专用凸轮数控加工技术研究
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摘要
随着各种先进制造技术的普及应用,新材料新工艺的发展,凸轮的设计与制造将会变得十分方便和精确,制造成本也会大幅下降,尤其是随着计算机的发展,凸轮机构的计算机辅助设计和制造已获得普遍地应用,从而提高了凸轮设计和加工的速度及质量,这也为凸轮机构的更广泛应用创造了条件,更好地促进自动机械的发展。
通过分析凸轮轮廓曲线的特征,本文提出了极坐标数控的凸轮加工方案,即通过控制旋转运动和直线运动,实现在极坐标下,对凸轮的数控加工。在极坐标下,利用极角与极径的关系,更容易设计理想的凸轮轮廓曲线,此方案避免了凸轮曲线方程从极坐标向直角坐标的转化,控制一旋转运动与一直线运动,插补出凸轮轮廓曲线。插补的算法采用数据采样插补,即在一个插补周期内,判断各轴的运动方向,计算出各轴的运动增量。另外还对插补误差进行了研究,并给出了插补误差控制方法,使其每一步插补均能满足精度要求。
本课题的控制系统设计,采用上位机(PC机)与下位机(PLC)相结合的方式。利用PC机强大的软硬件功能,实现对凸轮轮廓曲线的插补算法计算,求出满足精度要求的节点坐标、插补步长,并把这些信息传送给PLC,由PLC驱动伺服电机插补运动,完成加工。由于加工过程中,需要联动控制,因此,选择FM357作为定位模块,最多能同时控制四轴运动,满足控制系统的要求。
最后,本文根据凸轮轮廓曲线常用的运动规律,对各种运动规律的方程进行适当的修正,使其能根据设计的需要平滑过渡,并编写了凸轮轮廓曲线生成程序,利用MATLAB的绘图功能,生成所设计的凸轮轮廓曲线模型。有了凸轮轮廓曲线的数学模型,再利用MATLAB算法开发与强大的数学计算能力,即可进行凸轮轮廓曲线的插补算法仿真。通过编写插补程序,实时的插补误差控制,并利用MATLAB实时绘图功能,实现了凸轮轮廓曲线的动态仿真,证实了算法的可行性,最后对插补结果进行分析,验证了算法的正确性。另外,选用VB进行PC机应用软件的开发,编制了插补仿真界面,编写了VB与MATLAB接口程序,以及VB与PLC通信的程序。
With the development of new materials and new process, all kinds of advanced manufacture technology have been applied widely, so cam design and manufacture will be verily convenient and precise, and cam production cost will also be reduced. Especially, with the development of computer, Computer-Aided design and Computer-aided Manufacture are applied to cam mechanism, as a result, computer technique improve the quality and speed of cam design and manufacture, that creates good conditions for cam mechanism’s widespread use, then promote automatic mechanism’s development preferably.
By analyzing the feature of cam’s contour line, this paper proposes a machining solution of cam, and reasizes digital control processing about cam in Polar Coordinate by controling rotary motion and linear motion. It is easy to design cam’s contour line by utilizing angle and radius in Polar Coordinate. This plan avoids the conversion of Polar Coordinate and Rectangular Coordinate,and interpolates cam’s contour line by control rotary motion and linear motion. The algorithm of interpolation is data sampling interpolation, which judges axial direction and calculates axial incremental motion. Moreover, this paper also analyses the error of interpolation, and gives methods to control the error of interpolation, so makes every step interpolation always meat accuracy requirement.
This paper designs control system too, which adopts combine mode of upper computer and lower computer. It makes use of PC’s powerful software and hardware function, to calculate interpolation of cam’s contour line, then obtains coordinates of nodal point and interpolation step size and so on,and conveys the information to PLC. Lastly, PLC controls actuating motor to move until finish machining. Because of coordinated control in the course of machining, this paper chooses FM357 as the positioning module, which controls four axis at the same time, so it meats system need.
