Please wait a minute...
浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (1): 23-32    DOI: 10.3785/j.issn.1008-973X.2020.01.003
机械工程     
基于不规则元胞的主轴温度－结构场耦合热拓扑优化设计方法
邓小雷1,2,3(),盛泽枫1,张江林1,吕笑文1,贺忠1,王建臣1,3,傅建中2,*()
1. 衢州学院 浙江省空气动力装备技术重点实验室，浙江 衢州 324000
2. 浙江大学 浙江省三维打印工艺与装备重点实验室，浙江 杭州 310027
3. 浙江永力达数控科技股份有限公司，浙江 衢州 324000
Thermal topology optimization design method of spindle under temperature-structure field coupling condition based on irregular cell
Xiao-lei DENG1,2,3(),Ze-feng SHENG1,Jiang-lin ZHANG1,Xiao-wen LV1,Zhong HE1,Jian-chen WANG1,3,Jian-zhong FU2,*()
1. Key Laboratory of Air-driven Equipment Technology of Zhejiang Province, Quzhou University, Quzhou 324000, China
2. Key Laboratory of 3D Printing Process and Equipment of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
3. Zhejiang Yonglida CNC Technology Limited Company, Quzhou 324000, China
 全文: PDF(2639 KB)   HTML
摘要：

为了适应复杂的几何形状，避免传统的规则矩形元胞不能均匀地覆盖设计区域的问题，实现主轴结构耦合场热拓扑优化设计，提出基于不规则元胞的混合元胞自动机法（HCAM）耦合场主轴热拓扑优化设计方法. 该方法以数值传热学的相关理论为基础，用三角形元胞来替代传统的矩形元胞，并引入局部网格细化的思想，在应力集中或应变急剧变化的区域实现局部元胞细化，使得整个结构的元胞尺寸自适应变化. 通过案例对比分析验证了该方法的可行性，该方法可以有效地适应复杂结构形状、减少元胞单元和有限元网格的数量以及降低元胞单元与有限元网格之间映射的难度. 利用不规则元胞的HCAM对主轴结构进行不同工况下的温度－结构场耦合热拓扑优化设计研究，最终获得的热拓扑优化构形结果不仅减少了主轴结构材料，而且改善了其热态特性.
关键词： 不规则元胞;  主轴;  混合元胞自动机法;  温度－结构场耦合;  拓扑优化;  热拓扑设计    
Abstract:

A hybrid cellular automaton method (HCAM) applied with irregular cell was proposed to realize the thermal topological optimization design for the coupled field of spindle structure in order to adapt to the complex geometrical shape and avoid the problem which the traditional regular rectangular cells could not uniformly cover the design area. The traditional rectangular cell of HCAM was replaced by irregular cell based on the theory of numerical heat transfer. The idea of local mesh refinement was introduced to realize local cell refinement in the area where the stress could be concentrated or strain sharp changed, and the cell size of the whole structure could adaptively change. The comparison analysis results show that the method is feasible. The method can effectively adapt to the complex structure shape, reduce the number of cellular elements and finite element grids, and reduce the difficulty of mapping between cellular elements and finite element grids. The thermal topology optimization design of the temperature-structure field coupling spindle structure under different working conditions was analyzed by using the irregular cell HCAM. Results showed that the final thermal topology optimization results not only reduced the material of spindle, but also improved its thermal characteristics.
Key words: irregular cell    spindle    hybrid cellular automaton method    temperature-structure field coupling    topology optimization    thermal topology design
收稿日期: 2018-12-18 出版日期: 2020-01-05
CLC:  TH 161  
基金资助: 国家自然科学基金资助项目（51605253）；浙江省博士后择优资助项目（ZJ20180077）；浙江省基础公益研究计划资助项目（LGG18E050014）
通讯作者: 傅建中     E-mail: dxl@zju.edu.cn;fjz@zju.edu.cn
作者简介: 邓小雷（1981—），男，副教授，博士，从事数控装备及自动化技术和数字化设计与制造技术的研究. orcid.org/0000-0002-2868-6310. E-mail： dxl@zju.edu.cn
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
作者相关文章　　
邓小雷
盛泽枫
张江林
吕笑文
贺忠
王建臣
傅建中

引用本文:

邓小雷,盛泽枫,张江林,吕笑文,贺忠,王建臣,傅建中. 基于不规则元胞的主轴温度－结构场耦合热拓扑优化设计方法[J]. 浙江大学学报(工学版), 2020, 54(1): 23-32.

