Design of windmill power generation using multi generator and single rotor (horizontal blade)

Innovative Systems Design and Engineering www.iiste.org
ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online)
Vol 3, No 7, 2012

Design of Windmill Power Generation Using Multi-Generator and
Single Rotor (Horizontal Blade)
S. Siva Sakthi Velan
Department of Mechanical Engineering,

Mailam Engineering College, Mailam post, Tindivanam Taluk, Villupuram District, Tamilnadu state, India – 604304.
E-mail of the corresponding author: sivasakthivelan.s@gmail.com
Abstract
Wind energy is the environmental free and one of the best renewable energy for generation of electric power. The
main aim of the paper is “to produce current using multi generator and single rotor”. This paper proposes
multi-generator to address potential challenges: dimension, cost and reliability. The two permanent magnet D.C.
generators are desired to share the single shaft through straight bevel gears. These poles of the two generators will be
changed as alternate to parallel. This paper discussed about the design procedure of gears, gear life and wind turbine
rotors. The output current is stored in series of battery to appliances through converter and step up transformer. The
performances and practicalities of the proposed architecture are verified in simulation using prototype wind turbine.
Keywords: permanent magnet D.C. generator, wind turbine, straight bevel gear, poles of generator.

1. Introduction
The wind energy is an environment-friendly and efficient source of renewable energy. The kinetic energy of the wind
can be used to do work. This energy is harnessed by windmill in the past to do mechanical work. This is used for
water lifting pump and generating electricity. To generate the electricity, the rotary motion of the windmill is used to
turn the turbine of the electric generator. The output of single windmill is quite small and cannot be used for
commercial purposes. Therefore, a number of windmills are erected over a large area, which is known as wind
energy farm. The each and every windmill is coupled together to get a electricity for commercial purposes. The wind
speed should be higher than 15 Km/hr.

2. Literature review
The three-bladed rotor proliferates and typically has a separate front bearing, with low speed shaft connected to a
gearbox that provides an output speed suitable for the most popular four-pole (or two -pole) generators. This general
architecture commonly, with the largest wind turbines, the blade pitch will be varied continuously under active control
to regulate power in higher operational wind speeds. Support structures are most commonly tubular steel towers
tapering in some way, both in metal wall thickness and in diameter from tower base to tower top. Concrete towers,
concrete bases with steel upper sections and lattice towers, are also used but are much less prevalent. Tower height is
rather site specific and turbines are commonly available with three or more tower height options.

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Vol 3, No 7, 2012

3. Design of windmill

Figure 1. Experimental setup

The design is based on five steps as follows:
1. Design of wind turbine rotor; 2. Design of tower; 3. Yawn control; 4. Selection or Design of generator; 5. Design
of gear.

3.1 Design of wind turbine rotor
3.1.1 Selection of location
Place: Mailam Engineering College
Latitude: 12.1170; Longitude: 79.6150
Hub height: 20m; Wind speed: 4.8 ± 0.9
m/s
Min. & Max. Wind speed: 3.9 m/s; 5.7 m/s

Figure 2. Software calculations
Nomenclature for Windmill: PO = power contained in wind; ηE = efficiency of electrical generation; ηM = efficiency
of mechanical transmission; CP = power co-efficient; P = Required power output = 3600 W; V∞ = wind speed
velocity = 3.9 m/S; D = diameter of rotor; R = radius of rotor; a= axial interference factor; υ = Wind turbine velocity;
V2 = exit velocity of wind; ω = angular velocity of blade; v = n – bladed velocity; n = number of blades = 3 (assume);
N = speed of bladed rotor; θ = Angle separated between two blades; ta = Time taken by one blade move into the
position of preceding blade; TSR = tip speed rate; A = Area of blade; L = Length of blade; f = Width of blade; t =
Thickness of blade; H.R = Hub radius; V = Volume of blade; ρ = density of air = 1.225Kg/m3; A = area of rotor;
PMAX = Maximum exactable power; CF = Force coefficient; β = 1/3 (feasible) or 1 (constant); u = Aerofoil velocity; I
= Angle of inclination; (L/D) = Ratio of lift to drag; CL = Lift coefficient; CD = Drag co-efficient; Cmc/a =Moment co-
efficient; CDO = Profile drags co- efficient; i = Angle attack for infinite aspect ratio; w = relative velocity; Ab = Blade
area; FL = Lift force; FD = Drag force; ϵ = Eiffel polar; i = Angle attack for infinite aspect ratio; α = Pitch angle; PM =
power speed characteristic; CP = power co-efficient; CT = Torque co-efficient = CP / λ =0.1666; TM = Torque speed
characteristic; bP = width of profile = 0.106m; υ’ = kinematic viscosity; µ = absolute dynamic viscosity = 10-5 Pa =
10-5N/m2 (for air); µ = 8.16 x 10-6; ηa = aero dynamic efficiency

