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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2016, Vol. 11 Issue (4) : 388-402    https://doi.org/10.1007/s11465-016-0404-z
RESEARCH ARTICLE
Numerical analysis and experimental investigation of modal properties for the gearbox in wind turbine
Pengxing YI(),Peng HUANG,Tielin SHI
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract

Wind turbine gearbox (WTG), which functions as an accelerator, ensures the performance and service life of wind turbine systems. This paper examines the distinctive modal properties of WTGs through finite element (FE) and experimental modal analyses. The study is performed in two parts. First, a whole system model is developed to investigate the first 10 modal frequencies and mode shapes of WTG using flexible multi-body modeling techniques. Given the complex structure and operating conditions of WTG, this study applies spring elements to the model and quantifies how the bearings and gear pair interactions affect the dynamic characteristics of WTGs. Second, the FE modal results are validated through experimental modal analyses of a 1.5 WM WTG using the frequency response function method of single point excitation and multi-point response. The natural frequencies from the FE and experimental modal analyses show favorable agreement and reveal that the characteristic frequency of the studied gearbox avoids its eigen-frequency very well.
Keywords wind turbine gearbox      modal analysis      finite element analysis      modal frequency      bearing equivalence     
Corresponding Author(s): Pengxing YI   
Just Accepted Date: 25 October 2016   Online First Date: 17 November 2016    Issue Date: 29 November 2016
 Cite this article:   
Pengxing YI,Peng HUANG,Tielin SHI. Numerical analysis and experimental investigation of modal properties for the gearbox in wind turbine[J]. Front. Mech. Eng., 2016, 11(4): 388-402.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-016-0404-z
https://academic.hep.com.cn/fme/EN/Y2016/V11/I4/388
Fig.1  Structure of the WTG. (a) Scheme of WTG; (b) model of LS PGS

1?Flexible shaft; 2?Planetary carrier; 3?Planetary gear; 4?Ring gear; 5? Middle-speed shaft; 6?High-speed shaft; 7?Hollow shaft; and 8?Sun gear shaft

