Design of Front and Rear Spars for The Trainer Aircraft Wing.
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TEAM Team Members :
CAE
Akshay A. Pradeep S. Shet CAD
Pavan Kumar N. R. Raghunandan M. Lakshmana H. B. Chetan A. V.
Guide Co-ordinator
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Mr. H. N. Athavale Mr. Umanath Nayak
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OBJECTIVE CAD
To generate the CAD model of wing using the available data and prepare the assembly of all components
CAE
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Determine the Spar locations with respect to chord length.
Determine the dimensions for flange and web of the spars.
Estimate the number of ribs and their positioning
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SCOPE OF THE PROJECT CAE Estimation of spar position. Dimension calculations of front and rear spars. Calculations for number of ribs and their positions. CAD Profile creation of the wing using the given NACA standards. Creation of the wing geometry Use available data to develop CAD models for each individual component Prepare an assembly of all components using CATIA
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INPUT Root chord : 2400 mm Tip chord : 700 mm Semi Span length : 5500 mm Exposed Span : 4750 mm Airfoil (root) : NACA 64A1215 (tip) : NACA 64A1210 Aircraft weight : 14000 N Lift Load : 6g Design Factor : 1.5 Given Spar Position(in % of chord length) Front Spar : 18-25 Rear Spar : 62-70
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DERIVED INPUT
●
Limit load
: 14000 * 6= 84000 N
●
Design Load
: 84000 * 1.5= 126000 N
●
Load on semi-span
: 126000 / 2= 63000 N
●
Exposed wing area
: 7.3625 E6 mm2
●
Pressure load on wing
: 63000 / 7.3625 E6 = 8556.87 E-6 N/mm2
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WING GEOMETRY
TIP CHORD
700
SWEEP AT ¼ CHORD
2400
ROOT CHORD
LEADING EDGE
4750 TRAILING EDGE
Top View [RH] ALL DIMENSIONS ARE IN mm
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AIRFOIL
Generate the aerofoil section using the Coordinates of NACA 64A1215 and NACA 64A1210.
[source : http://www.pdas.com/sections6a.htm]
Generate the CAD model of the wing using CATIA- V5.
Aerofoil at Root NACA 64A1215
Aerofoil at Tip NACA 64A1210 CADES Proprietary
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DESIGN PROCEDURE
Calculation of the Shear force, Bending moment & Torsion for the given load. Calculation of load distribution between the front and rear spar. Estimation of spar positions. Generation of CAD Model and Drafting.
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DESIGN PROCEDURE Divide the wing area into number of divisions. Calculate the chord length at each section. Determine the C.G of each area. Calculate the shear force, bending moment and Torque at the respective sections. Shear force =pressure*area. Bending moment=shear force*CG distance. Torque = Shear force*Distance b/w CG and CP.
