数控工作台非线性动态特性的辨识研究
|
摘要
数控工作台是数控机床的主要组成部分之一。各部件之间的弹性变形、摩擦、间隙等已成为进给系统定位精度、跟踪精度等动态性能提高的瓶颈。对数控工作台的动态特性的研究很多,但针对其非线性特征的研究尚不多见。
本文采用“试验探讨——理论分析——试验验证”的研究途径和“综合——分析——综合”的研究步骤,从实测数控工作台的动态信号入手,对采集的时间序列进行一系列的分析,作出其动态特性的非线性判断;对数控工作台动力学系统建立了数学模型,对刚度和摩擦力的非线性动态特性进行了模型结构辨识、分岔与混沌分析,获得了大量关于数控工作台非线性动态特性的规律;通过试验研究进行了模型适用性检验;分析了非线性动态特征对数控加工性能的影响并提出了相应的应对措施。
主要包括以下几方面的内容。
首先,做出了数控工作台动态特性的混沌特征的判断,明确了系统的非线性性质;建立了系统的数学模型,清晰地表示出了数控工作台各组成部分之间的关系。
其次,对数控工作各个部分的刚度进行了研究,分析了滚珠丝杠的四种支承方式的力学模型和不同支承方式下的滚珠丝杠的轴向刚度、扭转刚度和弯曲挠度的变化规律,对轴承刚度、滚珠螺母刚度和支座刚度也作了简要地分析。着重对刚度的非线性特征进行了研究,提出了根据数控工作台的运动方向和工作位置不同,滚珠丝杠的刚度分别呈软弹簧特性或硬弹簧特性,其动态响应遵从软、硬特性的Duffing方程的结论。该结论对于研究螺旋传动机构等一类直线运动机构以及细长轴类零件加工系统的动力学特性具有普遍的适用性。
接着,简单介绍了摩擦力特性和摩擦模型。着重对摩擦力的非线性特征进行了研究,提出了根据工作台的运动速度和运动方向,非线性摩擦力的变化规律在Stribeck摩擦曲线的四个摩擦特性区间内的非线性摩擦力的响应分别遵从不同的规律。即在全液体润滑区域的作用效果相当于增加了系统的阻尼;在边界润滑和半液体润滑区域Stribeck曲线出现负斜率,其作用效果相当于减小了系统的阻尼,当系统出现负阻尼时其动态特性遵循Van der pol方程;在静摩擦区域Stribeck曲线斜率为正的大数值,其作用效果使系统阻尼瞬间陡增,遏制系统的动态响应。该上述结论对于研究机床导轨副、齿轮传动副、凸轮传动副和摩擦传动副的非线性摩擦特性,以及金属切削过程的非线性摩擦特性具有普适性。
同时提出了当系统出现负阻尼时,同时考虑弹簧力和摩擦力非线性作用,耦合系统遵循Lienard方程的具体形式Van Der Pol-Duffing耦合方程。该上述结论对于研究螺旋传动机构等一类直线运动机构以及细长轴类零件加工系统的非线性刚度和摩擦耦合特性具有普适性。
通过对不同工况下Duffing方程、Van der pol方程和Van Der Pol-Duffing耦合方程的解析分析、数值仿真、分岔与混沌分析,获得了大量关于数控工作台非线性动态特性的规律。
以华中数控公司生产的ZJK7532型数控钻铣床的工作台为测试对象进行试验研究,从不同角度验证了理论分析结论的有效性;根据理论分析和试验研究的所得的规律,分析了非线性动态特性对数控加工的影响,并提出一系列应对措施。
用MATLAB编程语言编写了一系列相关软件。其中关联维数分析等多种分析软件,对于混沌时间序列的分析和处理具有普遍的适用性;绘制系统分岔图等软件,对于具有确定数学模型的非线性系统的分岔与混沌分析具有普遍的适用性。
NC (numerical control) table is one of the main components of NC machine. Factors such as backlash, friction and elastic deformation among each part have become the bottleneck for feed system to enhance positioning precision, tracing precision and dynamic behaviors. There are many researches on dynamic behavior of NC table, but only few focused on its nonlinear dynamic characteristics.
Using 'experimental probe-theoretical analysis-experimental verification' approach and 'synthesis-analysis-synthesis' procedure, this research starts from testing the dynamic signals of NC table. By means of a series of analysis on the colleted time series, a judgment is made that its dynamic behavior is nonlinear. The mathematic model of its dynamic system is established. The model structure discrimination, bifurcation and chaotic analysis of the nonlinear dynamic characteristics of its stiffness and friction are made. Massive regulations about the nonlinear dynamic behaviors of NC table in different working conditions are obtained. The applicability of the model is tested via experiments. The effects on NC machining performances of its nonlinear dynamic characteristics are analyzed. A serise of corresponding improving measures are proposed. The main contributions of this dissertation are shown as follows.
Firstly, the judgment that the dynamic behaviors of NC table have chaotic characteristics is made. So the nonlinear properties of the system are clearly exhibited. The systematic mathematic model of NC table is established. It clearly shows the relationship of every components of NC table.
Secondly, stiffness of every component of NC table is analyzed separately. The mechanical models of four types of supporting ball screw are suggested. The varying regulation of axial stiffness, torsion stiffness and bending deflections of ball screw supported by each support types are analyzed. Stiffness of bearings, ball nut and sockets are briefly analyzed also. The nonlinear dynamic characteristics of stiffness are emphatically studied and the following conclusions are presented. Stiffness values vary with displacement and moving direction of NC table and show soft spring property or hard spring property. The responses of nonlinear springs obey soft or hard property Duffing equation. These conclusions above are of general applicability to the dynamic behavior reseaches on a kind of rectilinear movement mechanisms such as screw transmission mechanism and a kind of machining system to cut the slender pieces.