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Vol 3, No 7, 2012

3.1.2 Calculation of rotor diameter
Power, P = PO ηE ηM CP (1)
In the absence of above data we use fast or slow rotor formula as shown below
For slow rotor, P = 0.15 D2 V∞3 (2)
For fast rotor, P = 0.2 D2 V∞3 (3)
We use the fast rotor formula to calculate diameter
D = 17.42 m; R = 8.71m

3.1.3 Circumference, swept area of rotor
Circumference of rotor = π x D = 54.72m (4)
2 2
AS = π x R = 238.33m (5)

3.1.4 wind variation calculation
Axial interference factor, υ = V∞ (1 - a) (6)
2
= V∞ = 2.6 m/s (7)
3
a = 0.3333
V2 = 2υ - V∞ = 1.3 m/s (8)

3.1.5 Calculation of number of blades
Figure 2. windmill specification
ω 2π
≈ (9)
ν nD
ω = 0.3125 rad/sec
2πN
ω= (10)
60
N = 2.985 rpm

3.1.6 velocity of wind turbine rotor
πDN
V= = 2.723 m/s (11) Figure 3. wind transfer specification
60

3.1.7 Angle separated between two blades
360
θ= =1200 (12)
n

3.1.8 Time taken by one blade move into the position of preceding blade
2π
ta = = 6.7 sec (13)
nω

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Vol 3, No 7, 2012

.
3.1.9 Time taken for turbine disturbed by wind
D
tb = = 6.7 sec (14)
ν

3.1.10 Calculation of hub radius, Length of blade, thickness
of blade, width of blade
H.R = 0.14 x R = 1.22m; L = 0.86 x R = 7.49m; t = 0.2 x L =
1.50m; f = 0.1 x t = 0.15m

3.1.11 Area and Volume of blade
A = Lf = 1.1235 m2 (15)
3
V = Lft = 1.69 m (16) Figure 4. blade specification

3.1.12 Power contaminated in wind

3
ρAV∞
PO = (17)
2
A = π x R2 = 238.33 m2
P0 = 8659.37 W

3.1.13 Maximum exactable power
16
PMAX = PO = 5131.47 W (18)
27

3.1.14 Calculation of tip speed rate
V∞ × TSR × 60
revolutions (rpm) = (19)
6.28 × R
TSR = 7

blade tip speed
Tip speed rate = (20)
wind velocity
Blade tip speed = 27.23 m/s

3.1.15 Force coefficient

27 PMAX
CF = =2 (21)
8 Po

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Vol 3, No 7, 2012

3.1.16 Aerofoil velocity

u
=β (22)
V∞
u = 1.3

3.1.17 Angle of inclination
u
I = cot −1 = 63.40 (23)
ν

3.1.18 Power co-efficient

Power output from wind turbine
CP = ×100 (24)
power contaminated in wind
CP = 0.4142 x 100 = 41.42 ≈ 40%
From aerofoil data sheet National Advisory Committee of Aeronautics NACA 4412,
(L/D) = 20; CL = 1; CD = 0.20; Cmc/a = -0.08; CDO = 0.01; i = -2

3.1.19 Lift force
1
FL = ρAb w 2 C L (25)
2

w= u 2 + ν 2 = 2.91 m/s (26)
FL = 5.824 N

3.1.20 Drag force
1
FD = ρAb w 2 C D = 1.16 N (27)
2

3.1.21 Aerodynamic forces in aerofoil moving in direction of the
wind
where, FD = Drag force; FL = Lift force; u = Aerofoil velocity; V =
wind velocity