Finally, this paper amends equations of every law of motion becomingly, according to usual law of motion of cam outline curve, in order to meet the need of smooth transition, and writes generator programs of cam outline curve, then generates designed cam outline curve model, by using drawing function of MATLAB. Once having mathematical models of cam outline curve, then MATLAB can simulate the interpolation algorithm of cam outline curve, by using algorithm develop and math calculate capability of MATLAB. This paper compiles interpolation procedures, and controls real-time interpolation errors, then realizes dynamic simulation of cam’s contour line by using drawing function of MATLAB, and confirms feasibility of interpolation algorithm, besides, this paper also checkes validity of interpolation algorithm, by analyzing the interpolation results. In addition, this paper chooses VB to develop application software for PC, and designs interface of interpolation simulation, and compiles interface program of VB and MATLAB, as well as VB and PLC.
通过分析凸轮轮廓曲线的特征,本文提出了极坐标数控的凸轮加工方案,即通过控制旋转运动和直线运动,实现在极坐标下,对凸轮的数控加工。在极坐标下,利用极角与极径的关系,更容易设计理想的凸轮轮廓曲线,此方案避免了凸轮曲线方程从极坐标向直角坐标的转化,控制一旋转运动与一直线运动,插补出凸轮轮廓曲线。插补的算法采用数据采样插补,即在一个插补周期内,判断各轴的运动方向,计算出各轴的运动增量。另外还对插补误差进行了研究,并给出了插补误差控制方法,使其每一步插补均能满足精度要求。
本课题的控制系统设计,采用上位机(PC机)与下位机(PLC)相结合的方式。利用PC机强大的软硬件功能,实现对凸轮轮廓曲线的插补算法计算,求出满足精度要求的节点坐标、插补步长,并把这些信息传送给PLC,由PLC驱动伺服电机插补运动,完成加工。由于加工过程中,需要联动控制,因此,选择FM357作为定位模块,最多能同时控制四轴运动,满足控制系统的要求。
最后,本文根据凸轮轮廓曲线常用的运动规律,对各种运动规律的方程进行适当的修正,使其能根据设计的需要平滑过渡,并编写了凸轮轮廓曲线生成程序,利用MATLAB的绘图功能,生成所设计的凸轮轮廓曲线模型。有了凸轮轮廓曲线的数学模型,再利用MATLAB算法开发与强大的数学计算能力,即可进行凸轮轮廓曲线的插补算法仿真。通过编写插补程序,实时的插补误差控制,并利用MATLAB实时绘图功能,实现了凸轮轮廓曲线的动态仿真,证实了算法的可行性,最后对插补结果进行分析,验证了算法的正确性。另外,选用VB进行PC机应用软件的开发,编制了插补仿真界面,编写了VB与MATLAB接口程序,以及VB与PLC通信的程序。
With the development of new materials and new process, all kinds of advanced manufacture technology have been applied widely, so cam design and manufacture will be verily convenient and precise, and cam production cost will also be reduced. Especially, with the development of computer, Computer-Aided design and Computer-aided Manufacture are applied to cam mechanism, as a result, computer technique improve the quality and speed of cam design and manufacture, that creates good conditions for cam mechanism’s widespread use, then promote automatic mechanism’s development preferably.
By analyzing the feature of cam’s contour line, this paper proposes a machining solution of cam, and reasizes digital control processing about cam in Polar Coordinate by controling rotary motion and linear motion. It is easy to design cam’s contour line by utilizing angle and radius in Polar Coordinate. This plan avoids the conversion of Polar Coordinate and Rectangular Coordinate,and interpolates cam’s contour line by control rotary motion and linear motion. The algorithm of interpolation is data sampling interpolation, which judges axial direction and calculates axial incremental motion. Moreover, this paper also analyses the error of interpolation, and gives methods to control the error of interpolation, so makes every step interpolation always meat accuracy requirement.