Thirdly, the friction properties and friction models are introduced briefly. Nonlinear frictional dynamic characteristics of NC table are emphatically studied and the following conclusions are presented. The varying regulation of frictional force obeys Streibeck curve according the velocity and moving direction of NC table. The responses of nonlinear frictional forces in four different frictional regions on the Streibeck curve obey different regulations separately. These are as follows. In the full lubrication region, it's action effects are equivalent to increasing the systematic damping. In the boundary lubrication and half liquid lubrication regions, the negative slope of the Streibeck curve occurs and their action effects are equivalent to decreasing the systematic damping. When the negative systematic damping occurs, their responses obey Van Der Pol equation. In the static friction region, it's action effects are equivalent to increasing the systematic damping suddenly and the systematic responses are suppressed significantly. These conclusions above are of general applicability to the reseaches on nonlinear frictional dynamic behaviors of a kind of friction pairs such as machine tool guidway pair and a kind of metal machining processes.
Meantime, the conclusion that the coupling effect of nonlinear stiffness and friction,when the negative systematic damping occurs, obeys Van Der Pol-Duffing coupling equation, the concrete type of Lienard equation, is presented. This conclusion is of general applicability to the dynamic behavior reseaches on nonlinear stiffness and friction coupling of a kind of rectilinear movement mechanisms such as screw transmission mechanism and a kind of machining system to cut the slender pieces.
By means of analytic solutions, numerical simulation, bifurcation and chaotic analysis, massive regulations about the nonlinear dynamic behaviors of NC table in different working conditions are obtained.
A ZJK7532 NC drilling and milling machine made by Huazhong NC Company serves as a test object. The experiments are made to demonstrate the applicability of above theoretic analysis from different aspects. According to the regulations obtained via theoretic analysis and experiments, the effects on NC machining performances of its nonlinear dynamic characteristics are analyzed. A series of corresponding improving measures are proposed.
A series of related softwares are written using MATLAB. The softwares such as correlation dimension analysis software etc are of general applicability to analyzing and processing chaotic time senses. The softwares such as systematic bifurcation diagram drawing software etc are of general applicability to bifurcation and chaotic analysis on nonlinear systems with determinate mathematic model.
本文采用“试验探讨——理论分析——试验验证”的研究途径和“综合——分析——综合”的研究步骤,从实测数控工作台的动态信号入手,对采集的时间序列进行一系列的分析,作出其动态特性的非线性判断;对数控工作台动力学系统建立了数学模型,对刚度和摩擦力的非线性动态特性进行了模型结构辨识、分岔与混沌分析,获得了大量关于数控工作台非线性动态特性的规律;通过试验研究进行了模型适用性检验;分析了非线性动态特征对数控加工性能的影响并提出了相应的应对措施。
主要包括以下几方面的内容。
首先,做出了数控工作台动态特性的混沌特征的判断,明确了系统的非线性性质;建立了系统的数学模型,清晰地表示出了数控工作台各组成部分之间的关系。
其次,对数控工作各个部分的刚度进行了研究,分析了滚珠丝杠的四种支承方式的力学模型和不同支承方式下的滚珠丝杠的轴向刚度、扭转刚度和弯曲挠度的变化规律,对轴承刚度、滚珠螺母刚度和支座刚度也作了简要地分析。着重对刚度的非线性特征进行了研究,提出了根据数控工作台的运动方向和工作位置不同,滚珠丝杠的刚度分别呈软弹簧特性或硬弹簧特性,其动态响应遵从软、硬特性的Duffing方程的结论。该结论对于研究螺旋传动机构等一类直线运动机构以及细长轴类零件加工系统的动力学特性具有普遍的适用性。
接着,简单介绍了摩擦力特性和摩擦模型。着重对摩擦力的非线性特征进行了研究,提出了根据工作台的运动速度和运动方向,非线性摩擦力的变化规律在Stribeck摩擦曲线的四个摩擦特性区间内的非线性摩擦力的响应分别遵从不同的规律。即在全液体润滑区域的作用效果相当于增加了系统的阻尼;在边界润滑和半液体润滑区域Stribeck曲线出现负斜率,其作用效果相当于减小了系统的阻尼,当系统出现负阻尼时其动态特性遵循Van der pol方程;在静摩擦区域Stribeck曲线斜率为正的大数值,其作用效果使系统阻尼瞬间陡增,遏制系统的动态响应。该上述结论对于研究机床导轨副、齿轮传动副、凸轮传动副和摩擦传动副的非线性摩擦特性,以及金属切削过程的非线性摩擦特性具有普适性。
同时提出了当系统出现负阻尼时,同时考虑弹簧力和摩擦力非线性作用,耦合系统遵循Lienard方程的具体形式Van Der Pol-Duffing耦合方程。该上述结论对于研究螺旋传动机构等一类直线运动机构以及细长轴类零件加工系统的非线性刚度和摩擦耦合特性具有普适性。
通过对不同工况下Duffing方程、Van der pol方程和Van Der Pol-Duffing耦合方程的解析分析、数值仿真、分岔与混沌分析,获得了大量关于数控工作台非线性动态特性的规律。
以华中数控公司生产的ZJK7532型数控钻铣床的工作台为测试对象进行试验研究,从不同角度验证了理论分析结论的有效性;根据理论分析和试验研究的所得的规律,分析了非线性动态特性对数控加工的影响,并提出一系列应对措施。
用MATLAB编程语言编写了一系列相关软件。其中关联维数分析等多种分析软件,对于混沌时间序列的分析和处理具有普遍的适用性;绘制系统分岔图等软件,对于具有确定数学模型的非线性系统的分岔与混沌分析具有普遍的适用性。
NC (numerical control) table is one of the main components of NC machine. Factors such as backlash, friction and elastic deformation among each part have become the bottleneck for feed system to enhance positioning precision, tracing precision and dynamic behaviors. There are many researches on dynamic behavior of NC table, but only few focused on its nonlinear dynamic characteristics.
