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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front. Mech. Eng.    2014, Vol. 9 Issue (4) : 354-367    https://doi.org/10.1007/s11465-014-0319-5
RESEARCH ARTICLE
Multi-objective genetic algorithms based structural optimization and experimental investigation of the planet carrier in wind turbine gearbox
Pengxing YI(),Lijian DONG,Tielin SHI
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract

To improve the dynamic performance and reduce the weight of the planet carrier in wind turbine gearbox, a multi-objective optimization method, which is driven by the maximum deformation, the maximum stress and the minimum mass of the studied part, is proposed by combining the response surface method and genetic algorithms in this paper. Firstly, the design points’ distribution for the design variables of the planet carrier is established with the central composite design (CCD) method. Then, based on the computing results of finite element analysis (FEA), the response surface analysis is conducted to find out the proper sets of design variable values. And a multi-objective genetic algorithm (MOGA) is applied to determine the direction of optimization. As well, this method is applied to design and optimize the planet carrier in a 1.5 MW wind turbine gearbox, the results of which are validated by an experimental modal test. Compared with the original design, the mass and the stress of the optimized planet carrier are respectively reduced by 9.3% and 40%. Consequently, the cost of planet carrier is greatly reduced and its stability is also improved.
Keywords planet carrier      multi-objective optimization      genetic algorithms      wind turbine gearbox      modal experiment     
Corresponding Author(s): Pengxing YI   
Issue Date: 19 December 2014
 Cite this article:   
Pengxing YI,Lijian DONG,Tielin SHI. Multi-objective genetic algorithms based structural optimization and experimental investigation of the planet carrier in wind turbine gearbox[J]. Front. Mech. Eng., 2014, 9(4): 354-367.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0319-5
https://academic.hep.com.cn/fme/EN/Y2014/V9/I4/354
Fig.1  Schema of WTG
Fig.2  Simplified model of the planet carrier with planetary pins in WTG
Fig.3  Boundary conditions
Fig.4  FE meshing model
Fig.5  Selected design variables
Objective function Design variable
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
P11 (maximum deformation) 0.062 0.050 0.769 0.045 0.009 0.083 0.005 0.002 0.004 0.031
P12 (maximum stress) 0.008 0.006 0.006 0.021 0.048 0.031 0.830 0.009 0.005 0.014
P13 (mass) 0.130 0.053 0.358 0.145 0.023 0.229 0.008 0.020 0.004 0.135
Tab.1  Correlation coefficient between the design variables and objective functions
Designvariable The lower bound/mm The upperbound/mm The initialvalue/mm
P1 90 108 99
P3 315 355 325
P4 540 580 550
P6 370 410 400
P7 5 10 5
P10 620 635 629
Tab.2  The range of chosen design variables
Fig.6  Geometry representation of circumscribed CCDs
Fig.7  Distributions of design points for different design variables
Elastic modulus /MPa Poisson’s ratio Tensile strength /MPa Yield strength/MPa Density/(kg·m-3)
1.690×105 0.305 700 420 7355
Tab.3  Mechanical properties of material making the planet carrier
Fig.8  The deformation and stress of planet carrier with the initial design variables. (a) Total deformation; (b) X-direction deformation; (c) Y-direction deformation; (d) Z-direction deformation; (e) the stress of planet carrier; (f) the misalignment
Design point No. Design variable/mm Objective function
P1 P3 P4 P6 P7 P10 P11/mm P12/MPa P13/kg
1 99.0 335.0 560.0 390.0 7.5 623.5 0.2718 160.08 2409
2 90.0 335.0 560.0 390.0 7.5 623.5 0.2770 154.02 2345
3 108.0 335.0 560.0 390.0 7.5 623.5 0.2677 154.13 2474
4 99.0 315.0 560.0 390.0 7.5 623.5 0.2577 148.38 2515
5 99.0 355.0 560.0 390.0 7.5 623.5 0.2896 151.86 2303
6 95.2 343.4 568.4 398.4 6.4 627.1 0.2787 182.94 2356
… … … … … … … … … …
40 95.2 343.4 551.6 398.4 8.6 627.1 0.2759 157.66 2414
41 102.8 343.4 551.6 398.4 8.6 619.9 0.2755 154.60 2434
42 95.2 326.6 568.4 398.4 8.6 627.1 0.2660 167.83 2446
43 102.8 326.6 568.4 398.4 8.6 619.9 0.2659 160.20 2462
44 95.2 343.4 568.4 398.4 8.6 619.9 0.2834 181.12 2320
45 102.7 343.4 568.4 398.4 8.6 627.1 0.2749 181.13 2410
Tab.4  FE Computing results of the related parameters at each design point
Fig.9  The response surface of maximum deformation with two design variables
Fig.10  The response surface of the max-stress
Fig.11  The response surface of the mass
Fig.12  Scatter diagram of the optimization results
The objective function The maximum deformation The maximum stress The minimum mass
Weighted distribution, φ 1 0.333 0.667 1
Weighted distribution, φ 2 0.667 0.333 1
Weighted distribution, φ 3 0.667 1 1
Weighted distribution, φ 4 1 0.667 1
Weighted distribution, φ 5 1 1 1
Tab.5  The weighted distributions of objective functions
P1/mm P3/mm P4/mm P6/mm P7/mm P10/mm Deformation/mm Stress/MPa Mass/kg
99 317 570 370 9 623 0.269 141.15 2330
Tab.6  The optimum result of the chosen dimensions
Order number Natural frequency/Hz Order number Natural frequency/Hz
1 401.5 8 683.0
2 401.6 9 812.5
3 487.4 10 812.6
4 571.7 11 850.4
5 571.8 12 896.5
6 661.1 13 896.8
7 682.8 14 913.1
Tab.7  The non-zero order natural frequency of planet carrier
Fig.13  The modal testing schema of the planet carrier
Fig.14  Measurement points of response signals
Fig.15  Definition of coordinate system
Fig.16  The input excitation force signal
Fig.17  Response signal of acceleration sensor
Fig.18  Frequency response function at X direction
Fig.19  Frequency response function at Y direction
Fig.20  Frequency response function at Z direction
Order number FE natural frequency/Hz Experimental natural frequency/Hz Error/%
1 401.5 400.2 0.3
3 487.4 No No
4 571.7 553.2 3.2
6 661.1 664.5 0.5
7 682.8 681.0 0.2
9 812.5 808.1 0.6
11 850.4 848.5 0.2
12 896.5 895.6 0.1
14 913.1 910.3 0.3
Tab.8  Comparison between experimental modal results and theory modal results
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