基于接触区域的球头铣刀颤振稳定域预报方法研究
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摘要
运用半解析法精准搭建出球头铣刀与工件接触区域边界的投影方程,对铣削系统时滞动力学方程进行全离散时域数值求解,在单齿周期内球头铣刀视为圆弧切削的基础上,通过接触区域投影和切削刃投影不同时刻的关系,确定出数值求解方程中所需要的瞬时参与切削刀刃的实际切削部位,利用Floquet定理获得了不同转速下的临界切削深度,构建出了高精度的球头铣刀颤振稳定域叶瓣图,并在三轴数控机床上进行了试验验证,试验结果与预测结果相符合,表明了该方法的正确性。同时,与传统方法相比,这里所提供的方法拥有较高的预测精度,最后分析了不同参数对颤振稳定域的影响规律,为叶瓣图指导实际加工奠定了基础。
he equations for the boundaries of ball-end mill-workpiece engagement(BWE)are precisely established by a semi-analytical method at first.The differential dynamic equation derived from the ideal 2-Dof milling system is solved by the complete discrete method.Based on the cutter within a tooth passing period considered as arc path cutting,the instantaneous cutting positions required in the numerical solution are identified by the relationship of cutter edge and BWE.The stability lobe diagram is constructed by Floquet theory,which is subsequently verified on a three-axis NC machine tool.The experimental results are in good agreement with the predicted results,indicating the validity of this method.In contrast to traditional method,the proposed method shows higher prediction precision.The influence laws of different parameters on stability are analyzed at last,which can give a help for the actual machining.
he equations for the boundaries of ball-end mill-workpiece engagement(BWE)are precisely established by a semi-analytical method at first.The differential dynamic equation derived from the ideal 2-Dof milling system is solved by the complete discrete method.Based on the cutter within a tooth passing period considered as arc path cutting,the instantaneous cutting positions required in the numerical solution are identified by the relationship of cutter edge and BWE.The stability lobe diagram is constructed by Floquet theory,which is subsequently verified on a three-axis NC machine tool.The experimental results are in good agreement with the predicted results,indicating the validity of this method.In contrast to traditional method,the proposed method shows higher prediction precision.The influence laws of different parameters on stability are analyzed at last,which can give a help for the actual machining.
引文
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[11]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.HU Ruifei,YIN Ming,LIU Yan,et al.Optimization of milling parameters under constrain of process stability,Journal of Mechanical Engineering,2017,53(5):190-198.
[12]刘强,李忠群.数控铣削加工过程仿真与优化:建模、算法与工程应用[M].北京:航空工业出版社,2011.LIU Qiang,LI Zhongqun.Simulation and optimization of CNC milling progress:Modeling,algorithms and applications[M].Beijing:Aviation Industrial Publishing House,2011.
[2]MERDOL S,ALTINTAS Y.Multi frequency solution of chatter stability for low immersion milling[J].Journal of Manufacturing Science&Engineering,2004,126(3):459-466.
[3]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(1):117-141.
[4]LI Z,YANG Z,PENG Y,et al.Prediction of chatter stability for milling process using Runge-Kutta-based complete discretization method[J].The International Journal of Advanced Manufacturing Technology,2016,86(1):943-952.
[5]DING Y,ZHU L,ZHANG X,et al.Second-order full-discretization method for milling stability prediction[J].International Journal of Machine Tools&Manufacture,2010,50(10):926-932.
[6]LI M,ZHANG G,HUANG Y.Complete discretization scheme for milling stability prediction[J].Nonlinear Dynamics,2012,71(1-2):187-199.
[7]李忠群.复杂切削条件高速铣削加工动力学建模、仿真与切削参数优化研究[D].北京:北京航空航天大学,2008.LI Zhongqun.Dynamic modeling,simulation and optimization of high speed milling under complicated cutting conditions[D].Beijing:Beihang University,2008.
[8]李忠群,刘强.圆角铣削颤振稳定域建模与仿真研究[J].机械工程学报,2010,46(7):181-186.LI Zhongqun,LIU Qiang.Modeling and simulation of chatter stability for circular milling[J].Journal of Mechanical Engineering,2010,46(7):181-186.
[9]吴石,刘献礼,宋盛罡,等.铣刀磨损对铣削稳定性及表面位置误差的影响[J].振动、测试与诊断,2015,35(4):763-769.WU Shi,LIU Xianli,SONG Shenggang,et al.The influence of wear loss of milling cutter on milling stability and surface location error[J].Journal of Vibration,Measurement and Diagnosis,2015,35(4):763-769.
[10]宋盛罡.薄板件铣削过程颤振稳定域预测及实验研究[D].哈尔滨:哈尔滨理工大学,2015.SONG Shengang.Prediction and experimental study on the chatter stability in milling of thin part[D].Harbin:Harbin University of Science and Technology,2015.
[11]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.HU Ruifei,YIN Ming,LIU Yan,et al.Optimization of milling parameters under constrain of process stability,Journal of Mechanical Engineering,2017,53(5):190-198.
[12]刘强,李忠群.数控铣削加工过程仿真与优化:建模、算法与工程应用[M].北京:航空工业出版社,2011.LIU Qiang,LI Zhongqun.Simulation and optimization of CNC milling progress:Modeling,algorithms and applications[M].Beijing:Aviation Industrial Publishing House,2011.