Using 'experimental probe-theoretical analysis-experimental verification' approach and 'synthesis-analysis-synthesis' procedure, this research starts from testing the dynamic signals of NC table. By means of a series of analysis on the colleted time series, a judgment is made that its dynamic behavior is nonlinear. The mathematic model of its dynamic system is established. The model structure discrimination, bifurcation and chaotic analysis of the nonlinear dynamic characteristics of its stiffness and friction are made. Massive regulations about the nonlinear dynamic behaviors of NC table in different working conditions are obtained. The applicability of the model is tested via experiments. The effects on NC machining performances of its nonlinear dynamic characteristics are analyzed. A serise of corresponding improving measures are proposed. The main contributions of this dissertation are shown as follows.
Firstly, the judgment that the dynamic behaviors of NC table have chaotic characteristics is made. So the nonlinear properties of the system are clearly exhibited. The systematic mathematic model of NC table is established. It clearly shows the relationship of every components of NC table.
Secondly, stiffness of every component of NC table is analyzed separately. The mechanical models of four types of supporting ball screw are suggested. The varying regulation of axial stiffness, torsion stiffness and bending deflections of ball screw supported by each support types are analyzed. Stiffness of bearings, ball nut and sockets are briefly analyzed also. The nonlinear dynamic characteristics of stiffness are emphatically studied and the following conclusions are presented. Stiffness values vary with displacement and moving direction of NC table and show soft spring property or hard spring property. The responses of nonlinear springs obey soft or hard property Duffing equation. These conclusions above are of general applicability to the dynamic behavior reseaches on a kind of rectilinear movement mechanisms such as screw transmission mechanism and a kind of machining system to cut the slender pieces.
Thirdly, the friction properties and friction models are introduced briefly. Nonlinear frictional dynamic characteristics of NC table are emphatically studied and the following conclusions are presented. The varying regulation of frictional force obeys Streibeck curve according the velocity and moving direction of NC table. The responses of nonlinear frictional forces in four different frictional regions on the Streibeck curve obey different regulations separately. These are as follows. In the full lubrication region, it's action effects are equivalent to increasing the systematic damping. In the boundary lubrication and half liquid lubrication regions, the negative slope of the Streibeck curve occurs and their action effects are equivalent to decreasing the systematic damping. When the negative systematic damping occurs, their responses obey Van Der Pol equation. In the static friction region, it's action effects are equivalent to increasing the systematic damping suddenly and the systematic responses are suppressed significantly. These conclusions above are of general applicability to the reseaches on nonlinear frictional dynamic behaviors of a kind of friction pairs such as machine tool guidway pair and a kind of metal machining processes.
Meantime, the conclusion that the coupling effect of nonlinear stiffness and friction,when the negative systematic damping occurs, obeys Van Der Pol-Duffing coupling equation, the concrete type of Lienard equation, is presented. This conclusion is of general applicability to the dynamic behavior reseaches on nonlinear stiffness and friction coupling of a kind of rectilinear movement mechanisms such as screw transmission mechanism and a kind of machining system to cut the slender pieces.
By means of analytic solutions, numerical simulation, bifurcation and chaotic analysis, massive regulations about the nonlinear dynamic behaviors of NC table in different working conditions are obtained.
A ZJK7532 NC drilling and milling machine made by Huazhong NC Company serves as a test object. The experiments are made to demonstrate the applicability of above theoretic analysis from different aspects. According to the regulations obtained via theoretic analysis and experiments, the effects on NC machining performances of its nonlinear dynamic characteristics are analyzed. A series of corresponding improving measures are proposed.
