Vertical axis wind turbine

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Vertical axis wind turbine
Vertical Axis Wind Turbine
Lindsay Pellhum
Jordan Showalter
Derek Storms
Joseph Trosclair
ET 494
Spring 2017
Advisor:
Dr. Rana Mitra
Scope Of The Project
 To harness and utilize the available wind resources to help the Sustainability
Center, located on north campus, in their goal of using renewable energy
to one day power Greek Village
Tower Design
 The loading conditions on the tower
resolute from local wind speeds
provided by LSU AgCenter.
 Load and Resistance Factor Design
(LRFD) was then used for the
dimensions of the tower.
 The Teams Design
 Material: ASTM 500 Grade B
 Structure height: 30ft
 Tower 21.5ft
 Hub 8.5ft
 Tower diameter: 18 inches
Tower Design Formulas

Design Load Criteria (1.2 safety factor)
 Axial Load(lb): 4377.612996

Design Stress Check with accordance to
material (ASTM 500 Grade B (round))
𝑀
𝐼
 Moment Load (lb*ft): 48101.26851
 𝜎=
 Shear Load (lb/ft^2): 11.42116958
 4041psi ≤ 16,000 psi OK
 Axial Load
 Weight of the tower
 Density of Steel x Volume
 Moment Load
 M= 𝐹𝑤𝑖𝑛𝑑 × 𝐻𝑡
 Electronic Industries Association Wind Force Formula:
 𝐹𝑤𝑖𝑛𝑑 = 𝐴𝑔 × 𝑃 × 𝐶𝑑 × 𝐾𝑧 × 𝐺ℎ

𝐴𝑔 is Gross Area of tower

𝑃 is wind pressure

𝐶𝑑 is the drag coefficient

𝐾𝑧 is Exposure Coefficient , The basic wind speed measured in the fastest
mile was obtained from ASCE 7-05 wind speed

𝐺ℎ is the gust response factor
𝑦
Load Calculations
Height
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
volume of steel(ft^3)
Weight of Steel (lb/ft^3) Weight of Structure (lb) Area (ft^2) Diamater (ft)
z
Kz
Ag (Dia*H) (ft^2)
Force (lb) Moment Shear(lb/ft^2)
0.190895386
490
93.53873924 9.5448566
1.5 0.5 0.302
1.5 13.89233 13.89233 2.853856963
0.381790772
490
187.0774785 18.707626
1.5 1.5 0.413
3 38.02992 76.05984 3.985963263
0.572686159
490
280.6162177 27.870395
1.5 2.5 0.478
4.5 66.00883 198.0265 4.643927797
0.763581545
490
374.1549569 37.033164
1.5 3.5 0.527
6 96.89283 387.5713 5.130118136
0.954476931
490
467.6936962 46.195933
1.5 4.5 0.566
7.5 130.1325 650.6625 5.523426607
1.145372317
490
561.2324354 55.358702
1.5 5.5 0.599
9 165.3739 992.2436 5.857438363
1.336267703
490
654.7711746 64.521471
1.5 6.5 0.629
10.5 202.3684 1416.579 6.149855576