3.1.22 Tangent to the Eiffel polar Figure 5. Aerodynamic force in aerofoil

CD
Tan ∈= (28)
CL
ϵ = 21.80

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Vol 3, No 7, 2012

3.1.23 Calculation of pitch angle
α=I–i = 65.4 (29)

3.1.24 Calculation of specific rated capacity

power rating of the generator
SRC = = 7.553 (30)
rotor swept area
3.1.25 Calculation of power speed characteristic

ρC P πR 2 V∞ 3
PM = = 3593.57 W (31)
2

3.1.26 Torque speed characteristic
PM 1
or TM = ρCT πR V∞ = 12570.51N-m
3 3
TM = (32)
ω 2

3.1.27 Calculation of Reynolds number

V∞ b p
RE = (33)
ν'

µ
υ’ = (34)
ρ
RE = 2.1 x 105

3.1.28 Calculation of aero dynamic efficiency

1- (Tan ∈ Cot I)
ηA = ×100 = 44.45% (35)
1+ (Tan ∈ Tan I )

Table 1. Tower height selection
3.2. Design of Tower
Power Tower height
From the table 1, required power is 3.6KW. So, we taken as 20m
Upto 100 KW Upto 30m
100 - 300 KW 30 - 35m
3.3. Yaw control
300 - 500 KW 35 - 40m
The yaw control mechanism is used to control the speed of rotor. when
fan tail is placed perpendicular to the main turbine. so that the thrust force Above 500 KW Above 40m

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Vol 3, No 7, 2012

automatically pushes the turbine in the direction of wind.

3.4. Design or Selection of Generator
If the required power of different generators are present in market at low speed, we used that generator to make a
gear design. Until, we design the gear to design the generator. The selected generator is Permanent Magnet D.C.
Generator and required power is 3600W present in market at low speed of 480rpm and model name is GL – PMG –
1800. Specification is given below:

Figure 6. Specification of D.C. generator

3.5. Design of gear
3.5.1 Gear name: Straight Bevel Gear.
(NOTE: From PSG data book pg. no: 8.38, 8.39, 1.40, 8.53, 8.18, 8.51, 8.15, 8.17, 8.14, 8.16, 8.13, 8.13A)

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Vol 3, No 7, 2012

Figure 7. Specification of straight bevel gear Figure 8. Yawn control

Nomenclature for Gears: N2 = driver gear speed (Turbine speed = 2.985 rpm); N1 = driven gear speed = 480rpm; i =
Transmission ratio; Z1 = No. of teeth in driven gear ≥ 7 = 7; Z2 = No. of teeth in driver gear; δ2 = Pitch angle of driver
gear; δ1 = Pitch angle of driven gear; ZV1 = Virtual number of teeth of driven gear; ZV2 = Virtual number of teeth of
driver gear; P = Rated power = 3600 W; KO = Correction factor, 2 (assume high shock); V = Velocity of driven gear;
FT = tangential load on tooth; d1 = diameter of driven gear, (MT x Z1) millimeter; MT = transverse module; FD =
dynamic load; CV = velocity factor; b = face width = 10 MT; σB = bending stress for alloy steel 126 N/mm2; R = cone
distance; y' = lewis form factor; C = errors in action; e = Errors of tooth profile; V = mean velocity; Q' = Ratio factor;
Kw = Wear factor; n = speed of driven gear; T = life time in hrs; N = Life time in cycles; , Mτ = nominal twisting
moment transmitted by driven gear; Kd = dynamic load factor; K = load concentration factor; KBL = life factor for
bending; σ-1 = endurance limit stress in bending (σU + σY) + 120; σU = ultimate tensile stress = 700 N/mm2; σY =
yield stress = 360 N/mm2; n = factor of safety = 2; kσ = fillet stress concentration of factor = 1.2; CR = coefficient
depending on the surface hardness, 22; HRC = brinell or rockwel hardness number, 55 – 63 ≈ 59; KCL = life factor, 1;
ψY = 1; Eeq = Equivalent young’s modulus; [σC] = Compressive stress; MT = nominal twisting moment transmitted by
driven gear; Kd = dynamic load factor = 1.2; K = load concentration factor = 1.02.