This paper designs control system too, which adopts combine mode of upper computer and lower computer. It makes use of PC’s powerful software and hardware function, to calculate interpolation of cam’s contour line, then obtains coordinates of nodal point and interpolation step size and so on,and conveys the information to PLC. Lastly, PLC controls actuating motor to move until finish machining. Because of coordinated control in the course of machining, this paper chooses FM357 as the positioning module, which controls four axis at the same time, so it meats system need.
Finally, this paper amends equations of every law of motion becomingly, according to usual law of motion of cam outline curve, in order to meet the need of smooth transition, and writes generator programs of cam outline curve, then generates designed cam outline curve model, by using drawing function of MATLAB. Once having mathematical models of cam outline curve, then MATLAB can simulate the interpolation algorithm of cam outline curve, by using algorithm develop and math calculate capability of MATLAB. This paper compiles interpolation procedures, and controls real-time interpolation errors, then realizes dynamic simulation of cam’s contour line by using drawing function of MATLAB, and confirms feasibility of interpolation algorithm, besides, this paper also checkes validity of interpolation algorithm, by analyzing the interpolation results. In addition, this paper chooses VB to develop application software for PC, and designs interface of interpolation simulation, and compiles interface program of VB and MATLAB, as well as VB and PLC.
引文
[1]彭国勋,肖正扬.自动机械的凸轮机构设计[M].北京:机械工业出版社,1990:30-80.
[2]尚汗冀.内燃机配气凸轮机构的设计与计算[M].上海:复旦大学出版社,1988:95-150.
[3]葛正浩,冯涛.可以任意增加局部控制条件的凸轮机构通用多项式运动规律[J].机械科学与技术,1998,17(6):986-987.
[4]K.Yoon, S.Rao. Cam motion synthesis using cubic splines. Trans.ASME.J.Of Mech.Des, 1993,115(9):21-25.
[5]申永胜.机械原理基础教程[M].北京:清华大学出版社,1999:80-107.
[6]孙恒,傅则绍.机械原理[M].北京:高等教育出版社,1989:338-367.
[7]叶仲和.用瞬心法求滚子摆动从动件圆柱凸轮机构压力角和最小平均圆柱半径[J].机械科学与技术,1996,(2):191-194.
[8]吴炎辉,李刚炎,杨明忠.凸轮轮廓设计的速度瞬心法[J].机械科学与技术,1998,(3):397-398.
[9]Shin J H, Lee C M,Kim J S. Shape design of disk cam mechanisms using instant velocity centers. In: Proceedings of 6th international Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 1996:178-186.
[10]Fan Y Chen. Mechanics and Design of Cam Mechanisms. New York. Pergamon Press Inc,1992:45-51.
[11]D.Tsay, M.Wei. A general approach to determination of planar and spatial cam profiles ASME Journal of Mechanical Design, 1996,118(1):259-265.
[12]何有钧,邹慧君,郭为忠.圆柱滚子从动件凸轮廓面得等距曲面设计方法[J].上海交通大学学报,2000,(10):1336-1337.
[13]赵韩,丁爵曾,梁锦华.凸轮机构设计[M] .北京:高等教育出版社, 1993.12, 4-6.
[14]Chen,F.Y. Mechanics and Design of Cam Mechanisms, PergamonPiess Inc.Newyork,1982:36-43.
[15]Jensen,P.W. Cam Design and Manufacture. Marcel Dekker Inc,1987:58-72.
[16]牧野洋.凸轮自动设计[M].日本机械学会社,第84卷750号.
[17]中国机械工程学会机械传动专业学会机构专业委员会,全国第六届机构学术讨论会《论文摘要》,1988.
[18]张玉峰.基于UG的盘形凸轮参数化建模技术研究与实现[J].工具技术,2009 43(11):72-74.
[19]徐森亮.盘形凸轮轮廓曲线的参数化设计[J],现代机械,2009(2):8-10.