A series of related softwares are written using MATLAB. The softwares such as correlation dimension analysis software etc are of general applicability to analyzing and processing chaotic time senses. The softwares such as systematic bifurcation diagram drawing software etc are of general applicability to bifurcation and chaotic analysis on nonlinear systems with determinate mathematic model.
引文
[1]黄祖尧.精密高速滚珠丝杠副的发展及其应用.制造技术与机床,2002(5):8-11
[2]黄祖尧.从我国滚珠丝杠副标准的演变看其技术发展.制造技术与机床,1995,9:42-44
[3]肖正义.滚珠丝杠副的发展趋势.制造技术与机床,2000,4:11-13
[4]Pritschow G.A comparison of linear and conventional electromechanical drives.Annals of the CIRP,1998,47(2):541-548
[5]Brandenburg G,Bruckl S,Dormann J,et al.Comparative investigation of rotary and linear motor.Proceedings of the IEEE International Symposium on Industrial Electronics,1999,2:963-967
[6]杨春林.美国国际制造技术展览会(IMTS 2006)回眸.世界制造技术与装备市场,2006,6:29-37
[7]黄育全,喻忠志。我国滚珠丝杠副发展历程及未来趋势.机械传动,2004,10:61-62
[8]廖伯瑜,周新民,尹志宏.现代机械动力学及其工程应用——建模、分析、仿真、修改、控制、优化.北京:机械工业出版社,2003
[9]Leonard-Cristian Pop.Particularities of modeling ball screw based NC axes as finite degrees of freedom dynamic systems.Buletinul Institutului Polotehnic Din Iasi,2005,5:1-6
[10]Leonard-Cristian Pop,Mircea Cretu,Liviu Morar.Methods of evaluation of the mechanical characteristics influences on the NC balls screw drives dynamic behavior.Buletinul Institutului Polotehnic Din Iasi,2005,5:13-18
[11]Leonard-Cristian Pop,Liviu Morar.Axial pre-stress of NC machine tools ball screw drives.Buletinul Institutului Polotehnic Din Iasi,2005,5:7-12
[12]Kaan Erkorkmaz,Yusuf Altintas.High speed CNC design,part Ⅱ:Modeling and identification of feed drives.International Journal of Machine Tools &Manufacture,2001,41:1487-1509
[13]J.-S.Chen,Y.-K.Huang,C.-C.Cheng.Mechanical model and contouring analysis of high-speed ball-screw drive system with compliance effect.International Journal of Advanced Manufacturing Technology,2004,24:241-250
[14]Kripa K.Varanasi,Samir A.Nayfeh.The dynamics of lead-screw drives:low-order modeling and experiments.Journal of Dynamic Systems,measurement,and Control,2004,126:388-396
[15]C.L.Chen,M.J.Jang,K.C.Lin.Modeling and high-precision control of a ball-screw-drive stage.Precision Engineering,2004,28:483-495
[16]R.Whalley,M.Ebrahimi,A.A.Abdul-Ameer.Hybrid modeling of machine tool axis drives.International Journal of Machine Tools &Manufacture,2005,45:1560-1576
[17]R.Whalley,M.Ebrahimi,A.A.Abdul-Ameer et al.Optimum,Machine Tool Axis Traverse Regulation.International Journal of Machine Tools &Manufacture,2006,46:1835-1853
[18]George W.Younkin.Modeling machine tool feed servo drives using simulation techniques to predict performance.IEEE Transactions Industry Applications,1991,27:268-274
[19]U.C.Gu,C.C.Cheng.Vibration analysis of a high-speed spindle under the action of a moving mass.Journal of Sound and Vibration,2004,278:1131-1146
[20]Xuesong Mei,Masaomi Tsutsumi,Tao Tao et al.Study on the load distribution of ball screw with errors.Mechanism and Machine Theory,2003,38:1257-1269
[21]Zheng-Hong Tsai,Syh-shiuh Yeh,Pau-Lo Hsu.The integrated linear and nonlinear motion control design for precise CNC machine tools.Proceedings of the 2004IEEE International Conference on Control Applications,2004:724-729
[22]王军平,王安,敬忠良.基于内在反馈的机械系统低速运动平稳性研究.机械科学与技术,2001,20(6):819-832.
[23]R.Ramesh,M.A.Mannan,A.N.Poo.Tracking and contour error control in CNC servo systems.International Journal of Machine Tools & Manufacture,2005,45:301-326
[24]C Pislaru,VYMoreno-Castaneda,DG Ford.Dynamic model of a non-linear servo control system using transmission line modeling technique.Control 2004,University of Bath,UK,2004,9:ID118
[25]胡赤兵,吴建民,邬再新.滚珠丝杠副支承方式的力学模型及对加工精度的影响.机械传动,2004,28(3):51-53
[26]杨祖孝.进给滚珠丝杠副传动刚度的计算.制造技术与机床,1999,7:12-14
[27]黄其圣,胡鹏浩.滚珠螺旋传动系统的刚度计算.2000,34(2):29-32
[28]吴南星,胡如夫,孙庆鸿.数控车床丝杠进给系统刚度对定位精度的影响.中国工程科学,2004,6(9):46-49
[29]Yoshitaka Morimoto,Yoshio Ichida;Ryunosuke Sato et al.Measurement and vibration control of dynamic characteristic of feed table for machine tool.41 st SICE Annual Conference(SICE 2002),2002,1:492-494
[30]Xi Shi,Andreas A.Polycarpou.Measurement and modeling of normal contact stiffness and contact damping at the meso-scale.Journal of Vibration and Acoustics,2005,127:52-60
[31]赵联春,马家驹.球轴承的弹性接触振动.机械工程学报,2003,39(5):60-64
[32]赵联春,马家驹,马纯青.载荷对球轴承振动特性的影响.轴承,2003,5:38-41
[33]赵联春,马家驹,曹志飞.设计和应用参数对球轴承振动特性的影响.轴承,2006.1:4-8
[34]赵联春,马家驹,曹志飞等.润滑对球轴承振动特性的影响.摩擦学学报,2003,23(5):421-425.
[35]张迅雷等.球轴承振动的试验研究.轴承,2005,11:22-26
[36]刘强,尔联洁,刘金琨.摩擦非线性环节的特性、建模与控制补偿综述.系统工程与电子技术,2002,24(11):45-52
[37]朱华,葛世荣.摩擦学系统的混沌特性.机械工程学报,2004,40(12):10-13
