并联机床的动力学特性对加工精度影响的分析
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摘要
为了提高并联机床的加工精度,分析了并联机床的动力学特性对加工精度的影响。根据牛顿-欧拉方程,得到并联机床的动力学方程,解得连杆的驱动力;根据杆件轴向伸长量与受力之间的关系,得到连杆的长度误差;以无长度误差的连杆长度为优化目标,用优化的方法,得到动平台的位姿,并与连杆有长度误差时动平台的位姿比较,得动平台的位姿误差;根据刀具在动平台坐标系中位置,得刀具加工位置误差及对被加工零件精度的影响。结果表明:并联机床连杆的长度误差,引起刀具加工位置误差,使被加工零件产生形位误差和尺寸误差;并联机床电主轴偏心引起连杆的长度误差的扰动,产生刀具加工位置的扰动误差,影响被加工零件的表面粗糙度。
In order to improve the machining accuracy of a parallel machine tool,the effect of its dynamic characteristics on machining accuracy was analysed.The dynamic equation of the parallel machine tool was derived in the light of Newton-Euler method and the driving force of the leg was obtained from the solution of the dynamic equation.According to the relation between the axial extension length and leg driving force,the length error of the leg was calculated.Taking the accurate leg length as an optimization objective,the position and pose of the moving platform were achieved by using optimization method and their errors were analysed.According to tool position in the coordinate system of the moving platform,the error of machining position was calculated,and its effect on the accuracy of machined parts was discussed.The results show that the tool position error is caused by leg length error,which produces the errors of form,position and dimension of machined parts.The rotor eccentricity of the parallel machine tool may cause disturbances on leg length and tool position,which will effect the surface roughness of machined parts.
In order to improve the machining accuracy of a parallel machine tool,the effect of its dynamic characteristics on machining accuracy was analysed.The dynamic equation of the parallel machine tool was derived in the light of Newton-Euler method and the driving force of the leg was obtained from the solution of the dynamic equation.According to the relation between the axial extension length and leg driving force,the length error of the leg was calculated.Taking the accurate leg length as an optimization objective,the position and pose of the moving platform were achieved by using optimization method and their errors were analysed.According to tool position in the coordinate system of the moving platform,the error of machining position was calculated,and its effect on the accuracy of machined parts was discussed.The results show that the tool position error is caused by leg length error,which produces the errors of form,position and dimension of machined parts.The rotor eccentricity of the parallel machine tool may cause disturbances on leg length and tool position,which will effect the surface roughness of machined parts.
引文
[1]单鹏,谢里阳,田万禄,等.基于D-H矩阵的Stewart型并联机床位姿误差计算模型[J],机械工程学报,2010,46(9):186-191.SHAN Peng,XIE Li-yang,TIAN Wan-lu,et al.Modeling ofposition and pose error of Stewart machine tool based on D-Htransforming matrix[J],Chinese Journal of MechanicalEngineering,2010,46(9):186-191.
[2]高猛,李铁民,郑浩峻,等.并联机床铰链制造误差的补偿[J].清华大学学报(自然科学版),2003,43(5):617-620.GAO Meng,LI Tie-min,ZHENG Hao-jun,et al.Compensation for joint manufacturing errors in parallelkinematic machines[J].J T singhua Univ(Sci&Tech),2003,43(5):617-620.
[3]汪劲松,白杰文,高猛,等.Stewart平台铰链间隙的精度分析[J].清华大学学报(自然科学版),2002,42(6):758-761.WANG Jin-song,BAI Jie-wen,GAO Meng,et al.Accuracyanalysis of joint-clearances in a Stewart platform[J].J Tsinghua Univ(Sci&Tech),2002,42(6):758-761.
[4]Ropponen T,Arai T.Accuracy analysis of a modified Stewartplatform manipulator[C]//Proceedings of 1995 IEEEInternational Conference on Robotics and Automation,May 22-27,1995,Nagoya,Aichi,Japan.New York:IEEE,1995:521-525.
[5]Patel A J,Ehmann K F.Volumetric error analysis of aStewart platform-based machine tool[J].Annals of theCIRP,1997,46(1):287-290.
[6]李铁民,郑浩峻,汪劲松.并联机床不同位形下的运动精度评价指标[J].机械工程学报,2002,38(9):101-105.LI Tie-min,ZHENG Hao-jun,WANG Jin-song.Precisionmeasures for various configurations of parallel kinematicmachine tools[J].Chinese Journal of MechanicalEngineering,2002,38(9):101-105.
[7]胡明,田文元,蔡光起.并联机床驱动杆铰链位置误差分析[J].东北大学学报(自然科学版),2007,28(3):389-392.HU Ming,TIAN Wen-yuan,CAI Guang-qi.Position erroranalysis of drive rod hinges on a kind of 3-DOF parallelmachine tools[J].Journal of Northeastern University(NaturalScience),2007,28(3):389-392.
