Static and dynamic characteristic analysis and structure optimization for crossbeam structure of heavy-duty truss robot
Jin WANG1(),Xiang-kun WANG1,Jian-hui FU1,*(),Guo-dong LU1,Chao-chao JIN2,Yan-zhi CHEN3
1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China 2. Ningbo Welllih Robot Technology Limited Company, Ningbo 315480, China 3. Yuyao Zhejiang University Robot Research Center, Ningbo 315400, China
The finite element method was used to analyze the static and dynamic characteristics of the crossbeam structure of heavy-duty truss robot and optimize the structure in order to explore and improve the static and dynamic characteristics under extreme load pressure. The static analysis results showed that the maximum deformation of the crossbeam structure in the Y direction was 0.470 mm under the pressure of the limit load of 17800 N. The dynamic analysis results showed that the first six natural frequencies of the crossbeam structure were distributed from 47 to 134 Hz. Harmonic response analysis results showed the influence of the first three natural frequencies on the structure. The optimization results show that the experimental design method of OSF has better optimization effect under two different experimental design methods of CCD and OSF. The quality of the crossbeam structure was reduced by 1.47%, the total deformation was reduced by 18.41% and the frequency was reduced by 13.48% after the optimization of the OSF experimental design.
Jin WANG,Xiang-kun WANG,Jian-hui FU,Guo-dong LU,Chao-chao JIN,Yan-zhi CHEN. Static and dynamic characteristic analysis and structure optimization for crossbeam structure of heavy-duty truss robot. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 124-134.
为了探究并改善重载桁架机器人横梁结构在承受极限负载压力下的静动态特性，利用有限元方法分析该结构的静动态特性并进行结构优化. 静态分析结果表明，横梁结构在承受极限负载17 800 N的压力下，横梁结构在Y方向上的最大变形量为0.470 mm. 动态分析结果表明，横梁结构的前6阶固有频率为47~134 Hz. 谐响应分析结果显示了前3阶固有频率对结构的影响. 优化结果表明，在中心复合设计(CCD)与最佳填充空间设计(OSF)2种不同实验设计方法下，OSF实验设计方法具有更好的优化效果. OSF实验设计优化后，横梁结构的质量降低了1.47%，总变形量降低了18.41%，频率降低了13.48%.
关键词：
重载桁架机器人,
横梁结构,
模态分析,
谐响应分析,
结构尺寸优化
Fig.1Heavy-duty robot model and crossbeam structure model
结构
S/mm
L/mm
T/mm
E/(1011 Pa)
ρ/(kg·m?3)
横梁
400×400
7300
12
2
7850
滑轨
46×35
7280
?
2
7850
齿条
39×35
7000
?
2
7850
Tab.1Basic parameter of crossbeam，slide rail and rack model
Fig.2Cross-section of crossbeam structure and meshing result
Fig.3Simplified model of pressure load
单元
DA /mm
σA /MPa
DB/mm
σB/MPa
DC/mm
σC /MPa
Nd
ta /s
实体单元
0.192
20.743
0.406
22.973
0.470
22.436
339488
310
壳单元
0.192
19.882
0.403
22.645
0.466
23.190
136448
202
Tab.2Comparison of simulation results between solid elements and shell elements
Fig.4Deformation cloud diagrams of solid element and shell element for crossbeam structure
位置
Sb/mm
Sa/mm
DF/mm
位置A
0.249
0.236
0.013
位置B
0.528
0.509
0.019
位置C
0.586
0.581
0.005
Tab.3Comparison of maximum total deformation before and after simplification of cross section
Fig.5Comparison of beam cross section before and after simplification and mesh generation
Fig.6Theoretical mechanical model of fixed beam at both ends
