多轴CNC机床运动优化磨齿拓扑修形面齿轮
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摘要
为了求解利用碟形砂轮磨齿加工拓扑修形面齿轮CNC数控机床各轴运动参数的问题,提出一种数控机床各轴运动参数的优化求解方法。依据多轴CNC机床碟形砂轮磨齿加工各轴的运动关系,建立了多轴机床磨齿实际拓扑齿面的数学模型;将机床各轴运动表示为联系参数的6阶多项式函数,以各轴运动函数的多项式系数为优化参数,并以齿面目标偏差与实际偏差的误差最小作为评价函数,建立了各轴运动参数的优化模型;利用迭代最小二乘法对模型进行求解,获得加工拓扑修形齿面各轴的运动规律。通过拓扑修形面齿轮加工优化仿真和磨齿试验,实现了高精度拓扑修形面齿轮的数控磨齿,验证了各轴运动参数优化求解的正确性。
To obtain each axis motion of a multi-axis CNC machine for grinding double crowned topological tooth geometry of face gear,a novel methodology of optimum solution for multi-axis motions was proposed by grinding disc wheel application.A theoretical model of face gear grinding with disc grinding wheel was built based on meshing theory.According to the kinematical relations of CNC machine's each axis in the grinding process,a mathematical model of actual tooth flank was established and the initial motion of each axis was obtained.Each axis motion of CNC machine was formulated by six order polynomial function approximately,and an optimization process with the objective function of tooth flank form errors minimization between actual and target tooth flanks was established.By using least squares techniques,the polynomial coefficients of multi-axis motion functions were obtained precisely.The optimization simulation and actual grinding of topological tooth flanks for face gear were developed,and the result showed that the high precision actual tooth gear could be yield by application of optimization method.
To obtain each axis motion of a multi-axis CNC machine for grinding double crowned topological tooth geometry of face gear,a novel methodology of optimum solution for multi-axis motions was proposed by grinding disc wheel application.A theoretical model of face gear grinding with disc grinding wheel was built based on meshing theory.According to the kinematical relations of CNC machine's each axis in the grinding process,a mathematical model of actual tooth flank was established and the initial motion of each axis was obtained.Each axis motion of CNC machine was formulated by six order polynomial function approximately,and an optimization process with the objective function of tooth flank form errors minimization between actual and target tooth flanks was established.By using least squares techniques,the polynomial coefficients of multi-axis motion functions were obtained precisely.The optimization simulation and actual grinding of topological tooth flanks for face gear were developed,and the result showed that the high precision actual tooth gear could be yield by application of optimization method.
引文
[1]LITVIN F L.Gear geometry and applied theory[M].Englewood Cliffs,N.J.,USA:Prentice Hall Inc.,1994:491-525.
[2]LITVIN F L,GONZALEZ-PEREZ I,AZNAR A F,et al.Design generation and stress analysis of face-gear drive with helical pinion[J].Computer Methods Applacation Mechanical Engrg,2005,194(36-38):3870-3901.
[3]SHEN Y B,FANG Z D,ZHAO N,et al.Application of modified geometry of face-gear drive with double crowned helical pinion[M]//Advanced Design and Manufacture to Gain a Competitive Edge.Berlin,Germany:Springer-Verlag,2008:579-588.
[4]LITVIN F L,AZNAR A F,HOWKINS M.Design,generateon and TCA of new type of asymmetric face-gear drive with modified geometry[J].Comput.Methods Appl.Mech.Engrg.,2001,190(43/44):5837-5865.
[5]SHIH Y P.A novel ease-off flank modification methodology for spiral bevel and hypoid gears[J].Mechanism and Machine Theory,2010,45(8):1108-1124.
[6]SHIH Y P,FONG Z H.Flank modification methodology for face-hobbing hypoid gears based on ease-off topology[J].ASME Journal of Mechanical,2007,129(12):1294-1302.
[7]JIANG Jinke,FANG Zongde.Design and analysis of modified cylindrical gears with a higher-order transmission error[J].Mechanism and Machine Theory,2015,88:141-152.
[8]JIANG Jinke,FANG Zongde.High-order tooth flank correction for a helical gear on a six-axis CNC hob machine[J].Mechanism and Machine Theory,2015,91:227-237.
[9]ZHANG Hu,FANG Chenggang,GUO Erkuo,et al.Accurate lead modification of CNC gear profile grinding based on fiveaxis motions optimization[J].Computer Integrated Manufacturing Systems,2014,20(12):3058-3066(in Chinese).[张虎,方成刚,郭二廓,等.基于五轴运动优化的数控成形磨齿精密齿向修形[J].计算机集成制造系统,2014,20(12):3058-3066.]
[10]PENG Xianlong,FANG Zongde,SU Jinzhan,et al.Theory analysis for application grinding disk in face gear grinding[J].Journal of Aerospace Power,2012,27(5):1159-1165(in Chinese).[彭先龙,方宗德,苏进展,等.采用碟形砂轮的面齿轮磨齿方法理论分析[J].航空动力学报,2012,27(5):1159-1165.]
[11]TANG Jinyuan,YIN Feng,CHEN Xingming.The principle of profile modified face-gear grinding based on disk wheel[J].Mechanism and Machine Theory,2013,70(6):1-15.
