多级盘转子装配不平衡量预测与优化

刘洪慧; 刘亮; 李明华; 东晓; 孙清超

doi:10.13433/j.cnki.1003-8728.20200447

多级盘转子装配不平衡量预测与优化

doi: 10.13433/j.cnki.1003-8728.20200447

大连理工大学机械工程学院, 辽宁大连 116024

基金项目:

中央高校基本科研业务费项目 DUT19LAB17

辽宁省兴辽英才计划项目 XLYC1808016

详细信息

作者简介:
刘洪慧(1996-), 硕士研究生, 研究方向为先进加工工艺与数字化制造装备, 554532568@qq.com

通讯作者:
孙清超, 教授, 博士生导师, 博士, qingchao@dlut.edu.cn

中图分类号: V263.2
计量
- 文章访问数: 133
- HTML全文浏览量: 49
- PDF下载量: 21
- 被引次数: 0
出版历程
- 收稿日期: 2020-10-21
- 刊出日期: 2022-08-25

Prediction and Optimization of Assembly Unbalance of Multi-stage Disc Rotor

School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China

摘要

摘要: 多级盘转子装配是航空发动机转子制造过程中十分重要的一环，其中装配不平衡量的大小直接影响整机振动水平。为了对多级盘转子进行初始不平衡量的预测与优化，通过端面跳动及径向跳动等参数计算获得各单件的表示矩阵，经过堆叠计算获得在以回转轴线为轴的坐标系内的装配体空间位姿，进而获得各单件及整体的静、偶不平衡量，同时获得相对回转轴线位置的各单件质心分布情况，建立装配不平衡量预测模型; 基于预测模型以静、偶不平衡量及质心分布为目标，以装配相位为设计变量利用遗传算法进行多目标优化。结果表明：与原始装配方案相比，根据预测模型进行遗传算法优化之后的初始静不平衡量降低至5.11%，偶不平衡量降低至7.09%，质心分布范围降低至14.29%，优化效果显著，装配质量提升明显，并且与不考虑质心分布的优化相比证明能有效控制质心范围，与穷举法优化相比证明能有效的节约时间，对航空发动机的装配工艺的进步有一定的工程指导意义。
- 初始不平衡量 /
- 质心分布 /
- 装配 /
- 多级盘转子 /
- 预测 /
- 优化
Abstract: The assembly of multi-stage disc rotors is a very important part of the manufacturing process of aero-engine rotors, and the size of the assembly unbalance directly affects the vibration level of the whole aero-engine. In order to predict and optimize the initial unbalance of the multi-stage disc rotor, firstly obtain the representation matrix of each single piece by calculating the parameters such as end runout and radial runout. After stacking calculation, the spatial position and posture of the assembly in the coordinate system with the axis of rotation as the axis are obtained. Then calculate the static unbalance and even unbalance of each single piece and the whole. At the same time, obtain the gravity center distribution of each single piece relative to the position of the axis of rotation, and establish an assembly unbalance prediction model. Based on the predictive model, the genetic algorithm is used for multi-objective optimization. Among them, the static unbalance, the even unbalance and the gravity center distribution are taken as the target, and the assembly phase is taken as the design variable. The results show that compared with the original assembly scheme, the initial static unbalance after genetic algorithm optimization based on the prediction model is reduced to 5.11%, the even unbalance is reduced to 7.09%, and the gravity center distribution range is reduced to 14.29%. The optimization effect is significant, and the assembly quality is improved significantly. Moreover, compared with the other optimization that does not consider the gravity center distribution, it proves that the range of gravity center can be effectively controlled; and compared with the exhaustive method optimization, it proves that it can effectively save time. This study has certain engineering guiding significance for the advancement of aero-engine assembly technology.
- initial unbalance /
- gravity center distribution /
- assembly /
- multi-stage disc rotor /
- prediction /
- optimization

HTML全文

图 1 不平衡量类型

下载: 全尺寸图片幻灯片

图 2 单件偶不平衡量计算

下载: 全尺寸图片幻灯片

图 3 单件的表征方法

下载: 全尺寸图片幻灯片

图 4 轴承处不平衡质量矩计算

下载: 全尺寸图片幻灯片

图 5 整体不平衡量计算

下载: 全尺寸图片幻灯片

图 6 遗传算法NSGA-Ⅱ优化过程

下载: 全尺寸图片幻灯片

图 7 高压模拟转子模型

下载: 全尺寸图片幻灯片

图 8 结果对比

下载: 全尺寸图片幻灯片

图 9 质心分布范围及延回转轴线投影对比

下载: 全尺寸图片幻灯片

表 1 质心位置

零件	x	y	z
1	-0.001 35	-0.000 90	79.928
2	-0.004 65	0.000 26	259.007
3	-0.006 04	0.002 51	382.005
4	-0.007 43	0.004 01	534.981
5	-0.004 04	0.002 90	901.574
6	-0.000 28	0.000 28	1 061.393

