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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

邮发代号 80-975

2019 Impact Factor: 2.448

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Frontiers of Mechanical Engineering  2018, Vol. 13 Issue (3): 376-384   https://doi.org/10.1007/s11465-018-0500-3
  本期目录
Robust optimization of the billet for isothermal local loading transitional region of a Ti-alloy rib-web component based on dual-response surface method
Ke WEI, Xiaoguang FAN(), Mei ZHAN, Miao MENG
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710071, China
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Abstract：

Billet optimization can greatly improve the forming quality of the transitional region in the isothermal local loading forming (ILLF) of large-scale Ti-alloy rib-web components. However, the final quality of the transitional region may be deteriorated by uncontrollable factors, such as the manufacturing tolerance of the preforming billet, fluctuation of the stroke length, and friction factor. Thus, a dual-response surface method (RSM)-based robust optimization of the billet was proposed to address the uncontrollable factors in transitional region of the ILLF. Given that the die underfilling and folding defect are two key factors that influence the forming quality of the transitional region, minimizing the mean and standard deviation of the die underfilling rate and avoiding folding defect were defined as the objective function and constraint condition in robust optimization. Then, the cross array design was constructed, a dual-RSM model was established for the mean and standard deviation of the die underfilling rate by considering the size parameters of the billet and uncontrollable factors. Subsequently, an optimum solution was derived to achieve the robust optimization of the billet. A case study on robust optimization was conducted. Good results were attained for improving the die filling and avoiding folding defect, suggesting that the robust optimization of the billet in the transitional region of the ILLF was efficient and reliable.
Key words： isothermal local loading forming    rib-web component    transitional region    robust optimization    dual response surface method
收稿日期: 2017-07-27      出版日期: 2018-06-11
Corresponding Author(s): Xiaoguang FAN   
 引用本文:   
. [J]. Frontiers of Mechanical Engineering, 2018, 13(3): 376-384.
Ke WEI, Xiaoguang FAN, Mei ZHAN, Miao MENG. Robust optimization of the billet for isothermal local loading transitional region of a Ti-alloy rib-web component based on dual-response surface method. Front. Mech. Eng., 2018, 13(3): 376-384.
 链接本文:  
https://academic.hep.com.cn/fme/CN/10.1007/s11465-018-0500-3
https://academic.hep.com.cn/fme/CN/Y2018/V13/I3/376
Fig.1  
Fig.2  
Fig.3  
Control factors Uncontrolled factors
Outer array Inner array
Z1 1 1 … 3
Z2 1 2 … 3
Z3 1 2 … 2
Z4 1 2 … 1
x1 x2 x3 x4
1 1 2 3 f1,1 f1,2 … f1,j
1 2 3 2 f2,1 f2,2 … f2,j
1 3 1 1 f3,1 f3,2 … f3,j
… … … … … … … …
