薄壁件铣削变形预测与补偿策略研究
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摘要
薄壁件在航空航天领域的应用越来越广泛,但是薄壁件本身的特点决定了它的加工精度难以控制,薄壁件的特点是整体性,面积大,刚度低,加工困难,等等。如何在加工过程中合理的预测出加工变形误差并正确的预测出来,最后加以补偿以达到加工精度要求是现在科研工作者研究的热点。本文在总结前人研究的基础上分析了薄壁件在加工过程中的特点并做了以下工作。
首先,建立立铣刀铣削力模型,以正交切削为基础,分析切削力和材料各参数、刀具角度之间的关系,利用正交/斜交化关系并把立铣刀沿着刀轴方向分为若干切削力单元并建立每个单元的切削力,最后建立了立铣刀在切削过程中切削力模型,把次摆线切削刃轨迹转化为圆形轨迹,并计算了切削力计算切削力过程中关键参数,未变形切削厚度。
其次,分析了有限元模型建立过程中的应力场和温度场,并采用应力场温度场直接耦合的方式建立了薄壁件加工过程有限元模型。本文建立完成有限元模型后,采用了迭代算法来求解薄壁件加工过程中的变形误差曲线,最后采用插补的方法获得薄壁件在加工过程中的误差曲面。
再次,采用三轴和五轴补偿策略分别对误差曲面进行补偿。
最后,利用航空铝合金7075-T6进行了加工实验研究,实验结果和预测结果吻合的也很好,同时还做了三轴补偿和五轴补偿的加工试验,结果表明三轴和五轴补偿策略都能降低加工误差,但是五轴补偿更能发挥五轴加工中心的特点和获得更高的精度。
In aeronautic/aerospace field, more and more key functional parts or components with sculptured surfaces use thin-walled parts. However, the characteristics of thin-walled parts such as integrity, large area, low-rigidity, hard-machining etc. determined that the precision of them are difficulty to be controlled. How to predict deformation error and compensate it in milling process is a challenge for researchers and manufactures. Based on successful research findings of literatures, this paper analyzes the properties of the milling process and does some works as follows:
Firstly, cutting force model for end mill. Based on orthogonal milling process, analyzing the relationships between cutting forces and parameters of materials and the angles of the cutter, the cutting forces on every cutting element using orthogonal/inclined relationship are computed, finally, the total cutting forces impacted on the cutter are obtained, and the key parameters of the cutting force model, instantaneous uncut chip thickness, is computed in this paper.
Secondly, analyzing the temperature field and stress field, and the finite element model is set up adopting direct-coupling method, the using the iterative method, the deformation error curves are predicted and finally the deformation error surface is obtained through interpolation method.
Then, utilizing three and five-axis compensation method, the deformation surface is compensated.
Finally, using AL7075-T6, a series of experiments are executed, the results shows that there are consistent with each other, between experiment data and simulation data, further more, both three and five-axis compensation method can deduce the deformation error, but five-axis compensation method is of more precision and takes full advantage of five-axis machine center.
