非球头刀单触点宽行加工刀具运动优化方法
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摘要
将非球面刀具的单触点宽行加工复杂曲面问题归结为刀具曲面包络特征线在运动变换下逼近设计曲面的曲面拟合问题,提出复杂曲面非球面刀具单触点宽行加工的通用刀具运动优化方法—曲面包络逼近原理.该方法基于曲面自然活动标架理论,推导了由刀具曲面和设计曲面运动不变量参数描述的、通用规范的刀具相对工件运动的速度方程和运动变换矩阵;分别以加工效率和加工精度最优为目标,建立了能确保刀具相对工件运动连续光滑的刀位优化的泛函极值模型.最后通过一个圆锥面刀具和一个圆环面刀具的数控加工复杂曲面的仿真实例,论证了文中方法的精确性、有效性和通用性.
A universal envelope-approximation theory was presented to generate the sculptured surface by strip-width-maximization machining with single point contact using non-ball-end cutters, formulating the problem of multi-axis sculptured surface machining as that of approximating the cutter surface to the design surface under the movement transform. The speed equation and the movement transform matrix is deduced to determine the relative motion between the tool and the workpiece by intrinsic differential geometry based on the idea of the moving frame. The functional optimized model of the tool positioning was established to enable the relative motion between the tool and the workpiece to be smooth and continuous, aiming at the highest machining efficiency and machining accuracy respectively. Simulated examples demonstrate the improved machining efficiency and precision of the envelope-approximation Theory over current published methods.
A universal envelope-approximation theory was presented to generate the sculptured surface by strip-width-maximization machining with single point contact using non-ball-end cutters, formulating the problem of multi-axis sculptured surface machining as that of approximating the cutter surface to the design surface under the movement transform. The speed equation and the movement transform matrix is deduced to determine the relative motion between the tool and the workpiece by intrinsic differential geometry based on the idea of the moving frame. The functional optimized model of the tool positioning was established to enable the relative motion between the tool and the workpiece to be smooth and continuous, aiming at the highest machining efficiency and machining accuracy respectively. Simulated examples demonstrate the improved machining efficiency and precision of the envelope-approximation Theory over current published methods.
引文
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[14]ChenZhitong,YueYi,XuRufeng.Amiddle-point-errorcontrolmethodinstrip-widthmaximization-machining[J].ChineseJournalofMechanicalEngineering,2011,47(1):117-123(in Chinese)(陈志同,乐毅,徐汝锋.中点误差控制宽行加工算法[J].机械工程学报, 2011, 47(1):117-123)
[15]ZouQixiao,DongLei,CaoLixin.Leastsquarepositioning method of flank milling for non-developable ruled surface[J].ComputerIntegratedManufacturingSystems,2016,22(3):748-753(in Chinese)(邹启晓,董雷,曹利新.非可展直纹面侧铣加工的最小二乘刀位规划方法[J].计算机集成制造系统, 2016, 22(3):748-753)
[16]Dong Lei, Cao Lixin. Approximation method of tunnel surfaces with general cylindrical surfaces and its application in plunge millingofimpellers[J].ActaAeronauticaetAstronautica Sinica, 2014, 35(8):2331-2340(in Chinese)(董雷,曹利新.通道曲面的柱面逼近方法及其在叶轮插铣中的应用[J].航空学报, 2014, 35(8):2331-2340)
[17]ZhouKaihong.Researchonmeshingcharacteristics-based design&CNC technology of point-contact spiral bevel gears toothsurface[D].Changsha:CentralSouthUniversity,2009:54-63(in Chinese)(周凯红.基于预定啮合特性的螺旋锥齿轮点啮合齿面设计及CNC制造技术研究[D].长沙:中南大学, 2009:54-63)
[18]Zeidler E. Applied functional analysis main principles and their applications[M]. Heidelberg:Springer, 1995:167-279