Fig.2  Simplified model of WTG
Fig.3  FE meshing model and refinements. (a) Total mesh result; (b) refinements of mesh in specific regions
Location Radial stiffness/(MN·mm–1) Axial stiffness/(MN·mm–1) Tangential stiffness/(MN·mm–1) Type
Low-speed shaft 2874.3 0.0001 0.28 NU 1072 MA
2123.9 216.1000 8.83 32972
7616.4 1088.3000 33.30 32972
Middle-speed shaft 2199.8 0.0001 0.46 NU 2236
4004.7 0.0001 1.39 NU 2244 ECMA
High-speed shaft 2327.3 0.0001 0.34 NU 2232 ECMA
1457.8 0.0001 0.13 QJ 226 N2MA
Tab.1  Bearing parameters
Fig.4  Bearing equivalence of three directions. (a) Radial direction at middle-speed shaft; (b) axial direction at low-speed shaft; (c) tangential direction at low-speed shaft
Fig.5  Fixed support on the torque arm and planet carrier
Fig.6  Contact between the planet carrier and planetary pins
Pairs Average meshing stiffness/(109N·m–1)
Sun gear-planetary gear 22.31
Planetary gear-annular gear 21.04
Low-speed gear-middle-speed gear 21.53
Middle-speed gear-high-speed gear 22.87
Tab.2  Average meshing stiffness of different gear pairs
Fig.7  Modeling the interaction between meshing gear pairs. (a) Frictional contact among gear teeth; (b) equivalence of meshing stiffness
Order Natural frequency/Hz Mode shape Maximum deformation/mm Location of maximum deformation
1 46.6 Gearbox swings up and down 0.56 Output of high-speed shaft
2 111.8 Gearbox swings side to side 0.49 Gear on the low-speed shaft
3 127.7 Gearbox swings back and front 0.54 Output of high-speed shaft
4 209.1 Two-stage parallel shafts swings and gearbox twists 0.62 Input of planet carrier
5 214.7 Low-speed shaft swings and twists 0.70 Gear on the low-speed shaft
6 239.3 Gearbox twists up and down 0.71 Up box
7 284.6 Gearbox twists and swings 0.71 Planet carrier
8 297.8 Coupled twisting of the input and output shafts 0.92 Bearing bore of the input shaft at the bottom box
9 302.0 Output shaft swings side to side 0.82 End of output shaft
10 331.8 Planet carrier swings and twists 0.74 Planet carrier
Tab.3  Natural frequencies and mode shapes of WTG from the first to the tenth order with FE simulation
Fig.8  Variations of the first order mode shape with time. (a) 1/10 s; (b) 1/2 s; and (c) 9/10 s
Fig.9  Variations of the fourth order mode shape with time. (a) 1/10 s; (b) 1/2 s; and (c) 9/10 s
Fig.10  Variations of the eighth order mode shape with time. (a) 1/10 s; (b) 1/2 s; and (c) 9/10 s
Fig.11  Mode shapes of the WTG system with maximum vibration deformation. (a) Second order; (b) third order; (c) fifth order; (d) sixth order; (e) seventh order; (f) ninth order
Fig.12  Variation of modal frequencies and deformation. (a) First mode; (b) second mode; (c) third mode; (d) fourth mode
Location Mesh stiffness/(MN·mm–1)
Low-speed gear P1 21.53
High-speed gear P2 22.87
Tab.4  Parameters of gear mesh stiffness
Fig.13  Variation of the deformation. (a) First mode; (b) second mode; (c) third mode; (d) fourth mode
Fig.14  Variation of modal frequency. (a) First mode; (b) second mode; (c) third mode; (d) fourth mode
Fig.15  Scheme of experimental modal analysis
Fig.16  Modal testing experiment for a 1.5 WM WTG
PCB number X-axis sensitivity/(mv·g-1) Y-axis sensitivity/(mv·g-1) Z-axis sensitivity/(mv·g-1)
95482 103.4 100.9 100.1
95483 101.0 101.5 98.2
95484 102.1 101.8 103.0
95485 101.8 102.1 103.0
Tab.5  Parameters of the acceleration sensors
Fig.17  Distribution of response points. Response points (a) on the gearbox, (b) at the top of the gearbox, (c) at the joint of the gearbox, (d) on the annular gear, and (e) on the torque arm
Fig.18  Experimental tests: Application of impact
Fig.19  Connected sensors
NO. X Y Z 18 ?X ?Y Z 36 Z X Y 54 ?Y ?Z X 72 ?X ?Y Z 90 Y X ?Z
1 ?X ?Y Z 19 Z X Y 37 Z X Y 55 ?Y ?Z X 73 ?Y Z ?X 91 Y X ?Z
2 Z X Y 20 Z X Y 38 Z X Y 56 ?Y X Z 74 ?Y Z ?X 92 ?Z Y X
3 Z X Y 21 Z X Y 39 Z Y ?X 57 ?Y X Z 75 ?Y ?X ?Z 93 ?Z X ?Y
4 Z X Y 22 Z X Y 40 Z Y ?X 58 ?Y X Z 76 ?X Y ?Z 94 ?Z X ?Y
5 Z X Y 23 Z X Y 41 Z ?X ?Y 59 ?Y X Z 77 ?X Y ?Z 95 ?Z X ?Y
6 Z X Y 24 Z X Y 42 Z X Y 60 ?Y X Z 78 ?Y ?Z X 96 ?Z X ?Y
7 Z X Y 25 Z X Y 43 Z X Y 61 Y Z X 79 ?Y ?Z X 97 ?Z X ?Y
8 ?X ?Y Z 26 Z X Y 44 ?Y X Z 62 Y ?X Z 80 ?Y ?Z X 98 ?Z X ?Y
9 Y X ?Z 27 Z X Y 45 ?Y X Z 63 ?Y ?X ?Z 81 ?Y ?Z X 99 ?Z X ?Y
10 Z X Y 28 Z X Y 46 ?Y X Z 64 Y X ?Z 82 ?Y X Z 100 ?Z X ?Y
11 Z X Y 29 Z Y ?X 47 ?Y X Z 65 Y Z X 83 ?Y X Z 101 ?Z X ?Y
12 Z X Y 30 Z Y ?X 48 ?Y X Z 66 ?Y ?Z X 84 ?Y X Z 102 ?Z X ?Y
13 Z X Y 31 Z Y ?X 49 Y Z X 67 ?Y ?Z X 85 Y ?X Z 103 ?Z X ?Y
14 Z X Y 32 Z ?Y X 50 Y ?X Z 68 ?X Y ?Z 86 Y Z X 104 ?Z X ?Y
15 Y X ?Z 33 Z X Y 51 ?Y ?X ?Z 69 X ?Z Y 87 Y Z X 105 ?Z X ?Y
16 Z X Y 34 Z X Y 52 Y X ?Z 70 ?Y ?Z X 88 Y Z X 106 ?Z X ?Y
17 Z X Y 35 Z X Y 53 Y Z X 71 ?Y X Z 89 Y Z X 107 ?Z X ?Y
Tab.6  Coordinate of the response points to the absolute coordinate
Fig.20  Modal response of testing Point 7. (a) Incentive force signal; (b) acceleration response signal; (c) X direction frequency function; (d) Y direction frequency function; (e) Z direction frequency function
Fig.21  Real part of the frequency response function. Comparison of the (a) X, (b) Y, and (c) Z directions
Order Simulation/Hz Experiment/Hz Deviation/%
1 46.6 49.3 5.5
2 111.8 105.5 5.9
3 127.7 134.9 5.3
4 209.1 198.6 6.9
5 214.7 203.8 5.3
6 239.3 250.2 4.4
7 284.6 300.7 5.4
8 297.8 308.6 3.5
9 302.0 318.5 5.2
10 331.8 343.1 3.3
Tab.7  Comparison of the FE and experimental modal analyses
Location Frequency/Hz
Rotational frequency of the main axle 1.855
Rotational frequency of the middle-speed shaft 8.065
Rotational frequency of the high-speed shaft 21.700
Gear mesh of the sun and planet gears 38.900
Gear mesh of the low- and middle-speed shafts 185.500
Gear mesh of the middle- and high-speed shafts 758.100
Tab.8  Characteristic frequency of the gearbox system
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