可重构三轴机床几何误差敏感性变化规律预测
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摘要
机床的几何误差敏感源辨识是对机床精准设计的一项重要挑战,特别是其运动轴间的位姿关系在机床重构后会改变,如何快速地鉴别机床重构后的空间误差敏感项对后续加工有较大影响。本文以可重构三轴机床为研究对象,采用齐次坐标变换矩阵方法,提出了基于模块化误差矩阵的综合空间误差模型快速重建方法。运用矩阵微分求得各几何误差的敏感性系数,分析不同的三轴机床结构与敏感误差源变化规律的映射关系,对不同配置的机床进行敏感性规律验证。结果表明:机床在不同的重构配置下均符合该变化规律,有利于可重构机床的设计和加工精度的提高。
The geometric error sensitive source identification of machine tools is an important challenge to the precise design of machine tools, as the position and orientation relations between the motion axes would be changed after the machine reconfiguration. How to quickly identify the space error sensitive items after machine reconfiguration has great influence on the subsequent machining. A comprehensive spatial error model for rapid reconstruction based on modular error matrix was proposed for reconfigurable three axis machine tool with the use of homogeneous coordinate transformation matrix to the reconfigurable characteristics of reconfigurable machine tools. The sensitivity coefficients of various geometric errors were obtained by matrix differentiation. The mapping relationship between the different three axis machine tool structures and the sensitive error source was analyzed, and the sensitivity rules of different configurations of machine tool were verified. Results showed that the machine tool met the change rule under different reconfigurations, which was beneficial to the design of reconfigurable machine tool and the improvement of machining precision.
The geometric error sensitive source identification of machine tools is an important challenge to the precise design of machine tools, as the position and orientation relations between the motion axes would be changed after the machine reconfiguration. How to quickly identify the space error sensitive items after machine reconfiguration has great influence on the subsequent machining. A comprehensive spatial error model for rapid reconstruction based on modular error matrix was proposed for reconfigurable three axis machine tool with the use of homogeneous coordinate transformation matrix to the reconfigurable characteristics of reconfigurable machine tools. The sensitivity coefficients of various geometric errors were obtained by matrix differentiation. The mapping relationship between the different three axis machine tool structures and the sensitive error source was analyzed, and the sensitivity rules of different configurations of machine tool were verified. Results showed that the machine tool met the change rule under different reconfigurations, which was beneficial to the design of reconfigurable machine tool and the improvement of machining precision.
引文
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[2] BI Zhiming,LANG S Y T,VERNER M,et al.Development of reconfigurable machines[J].International Journal of Advanced Manufacturing Technology,2008,39(11/12):1224.
[3] SCHMIDT K W.A computation of supervisors for reconfigurable machine tools[J].Discrete Event Dynamic Systems,2015,25(1):125.
[4] XIE Nan,LI Aiping,XUE Wei.Cooperative optimization of reconfigurable machine tool configurations and production plan[J].Chinese Journal of Mechanical Engineering,2012,25(5):982.
[5] 曾法力,李爱平,谢楠,等.基于图重写规则的可重构机床配置规划[J].计算机集成制造系统,2011,17(8):1766.
[6] SHEN H Y,FU J Z,HE Yong,et al.On-line asynchronous compensation methods for static/quasi-static error implemented on CNC machine tools[J].International Journal of Machine Tools & Manufacture,2012,60(1):14.
[7] 程强,刘广博,刘志峰,等.基于敏感度分析的机床关键性几何误差源识别方法[J].机械工程学报,2012,48(7):171.
[8] LEETE D L.Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes[J].International Journal of Machine Tool Design and Research,1961,1(4):293.
[9] SCHULTSCHIK R.The components of volumetric accuracy[J].CIRP Annals(Manufacturing Technology),2014,228(17):3141.
[10] RICO J M,GALLARDO J,DUFFY J.Screw theory and higher order kinematic nanlysis of open serial and closed chains[J].Mechanism & Machine Theory,1999,34(4):559.
[11] OKAFOR A C,ERTEKIN Y M.Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics[J].International Journal of Machine Tools & Manufacture,2000,48(8):1199.
[12] KONG L B,CHEUNG C F,TO S,et al.A kinematics and experimental analysis of form error compensation in ultra-precision machining[J].International Journal of Machine Tools & Manufacture,2008,48(12):1408.
[13] GIRI D,MOON Y M.Error modeling in a reconfigurable machine tool[C]//ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.[S.l.]:ASME,2005∶1001.
[14] TIAN W J,GAO W G,ZHANG D W,et al.A general approach for error modeling of machine tools [J].International Journal of Machine Tools & Manufacture,2014,228(17):3141.
[15] 赵强强,洪军,刘志刚,等.任意拓扑结构机床运动轴误差传递链建模方法[J].机械工程学报,2016,52(21):130.
[16] CHENG Q,ZHAO H W,ZHANG G J,et al.An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis[J].International Journal of Advanced Manufacturing Technology,2014,75(1/2/3/4):107.
[17] LI J,XIE F G,LIU X J.Geometric error modeling and sensitivity analysis of a five-axis machine tool[J].International Journal of Advanced Manufacturing Technology,2015,7(5):1.
[18] 时修丽,黄筱调,袁鸿,等.多因素影响下的大重型数控转台的传动精度分析[J].计算机集成制造系统,2014,20(1):148.
[19] 郭世杰,梅雪松,姜歌东,等.数控机床几何误差相关性分析方法研究[J].农业机械学报,2016,47(10):383.