[38]F.M-Bender,W.Symens.Dynamic characterization of hysteresis elements in mechanical systems Ⅰ.Theoretical analysis.Chaos15,2005,013105:1-11
[39]W.Symens,E Ai-Bender.Dynamic characterization of hysteresis elements in mechanical systems.Ⅱ.Experimental validation.Chaos 15,2005,013106:1-9
[40]Dumitru Olaru,George C.Puiu,Liviu C.Balan et al.A new model to estimate friction torque in ball screw system.Springer Netherlands press,2005
[41]Ding Wenjing,Fan Shichao,Lu Mingwan.A new criterion for occurrence of stick-slip motion in drive mechanism.ACTA MECHANICA SINICA(English Series),2000,16(3):273-281
[42]吴南星,孙庆鸿,冯景华.机床进给伺服系统非线性摩擦特性及控制补偿研究.东南大学学报(自然科学版),2004,34(6):771-774
[43]卢泽生,曹东海.爬行物理模型的建立与仿真分析.机械工程学报,2004,40(11):107-111
[44]梅雪松,陶涛,堤正臣等.高速高精度数控伺服工作台摩擦误差的研究.机械工程学报,2001,37(6):76-81
[45]Pai-Yi Huang,Yung-Yaw Chen,Min-Shin Chen.Position-dependent Friction Compensation for Ball-screw Tables.Proceedings of the 1998 IEEE International Conference on Control Applications,1998:863-867
[46]胡旭晓.机床进给系统摩擦特性分析及改善措施研究.机械工程学报,2005,41(8):185-189
[47]崔宪莉,孙容磊,熊有伦.速度反向区间的非线性摩擦分析与控制补偿研究.控制与检测,2006,3:39-46
[48]王军平,王安,敬忠良.基于内在反馈的机械系统低速运动平稳性研究.机械科学与技术,2001,20(6):819-832
[49]Zheng-Hong Tsai,Syh-shiuh Yeh,Pau-Lo Hsu.The integrated linear and nonlinear motion control design for precise CNC machine tools.Proceedings of the 2004IEEE International Conference on Control Applications,2004:724-729
[50]Ji Zhong,Jin Tao,Qin Shuren.Signal feature extraction based upon independent component analysis and wavelet transform.Chinese Journal of Mechanical Engineering,2005,18(1):123-126
[51]Jing Lin,Liangsheng Qu.Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis.Journal of Sound and Vibration,2000,234(1):135-148
[52]G.Y.Luo,D.Osypiw,M.Irle.Vibration modeling with fast Gaussian wavelet algorithm.Advances in Engineering Software,2003,33:191-197
[53]徐玉秀,原培新,黄海英.基于广义维数的故障特征提取及诊断研究.机械强度,2004,26(5):587-590
[54]黄文虎,武新华,焦映厚等.非线性转子动力学研究综述.振动工程学报,2000,13(4):497-509
[55]孟光.转子动力学研究的回顾与展望[J].振动工程学报,2002,15(1):1-9
[56]吏习智.信息处理于软计算.北京:高等教育出版社,2003
[57]Hsu C S.Cell-to-cell mapping:A method of global analysis for nonlinear systems.New York:Springer-Verlag,1987
[58]Kreuzer K.非线性动力学系统的数值研究.凌复华译.上海:上海交通大学出版社,1989
[59]Thomas S P,Chua L O.Practical numerical algorithms for chaotic systems.New York:Springer-Verlag,1989
[60]Nusse H E,Yorke J A.Dynamics:Numerical explorations.New York:Springer-Verlag,1994
[61]Kawakami H.Numerical methods for chaotic dynamical systems Singapore:World Scientific,1998
[62]刘延柱,陈立群.非线性振动.北京:高等教育出版社,2001
[63]N H Packard et al.Geometry from a time series.Phys.Rev.Lett.1980,45:712-715
[64]F Yakens.Detecting strange attractors in turbulence.In:Dynamical system and turbulence,Eds.D A Rand and L S Young.New York:Springer-Verlag,1980:366-381
[65]刘秉正,彭建华.非线性动力学.北京:高等教育出版社,2004
[66]李扬,姚锦绣,汪仁煌.关联维计算及其在旋转机组振动故障征兆提取中的应用.机电工程技术,2002,6:51-59
[67]王林鸿,郭俊杰,吴波,杨叔子.液压缸运行动态特性的关联维数分析.机床与液压,2006,9:99-102
[68]徐玉秀,张剑,侯荣涛著.机械系统动力学分形特征及故障诊断方法.北京:国防工业出版社,2006
[69]Akira Kawamura,Alistair I.Mckcrchar,Robert H.Spigel et al.Chaotic characteristics of thr southern oscillation index time series.Journal of Hydrology,1998,204:168-181
[70]K.Shin,J.K.Hammond.The instantaneous Lyapunov exponent and its application to chaotic dynamical systems.Journal of Sound and Vibration,1998,218(3):389-403
[71]段礼祥,张来斌,王朝晖等.柴油机振动信号的小波包奇异值降噪.中国石油大学学报(自然科学版),2006,30(1):93-97
[72]Linhong WANG,Bo WU,Runsheng DU,Shuzi YANG.Dynamic characteristics of NC table with SVD.Frontiers of Mechanical Engineering in China,2008,3(4):385-391
[73]张伯鹏等.制造信息学.北京:清华大学出版社,2003
[74]耿俊豹,黄树红,金家善等.基于信息熵贴近度和证据理论的旋转机械故障诊断方法.机械科学与技术,2006,25(6):663-666
[75]卢文祥,杜润生.机械工程测试信息信号分析.武汉:华中科技大学出版社,1999
[76]王林鸿,吴波,杜润生,杨叔子.基于奇异值分解和奇异熵的数控工作台动态特征.仪器仪表学报,2008,8(增刊Ⅰ):135-140
[77]Thompson J M T,Stewart H B.Nonlinear dynamics and chaos:Geometrical methods for engineers and scientists.New York:John Wiley & Sons Co,1986
[78]R Whalley,MEbrahimi,A A Abdul-Ameer.Machine tool axis dynamics.Proc.IMechE 2006,Vol.220Part C:J.Mechanical Engineering Science:403-419
[79]M.Aleyaasin,M.Ebrahimi,R.Whally.Vibration analysis of distributed-lumped rotor systems.Comput.Methods Appl.Mech.Engrg.2000,189:545-558
[80]H Bartlett,R Whally.Distributed rotor dynamics.Proc.IMechE 1998,Vol.212PartⅠ:249-265
[81]胡赤兵,吴建民,邬再新.滚珠丝杠副支承方式的力学模型及对加工精度的影响.机械传动,2004,28(3):51-53
[82]唐云冰,高德平,罗贵火.滚动轴承非线性轴承力及其对轴承系统振动特性的 影响.航空动力学报,2006,21(2):366-373
[83]黄其圣,胡鹏浩.滚珠螺旋传动系统的刚度计算.工具技术,2000,34(2):29-32
[84]单辉祖.材料力学.北京:高等教育出版社,2004
[85]王林鸿,杜润生,吴波,杨叔子.数控工作台的非线性动态特性.中国机械工程,2008年11月4日录用
[86]吴胜强,李明.Duffing振子混沌运动的数值仿真分析.邢台职业技术学院学报,2004,21(5):64-66
[87]师汉民.机械振动系统.武汉:华中科技大学出版社,2004
[88]飞思科技产品研发中心.MATLAB7辅助信号处理技术与应用.北京:电子工业出版社,2005
[89]温诗铸,黄平.摩擦学原理.北京:清华大学出版社,2002.