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METHODS AND METHODOLOGY L9
L2
L1
700 2400
A10
A9
A8
A7
A6
A5
A4
A3
A2
A1
475
ALL DIMENSIONS IN mm
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DESIGN PROCEDURE Chord Length, L1= Lroot -((Lroot -Ltip ) / S) * x At section 2, L1 = 2400-((2400-700)/4750)*4275 Lroot L1 = 870 mm Area of Trapezium, A1 = 0.5*(L1+Ltip )*h A1 = 0.5*(870+700)*475 A1 = 373 E3 mm2
L1 x
A1
Ltip
h
S
CG of Trapezoid Section = h/3*((Ltip +2L1)/(Ltip +L1)) CG=475/3*((700+2*870)/(700+870)) CG = 246 mm from Ltip
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DESIGN PROCEDURE Limit load = 84000 N Design Load = Limit Load*Design factor Design load on wing, = 84000*1.5 = 1,26,000 N Design load on semi-span wing, = 63000 N pressure load on wing [P] = 8556.87 E-6 N/mm2 Load At Section 2, = P2+P1 = P*A2+P1 = 8557 E-6 * 453625 + 3190.65 = 3881.6 + 3190.65 = 7072.25 N Bending Moment At Section 2, M2 = P2 * CG2 + P1 * (CG1 + L2) M2 = 3881.6 * 230 + 3190.65 * (229 + 475) M2 = 3248260 N-mm CADES Proprietary
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SHEAR FORCE
Shear force diagram for the wing 70000.00
63000.00
Shear force [N]
60000.00
53590.65
50000.00
44872.25 36844.85
40000.00
29508.40
30000.00
22862.90 16908.39 11644.85 7072.25 3190.65 3190.65
20000.00 10000.00 0.00 Root 0
475
950 1425 1900 2375 2850 3325 3800 4275 TIP 4750
Wing span [Root to tip] [mm] CADES Proprietary
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BENDING MOMENT
Bending moment diagram for the wing span Bending moment [N-mm]
140000000
123020000
120000000 100000000
95259000
80000000
71809000 52341000
60000000
36527000 24039000 14548000 7727860 3248260 781700
40000000 20000000 0 ROO T 0
475
950
1425
1900
2375
2850
3325
3800
0
4275 TIP 4750
Wing span [root to tip] [mm] CADES Proprietary
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LOAD DISTRIBUTION Centre of Pressure, CP = 45% of Chord Length (C) from LE [870mm] Front Spar Position = 25% of C from LE [217.5mm] Rear Spar Position = 62% of C from LE [539.4mm]
[1]
45% of C
Chord CP
RA 25% of C
FS
a
RB
b
RS a=174mm b=148mm
c
c=322mm
62% of C
C=870mm Chord Length 'C'
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Shear Force Distribution: Shear Force on Front Spar, = Load * b/c At Section 1, SFFS = 3190.65 * (148/322) SFFS = 1465.974 N Shear Force on Rear Spar SFRS = 3190.65 - 1465.974 SFRS = 1724.676 N SF on Front Spar SF on Rear Spar
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= 45.9% of total load = 54.1% of total load
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Bending Moment Distribution: Moment is distributed in same ratio as that of the Shear force. Bending Moment on Front Spar, MFS = 0.459 * 781700 MFS = 359159 N-mm Bending Moment on Rear Spar, MRS = 781700 - 359159 MRS = 422541N-mm
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SHEAR FORCE & BENDING MOMENT
Front Spar
Rear Spar
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MATERIAL Material Ultimate tensile strength, σ Shear strength Density Young's Modulus, E Poisson's Ratio
: AA 2024-T6 : 427 MPa : 283MPa : 2.79 E-6 kg/mm3 : 72400 Mpa : 0.33 [Aluminum Association, Inc]. [7]
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Moment of Inertia: I = M*y/σ
Where, I M y σ
= Moment of Inertia, in mm4 = Bending Moment, in N-mm = distance b/w neutral axis to top surface, in mm = Tensile strength, in MPa
Moment of Inertia on Front Spar, IFS IFS
= 359159 * 52.8 / 427 = 44412 mm4
Moment of Inertia on Rear Spar, IRS IRS
= 422541 * 43.44 / 427 = 42987 mm4
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MOMENT OF INERTIA
Front Spar
Rear Spar
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TORSION
Area of Torque Box, A1 CG of Torque Box Distance Between CG & CP Torque, T = Load*d
= 30980.3 mm2 = 165 mm From Rear spar = 18.268 mm = 3190.65 * 18.268
T = 58286 N-mm Shear flow, q1 = T/(2*A1) [2] q1 = 58286 / (2 * 30980.3) q1 = 0.941 N/mm CADES Proprietary
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CG OF TORQUE BOX
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Torque
Shear Flow
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TORQUE DIAGRAM
Torque diagram for the wing span 11857039.54
12000000
Torque [N-mm]
10000000
8689789.08
