摘要
随着航空飞行器综合性能的不断提高,对航空器结构提出了更高的要求,例如更轻的结构重量、更高的结构强度、更长的应力疲劳寿命等。对于薄壁类结构零件来说,铣削加工是决定其加工精度和加工效率的关键技术,很大程度上决定了航空结构件的加工质量和使用寿命。由于较低的结构刚度,薄壁类结构件铣削加工过程中容易出现严重的切削振动和颤振、刀具及工件的弹性变形等现象,造成工件表面粗糙度下降以及工件的让刀误差。科学统计表明,造成航空薄壁件加工质量不满足加工精度要求的情况中,超过70%是工件表面让刀误差造成的。由此可知,加工让刀误差大大制约了薄壁类结构件的加工精度和效率,也很大程度上限制了高端航空飞行器的研发速度和规模生产。
论文首先分析了整体铣刀三维切削力模型构建方法。根据Yusuf建立的钛合金直角切削力预测模型,将切削速度和刀具前角对切削力的影响规律引入预测系数模型,并通过钛合金直角切削实验重新标定了直角切削预测系数；借助等效前角将直角切削力预测系数应用至斜角切削力的预测,并通过整体刀具离散化建模和切削力向量迭加,建立了以切削中心角为自变量的整体铣刀三维切削力预测模型。
提出并定义了薄壁件铣削中刀具-工件接触副的概念,包括了铣削过程中刀具-工件接触线方程、接触区域切削中心角范围、以及铣削层厚度建模等关键技术部分。首先根据刀具参数和工艺参数,研究了以切削中心角为自变量刀具-工件接触线数学模型,并在考虑工件边界范围的基础上对切削中心角范围随切削时间的变化进行了分析；根据相邻刀刃余摆线运动轨迹,借助泰勒级数展开法建立了薄壁件铣削层厚度的精确模型。进而分析了多个切削刃同时参与切削情况下的接触副建模方法。
薄壁结构件加工过程中,刀具挠度变形对工件表面让刀误差有比较显著的影响。同时对工件弹性变形和刀具弹性变形展开研究是困难的,因此首先对铣削过程中整体铣刀的挠度变形预测方法进行了研究。构建了等效直径刀具悬臂梁模型,通过离散整体刀具及作用在切削刃上的铣削载荷,分析了刀具在任意方向集中载荷单独作用下,沿特定方向挠度变形的求解方法。进而借助材料力学挠度叠加原理,,通过各个方向挠度向量的叠加,构建了切削载荷条件下整体刀具沿特定方向挠度变形的理论预测模型。并讨论了多刃同时切削情况下的刀具挠度变形求解方法。最终构建了以刀具挠度变形为反馈的工件表面让刀误差及切削力柔性预测模型。借助Matlab运算工具实现了理论模型的预测,并通过钛合金Ti6A14V刚性工件铣削实验验证了理论模型的预测精度。
分析了利用薄板弹塑性力学求解薄壁件切削载荷下弯曲变形的可行性和关键步骤,并借助李滋公式具体形式构建了薄壁结构随切削过程的刚度时变特性数学模型,实现了对薄壁结构刚度时变特性的定量描述。通过分析刀具挠度变形和工件弯曲变形对刀具-工件接触副的耦合作用规律,建立了考虑刀具-工件变形对铣削层厚度影响的薄壁变形控制方程载荷矩阵。借助数学迭代方法,构建了以刀具-工件变形变形为反馈的薄壁件铣削加工表面让刀误差及切削力柔性预测系统方法。并借助Matlab实现了理论模型预测功能,进行了钛合金Ti6Al4V薄壁件铣削实验验证了理论模型的预测精度。
With the development of the aircraft variable functions, the properties requirements for the aircraft structure are more critical, such as less weight, more structure strength, and better stress fatigue life. Due to the low level of structure rigidity of the thin wall part, serious vibration and chatter of the machining system and the deflections of the tool and part are the main problem for the manufacturers, which will generate low quality surface roughness and surface dimension error. Involving to the previous researches and surveys, more than70%of the machining part out of the precious requirement is caused by the deflection dimension error, which is the primary element limiting the machining precious and efficiency, even more, the design and manufacture of the advanced aircrafts.