下载: 导出CSV

表 2 各单件静不平衡量

零件	大小/(g·mm)	相位/(°)	在Z轴位置/mm
1	13.5	-146.2	79.928
2	32.6	176.7	259.007
3	79.4	157.4	382.005
4	165.2	151.6	534.981
5	264.4	144.2	901.574
6	2.0	135.1	1 061.393

下载: 导出CSV

表 3 各单件偶不平衡量

零件	大小/(g·mm²)	上相位/(°)
1	1 203.3	-146.2
2	-2 274.0	120.3
3	-695.1	129.5
4	-2 347.8	133.4
5	-1 444.6	-30.5
6	88.7	-44.9

下载: 导出CSV

表 4 整个装配体不平衡量

类型	大小	相位/(°)
静不平衡量	544.1 g·mm	151.6
偶不平衡量	36 997 g·mm²	112.9

下载: 导出CSV

表 5 非劣解组

个体	x₁	x₂	x₃	x₄	x₅	F₁	F₂	F₃
1	0	210	170	45	60	115.26	119	0.001 7
2	0	220	150	45	60	74.78	2469	0.001 1
3	0	220	140	45	60	56.74	3631	0.001 1
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
198	350	250	120	60	40	37.80	3806	0.001 0
199	350	250	120	45	60	9.56	7769	0.000 9
200	350	230	120	75	40	51.92	11 187	0.000 9

下载: 导出CSV

表 6 优化结果

	x₁	x₂	x₃	x₄	x₅	F₁	F₂	F₃
初始	0	0	0	0	0	544.1	36 997	0.008 4
优化	40	250	110	45	60	27.84	2 622	0.001 2
优化/初始						5.11%	7.09%	14.29%

下载: 导出CSV

表 7 结果对比

	x₁	x₂	x₃	x₄	x₅	F₁	F₂	F₃
初始	0	0	0	0	0	544.1	36 997	0.008 4
随机1	110	270	60	195	100	664.1	96 583	0.008 1
随机2	70	320	210	300	160	500.6	49 768	0.006 2
随机3	130	150	180	75	140	314.5	75 689	0.004 7
优化	40	250	110	45	60	27.8	2 622	0.001 2

下载: 导出CSV

表 8 两优化方法比较

方法	静不平衡量/(g·mm)	偶不平衡量/(g·mm²)	质心分布/mm
不考虑质心分布的优化	6.31	1 220	0.001 86
考虑质心分布的优化	27.84	2 622	0.001 16

下载: 导出CSV

表 9 遗传算法与穷举法对比

	静不平衡量/(g·mm)	偶不平衡量/(g·mm²)	质心分布/mm	时间/s
穷举法	12.64	2449	0.00119	12600
遗传算法	27.84	2622	0.00116	7.54

下载: 导出CSV

参考文献(21)

