基于空间统计学的机床动力学特性

doi:10.3901/JME.2015.21.087

摘要/Abstract

摘要：

机床刚度、固有频率等动力学特性随着机床部件位置、姿态在工作空间中的变化而变化。对机床动力学特性的研究不仅需要考虑到机床质量、刚度、阻尼值的大小，还应重视机床加工点的空间位置变化。采用空间统计学方法，以超精密机床固有频率这一关键动力学性能为例，分析机床动力学性能与机床位置姿态之间的数学关系，选取机床动态特性变异函数，建立动力学性能变化预测的Kriging方法模型，研究动力学特性在工作空间中的变化规律以及动力学特性空间信息的表述方法。将所建立的模型与正交多项式方法、径向基神经网络方法、二阶响应面方法等方法建立动力学性能预测分析模型比较，空间统计学Kriging方法所建立的模型R²检验大于0.96，在四种模型建构方式中为精确度最优，能够在完整工作空间中准确地描述机床动力学特性。基于空间统计学的机床动力学特性研究为机床的动力学设计提供了新的设计分析方法及相应的技术支持。

关键词: Kriging模型, 固有频率, 加工空间, 空间统计学, 机床动力学

Abstract:

The dynamic characteristics of machine tools, such as stiffness and natural frequency vary with the changing of position and posture of the machine components in working space. Not only the mass, stiffness, damping ratios should be considered during the research of the dynamic characteristics of machine tools, the spatial position change of machining point should also be paid more attention. Spatial statistical method is adopted, and the machine tool’s natural frequency is taken as the critical dynamic characteristic, thus the mathematical relation between the machine tool’s dynamic characteristics and its position and posture is analyzed. The machine tool’s dynamic performance variation function is selected, and the Kriging method model to predict dynamic characters is established, then the prediction of the changing rules of machine tool’s dynamic characteristics is realized. The established model is compared with the dynamic characteristics predication models established by using orthogonal polynomial method, the RBF neural network method and the second order response surface method, and result shows that the R-Squared value of the model using spatial statics Kriging method is 0.96, which is the optimum in the four models, thus it can accurately describe the machine tool’s dynamic characteristics in complete working space. The research of machine tools dynamics based on spatial statistics provides a new design and analyze method and technical support for the dynamic design of the ultra-precision machine tools.

Key words: Kriging model, manufacturing space, natural frequency, spatial statistics, machine tools dynamics

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.

参考文献

[1] ALTINTAS Y，BRECHER C，WECK M，et al. Virtual machine tool[J]. CIRP Keynote Paper，2005，54(2)：STCM.

[2] ZAEH M，SIEDL D. A new method for simulation of machining performance by integrating finite element and multi-body simulation for machine tools[J]. CIRP Annals- Manufacturing Technology，2007，56(1)：383-386.

[3] YANG Qingdong，LIU Guoqing，WANG Keshe. Dynamics analysis of special structure of milling-head machine tool[J]. Chinese Journal of Mechanical Engineering，2008，21(6)：103-107.

[4] CHANAL H，DUC E，RAY P. A study of the impact of machine tool structure on machining processes[J]. International Journal of Machine Tools and Manufacture，2006，46(2)：98-106.

[5] ZAGHBANI I，SONGMENE V. Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis[J]. International Journal of Machine Tools and Manufacture，2009，49(12-13)：947-957.

[6] 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.

[7] 刘海涛. 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. Dynamic characteristic analysis for machine tools based on concept of generalized manufacturing space[J]. Journal of Mechanical Engineering，2010，46(21)：54-60.

[8] CHENG Kai. Machine tool design[M]. London：Springer，2009.

[9] 闫蓉，陈威，彭芳瑜. 多轴加工系统闭链刚度场建模与刚度性能分析[J]. 机械工程学报，2012，48(1)：177-184. YAN Rong, CHEN Wei, PENG Fangyu. Closed-loop stiffness modeling and stiffness index analysis for multi-axis machining system[J]. Journal of Mechanical Engineering，2012，48(1)：177-184.

[10] WU Wenjing，LIU Qiang. Dynamics analysis of a parallel mill-turn tool spindle head driven by dual-linear motors using extended transfer matrix method[J]. Chinese Journal of Mechanical Engineering，2011，24(5)：859-869.

[11] GIUNTA A，WATSON L. A comparison of approximation modeling techniques：Polynomial vs. interpolating models[J]. AIAA，1998，1：392-404.

[12] LOPHAVEN S，NIELSEN H，SONDERGAARD J. DACE — a Matlab Kriging toolbox，informatics and mathematical modelling[J]. Experimental Methods for the Analysis of Optimization Algorithms，2010：337-362.

[13] GAO Yuehua，WANG Xicheng. An effective warpage optimization method in injection molding based on the Kriging model[J]. International Journal of Advanced Manufacture Technology，2008，37：953-960.

[14] HONG J，TALBOT D，KAHRAMAN A. Load distribution analysis of clearance-fit spline joints using finite elements[J]. Mechanism and Machine Theory，2014，74：42-57.

[15] BOSETTI P，FRANCESCO B，BORTOLUZZI D. Design，manufacturing，and performance verification of a Roberts linkage for inertial isolation[J]. Precision Engineering，2014，38(1)：138-147.

[16] PARK D，KOLIVAND M，KAHRAMAN A. An approximate method to predict surface wear of hypoid gears using surface interpolation[J]. Mechanism and Machine Theory，2014，71：64-78.

[17] DRAZUMERIC R，BADGER J，KRAJNIK P. Geometric，kinematical and thermal analyses of non-round cylindrical grinding[J]. Journal of Materials Processing Technology，2014，214(4)：818-827.

[18] 阳红. 基于热误差神经网络预测模型的机床重点热刚度辨识方法研究[J]. 机械工程学报，2011，47(11)：117-124. YANG Hong. Method of key thermal stiffness identification on a machine tool based on the thermal errors neural network prediction model[J]. Journal of Mechanical Engineering，2011，47(11)：117-124.

[19] AHILAN C，SOMASUNDARAM K，SIVAKUMARAN N，et al. Modeling and prediction of machining quality in CNC turning process using intelligent hybrid decision making tools[J]. Applied Soft Computing，2013，13(3)：1543-1551.