In this study, the3D milling force modeling method is talking about firstly base on the orthogonal cutting force prediction model, which is modified by taking account the cutting speed and tool rake angel into the prediction coefficients by titanium orthogonal cutting experiments. The cutting force model in oblique cutting is achieved with the transformation of orthogonal cutting force prediction model by equivalent rake angle. Finally, cutting force model for solid milling tool is established with the cutting center angle as the variable involving with tool discretization and cutting force vector superposition.
The modeling of tool-workpiece contacting area, named tool-workpiece pair in this study, is proposed, which includes the undeformed chip thickness, tool-workpiece contacting curve, and range of center angle. In this study, the trace of solid tool cutting edges varying with machining time is described with the cylindrical spiral function firstly. And then, the cutting center angle range is achieved base on the analysis of tool-workpiece contacting relationship. The thickness of undeformed chip in milling thin wall part is detennined with respect to teeth trajectories.The model of multi-contacting-pair in milling process is approached by taking account tool and processing parameters.
The influence of tool deflection on workpiece geometric error cannot be ignored in milling thin wall part. However, it is very difficult to model tool deflection and workpiece deflection synchronously. In this study, the tool'deflection prediction method is achieved with taking account the solid workpiece with high level of structure rigidity. Tool deflection on specific direction under the condition of variant concentrated force is achieved by cantilever model. Furthermore, the models of tool deflection with one single cutting edge and multi cutting edges under cutting force condition are achieved based on superposition principle involving to elastic mechanics. Finally, the prediction model of surface error and cutting force in milling rigidity workpiece, with the tool deflection as system feedback, is achieved. The theoretical model is realized in software of Matlab and milling experiments of Ti6A14V workpiece are carried out to invalidate the precision of prediction model.
The key methodologies of deflection in milling thin wall component are analyzed based on thin plate elastic mechanics. The time-variant rigidity of thin wall workpiece in milling process is model with respect to Ritg function. Loading matrix is achieved by taken account the influence of tool and workpiece deflections on tool-workpiece contacting pair. Furthermore, the prediction model of surface error and cutting force in milling thin wall component is proposed by taking account tool and workpiece deflections as the system feedback, which is realized in Matlab. Finally, milling experiments on Ti6A14V alloy thin wall components are carried out to invalidate the precision of prediction model.
引文
[1].王道荫.迈向21世纪的航空制造技术fB].北京：航空工业出版社,1994.
[2].路甬祥.团结奋斗开拓创新建设制造强国[J].机械工程学报.2003,19(1)：1-9.
[3].刘强,郇极.航空航天制造与现代数控技术及装备[J].中国制造业信息化,2005，3：64-66.
[4].航空制造工程手册总编委会.航空制造工程手册[B].航空工业出版社,1995.
[5].汤爱君.薄壁件高速铣削三维稳定性及加工变形研究[D].山东大学博士学位论文,2006.
[6].Martellotti M E. An analysis of the milling process. Journal of Engineering for Industry [J],1941,63:677-700.
[7].Zheng L, Chiou Y S, Liang Y S. Three dimensional cutting force analysis in end milling [J], Int. J. Mech. Sci.1996,38(3):259-269.
[8].Budak E, Altintas Y. Modeling and avoidance of static form errors in peripheral milling of plates [J], Int. Journal of Machine Tools & Manufacture.1995,35(3): 459-476.
[9].Altintas Y, Spence A. End milling force algorithms for CAD systems [J], CIRP Ann.1991,40(1):31-34.
[10]. Wan M, Zhaag W H, Tan G. Systematic simulation procedure of peripheral milling process of thin-walled workpiece [J], Journal of Materials Processing Technology,2008,197:122-131.
[11].万敏,张卫红.薄壁件周铣铣削力建模与表面误差预测方法研究[J].航空学报,2005,26(5)：598-603.
[12]. Wan M, Zhang W H. Efficient algorithms for calculations of static form errors in peripheral milling[J]. Journal of Materials Processing Technology,2006,171: 156-165.
