基于径向基函数法的五轴数控机床空间动态性能研究
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摘要
在对数控机床进行动态性能分析时,局限于某一固定位姿获取的动态特性信息不足以描述整个加工空间内的机床动态特性。针对这一问题,提出一种基于径向基函数理论的五轴数控机床空间动态特性分析方法,利用机床实测试验数据和径向基函数法来构建五轴联动数控机床的空间动态特性函数模型。该方法以机床固有频率这一关键动力学性能指标为例,建立机床整机动态特性与机床位姿之间的数学关系。以一五轴数控机床为研究对象,将试验设计方案确定的各联动轴的坐标作为试验样本点,采用德国M+P振动试验设备提取样本点的试验数据,构建反映机床空间位姿与机床前6阶固有频率关系的函数表达式,并通过计算模型质量评价指标验证该模型的有效性。结果表明,该方法能有效预测在加工空间内固有频率的分布规律及其各轴向位移变化的灵敏度,为合理规划工艺路线提高加工精度提供技术支持。
Dynamic performance analysis of NC machine tools is limited to the dynamic characteristics of a fixed position. Thus, a method to research five-axis linkage machine tool's dynamic characteristics in the generalized machining space is proposed based on the machine tools measured test data and the radial basis function method. In this method, the natural frequency is taken as the critical index to describe the whole machine tool dynamic characteristics, with which the mathe-matic relationship between dynamic characteristics and spatial poses are analyzed. The proposed method is applied in a five-axis machining center to verify its feasibility.The various pose combinations of the moving parts are arranged as the samples by the Hierarchical Latin hypercube experiment design, and the first six orders natural frequencies are acquired by machine tool test with the M+P system, a mathmatic function model is established to describe the connections between the pose features and the natural frequencies. And the accuracy of the established model is validated after calculating the valuating indexes. Results show that the method could effectively predict the machining space distribution law of the natural frequency and the axial displacement change sensitivity, providing a theoretical support for the process planning and dynamic optimization of the machine tool.
Dynamic performance analysis of NC machine tools is limited to the dynamic characteristics of a fixed position. Thus, a method to research five-axis linkage machine tool's dynamic characteristics in the generalized machining space is proposed based on the machine tools measured test data and the radial basis function method. In this method, the natural frequency is taken as the critical index to describe the whole machine tool dynamic characteristics, with which the mathe-matic relationship between dynamic characteristics and spatial poses are analyzed. The proposed method is applied in a five-axis machining center to verify its feasibility.The various pose combinations of the moving parts are arranged as the samples by the Hierarchical Latin hypercube experiment design, and the first six orders natural frequencies are acquired by machine tool test with the M+P system, a mathmatic function model is established to describe the connections between the pose features and the natural frequencies. And the accuracy of the established model is validated after calculating the valuating indexes. Results show that the method could effectively predict the machining space distribution law of the natural frequency and the axial displacement change sensitivity, providing a theoretical support for the process planning and dynamic optimization of the machine tool.
引文
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[2]TOH C K.Vibration analysis in high speed rough and finish milling hardened steel[J].Journal of Sound and Vibration,2004,278(1-2):101-115.
[3]Al TINTAS Y,BRECHER C,WECK M,et al.Virtual machine tool[J].CIRP Annals-Manufacturing Technology,2005,54(2):115-138.
[4]YIGIT A S,ULOSY A G.Dynamic stiffness evaluation for reconfigurable machine tools including weakly non-linear joint characteristics[J].Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture,2002,2016(1):87-101.
[5]ZAGHBAN I,SONGMENE V.Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis[J].International Journal of Machine Tools&Manufacture,2009,49(12):947-957.
[6]LAW M,ALTINTAS Y,SRIKANTHA P A.Rapid evaluation and optimization of machine tools with position dependent stability[J].International Journal of Machine Tools&Manufacture,2013,68(3):81-90.
[7]刘海涛,赵万华.基于广义加工空间概念的机床动态特性分析[J].机械工程学报,2010,46(21):54-60.LIU Haitao,ZHAO Wanghua.Dynamic characteristic analysis for machine tools based on concept of generalized manufacturing space[J].Journal of Mechanical Engineering,2010,46(21):54-60.
[8]孙明楠,殷国富,胡腾,等.基于广义动态信息模型的机床结合部动刚度参与因子辨识方法[J].机械工程学报,2013,49(11):61-69.SUN Mingnan,YIN Guofu,HU Teng,et al.Method of dynamic stiffness participation factors identification of machine tool joints based on the generalized dynamic information model[J].Journal of Mechanical Engineering,2013,49(11):61-69.
[9]邓聪颖,刘蕴,殷国富,等.基于响应面方法的数控机床空间动态特性研究[J].工程科学与技术,2017,49(4):211-218.DENG Congying,LIU Yun,YIN Guofu,et al.Research on machine tool spatial dynamic characteristics based on response surface method[J].Advanced Engineering Sciences,2017,49(4):211-218.
[10]WU Jun,WANG Jinsong,WANG Liping,et al.Study on the stiffness of a 5-DOF hybrid machine tool with actuation redundancy[J].Mechanism and Machine Theory,2009,44(2):289-305.
[11]李天箭,丁晓红,程凯.基于空间统计学的机床动力学特性[J].机械工程学报,2015,51(21):87-94.LI Tianjian,DING Xiaohong,CHENG Kai.Machine tool dynamics based on spatial statistics[J].Journal of Mechanical Engineering,2015,51(21):87-94.
[12]董冠华,殷勤,殷国富,等.基于模态分析理论的结合部动刚度辨识[J].振动与冲击,2017(36):125-131.DONG Guanhua,YIN Qin,YIN Guofu.et al.A study on the identification of joints dynamic stiffness based on modal analysis[J].Journal of Vibration and Shock,2017(36):125-131.
[13]隋云康,宇慧平.响应面方法的改进及其对工程优化的应用[M].北京:科学出版社,2011.SUI Yunkang,YU Huiping.Modification of response surface method and its application on engineering optimization[M].Beijing:Science Press,2011.
[14]于志玲,张阳.最佳一致逼近理论中哈尔(Haar)条件的等价定义[J].南开大学学报,2006,39(3):101-103.YU Zhiling,ZHANG Yang.The equivalent definition of Haar in the theory of optimal consensus approximation[J].Journal of Nankai University,2006,39(3):101-103.
[15]FANG H B,HORSTEMEYER M F.Global response approximation with radial basis functions[J].Engineering Optimization,2006,38(4):407-424.
[16]WU Z M.Generalized bochner’s theorem for radial function[J].Approximation Theory and Its Application,1997,13:47-57
[17]李云雁,胡传荣.试验设计与数据处理[M].北京:化学工业出版社,2005.LI Yunyan,HU Chuanrong.Experimental design and data processing[M].Beijing:Chemical Industry Press,2005.
[18]吴振君,王水林,葛修润.LHS方法在边坡可靠度分析中的应用[J].岩土力学,2010,31(4):1047-1053.WU Zhenjun,WANG Shuilin,GE Xiurun.Application of LHS method in slope reliability analysis[J].Geotechnical Mechanics,2010,31(4):1047-1053.