[90]E.Rabinowicz.The nature of the static and kinetic coefficients of friction.Journal of Applied Physics,1951,22(11):1373-1379
[91]V.I.Johannes,M.A.Green,C.A.Brockley.The role of the rate of application of the tangential force in determining the static friction coefficient.Wear,1973,24:381-385
[92]R.S.H.Richardson,H.Nolle.Surface friction under time-dependent loads.Wear,1976,37(1):87-101
[93]D.P.Hess,A.Soom.Friction at a lubricated line contact operating at oscillating sliding velocities.Journal of Tribology,1990,112:147-152
[94]Brian Armstrong-Helouvry,Pierre Dupont,Carlos Canudas De Wit.A survey of models,analysis tools and compensation methods for the control of machines with friction.Automatic,1994,30(7):1083-1138
[95]魏立新.x-y数控平台运动摩擦补偿及边缘跟踪力控制研究.[燕山大学博士学位论文].2005:27-36
[96]Cao J S.Existence for periodic solution of forced Lienard equation.Journal of Nanjing Normal University(Natural Science),1997,20(4):14-19
[97]周进.Lienard方程周期解不存在的充分条件.应用数学,1998,11:41-43
[98]沈松,应怀樵,雷速华等.用锤击法和变时基技术进行黄河铁路桥的模态试验 分析.振动工程学报,2000,13(3):492-495
[99]褚衍东,李险峰,张建刚.Van der pol-Duffing耦合系统的分岔与混沌.江南大学学报(自然科学版),2007,6(1):119-123
[100]H.S.Lee.Robust digital tracking controllers for high-speed/accuracy positioning systems.University of California at BERKELEY Dissertation,1994:1-20
[101]克晶.高精度转台摩擦补偿研究.[哈尔滨工业大学工学博士学位论文].2003:13-15
[102]王茂华,于俊一,张永亮.电流变技术在机床颤振控制中应用的研究.机械工程学报,2000,36(11):94-97
[2]黄祖尧.从我国滚珠丝杠副标准的演变看其技术发展.制造技术与机床,1995,9:42-44
[3]肖正义.滚珠丝杠副的发展趋势.制造技术与机床,2000,4:11-13
[4]Pritschow G.A comparison of linear and conventional electromechanical drives.Annals of the CIRP,1998,47(2):541-548
[5]Brandenburg G,Bruckl S,Dormann J,et al.Comparative investigation of rotary and linear motor.Proceedings of the IEEE International Symposium on Industrial Electronics,1999,2:963-967
[6]杨春林.美国国际制造技术展览会(IMTS 2006)回眸.世界制造技术与装备市场,2006,6:29-37
[7]黄育全,喻忠志。我国滚珠丝杠副发展历程及未来趋势.机械传动,2004,10:61-62
[8]廖伯瑜,周新民,尹志宏.现代机械动力学及其工程应用——建模、分析、仿真、修改、控制、优化.北京:机械工业出版社,2003
[9]Leonard-Cristian Pop.Particularities of modeling ball screw based NC axes as finite degrees of freedom dynamic systems.Buletinul Institutului Polotehnic Din Iasi,2005,5:1-6
[10]Leonard-Cristian Pop,Mircea Cretu,Liviu Morar.Methods of evaluation of the mechanical characteristics influences on the NC balls screw drives dynamic behavior.Buletinul Institutului Polotehnic Din Iasi,2005,5:13-18
[11]Leonard-Cristian Pop,Liviu Morar.Axial pre-stress of NC machine tools ball screw drives.Buletinul Institutului Polotehnic Din Iasi,2005,5:7-12
[12]Kaan Erkorkmaz,Yusuf Altintas.High speed CNC design,part Ⅱ:Modeling and identification of feed drives.International Journal of Machine Tools &Manufacture,2001,41:1487-1509
[13]J.-S.Chen,Y.-K.Huang,C.-C.Cheng.Mechanical model and contouring analysis of high-speed ball-screw drive system with compliance effect.International Journal of Advanced Manufacturing Technology,2004,24:241-250
[14]Kripa K.Varanasi,Samir A.Nayfeh.The dynamics of lead-screw drives:low-order modeling and experiments.Journal of Dynamic Systems,measurement,and Control,2004,126:388-396
[15]C.L.Chen,M.J.Jang,K.C.Lin.Modeling and high-precision control of a ball-screw-drive stage.Precision Engineering,2004,28:483-495
[16]R.Whalley,M.Ebrahimi,A.A.Abdul-Ameer.Hybrid modeling of machine tool axis drives.International Journal of Machine Tools &Manufacture,2005,45:1560-1576
[17]R.Whalley,M.Ebrahimi,A.A.Abdul-Ameer et al.Optimum,Machine Tool Axis Traverse Regulation.International Journal of Machine Tools &Manufacture,2006,46:1835-1853
[18]George W.Younkin.Modeling machine tool feed servo drives using simulation techniques to predict performance.IEEE Transactions Industry Applications,1991,27:268-274
[19]U.C.Gu,C.C.Cheng.Vibration analysis of a high-speed spindle under the action of a moving mass.Journal of Sound and Vibration,2004,278:1131-1146
[20]Xuesong Mei,Masaomi Tsutsumi,Tao Tao et al.Study on the load distribution of ball screw with errors.Mechanism and Machine Theory,2003,38:1257-1269
[21]Zheng-Hong Tsai,Syh-shiuh Yeh,Pau-Lo Hsu.The integrated linear and nonlinear motion control design for precise CNC machine tools.Proceedings of the 2004IEEE International Conference on Control Applications,2004:724-729
[22]王军平,王安,敬忠良.基于内在反馈的机械系统低速运动平稳性研究.机械科学与技术,2001,20(6):819-832.