首先,建立立铣刀铣削力模型,以正交切削为基础,分析切削力和材料各参数、刀具角度之间的关系,利用正交/斜交化关系并把立铣刀沿着刀轴方向分为若干切削力单元并建立每个单元的切削力,最后建立了立铣刀在切削过程中切削力模型,把次摆线切削刃轨迹转化为圆形轨迹,并计算了切削力计算切削力过程中关键参数,未变形切削厚度。
其次,分析了有限元模型建立过程中的应力场和温度场,并采用应力场温度场直接耦合的方式建立了薄壁件加工过程有限元模型。本文建立完成有限元模型后,采用了迭代算法来求解薄壁件加工过程中的变形误差曲线,最后采用插补的方法获得薄壁件在加工过程中的误差曲面。
再次,采用三轴和五轴补偿策略分别对误差曲面进行补偿。
最后,利用航空铝合金7075-T6进行了加工实验研究,实验结果和预测结果吻合的也很好,同时还做了三轴补偿和五轴补偿的加工试验,结果表明三轴和五轴补偿策略都能降低加工误差,但是五轴补偿更能发挥五轴加工中心的特点和获得更高的精度。
In aeronautic/aerospace field, more and more key functional parts or components with sculptured surfaces use thin-walled parts. However, the characteristics of thin-walled parts such as integrity, large area, low-rigidity, hard-machining etc. determined that the precision of them are difficulty to be controlled. How to predict deformation error and compensate it in milling process is a challenge for researchers and manufactures. Based on successful research findings of literatures, this paper analyzes the properties of the milling process and does some works as follows:
Firstly, cutting force model for end mill. Based on orthogonal milling process, analyzing the relationships between cutting forces and parameters of materials and the angles of the cutter, the cutting forces on every cutting element using orthogonal/inclined relationship are computed, finally, the total cutting forces impacted on the cutter are obtained, and the key parameters of the cutting force model, instantaneous uncut chip thickness, is computed in this paper.
Secondly, analyzing the temperature field and stress field, and the finite element model is set up adopting direct-coupling method, the using the iterative method, the deformation error curves are predicted and finally the deformation error surface is obtained through interpolation method.
Then, utilizing three and five-axis compensation method, the deformation surface is compensated.
Finally, using AL7075-T6, a series of experiments are executed, the results shows that there are consistent with each other, between experiment data and simulation data, further more, both three and five-axis compensation method can deduce the deformation error, but five-axis compensation method is of more precision and takes full advantage of five-axis machine center.
引文
[1]石光酶译,罗伯特.虎克.《力学与实践》[M].1981,3(3)：70-73.
[2]F.W.Taylor. On the Art of cutting Metal [J]. ASME Transactions. Vol.1907(28):31-35.
[3]HerbetEG. Cutting tools research committee [J]. Report on Machinability. Proceeding, I Mech E,1928(114):175-825.
[4]Chao BT, Bisacre GH. The effect of feed and speed on the mechanics of metal cutting[J]. Proceeding,I mech E,1951(165):1-1.
[5]Shaw MC. Metal Cutting Principles[M]. Oxford:Clarendon Press,1984.
[6]艾兴,肖诗纲。切削用量手册[M],北京：机械工业出版社,1984.
[7]付秀丽,艾兴,张松潘,永智.航空整体结构件的高速切削加工[M].工具技术,2006.
[8]李亮,何宁,何磊,王珉.高速铣削铝合金时切削力和表面质量影响因素的试验研究[J],工具技术,2004.4.
[9]黄志刚.整体结构件铣削加工变形的有限元模拟理论及方法[D],杭州：浙江大学机械工程学院,2003.
[10]Lajczok, MRA study of some aspects of metal cutting by the finite element method[D]. [Ph D dissertation]. N C State University 1980.
[11]E. Usui, T. Shirakashi, Mechanics of metal machining-from "descriptive" to "predictive" theory, on the art of cutting metals:A tribute to F. W. Taylor, PED7 [C],The winner annual meeting of the American Society of Mechanical Engineers, Ed. Kops, L., Ramalingam, S.,1982.
[12]Strenkowski JS, Moon K J. Finite element prediction of chip geometry and tool /workpiece temperature distribution in orthogonal metal cutting[J]. Tran ASME J Eng Ind,1990,112(4):311-318.
[13]Lin, Z. C, Lin, S. Y, A Couple finite element model of thermo-elastic large deformation of orthogonal cutting[J], Journal of Engineering Material and Technology,1992,114(2):218-226.
[14]Shih, A. J., Yang, H. T. Y., Experimental and finite element predictions on the residual stresses due to orthogonal metal cutting[J], International Journal for Numerical Methods in Engineering,1993,36(8):1487-1507.