[13].Desai K A, Rao P V M. Effect of direction of parameterization on cutting forces and surface error in machining curved geometries [J], Int. J. Mach. Tools Manufact.2008,48:249-259.
[14].Omar O E E K. An improved cutting force and surface topography prediction model in end milling [J], Int. J. Mach. Tools Manufact.2007,47:1263-1275.
[15].Shirase K. Altintas Y. Cutting force and dimensional surface error generation in peripheral milling with variable pitch helical end mills[J]. Int. J. Mach. Tools Manufact.1996,36(5):567-584.
[16].Merdol S D, Altintas Y. Mechanics and dynamics of serrated cylindrical and tapered end mills [J]. Journal of Manufacturing Science and Engineering.2004, 126:317-326.
[17]. Altintas Y, Lee P. Mechanics and dynamics of ball end milling [J]. Journal of Manufacturing Science and Engineering,1998,120:684-692.
[18].Engin S, Altintas Y. Mechanics and dynamics of general milling cutters Part Ⅰ: helical end mills[J]. Int. J. Mach. Tools Manufact.2001,41:2195-2212.
[19].Gradisek J, Kalveram M, Weinert K. Mechanistic identification of specific force coefficients for a general end mill [J]. Int. J. Mach. Tools Manufact.2004,44: 401-414.
[20]. Jayaram S, Kapoor S G, Devor R E. Estimation of the specific cutting pressure for mechanistic cutting force models [J]. International Journal of Machine Tools & Manufacture,2001,41:265-281.
[21].Melkote S M, Endres W J. The importance of including size effect when modeling slot milling [J]. Transactions of the ASME Journal of Manufacturing Science and Engineering,1998,120:68-75.
[22].Kilne W A, DeVor R E, Shareef I A. The prediction of surface accuracy in end milling [J]. Transactions of the ASME Journal of Engineering for Industry,1982, 104:272-278.
[23]. Sutherland J W, DeVor R E. An improved method for cutting force and surface error prediction in flexible end milling systems [J]. Transactiom of the ASME Journal of Engineering for Industry,1986,108:269-279.
[24].Liao C L, Tsai J S. Dynamic response analysis in end milling using pretwisted beam finite element [J]. Transssaction of the ASME Journal of Vibration and Acoustics,1995,117:1-10.
[25].Tlusty J, NacNeil P. Dynamics of cutting force in end milling [J]. Annals of the CIRP,1975,24:21-25.
[26].Budak E, Altintas Y. Peripheral milling conditions for improvedl dimensional accuracy[J]. International Journal of Machine Tools & Manufacturing,1994, 34(7):907-918.
[27].武凯.何宁,螯澄宇.立铣空间力学模型分析研究[J].南京航空航天大学学报,2002,34(6)：553-556.
[28].康永刚,王仲奇,吴建军,姜澄字.立铣切削力分类研究及精确铣削力模型的建立[J].航空学报,2007,28(2)：481-489.
[29].Armorego EJA, Deshpande ND. Force prediction models and CAD/CAM software for helical tooth milling processes III:End-milling and slot operations [J]. International Journal of Product Research,1994,32(7):1715-1738.
[30].Budak E, Altintas Y, Armorego EJA. Prediction of milling force coefficients from orthogonal cutting data [J]. ASME Journal of Manufacture Science and Engineering,1996,118:216-224.
[31]. Li H Z, Zhang W B, Li X P. Modeling of cutting forces in helical end milling using a predictive machining theory [J]. International Journal of Mechanical Science,2001,43:1711-1730.
[32].Oxley PLB. Mechanics of Machining [M]. Chichester:Ellie Horwood Limited, 1989.
[33].胡创国.薄壁件精密切削变形控制与误差补偿技术研究[D].西安：西北工业大学,2007.
[34].Luo T, Lu W, Krishnamurthy K. A neural network approach for force and contour error control in multi-dimensional end milling operations [J]. Journal of Material Processing Technology,1998,38:1343-1359.