[23]R.Ramesh,M.A.Mannan,A.N.Poo.Tracking and contour error control in CNC servo systems.International Journal of Machine Tools & Manufacture,2005,45:301-326
[24]C Pislaru,VYMoreno-Castaneda,DG Ford.Dynamic model of a non-linear servo control system using transmission line modeling technique.Control 2004,University of Bath,UK,2004,9:ID118
[25]胡赤兵,吴建民,邬再新.滚珠丝杠副支承方式的力学模型及对加工精度的影响.机械传动,2004,28(3):51-53
[26]杨祖孝.进给滚珠丝杠副传动刚度的计算.制造技术与机床,1999,7:12-14
[27]黄其圣,胡鹏浩.滚珠螺旋传动系统的刚度计算.2000,34(2):29-32
[28]吴南星,胡如夫,孙庆鸿.数控车床丝杠进给系统刚度对定位精度的影响.中国工程科学,2004,6(9):46-49
[29]Yoshitaka Morimoto,Yoshio Ichida;Ryunosuke Sato et al.Measurement and vibration control of dynamic characteristic of feed table for machine tool.41 st SICE Annual Conference(SICE 2002),2002,1:492-494
[30]Xi Shi,Andreas A.Polycarpou.Measurement and modeling of normal contact stiffness and contact damping at the meso-scale.Journal of Vibration and Acoustics,2005,127:52-60
[31]赵联春,马家驹.球轴承的弹性接触振动.机械工程学报,2003,39(5):60-64
[32]赵联春,马家驹,马纯青.载荷对球轴承振动特性的影响.轴承,2003,5:38-41
[33]赵联春,马家驹,曹志飞.设计和应用参数对球轴承振动特性的影响.轴承,2006.1:4-8
[34]赵联春,马家驹,曹志飞等.润滑对球轴承振动特性的影响.摩擦学学报,2003,23(5):421-425.
[35]张迅雷等.球轴承振动的试验研究.轴承,2005,11:22-26
[36]刘强,尔联洁,刘金琨.摩擦非线性环节的特性、建模与控制补偿综述.系统工程与电子技术,2002,24(11):45-52
[37]朱华,葛世荣.摩擦学系统的混沌特性.机械工程学报,2004,40(12):10-13
[38]F.M-Bender,W.Symens.Dynamic characterization of hysteresis elements in mechanical systems Ⅰ.Theoretical analysis.Chaos15,2005,013105:1-11
[39]W.Symens,E Ai-Bender.Dynamic characterization of hysteresis elements in mechanical systems.Ⅱ.Experimental validation.Chaos 15,2005,013106:1-9
[40]Dumitru Olaru,George C.Puiu,Liviu C.Balan et al.A new model to estimate friction torque in ball screw system.Springer Netherlands press,2005
[41]Ding Wenjing,Fan Shichao,Lu Mingwan.A new criterion for occurrence of stick-slip motion in drive mechanism.ACTA MECHANICA SINICA(English Series),2000,16(3):273-281
[42]吴南星,孙庆鸿,冯景华.机床进给伺服系统非线性摩擦特性及控制补偿研究.东南大学学报(自然科学版),2004,34(6):771-774
[43]卢泽生,曹东海.爬行物理模型的建立与仿真分析.机械工程学报,2004,40(11):107-111
[44]梅雪松,陶涛,堤正臣等.高速高精度数控伺服工作台摩擦误差的研究.机械工程学报,2001,37(6):76-81
[45]Pai-Yi Huang,Yung-Yaw Chen,Min-Shin Chen.Position-dependent Friction Compensation for Ball-screw Tables.Proceedings of the 1998 IEEE International Conference on Control Applications,1998:863-867
[46]胡旭晓.机床进给系统摩擦特性分析及改善措施研究.机械工程学报,2005,41(8):185-189
[47]崔宪莉,孙容磊,熊有伦.速度反向区间的非线性摩擦分析与控制补偿研究.控制与检测,2006,3:39-46
[48]王军平,王安,敬忠良.基于内在反馈的机械系统低速运动平稳性研究.机械科学与技术,2001,20(6):819-832
[49]Zheng-Hong Tsai,Syh-shiuh Yeh,Pau-Lo Hsu.The integrated linear and nonlinear motion control design for precise CNC machine tools.Proceedings of the 2004IEEE International Conference on Control Applications,2004:724-729
[50]Ji Zhong,Jin Tao,Qin Shuren.Signal feature extraction based upon independent component analysis and wavelet transform.Chinese Journal of Mechanical Engineering,2005,18(1):123-126
[51]Jing Lin,Liangsheng Qu.Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis.Journal of Sound and Vibration,2000,234(1):135-148
[52]G.Y.Luo,D.Osypiw,M.Irle.Vibration modeling with fast Gaussian wavelet algorithm.Advances in Engineering Software,2003,33:191-197
[53]徐玉秀,原培新,黄海英.基于广义维数的故障特征提取及诊断研究.机械强度,2004,26(5):587-590
[54]黄文虎,武新华,焦映厚等.非线性转子动力学研究综述.振动工程学报,2000,13(4):497-509
[55]孟光.转子动力学研究的回顾与展望[J].振动工程学报,2002,15(1):1-9
[56]吏习智.信息处理于软计算.北京:高等教育出版社,2003
[57]Hsu C S.Cell-to-cell mapping:A method of global analysis for nonlinear systems.New York:Springer-Verlag,1987
[58]Kreuzer K.非线性动力学系统的数值研究.凌复华译.上海:上海交通大学出版社,1989
[59]Thomas S P,Chua L O.Practical numerical algorithms for chaotic systems.New York:Springer-Verlag,1989