8000000 6187429.48
6000000
4252608.34
4000000
2795550.39 1734041.9 992888.78 506210.31 212789.99 58285.91
2000000 0
ROOT 0
475
950
1425
1900
2375
2850
3325
3800
0
4275 TIP 4750
Wing span [root to tip] [mm]
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SHEAR FORCE DUE TO TORSION Shear force (SF) on Front Spar SFFS = q * hFS SFFS = 0.941*105.6 = 99.34 N Total SF on FS = 1465.974+99.34 = 1565.313 N On Rear Spar SFRS = q*hRS SFRS = 0.941*86.88 SFRS = 81.729 N Total SF on RS = 1724.676+81.729 = 1806.405 N
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SHEAR FORCE DUE TO TORSION
Front Spar
Rear Spar
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TOTAL SHEAR FORCE
Front Spar
Rear Spar
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WEB THICKNESS Thickness of the Web can be calculated from the following formula,
حshearstrength
= SFFS / A web
Where, حshearstrength
= Shear strength of the material AA 2024-T6 in MPa
A web = Area of the web = (height * thickness) in mm
283 = 1565.313 / (105.602 * t web ) t web = 0.052 mm Area of the web = height * thickness = 105.602 * 0.052 A web = 5.531 mm2 Moment of Inertia of Web: Moment of Inertia of a rectangular section web is given by, I web = t web * (hFS )3 / 12 I web = 0.052 * (105.602)3 / 12 I web = 5140.175 mm4 CADES Proprietary
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WEB
Front Spar
Rear Spar
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FLANGE MOIflange = MOIFrontSpar
- MOIWeb I flange = IFS - Iweb = 44411 - 5140.175
I flange = 39270.825 mm4 Also Moment of Inertia of the flange is given by, I flange = Aflange * (yFS )2 Where, Iflange = Moment of Inertia of flange in mm4 yFS = height from neutral axis to top surface of the flange in mm Hence, Aflange = Iflange / (yFS )2 = 39270.825 / (52.801)2 Aflange = 14.086 mm2 CADES Proprietary
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FLANGE
Front Spar
Rear Spar
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MASS CALCULATIONS AFS = Aflange + Aweb AFS = 14.09 + 5.53 = 19.62 mm2 VFS = AFS * 475 = 19.62 * 475 VFS = 9318.3 mm3
Mass = Density * Total Volume = 2.78 E-6 * 4218551.12 Mass = 11.73 kg
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MASS CALCULATIONS 14.00
13.49
13.50
13.32
13.33
13.34
13.17
13.17
13.18
13.18
13.02
13.02
13.02
13.02
13.02
12.88
12.88
12.88
12.88
12.87
12.87 12.77 12.68
Mass [kg]
13.50
13.00 12.75
12.74
12.74
12.74
12.73
12.72
12.62 12.49 12.37 12.25 12.13 12.01 11.89
12.61
12.61
12.60
12.50 12.5012.39 12.27 12.16 12.05 12.0011.95 11.84
12.62 12.50 12.38 12.26 12.15 12.03 11.92 11.81
12.59
12.49
12.48
12.46
12.36
12.34
12.23 12.11
12.33
12.45 12.34
12.59 12.51
12.21
12.19
11.50 62
63
64
11.73
12.08
11.98
65
66
67
Rear spar position in %
68
69
18 19 20 21 22 23 24 25
Front spar position
13.67
70
Hence, from the Calculations it is found that (25% - 62%) combination of Spar Position was found suitable. The Mass of this combination is 11.73 Kg which is least than any other combinations CADES Proprietary
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BUCKLING To Check whether the web fails under shear buckling. Condition: Shear stressinduced < Buckling stress (safe design) The thickness calculation is based on iterations,
●
Finduced = q / tweb Fcritical = k*E*(tweb / b)2 where,
[4]
q = shear flow, in N/mm E = Young's Modulus, in MPa b = height of spar, in mm tweb = web thickness, in mm
[4]
k = shear buckling coefficient from graph CADES Proprietary
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BUCKLING CALCULATIONS ITERATION 1. RIB SPACING FOR EQUAL DISTANCE OF 475mm Web thickness's of front spar at section 1 is as follows, Finduced = q1 / t web ------------ (1) = 0.941 / 0.052 Finduced = 18.09 N/mm2 Fallowable = K * E * (t web / b)2-----------(2) 18.09 = 5 * 72400 * (t web / 105.602)2 The value calculated for tweb is re substituted in Eqn.(1) and this loop will continue till we get equal consecutive thickness. Hence, the thickness of the web is 0.30 mm at section 1. Same calculations were repeated for all sections of front spar to optimize the web thickness
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Front Spar
Rear Spar
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MASS CALCULATION
Web design is safe under buckling.