[15]S. Ratchev, S. Liu*, W. Huang, A. A. Becker. Milling error prediction and compensation in machining of low-rigidity parts [J], International Journal of Machine Tools & Manufacture,2004 (44):1629-1641.
[16]W. A. KLINE, R. E. DEVOR and I. A. SrmmSEF. The prediction of surface accuracy in end milling[J]. Trans. ASME J. Engng Ind.1982 (104):272-278.
[17]J. W. Sutherland and R. E. Devor, An improved method for cutting force and surface error prediction in flexible end milling systems [J]. Trans. ASME J. Engng Ind.1986 (108):269-279.
[18]Erhan Budak, Yusuf Altintas. MODELING AND AVOIDANCE OF STATIC FORM ERRORS IN PERIPHERAL MILLING OF PLATES [J], Int. J. Math. Tools Manufact.1995,35(3): 459-476.
[19]Svetan Ratchev, Shulong Liu, Wei Huang, Adib A. Becker, Machining simulation and system integration combining FE analysis and cutting mechanics modeling [J], Int J Adv Manuf Technol 2007(35):55-65.
[20]路冬. 航空整体结构件加工变形预测及装夹布局优化[D],济南： 山东大学机械工程学院,2007.
[21]刘亚俊,夏伟.金属切削理论发展的历史回顾[J],力学与实践,2001.
[22]李带娣, 基于铣削力预测模型的加工进给率优化研究[D].大连：大连理工大学,2007.
[23]陈玉安,周上祺.残余应力X射线测定方法的研究现状[J],无损检测,2001,23(1)：19-22.
[24]Liu Gang. Study on deformation of titanium thin-walled part in milling process[J], Journal of Materials processing technology,2009 (209):2788-2793.
[25]Budak, E., Altintas, Y., Modeling and avoidance of static form errors in eripheral milling of plates[J]. International Journal of Machine Tools & Manufacture. 1995(35):459-476.
[26]Shi, H. R., Hae, S. L., Chong, N. C., The form error prediction in side wall machining considering tool deflection[J], International Journal of Machine Tools & Manufacture,2003(43):1405-1411.
[27]Svetan, R., Huang, W., Liu, S., Modeling and simulation environment for machining of low-rididity components[J]. Journal of Materals processing Technology, 2004(153-154):67-73.
[28]Tsai.J. S., Liao, G. L., Finite-element modeling of static surface errors in the peripheral milling of thin-walled workpieces[J], Journal of Materials Processing Technology,1999(94):235-346.
[29]Wan, M. Zhang, W. H., Qiu, K. P., 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):13-22.
[30]Svetan, R., Evan, G., Stan, N., Force and deflection modeling in milling of low-rigidity complex part[J], Journal of Materials Processing Technology, 2003(143-444):796-801.
[31]M. Rahman, J. Heikkala, K. Lappalainen, Modeling, measurement and error compemsation of multi-axis machine tools [J]. Part Ⅰ:theory, International Journal of Machine Tools & Manufacture 2000(40):1535-1546.
[32]T.S. Suneel, S. S. Pande, Intelligent tool path correction for improving profile accuracy in CNC turning. International Journal Production Research, 2000(38):3181-3202.
[33]S. M. Wang, Y.L. Liu, Y. Kang, An efficient error compensation system for CNC multi-axis machines, International Journal of Machine tools & Manufacturing,2002 (42):1235-1245.
[34]K. M. Y. Law, A. Geddam, Error compensation in the end milling of pockets:a methodology[J], Journal of Materials Processing Technology,2003(139) 21-27.
[35]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): 673-681.
[36]S. Ratchev, S. Liu, W. Huang, A. A. Becker, Milling error prediction and compensation in machining of low-rigidity parts [J], International Journal of Machine Tools and Manufacture.2004(44):1629-1641.
[37]S. Ratchev, S. Liu, W. Huang, A. A. Becker, An advanced FEA based force induced error compensation strategy in milling[J], International Journal of Machine Tools and Manufacture 2006 (46):542-551.