1.52716309
490
748.3099139 73.684241
1.5 7.5 0.655
12 240.9301 1927.441 6.411255134
1.718058476
490
841.8486531 82.84701
1.5 8.5 0.679
13.5 280.9147 2528.232 6.648506799
1.908953862
490
935.3873924 92.009779
1.5 9.5 0.701
15 322.2057 3222.057 6.866347762
2.099849248
490
1028.926132 101.17255
1.5 10.5 0.721
16.5 364.7075 4011.782
7.06819544
2.290744634
490
1122.464871 110.33532
1.5 11.5 0.74
18 408.3395 4900.074 7.256603687
2.481640021
490
1216.00361 119.49809
1.5 12.5 0.758
19.5 453.033 5889.429 7.433535911
2.672535407
490
1309.542349 128.66086
1.5 13.5 0.775
21 498.7285 6982.199 7.600537172
2.863430793
490
1403.081089 137.82362
1.5 14.5 0.791
22.5 545.3739 8180.608 7.758847254
3.054326179
490
1496.619828 146.98639
1.5 15.5 0.806
24 592.9231 9486.77 7.909477589
3.245221565
490
1590.158567 156.14916
1.5 16.5 0.82
25.5 641.3352 10902.7 8.053265138
3.436116952
490
1683.697306 165.31193
1.5 17.5 0.834
27 690.5734 12430.32 8.190911108
3.627012338
490
1777.236045 174.4747
1.5 18.5 0.848
28.5 740.6044 14071.48 8.323009381
3.817907724
490
1870.774785 183.63747
1.5 19.5 0.86
30 791.398 15827.96 8.450067784
4.00880311
490
1964.313524 192.80024
1.5 20.5 0.873
31.5 842.9266 17701.46 8.572524289
4.199698496
490
2057.852263 201.96301
1.5 21.5 0.885
33 895.1648 19693.63 8.690759525
4.390593882
490
2151.391002 211.12578
1.5 22.5 0.896
34.5 948.0895 21806.06 8.805106576
4.581489269
490
2244.929742 220.28855
1.5 23.5 0.908
36 1001.679 24040.29 8.915858751
4.772384655
490
2338.468481 229.45132
1.5 24.5 0.918
37.5 1055.913 26397.83 9.023275808
4.963280041
490
2432.00722 238.61408
1.5 25.5 0.929
39 1110.774 28880.12 9.127588992
5.154175427
490
2525.545959 247.77685
1.5 26.5 0.939
40.5 1166.243 31488.56 9.229005154
5.345070813
490
2619.084699 256.93962
1.5 27.5 0.949
42 1222.305 34224.54 9.327710135
5.5359662
490
2712.623438 266.10239
1.5 28.5 0.959
43.5 1278.944 37089.38 9.423871585
5.726861586
490
2806.162177 275.26516
1.5 29.5 0.968
45 1336.146 40084.39 9.517641314
Foundation Design
 Types of Foundation Design: Spread, Drilled, or Anchored
 Spread Footing
 Circular, hexagonal, octagonal, square
 Spread Footing (square) Design
 Assumed an 8’ x 8’ x 3’
 Using 7.5’ x 7.5’ x 3’ to reduce cost
 Most notable calculation