1 2 2 2 fi,1 fi,2 … fi,j
Tab.1  
Fig.4  
Fig.5  
Feature Parameter Value
Rib 1 Width, W1/mm 15
Height, H1/mm 44
Rib 2 Width, W2/mm 13
Height, H2/mm 43
Rib 3 Width, W3/mm 12
Height, H3/mm 45
Rib 4 Width, W4/mm 12
Height, H4/mm 44
Rib 5 Width, W5/mm 16
Height, H5/mm 45
Distance to the left side of Rib 1 D01/mm 35
Distance between Ribs 1 and 2 D12/mm 60
Distance between Ribs 2 and 3 D23/mm 75
Distance to the right side of Rib 3 D30/mm 30
Thickness of Web 1 Tweb1/mm 13
Thickness of Web 2 Tweb2/mm 13
Thickness of Web 3 Tweb3/mm 14
Thickness of Web 4 Tweb4/mm 14
Thickness of Web 5 Tweb5/mm 12
Thickness of Web 6 Tweb6/mm 12
All fillet radii R/mm 5
All drafts γ/(° ) 2
Width of the eigenstructure Weigen/mm 100
Volume of the eigenstructure Veigen/mm3 5.63×105
Tab.2  
Fig.6  
Factor type Variables Minimum values Maximum values
Control factors a: H1/He 0.75 1.15
b: H3/He 0.75 1.15
c: lleft/Lleft 0.60 1.00
d: lright/Lright 0.60 1.00
Uncontrolled factors MFerror −0.1 mm 0.1 mm
m 0.3 0.5
Lerror 13.9 mm 14 mm
Tab.3  
BBD NO. Control factors Uncontrolled factors Responses
a b c d UD 1 2 3 4 5 fiμ fiσ
MFerror –0.10 –0.05 0.00 0.05 0.10
m 0.35 0.45 0.30 0.40 0.50
Lerror 13.975 13.950 13.925 13.900 14.000
1 1.15 0.95 0.8 0.6 1.29 1.32 1.49 1.30 1.58 1.40 0.13
2 0.95 1.15 0.8 0.6 4.30 5.24 4.00 5.06 5.32 4.78 0.59
3 0.75 0.95 0.6 0.8 4.88 4.93 4.07 4.82 5.07 4.75 0.39
4 1.15 1.15 0.8 0.8 1.84 2.58 1.30 2.60 2.34 2.13 0.56
5 0.95 0.95 1.0 1.0 1.23 1.39 1.12 1.12 1.62 1.29 0.21
6 0.95 0.95 0.8 0.8 1.43 1.48 1.27 1.30 1.65 1.43 0.15
7 1.15 0.95 1.0 0.8 1.22 1.13 1.29 1.04 0.92 1.12 0.15
8 0.95 0.95 0.6 0.6 1.73 1.35 1.55 1.52 1.59 1.55 0.14
9 0.95 0.95 0.6 1.0 1.51 1.28 1.52 1.54 1.62 1.49 0.13
10 0.75 0.95 1.0 0.8 2.20 2.58 2.08 3.25 3.79 2.78 0.73
11 0.95 1.15 0.6 0.8 3.95 4.82 3.46 4.29 4.77 4.26 0.57
12 0.95 0.75 0.6 0.8 1.35 1.80 1.35 1.42 1.24 1.43 0.21
13 0.75 0.95 0.8 0.6 2.91 3.46 2.69 3.69 3.85 3.32 0.50
14 0.75 0.95 0.8 1.0 3.48 3.96 3.23 4.23 4.41 3.86 0.50
15 0.95 0.95 0.8 0.8 1.59 1.25 1.37 1.30 1.63 1.43 0.17
16 0.95 0.75 0.8 1.0 1.35 1.49 1.10 1.53 1.05 1.30 0.22
17 0.95 0.95 0.8 0.8 1.56 1.60 1.32 1.32 1.59 1.48 0.15
18 1.15 0.95 0.8 1.0 1.23 1.26 1.35 1.34 1.52 1.34 0.11
19 1.15 0.75 0.8 0.8 2.76 2.81 2.63 2.59 2.79 2.72 0.10
20 0.95 0.75 1.0 0.8 1.21 1.14 1.03 1.35 0.57 1.06 0.30
21 0.95 0.75 0.8 0.6 1.35 1.54 1.24 1.46 1.01 1.32 0.21
22 0.75 0.75 0.8 0.8 1.96 1.97 0.97 2.81 2.42 2.03 0.69
23 0.95 1.15 1.0 0.8 4.14 5.11 3.15 4.93 4.66 4.40 0.79
24 0.95 0.95 0.8 0.8 1.45 1.21 1.42 1.36 1.61 1.41 0.15
25 0.95 0.95 0.8 0.8 1.46 1.23 1.40 1.32 1.63 1.41 0.15
26 0.95 1.15 0.8 1.0 3.92 4.60 3.34 4.42 4.63 4.18 0.55
27 1.15 0.95 0.6 0.8 1.67 1.73 1.76 1.89 1.91 1.79 0.11
28 0.75 1.15 0.8 0.8 7.05 8.20 6.42 7.59 7.99 7.45 0.73
29 0.95 0.95 1.0 0.6 1.03 1.20 1.21 1.37 0.87 1.14 0.19
Tab.4  
Optimization type a b c d fiμ fiσ
Robust optimization 1.12 0.93 0.65 1 1.23 0.09
Deterministic optimization 1.13 0.96 1.00 1 1.26 0.15
Tab.5  
Fig.7  
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