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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (10): 2009-2017    DOI: 10.3785/j.issn.1008-973X.2020.10.019
能源工程、机械工程     
基于空间动力学优化的机床结构件质量匹配设计
黄华(),邓文强,李源,郭润兰
兰州理工大学 机电工程学院，甘肃 兰州 730000
Mass matching design of machine tool parts based on spatial dynamics optimization
Hua HUANG(),Wen-qiang DENG,Yuan LI,Run-lan GUO
School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730000, China
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摘要：

提出基于整机空间动力学预测模型、以移动结构件质量为设计变量的多目标匹配设计方法. 基于机床移动件的工作行程构建整机工作空间，运用正交试验法进行空间位姿试验设计，建立整机空间固有频率预测模型；在工作空间内对机床进行动力学性能的灵敏度分析，识别动力学的最优位姿和最差位姿；以最差位姿机床固有频率为优化目标，采用多目标质量匹配法对移动部件的质量进行最佳分布设计；重新计算优化后机床的固有频率，通过频率响应分析，比较优化前、后机床在最差和最优位姿下的动力学性能. 结果表明，经过多目标质量匹配优化后，机床的固有频率得到了提高，刀尖节点的最大频响振幅明显降低，机床的整机动力学性能有了较大程度的改善.
关键词： 空间位姿;  预测模型;  动态特性;  多目标优化;  质量匹配    
Abstract:

A multi-objective matching design method based on the whole machine space dynamics prediction model was proposed by taking the moving structure mass as design variables. The whole machine workspace was constructed based on the working stroke of the moving parts of the machine tool. Then the orthogonal test method was used to design the spatial pose, and the prediction model of the spatial natural frequency was established. The sensitivity analysis of the machining path was conducted in the workspace. The best and worst position was identified. Then the optimal distribution of the mass of moving parts was designed by multi-objective mass matching method by taking the natural frequency of the machine tool with the worst position as the optimization objective. The natural frequency of the optimized machine tool was calculated. The dynamic characteristics of the best and worst position before and after optimization were analyzed and compared. Results show that the natural frequency of the machine tool was improved with the optimization of multi-objective mass matching, and the maximum frequency response amplitude of the tool tip was significantly reduced. The dynamic performance of the machine tool was greatly improved.
Key words: spatial pose    prediction model    dynamic characteristics    multi-objective optimization    mass matching
收稿日期: 2019-11-12 出版日期: 2020-10-28
CLC:  TG 502  
基金资助: 国家自然科学基金资助项目（51965037、51565030）
作者简介: 黄华（1978—），男，副教授，博士，从事数控技术及装备的研究.orcid.org/0000-0002-4945-5888. E-mail： hh318872@126.com
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引用本文:

黄华,邓文强,李源,郭润兰. 基于空间动力学优化的机床结构件质量匹配设计[J]. 浙江大学学报(工学版), 2020, 54(10): 2009-2017.

Hua HUANG,Wen-qiang DENG,Yuan LI,Run-lan GUO. Mass matching design of machine tool parts based on spatial dynamics optimization. Journal of ZheJiang University (Engineering Science), 2020, 54(10): 2009-2017.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.10.019    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I10/2009

