平底立铣刀的切削力尺寸效应研究及其系数估算
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摘要
检验基于三元切削力机理模型的平底立铣刀尺寸效应,并探索一种简便的切削力系数估算方法。论证了在切削厚度较小时可忽略刀具螺旋角对切削力的影响,据此构建平底立铣刀单个刀齿的三元切削力简化模型。基于该模型,用各齿径向跳动量补偿瞬时切削厚度,用切削试验数据拟合各齿切削力峰值与切削深度及瞬时切削厚度的线性方程式,发现各拟合式的确定系数总体上接近1,表明同一刀齿的切削力系数大体为常数,这意味着平底立铣刀的尺寸效应不显著。据此采用刀具的平均切削力峰值估算切削力系数,该方法不用考虑刀具偏心,且计算比较简便,模拟得到的切削力波形与实测波形相近,表明估算方法比较有效。研究结果可供铣削力尺寸效应机理研究及平底立铣刀应用领域参考。
The size effect of flat end mills based on the ternary cutting force model is checked, and then a simple method estimating coefficients of cutting force is explored. The effect of helical angle on cutting force is proved to be negligible when cutting depth is little, then a simplified ternary mathematical model of force for single tooth of flat end mills is built. Based on this model, the instantaneous cutting thicknesses for every tooth are compensated with tooth run-out, and data of cutting experiments are used to fit the linear equations of peak cutting forces with cutting depth and instantaneous cutting thickness for every tooth, their R-squares are found to be near 1 as a whole, this indicates that the coefficients of cutting force for one tooth be constant, which means that the size effect of flat end mills be not significant. Accordingly, the average peak force of tool is used to estimate cutting force, with this estimation method, tool eccentricity need not to be considered, and calculation is rather simple, its simulated force waveform is close to the measured, which indicates that the estimating method be rather effective. These research results can be used as reference in the research of size effect for milling force, and in the application of flat end mills.
The size effect of flat end mills based on the ternary cutting force model is checked, and then a simple method estimating coefficients of cutting force is explored. The effect of helical angle on cutting force is proved to be negligible when cutting depth is little, then a simplified ternary mathematical model of force for single tooth of flat end mills is built. Based on this model, the instantaneous cutting thicknesses for every tooth are compensated with tooth run-out, and data of cutting experiments are used to fit the linear equations of peak cutting forces with cutting depth and instantaneous cutting thickness for every tooth, their R-squares are found to be near 1 as a whole, this indicates that the coefficients of cutting force for one tooth be constant, which means that the size effect of flat end mills be not significant. Accordingly, the average peak force of tool is used to estimate cutting force, with this estimation method, tool eccentricity need not to be considered, and calculation is rather simple, its simulated force waveform is close to the measured, which indicates that the estimating method be rather effective. These research results can be used as reference in the research of size effect for milling force, and in the application of flat end mills.
引文
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[7]ADETORO O B,WEN P H.Prediction of mechanistic cutting force coefficients using ALE formulation[J].International Journal of Advanced Manufacturing Technology,2010,46:79-90.
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[11]WAN M,ZHANG W,YANG Y.Phase width analysis of cutting forces considering bottom edge cutting and cutter runout calibration in flat end milling of titanium alloy[J].Journal of Materials Processing Technology,2011,211:1852-1863.
[12]WAN M,LU M,ZHANG W,et al.A new ternary-mechanism model for the prediction of cutting forces in flat end milling[J].International Journal of Machine Tools&Manufacture,2012,57:34-45.
[13]SHIN Y C,WATERS A J.A new procedure to determine instantaneous cutting force coefficients for machining force prediction[J].International Journal of Machine Tools&Manufacture,1997,37(9):1337-1351.
[14]ALTINTAS Y,SPENCE A.End milling force algorithms for CAD systems[J].Annals of the CIRP,1991,40(1):31-34.
[15]SRINIVASA Y V,SHUNMUGAM M S.Mechanistic model for prediction of cutting forces in micro end-milling and experimental comparison[J].International Journal of Machine Tools&Manufacture,2013,67:18-27.