[35].Szecsi T. Cutting force modeling using artificial neural networks [J]. Journal of Material Processing Technology,1999,92:344-349.
[36]. Yang Yong, Li Changhe, Sun Jie. Three-dimensional numerical simulation of cutting force during milling of titanium alloy Ti6A14V [J]. Yingyong Jichu yu Gongcheng Kexue Xuebao/Journal of Basic Science and Engineering, 18(3):493-502.(EI收录)
[37].陈建岭,李剑峰,孙杰，宋良煜,徐志平.钛合金高速切削切屑形成机理的有限元分析[J].组合机床与自动化加工技术,2007,1：25-31.
[38].陈建岭,李剑峰,孙杰,王中秋,徐志平.The Influence of Material Constitutive Constants on Numerical Simulation of Orthogonal Cutting of Titanium Alloy Ti6A14V [J]. Key engineering material,2008,375-376:182-186.1(EI收录)
[39].姜峰,李剑峰,孙杰,张松,李方义.钛合金高速加工的铣削力建模新方法[D].山东大学,2007.
[40]. Philippe Depince, Jean-Yves Hascoet. Active integration of tool deflection effects in end milling. Part 1. Prediction of milled surfaces[J]. International Journal of Machine Tools & Manufacture,2006,46:937-944.
[41].Seo, T.I., Integration of tool deflection during the generation of tool path [D], PhD thesis (In French), Universite of Nantes-Ecole Centrale of Nantes,1998.
[42J.K.M.Y. Law. A. Geddam, V.A. Ostaflev, A process-design approach to error compensation in the end milling pockets[J], Journal of Materials Processing Technology 89-90 (1999) 238-244.
[43]. L. Kops, D.T. Vo, Determination of the equivalent diameter of an end mill based on its compliance [J], Annals of the CIRP 39 (1990) 93-96.
[44].S.H. Ryu, H.S. Lee, C.N. Chu, The form error prediction in side wall machining considering tool deflection [J], International Journal of Machine tools and Manufacture 43 (2003) 1405-1411.
[45].陈蔚芳,楼佩煌,陈华,薄壁件加工变形主动补偿方法[J],航空学报,2009,30(3),570-576.
[46]. Sutherland J W, DeVor R E. An improved method for cutting force and surface error prediction in flexible end milling systems [J]. Transactions of the ASME Journal of Engineering for Industry,1986,108:269-279.
[47].Budak E, Altintas Y Flexible milling force model for improved surface error predictions [C]. In:Proceedings of Engineering System Design and Analysis, Istanbul, Turkey,1992,47(1):89-94.
[48].Ratchev S, Liu S, Huang W, Becker A.A. Milling error prediction and compensation in machining of low-rigidity parts [J]. International Journal of Machine Tools & Manufacture,2004,44:1629-1641.
[49].Ratchev S, Liu S, Huang W, Becker A.A. A flexible force model for end milling of low-rigidity parts [J]. Journal of Materials Processing Technology,2004, 153-154:134-138.
[50].Ratchev S, Govender E, Nikov S. Force and deflection modeling in milling of low-rigidity complex parts [J]. Journal of Materials Processing Technology,2003, 143-144:796-801.
[51].Ratchev S, Liu S, Huang W, Becker A.A. An advanced FEA based force induced error compensation strategy in milling [J]. International Journal of Machine Tools & Manufacture,2006,46:542-551.
[52]. Tang Aijun, Liu Zhanqiang. Deformations of thin-walled plate due to static end milling force [J]. Journal of Materials Processing Technology. (2008), doi: 10.1016/j jmatprotec.2007.12.089.
[53].王志刚,何宁,武凯.薄壁零件加工变形分析及控制方案[J].中国机械工程,2002,13(2)：114-117.
[54].万敏,张卫红.薄壁件周铣铣削力建模与表面误差预测方法研究[J].航空学报,2005,26(5)：598-603.
[55]. Wan M, Zhang W H. Efficient algorithms for calculations of static form errors in peripheral milling [J]. Journal of Materials Processing Technology,2006, 171:156-165.
