薄壁铣削加工颤振稳定性研究综述

PDF(758 KB)

振动与冲击 ›› 2021, Vol. 40 ›› Issue (8) : 50-61.

论文

薄壁铣削加工颤振稳定性研究综述

卢晓红，杨昆，栾贻函，侯鹏荣，顾瀚

作者信息 +

A review on chatter stability in thin-wall milling

LU Xiaohong，YANG Kun，LUAN Yihan，HOU Pengrong，GU Han

Author information +

文章历史 +

摘要

针对薄壁铣削过程中的颤振问题。论述了薄壁铣削加工再生型颤振理论模型的研究进展；深入探讨颤振的根源—铣削力模型，对比分析薄壁铣削力经验模型、有限元模型及解析模型的优缺点；对薄壁铣削系统动态特性进行详细论述；刀尖频响函数求取法分为试验法、模态综合法和动柔度子结构耦合法；薄壁件动态特性研究法分为试验法、有限元法及解析法，详细论述了各种方法的原理、研究现状及优缺点。详细对比分析了频域法和时域法这两种稳定性求解方法，对介观尺度薄壁微铣削颤振稳定性相关研究进行探讨；并对薄壁铣削加工颤振稳定性研究现状和后续研究方向进行归纳和探讨。

Abstract

Aiming at the chatter problems in thin-wall milling, the research progress of regenerative chatter theoretical models of thin-wall milling was discussed firstly in this work. Then, the milling force model, which is the root of the chatter, was discussed in depth, and the advantages and disadvantages of empirical models, finite element models, and analytical models of milling force were comparatively analyzed. Afterwards, the dynamic characteristics of thin-wall milling systems were discussed in detail. The methods of calculating the frequency response function of the tool tip were divided into experimental method, finite element method, and analytical method. The principles, research status, advantages, and disadvantages of these methods were discussed. Frequency-domain methods and time-domain methods for solving stability problems were comparatively analyzed. Related research on chatter stability of micro-milling meso-scale thin-wall was discussed. Finally, the research status and future directions of chatter stability of milling thin-walled parts were summarized and explored.

导出引用

卢晓红，杨昆，栾贻函，侯鹏荣，顾瀚. 薄壁铣削加工颤振稳定性研究综述[J]. 振动与冲击, 2021, 40(8): 50-61

LU Xiaohong，YANG Kun，LUAN Yihan，HOU Pengrong，GU Han. A review on chatter stability in thin-wall milling[J]. Journal of Vibration and Shock, 2021, 40(8): 50-61

参考文献

［1］蒋宇平,龙新华,孟光.薄壁结构件铣削加工振动稳定性分析［J］. 振动与冲击, 2016,35(2): 45-50.
JIANG Yuping, LONG Xinhua, MENG Guang. Stability analysis for thin-walled milling processes［J］. Journal of Vibration and Shock, 2016,35(2): 45-50.

［2］JIN X, SUN Y W, GUO Q, et al. 3D stability lobe considering the helix angle effect in thin-wall milling［J］. International Journal of Advanced Manufacturing Technology, 2016,82(9/10/11/12): 2123-2136.

［3］BUDAK E. Mechanics and dynamics of milling thin walled structures［D］. Vancouver: University of British Columbia, 1994.

［4］LAPUJOLADE F, MABROUKI T, RASSI K. Prédiction du comportement vibratoire du fraisage latéral de finition des pièces à parois minces［J］. Mecanique et Industries, 2002,3(4): 403-418.

［5］THEVENOT V, ARNAUD L, DESSEIN G, et al. Influence of material removal on the dynamic behavior of thin-walled structures in peripheral milling［J］. Machining Science and Technology, 2006,10(3): 275-287.

［6］THEVENOT V, ARNAUD L, DESSEIN G, et al. Integration of dynamic behavior variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling［J］. International Journal of Advanced Manufacturing Technology, 2006,27(7/8): 638-644.

［7］LI Z Y, SUN Y N, GUO D M. Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece［J］. International Journal of Advanced Manufacturing Technology, 2017,89(9/10/11/12): 2663-2674.

［8］张雪薇，于天彪，王宛山. 薄壁零件铣削三维颤振稳定性建模与分析［J］. 东北大学学报(自然科学版), 2015,36(1): 99-103.
ZHANG Xuewei，YU Tianbiao，WANG Wanshan. Modeling and analysis for 3D chatter stability of thin-walled parts in milling process［J］. Journal of Northeastern University(Natural Science), 2015,36(1): 99-103.