●
From buckling calculation the total mass of the spars is 16.14 kg.
●
By this, mass of the spars got increased by 4.41 kg.
●
To decrease the mass, one more iteration has been carried out.
●
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ITERATION-2 Rib no.
Rib dist. From root
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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[mm] TIP4750 4440 4110 3780 3450 3120 2790 2470 2150 1830 1520 1210 900 600 300 Root 0
●
For optimum Rib spacing, (a/b) ratio >= 1
Spar heights FS RS [mm] 64.49 81.97 100.58 119.19 137.8 156.41 175.02 193.06 211.11 229.15 246.63 264.11 281.59 298.51 315.43 332.35
(a/b) ratio FS RS
[mm] 54.05 68.4 83.67 98.94 114.22 129.49 144.76 159.57 174.38 189.19 203.53 217.88 232.23 246.11 259.99 273.88
0 3.78 3.28 2.77 2.39 2.11 1.89 1.66 1.52 1.40 1.26 1.17 1.10 1.00 1.05 1.11
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0.00 4.53 3.94 3.34 2.89 2.55 2.28 2.01 1.84 1.69 1.52 1.42 1.33 1.22 1.15 1.10
K from graph
FS
RS
5.10
5.00
5.17
5.08
5.30
5.15
5.50
5.20
5.75
5.40
6.00
5.60
6.30
5.80
6.55
6.20
6.90
6.25
7.25
6.55
7.60
6.80
7.80
7.00
8.20
7.35
8.00
7.60
7.80
7.80
Web thickness FS RS
Web volume FS RS 3 3 [mm ] [mm ]
[mm] [mm] 0.22 0.2 5590.56 4240.8 0.34 0.3 11285.3 8283.53 0.44 0.39 17306.53 12734.09 0.53 0.48 24101.05 18091.81 0.64 0.57 33033.37 24356.69 0.74 0.67 42739.15 32006.44 0.84 0.76 51894.8 38807.18 0.94 0.84 63500.68 46872.81 1.03 0.94 75528.17 56907.75 1.12 1.02 85630.63 64357.45 1.2 1.1 98250.04 74297.42 1.31 1.19 114355.32 85668.54 1.39 1.26 124479.09 93029.96 1.51 1.35 142888.88 105297.57 1.63 1.43 162519.15 117494.52 Total volume 1053102.72 782446.56 Web volume 1835549.28
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WEIGHT CALCULATION
Finally mass of the spars reduced by 0.89 kg when compared to 1st iteration.
