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Effect of Geometrical Imperfections of Gears in Large Offshore Wind Turbine Gear Trains: 0.6–10 MW Case
Studies Amir Rasekhi Nejad Torgeir Moan IMT, CeSOS, NTNU Trondheim, Norway
CeSOS, NTNU Trondheim, Norway
[email protected] [email protected] EWEA 2012, Copenhagen, Denmark
Keywords: Gear geometrical imperfections, large wind turbine gear trains, offshore drivetrains
Abstract Current wind turbine gear design standards,
such as ISO/IEC 61400-4 [1] and ANSI/AGMA/ AWEA 6006-A03 [2] cover turbines with capacity up to 2 MW. According to these design codes, gear geometrical tolerances shall be taken from ISO 1328-1 & 2 [3,4] where gear quality is classified in grades. For instance based on AWEA wind turbine design code [2], the maximum quality grade for carburized external gears shall not be more than 6 in ISO 1328-1 [3] ranking level. However, in absence of design guidelines for above 2 MW turbines, selecting right gear quality grade is a challenge for designers.
In this paper, the effect of gear geometrical variation in large wind turbines is investigated. In general gear geometrical imperfections are classified in two groups of assembly dependent and assembly independent variations. They influence gear load sharing, vibration, contact pattern, contact stress and finally reaction loads imposed on bearings. Both two groups of variations are considered in this study and their effect on contact stress, vibration and bearing load variation is evaluated through case studies of 0.6 to 10 MW. The outcome presents the effect of gear quality changes in large wind turbine gear trains and sensitivity to each category of imperfection.
1. Introduction Wind is taking the industry further offshore and
deeper water exposing wind turbine machineries to extreme loads and higher design uncertainties. Without doubt, current challenges with land based and fixed offshore wind turbines needs to be well understood in order to limit uncertainties for future floating fleets. Particularly for large multi mega watts offshore wind turbines as blade diameter increases, the rotational speed decreases, thus, drive trains with higher ratio are needed.
In this paper, the effect of gear geometrical quality in large wind turbines is investigated. Manufacturing deviations create nonlinearity in the dynamic behaviour of the gears as indicated by gear researchers [5,6,7]. According to Musial W. et al [8] some common issues have been observed in wind turbine drivetrain failures: “most of the problems with the current fleet of wind turbine
gearboxes are generic in nature, meaning that the problems are not specific to a single gear manufacturer or turbine model. Most gearbox failures do not begin as gear failures or gear-tooth design deficiencies”. One of possible failure reasons highlighted by Musial W. et al [8] is that the transfer of loads from gears and bearings to shafts is occurring in non-linear or unpredicted manner meaning that observed experimental loads are higher than expected values obtained from simulations.
Although research works directly addressing gear trains in wind turbines, to the author’s best knowledge, are rather limited [9-11], nonlinear dynamic behaviour of gear trains has been studied for both spur and helical gears and manufacturing imperfections are claimed to be important players in this nonlinear performance [12-17].
Wind turbine geometrical manufacturing imperfections of gears can be classified in four general categories: Tooth profile deviations (assembly
independent) Misalignment (assembly dependent) Backlash (assembly dependent) Mesh phasing (assembly dependent)
The influence of each category is investigated in reference [18] but in the current study, first two groups are assessed.
2. Study method & case studies There are well established standard
calculation methods for gear contact stress, transmission error and bearing reaction specified in design codes like ISO 6336 [19] which are reflected in gear design tools. In this paper, imperfection effects are investigated through study of gear trains in various sizes by means of design and analysis software, KISSsoft [20]. The gear parameters are calculated by this program in rated wind speed.
In accordance with ANSI/AGMA/AWEA 6006-A03 [2] the gear quality shall follow grading level listed in table 1 in which the higher grade number means the larger tolerances and lower quality. Gear quality grade limits gear tooth tolerances including profile deviations which are assembly independent. There are other manufacturing limits
like axial misalignment that are not dictated by the gear quality grade.