[16]刘璨,吴敬权,李广慧,等.基于单刃铣削力峰值的铣刀偏心辨识[J].机械工程学报,2013,49(1):185-190.LIU Can,WU Jingquan,LI Guanghui,et al.Identification of mills eccentricity based on peak force of single edge[J].Journal of Mechanical Engineering,2013,49(1):185-190.
[17]刘显波,龙新华,孟光,等.基于频域多目标优化的铣削力系数及偏心参数识别[J].机械工程学报,2011,47(7):185-190.LIU Xianbo,LONG Xinhua,MENG Guang,et a1.The identifications of milling force coeficients and eccentricity based on multi-objective optimization in frequency-domain[J].Journal of Mechanical Engineering,2011,47(7):185-190.
[2]KOENIGSBERGER F,SABBERWAL A J P.An investigation into the cutting force pulsations during milling operations[J].International Journal of Machine Tool Design and Research,1961,1:15-33.
[3]KO J H,YUN W,CHO D,et al.Development of a virtual machining system,part 1:Approximation of the size effect for cutting force prediction[J].International Journal of Machine Tools&Manufacture,2002,42:1595-1605.
[4]ZHANG Z,ZHENG L,ZHANG L,et al.A study on calibration of coefficients in end milling forces model[J].International Journal of Advanced Manufacturing Technology,2005,25:652-662.
[5]CHENG P J,TSAY J T,LIN S C.A study on instantaneous cutting force coefficients in face milling[J].International Journal of Machine Tools&Manufacture,1997,37(10):1393-1408.
[6]WANG M,GAO L,ZHENG Y.An examination of the fundamental mechanics of cutting force coefficients[J].International Journal of Machine Tools&Manufacture,2014,78:1-7.
[7]ADETORO O B,WEN P H.Prediction of mechanistic cutting force coefficients using ALE formulation[J].International Journal of Advanced Manufacturing Technology,2010,46:79-90.
[8]GONZALO O,BERISTAIN J,JAUREGI H,et al.Amethod for the identification of the specific force coefficients for mechanistic milling simulation[J].International Journal of Machine Tools&Manufacture,2010,50:765-774.
[9]CAMPATELLI G,SCIPPA A.Prediction of milling cutting force coefficients for Aluminum 6082-T4[J].Procedia CIRP,2012,1:563-568.
[10]DANG J,ZHANG W,YANG Y,et al.Cutting force modeling for flat end milling including bottom edge cutting effect[J].International Journal of Machine Tools&Manufacture,2010,50:986-997.
[11]WAN M,ZHANG W,YANG Y.Phase width analysis of cutting forces considering bottom edge cutting and cutter runout calibration in flat end milling of titanium alloy[J].Journal of Materials Processing Technology,2011,211:1852-1863.
[12]WAN M,LU M,ZHANG W,et al.A new ternary-mechanism model for the prediction of cutting forces in flat end milling[J].International Journal of Machine Tools&Manufacture,2012,57:34-45.
[13]SHIN Y C,WATERS A J.A new procedure to determine instantaneous cutting force coefficients for machining force prediction[J].International Journal of Machine Tools&Manufacture,1997,37(9):1337-1351.
[14]ALTINTAS Y,SPENCE A.End milling force algorithms for CAD systems[J].Annals of the CIRP,1991,40(1):31-34.
[15]SRINIVASA Y V,SHUNMUGAM M S.Mechanistic model for prediction of cutting forces in micro end-milling and experimental comparison[J].International Journal of Machine Tools&Manufacture,2013,67:18-27.
[16]刘璨,吴敬权,李广慧,等.基于单刃铣削力峰值的铣刀偏心辨识[J].机械工程学报,2013,49(1):185-190.LIU Can,WU Jingquan,LI Guanghui,et al.Identification of mills eccentricity based on peak force of single edge[J].Journal of Mechanical Engineering,2013,49(1):185-190.
[17]刘显波,龙新华,孟光,等.基于频域多目标优化的铣削力系数及偏心参数识别[J].机械工程学报,2011,47(7):185-190.LIU Xianbo,LONG Xinhua,MENG Guang,et a1.The identifications of milling force coeficients and eccentricity based on multi-objective optimization in frequency-domain[J].Journal of Mechanical Engineering,2011,47(7):185-190.