［9］SEGUY S, DESSEIN G, ARNAUD L. Surface roughness variation of thin wall milling, related to modal interactions［J］. International Journal of Machine Tools and Manufacture, 2008,48(3/4): 261-274.

［10］葛茂杰,单国峰,于健,等.钛合金薄壁件相关铣削力模型的试验研究［J］. 工具技术, 2015,49(10): 44-47.
GE Maojie, SHAN Guofeng, YU Jian, et al. Experimental research on milling force model of titanium alloy thin wall workpiece ［J］. Tool Engineering, 2015,49(10): 44-47.

［11］武凯, 何宁, 廖文和, 等. 薄壁腹板加工变形规律及其变形控制方案的研究［J］. 中国机械工程, 2004,15(8): 670-674.
WU Kai, HE Ning, LIAO Wenhe, et al. Study on machining deformations and their control approaches of the thin-web in end milling［J］. China Mechanical Engineering, 2004,15(8): 670-674.

［12］何永强, 曹岩. 基于薄壁件铣削力模型的应用分析［J］. 机械工程师, 2007(10): 4-6.
HE Yongqiang, CAO Yan. Study on application of force models of thin-wall part milling［J］. Mechanical Engineer, 2007(10): 4-6.

［13］乔帆,任斐,刘晓,等.薄壁零件端铣建模与试验研究［J］.机械制造, 2019,57(8): 80-83.
QIAO Fan, REN Fei, LIU Xiao, et al. Modeling and experimental research on end milling of thin-walled parts［J］. Machinery, 2019,57(8): 80-83.

［14］丁杰, 孙博, 刘践丰, 等. 端铣刀五坐标曲面加工刀位计算方法研究［J］. 机械制造, 2015,53(7): 58-60.
DING Jie, SUN Bo, LIU Jianfeng, et al. Research on the calculation method of cutter position in five-coordinate surface machining of end milling cutter［J］. Machinery, 2015,53(7): 58-60.

［15］郑金兴. 粒子群优化人工神经网络在高速铣削力建模中的应用［J］. 计算机集成制造系统, 2008,14(9): 1710-1716.
ZHENG Jinxing. Application of particle-swarm optimization-trained artificial neural network in high speed milling force modeling［J］. Computer Integrated Manufacturing Systems, 2008,14(9): 1710-1716.

［16］王凌云, 黄红辉, 谢志江. 航空铝合金薄壁零件高速加工铣削力［J］. 中南大学学报(自然科学版), 2017,48(7): 1756-1761.
WANG Lingyun, HUANG Honghui, XIE Zhijiang. Milling force of aerospace aluminum alloy thin-wall parts in high-speed machining［J］. Journal of Central South University (Science and Technology), 2017,48(7): 1756-1761.

［17］王飞, 程祥, 杨先海, 等. 微型薄壁件的微细铣削机理与工艺研究［J］. 组合机床与自动化加工技术, 2018(7): 160-163.
WANG Fei, CHENG Xiang, YANG Xianhai, et al. Study of mechanism and technology for miniature thin wall in micro-milling［J］. Modular Machine Tool and Automatic Manufacturing Technique, 2018(7): 160-163.

［18］岳彩旭, 刘鑫, 何耿煌, 等. 钛合金薄壁件铣削过程有限元仿真分析［J］. 航空制造技术, 2019,62(13): 60-66.
YUE Caixu, LIU Xin, HE Genghuang, et al. Finite element simulation analysis of titanium alloy thin-walled milling process［J］. Aeronautical Manufacturing Technology, 2019,62(13): 60-66.

［19］TSAI J S, LIAO C L. Finite-element modeling of static surface errors in the peripheral milling of thin-walled workpieces［J］. Journal of Materials Processing Technology, 1999,94(2/3): 235-246.

［20］车现发. 高强度铝合金航空薄壁件铣削加工变形控制的工艺研究［D］. 南京：南京航空航天大学, 2011.

［21］宋戈. 基于切削力精确建模的钛合金薄壁件让刀变形预测研究［D］. 济南：山东大学, 2012.

［22］RATCHEV S, LIU S, HUANG W, et al. A flexible force model for end milling of low-rigidity parts［J］. Journal of Materials Processing Technology, 2004,153/154(1/2/3): 134-138.