[2]WuBaohai,WangShangjin.5-Axisflankmachining sculpturedsurfacesbasedonsignedDupinindicatrix[J].ChineseJournalofMechanicalEngineering,2007,42(11):192-196(in Chinese)(吴宝海,王尚锦.基于正向杜邦指标线的五坐标侧铣加工[J].机械工程学报, 2006, 42(11):192-196)
[3]Rao N, Bedi S, Buchal R. Implementation of the principal-axis methodformachiningofcomplexsurfaces[J].The International Journal of Advanced Manufacturing Technology,1996, 11(4):249-257
[4]Li C G, Bedi S, Mann S. Flank milling of ruled surface with conicaltools-anoptimizationapproach[J].TheInternational JournalofAdvancedManufacturingTechnology,2006,29(11/12):1115-1124
[5]WarkentinA,IsmailF,BediS.Multi-pointtoolpositioning strategyfor5-axismachiningofsculpturedsurfaces[J].Computer Aided Geometric Design, 2000, 17(1):83-100
[6]Chiou C J, Lee Y S. A machining potential field approach to toolpathgenerationformulti-axissculpturedsurface machining[J]. Computer Aided Design, 2002, 34(5):357-371
[7]FanJH,BallA.Quadricmethodforcutterorientationin five-axis sculptured surface machining[J]. International Journal of Machine Tools and Manufacture, 2008, 48(7/8):788-801
[8]ZhuLM,DingH,XiongYL.Thirdorderpointcontact approachforfive-axissculpturedsurfacemachiningusing non-ballendtolls-PartI:thirdorderapproximationoftool envelopesurface[J].ScienceChinaTechnologicalSciences,2010, 53(7):1904-1912
[9]ZhuLM,DingH,XiongYL.Thirdorderpointcontact approachforfive-axissculpturedsurfacemachiningusing non-ball end tools-Part II:tool positioning strategy[J]. Science China Technological Sciences, 2010, 53(8):2190-2197
[10]Zhu L M, Zheng G, Ding H, et al. Global optimization of tool pathforfive-axisflankmillingwithaconicalcutter[J].Computer-Aided Design, 2010, 42(10):903-910
[11]ZhuLimin,LuYaoan.Modelingsweptenvelopesofrotary cuttingtoolswithapplicationtofive-axisflankmilling[J].ChineseJournalofMechanicalEngineering,2013,49(7):176-183(in Chinese)(朱利民,卢耀安.回转刀具侧铣加工扫掠包络面几何造型及其应用[J].机械工程学报, 2013, 49(7):176-183)
[12]Gong H, Wang N. 5-axis flank milling free-form surfaces consider ing constraints[J]. Computer-Aided Design, 2011, 43(6):563-572
[13]ChenZhitong,HeYing.Anunifiedmethodforstrip-widthmaximizationendmillingmachiningtoolpathgeneration.China:201310335002.1,2013.11.27[P]. 2013-11-27(in Chinese)(陈志同,贺英.一种宽行端铣加工刀轨生成统一方法.中国:201310335002.1,2013.11.27[P]. 2013-11-27
[14]ChenZhitong,YueYi,XuRufeng.Amiddle-point-errorcontrolmethodinstrip-widthmaximization-machining[J].ChineseJournalofMechanicalEngineering,2011,47(1):117-123(in Chinese)(陈志同,乐毅,徐汝锋.中点误差控制宽行加工算法[J].机械工程学报, 2011, 47(1):117-123)
[15]ZouQixiao,DongLei,CaoLixin.Leastsquarepositioning method of flank milling for non-developable ruled surface[J].ComputerIntegratedManufacturingSystems,2016,22(3):748-753(in Chinese)(邹启晓,董雷,曹利新.非可展直纹面侧铣加工的最小二乘刀位规划方法[J].计算机集成制造系统, 2016, 22(3):748-753)
[16]Dong Lei, Cao Lixin. Approximation method of tunnel surfaces with general cylindrical surfaces and its application in plunge millingofimpellers[J].ActaAeronauticaetAstronautica Sinica, 2014, 35(8):2331-2340(in Chinese)(董雷,曹利新.通道曲面的柱面逼近方法及其在叶轮插铣中的应用[J].航空学报, 2014, 35(8):2331-2340)
[17]ZhouKaihong.Researchonmeshingcharacteristics-based design&CNC technology of point-contact spiral bevel gears toothsurface[D].Changsha:CentralSouthUniversity,2009:54-63(in Chinese)(周凯红.基于预定啮合特性的螺旋锥齿轮点啮合齿面设计及CNC制造技术研究[D].长沙:中南大学, 2009:54-63)
[18]Zeidler E. Applied functional analysis main principles and their applications[M]. Heidelberg:Springer, 1995:167-279