图 1  HMC630卧式加工中心
水平 因素
x/m y/m z/m
1 0.02 0.02 0.02
2 0.2 0.175 0.1375
3 0.4 0.35 0.275
4 0.6 0.525 0.4125
5 0.78 0.68 0.53
表 1  正交试验因素与水平
试验号 位姿坐标
x/m y/m z/m
1 0.02 0.02 0.02
2 0.02 0.175 0.1375
3 0.02 0.35 0.275
4 0.02 0.525 0.4125
5 0.02 0.68 0.53
6 0.2 0.02 0.1375
7 0.2 0.175 0.275
8 0.2 0.35 0.4125
9 0.2 0.525 0.53
10 0.2 0.68 0.02
11 0.4 0.02 0.275
12 0.4 0.175 0.4125
13 0.4 0.35 0.53
14 0.4 0.525 0.02
15 0.4 0.68 0.1375
16 0.6 0.02 0.4125
17 0.6 0.175 0.53
18 0.6 0.35 0.02
19 0.6 0.525 0.1375
20 0.6 0.68 0.275
21 0.78 0.02 0.53
22 0.78 0.175 0.02
23 0.78 0.35 0.1375
24 0.78 0.525 0.275
25 0.78 0.68 0.4125
表 2  位姿正交试验表
材料 ρ/(kg·m?3) E/GPa μ ξ
钢 7850 200 0.30 0.28
铸铁 7200 110 0.28 0.006
表 3  钢和铸铁的材料参数
结合部类型 k / (N·m?1) ζ / (N·s·m?1)
导轨滑块法向 4.9×106 3150
导轨滑块切向 4.2×106 1400
丝杆螺母轴向 1.7×106 3200
螺栓法向 9.0×106 6860
螺栓切向 7.8×106 5500
表 4  主要结合部的等效刚度和阻尼参数
试验号 f1/Hz f2/Hz f3/Hz f4/Hz f5/Hz
1 64.215 71.125 148.50 199.19 212.03
2 65.631 72.928 147.55 205.56 217.52
3 65.630 73.673 145.08 211.32 221.69
4 63.995 71.216 139.55 210.05 224.00
5 69.530 80.051 139.90 239.68 243.26
6 64.211 70.475 146.21 201.19 215.28
7 65.098 71.842 143.10 206.99 220.27
8 64.254 72.413 140.08 211.84 224.32
9 62.146 70.023 135.10 209.57 224.63
10 64.607 71.649 150.37 201.22 213.29
11 63.682 69.430 141.86 202.19 218.09
12 64.573 71.680 139.53 210.28 225.33
13 70.307 85.978 140.70 238.65 252.55
14 65.857 74.416 151.69 206.07 215.94
15 64.571 70.841 147.78 203.02 216.33
16 62.404 68.259 137.13 202.42 220.20
17 61.911 69.460 133.94 207.20 223.36
18 66.171 75.681 152.24 206.73 216.89
19 65.849 73.548 149.12 208.59 218.43
20 64.069 69.794 143.28 203.77 219.17
21 60.671 67.130 132.92 202.07 220.87
22 65.646 73.803 150.05 203.48 214.90
23 66.163 74.787 149.68 209.48 219.10
24 65.322 72.449 144.50 209.89 221.29
25 62.833 68.567 138.40 203.60 221.10
表 5  正交试验结果
ω R2 ω R2
ω1 0.996 5 ω4 0.998 4
ω2 0.998 6 ω5 0.998 7
ω3 0.999 2 ? ?
表 6  预测模型精度检验
图 2  机床空间固有频率预测模型
图 3  固有频率对坐标轴的全局效应
图 4  最差位姿坐标迭代历程图
图 5  最优位姿坐标迭代历程图
kg
水平 m1 m2 m3
?1 1209.115 2245.745 293.764
0 1511.400 2807.200 367.200
1 1813.672 3368.618 440.646
表 7  移动件质量试验设计水平表
kg
试验号 移动件质量
m1 m2 m3
1 1209.115 2245.745 293.764
2 1209.115 3368.618 367.200
3 1813.672 2245.745 367.200
4 1813.672 3368.618 367.200
5 1209.115 2807.200 293.764
6 1209.115 2807.200 440.646
7 1813.672 2807.200 293.764
8 1813.672 2807.200 440.646
9 1511.400 2245.745 293.764
10 1511.400 2245.745 440.646
11 1511.400 3368.618 293.764
12 1511.400 3368.618 440.646
13 1511.400 2807.200 367.200
表 8  移动件质量分布试验表
图 6  移动件质量对机床各阶固有频率的主效应
kg
状态 m1 m2 m3
优化前 1511.400 2807.200 367.200
优化后 1639.916 2245.745 293.801
表 9  优化前、后各移动件质量变化对比
状态 f1/Hz f2/Hz f3/Hz f4/Hz f5/Hz
优化前 59.534 65.709 133.986 197.342 220.331
优化后 68.056 77.534 150.375 229.642 249.632
表 10  优化前、后机床最差位姿前5阶固有频率
状态 f1/Hz f2/Hz f3/Hz f4/Hz f5/Hz
优化前 64.397 70.327 145.61 203.57 217.91
优化后 71.946 78.541 162.53 226.94 243.00
表 11  优化前、后机床最优位姿前5阶固有频率
图 7  最差位姿频率响应曲线
图 8  最优位姿频率响应曲线
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