［23］丁洋. 一种面向钛合金薄壁件的铣削颤振预测方法的研究［D］. 沈阳：东北大学, 2017.

［24］王灼建,贺辛亥,董红坤,等.铝合金薄壁零件铣削力模型的研究［J］. 机床与液压, 2016,44(3): 154-157.
WANG Zhuojian, HE Xinhai, DONG Hongkun, et al. Research on model of milling force of thin-walled parts with aluminum［J］. Machine Tool and Hydraulics, 2016,44(3): 154-157.

［25］MESHREKI M. Dynamics of thin-walled aerospace structures for fixture design in multi-axis milling［M］. Montreal: McGill University ProQuest Dissertations Publishing, 2009.

［26］EKSIOGLU C, KILIC Z M, ALTINTAS Y. Discrete-time prediction of chatter stability, cutting forces, and surface location errors in flexible milling systems［J］. Journal of Manufacturing Science and Engineering, 2012,134(6): 061006.

［27］MERDOL S D, ALTINTAS Y. Multi frequency solution of chatter stability for low immersion milling［J］. Journal of Manufacturing Science and Engineering, 2004,126(3): 459-466.

［28］宋盛罡,边立健,冯闯.考虑加工余量的叶轮颤振稳定域预测分析［J］. 机械工程师, 2018(11): 125-128.
SONG Shenggang, BIAN Lijian, FENG Chuang. Prediction and analysis of impeller flutter stability region considering machining margin［J］. Mechanical Engineer, 2018(11): 125-128.

［29］赵慧楠. 基于过程阻尼的铣削加工薄壁件颤振稳定性及参数优化研究［D］. 沈阳：东北大学,2015.

［30］AHMADI K. Machining chatter in flank milling and investigation of process damping in surface generation［D］. Waterloo: University of Waterloo, 2011.

［31］YUE C X, GAO H N, LIU X L, et al. Analytical prediction of part dynamics and process damping for machining stability analysis［J］. Procedia CIRP, 2018,72: 1463-1468.

［32］LI Z Y, JIANG S L, SUN Y W. Chatter stability and surface location error predictions in milling with mode coupling and process damping［J］. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2019,233(3): 686-698.

［33］WANG D Q, LSER M, IHLENFELDT S, et al. Milling stability analysis with considering process damping and mode shapes of in-process thin-walled workpiece［J］. International Journal of Mechanical Sciences, 2019,159: 382-397.

［34］DING Y, ZHU L D. Investigation on chatter stability of thin-walled parts considering its flexibility based on finite element analysis［J］. International Journal of Advanced Manufacturing Technology, 2018,94(9/10/11/12): 3173-3187.

［35］赵福桂, 戚厚军.考虑刀具和工件动态耦合特性的薄壁件铣削稳定性研究［J］. 机械工程师, 2016(1): 6-8.
ZHAO Fugui, QI Houjun. Study on the milling stability of thin-walled components considering the dynamic coupling characteristics between tool and workpiece［J］. Mechanical Engineer, 2016(1): 6-8.

［36］敦艺超. 面向薄壁件的铣削颤振稳定性及参数优化的研究［D］. 沈阳：东北大学, 2017.

［37］BUDAK E, ALTINTAS Y. Analytical prediction of chatter stability in milling. Part Ⅰ: general formulation［C］//Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, ASME Dynamic Systems and Control Division 1995.San Francisco: ASME, 1995.

［38］KIVANC E B, BUDAK E. Structural modeling of end mills for form error and stability analysis［J］. International Journal of Machine Tools & Manufacture, 2004,44(11): 1151-1161.

［39］SINGH K K, KULKARNI S S, KARTIK V, et al. A free interface component mode synthesis approach for determining the micro-end mill dynamics［J］. Journal of Micro and Nano-Manufacturing, 2018,6(3): 031005.

［40］SCHMITZ T L, DONALSON R R. Predicting high-speed machining dynamics by substructure analysis［J］. CIRP Annals-Manufacturing Technology, 2000,49(1): 303-308.

［41］SCHMITZ T L, DAVIES M A, KENNEDY M D. Tool point frequency response prediction for high-speed machining by RCSA［J］. Journal of Manufacturing Science and Engineering, 2001,123(4): 700-707.

［42］MASCARDELLI B A, PARK S S, FREIHEIT T. Substructure coupling of microend mills to aid in the suppression of chatter［J］. Journal of Manufacturing Science and Engineering, 2008,130(1): 119-129.