[8]姜虹,蔡永琳,王小椿.一种并联机构结构误差识别与修正的新算法[J].北京交通大学学报,2007,31(1):46-49.JIANG Hong,CAI Yong-lin,WANG Xiao-chun.A new kindof algorithm on parallel mechanism structural errors detectionand modification[J].Journal of Beijing Jiaotong University,2007,31(1):46-49.
[9]吴海兵,刘远伟,左敦稳.交叉式并联机床工作空间分析[J].机械科学与技术,2009,28(4):472-475.WU Hai-bing,LIU Yuan-wei,ZUO Dun-wen.Workspaceanalysis of a cross-legged parallel Machine tool[J].Mechanical Science and Technology for AerospaceEngineering,2009,28(4):472-475.
[10]郭祖华,陈五一,陈鼎昌.6-UPS型并联机构的刚体动力学模型[J].机械工程学报,2002,38(11):53-57.GUO Zu-hua,CHEN Wu-yi,CHEN Ding-chang.Dynamicsmodel on the 6-UPS parallel machanism[J].ChineseJournal of Mechanical Engineering,2002,38(11):53-57.
[11]舒强,施宁平,饶学军,等.一种新型并联XYY微定位平台动力学建模及控制仿真[J].振动与冲击,2012,31(8):130-135,147.SHU Qiang,SHI Ning-ping,Rao Xue-jun,et al.Dynamicmodeling and control simulation for a novel parallel XYYmicro positioner[J].Journal of Vibration and Shock,2012,31(8):130-135,147.
[12]刘鸿文.材料力学(上册)[M].北京:人民教育出版社,1979:41-43.
[2]高猛,李铁民,郑浩峻,等.并联机床铰链制造误差的补偿[J].清华大学学报(自然科学版),2003,43(5):617-620.GAO Meng,LI Tie-min,ZHENG Hao-jun,et al.Compensation for joint manufacturing errors in parallelkinematic machines[J].J T singhua Univ(Sci&Tech),2003,43(5):617-620.
[3]汪劲松,白杰文,高猛,等.Stewart平台铰链间隙的精度分析[J].清华大学学报(自然科学版),2002,42(6):758-761.WANG Jin-song,BAI Jie-wen,GAO Meng,et al.Accuracyanalysis of joint-clearances in a Stewart platform[J].J Tsinghua Univ(Sci&Tech),2002,42(6):758-761.
[4]Ropponen T,Arai T.Accuracy analysis of a modified Stewartplatform manipulator[C]//Proceedings of 1995 IEEEInternational Conference on Robotics and Automation,May 22-27,1995,Nagoya,Aichi,Japan.New York:IEEE,1995:521-525.
[5]Patel A J,Ehmann K F.Volumetric error analysis of aStewart platform-based machine tool[J].Annals of theCIRP,1997,46(1):287-290.
[6]李铁民,郑浩峻,汪劲松.并联机床不同位形下的运动精度评价指标[J].机械工程学报,2002,38(9):101-105.LI Tie-min,ZHENG Hao-jun,WANG Jin-song.Precisionmeasures for various configurations of parallel kinematicmachine tools[J].Chinese Journal of MechanicalEngineering,2002,38(9):101-105.
[7]胡明,田文元,蔡光起.并联机床驱动杆铰链位置误差分析[J].东北大学学报(自然科学版),2007,28(3):389-392.HU Ming,TIAN Wen-yuan,CAI Guang-qi.Position erroranalysis of drive rod hinges on a kind of 3-DOF parallelmachine tools[J].Journal of Northeastern University(NaturalScience),2007,28(3):389-392.
[8]姜虹,蔡永琳,王小椿.一种并联机构结构误差识别与修正的新算法[J].北京交通大学学报,2007,31(1):46-49.JIANG Hong,CAI Yong-lin,WANG Xiao-chun.A new kindof algorithm on parallel mechanism structural errors detectionand modification[J].Journal of Beijing Jiaotong University,2007,31(1):46-49.
[9]吴海兵,刘远伟,左敦稳.交叉式并联机床工作空间分析[J].机械科学与技术,2009,28(4):472-475.WU Hai-bing,LIU Yuan-wei,ZUO Dun-wen.Workspaceanalysis of a cross-legged parallel Machine tool[J].Mechanical Science and Technology for AerospaceEngineering,2009,28(4):472-475.
[10]郭祖华,陈五一,陈鼎昌.6-UPS型并联机构的刚体动力学模型[J].机械工程学报,2002,38(11):53-57.GUO Zu-hua,CHEN Wu-yi,CHEN Ding-chang.Dynamicsmodel on the 6-UPS parallel machanism[J].ChineseJournal of Mechanical Engineering,2002,38(11):53-57.
[11]舒强,施宁平,饶学军,等.一种新型并联XYY微定位平台动力学建模及控制仿真[J].振动与冲击,2012,31(8):130-135,147.SHU Qiang,SHI Ning-ping,Rao Xue-jun,et al.Dynamicmodeling and control simulation for a novel parallel XYYmicro positioner[J].Journal of Vibration and Shock,2012,31(8):130-135,147.
[12]刘鸿文.材料力学(上册)[M].北京:人民教育出版社,1979:41-43.