[1]	李常有, 徐敏强, 郭耸, 等. 基于模型的转子系统不平衡量的估计[J]. 航空动力学报, 2009, 24(7): 1530-1536 https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI200907017.htm LI C Y, XU M Q, GUO S, et al. Estimation of the unbalance magnitude of rotor system based on model[J]. Journal of Aerospace Power, 2009, 24(7): 1530-1536 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKDI200907017.htm
[2]	张冬梅, 吴法勇, 孟庆明, 等. 基于转子初始不平衡量控制的整机振动排故方法[J]. 航空维修与工程, 2014(2): 62-65 doi: 10.3969/j.issn.1672-0989.2014.02.033 ZHANG D M, WU F Y, MENG Q M, et al. Troubleshooting based on rotor original unbalance controlled in aero-engine vibration[J]. Aviation Maintenance & Engineering, 2014(2): 62-65 (in Chinese) doi: 10.3969/j.issn.1672-0989.2014.02.033
[3]	纪福森, 翟贤超. 某压气机试验件转子平衡精度分析[J]. 航空发动机, 2016, 42(1): 88-91 https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201601019.htm JI F S, ZHAI X C. Analysis of balance precision for a compressor test rig[J]. Aeroengine, 2016, 42(1): 88-91 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201601019.htm
[4]	MANTRIPRAGADA R, WHITNEY D E. Modeling and controlling variation propagation in mechanical assemblies using state transition models[J]. IEEE Transactions on Robotics and Automation, 1999, 15(1): 124-140 doi: 10.1109/70.744608
[5]	WHITNEY D E, GILBERT O L, JASTRZEBSKI. Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies[J]. Research in Engineering Design, 1994, 6(4): 191-210 doi: 10.1007/BF01608399
[6]	孙传智. 基于矢量投影的多级转子同轴度测量方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2017 SUN C Z. Research on coaxiality measurement method based on vector projection for multi-stage rotor[D]. Harbin: Harbin Institute of Technology, 2017 (in Chinese)
[7]	刘泽伟. 航空发动机转子同轴度和不平衡量双目标优化装配方法[D]. 哈尔滨: 哈尔滨工业大学, 2019 LIU Z W. Double objective optimation assembly method of coaxiality and initial unbalance for aero-engine rotors[D]. Harbin: Harbin Institute of Technology, 2019 (in Chinese)
[8]	YANG Z, MCWILLIAM S, POPOV A A, et al. A probabilistic approach to variation propagation control for straight build in mechanical assembly[J]. The International Journal of Advanced Manufacturing Technology, 2013, 64(5-8): 1029-1047 doi: 10.1007/s00170-012-4071-x
[9]	YANG Z, HUSSAIN T, POPOV A A, et al. Novel optimization technique for variation propagation control in an aero-engine assembly[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2011, 225(1): 100-111 doi: 10.1243/09544054JEM2043
[10]	YANG Z, POPOV A A, MCWILLIAM S. Variation propagation control in mechanical assembly of cylindrical components[J]. Journal of Manufacturing Systems, 2012, 31(2): 162-176 doi: 10.1016/j.jmsy.2011.09.003
[11]	刘鑫. 航空发动机转子装配精度预测及堆叠[D]. 大连: 大连理工大学, 2019 LIU X. Assembly accuracy prediction and stacking of aeroengine rotor[D]. Dalian: Dalian University of Technology, 2019 (in Chinese)
[12]	SUN Q C, ZHAO B B, LIU X, et al. Assembling deviation estimation based on the real mating status of assembly[J]. Computer-Aided Design, 2019, 115: 244-255 doi: 10.1016/j.cad.2019.06.001
[13]	曹茂国. 多级盘结构转子的工艺装配优化设计方法[J]. 航空发动机, 1994(3): 48-52 https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ199403005.htm CAO M G. Optimal design method for assembly technology of rotor with multi-stage disc structure[J]. Aeroengine, 1994(3): 48-52 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ199403005.htm
[14]	李立新, 艾延廷, 王志, 等. 基于遗传算法的多级盘转子平衡方案优化设计[J]. 振动、测试与诊断, 2008, 28(2): 139-142 doi: 10.3969/j.issn.1004-6801.2008.02.013 LI L X, AI Y T, WANG Z, et al. Optimum design for balance in multi-disk rotor installation based on genetic algorithm[J]. Journal of Vibration, Measurement & Diagnosis, 2008, 28(2): 139-142 (in Chinese) doi: 10.3969/j.issn.1004-6801.2008.02.013
[15]	刘君, 吴法勇, 王娟. 航空发动机转子装配优化技术[J]. 航空发动机, 2014, 40(3): 75-78 https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201403021.htm LIU J, WU F Y, WANG J. Optimization technique of aeroengine rotor assembly[J]. Aeroengine, 2014, 40(3): 75-78 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201403021.htm
[16]	吴法勇, 王娟. 基于同心度测量的转子不平衡量装配优化技术[C]//第十五届中国科协年会分动、与会论文集. 中贵阳: 中国科学技术协会, 2013 WU F Y, WANG J. Rotor unbalance assembly optimization technology based on concentricity measurement[C]//The 13th session of the 15th China Association for Science and Technology Annual Conference. Guiyang: Aeroengine Design, Manufacturing and Application Technology Seminar, 2013 (in Chinese)
[17]	琚奕鹏, 吴法勇, 金彬, 等. 基于转子跳动和初始不平衡量优化的多级盘转子结构装配工艺[J]. 航空发动机, 2018, 44(6): 83-90 https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201806016.htm JU Y P, WU F Y, JIN B, et al. Structure assembly technique of multi-stage disc rotor based on rotor runout and unbalance optimization[J]. Aeroengine, 2018, 44(6): 83-90 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201806016.htm
[18]	石宏. 航空发动机装配工艺技术[M]. 北京: 北京航空航天大学出版社, 2015 SHI H. Assembly process technology of aeroengine[M]. Beijing: Beihang University Press, 2015 (in Chinese)
[19]	周仁睦. 转子动平衡-原理、方法和标准[M]. 北京: 化学工业出版社, 1992 ZHOU R M. Rotor dynamic balance[M]. Beijing: Chemical Industry Press, 1992 (in Chinese)
[20]	毛荣宝. 刚体绕非惯性主轴转动时不平衡力偶的计算方法[J]. 力学与实践, 1994, 16(6): 63-65 https://www.cnki.com.cn/Article/CJFDTOTAL-LXYS406.018.htm MAO R B. Calculation method of unbalanced couple when a rigid body rotates around a non-inertial main shaft[J]. Mechanics and Practice, 1994, 16(6): 63-65 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXYS406.018.htm
[21]	ISO. ISO 1101 Geometrical product specifications (GPS)- geometrical tolerancing-tolerances of form, orientation, location and run-out[S]. ISO, 2012