[56]. Wan M, Zhang W H, Tan C; Qin G H. Systematic simulation procedure of peripheral milling process of thin-walled workpiece [J]. Journal of Materials Processing Technology,2008,197:122-131.
[57]. Wan Min, Zhang Weihong, Qiu Kepeng, Gao Tong. Numerical prediction of static form errors in peripheral milling of thin-walled workpiece with irregular meshes [J]. Journal of Manufacturing Science and Engineering,2005,127:13-22.
[58]. Wan M, Zhang W H, Tan C, Qin G H. An in-depth analysis of the synchronization between the measured and prediction cutting forces for developing instantaneous milling force model [J]. International Journal of Machine Tools & Manufacture.2007,47:2018-2030.
[59].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.
[60].董辉跃,柯映林,杨慧香.博壁板高速铣削加工过程中的让刀误差预测[J].浙江大学学报,2006,40(4)：634-637.
[61].王运巧,梅中义,范玉青.薄壁弧形件装夹布局有限元优化[J].机械工程学报,2005,41(6)：214-217.
[62]. Liu Shaogang, Zheng L, Zhang Z H. Optimal fiucture design in peripheral milling of thin-walled workpiece[J]. International Journal of Advanced Manufacture Technology,2005, doi:10.1007/s00170-004-2425-8.
[63].黄志刚.航空整体结构件铣削加工变形的有限元模拟理论及方法研究[D].杭州：浙江大学博士学位论文,2003.
[64].王立涛.基于铣削力要素的航空结构件加工变形机理研究及有限元模[D].杭州：浙江大学博士学位论文,2002.
[65].Hiroyasul IWABE. Hiroyasu IWABE. High accurate machining of thin wall shape workpiece by end mill [C]. 日本机械学会论文集,1997,63:605-610.
[66]. J. Tlusty, S. Smith, J. Bsdrawy. Design of a high speed machine for aluminum aircraft parts [J]. Manufacturing Science and Technology.1997,2:253-259.
[67]. J. Tlusty, S. Smith, W. R. Winfough. Techniques for the use of long slender end mills in high speed milling [J]. Annals of the CIRP,1996.45(1):393-396.
[68].Haruki Obara, Takahiro Watanabe, Tsuyoshi Ohsumi, Eiji Ninomiya, Masatoshi Hatano. A method to machine three-dimensional thin parts [J]. Initiatives of Precision Engineering at the Beginning of a Millennium.2002,1:87-91.
[69]. W. A. Kline, R. E. Devor. The prediction of surface accuracy in end milling [J]. ASME Journal of Engineering for Industry.1982,104(3):272-278.
[70]. S. Ratchev, S. Liu, W. Huang, et al. An advanced FEA based force induced error compensation strategy in milling [J]. International Journal of Machine Tools and Manufacture.2006,46(5):542-551.
[71]. S. Ratchev, S. Liu, A. A. Becker. Error compensation strategy in milling flexible thin-wall parts [J]. Journal of Materials Processing Technology.2005, 162-163(15):673-681.
[72]. S. Ratchev, K. Phuah, G. Lammel, et al. An experimental investigation of fixture-workpiece contact behaviour for the dynamic simulation of complex fixture-workpiece systems [J]. Journal of Materials Processing Technology.2005, 164-165(15):1597-1606.
[73]. S. Ratchev, S. Liu, W. Huang. Milling error prediction and compensation in machining of low-rigidity parts [J]. International Journal of Machine Tools and Manufacture.2004,44(15):1629-1641.
[74]. S. Ratchev, W. Huang, S. Liu, et al. Modelling and simulation environment for machining of low-rigidity components [J]. Journal of Materials Processing Technology.2004,153-154(10):67-73.
[75]. S. Ratchev, S. Liu, W.Huang, et al. A flexible force model for the end milling of low-rigidity parts [J]. Journal of Materials Processing Technology.2004, 153-154(10):134-138.
[76].Svetan Ratchev, Stan Nikov, Idir Moualek. Material removal simulation of peripheral milling of thin wall low-rigidity structures using FEA [J]. Advances in Engineering Software.2004,35(8-9):481-491.