Table 1: required gear accuracy [2]
Gear type Heat treatment Max. Accuracy per
ISO 1328-1 External Carburized 6 Internal Carburized 7
Internal Nitrided 7 (with 8 for runout
and total cumulative pitch deviation)
Internal Through hardened
8
In this study both groups are considered by
case studies listed in table 2 and 3. Gear quality investigation is carried through R1 and C1 cases. R1 reflects the lowest permitted quality in accordance with wind turbine design codes [1,2] while gears in C1 are one grade lower than permissible level. It is worthwhile to indicate that lower quality than C1 case is not possible because the tooth thickness tolerances are out of the acceptable standard range.
Table 2: Assembly independent study cases
Case # Gear quality grade
(ISO1328-1) Wind speed
External Internal R1 6 7 Rated C1 7 8 Rated Case R2 and C2 in table 3 cover the axial
misalignment – shown in Fig. 1 – which is an assembly dependent parameter. The misalignment values selected for C2 and R2 cases are based on experimental observations [11] and standard values of total helix deviations [3]. The axial misalignment is then applied only on planets as the floating sun concept is assumed for all case studies.
Fig. 1: Axial misalignment
Table 3: Assembly dependent study cases
Case #
Axial misalignment ( f ) Wind speed
R2 50 Rated C2 200 Rated
It is known that gear geometrical imperfections
influence contact and root stresses, contact pattern, support reactions and vibration throughout the system. Therefore in order to capture their effects, following parameters are calculated for each case:
Bearing reactions: by measuring planet bearing force
Vibration: by measuring transmission error (TE)
Contact stress : by measuring contact stress along line of action
Variation of force along the face width: by
measuring HK ; face load factor
Bearing reaction varies in each gear rotation cycle. Geometrical imperfections influence load distribution on the bearing which is captured by
recording the reaction and HK in each case study.
Transmission Error (TE) is another important factor which is affected by the manufacturing imperfections. Transmission error is the single most important factor in the generation of gear vibration and is defined as “the difference between the actual position of the output gear and the position it would occupy if the gear were perfectly conjugate” [21]. Transmission error is the combination of gear pitch, profile and helix errors together with tooth bending, gear body deformation and support deflections which give an overall relative deflection at the meshing point between the gears and the deviation from the true involute profile. The mean value of TE is not important in vibration generation as it is due to elastic tooth deflection but the varying part is causing the oscillating acceleration and vibration through the system.
Contact stress is also measured for each case through the line of action for planet in the middle section of face width.
The design concept of case studies covers high ratio gear trains suitable for high speed generators with specification listed in table 4 and 5. Besides that, since scope of this study is limited to the gear quality, shaft and gear train support deflections are excluded.
Table 4: Rotor speed and generated power
of study cases (rpm/MW) Capacity(MW) Cut in Rated
0.6 12/0.05 24/0.6 2 9/0.18 15/2 5 7/0.35 12/5
10 5/0.70 12/10
Table 5: Gear trains of study cases Capacity (MW)
1st
stage 2nd
stage 3rd
stage 4th
stage
0.6 Type P H H Ratio 1:4.07 1:4.00 1:3.77
2 Type P P H Ratio 1:4.03 1:5.06 1:5.09
5 Type P P P H Ratio 1:4.00 1:4.00 1:4.00 1:1.95
10 Type P P P H Ratio 1:4.00 1:4.00 1:4.00 1:1.97
P: Planetary, H: Parallel Helical
2.1. 0.6 MW case study Fig. 2 presents the schematic of a 0.6 MW
model consisting of one planetary and two helical stages.
Fig. 2: 0.6 MW, 3 stage gear train
In Fig. 3 planet bearing, contact stress and TE
for cases R1 and C1 is presented. The noticeable observation is the increase of TE for gear quality of 7.
