the critical strain level.The trends are almostconstant when the core shear modulus increases. Critical bucklingstrains are proportional with the increase in core thickness. As such,core thickness is another major aspect in sandwich bucklingresistance.The results are expanded in Figure 10 to include additionalface sheet layer combinations.

Figure 9. Critical buckling strain versus core transverse shear modulus in 20, 30, 40mm core. 1 facing layer. Flat-section sandwich panel.

Figure 10. Critical buckling strain versus core transverse shear modulus in 20, 30, 40mm core. All 5 facing layers. Flat panel. 1m width

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240

C r i t i c a l b u c k l i n g s t r a i n ε

( % )

Transverse shear modulus

1 facing

40m

30mm

20mm

Q5

Q5

Q5

M

M

M

M4

M4

M4

M2

M2

M2

M1

M1

M1

Q1

Q1

Q1

Q2 Q3 Q4

Q4

Q4

Q3

Q3

0

0.1

0.2

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0.5

0.6

0.7

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1

20 70 120 170 220

C r i t

i c a l b u c k l i n g s t r a i n ε

( % )

Transverse shear modulus (Mpa)

40mm

30mm

20mm

5 layer4 layer3 layer2 layer1 layer







Curved Panel Curvature Ratio and Core Thickness StudyIn the curved-section sandwich panel models (see Figure 11), theresults clearly indicate that the buckling loads increase quickly withcurvature of the plate, core thickness, and number of facing layers. It isalso shown that the ‘critical curvature ratio’ exists for a fixed corematerial and thickness, where the trends of the critical buckling loadsreach a high point and then level off. Local buckling occurs after that.For the lower shear modulus core materials, the ‘critical curvatureratio’ occurs earlier than those with high shear modulus. In the practicaldesign, it reveals those sandwich panels made of lower shear modulus

core materials are not suitable to be made with large curvature ratio toresist buckling. Alternatively, when the core shear modulus is high, thetrend is still upward (no critical point is reached).For the critical buckling strains in the curved-section panel models(Figure 12), the plots show that the strains decrease and then increaseas the curvature of the plate increases. The results of variations in thetransverse shear modulus in curved-section sandwich panel models areshown in Figure 13. The critical buckling strain increases when thecore thickness and section curvature ratio increases

Figure 11. Critical buckling load versus panel curvature ratio for core material M1, M2, M3, M4 in 20, 30, 40mm core thickness and all five facinglayers. Curved-section panel.

0

2

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14

0 5 10 15 20 25 0

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0

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2025

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35

40

45

0 5 10 15 20 250

20

40

60

80

100

120

140

0 5 10 15 20 25





Figure 12. Critical buckling strain versus panel curvature ratio for core material M1, M2, M3, M4 in 20, 30, 40mm core thickness and all five facinglayers. Curved-section panel.

0

0.1

0.2

0.3

0.4

0.5

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0 10 200

0.2

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0 5 10 15 20 25

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0 5 10 15 20 250

0.2

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1.4

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0 5 10 15 20 25





Figure 13. Critical buckling strain versus transverse shear modulus in 5%, 10%, 25% curvature, 20mm core, Curved panel, all 5 layers.

PRELIMINARY DESIGN EXAMPLE

Figure 14 shows a repeat of Figure 6 to be used as a design example.In this example, the critical buckling design strain has been previouslychosen based on other factors (maximum blade deflection, joining,damage tolerance, etc.), and required to be equal to or greater than0.5%. Several combinations of core selection, core thickness, andfacing thickness are depicted in Figure 14 (only three are shown of apossible 12 curve intersections):

A. approximately 27mm thickness of core M4 with 5 facing layers;B. approximately 33mm thickness of core M3 with 1 facing layers;C. approximately 41mm thickness of core M4 with 2 facing layers;

Based on the cost and weight of facing materials and core materials, theoptimal choice can be made to minimize or balance the cost and theweight of the structure.

Figure 14. Critical buckling strain versus core thickness for all five facing layers and all four core materials. Flat-section. 1m width sandwich panel.

00.10.20.30.40.50.60.70.80.9

1

20 70 120 170 220Transverse shear modulus (Mpa)

20mm Core

C r i t i c a l

b u c k l i n g s t r a i n ε ( %

)

25%

10%

5%

5 layer4 layer

3layer2 layer

5 layer4 layer3layer2 layer1 layer5 layer4 layer3layer2 layer1 layer

0

0.2

0.4

0.6

0.8

1

1.2

20 25 30 35 40 45

M1

M2

b=1m5layer4layer

1 layer

2 layer

3 layer4 layer5 layer

Core thickness

C r i t

i c a l b u c k

l i n s t r a i n

ε

0.5

A B





CONCLUSIONS

A finite element based study of the buckling of composite sandwichpanels (as seen in wind turbine blade shells) was conducted to examinethe sensitivity of critical buckling load and strain levels to multipledesign parameters, including the core transverse modulus, corethickness, number of facing layers, panel width, and panel curvature.The results of this project provide a more efficient preliminary designmethod to assess sandwich panel buckling in wind turbine blade design.