[77].Svetan Ratchev, Evan Govender, Stan Nikov, et al. Force and deflection modelling in milling of low-rigidity complex parts [J]. Journal of Materials Processing Technology.2003,143-144(20):796-801.
[78].Depince P, Hascoet J Y. Active integration of tool deformation effects in end milling. Part 1:prediction of milled surfaces [J]. International Journal of Machine Tools and Manufacture,2006,46(9):937-944.
[79].Depince P, Hascoet J Y. Active integration of tool deformation effects in end milling. Part 2:compensation of tool deformation [J]. International Journal of Machine Tools and Manufacture,2006,46(9):945-956.
[80].Lim E M, Menq C H, Yen D W. Integrated planning for precision machining of complex surfaces-Ⅲ compensation of dimensional errors [J]. International Journal of Machine Tools and Manufacture,1997,37 (9):1313-1326.
[81]. Rao V S, Rao P V M. Tool deflection compensation in peripheral milling of curved geometries [J]. International Journal of Machine Tools and Manufacture, 2006,46(15):2036-2043.
[82].Lee C M, Kim S W, Lee Y H, et al. The optimal cutter orientation in ball end milling of cantilever-shaped thin plate [J]. Journal of Materials Processing Technology,2004,153-154:900-906.
[83].毕运波,董辉跃,柯映林.航空铝合金薄壁件加工变形有限元仿真与分析[J].浙江大学学报(工学版).2008,42(3)：397-402.
[84].成群林,董辉跃,柯映林,等.航空整体结构件铣削加工变形预测研究[J].浙江大学学报(工学版).2007,41(5)：799-803.
[85].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.
[86].武凯,何宁,廖文和,等.基于变形控制的薄壁结构件高速铣削参数选择[J].机械科学与技术.2005,24(7)：788-791.
[87].武凯,何宁,廖文和,等.阶梯对称铣削工艺在薄壁件精密加工中的应用[J].航空精密制造技术.2005,41(5)：37-39.
[88].武凯,何宁,廖文和,等.基于薄壁件变形分析的铣削加工瞬态力学模型研究[J].应用科学学报.2005,23(6)：631-634.
[89].梅中义,王运巧,范玉青.飞机结构件数控加工变形控制研究与仿真[J].航空学报.2005, 26(2)：234-239.
[90].王运巧,梅中义,范玉青.航空薄壁结构件数控加工变形控制研究[[J].现代制造工程.2005,(1)：31-33.
[91].王运巧,梅中义,范玉青.航空薄壁弧形件加工变形的非线性有限元分析[J].航空制造技术.2004,(6)：84-86.
[92].万敏,张卫红,谭刚.薄壁件周铣过程中材料去除效应的快速仿真[J].航空学报.2007, 28(5)：1247-1251.
[93], M. Wan, W H. Zhang, K. P. Qiu, et al. Numerical prediction of static form errors in peripheral milling of thin-walled workpieces with irregular meshes [J]. Journal of Manufacturing Science and Engineering.2005,127(1):13-22.
[94].万敏.薄壁件周铣加工过程中表面静态误差预测关键技术研究[D].西安：西北工业大学硕士学位论文,2005.
[95]. M. Wan, W. H. Zhang. Efficient algorithms for calculations of static form errors in peripheral milling [J]. Journal of Materials Processing Technology.2006, 171(1):156-165.
[96]. Huang Panling, Li Jianfeng, Sun Jie. Simulation and optimal selection of Pitch Angles Distribution for Variable Pitch Angles Helix End Mills [J].Key Engineering Materials,2010, (443):285-290.
[97]. Huang Panling, Li Jianfeng, Sun Jie. Structure Optimization of Variable Pitch Helix End Mills Based on FEM Simulation [J]. Key EngineeringMaterials.2010, (443):291-296.
[98]. Huang Panling, Li Jianfeng, Sun Jie, Ge Maojie. Milling force vibration analysis in high-speed-milling titanium alloy using variable pitch angle mill [J]. International Journal of Advanced Manufacturing Technology,2012, (58):153-160.(EI收录)
[99].皇攀凌,李剑锋.面向钛合金铣削的变齿距立铣刀研究[D].山东大学,2011.