-10 -5 0 5 10 15 207.5
8
8.5
9
9.5x 10
4 Bearing Force (N)
Pla
net,
1st s
tag
e
-10 -5 0 5 10 15 20 257
7.5
8
8.5x 10
4
Gea
r, 2
nd
sta
ge
-10 -5 0 5 10 15 20 252.8
3
3.2
3.4
3.6x 10
4
Rotation Angle(degree)
Gea
r, 3
rd s
tage
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 3-1: 0.6 MW, effect of gear quality on bearing
force
-10 -8 -6 -4 -2 0 2 40
500
1000
1500Contact Stress (Mpa)
1st
sta
ge
-20 -15 -10 -5 0 5 10 15600
800
1000
1200
1400
2nd
sta
ge
-20 -15 -10 -5 0 5 10400
600
800
1000
1200
1400
Rotation Angle(degree)
3rd
stag
e
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 3-2: 0.6 MW, effect of gear quality on contact
stress
-10 -5 0 5 10 15 20-230
-225
-220
-215
-210
-205Transmission Error (micron)
Sun
/Pla
net
TE
1st
sta
ge
-10 -5 0 5 10 15 20 25-220
-218
-216
-214
-212
-210
Pin
ion/
Gea
r T
E 2
nd s
tag
e
-10 -5 0 5 10 15 20 25-180
-175
-170
-165
Rotation Angle(degree)
Pin
ion/
Ge
ar T
E 3
rd s
tag
e
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 3-3: 0.6 MW, effect of gear quality on TE
In this case as it shown in above figures, the
effect of gear quality is limited to TE variation. The misalignment effect (R2 and C2 cases) is shown in
Fig. 4-1 to 4-3 with HK in table 6.
Table 6: 0.6 MW, HK
CASE # 1st stage 2nd stage 3rd stageR2 1.42 1.34 1.51 C2 2.56 2.29 2.83
-10 -5 0 5 10 15 206
6.5
7
7.5
8
8.5x 10
4 Bearing Force (N)
Pla
net
, 1
st s
tag
e
-10 -5 0 5 10 15 20 258
8.5
9
9.5
10
10.5x 10
4
Gea
r, 2
nd
sta
ge
-10 -5 0 5 10 15 20 253.5
4
4.5
5x 10
4
Rotation Angle(degree)
Gea
r, 3
rd s
tage
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 4-1: 0.6 MW, effect of gear misalignment on
bearing force
-10 -8 -6 -4 -2 0 2 40
500
1000
1500Contact Stress (Mpa)
1st
sta
ge
-20 -15 -10 -5 0 5 10 150
500
1000
1500
2nd
sta
ge
-20 -15 -10 -5 0 5 100
500
1000
1500
Rotation Angle(degree)
3rd
stag
e
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 4-2: 0.6 MW, effect of gear misalignment on
contact stress
-10 -5 0 5 10 15 20-230
-220
-210
-200
-190Transmission Error (micron)
Sun
/Pla
net
TE
1st
sta
ge
-10 -5 0 5 10 15 20 25-230
-220
-210
-200
-190
Pin
ion/
Gea
r T
E 2
nd s
tage
-10 -5 0 5 10 15 20 25-180
-170
-160
-150
-140
-130
Rotation Angle(degree)
Pin
ion/
Ge
ar T
E 3
rd s
tage
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 4-3: 0.6 MW, effect of gear misalignment on TE
Misalignment of 200 m appears too large for
this gear train as the face load distribution factor is too high. Because of large face load factor, the load is not distributed equally along the face. Thus, the bearing force and contact stress obtained from middle of the gear is less than the 50 m case.
2.2. 2 MW case study
The 2 MW gear train includes two planetary stages and one parallel helical as shown in Fig. 5.
Fig. 5: 2 MW, 3 stage gear train
-10 -5 0 5 10 15 201.9
2
2.1
2.2
2.3x 10
5 Bearing Force (N)
Pla
ne
t, 1
st s
tag
e
-10 -5 0 5 10 15 207.5
8
8.5
9
9.5x 10
4
Pla
net,
2nd
stag
e
-10 -5 0 5 10 15 20 256
6.5
7
7.5x 10
4
Rotation Angle(degree)
Gea
r, 3
rd s
tage
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 6-1: 2 MW, effect of gear quality on bearing
force
-14 -12 -10 -8 -6 -4 -2 0 2 4400
600
800
1000
1200Contact Stress (Mpa)
1st
sta
ge
-10 -5 0 50
500
1000
1500
2nd
sta
ge
-15 -10 -5 0 5 10 150
500
1000
1500
Rotation Angle(degree)
3rd
sta
ge
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 6-2: 2 MW, effect of gear quality on contact
stress
-10 -5 0 5 10 15 20-250
-245
-240
-235
-230
-225Transmission Error (micron)
Sun
/Pla
net
TE
1st
sta
ge
-10 -5 0 5 10 15 20-206
-204
-202
-200
-198
-196
Sun
/Pla
net
TE
2n
d st
age
-10 -5 0 5 10 15 20 25-275
-270
-265
-260
-255
-250
Rotation Angle(degree)
Pin
ion/
Ge
ar T
E 3
rd s
tag
e
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 6-3: 2 MW, effect of gear quality on TE
Fig.6 presents the effect of gear quality and
Fig. 7 the misalignment influence.