[12]WANG Yanzhong,LAN Zhou,HOU Liangwei.A precision generating grinding method for face gear using CBN wheel[J].International Journal of Advanced Manufacturing Technology,2015,79(9):1839-1848.
[13]WANG Yanzhong,HOU Liangwei,LAN Zhou,et al.Research on processing method of grinding face gear with involute disc wheel[J].Journal of Aerospace Power,2015,30(8):2033-2041(in Chinese).[王延忠,侯良威,兰州,等.渐开线碟形砂轮磨削面齿轮数控加工研究[J].航空动力学报,2015,30(8):2033-2041.]
[14]GUO Hui,ZHAO Ning,ZHANG Shuyan.Enveloperesiduals research of face gear based on disc grinding wheel tooth grinding[J].Journal of Aerospace Power,2014,29(11):2743-2750(in Chinese).[郭辉,赵宁,张淑艳.基于碟形砂轮磨齿的面齿轮包络残差研究[J].航空动力学报,2014,29(11):2743-2750.]
[15]SUN Yongsheng,HAN Xianguo,CHEN Wuyi.High efficient approach of direct problem with extensive convergence on parallel mechanism[J].Computer Integrated Manufacturing Systems,2012,18(5):981-987(in Chinese).[孙永生,韩先国,陈五一.并联机构大范围收敛高效正解法[J].计算机集成制造系统,2012,18(5):981-987.]
[2]LITVIN F L,GONZALEZ-PEREZ I,AZNAR A F,et al.Design generation and stress analysis of face-gear drive with helical pinion[J].Computer Methods Applacation Mechanical Engrg,2005,194(36-38):3870-3901.
[3]SHEN Y B,FANG Z D,ZHAO N,et al.Application of modified geometry of face-gear drive with double crowned helical pinion[M]//Advanced Design and Manufacture to Gain a Competitive Edge.Berlin,Germany:Springer-Verlag,2008:579-588.
[4]LITVIN F L,AZNAR A F,HOWKINS M.Design,generateon and TCA of new type of asymmetric face-gear drive with modified geometry[J].Comput.Methods Appl.Mech.Engrg.,2001,190(43/44):5837-5865.
[5]SHIH Y P.A novel ease-off flank modification methodology for spiral bevel and hypoid gears[J].Mechanism and Machine Theory,2010,45(8):1108-1124.
[6]SHIH Y P,FONG Z H.Flank modification methodology for face-hobbing hypoid gears based on ease-off topology[J].ASME Journal of Mechanical,2007,129(12):1294-1302.
[7]JIANG Jinke,FANG Zongde.Design and analysis of modified cylindrical gears with a higher-order transmission error[J].Mechanism and Machine Theory,2015,88:141-152.
[8]JIANG Jinke,FANG Zongde.High-order tooth flank correction for a helical gear on a six-axis CNC hob machine[J].Mechanism and Machine Theory,2015,91:227-237.
[9]ZHANG Hu,FANG Chenggang,GUO Erkuo,et al.Accurate lead modification of CNC gear profile grinding based on fiveaxis motions optimization[J].Computer Integrated Manufacturing Systems,2014,20(12):3058-3066(in Chinese).[张虎,方成刚,郭二廓,等.基于五轴运动优化的数控成形磨齿精密齿向修形[J].计算机集成制造系统,2014,20(12):3058-3066.]
[10]PENG Xianlong,FANG Zongde,SU Jinzhan,et al.Theory analysis for application grinding disk in face gear grinding[J].Journal of Aerospace Power,2012,27(5):1159-1165(in Chinese).[彭先龙,方宗德,苏进展,等.采用碟形砂轮的面齿轮磨齿方法理论分析[J].航空动力学报,2012,27(5):1159-1165.]
[11]TANG Jinyuan,YIN Feng,CHEN Xingming.The principle of profile modified face-gear grinding based on disk wheel[J].Mechanism and Machine Theory,2013,70(6):1-15.
[12]WANG Yanzhong,LAN Zhou,HOU Liangwei.A precision generating grinding method for face gear using CBN wheel[J].International Journal of Advanced Manufacturing Technology,2015,79(9):1839-1848.
[13]WANG Yanzhong,HOU Liangwei,LAN Zhou,et al.Research on processing method of grinding face gear with involute disc wheel[J].Journal of Aerospace Power,2015,30(8):2033-2041(in Chinese).[王延忠,侯良威,兰州,等.渐开线碟形砂轮磨削面齿轮数控加工研究[J].航空动力学报,2015,30(8):2033-2041.]
[14]GUO Hui,ZHAO Ning,ZHANG Shuyan.Enveloperesiduals research of face gear based on disc grinding wheel tooth grinding[J].Journal of Aerospace Power,2014,29(11):2743-2750(in Chinese).[郭辉,赵宁,张淑艳.基于碟形砂轮磨齿的面齿轮包络残差研究[J].航空动力学报,2014,29(11):2743-2750.]
[15]SUN Yongsheng,HAN Xianguo,CHEN Wuyi.High efficient approach of direct problem with extensive convergence on parallel mechanism[J].Computer Integrated Manufacturing Systems,2012,18(5):981-987(in Chinese).[孙永生,韩先国,陈五一.并联机构大范围收敛高效正解法[J].计算机集成制造系统,2012,18(5):981-987.]