基于Cotes求积法和神经网络的稳定域判断及铣削参数优化新方法

doi:10.12382/bgxb.2022.0673

摘要/Abstract

摘要：

再生效应引起的铣削颤振,是制约加工效率和工件质量的主要因素之一。准确高效地识别铣削颤振的稳定域,是抑制颤振、提高生产效率的关键步骤。为此,根据铣削振动微分方程,利用柯特斯积分法(Cotes Integration Method,CIM)提出一种新的铣削稳定域预测方法。利用CIM获得主轴转速-轴向切深平面二维稳定性叶瓣图(Stability Lobe Diagram,SLD),与半离散法(Semi-discretization Method,SDM)和全离散法(Full-discretization Method,FDM)等方法进行比较,结果表明CIM的收敛性更优。考虑径向切深的影响,建立三维SLD的迭代计算方法,通过等效地离散三维SLD曲面为节点集合,随机以90%的节点作为训练集,构建轴向切深与主轴转速、径向切深之间的神经网络预测模型。10%验证集的预测结果表明神经网络的预测误差不超过6%。以材料去除率为效率目标,刀具寿命为成本目标,建立稳定铣削多目标优化模型并应用基于分解的多目标进化算法(Multiobjective Evolutionary Algorithm Based on Decomposition, MOEA/D)求解,为获得高效率、低成本的最优铣削参数提供基础理论和技术支撑。

关键词: 铣削, 颤振, Cotes积分, 神经网络, 遗传算法

Abstract:

Milling chatter caused by regeneration effect is one of the main factors restricting machining efficiency and workpiece quality. The accurate and efficient identification of milling chatter stability is crucial to suppress the chatter and improve the production efficiency. Therefore, a predication method for milling chatter stability is investigated using the Cotes integration method (CIM) on basis of the milling vibration differential equation. The 2D stability lobe diagram (SLD) is obtained by CIM, which is compared with 1st semi-discretization method (SDM), 1st semi-discretization method (FDM) and 2nd FDM. The results show that CIM is of better convergence. Considering the effect of radial depth of cut on SLD, an iterative calculation method of 3D SLD is established. After equivalently discretizing 3D SLD surfaces as a set of nodes, a neural network prediction model between axial depth of cut and spindle speed and radial depth of cut is constructed by randomly using 90% of the nodes as the training set and 10% of the nodes as the validation set. The predicted results show that the predicted error of neural network is no more than 6%. Finally, a multi-objective optimization model of stable milling is suggested with the objective of the material removal rate and tool life in addition to the corresponding MOEA/D. It provides basic theory and technical support for obtaining the optimal milling parameters with high efficiency and low cost.

Key words: milling operation, chatter, cotes integration, neural network, genetic algorithm

中图分类号:

TH161

秦国华, 娄维达, 林锋, 徐勇. 基于Cotes求积法和神经网络的稳定域判断及铣削参数优化新方法[J]. 兵工学报, 2024, 45(2): 516-526.

QIN Guohua, LOU Weida, LIN Feng, XU Yong. A Novel Method of Stability Judgment and Milling Parameter Optimization Based on Cotes Integration Method and Neural Network[J]. Acta Armamentarii, 2024, 45(2): 516-526.