-10 -5 0 5 10 15 201.4
1.6
1.8
2
2.2x 10
5 Bearing Force (N)
Pla
net,
1st
sta
ge
-10 -5 0 5 10 15 205
6
7
8x 10
4
Pla
net,
2nd
stag
e
-10 -5 0 5 10 15 20 256
7
8
9
10x 10
4
Rotation Angle(degree)
Gea
r, 3
rd s
tage
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 7-1: 2 MW, effect of gear misalignment on
bearing force
-14 -12 -10 -8 -6 -4 -2 0 2 40
500
1000
1500Contact Stress (Mpa)
1st
sta
ge
-10 -5 0 50
500
1000
1500
2nd
sta
ge
-15 -10 -5 0 5 100
500
1000
1500
Rotation Angle(degree)
3rd
sta
ge
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 7-2: 2 MW, effect of gear misalignment on
contact stress
-10 -5 0 5 10 15 20-260
-240
-220
-200Transmission Error (micron)
Sun
/Pla
net
TE
1st
sta
ge
-10 -5 0 5 10 15 20-210
-200
-190
-180
-170
-160
Pin
ion/
Gea
r T
E 2
nd s
tag
e
-10 -5 0 5 10 15 20 25-280
-270
-260
-250
-240
-230
Rotation Angle(degree)
Pin
ion/
Ge
ar T
E 3
rd s
tag
e
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 7-3: 2 MW, effect of gear misalignment on TE
Table 7: 2 MW, HK
CASE # 1st stage 2nd stage 3rd stageR2 1.30 1.52 1.35 C2 2.19 2.86 2.34
The change of gear quality does not have a
considerable impact on measured parameters shown in fig. 6, while changes in planet axial misalignment has increased TE variation, causing loss of contact. The effect of misalignment appears to be not the same for each stage. The first stage is less sensitive to the misalignment than others. The load reduction observed in bearing reactions, confirms the unequal load distribution along the face width.
2.3. 5 MW case study
The 5 MW example gear train consists of three planetary stages (Fig. 8) and one helical stage.
Fig. 8: 5 MW, 4 stage gear train
-5 0 5 10 15 203
3.5
4x 10
5 Bearing Force (N)
Pla
net,
1st s
tag
e
-10 -5 0 5 10 15 201.4
1.5
1.6
1.7x 10
5
Pla
net
, 2n
d st
age
-10 -5 0 5 10 15 206
6.5
7x 10
4
Pla
net,
3rd
stag
e
-6 -4 -2 0 2 4 6 8 10 12 145.5
6
6.5x 10
4
Rotation Angle(degree)
Gea
r, 4
th s
tage
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 9-1: 5 MW, effect of gear quality on bearing
force
-12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500Contact Stress (Mpa)
1st
sta
ge
-14 -12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
2nd
sta
ge
-12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
3rd
sta
ge
-10 -8 -6 -4 -2 0 2 4 6 8400
600
800
1000
Rotation Angle(degree)
Gea
r, 4
th s
tage
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 9-2: 5 MW, effect of gear quality on contact
stress
-5 0 5 10 15 20-330
-320
-310
-300Transmission Error (micron)
S/P
TE
1st
sta
ge
-10 -5 0 5 10 15 20-250
-240
-230
-220
S/P
TE
2nd
sta
ge
-10 -5 0 5 10 15 20-210
-205
-200
S/P
TE
3rd
sta
ge
-6 -4 -2 0 2 4 6 8 10 12 14-240
-235
-230
-225
Rotation Angle(degree)
TE
4th
sta
ge
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 9-3: 5 MW, effect of gear quality on TE
Table 8: 5 MW, HK
CASE # 1st stage 2nd stage 3rd stage 4th
stage R2 1.14 1.19 1.52 1.38 C2 1.78 2.04 2.85 2.44
-5 0 5 10 15 202.5
3
3.5
4x 10
5 Bearing Force (N)
Pla
net,
1st s
tag
e
-10 -5 0 5 10 15 201
1.2
1.4
1.6x 10
5
Pla
net
, 2n
d st
age
-10 -5 0 5 10 15 204
5
6
7x 10
4
Pla
net,
3rd
stag
e
-6 -4 -2 0 2 4 6 8 10 12 146
7
8x 10
4
Rotation Angle(degree)
Gea
r, 4
th s
tage
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 10-1: 5 MW, effect of gear misalignment on
bearing force
-10 -8 -6 -4 -2 0 2 4 60
500
1000
1500Contact Stress (Mpa)
1st
stag
e
-14 -12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