3.5.2 Calculation of transmission ratio

N1
i= = 160.80 ≈ 161 (36)
N2 `

3.5.3 Calculation of number of teeth
Z2 = i Z1 = 1127 (37)

3.5.4 Material
For pinion: C 45 (Forged steel, Case hardened)
Allowable static stress σB = 126 N/mm2; Compersible static stress σC = 1150 N/mm2; Tensile strength σU = 700
N/mm2; Yield point stress σy = 360 N/mm2; BHN = 229
For wheel: Case steel graded

3.5.5 Calculation of pitch angles and virtual number of teeth
Pitch angles, δ2 = Tan-1 i = 89.640 (38)
0 0
δ1 = 90 - δ2 = 0.356 (39)

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Vol 3, No 7, 2012

Z1
Virtual number of teeth, ZV 1 = =7 (40)
Cosδ1

Z2
ZV 2 = = 179368.8 ≈ 179369 (41)
Cosδ 2

3.5.6 Calculation of tangential load on tooth (FT)
P
FT = 譑 O (42)
V
π譫 I 譫 1
V= (43)
60
V = 0.1759 MT m/s.

40925.557
FT = N
MT

3.5.7 Calculation of dynamic load (FD)

FT
FD = (44)
CV

5.6
CV = (45)
5.6 + V
Where, V = velocity, 5m/s (assume)

57238.541
CV = 0.715; FT = N → (1)
MT

3.5.8 Calculation of beam strength (FS)
(R - b)
FS = πM T bσ B y' (46)
R
0.912
y ' = 0.154 − (47)
Z v1
y’ = 0.1084 [for 200 involute]

R= 0.5 譓 T 譓 2
1 + Z2 = 563.511 MT
2 (48)

FS = 421.476 MT2 → (2)

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Vol 3, No 7, 2012

3.5.9 Calculation of transverse module
From (1) and (2), FS ≥ FT
MT ≥ 4.59 mm ≈ 5 mm

3.5.10 Calculation of b, V, d
Face width, b = 10 MT = 50 mm = 0.05 m (49)
Reference diameter, d1 = MT x Z1 = 35 mm = 0.035 m (50)
d2 = MT x Z2 = 5635 mm = 5.635 m (51)
π譫 I 譫 1
Velocity, V= = 0.879 m/s (52)
60

3.5.11 Revision of beam strength
(R - b)
FS = πM T bσ B y' (53)
R
R = 563.511 MT = 2817.555 mm = 2.8176 m
FS = 10536.9 N

3.5.12 Calculation of accurate dynamic load

21V(bC + FT )
FD = FT + (54)
21V + (bC + FT )
C = 8150 e; e = 0.022; C = 179.3 mm (55)
P
FT = = 4.09556 N (in mm) (56)
V
FD = 8927.4 N → (4)

3.5.13 Check the beam strength
From (3) and (4), FD ≤ FS; So, design is safe and satisfactory.

3.5.14 Calculation of maximum wear load

0.75d1bQ'(K W )
FW = (57)
Cosδ1

2ZV2
Q' = = 1.980 (58)
ZV1 + ZV2
Kw = 0.919 N/mm2; FW = 2388.297 N → (5)

3.5.15 Check for beam strength
From (5) and (4), FD ≤ FW

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Vol 3, No 7, 2012

So, design is safe and satisfactory.

3.5.16 Gear life
Life time: 10, 00, 000 hrs (assume)
N = 60n T = 2.88 x 1010 cycles (59)

3.5.17 Calculation of twisting moment
[Mτ] = Mτ x K x Kd (60)
WhereK. Kd = 1.3

P? 0
MT = = 71.61972 N-m (61)
2πN1
[Mτ] = 93.105 N-m

3.5.18 Calculation of Eeq, [σB], [σC]
Equivalent young’s modulus Eeq = 2.15 x 105 N/mm2

K BL σ -1
Bending stress [σ B ] = (62)
nK σ
σ-1 = 0.22 (σU + σY) + 120 = 353.2 N/mm2 (63)
2
bending stress [σB] = 103.01 N/mm
Compressive stress, [σC] = CR x HRC x KCL = 1122 N/mm2 (64)