［43］SCHMITZ T L, HONEYCUTT A. Analytical solutions for fixed-free beam dynamics in thin rib machining［J］. Journal of Manufacturing Processes, 2017,30: 41-50.

［44］SCHMITZ T L, DUNCAN G S. Three-component receptance coupling substructure analysis for tool point dynamics prediction［J］. Journal of Manufacturing Science and Engineering, 2005,127(4): 781-790.

［45］LIU W. Structural dynamic analysis and testing of coupled structures［D］. London: Imperial College London, 2000.

［46］MOVAHHEDY M R, GERAMI J M. Prediction of spindle dynamics in milling by sub-structure coupling［J］. International Journal of Machine Tools & Manufacture, 2006,46(3/4): 243-251.

［47］LU X H, JIA Z Y, ZHANG H X, et al. Tool point frequency response prediction for micro-milling by receptance coupling substructure analysis［J］. Journal of Manufacturing Science and Engineering, 2017,139(7): 071004.

［48］NAMAZI M, ALTINTAS Y, ABE T, et al. Modeling and identification of tool holder-spindle interface dynamics［J］. International Journal of Machine Tools & Manufacture, 2007,47(9): 1333-1341.

［49］FILIZ S, CHENG C H, POWELL K B, et al. An improved tool-holder model for RCSA tool-point frequency response prediction［J］. Precision Engineering, 2009,33(1): 26-36.

［50］ERTRK A, ZGVEN H N, BUDAK E. Analytical modeling of spindle-tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF［J］. International Journal of Machine Tools and Manufacture, 2006,46(15): 1901-1912.

［51］SCHMITZ T L. Torsional and axial frequency response prediction by RCSA［J］. Precision Engineering, 2010,34(2): 345-356.

［52］SCHMITZ T L, DONALSON R R. Predicting high-speed machining dynamics by substructure analysis［J］. CIRP Annals-Manufacturing Technology, 2000,49(1): 303-308.

［53］王二化, 吴波, 胡友民, 等. 主轴－刀柄－刀具系统刀尖频响函数的预测方法研究［J］. 振动与冲击, 2015,34(13): 83-88.
WANG Erhua, WU Bo, HU Youmin, et al. Tool nose FRF prediction of a spindle-holder-tool system［J］. Journal of Vibration and Shock, 2015,34(13): 83-88.

［54］MANCISIDOR I, ZATARAIN M, MUNOA J, et al. Fixed boundaries receptance coupling substructure analysis for tool point dynamics prediction［J］. Advanced Materials Research, 2011,223: 622-631.

［55］KIVANC E B, BUDAK E. Structural modeling of end mills for form error and stability analysis［J］. International Journal of Machine Tools & Manufacture, 2004,44(11): 1151-1161.

［56］MANCISIDOR I, URKIOLA A, BARCENA R, et al. Receptance coupling for tool point dynamic prediction by fixed boundaries approach［J］. International Journal of Machine Tools and Manufacture, 2014,78: 18-29.

［57］JUN M B G, LIU X Y, DEVOR R E, et al. Investigation of the dynamics of microend milling. Part Ⅰ: model development［J］. Journal of Manufacturing Science and Engineering, 2006,128: 893-900.

［58］王二化, 许志荣, 叶锋. 立式铣床刀尖频响函数预测方法研究［J］. 机床与液压, 2017,45(11): 138-142.
WANG Erhua, XU Zhirong, YE Feng. Prediction method research of tool point FRF of vertical milling machine［J］. Machine Tool and Hydraulics, 2017,45(11): 138-142.

［59］LU X H, JIA Z Y, LIU S Q, et al. Chatter stability of micro-milling by considering the centrifugal force and gyroscopic effect of the spindle［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2019,141(11): 1-32.

［60］ALBERTELLI P, GOLETTI M, MONNO M. A new receptance coupling substructure analysis methodology to improve chatter free cutting conditions prediction［J］. International Journal of Machine Tools and Manufacture, 2013,72: 16-24.

［61］DENG C Y, MIAO J G, WEI B, et al. Evaluation of machine tools with position-dependent milling stability based on Kriging model［J］. International Journal of Machine Tools and Manufacture, 2018,124: 33-42.

［62］WANG D Q, WANG X B, LIU Z B, et al. Surface location error prediction and stability analysis of micro-milling with variation of tool overhang length［J］. International Journal of Advanced Manufacturing Technology, 2018,99(1/2/3/4): 919-936.