2nd
sta
ge
-12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
3rd
stag
e
-10 -8 -6 -4 -2 0 2 4 6 80
500
1000
Rotation Angle(degree)
4th
sta
ge
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 10-2: 5 MW, effect of gear misalignment on
contact stress
-5 0 5 10 15 20-340
-320
-300
-280Transmission Error (micron)
S/P
TE
1st
sta
ge
-10 -5 0 5 10 15 20-260
-240
-220
-200
S/P
TE
2nd
sta
ge
-10 -5 0 5 10 15 20-220
-200
-180
-160
S/P
TE
3rd
sta
ge
-6 -4 -2 0 2 4 6 8 10 12 14-240
-230
-220
-210
Rotation Angle(degree)
TE
4th
sta
ge
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 10-3: 5 MW, effect of gear misalignment on TE According to figures 9-1 to 9-3, low gear
quality of 7 has minor influence on the bearing reaction, vibration and planet contact stress for 5 MW gear train. In axial misalignment cases, the 1st and 2nd stage accept more misalignment than the last two stages. Table 8 shows a decline in face load factor comparative with the 0.6 and 2 MW gear trains.
2.4. 10 MW case study
The 10 MW gear train includes three stage planetary with one stage parallel helical gear as illustrated in Fig. 11. The overall gear ratio of this gear train is 1:126 which is suitable for high speed generators.
Fig. 11: 10 MW, 4 stage gear train
-10 -5 0 5 10 15 205.5
6
6.5
7x 10
5 Bearing Force (N)
Pla
net,
1st s
tag
e
-10 -5 0 5 10 15 202.2
2.4
2.6
2.8x 10
5
Pla
net
, 2n
d st
age
-10 -5 0 5 10 15 208
9
10
11x 10
4
Pla
net,
3rd
stag
e
-5 0 5 10 15 209
9.5
10
10.5x 10
4
Rotation Angle(degree)
Gea
r, 4
th s
tage
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 12-1: 10 MW, effect of gear quality on bearing
force
-12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500Contact Stress (Mpa)
1st
sta
ge
-14 -12 -10 -8 -6 -4 -2 0 2 40
500
1000
1500
2nd
stag
e
-14 -12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
3rd
stag
e
-12 -10 -8 -6 -4 -2 0 2 4 6 80
500
1000
1500
Rotation Angle(degree)
Gea
r, 4
th s
tage
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 12-2: 10 MW, effect of gear quality on contact
stress
-10 -5 0 5 10 15 20-325
-320
-315
-310Transmission Error (micron)
S/P
TE
1st
sta
ge
-10 -5 0 5 10 15 20-295
-290
-285
-280
S/P
TE
2nd
sta
ge
-10 -5 0 5 10 15 20-215
-210
-205
-200
S/P
TE
3rd
sta
ge
-5 0 5 10 15 20-280
-270
-260
-250
-240
Rotation Angle(degree)
TE
4th
sta
ge
Blue: Gear Quality Grade 6Green: Gear Quality Grade 7
Fig. 12-3: 10 MW, effect of gear quality on TE
Table 9: 10 MW, HK
CASE # 1st stage 2nd stage 3rd stage 4th
stage R2 1.20 1.30 1.46 1.27 C2 1.78 2.19 2.70 2.07
-10 -5 0 5 10 15 204
5
6
7x 10
5 Bearing Force (N)
Pla
net,
1st
stag
e
-10 -5 0 5 10 15 201.5
2
2.5
3x 10
5
Pla
net,
2nd
sta
ge
-10 -5 0 5 10 15 206
8
10x 10
4
Pla
net,
3rd
stag
e
-5 0 5 10 15 200.8
1
1.2
1.4x 10
5
Rotation Angle(degree)
Gea
r, 4
th s
tage
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 13-1: 10 MW, effect of gear misalignment on
bearing force
-12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500Contact Stress (Mpa)
1st
sta
ge
-14 -12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
2nd
sta
ge
-14 -12 -10 -8 -6 -4 -2 0 2 4 60
500
1000
1500
3rd
sta
ge
-12 -10 -8 -6 -4 -2 0 2 4 6 80
500
1000
1500
Rotation Angle(degree)
4th
stag
e
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 13-2: 10 MW, effect of gear misalignment on
contact stress
-10 -5 0 5 10 15 20-330
-320
-310
-300Transmission Error (micron)
S/P
TE
1st
sta
ge
-10 -5 0 5 10 15 20-300
-290
-280