图/表 18

参考文献 23

[1]	ALTINTAŞ Y, BUDAK E. Analytical prediction of stability lobes in milling[J]. CIRP Annals-Manufacturing Technology, 1995, 44(1): 357-362. doi: 10.1016/S0007-8506(07)62342-7 URL
[2]	INSPERGER T, STEPAN G. Updated semi-discretization method for periodic delay-differential equations with discrete delay[J]. International Journal for Numerical Methods in Engineering, 2004, 61: 117-141. doi: 10.1002/nme.v61:1 URL
[3]	INSPERGER T, STEPAN G, TURI J. On the higher-order semi-discretizations for periodic delayed systems[J]. Journal of Sound and Vibration, 2008, 313(1): 334-341. doi: 10.1016/j.jsv.2007.11.040 URL
[4]	DING Y, ZHU L M, ZHANG X J, et al. A full-discretization method for prediction of milling stability[J]. International Journal of Machine Tools and Manufacture, 2010, 50(5): 502-509. doi: 10.1016/j.ijmachtools.2010.01.003 URL
[5]	CHEN D, ZHANG X J, DING H. A novel Chebyshev-Gauss pseudospectral method for accurate milling stability prediction[J]. The International Journal of Advanced Manufacturing Technology, 2021, 117(9): 2867-2881. doi: 10.1007/s00170-021-07713-z
[6]	WU Y, YOU Y P, LIU A M. et al. A correction method for milling stability analysis based on local truncation error[J]. The International Journal of Advanced Manufacturing Technology, 2021, 115: 2873-2887. doi: 10.1007/s00170-021-07262-5
[7]	ZHAN D N, JIANG S L, LI S K, et al. A hybrid multi-step method based on 1/3 and 3/8 Simpson formulas for milling stability prediction[J]. The International Journal of Advanced Manufacturing Technology, 2022, 120(1): 265-277. doi: 10.1007/s00170-022-08705-3
[8]	WAN M, DANG X B, ZHANG W H, et al. Optimization and improvement of stable processing condition by attaching additional masses for milling of thin-walled workpiece[J]. Mechanical Systems and Signal Processing, 2018, 103: 196-215. doi: 10.1016/j.ymssp.2017.10.008 URL
[9]	YUAN H, WAN M, YANG Y, et al. A tunable passive damper for suppressing chatters in thin-wall milling by considering the varying modal parameters of the workpiece[J]. The International Journal of Advanced Manufacturing Technology, 2019, 104(9): 4605-4616. doi: 10.1007/s00170-019-04316-7
[10]	秦国华, 娄维达, 吴竹溪, 等. 基于过程阻尼和结构模态耦合的铣削稳定性分析与实验验证[J]. 中国科学:技术科学, 2020, 50(9): 1211-1225.
	QIN G H, LOU W D, WU Z X, et al. Milling stability analysis and validation based on the coupling of process damping and structural mode[J]. SCIENTIA SINICA Technologica, 2020, 50(9): 1211-1225 (in Chinese) doi: 10.1360/SST-2019-0325 URL
[11]	张洁, 刘成颖, 郑烽, 等. 基于铣削动力学的刀具强迫振动抑制研究[J]. 机械工程学报, 2018, 54(17): 94-99. doi: 10.3901/JME.2018.17.094
	ZHANG J, LIU C Y, ZHENG F, et al. Research on suppression of the forced vibration of the cutter based on the milling dynamics[J]. Journal of Mechanical Engineering, 2018, 54(17): 94-99. (in Chinese) doi: 10.3901/JME.2018.17.094
[12]	GUO J J, LEE K M, YU M, et al. Regenerative effects of orthogonal chip dimensions on turning stability of thin-wall workpiece-tool coupled dynamics[J]. IEEE/ASME Transactions on Mechatronics, 2022, 27(5):3601-3612. doi: 10.1109/TMECH.2021.3135808 URL
[13]	曾莎莎, 彭卫平, 雷金. 基于混合算法的薄壁件铣削加工工艺参数优化[J]. 中国机械工程, 2017, 28(7): 842-845, 851.
	ZENG S S, PENG W P, LEI J. Optimization of milling process parameters based on hybrid algorithm for thin-walled workpieces[J]. China Mechanical Engineering, 2017, 28(7): 842-845, 851. (in Chinese)
[14]	RINGGAARD K, MOHAMMADI Y, MERRILD C, et al. Optimization of material removal rate in milling of thin-walled structures using penalty cost function[J]. International Journal of Machine Tools and Manufacture, 2019, 145: 103430. doi: 10.1016/j.ijmachtools.2019.103430 URL
[15]	THANGARASU S K, SHANKAR S, DEVENDRAN K, et al. Tool wear prediction in hard turning of EN8 steel using cutting force and surface roughness with artificial neural network[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2020, 234(1): 329-342. doi: 10.1177/0954406219873932 URL
[16]	郭强, 李红霞, 李玉晓. 基于改进粒子群算法的数控加工参数优化研究[J]. 机械制造与自动化, 2021, 50(3): 132-135.
	GUO Q, LI H X, LI Y X. Research on optimization of NC machining parameters based on improved particle swarm optimization[J]. Machine Building & Automation, 2021, 50(3): 132-135. (in Chinese)
[17]	刘献礼, 孙庆贞, 岳彩旭, 等. 基于数据挖掘技术的钛合金铣削工艺参数优化[J]. 计算机集成制造系统, 2022, 28(8): 2440-2448.
	LIU X L, SUN Q Z, YUE C X, et al. Optimization of milling process parameters of titanium alloy based on data mining technology[J]. Computer Integrated Manufacturing Systems, 2022, 28(8): 2440-2448. (in Chinese)
[18]	曹宏瑞, 陈雪峰, 何正嘉. 主轴-切削交互过程建模与高速铣削参数优化[J]. 机械工程学报, 2013, 49(5): 161-166.
	CAO H R, CHEN X F, HE Z J. Modeling of spindle-process interaction and cutting parameters optimization in high-speed milling[J]. Journal of Mechanical Engineering, 2013, 49(5): 161-166. (in Chinese)
[19]	胡瑞飞, 殷鸣, 刘雁, 等. 切削稳定性约束下的铣削参数优化技术研究[J]. 机械工程学报, 2017, 53(5): 190-198. doi: 10.3901/JME.2017.05.190
	HU R F, YIN M, LIU Y, et al. Optimization of milling parameters under constrain of process stability[J]. Journal of Mechanical Engineering, 2017, 53(5): 190-198. (in Chinese) doi: 10.3901/JME.2017.05.190
[20]	DING Y, ZHU L M, ZHANG X J, et al. Second-order full-discretization method for milling stability prediction[J]. International Journal of Machine Tools and Manufacture, 2010, 50(5): 926-932. doi: 10.1016/j.ijmachtools.2010.05.005 URL
[21]	PALUZO-HIDALGO E, GONZALEZ-DIAZ R, GUTIÉRREZ-NARANJO M A. Two-hidden-layer feed-forward networks are universal approximators: a constructive approach[J]. Neural Networks, 2020, 131: 29-36. doi: 10.1016/j.neunet.2020.07.021 URL
[22]	秦国华, 高杰, 叶海潮, 等. 基于融合指标和神经网络的刀具磨损预测[J]. 兵工学报, 2021, 42(9): 2013-2023. doi: 10.3969/j.issn.1000-1093.2021.09.022
	QIN G H, GAO J, YE H C, et al. Tool wear prediction based on fusion evaluation index and neural network[J]. Acta Armamentarii, 2021, 42(9): 2013-2023. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.09.022
[23]	ZHANG Q F, LI H. MOEA/D: a multiobjective evolutionary algorithm based on decomposittion[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712-731. doi: 10.1109/TEVC.2007.892759 URL