［63］刘圣前. 考虑离心力和陀螺效应的微铣削稳定性研究［D］.大连：大连理工大学,2018.

［64］孙超. 基于刀具和工件刚度特性的钛合金薄壁件切削稳定性研究［D］. 济南：山东大学,2012.

［65］KOLLURU K, AXINTE D. Coupled interaction of dynamic responses of tool and workpiece in thin wall milling［J］. Journal of Materials Processing Technology, 2013,213(9): 1565-1574.

［66］杨昀. 薄壁件铣削系统动力学建模及稳定性预测方法研究［D］.西安：西北工业大学,2016.

［67］BRAVO U, ALTUZARRA O, DE LACALLE L N L, et al. Stability limits of milling considering the flexibility of the workpiece and the machine［J］. International Journal of Machine Tools and Manufacture, 2005,45(15): 1669-1680.

［68］刘冬生,张定华,罗明,等.基于PVDF薄膜传感器的薄壁件铣削振动在线监测与分析［J］.机械工程学报, 2018,54(17): 116-123.
LIU Dongsheng, ZHANG Dinghua, LUO Ming, et al. On-line vibration monitoring and analysis of thin-walled workpiece based on PVDF film sensor in milling process［J］. Journal of Mechanical Engineering, 2018,54(17): 116-123.

［69］ALTINTAS Y, MONTGOMERY D, BUDAK E. Dynamic peripheral milling of flexible structures［J］. Journal of Engineering for Industry, 1992,114(2): 137-145.

［70］CAMPOMANES M L, ALTINTAS Y. An improved time domain simulation for dynamic milling at small radial immersions［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2003,125(3): 416-422.

［71］LI H Q, SHIN Y C. A comprehensive dynamic end milling simulation model［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2006,128(1): 86-95.

［72］LORONG P, COFFIGNAL G, COHEN-ASSOULINE S. Simulation du comportement dynamique dún système usinant: modélisation de línteraction outil/matière en présence dúne pièce flexible［J］. Mecanique et Industries, 2008,9(2): 117-124.

［73］SEGUY S, DESSEIN G, ARNAUD L. Surface roughness variation of thin wall milling, related to modal interactions［J］. International Journal of Machine Tools and Manufacture, 2008,48(3/4): 261-274.

［74］TSAI M P, TSAI N C, YEH C W. On milling of thin-wall conical and tubular workpieces［J］. Mechanical Systems and Signal Processing, 2016,72/73: 395-408.

［75］CHEUNG Y K. Finite strip method in structural analysis［M］. Amsterdam: Elsevier, 2013.

［76］SINGIRESU S R. Vibration of continuous systems［M］. New York: Wiley, 2007.

［77］MESHREKI M, ATTIA H, KVECSES J. Development of a new model for the varying dynamics of flexible pocket-structures during machining［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2011,133(4): 041002.

［78］AHMADI K. Finite strip modeling of the varying dynamics of thin-walled pocket structures during machining［J］. The International Journal of Advanced Manufacturing Technology, 2017,89(9/10/11/12): 2691-2699.

［79］杨昀, 张卫红, 党建卫, 等. 航空薄壁件铣削加工动力学仿真技术［J］. 航空制造技术, 2018,61(7): 42-47.
YANG Yun, ZHANG Weihong, DANG Jianwei, et al. Simulation technology of machining dynamics of aviation thin wall parts［J］. Aeronautical Manufacturing Technology, 2018,61(7): 42-47.

［80］SONG Q H, LIU Z Q, WAN Y, et al. Application of sherman-morrison-woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component［J］. International Journal of Mechanical Sciences, 2015,96/97: 79-90.

［81］JU G G, SONG Q H, LIU Z Q, et al. Instantaneous dynamics of multi-axis milling thin-walled workpiece with complex curved surface［J］. Materials Science Forum, 2016,836/837: 529-535.

［82］YANG Y, ZHANG W H, MA Y C, et al. Chatter prediction for the peripheral milling of thin-walled workpieces with curved surfaces［J］. International Journal of Machine Tools and Manufacture, 2016,109: 36-48.

［83］BUDAK E, TUN L T, ALAN S, et al. Prediction of workpiece dynamics and its effects on chatter stability in milling［J］. CIRP Annals-Manufacturing Technology, 2012,61(1): 339-342.