[38]Zhigang Wang, Ning He, Kai Wu, et al., Analysis and control approach for machining deformation of thin-walled workpiece[J], China Mechanical Engi-neering.2002(13): 113-117.
[39]Lianyu Zhen, Shuchun Wang, Approaches to improve the process quality of thin-walled workpiece in machining[J], Acta Aeronautica et Astronautica Sinica.2001(22): 424-428.
[40]WeifangChen a, JianbinXue, DunbingTang a, HuaChen a, ShaopengQub, Deformation prediction and error compensation in multilayer milling processes for thin-walled parts[J], International Journal of Machine Tools & Manufacture, doi:10.1016/j.ijmachtools.2009.05.006.
[41]Jitender K. Rai*, Paul Xirouchakis*, Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components [J]. International Journal of Machine Tools & Manufacture, 2008(48):629-643.
[2]F.W.Taylor. On the Art of cutting Metal [J]. ASME Transactions. Vol.1907(28):31-35.
[3]HerbetEG. Cutting tools research committee [J]. Report on Machinability. Proceeding, I Mech E,1928(114):175-825.
[4]Chao BT, Bisacre GH. The effect of feed and speed on the mechanics of metal cutting[J]. Proceeding,I mech E,1951(165):1-1.
[5]Shaw MC. Metal Cutting Principles[M]. Oxford:Clarendon Press,1984.
[6]艾兴,肖诗纲。切削用量手册[M],北京：机械工业出版社,1984.
[7]付秀丽,艾兴,张松潘,永智.航空整体结构件的高速切削加工[M].工具技术,2006.
[8]李亮,何宁,何磊,王珉.高速铣削铝合金时切削力和表面质量影响因素的试验研究[J],工具技术,2004.4.
[9]黄志刚.整体结构件铣削加工变形的有限元模拟理论及方法[D],杭州：浙江大学机械工程学院,2003.
[10]Lajczok, MRA study of some aspects of metal cutting by the finite element method[D]. [Ph D dissertation]. N C State University 1980.
[11]E. Usui, T. Shirakashi, Mechanics of metal machining-from "descriptive" to "predictive" theory, on the art of cutting metals:A tribute to F. W. Taylor, PED7 [C],The winner annual meeting of the American Society of Mechanical Engineers, Ed. Kops, L., Ramalingam, S.,1982.
[12]Strenkowski JS, Moon K J. Finite element prediction of chip geometry and tool /workpiece temperature distribution in orthogonal metal cutting[J]. Tran ASME J Eng Ind,1990,112(4):311-318.
[13]Lin, Z. C, Lin, S. Y, A Couple finite element model of thermo-elastic large deformation of orthogonal cutting[J], Journal of Engineering Material and Technology,1992,114(2):218-226.
[14]Shih, A. J., Yang, H. T. Y., Experimental and finite element predictions on the residual stresses due to orthogonal metal cutting[J], International Journal for Numerical Methods in Engineering,1993,36(8):1487-1507.
[15]S. Ratchev, S. Liu*, W. Huang, A. A. Becker. Milling error prediction and compensation in machining of low-rigidity parts [J], International Journal of Machine Tools & Manufacture,2004 (44):1629-1641.
[16]W. A. KLINE, R. E. DEVOR and I. A. SrmmSEF. The prediction of surface accuracy in end milling[J]. Trans. ASME J. Engng Ind.1982 (104):272-278.
[17]J. W. Sutherland and R. E. Devor, An improved method for cutting force and surface error prediction in flexible end milling systems [J]. Trans. ASME J. Engng Ind.1986 (108):269-279.
[18]Erhan Budak, Yusuf Altintas. MODELING AND AVOIDANCE OF STATIC FORM ERRORS IN PERIPHERAL MILLING OF PLATES [J], Int. J. Math. Tools Manufact.1995,35(3): 459-476.