Xiao-lei DENG,Ze-feng SHENG,Jiang-lin ZHANG,Xiao-wen LV,Zhong HE,Jian-chen WANG,Jian-zhong FU. Thermal topology optimization design method of spindle under temperature-structure field coupling condition based on irregular cell. Journal of ZheJiang University (Engineering Science), 2020, 54(1): 23-32.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.01.003    或    http://www.zjujournals.com/eng/CN/Y2020/V54/I1/23

图 1  不规则元胞的邻胞
图 2  C型结构及其不规则元胞（网格）划分
图 3  不同优化算法的C型结构优化结果对比
图 4  半圆环型结构及其不规则元胞（网格）划分
图 5  不同优化算法的半圆环型结构优化结果对比
图 6  温度-结构场耦合的平板结构及不规则元胞（网格）划分
图 7  HCAM得到的平板结构拓扑优化构形图
图 8  平板结构优化前、后的结果比较
图 9  HCAM的性能指标和质量比历程曲线图
图 10  温度载荷作用下的主轴测试用例
图 11  主轴结构的不规则元胞（网格）
图 12  HCAM得到的主轴测试用例拓扑优化构形图
图 13  主轴测试用例优化前、后的结果比较
图 14  HCAM的性能指标和质量比历程曲线图
图 15  热流作用下的主轴测试用例
图 16  HCAM得到的主轴测试用例拓扑优化构形图
图 17  主轴测试用例优化前、后的结果比较
图 18  HCAM的性能指标和质量比历程曲线图
1 MAYR J, JEDRZEJEWSKI J, UHLMANN E, et al Thermal issues in machine tools[J]. CIRP Annals-Manufacturing Technology, 2012, 61 (2): 771- 791
doi: 10.1016/j.cirp.2012.05.008
2 LIU J F, ZHANG P Thermo-mechanical behavior analysis of motorized spindle based on a coupled model[J]. Mechancial Engineering, 2018, 10 (1): 1- 12
3 ABELE E, ALTINTAS Y, BRECHER C Machine tool spindle units[J]. CIRP Annals - Manufacturing Technology, 2010, 59 (2): 781- 802
doi: 10.1016/j.cirp.2010.05.002
4 邓小雷, 林欢, 王建臣, 等 机床主轴热设计研究综述[J]. 光学精密工程, 2018, 26 (6): 1415- 1429
DENG Xiao-lei, LIN Huan, WANG Jian-chen, et al Review on thermal design of machine tools’ spindle[J]. Optics and Precision Engineering, 2018, 26 (6): 1415- 1429
5 邓小雷, 傅建中, 贺永, 等 精密数控机床主轴系统多物理场耦合热态特性[J]. 浙江大学学报: 工学版, 2013, (10): 1863- 1870
DENG Xiao-lei, FU Jian-zhong, HE Yong, et al Multi-field coupling thermal characteristics analysis for spindle system of the precision CNC machine tool[J]. Journal of Zhejiang University: Engineering Science, 2013, (10): 1863- 1870
6 BOCHENEK B, KATARZYNA T Novel local rules of cellular automata applied to topology and size optimization[J]. Engineering Optimization, 2012, 44 (1): 23- 25
doi: 10.1080/0305215X.2011.561843
7 FARAMARZI A, AFSHAR M H Application of cellular automata to size and topology optimization of truss structures[J]. Scientia Iranica, 2012, 19 (3): 373- 380
doi: 10.1016/j.scient.2012.04.009
8 BAETENS J M, DE LOOF K, DE BAETS B Influence of the topology of a cellular automaton on its dynamical properties[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18 (3): 651- 668
doi: 10.1016/j.cnsns.2012.08.018
9 TOVAR A, QUEVEDO W I, PATEL N M, et al. Hybrid cellular automata with local control rules: a new approach to topology optimization inspired by bone functional adaptation [C] // 6th World Congresses of Structural and Multidisciplinary Optimization. Rio de Janeiro: WCSMO, 2005: Brazil: 1-11.
10 TOVAR A, PATEL N M, KAUSHIK A K, et al Optimality conditions of the hybrid cellular automata for structural optimization[J]. AIAA Journal, 2007, 45 (3): 673- 683
doi: 10.2514/1.20184
11 TOVAR A, PATEL N M, NIEBUR G L, et al Topology optimization using a hybrid cellular automaton method with local control rules[J]. Journal of Mechanical Design, 2006, 128: 1205- 1216