f.o.s =
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑀𝑜𝑚𝑒𝑛𝑡
𝑂𝑣𝑒𝑟𝑡𝑢𝑟𝑛𝑖𝑛𝑔 𝑀𝑜𝑚𝑒𝑛𝑡
>2

RM is the Weight of the concert multiplied by the distance from the midpoint of the foundation to the edge.

OM is the wind force multiplied by the total height (tower and foundation)

Using 7.5’ x 7.5’ x 3’ → RM/OM = 2.03 OK
Foundation in AutoCAD
Foundation Cont’
Foundation Column
 2.5ft x 2.5ft x 2ft
 1ft is covered in soil.
Rebar Reinforcement
 Footing Top:
 Use 15 #6 Z-Bars
 Use 15 #6 X-Bars
 Footing Bottom:
 Use 15 #6 Z-Bars
 Use 15 #6 X-Bars
 Colum
 Use 12 #6 longitudinal Bar
 Use ties #4 transverse reinforcement
Foundation Rebar in AutoCAD
Baseplate Design
 Baseplate, always the first installed but the last to be designed
 Cases: Axial, Axial load plus Moment, and axial load plus shear
 Axial: Load is perpendicular to the plate and through the column centroid.
 Axial load plus moment: this kind of connection would be used at the base of moment
resistant frames where moment capacity is needed.
 Axial load plus shear: important when bracing is connected to the base of the column.
Baseplate Design Con’t
 The team’s design
 30” x 30” x ¾”
 Four 1”-dia holes
 Anchor rods: F1554-36 rods with
each using hairpins #4.
 Baseplate material: ASTM A36
 Layer of grout 1½”
Foundation and baseplate design
codes
 Base plate: AISC DG #1
 Anchorage: ACI 318-14 Ch. 17
 Concrete: ACI 318-14
Blade Design
 Part of the turbine
 Connected to the hub
 Consist of airfoils
 Turbine height: 8.5ft
 Turbine diameter: 7.5ft
 Swept area: 63.75𝑓𝑡 2
 Inclination angle: 47.27°
 Closed cell foam, fiberglass,
carbon fiber
Airfoils
 Shape of wing, blade, or sail
 Camber
 Angle of attack
 Tip Speed Ratio
 Power, Lift, Drag, Stall
 Coefficients
 Reynolds number
 Betz Limit
NACA 0015
 National Advisory Committee for Aeronautics (NACA)
 Aerodynamic center located at ¼ chord
 4 digit series airfoil
 Symmetrical
 SOLIDWORKS
 AutoCAD
 MATLAB
Double-Multiple Streamtube Model
with Interference Factor (DMSV)
 Analytical model of accurately testing design of helical Darrieus VAWTs
 Predicts rotor performance and aerodynamic forces on blades
 Upstream and downstream half-cycles
 Induced velocities
 Actuator Disk Theory
 MATLAB
 Ion Paraschioiu
DMSV Continued
DMSV Continued
 𝑉𝑢 = 𝑉𝑜 𝑎𝑢
 𝑉𝑑 = 𝑉𝑒 𝑎𝑑
 𝑉𝑒 = 𝑉𝑜 (2𝑎𝑢 − 1)
 𝐶𝑝 = 𝐶𝑝𝑑 + 𝐶𝑝𝑢
 𝑇(Θ) = 0.5𝜌𝑐𝑅𝐿𝑊 2 𝐶_𝑡
 𝑇𝑎𝑣𝑔 =
𝑁 π/2
𝑇(Θ)𝑑Θ
2π −π/2
 𝑃𝑜𝑤𝑒𝑟 = 𝑇𝜔
MATLAB Code (Small Portion)
Power and Torque Output
Blade Composition
 Made of closed cell foam, fiberglass, and carbon fiber
 Closed cell foam laser cut to the blade dimensions
 Closed cell foam is then coated with liquid fiberglass
 Carbon fiber is then placed over the closed cell foam and fiberglass
Hub
 Hollow cylinder
 4 inch diameter
 1 inch thick
 Material: A36 steel
 Material yield strength: 36,000 psi
 Equivalent stress from wind:
 𝜎𝐸 =
𝜎𝑏2
1
+
3𝜏 2 2
= 22,276.8 psi
Support Plates
 3 support plates
 Bottom, middle, and top of rotor
 2 inches wide connecting to the blades
 3/8 inches thick
 Material: Cast ASTM Ductile Iron
 Material yield strength: 45,000 psi
 Equivalent stress from wind:
 𝜎𝐸 =
𝜎𝑏2
1
+
3𝜏 2 2
= 32,404.1 psi
Coupling
 Rigid coupling
 Connects the rotor to the gear box
 30.5 inches in diameter
 Diameter of bolts using Goodman Method:

1
𝑁
=
𝜏𝑚
𝑠𝑠𝑢
+
𝐾𝑡 𝜏𝑎
𝑠′𝑠𝑛
 Minimum bolt diameter = 0.248 inches
 Chosen bolt diameter = 0.5 inches
Brake System
 Centrifugal clutch connected to
output shaft of the gear box
 Engages at 25 mph (2800 prm)
 Engagement depends on spring
selection
 Engages when centrifugal force is
greater than spring force
 Clutch radius: 0.0425 m
 Spider radius: 0.0375 m
 Calculated centrifugal force:
 𝐹𝑐 = m ∗ 𝜔2 ∗ 𝑟 = 225.7 N
 Calculated spring force:
 𝐹𝑠 = 𝑚 ∗ 𝜔12 ∗ 𝑟 = 126.9 N
 Net outward radial force:
 𝐹 = 𝐹𝑐 − 𝐹𝑠 = 98.7 N
Power Transmission
 Consists of a single gearbox with multi-stage gear train.
 3 stages each with a gear ratio of 1:3.133
 12mph wind speed translates to 93rpm input and 2800rpm output
 Gear designed for 35mph wind speeds
 2 main cause of failure in gear teeth
 Bending stress
 Contact stress
Modified Lewis Bending Equation &
Modified Contact Stress Equation
𝜎
𝑊𝑡 ∗ 𝑃𝑑
𝑏= 𝐹∗𝐽 ∗ 𝐾𝑜 ∗𝐾𝑠 ∗𝐾𝑏 ∗𝐾𝑚 ∗𝐾𝑣 ∗𝐾𝑖
 Determines the allowable bending stress on the gear teeth.
𝜎𝑐 = 𝐶𝑝 ∗
𝑊𝑡 ∗ 𝑘𝑜 ∗𝑘𝑠 ∗𝑘𝑚 ∗𝑘𝑣 ∗𝑘𝑖
𝐹∗𝐷𝑝 ∗ 𝐼
 Determines the allowable contact stresses in the gear teeth.
Two most common causes of failure in spur gears.
 Values calculated must be adjusted by reliability, Safety, and cycle factors
Planetary Gear Train Specified Gear
Materials
 Computed Ring Stress
 88 ksi
 Material: AISI 3140 OQT 1300
 Ys = 94 ksi
 Computed Planet Stress
 131.6 ksi ksi
 Material: AISI 1137 OQT 400
 Ys = 136 ksi
 Computed Sun Stress
 264 ksi
 Material: AISI 4140 OQT400
 Ys = 270 ksi
Shaft Design
 Gearbox contains Input shaft, 3 stage shafts, and an output shaft to
generator
 Each shaft treated as a loaded beam
 Preliminary layout made with placement of gear force loads and bearing
reaction locations
 Bearing reaction forces calculated in both planes
 Summation of forces, summation of moments
 Shear force diagram and bending moment diagram created
Shaft diameter
 After each shaft Analyzed, minimum diameter could be computed at
each critical point
 Requires a combined stress approach using bending moment and torsional
shear
 Represented by the equation:
D =
32∗𝑁
𝜋
∗
𝐾𝑡 ∗𝑀 2
𝑆𝑛′
+
3 𝑇
4 𝑆𝑦
2
1
^3
Shaft Material Selection
• A preliminary material selection had to be made
• AISI 1144 OQT 400 Machined or cold drawn
• Sy = 83ksi Su = 118ksi Sn = 42ksi 19% elongation
Shaft diameter cont.
 Design factor of 3 used for possible uncertainty in design
 Adjusted Endurance strength of 27,216 psi
 𝑆𝑛′ = 𝑆𝑛 ∗ 𝐶𝑠 ∗ 𝐶𝑅 = 42,000psi * .75 * .81
 Size factor = .75
 Reliability factor = .81 for 99%
 Stress concentration factors 𝐾𝑡 used for key seats, fillets, and retaining rings
 1.5-2.5
Maximum Stress Computation
 To determine maximum stress due to torsion and bending along each shaft,
the following formulas used:
𝜏 =
𝑇∗𝑟
𝐽
𝜎𝑏 =
𝑀∗𝑦
𝐼
 Diameter calculated, max torque and bending moments used to
determine max stresses
 Compare the calculated values against adjusted endurance strength
to determine if pre-selected material makes a safe design.
 If unsafe, either adjust diameter and recalculate or pic stronger
material and recalculate diameter required.
Bearing Selection
 Using magnitude of reaction forces in each bearing with the minimum bore
diameter, bearings can be selected for each point on the shaft.
 𝑅𝐵 =
𝑅𝑥2 + 𝑅𝑦2
 6200 series single-row, deep-groove, Conrad-type ball bearings selected for use
in the shaft supports.
 Offer wide variety of diameter types and high dynamic load
handling capability
 6214 & 6217 chosen for design
 Can withstand 10,800 & 14,600 lb. dynamic loading
respectively, and are closest to required seat size.
Deliverables Achieved
 Tower design and calculations
 Foundation design and calculations
 Base plate design
 Blades designed in AutoCAD
 Airfoil calculations
 DMSV calculations
 Planetary gear material and calculations
 Gear box shaft dimensions and material determined
 Support bearing loads determined, bearings selected
 Rotor hub and support plates
 Brake system

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