参数	数值
阻尼比ζ	0.011
固有圆频率ω_n/Hz	922×2π
刀具模态质量m_t/kg	0.03993
切向切削力系数K_t/(N·m^-2)	6×10⁸
径向切削力系数K_r/(N·m^-2)	2×10⁸
铣刀齿数N	2
铣刀直径D/mm	19.05
径向切深a_e/mm	19.05
铣削方式	顺铣

参数	数值
阻尼比ζ	0.011
固有圆频率ω_n/Hz	922×2π
刀具模态质量m_t/kg	0.03993
切向切削力系数K_t/(N·m^-2)	6×10⁸
径向切削力系数K_r/(N·m^-2)	2×10⁸
铣刀齿数N	2
铣刀直径D/mm	19.05
径向切深a_e/mm	19.05
铣削方式	顺铣

参数	数值
模态阻尼c/(N·s·m^-1)	18.16
固有频率ω_n/Hz	1423
模态质量m_t/kg	0.029
模态刚度/(10⁶N·m^-1)	2.31
切向切削力系数K_t/(10⁸N·m^-2)	13.85
径向切削力系数K_r/(10⁸N·m^-2)	11.65
铣刀齿数N	3
铣刀直径D/mm	12

参数	数值
模态阻尼c/(N·s·m^-1)	18.16
固有频率ω_n/Hz	1423
模态质量m_t/kg	0.029
模态刚度/(10⁶N·m^-1)	2.31
切向切削力系数K_t/(10⁸N·m^-2)	13.85
径向切削力系数K_r/(10⁸N·m^-2)	11.65
铣刀齿数N	3
铣刀直径D/mm	12

序号	转速x₁/ (r·min^-1)	径向浸入比x₂	轴向切深y/m		误差/ %
序号	转速x₁/ (r·min^-1)	径向浸入比x₂	原始值	预测值	误差/ %
1	5800	0.01	0.003788942	0.003698179	2.3955
2	5760	0.05	0.001762478	0.001754662	0.4434
3	5800	0.1	0.001344508	0.00130052	3.2716
4	2780	0.15	0.000550624	0.000544134	1.1786
5	5900	0.2	0.000649173	0.000624724	3.7663
6	3180	0.25	0.000507705	0.000504448	0.6416
7	5000	0.3	0.000367626	0.000358995	2.3478
8	4800	0.35	0.000513988	0.000517069	-0.5993
9	5780	0.4	0.000525816	0.000498949	5.1096
10	4820	0.45	0.00036719	0.000353512	3.7250
11	5800	0.5	0.000340852	0.000330868	2.9290
12	2900	0.55	0.000190949	0.000180258	5.5987
13	3360	0.6	0.000141559	0.000140361	0.8458
14	3060	0.65	0.000141542	0.000142642	-0.7772
15	5660	0.7	0.00027032	0.000270943	-0.2305
16	3120	0.75	0.000145395	0.000148787	-2.3335
17	4940	0.8	0.000115155	0.000111805	2.9092
18	3640	0.9	0.000107789	0.00010285	4.5815
19	4020	0.95	0.000129277	0.000131375	-1.6234
20	5520	1	0.000115811	0.000116823	-0.8742