[100].葛茂杰,孙杰,李剑峰.石蜡辅助加固钛合金薄壁件铣削稳定性研究[J].山东大学学报,2011,41(1).
[101].葛茂杰,孙杰,李剑峰.Study on processing property of thin-walled titanium alloy component with paraffin reinforcement [J]. Advanced Materials.
[102].路东,王中秋,康小明,姜亦涛,孙玉晶等分别就航空薄壁件的装夹、校正、变形预测和控制等进行了研究。
[103].路冬,李剑峰,孙杰,姜峰.航空框类零件加工动态夹紧力确定有限元分析[J].山东大学学报,2007,37(1)：19-22
[104].王中秋,李剑峰,孙杰,姜亦涛.基于回弹曲线的航空整体结构件三点压弯校正分析[J].山东大学学报(工学版),2009/Vol.32/No.2:78-81.
[105].王中秋,李剑峰,孙杰,李桂玉.航空整体结构件侧壁滚压校正的有限元分析[J].中国机械工程,2009,(5)：612-616.
[106].姜亦涛,孙杰,王中秋,李剑峰,丁宏勃.振动时效技术在航空整体结构件 变形校正中的应用[J].山东大学学报：工学版,2009,39(2)：82-86.
[107].康小明,孙杰,苏财茂.飞机整体结构件加工变形的产生和对策[J].中国机械工程.2004.
[108].孙玉晶,孙杰,李剑峰,何勇.铣削参数对钛合金薄壁件表面粗糙度和让刀量的影响[J].粉末冶金材料科学与工程,2010,15(6)：586-592.
[109].孙杰,柯映林.隔框类航空整体结构件变形校正关键技术研究[J].浙江大学学报(工学版).2004.
[110].孙杰,柯映林.残余应力对航空整体结构件加工变形的影响分析[J].机械工程学报,2005,41(2)：117-122.
[111].孙杰,柯映林,吴群,许德.大型整体结构件数控加工变形校正的关键技术研究[J].机械工程学报,2003,39(8)：120-124.
[112].孙杰,李剑峰,王中秋,宋良煜,何勇.航空整体结构件加工变形控制与校正关键技术[J].航空制造技术,2009,(23)：62-66.
[113].孙杰,李剑峰.钛合金整体结构件加工关键技术研究[J].山东大学学报：工学版,2009,39(3)：81-88.
[114].孙杰.有限元技术在航空整体结构件加工中的应用[J].航空制造技术,2009,(21)：48-52
[115].胡创国.薄壁件精密切削变形控制与误差补偿技术研究[D].西安：西北工业大学机电学院,2007.
[116].楼文明.航空薄壁件加工变形补偿技术研究[D].西安：西北工业大学机电学院,2007.
[117].康永刚,王仲奇,吴建军,等.基于实际切深的薄壁件加工变形误差的预测[J].西北工业大学学报,2007,25(2)：251-256.
[118].王增强,孟晓娴,任军学,等.复杂薄壁零件数控加工变形误差控制补偿技术研究[J].机床与液压,2006(4)：61-63.
[119].孙杰,李剑峰,李方义,等.制造过程关键工艺环节的有限元仿真分析[J].山东大学学报,2005,35(1)：17-21.
[120].赵威,何宁,武凯.航空薄壁件的刀具偏摆数控补偿加工技术[J].机械制造及自动化,2002(5)：18-20.
[121].王志刚,何宁,武凯,等.薄壁零件加工变形分析及控制方案[J].中国机械工程,2002,13(2)：113-117.
[122].万敏,张卫红.铣削过程中误差预测与补偿技术研究进展[J].航空学报,2008,29(5)：1340-1349.
[123].Altintas, Y., Manufacturing Automation:Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design [B], Cambridge University Press,2000.
[124].H.Z. Li, K. Liu, X.P. Li, A new method for determining the undeformed chip thickness in milling, Materials Processing Technology [J],2001,113:378-384
[125].曲庆璋.弹性板理论[D].人民交通出版社.1999：27-30.