3.5.19 Calculation of cone distance
2
E eq M T  0.72 
R ≥ ψY 2
(i +1) 3 ×  (65)
i  (ψ Y - 0.53)[σ C ] 
R ≥ 0.5688
3.5.20 Revision of center distance

R = cone distance = 0.5 譓 T 譓 2
1 + Z2 = 563.51 mm
2 (66)

Design is satisfactory

3.5.21 Calculation of ψY
ψY = b/d1 = 1.428 (67)

3.5.22 Select the suitable quality
The preferred quality is 10 or 12.
IS quality is coarse.

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Vol 3, No 7, 2012

3.5.23 Revision of design torque
[Mτ] = Mτ x K x Kd = 87.6 N-mm (68)

3.5.24.Calculation of revision of bending stress

R i 2 + 1[ M T ]
σB = (69)
( R − 0.5b) 2 bM T YV 1
Where, YV1 = 0.389
σB = 0.0455 N/mm2

3.5.25 Check for bending
σB ≤ [σB]; Therefore, design is safe and satisfactory

3.5.26 Calculation of revision of wear strength
1

σC =
0.72 
 (i 2
+ 1)
3 2
Eeq [ M T ] = 132.1 N/mm2 (70)
R − 0.5b  ib 
 

3.5.27 Check for wear strength
σC ≤ [σC]; Therefore, design is safe and satisfactory

3.5.28 Basic calculations

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Vol 3, No 7, 2012

Transverse module, MT = 5 mm Whole depth: h = 1.2 MT = 1.2 mm
No. of teeth, Z1 = 7; Z2 = 1127 Middle circle diameter:
Cone distance, R = 563.51 mm dm1 = d1 - b sin δ1 = 10.05 mm
Face width, b = 50 mm dm2 = d2 - b Cos δ2 = 100.05 mm
0 0
Pitch angle, δ1 = 0.356 ; δ2 = 89.64 Addendum: ha1 = ha2 = MT = 1 mm
Reference diameter, d1 = MT x Z1 = 35 mm Dedendum: hf1 = hf2 = 1.2 MT = 1.2 mm
d2 = MT x Z2 = 5635 mm Face angle:
Tip diameter, da1 = MT (Z1 + Cos δ1) = 20.995 mm δa1 = δ1 + θa1 = 6.2810
da2 = MT (Z2 + Cos δ2) = δa2 = δ2 + θa2 = 71.630
200.099 mm Back cone distance:
Height factor, f0 = 1 Ra1 = R tan δ1 = 10.05 mm
M Tf0 Ra2 = R tan δ2 = 1005.1 mm
Addendum angle, T anθ a1 = T anθ a2 =
R Middle module: Mm = dm1 / Z1 = 0.5025 mm
θa1 = θa2 = 0.57 0 Crown height:
M T (f 0 + C ) Ch1 = (d2 / 2) – (MT sin δ1) = 99.9 mm
Dedendum angle, T an θ f1 = T an θ f2 =
R
Ch1 = (d1 / 2) – (MT sin δ2) = 9.0 mm
θf1= θf2 = 0.01190
Shift angle: ∑ = δ1 + δ2 = 900
4. Conclusions
This paper presents a new methodology for power generation using two same generators of single rotor, further
advantage of the method is cost efficient and generating high power with a same torque. Theoretical analysis and
experimental work is carried out confirm validity of the analytical work.

5. References
S. N. Bhadra, D. kastha, S. Banerjee (2005), wind electrical system, New Delhi: oxford university press, ISBN – 13:
978-0-19-567093-6; ISBN – 10: 0-19-567093-0.
Faculty of mechanical engineering (2011), design data book of engineering, Coimbatore: kalaikathir achagam page
no.: 1.40, 8.1 – 8.53.
Fujin Deng, Zhe Chen (2010), wind turbine based on multiple generators drive-train configuration,
E-ISBN: 978-1-4244-8509-3, Print ISBN: 978-1-4244-8508-6 page no.: 1- 8.
Shigley J. E., Mischke. C.R., Mechanical Engineering Design, Sixth Edition, Tata Mcgraw – Hill, 2003.
Ugural A. C., Mechanical Design An Integrated Approach, Mcraw – Hill, 2003.
Bhandari. V. B., Design of Machine Elements, Tata Mcgraw – Hill Publishing Company Ltd., 1994.

51

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