［84］YANG Y, ZHANG W H, MA Y C, et al. An efficient decomposition-condensation method for chatter prediction in milling large-scale thin-walled structures［J］. Mechanical Systems and Signal Processing, 2019,121: 58-76.

［85］TUYSUZ O, ALTINTAS Y. Time-domain modeling of varying dynamic characteristics in thin-wall machining using perturbation and reduced-order substructuring methods［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2018,140(1): 011015.

［86］BAUMANN M, EBERHARD P. Interpolation-based parametric model order reduction for material removal in elastic multibody systems［J］. Multibody System Dynamics, 2017,39(1/2): 21-36.

［87］OZOEGWU C G. Polynomial tensor-based stability identification of milling process: application to reduced thin-walled workpiece［M］//IUTAM Bookseries.Stuttgart: Springer, 2020.

［88］HAMANN D, EBERHARD P. Stability analysis of milling processes with varying workpiece dynamics［J］. Multibody System Dynamics, 2018,42(4): 383-396.

［89］ZHANG X W, YU T B, WANG W S, et al. Three-dimensional process stability prediction of thin-walled workpiece in milling operation［J］. Machining Science and Technology, 2016,20(3): 406-424.

［90］余满. 基于多模态的薄壁工件位移/应变场在线重构方法与切削稳定性分析［D］. 武汉：华中科技大学, 2018.

［91］DOZIO L, CARRERA E. A variable kinematic Ritz formulation for vibration study of quadrilateral plates with arbitrary thickness［J］. Journal of Sound and Vibration, 2011,330(18/19): 4611-4632.

［92］SHI J H, SONG Q H, LIU Z Q, et al. A novel stability prediction approach for thin-walled component milling considering material removing process［J］. Chinese Journal of Aeronautics, 2017,30(5): 1789-1798.

［93］SHI J H, GAO J, SONG Q H, et al. Dynamic deformation of thin-walled plate with variable thickness under moving milling force［C］//16th CIRP Conference on Modelling of Machining Operations.Cluny: CIRP CMMO, 2017.

［94］QU Y G, CHEN Y, LONG X H, et al. A modified variational approach for vibration analysis of ring-stiffened conical-cylindrical shell combinations［J］. European Journal of Mechanics-A/Solids, 2013,37: 200-215.

［95］REN S, LONG X H, QU Y G, et al. A semi-analytical method for stability analysis of milling thin-walled plate［J］. Meccanica, 2017,52(11/12): 2915-2929.

［96］田卫军. 薄壁叶片多轴加工颤振抑制方法研究［D］.西安：西北工业大学,2018.

［97］SONG Q H, SHI J H, LIU Z Q, et al. A time-space discretization method in milling stability prediction of thin-walled component［J］. International Journal of Advanced Manufacturing Technology, 2017,89(9/10/11/12): 2675-2689.

［98］MERRITT H E. Theory of self-excited machine-tool chatter: contribution to machine-tool chatter research—1［J］. Journal of Engineering for Industry, 1965,87(4): 447-454.

［99］农胜隆,高尚晗,黄艳.薄壁件铣削系统加工稳定性分析［J］.机械强度, 2018,40(6): 1419-1424.
NONG Shenglong, GAO Shanghan, HUANG Yan. Analysis of stability in the process of milling thin-walled workpiece［J］. Journal of Mechanical Strength, 2018,40(6): 1419-1424.

［100］FENG J L, HOU N, JIAN Z, et al. An efficient method to predict the chatter stability of titanium alloy thin-walled workpieces during high-speed milling by considering varying dynamic parameters［J］. International Journal of Advanced Manufacturing Technology, 2020,106(11/12): 5407-5420.

［101］ZHU L D, LIU B G, CHEN H Y. Research on chatter stability in milling and parameter optimization based on process damping［J］. Journal of Vibration and Control, 2018,24(12): 2642-2655.

［102］ALTINTAS Y, STEPAN G, MERDOL D, et al. Chatter stability of milling in frequency and discrete time domain［J］. CIRP Journal of Manufacturing Science and Technology, 2008,1(1): 35-44.

［103］MERDOL S D, ALTINTAS Y. Multi frequency solution of chatter stability for low immersion milling［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2004,126(3): 459-466.

［104］TANG A J, LIU Z Q. Three-dimensional stability lobe and maximum material removal rate in end milling of thin-walled plate［J］. International Journal of Advanced Manufacturing Technology, 2009,43(1/2): 33-39.

