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Frontiers of Mechanical Engineering

Front. Mech. Eng.
RESEARCH ARTICLE
Multidisciplinary co-design optimization of structural and control parameters for bucket wheel reclaimer
Yongliang YUAN, Liye LV, Shuo WANG, Xueguan SONG()
School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China
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Abstract

Bucket wheel reclaimer (BWR) is an extremely complex engineering machine that involves multiple disciplines, such as structure, dynamics, and electromechanics. The conventional design strategy, namely, sequential strategy, is structural design followed by control optimization. However, the global optimal solution is difficult to achieve because of the discoordination of structural and control parameters. The co-design strategy is explored to address the aforementioned problem by combining the structural and control system design based on simultaneous dynamic optimization approach. The radial basis function model is applied for the planning of the rotation speed considering the relationships of subsystems to minimize the energy consumption per volume. Co-design strategy is implemented to resolve the optimization problem, and numerical results are compared with those of sequential strategy. The dynamic response of the BWR is also analyzed with different optimization strategies to evaluate the advantages of the strategies. Results indicate that co-design strategy not only can reduce the energy consumption of the BWR but also can achieve a smaller vibration amplitude than the sequential strategy.

Keywords bucket wheel reclaimer      co-design      energy-minimum optimization      sequential strategy     
Corresponding Authors: Xueguan SONG   
Just Accepted Date: 17 February 2020   Online First Date: 11 March 2020   
 Cite this article:   
Yongliang YUAN,Liye LV,Shuo WANG, et al. Multidisciplinary co-design optimization of structural and control parameters for bucket wheel reclaimer[J]. Front. Mech. Eng., 11 March 2020. [Epub ahead of print] doi: 10.1007/s11465-019-0578-2.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0578-2
http://journal.hep.com.cn/fme/EN/Y/V/I/0
Fig.1  Whole structure of the bucket wheel reclaimer.
Fig.2  Excavation technology of the bucket wheel reclaimer: (a) Hierarchical and (b) fixed-point operations.
Fig.3  (a) Schematic of bucket wheel reclaimer; (b) excavation trajectory.
Basis function Φ(x)
Multi-quadrics ( x2+δ2)1/2, δ0,
Inverse multi-quadrics ( x2+δ2) 1/2, δ0
Gaussian e x2/δ 2, δ 0
Tab.1  Choices of Φ for the interpolation matrix
Fig.4  Typical speed curve of the motor.
Fig.5  Configuration of the bucket wheel reclaimer.
Fig.6  Resistance analysis of the bucket wheel reclaimer.
Fig.7  Characteristic curve of the motor.
Interpolation point Mean value/(kJ·kg−1) Best value/(kJ·kg−1) Worst value/(kJ·kg−1) Standard deviation/(kJ·kg−1)
6 34.80 34.46 41.29 43.90
8 33.79 33.51 39.46 41.31
10 36.03 35.18 43.45 46.97
12 1.13 0.84 2.00 2.84
Tab.2  The influence of the different interpolation points on energy consumption
Fig.8  Convergence histories of the different interpolation points on energy consumption.
Fig.9  Convergence histories of co-design strategy and sequential strategy for the bucket wheel reclaimer.
Design variable Initial value Sequential strategy Co-design strategy
Optimal value Improved/% Optimal value Improved/%
x1 3.50 m 4.19 m +19.71 4.20 m +20.00
x2 3.50 m 2.64 m ?24.57 3.53 m +0.83
x3 3.50 m 2.79 m ?20.29 2.56 m ?26.81
x4 5.60 m 5.33 m ?4.82 5.50 m ?1.87
x5 3.00 m 4.20 m +40.00 4.19 m +39.67
x6 6.00 m 2.75 m ?8.33 5.62 m ?6.26
x7 3.00 m 2.90 m ?3.33 3.29 m +9.70
x8 6.00 m 2.84 m ?5.33 5.61 m ?6.53
x9 3.00 m 2.80 m ?6.67 2.97 m ?1.13
x10 6.00 m 2.84 m ?5.33 5.23 m ?12.86
x11 1.079×10−2 m2 1.19×10−2 m2 +10.28 1.29×10−2 m2 +19.49
x12 3.50×10−2 m2 4.46×10−2 m2 +27.60 2.77×10−2 m2 ?20.71
x13 2.83×10−3 m2 3.12×10−3 m2 +10.35 2.84×10−3 m2 +0.37
x14 4.92×10−2 m2 5.07×10−2 m2 +3.29 5.25×10−2 m2 +6.95
x15 1.08×10−2 m2 1.35×10−2 m2 +25.11 1.17×10−2 m2 +8.58
x16 7.78 m 8.85 m +13.75 8.89 m +14.25
x17 4.80 m 5.16 m +7.50 4.52 m ?5.80
x18 1.08×10−2 m2 1.21×10−2 m2 +11.95 1.36×10−2 m2 +25.87
x19 4.37 m 3.74 m ?14.42 3.66 m ?16.25
x20 3.00 m 4.34 m +44.67 2.17 m ?27.56
x21 4.29×10−3 m2 5.02×10−3 m2 +16.94 5.65×10−3 m2 +31.71
x22 3.77 m 3.19 m ?15.38 3.72 m ?1.22
x23 8.50×10−3 m2 1.12×10−3 m2 +31.85 6.98×10−3 m2 ?17.79
x24 70.00° 61.42° ?12.26 57.79° ?17.44
x25 9.00° 7.78° ?13.56 7.78° ?13.56
x26 26.00° 19.86° ?23.62 20.96° ?19.39
x27 9.00° 7.15° ?20.56 7.20° ?20.00
v1 3.00×10−2 rad/s 2.72×10−2 rad/s ?9.47 2.61×10−2 rad/s ?13.10
v2 4.00×10−2 rad/s 3.83×10−2 rad/s ?4.24 4.26×10−2 rad/s +6.52
v3 6.50×10−2 rad/s 7.96×10−2 rad/s +22.51 5.90×10−2 rad/s ?9.29
v4 8.00×10−2 rad/s 7.05×10−2 rad/s ?11.86 7.58×10−2 rad/s ?5.27
v5 5.80×10−2 rad/s 4.92×10−2 rad/s ?15.09 4.88×10−2 rad/s ?15.87
v6 7.50×10−2 rad/s 6.48×10−2 rad/s ?13.58 7.88×10−2 rad/s +5.00
v7 6.30×10−2 rad/s 6.19×10−2 rad/s ?1.75 5.07×10−2 rad/s ?19.56
v8 5.00×10−2 rad/s 4.05×10−2 rad/s ?19.04 3.84×10−2 rad/s ?23.24
Best value 79.45 kJ/kg 61.86 kJ/kg ?22.14 57.72 kJ/kg ?27.31
Worst value ? 67.59 kJ/kg ?14.93 63.90 kJ/kg ?19.57
Mean value ? 64.71 kJ/kg ?18.55 60.71 kJ/kg ?23.59
Standard deviation ? 2.14 kJ/kg 1.93 1.95 kJ/kg 1.92
Tab.3  Optimization results of co-design strategy and sequential strategy for the bucket wheel reclaimer
Fig.10  Speed and power of the motor with co-design strategy: (a) Control speed and (b) output power of the rotation motor.
Fig.11  Dynamic response of the bucket wheel reclaimer with different optimization strategies.
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