●
●
These dimensions are taken for modelling
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RESULTS AND DISCUSSION WEB THICKNESS FOR FRONT SPAR THICKNESS OF WEB[mm]
2.00 1.63
1.60
1.51 1.39
1.31 1.20
1.20 0.80
1.12
1.03
0.94
0.84
0.74
ACTUAL FROM BUCKLING
0.64 0.53
0.44 0.39 0.36 0.34 0.34 0.32 0.29 0.40 0.27 0.25 0.22 0.20 0.22 0.17 0.15 0.12 0.10 0.07 0.04
0.00
-0.40
Root 0 300
600
900
1210 1520 1830 2150 2470 2790 3120 3450 3780 4110 4440 4750
FROM ROOT TO TIP [mm]
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WEB THICKNESS FOR REAR SPAR THICKNESS OF WEB[mm]
2.00 1.60
1.43
1.35
1.26
1.20
1.19
0.80
1.10
1.02
0.94
0.84
0.76
0.67
ACTUAL FROM BUCKLING
0.57 0.52 0.49 0.48 0.46 0.43 0.39 0.36 0.39 0.33 0.30 0.40 0.30 0.26 0.23 0.20 0.20 0.16 0.13 0.10 0.06
0.00 -0.40
Root 0 300
600
900
1210 1520 1830 2150 2470 2790 3120 3450 3780 4110 4440 4750
FROM ROOT TO TIP
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CONCLUSION
●
Front Spar positioning is estimated to 25% and Rear Spar to 62% of the
Chord Length. ●
Flange and web dimensions are calculated and suitable changes in
dimensions are incorporated from manufacturing point of view. ●
Number of Ribs and their positioning for the prevention of bending and
buckling of Spars is calculated. ●
Mass of the spars calculated from iterations is 15.25 kg.
●
The Detail drawings for the front and rear spars are provided using CATIA V5.
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SCOPE FOR FURTHER WORK
●
●
●
●
Spar position can be optimized based on buckling calculations. Further optimization of Rib is possible. --Varying number of Ribs and spacing of Ribs. Use of other materials for the design of spars can be thought of. Detail stress analysis of individual components and its validation with calculations can be carried out.
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CAD
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CAD MODELING OF THE WING SPAR Taking values from NACA Standards At Root: Profile: NACA 64A1215. Leading Edge radius = 1.556% c. Slope of mean line at leading edge = 0.0842. At Tip: Profile: NACA 64A1210. Leading Edge radius = 0.701% c. Slope of mean line at leading edge = 0.0842.
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1. Generation of the profiles at the root and tip using the NACA profiles.
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●
INCORPORATING THE LEADING EDGE RADIUS AS SPECIFIED IN THE PROFILE STANDARD.
1.Giving the slope in the sketcher mode
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2.Creating the arc of the required dimension coming out of sketcher.
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Using the connect curve option to join the leading edge radius and the aerofoil profile. ●
●
Create the surface using multi section surface option.
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INTERSECTION OF THE PROFILES Creating the planes at the four sections at ½, ¼, ¾ of the span of the wing. ● Intersecting the lofted surface on the planes creating unique sketches on them. ●
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ANGLE OF ATTACK ●
Create a point at the quarter chord and draw a line for reference.
●
Rotate the intersected profiles as 0.60 at the quarter, 1.10 at mid span, 1.60 at three fourths and 20 at the tip.
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CREATE THE SURFACE USING MULTI SECTION SURFACE OPTION By considering the profiles generated with angle of attack at different sections, the wing surface is created using multi-section surface option.
Thus the surface is created as per the requirements incorporating all the necessary data.
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CREATION OF REFERENCE AEROFOIL SECTIONS 15 planes are created at rib positions along the wing span. ● The intersections created are used as the reference for the creation of the spar. ●
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CONSIDERATIONS MADE DURING THE DESIGN OF SPAR ELEMENTS
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The maintenance of the nose box is made easy.
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The front spar is I – section.
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The rear spar is C – section.
●
Minimum distance required for a single row riveting is kept as 15 mm.
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DESIGNING OF SPAR ON MANUFACTURING BASIS
➢
The front spar is placed at 25% of chord length from leading edge.
➢
The rear spar is placed at 62% of chord length from leading edge.
➢
Thicknesses of the flanges and webs are different.
➢
The flanges are made of T-sections and L- sections.
➢
The webs are made with sheet metal.
➢
The thicknesses are optimized based on the availability of the standard gages of sheet metal.