［105］WANG M H, GAO L, ZHENG Y H. Prediction of regenerative chatter in the high-speed vertical milling of thin-walled workpiece made of titanium alloy［J］. International Journal of Advanced Manufacturing Technology, 2014,72(5/6/7/8): 707-716.

［106］YAN B L, ZHU L D. Research on milling stability of thin-walled parts based on improved multi-frequency solution［J］. International Journal of Advanced Manufacturing Technology, 2019,102(1/2/3/4): 431-441.

［107］ZHANG Z, LI H G, LIU X B, et al. Chatter mitigation for the milling of thin-walled workpiece［J］. International Journal of Mechanical Sciences, 2018,138/139: 262-271.

［108］孙海勇. 叶片侧铣颤振变形耦合建模及仿真分析［D］.哈尔滨：哈尔滨工业大学, 2019.

［109］INSPERGER T, STPN G. Semi-discretization method for delayed systems［J］. International Journal for Numerical Methods in Engineering, 2002,55(5): 503-518.

［110］INSPERGER T, STPN G. Updated semi-discretization method for periodic delay-differential equations with discrete delay［J］. International Journal for Numerical Methods in Engineering, 2004,61(1): 117-141.

［111］SONG Q H, AI X, TANG W X. Prediction of simultaneous dynamic stability limit of time-variable parameters system in thin-walled workpiece high-speed milling processes［J］. International Journal of Advanced Manufacturing Technology, 2011,55(9/10/11/12): 883-889.

［112］李钟昀. 考虑模态耦合与过程阻尼的钛合金铣削稳定性及表面位置误差研究［D］. 大连: 大连理工大学, 2017.

［113］DUN Y C, ZHU L D, WANG S H. Multi-modal method for chatter stability prediction and control in milling of thin-walled workpiece［J］. Applied Mathematical Modelling, 2020,80: 602-624.

［114］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 & Manufacture, 2010,50(5): 502-509.

［115］ZHANG X J, XIONG C H, DING Y, et al. Stability analysis in milling of thin-walled workpieces with emphasis on the structural effect［J］. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2010,224(4): 589-608.

［116］ZHANG X J, XIONG C H, DING Y. Improved full-discretization method for milling chatter stability prediction with multiple delays［C］//3rd International Conference on Intelligent Robotics and Applications. Shanghai: ICIRA, 2010.

［117］GAO H N, LIU X L. Stability research considering non-linear change in the machining of titanium thin-walled parts［J］. Materials, 2019,12(13): 2083.

［118］闫正虎, 刘志兵, 王西彬,等. 基于径向基函数的AL2A12薄壁件铣削稳定性研究［J］. 振动与冲击, 2017,36(3): 202-208.
YAN Zhenghu, LIU Zhibing, WANG Xibin, et al. Milling stability prediction of AL2A12 thin walled workpiece based on radial basis function［J］. Journal of Vibration and Shock, 2017,36(3): 202-208.

［119］BAYLY P V, HALLEY J E, MANN B P, et al. Stability of interrupted cutting by temporal finite element analysis［J］. Journal of Manufacturing Science and Engineering, 2003,125(2): 220-225.

［120］BAYLY P V, SCHMITZ T L, STEPAN G, et al. Effects of radial immersion and cutting direction on chatter instability in end-milling［C］//ASME International Mechanical Engineering Congress and Exposition. New Orleans: ASME, 2002.

［121］张玲利. 铣削系统颤振稳定性分析及稳定性的影响因素［D］. 沈阳：东北大学, 2015.

［122］LI Z Y, SUN Y W, GUO D M. Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece［J］. International Journal of Advanced Manufacturing Technology, 2017,89(9/10/11/12): 2663-2674.

［123］杨星焕. 铣削过程加工变形及颤振在线监测技术研究［D］.天津：天津大学, 2017.

［124］GAO J H, SONG Q, LIU Z Q. Chatter detection and stability region acquisition in thin-walled workpiece milling based on CMWT［J］. International Journal of Advanced Manufacturing Technology, 2018,98(1/2/3/4): 699-713.

［125］张钊. 薄壁结构铣削过程颤振分析及抑制研究［D］. 上海：上海交通大学, 2018.

［126］田卫军,任军学,李郁,等.基于过程模态的薄壁件铣削稳定性试验研究［J］.机电工程, 2018,35(7): 668-673.
TIAN Weijun, REN Junxue, LI Yu, et al. Experiment on milling stability of thin-walled parts based on process variable mode［J］. Journal of Mechanical and Electrical Engineering, 2018,35(7): 668-673.