-270
S/P
TE
2nd
sta
ge
-10 -5 0 5 10 15 20-220
-200
-180
S/P
TE
3rd
sta
ge
-5 0 5 10 15 20-280
-260
-240
-220
Rotation Angle(degree)
TE
4th
sta
ge
Blue: misalignment 50 micronGreen: misalignment 200 micron
Fig. 13-3: 10 MW, effect of gear misalignment on TE From Fig. 12 it is observed that change of gear
quality, does not affect the 10 MW gear train considerably. Similar to 5 MW case, 1st and 2nd stages are less sensitive to the misalignment shown in Fig. 13.
3. Comparison In above case studies, planet bearing force, transmission error, face load factor and contact stress were measured for two groups of gear grades and axial misalignment. In Fig. 14 and 15, the mean value of these parameters among the stages are drawn and compared. For bearing force, relative maximum variations are considered in comparison while for TE, standard deviations are compared. In contact stress, the maximum values are considered.
From Fig. 14 and 15 it is observed that misalignment holds stronger influence than gear quality on gear load sharing, vibration and contact stress variation. As the gear train capacity goes
higher to 10 MW, the face load factor ( HK )
declines, but it still remains in the range above 2 for 200 m misalignment which is not an
acceptable value. The same trend is observed for transmission error and contact stress in 200 m
for 10 MW gear train.
Fig. 14: Effect of gear quality grade, 0.6 to 10 MW
Fig. 15: Effect of misalignment, 0.6 to 10 MW
4. Conclusion The effect of gear quality grade and axial
misalignment for a range of medium to large wind turbine gear trains are investigated. Bearing reaction force, face load distribution factor, transmission error and maximum contact stress
are measured for each case study with varying gear quality and planet axial misalignment. In large gear trains such as 5 and 10 MW it is found that the gear quality of 7 for external gear and 8 for internal do not affect the measured parameters considerably even though they are one grade lower than permitted level. Transmission Error is the only parameter changes but within a small
range. However, larger TE variation can influence the load sharing behaviour of planets especially under low speed.
For assembly dependent imperfections like axial misalignment although a negative trend is observed for face load factor and contact stress toward larger wind turbines for large misalignment, they are found still not within acceptable range. Therefore, the assembly dependent tolerances still remain crucial even for large gear trains. This shows that the special consideration shall be taken in design of large turbines to accommodate the assembly imperfections or load dependent deformations because they are not less sensitive than small turbines to the misalignments.
It is also observed that each stage behave different than others to the misalignment. For instance the first two stages in 5 and 10 MW gear trains can hold larger misalignment than the other stages.
This study is conducted in rated wind speed for all the cases. Since the transmission error variation is higher in low wind speed, it is required to evaluate all cases in both low and rated wind speeds to confirm the results which are carried further in reference [18].
Acknowledgement The first author would like to thank KISSsoft
AG, Switzerland and Dr. Stefan Beermann for providing KISSsoft and KISSsys programs.
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