Fig.7Equivalent mechanical model of beam
位置
Dth/mm
Ds/mm
Der/mm
位置A
0.074
0.084
0.010
位置B
0.281
0.284
0.003
位置C
0.353
0.349
0.004
Tab.4Comparison between theoretical deformation and simulation deformation of beam structure
Fig.8Deformation cloud image of beam section at the biggest deflection
阶数
f/Hz
阶数
f/Hz
1
47.713
6
133.860
2
49.495
7
171.090
3
109.290
8
173.640
4
117.900
9
176.920
5
121.220
10
177.690
Tab.5First 10 natural frequencies of crossbeam structure
Fig.9Cloud diagram of first 6 modes of model shapes
Fig.10Position of horizontal plane (up) and vertical plane (down)
Fig.11Displacement response curve of crossbeam structure
尺寸范围
P1
P2
P3
P4
P5
P6
P7
初始值
12
12
376
376
44
46
32
下限
9
9
280
280
35
40
25
上限
14
14
420
420
50
60
35
Tab.6Variation range of cross-beam section size parameters mm
Fig.12Optimized cross-sectional structure (left) and meshed cross-section (right)
Fig.13CCD and OSF design sample points and response points
评判参数
CCD
OSF
f
m
d
σ
f
m
d
σ
测定系数
0.999
1.000
0.999
1.000
0.999
1.000
1.000
0.999
最大相对残差
0.000
0.000
0.011
0.000
0.000
0.000
0.000
0.000
均方根误差
0.000
0.000
0.000
0.000
0.000
0.002
0.000
0.000
相对均方根误差
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
相对最大 绝对误差
0.033
0.000
0.067
0.000
0.018
0.000
0.000
0.027
相对平均 绝对误差
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Tab.7Fitting accuracy of CCD and OSF
Fig.14Optimization process of beam structural size
Fig.15CCD design Pareto solution set and OSF design Pareto solution set
mm
方案
P1
P2
P3
P4
P5
P6
P7
1
11.15
12.61
344.90
392.34
41.75
52.49
29.95
2
11.14
12.48
342.28
392.19
41.89
52.59
29.94
3
11.16
12.61
344.14
391.83
41.38
52.52
29.98
4
11.19
12.27
344.18
392.17
42.82
52.64
29.94
5
11.16
12.61
343.98
392.31
41.39
52.48
29.95
原始
12.00
12.00
376.00
376.00
44.00
46.00
32.00
Tab.8Size optimization results of CCD experiment design
mm
方案
P1
P2
P3
P4
P5
P6
P7
1
10.96
12.95
333.13
393.66
42.99
54.67
29.72
2
12.38
12.44
312.45
411.90
41.11
48.11
31.48
3
11.00
12.82
323.83
411.26
43.63
51.20
29.64
4
11.00
12.82
323.64
409.63
42.49
54.68
29.65
5
11.00
12.82
323.64
409.63
42.49
54.73
29.65
原始
12.00
12.00
376.00
376.00
44.00
46.00
32.00
Tab.9Size optimization results of OSF experiment design
方案
CCD
OSF
f/Hz
vf/%
d/μm
vd/%
m/kg
vm/%
f/Hz
vf/%
d/μm
vd/%
m/kg
vm/%
1
44.72
?8.08
476.10
?16.03
1234.70
?0.11
42.45
?12.74
458.56
?19.13
1234.32
?0.14
2
44.34
?8.86
476.32
?16.00
1225.20
?0.87
41.13
?15.46
459.67
?18.93
1233.54
?0.20
3
44.61
?8.30
476.50
?15.96
1232.71
?0.27
42.09
?13.48
462.59
?18.41
1217.82
?1.47
4
44.70
?8.12
476.60
?15.94
1227.28
?0.71
41.74
?14.20
463.84
?18.20
1219.58
?1.33
5
44.59
?8.35
476.70
?15.93
1231.95
?0.33
41.74
?14.20
464.20
?18.13
1219.42
?1.34
原始
48.65
0.00
567.00
0.00
1236.00
0.00
48.65
0.00
567.00
0.00
1236.00
0.00
Tab.10Optimization results of frequency, deformation, mass of CCD and OSF experiment design
Fig.16Comparison of CCD and OSF design optimization effect and original model
Fig.17Comparison of optimization results between CCD experiment design and OSF experiment design
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