覆盖件模具曲面曲率特征对球头刀铣削力的影响
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摘要
针对自由曲面模具的铣削加工,提出一种综合考虑曲面曲率、刀具前倾角和侧偏角的瞬时铣削力预报方法。基于曲面几何特征,研究了进给方向、行距方向曲率半径对刀具切削角度的影响,以及刀具前倾角和轴向切触角对未变形切屑厚度的影响;基于微分思想,将自由曲面加工中任意刀齿切削周期内的切触区进行离散,结合三维次摆线切削轨迹建立未变形切屑模型,得到适合于自由曲面三轴球头铣削的瞬态铣削力,该模型能够综合考虑曲面曲率特征变化、刀具工件切触角度变化;基于二次曲面模具模型进行铣削加工试验,试验测试结果表明,预报的铣削力和试验测量结果在幅值上和变化趋势上具有一致性,在平稳切削时最大铣削力预测误差值在12%以内,验证了该方法能有效地预报自由曲面模具的球头铣削的瞬态铣削力。
A instantaneous milling force prediction method considering of the curvature, the lead angle and the tilt angle, is proposed for sculptured surface mould machining. In view of geometry features of the sculptured surface, the impacts of the curvature radius on feed direction and cross feed direction on cutting angles are explored. Furthermore, the impacts of the lead angle and axial tangential angle on the undeformed chip thickness are studied. By means of differential theory, the cutter-workpiece contact area in arbitrary rotation period of sculptured surfaces machining is discretized. Based on the 3D trochoidal tooth trajectory, the model of the undeformed chip thickness is established and the instantaneous milling force considering of the curvature features and cutting angles is obtained for three axis ball end milling of sculptured surfaces. Finally, experiments of machining mould with quadric surface are conducted to measure the milling force. The estimated milling forces match well with the actual cutting forces obtained from experiments. The error rate of estimated instantaneous milling forces is approximately 12%, which verifies the efficiency of this method to estimate the instantaneous milling force in milling of sculptured surface mould with sculptured surfaces.
A instantaneous milling force prediction method considering of the curvature, the lead angle and the tilt angle, is proposed for sculptured surface mould machining. In view of geometry features of the sculptured surface, the impacts of the curvature radius on feed direction and cross feed direction on cutting angles are explored. Furthermore, the impacts of the lead angle and axial tangential angle on the undeformed chip thickness are studied. By means of differential theory, the cutter-workpiece contact area in arbitrary rotation period of sculptured surfaces machining is discretized. Based on the 3D trochoidal tooth trajectory, the model of the undeformed chip thickness is established and the instantaneous milling force considering of the curvature features and cutting angles is obtained for three axis ball end milling of sculptured surfaces. Finally, experiments of machining mould with quadric surface are conducted to measure the milling force. The estimated milling forces match well with the actual cutting forces obtained from experiments. The error rate of estimated instantaneous milling forces is approximately 12%, which verifies the efficiency of this method to estimate the instantaneous milling force in milling of sculptured surface mould with sculptured surfaces.
引文
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[16]YANG Yun,ZHANG Weihong,WAN Min,et al.A solid trimming method to extract cutter–workpiece engagement maps for multi-axis milling[J].International Journal of Advanced Manufacturing Technology,2013,68(9-12):2801-2813.
[17]CAO Qingyuan,ZHAO Jun,HAN Shiguo,et al.Force coefficients identification considering inclination angle for ball-end finish milling[J].Precision Engineering,2012,36(2):252-260.
[18]LEE P,ALTINTAS Y.Prediction of ball-end milling forces from orthogonal cutting data[J].International Journal of Machine Tools and Manufacture,1996,36(9):1059-1072.
[2]ZHANG L,ZHENG L.Prediction of cutting forces in milling of circular corner profiles[J].International Journal of Machine Tools and Manufacture,2004,44(2-3):225-235.
[3]WEI Zhaocheng,WANG Minjie,MA Riguang,et al.Modeling of process geometry in peripheral milling of curved surfaces[J].Journal of Materials Processing Technology,2010,210(5):799-806.
[4]WEI Zhaocheng,WANG Minjie,HAN Xianguo.Cutting forces prediction in generalized pocket machining[J].International Journal of Advanced Manufacturing Technology,2010,50(5):449-458.
[5]WEI Zhaocheng,WANG Minjie,ZHU J N,et al.Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path[J].International Journal of Machine Tools and Manufacture,2011,51(5):428-432.
[6]TUYSUZ O,ALTINTAS Y,FENG H Y.Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect[J].International Journal of Machine Tools and Manufacture,2013,66:66-81.
[7]WOJCIECHOWSKI S.The estimation of cutting forces and specific force coefficients during finishing ball end milling of inclined surfaces[J].International Journal of Machine Tools and Manufacture.2015,89:110-123.
[8]LOTFI B,ZHONG Z W,KHOO L P.Prediction of cutting forces along Pythagorean-hodograph curves[J].International Journal of Advanced Manufacturing Technology,2009,43:872-882.
[9]RAO V S,RAO P V M.Modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces[J].International Journal of Machine Tools and Manufacture,2005,45(6):617-630.
[10]SUN Yuwen,REN Fei,GUO Dongming,et al.Estimation and experimental validation of cutting forces in ball-end milling of sculptured surfaces[J].International Journal of Machine Tools and Manufacture,2009,49(15):1238-1244.
[11]GUO Dongming.,REN Fei,SUN Yuwen.An approach to modeling cutting forces in five-axis ball-end milling of curved geometries based on tool motion analysis[J].Journal of Manufacturing Science and Engineering,2010,132(4):041004.
[12]SUN Yuwen,GUO Dongming.Numerical simulation and prediction of cutting forcer in five-axis milling processes with cutter run-out[J].International Journal of Machine Tools and Manufacture,2011,51(10/11):806-815.
[13]LIANG Xinguang,YAO Zhenqiang.An accuracy algorithm for chip thickness modeling in 5-axis ball finish milling[J].Computer-Aided Design,2011,43(8):971-978.
[14]HUANG Tao,ZHANG Xiaoming,DING Han.Decoupled chip thickness calculation model for cutting force prediction in five-axis ball-end milling[J].International Journal of Advanced Manufacturing Technology,2013,69(5):1203-1217.
[15]GENG L,LIU P L,LIU Kui.Optimization of cutter posture based on cutting force prediction for five-axis machining with ball-end cutters[J].International Journal of Advanced Manufacturing Technology,2015,78:1289-1303.
[16]YANG Yun,ZHANG Weihong,WAN Min,et al.A solid trimming method to extract cutter–workpiece engagement maps for multi-axis milling[J].International Journal of Advanced Manufacturing Technology,2013,68(9-12):2801-2813.
[17]CAO Qingyuan,ZHAO Jun,HAN Shiguo,et al.Force coefficients identification considering inclination angle for ball-end finish milling[J].Precision Engineering,2012,36(2):252-260.
[18]LEE P,ALTINTAS Y.Prediction of ball-end milling forces from orthogonal cutting data[J].International Journal of Machine Tools and Manufacture,1996,36(9):1059-1072.