［127］葛茂杰,杜永斌,贾明华,等.薄壁件模态分析及铣削稳定性分析［J］. 工具技术, 2018,52(1): 93-96.
GE Maojie, DU Yongbin, JIA Minghua, et al. Model analysis and milling stability of thin-walled workpiece［J］. Tool Engineering, 2018,52(1): 93-96.

［128］SUN Y W, JIANG S L. Predictive modeling of chatter stability considering force-induced deformation effect in milling thin-walled parts［J］. International Journal of Machine Tools and Manufacture, 2018,135: 38-52.

［129］MINIS I, YANUSHEVSKY R. A new theoretical approach for the prediction of machine tool chatter in milling［J］. Journal of Engineering for Industry-Transactions of the ASME, 1993,115(1): 1-8.

［130］EYNIAN M, ALTINTAS Y. Analytical chatter stability of milling with rotating cutter dynamics at process damping speeds［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2012,132(2): 0210121-02101214.

［131］SASTRY S, KAPOOR S G, DEVOR R E. Floquet theory based approach for stability analysis of the variable speed face-milling process［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2001,124(1): 10-17.

［132］LI Z Q, LIU Q. Solution and analysis of chatter stability for end milling in the time-domain［J］. Chinese Journal of Aeronautics, 2008,21(2): 169-178.

［133］WU S, LI R Y, LIU X L, et al. Experimental study of thin wall milling chatter stability nonlinear criterion［J］. Procedia CIRP, 2016,56: 422-427.

［134］吴石, 边立健, 刘献礼, 等. 薄板件铣削颤振稳定性的非线性判据试验研究［J］. 振动与冲击, 2016,35(17): 191-196.
WU Shi, BIAN Lijian, LIU Xianli, et al. Tests for milling chatter stability nonlinear criterion of thin parts［J］. Journal of Vibration and Shock, 2016,35(17): 191-196.

［135］李红涛,来新民,李成锋,等.介观尺度微型铣床开发及性能试验［J］. 机械工程学报, 2006,42(11): 162-167.
LI Hongtao, LAI Xinmin, LI Chengfeng, et al. Development and performance test of mesoscopic miniature milling machine［J］. Journal of Mechanical Engineering, 2006,42(11): 162-167.

［136］LIU Y, LI P F, LIU K, et al. Micro milling of copper thin wall structure［J］. International Journal of Advanced Manufacturing Technology, 2016,90(1/2/3/4): 405-412.

［137］ZARIATIN D L, KISWANTO G, KO T J. Investigation of the micro-milling process of thin-wall features of aluminum alloy 1100［J］. International Journal of Advanced Manufacturing Technology, 2017,93(5/6/7/8): 2625-2637.

［138］KIM C J, BONO M, NI J. Experimental analysis of chip formation in micro-milling［J］. Technical Paper-Society of Manufacturing Engineers, 2002(MR02-159): 1-8.

［139］VOGLER M P, DEVOR R E, KAPOOR S G. On the modeling and analysis of machining performance in micro-endmilling. Part Ⅰ: surface generation［J］. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2004,126(4): 685-694.

［140］ANNONI M, REBAIOLI L, SEMERARO Q. Thin wall geometrical quality improvement in micromilling［J］. International Journal of Advanced Manufacturing Technology, 2015,79(5/6/7/8): 881-895.

［141］FRIEDRICH C R. Micromechanical machining of high aspect ratio prototypes［J］. Microsystem Technologies, 2002,8(4/5): 343-347.

［142］ANNONI M, REBAIOLI L, SEMERARO Q. Thin wall geometrical quality improvement in micromilling［J］. The International Journal of Advanced Manufacturing Technology, 2015,79(5/6/7/8): 881-895.

［142］POPOV K, DIMOV S, PHAM D T, et al. Micromilling strategies for machining thin features［J］. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2006,220(11): 1677-1684.

［143］THEPSONTHI T, ZEL T. An integrated toolpath and process parameter optimization for high-performance micro-milling process of Ti-6Al-4V titanium alloy［J］. International Journal of Advanced Manufacturing Technology, 2014,75(1/2/3/4): 57-75.

［144］LLANOS I, AGIRRE A, URRETA H, et al. Micromilling high aspect ratio features using tungsten carbide tools［J］. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2014,228(11): 1350-1358.