[20]韩利芬,马秋成.基于UG平台摆动推杆盘形凸轮的实体建模[J].机械设计与研究,2003 19(2):25-26.
[21]王文刚.基于Pro/E盘形凸轮精确参数化建模及运动仿真[J].机械与电子,2009(9):70-74.
[22]孙桓,陈作模.机械原理[M].北京:高等教育出版社,2004:248-252.
[23]管荣法.凸轮与凸轮机构[M].北京:国防工业出版社,1993:15-17.
[24]赵国文,安承业.凸轮几何学[M].北京:机械工业出版社,1989:33-36.
[25]郁增才,赵国文.用啮合线设计盘形凸轮实际廓线的解析法[J].机械设计与制造,1986(6):14-15.
[26]Fan Yichen . Mechanics and Design of Cam Mechanisms . Pergramon Press Inc , 1982:58-63.
[27]廖常初.PLC应用技术问答[M].北京,机械工业出版社,2006:78-82.
[28]魏焕兵.基于PLC的数控磨沟机的研制[D].硕士学位论文,南京,南京航空航天大学,2006:5-6.
[29]Schickhuber.Mccarthy Distributed Fieldbus and Control Network System [J].Computing & Control Engineering Journal , 1997 , 8 (1):98-103.
[30]贾德胜.PLC应用开发实用子程序[M].北京:人民邮电出版社,2006:2-4.
[31]刘美俊.西门子S7系列PLC的应用于维护[M].北京:机械工业出版社,2009:1-3.
[32]赵韩,丁爵曾.凸轮机构设计[M].北京:高等教育出版社,1993 :9-22.
[33]Wang Yun Ju Ping. A simple method to calculate cam profile for the disc cam with offset, China International Symposium on Machine Elements, 1996:52-55.
[34]李恩林.插补原理[M].北京:机械工业出版社,1984:15-18.
[35]李恩林.数控系统插补原理通论[M].北京:国防工业出版社,2008:1-5.
[36]金建新.机床CNC系统中任意空间曲线的可控步长插补方法[J].机械工程学报,2000.36(4):95-97.
[37]廖效果,朱启逑.数字控制机床[M].武汉:华中科技大学出版社,2005:87-89.
[38]吴中俊,黄永红.可编程序控制器原理及应用[M].机械工业出版社,2009:32-33.
[39]龚仲华.S7-200/300/400 PLC应用技术-通用篇[M].北京:人民邮电出版社,2007:120-180.
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[41]Tarek Sobh, Khaled Elleithy.A Simplified and Systematic Technique to Develop and Implement PLC Program for a Control Process Springer Advances in Systems.Computing Sciences and Software Engineering, 2007 (9): 171-178 .
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[2]尚汗冀.内燃机配气凸轮机构的设计与计算[M].上海:复旦大学出版社,1988:95-150.
[3]葛正浩,冯涛.可以任意增加局部控制条件的凸轮机构通用多项式运动规律[J].机械科学与技术,1998,17(6):986-987.
[4]K.Yoon, S.Rao. Cam motion synthesis using cubic splines. Trans.ASME.J.Of Mech.Des, 1993,115(9):21-25.
[5]申永胜.机械原理基础教程[M].北京:清华大学出版社,1999:80-107.
[6]孙恒,傅则绍.机械原理[M].北京:高等教育出版社,1989:338-367.
[7]叶仲和.用瞬心法求滚子摆动从动件圆柱凸轮机构压力角和最小平均圆柱半径[J].机械科学与技术,1996,(2):191-194.
[8]吴炎辉,李刚炎,杨明忠.凸轮轮廓设计的速度瞬心法[J].机械科学与技术,1998,(3):397-398.
[9]Shin J H, Lee C M,Kim J S. Shape design of disk cam mechanisms using instant velocity centers. In: Proceedings of 6th international Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 1996:178-186.