The results from this study in practical design optimization wouldinvolve assessing the variables listed above, then comparing the costand weight of the various solutions toward the design objectives suchas minimizing cost or weight.

ACKNOWLEDGEMENT

The discussions with Fred Stoll of Milliken & Co. are gratefullyappreciated.

REFERENCES

ABAQUS User’s Manuals, Version 6.10 ( Volume I-III, Hibbitt:Karlson and Sorensen, Inc. , Pawtucket, RI. )

Allen HG. Analysis and design of structural sandwich panels.Pergamon Press, Oxford 1969.

E_TLX5500. http://www.vectorply.com/pdf/e-tlx%205500.pdf.Accessed 15 December 2011.

Eringen AC. Bending and buckling of rectangular plates. Proceedingsof the first U.S. National congress of applied mechanics, ASME NewYork 1952. 381-390.

Gambhir ML. Stability analysis and design of structure. Springer 2004.

http://proquest.umi.com/pqdlink?did=1537815401&Fmt=7&clientI%20d=79356&RQT=309&VName=PQD. Accessed 15 December 2011.

http://www.gurit.com/files/documents/3_Blade_Structure.pdf Jackson, K, Zuteck, M, van Dam, C, Standish, ., Berry, D. InnovativeDesign Approaches for Large Wind Turbine Blades. Wind Energy2005; 8:141 – 171.

Leissa AW. Buckling of laminated composite plates and shell panels. Air Force Wright Aeronautical Laboratories 1985, Final Report, No.AFWAL-TR-85-3069.

Lund E, Johansen LS, On Buckling Optimization of a Wind TurbineBlade. Mechanical Response of Composites, Computational Methods in

Applied Sciences 2008, Volume 10, 243-260.

Lund E. On Structural Optimization of Composite Shell StructuresUsing a Discrete Constitutive Parametrization. Wind Energy 20058:109 – 124.

Mishnaevsky, L., Brøndsted, P., Nijssen, R., Lekou, D. and Philippidis,T. Materials of large wind turbine blades: recent results in testing andmodeling. Wind Energy 2011.

Morovvati MR. Buckling of Generally Anisotropic Sandwich Shells. American Society of Composites 26th Annual Technical Conference2011, 1143.

Narita Y, Leissa AW. Buckling studies for simply supportedsymmetrically laminated rectangular plates. Int. J. Mech. Science 1990Volume 32, No. 11, 909-924.

Nemeth MP. Buckling Behavior of Long Anisotropic Plates Subjectedto Combined Loads. National Aeronautics and Space Administration

Langley Research Center 1995, 1-37.

Nemeth MP. Buckling of long compression-loaded anisotropic platesrestrained against inplane lateral and shear deformations. Thin-WalledStructures 2004. Volume 42 639 – 685.

Roczek A. Optimization of trailing edge sandwich panels for a windturbine blade. 9th International Conference on Sandwich Structures2010.

Toubia EA. Web buckling behavior under in-plane compression andshear loads for web reinforced composite sandwich core, Ph.D.dissertation, University of Dayton 2008, available at:Vinson JR. The behavior of sandwich structures of isotropic andcomposite materials. TECHNOMIC Publishing Company, Inc 1999.

WE Handbook- 3- Structural Design. Available at:Weaver PM, Nemeth MP. Bounds on Flexural Properties and BucklingResponse for Symmetrically Laminated Composite Plates. Journal of

Engineering Mechanics 2007, 1178-1191

Table 1: Candidate Material PropertiesFace/Core E 1 E2 E3 ν 12 ν 13 ν 23 G12 G13(G1) G23(G2)

MPa MPa MPa MPa MPa Mpa

E_TLX 5500(face sheet)

21400 10000 0.4 6000 3740 3740

M1 50 50 50 0.33 0.22 0.1 20 20 20

M2 100 100 100 0.2 0.2 0.2 30 50 50

M3 284 250 210 0.39 0.25 0 146 108 72

M4 400 400 400 0.2 0.2 0.2 250 250 250





Table 2: Panel Model information

Variables Range Description

Number of facing layers analyzed 1~5 Increased by 1Thickness of each layer (m) 0.0015 Increased by 0.0015

Range of core thickness (m) 0.02~0.045 Increased by 0.005Range of panel width b (m) 1~5 1m, 3m, 5mRange of panel curvature ratio (%) 0~25% Flat, 5%, 10%, 25%Aspect ratio (length/width; a/b) 5 ConstantShell edge load (N/m) 1 Uniformly distributed

Table 3: Additional Core Material Properties

Face/Core E 1 E2 E3 ν 12 ν 13 ν 23 G12 G13(G1) G23(G2)

MPa MPa MPa MPa MPa Mpa

Q1 150 150 150 0.2 0.2 0.2 100 100 100

Q2 200 200 200 0.2 0.2 0.2 120 120 120

Q3 250 250 250 0.2 0.2 0.2 150 150 150

Q4 350 350 350 0.2 0.2 0.2 200 200 200

Q5 250 250 250 0.2 0.2 0.2 200 200 200


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