➢
The final assembly of elements can be fastened with rivets.
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CROSS SECTION SPAR
Skin area,
As = (b +2*20*ts) mm2 Effective flange area = (Af- As)/2
where , b= flange width in mm ts =skin thickness in mm Af =designed flange area in mm2
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FRONT SPAR DIMENSIONS Rib no. Dist. From root Flange W idth Skin Area Available area Flange Thickness Effective Flange areaW eb thickness From root (mm) (mm) (mm2) (mm2) (mm) (mm2) (mm) 1 Root 0 70 220 266.94 3.81 266.94 1.63 2 300 70 220 215 3.07 215 1.63 3 600 70 220 175 2.5 175 1.63 4 900 65 210 150 2.31 150 1.29 5 1210 65 155.2 144.9 2.23 144.9 1.29 6 1520 60 147.2 116.4 2 120 1.29 7 1830 60 147.2 86.4 2 120 1.29 8 2150 55 139.2 60.4 2 110 0.91 9 2470 50 88.8 55.6 2 100 0.91 10 2790 45 82.8 36.1 2 90 0.91 11 3120 40 76.8 16.6 2 80 0.64 12 3450 35 70.8 -0.4 2 70 0.64 13 3780 30 64.8 -12.4 2 60 0.64 14 4110 30 64.8 -19.9 2 60 0.64 15 4440 30 64.8 -24.9 2 60 0.64 16 NO RIB 4750
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REAR SPAR DIMENSIONS Rib no. Dis t. F rom root F lange W idthS k in A rea A vailable areaF lange Thic k nesEsffec tive F lange area W eb thic k nes s F rom root (m m ) (m m ) (m m2) (m m2) (m m ) (m m2) (m m ) 1 R oot 0 90 260 415.01 4.61 415.01 1.45 2 300 90 260 340 3.78 340 1.45 3 600 80 240 295 3.69 295 1.45 4 900 75 230 257.5 3.43 257.5 1.15 5 1210 70 204 223 3.19 223 1.15 6 1520 65 194 180.5 2.78 180.5 1.15 7 1830 60 184 138 2.3 138 1.15 8 2150 55 174 100.5 2 110 0.91 9 2470 50 148 73.5 2 100 0.91 10 2790 45 138 48.5 2 90 0.91 11 3120 40 128 21 2 80 0.64 12 3450 35 118 4 2 70 0.64 13 3780 30 108 -19 2 60 0.64 14 4110 30 108 -36.5 2 60 0.64 15 4440 30 108 -43 2 60 0.64 16 N O R IB 4750
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CREATION OF THE SPAR SECTIONS 1. Two T sections for the flange, and web section for the front spar. 2. Two L sections for the flange, and web section for the rear spar.
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FULL PROFILE
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GENERATING SPAR USING DIFFERENT SECTIONS
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CRIMP HOLES OR LIGHTENING HOLES The lightening holes are made in the element in order to reduce the weight of the element. the crimp holes are made to the web element of the spar. These holes provided in between the two successive rib locations.
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SPAR WITH LIGHTENING HOLES
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REPRESENTATION OF RIVET HOLES
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FINAL SPAR ASSEMBLY
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BIBLIOGRAPHY 1] Abbot & Albert,'Theory of wing sections',Dover publication,1949. 2] David J. Perry,'Aircraft structures',Mc-Graw Hill publication,1950. 3] E. F. Bruhn,'Analysis and design of flight vehicle structures',1973. 4] Michael C. Y. Niu, 'Airframe Stress Analysis and Sizing', 2001. 5] Michael C. Y. Niu, 'Airframe structural design', Conmilit press Ltd., 1989. 6] Kuethe and Schetzer, 'Foundations of Aerodynamics', 2nd Edition, John Wiley and Sons, New York, 1959. 7] ASM Material Data Sheet 8] MIL Handbook. & CADES Library. CADES Proprietary
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