[10]Fan Y Chen. Mechanics and Design of Cam Mechanisms. New York. Pergamon Press Inc,1992:45-51.
[11]D.Tsay, M.Wei. A general approach to determination of planar and spatial cam profiles ASME Journal of Mechanical Design, 1996,118(1):259-265.
[12]何有钧,邹慧君,郭为忠.圆柱滚子从动件凸轮廓面得等距曲面设计方法[J].上海交通大学学报,2000,(10):1336-1337.
[13]赵韩,丁爵曾,梁锦华.凸轮机构设计[M] .北京:高等教育出版社, 1993.12, 4-6.
[14]Chen,F.Y. Mechanics and Design of Cam Mechanisms, PergamonPiess Inc.Newyork,1982:36-43.
[15]Jensen,P.W. Cam Design and Manufacture. Marcel Dekker Inc,1987:58-72.
[16]牧野洋.凸轮自动设计[M].日本机械学会社,第84卷750号.
[17]中国机械工程学会机械传动专业学会机构专业委员会,全国第六届机构学术讨论会《论文摘要》,1988.
[18]张玉峰.基于UG的盘形凸轮参数化建模技术研究与实现[J].工具技术,2009 43(11):72-74.
[19]徐森亮.盘形凸轮轮廓曲线的参数化设计[J],现代机械,2009(2):8-10.
[20]韩利芬,马秋成.基于UG平台摆动推杆盘形凸轮的实体建模[J].机械设计与研究,2003 19(2):25-26.
[21]王文刚.基于Pro/E盘形凸轮精确参数化建模及运动仿真[J].机械与电子,2009(9):70-74.
[22]孙桓,陈作模.机械原理[M].北京:高等教育出版社,2004:248-252.
[23]管荣法.凸轮与凸轮机构[M].北京:国防工业出版社,1993:15-17.
[24]赵国文,安承业.凸轮几何学[M].北京:机械工业出版社,1989:33-36.
[25]郁增才,赵国文.用啮合线设计盘形凸轮实际廓线的解析法[J].机械设计与制造,1986(6):14-15.
[26]Fan Yichen . Mechanics and Design of Cam Mechanisms . Pergramon Press Inc , 1982:58-63.
[27]廖常初.PLC应用技术问答[M].北京,机械工业出版社,2006:78-82.
[28]魏焕兵.基于PLC的数控磨沟机的研制[D].硕士学位论文,南京,南京航空航天大学,2006:5-6.
[29]Schickhuber.Mccarthy Distributed Fieldbus and Control Network System [J].Computing & Control Engineering Journal , 1997 , 8 (1):98-103.
[30]贾德胜.PLC应用开发实用子程序[M].北京:人民邮电出版社,2006:2-4.
[31]刘美俊.西门子S7系列PLC的应用于维护[M].北京:机械工业出版社,2009:1-3.
[32]赵韩,丁爵曾.凸轮机构设计[M].北京:高等教育出版社,1993 :9-22.
[33]Wang Yun Ju Ping. A simple method to calculate cam profile for the disc cam with offset, China International Symposium on Machine Elements, 1996:52-55.
[34]李恩林.插补原理[M].北京:机械工业出版社,1984:15-18.
[35]李恩林.数控系统插补原理通论[M].北京:国防工业出版社,2008:1-5.
[36]金建新.机床CNC系统中任意空间曲线的可控步长插补方法[J].机械工程学报,2000.36(4):95-97.
[37]廖效果,朱启逑.数字控制机床[M].武汉:华中科技大学出版社,2005:87-89.
[38]吴中俊,黄永红.可编程序控制器原理及应用[M].机械工业出版社,2009:32-33.
[39]龚仲华.S7-200/300/400 PLC应用技术-通用篇[M].北京:人民邮电出版社,2007:120-180.
[40]龚仲华.S7-200/300/400 PLC应用技术-提高篇[M].北京:人民邮电出版社,2007:464-500.
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