doi: 10.1115/1.2336251
12 BANDI P, SCHMIEDELER J P, TOVAR A Design of crashworthy structures with controlled energy absorption in the hybrid cellular automaton framework[J]. Journal of Mechanical Design, 2013, 135: 091002-1- 11
13 SOOBUM L, ANDRE′S T Topology optimization of piezoelectric energy harvesting skin using hybrid cellular automata[J]. Journal of Mechanical Design, 2013, 135: 1- 11
14 GOETZ J, TAN H, RENAUD J, et al Two-material optimization of plate armor for blast mitigation using hybrid cellular automata[J]. Engineering Optimization, 2012, 44 (8): 985- 1005
doi: 10.1080/0305215X.2011.624182
15 郭连水, PUNIT B, JOHN E R 一种大变形多空间域连续体结构拓扑优化方法[J]. 北京航空航天大学学报, 2009, 35 (2): 227- 230
GUO Lian-shui, PUNIT B, JOHN E R Method of multi-domain topology optimization for continuum structures[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35 (2): 227- 230
16 GUO L S, TOVAR A, PENNINGER C L, et al Strain-based topology optimization for crashworthiness using hybrid cellular automata[J]. International Journal of Crashworthiness, 2011, 13 (3): 239- 252
17 高云凯, 张玉婷, 方剑光 基于混合元胞自动机的铝合金保险杠横梁设计[J]. 同济大学学报: 自然科学版, 2015, 43 (3): 456- 461
GAO Yun-kai, ZHANG Yu-ting, FANG Jian-guang Design of an aluminum bumper beam based on hybrid cellular automata[J]. Journal of Tongji University: Natural Science, 2015, 43 (3): 456- 461
18 DA D C, CHEN J H, CUI X Y, et al Design of materials using hybrid cellular automata[J]. Structural and Multidisciplinary Optimization, 2017, 56: 131- 137
doi: 10.1007/s00158-017-1652-1
19 WENG S B, DENG X L, LIN H, et al Research on thermal topology design method of spindle based on HCAM[J]. IOP Conference Series: Materials Science and Engineering, 2017, 281: 012048
doi: 10.1088/1757-899X/281/1/012048
20 BOCHENEK B, KATARZYNA T Z GOTICA - generation of optimal topologies by irregular cellular automata[J]. Structural and Multidisciplinary Optimization, 2017, 55 (6): 1989- 2001
doi: 10.1007/s00158-016-1614-z
[1] 高云凯,马超,刘哲,徐亚男. 基于畸变比能全局化策略的应力拓扑优化[J]. 浙江大学学报(工学版), 2020, 54(11): 2169-2178.
[2] 谢杰, 黄筱调, 方成刚, 周宝仓, 陆宁. 磨齿机电主轴热特性及热误差建模[J]. 浙江大学学报(工学版), 2018, 52(2): 247-254.
[3] 于东, 张进华, 王东峰, 李小虎, 洪军. RV减速器主轴承摩擦力矩理论计算及特性分析[J]. 浙江大学学报(工学版), 2017, 51(10): 1928-1936.
[4] 熊飞,郝志勇,郑旭,刘瑞骏. 多目标拓扑优化的低响度正时罩设计[J]. 浙江大学学报(工学版), 2016, 50(5): 970-977.
[5] 李特, 芮执元, 雷春丽, 郭俊锋, 胡赤兵. 考虑气隙变化的高速电主轴热特性仿真[J]. 浙江大学学报(工学版), 2016, 50(5): 941-948.
[6] 黄伟迪,甘春标,杨世锡. 一类高速电主轴的动力学建模及振动响应分析[J]. 浙江大学学报(工学版), 2016, 50(11): 2195-2206.
[7] 马驰,杨军,赵亮,梅雪松,施虎,王新孟. 高速主轴系统热特性分析与实验[J]. 浙江大学学报(工学版), 2015, 49(11): 2092-2102.
[8] 邓小雷,傅建中,沈洪垚,陈子辰. 精密数控机床多主轴系统热平衡试验[J]. 浙江大学学报(工学版), 2014, 48(9): 1646-1653.
[9] 杨朝晖, 张进华, 洪军, 姚建国, 王煜. 超高精度滚动轴承旋转精度测试系统误差分析[J]. 浙江大学学报(工学版), 2014, 48(6): 1095-1101.
[10] 杨朝晖, 张进华, 洪军, 姚建国, 王煜. 超高精度滚动轴承旋转精度测试系统误差分析[J]. J4, 2014, 48(1): 0-00.
[11] 李晟,姚鑫骅,傅建中. 基于通信质量约束的主轴热监测无线传感器布点优化[J]. J4, 2013, 47(7): 1281-1286.
[12] 张焕宇, 郝志勇. 飞轮壳结构刚度对机体NVH性能的影响[J]. J4, 2013, 47(2): 261-266.
[13] 单艳玲, 高博青. 基于连续体拓扑优化的网壳结构鲁棒构型分析[J]. J4, 2013, 47(12): 2118-2124.
[14] 邓小雷, 傅建中, 贺永, 陈子辰. 精密数控机床主轴系统多物理场耦合热态特性[J]. J4, 2013, 47(10): 1863-1870.
[15] 蒋君侠, 范子春, 郭志敏, 柯映林. 适用于三段大部件对接的柔性装配平台设计与优化[J]. J4, 2010, 44(9): 1798-1804.