[19]Svetan Ratchev, Shulong Liu, Wei Huang, Adib A. Becker, Machining simulation and system integration combining FE analysis and cutting mechanics modeling [J], Int J Adv Manuf Technol 2007(35):55-65.
[20]路冬. 航空整体结构件加工变形预测及装夹布局优化[D],济南： 山东大学机械工程学院,2007.
[21]刘亚俊,夏伟.金属切削理论发展的历史回顾[J],力学与实践,2001.
[22]李带娣, 基于铣削力预测模型的加工进给率优化研究[D].大连：大连理工大学,2007.
[23]陈玉安,周上祺.残余应力X射线测定方法的研究现状[J],无损检测,2001,23(1)：19-22.
[24]Liu Gang. Study on deformation of titanium thin-walled part in milling process[J], Journal of Materials processing technology,2009 (209):2788-2793.
[25]Budak, E., Altintas, Y., Modeling and avoidance of static form errors in eripheral milling of plates[J]. International Journal of Machine Tools & Manufacture. 1995(35):459-476.
[26]Shi, H. R., Hae, S. L., Chong, N. C., The form error prediction in side wall machining considering tool deflection[J], International Journal of Machine Tools & Manufacture,2003(43):1405-1411.
[27]Svetan, R., Huang, W., Liu, S., Modeling and simulation environment for machining of low-rididity components[J]. Journal of Materals processing Technology, 2004(153-154):67-73.
[28]Tsai.J. S., Liao, G. L., Finite-element modeling of static surface errors in the peripheral milling of thin-walled workpieces[J], Journal of Materials Processing Technology,1999(94):235-346.
[29]Wan, M. Zhang, W. H., Qiu, K. P., 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):13-22.
[30]Svetan, R., Evan, G., Stan, N., Force and deflection modeling in milling of low-rigidity complex part[J], Journal of Materials Processing Technology, 2003(143-444):796-801.
[31]M. Rahman, J. Heikkala, K. Lappalainen, Modeling, measurement and error compemsation of multi-axis machine tools [J]. Part Ⅰ:theory, International Journal of Machine Tools & Manufacture 2000(40):1535-1546.
[32]T.S. Suneel, S. S. Pande, Intelligent tool path correction for improving profile accuracy in CNC turning. International Journal Production Research, 2000(38):3181-3202.
[33]S. M. Wang, Y.L. Liu, Y. Kang, An efficient error compensation system for CNC multi-axis machines, International Journal of Machine tools & Manufacturing,2002 (42):1235-1245.
[34]K. M. Y. Law, A. Geddam, Error compensation in the end milling of pockets:a methodology[J], Journal of Materials Processing Technology,2003(139) 21-27.
[35]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): 673-681.
[36]S. Ratchev, S. Liu, W. Huang, A. A. Becker, Milling error prediction and compensation in machining of low-rigidity parts [J], International Journal of Machine Tools and Manufacture.2004(44):1629-1641.
[37]S. Ratchev, S. Liu, W. Huang, A. A. Becker, An advanced FEA based force induced error compensation strategy in milling[J], International Journal of Machine Tools and Manufacture 2006 (46):542-551.
[38]Zhigang Wang, Ning He, Kai Wu, et al., Analysis and control approach for machining deformation of thin-walled workpiece[J], China Mechanical Engi-neering.2002(13): 113-117.
[39]Lianyu Zhen, Shuchun Wang, Approaches to improve the process quality of thin-walled workpiece in machining[J], Acta Aeronautica et Astronautica Sinica.2001(22): 424-428.
[40]WeifangChen a, JianbinXue, DunbingTang a, HuaChen a, ShaopengQub, Deformation prediction and error compensation in multilayer milling processes for thin-walled parts[J], International Journal of Machine Tools & Manufacture, doi:10.1016/j.ijmachtools.2009.05.006.
[41]Jitender K. Rai*, Paul Xirouchakis*, Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components [J]. International Journal of Machine Tools & Manufacture, 2008(48):629-643.