[60]Nusse H E,Yorke J A.Dynamics:Numerical explorations.New York:Springer-Verlag,1994
[61]Kawakami H.Numerical methods for chaotic dynamical systems Singapore:World Scientific,1998
[62]刘延柱,陈立群.非线性振动.北京:高等教育出版社,2001
[63]N H Packard et al.Geometry from a time series.Phys.Rev.Lett.1980,45:712-715
[64]F Yakens.Detecting strange attractors in turbulence.In:Dynamical system and turbulence,Eds.D A Rand and L S Young.New York:Springer-Verlag,1980:366-381
[65]刘秉正,彭建华.非线性动力学.北京:高等教育出版社,2004
[66]李扬,姚锦绣,汪仁煌.关联维计算及其在旋转机组振动故障征兆提取中的应用.机电工程技术,2002,6:51-59
[67]王林鸿,郭俊杰,吴波,杨叔子.液压缸运行动态特性的关联维数分析.机床与液压,2006,9:99-102
[68]徐玉秀,张剑,侯荣涛著.机械系统动力学分形特征及故障诊断方法.北京:国防工业出版社,2006
[69]Akira Kawamura,Alistair I.Mckcrchar,Robert H.Spigel et al.Chaotic characteristics of thr southern oscillation index time series.Journal of Hydrology,1998,204:168-181
[70]K.Shin,J.K.Hammond.The instantaneous Lyapunov exponent and its application to chaotic dynamical systems.Journal of Sound and Vibration,1998,218(3):389-403
[71]段礼祥,张来斌,王朝晖等.柴油机振动信号的小波包奇异值降噪.中国石油大学学报(自然科学版),2006,30(1):93-97
[72]Linhong WANG,Bo WU,Runsheng DU,Shuzi YANG.Dynamic characteristics of NC table with SVD.Frontiers of Mechanical Engineering in China,2008,3(4):385-391
[73]张伯鹏等.制造信息学.北京:清华大学出版社,2003
[74]耿俊豹,黄树红,金家善等.基于信息熵贴近度和证据理论的旋转机械故障诊断方法.机械科学与技术,2006,25(6):663-666
[75]卢文祥,杜润生.机械工程测试信息信号分析.武汉:华中科技大学出版社,1999
[76]王林鸿,吴波,杜润生,杨叔子.基于奇异值分解和奇异熵的数控工作台动态特征.仪器仪表学报,2008,8(增刊Ⅰ):135-140
[77]Thompson J M T,Stewart H B.Nonlinear dynamics and chaos:Geometrical methods for engineers and scientists.New York:John Wiley & Sons Co,1986
[78]R Whalley,MEbrahimi,A A Abdul-Ameer.Machine tool axis dynamics.Proc.IMechE 2006,Vol.220Part C:J.Mechanical Engineering Science:403-419
[79]M.Aleyaasin,M.Ebrahimi,R.Whally.Vibration analysis of distributed-lumped rotor systems.Comput.Methods Appl.Mech.Engrg.2000,189:545-558
[80]H Bartlett,R Whally.Distributed rotor dynamics.Proc.IMechE 1998,Vol.212PartⅠ:249-265
[81]胡赤兵,吴建民,邬再新.滚珠丝杠副支承方式的力学模型及对加工精度的影响.机械传动,2004,28(3):51-53
[82]唐云冰,高德平,罗贵火.滚动轴承非线性轴承力及其对轴承系统振动特性的 影响.航空动力学报,2006,21(2):366-373
[83]黄其圣,胡鹏浩.滚珠螺旋传动系统的刚度计算.工具技术,2000,34(2):29-32
[84]单辉祖.材料力学.北京:高等教育出版社,2004
[85]王林鸿,杜润生,吴波,杨叔子.数控工作台的非线性动态特性.中国机械工程,2008年11月4日录用
[86]吴胜强,李明.Duffing振子混沌运动的数值仿真分析.邢台职业技术学院学报,2004,21(5):64-66
[87]师汉民.机械振动系统.武汉:华中科技大学出版社,2004
[88]飞思科技产品研发中心.MATLAB7辅助信号处理技术与应用.北京:电子工业出版社,2005
[89]温诗铸,黄平.摩擦学原理.北京:清华大学出版社,2002.
[90]E.Rabinowicz.The nature of the static and kinetic coefficients of friction.Journal of Applied Physics,1951,22(11):1373-1379
[91]V.I.Johannes,M.A.Green,C.A.Brockley.The role of the rate of application of the tangential force in determining the static friction coefficient.Wear,1973,24:381-385
[92]R.S.H.Richardson,H.Nolle.Surface friction under time-dependent loads.Wear,1976,37(1):87-101
[93]D.P.Hess,A.Soom.Friction at a lubricated line contact operating at oscillating sliding velocities.Journal of Tribology,1990,112:147-152
[94]Brian Armstrong-Helouvry,Pierre Dupont,Carlos Canudas De Wit.A survey of models,analysis tools and compensation methods for the control of machines with friction.Automatic,1994,30(7):1083-1138
[95]魏立新.x-y数控平台运动摩擦补偿及边缘跟踪力控制研究.[燕山大学博士学位论文].2005:27-36
[96]Cao J S.Existence for periodic solution of forced Lienard equation.Journal of Nanjing Normal University(Natural Science),1997,20(4):14-19
[97]周进.Lienard方程周期解不存在的充分条件.应用数学,1998,11:41-43
[98]沈松,应怀樵,雷速华等.用锤击法和变时基技术进行黄河铁路桥的模态试验 分析.振动工程学报,2000,13(3):492-495
[99]褚衍东,李险峰,张建刚.Van der pol-Duffing耦合系统的分岔与混沌.江南大学学报(自然科学版),2007,6(1):119-123
[100]H.S.Lee.Robust digital tracking controllers for high-speed/accuracy positioning systems.University of California at BERKELEY Dissertation,1994:1-20
[101]克晶.高精度转台摩擦补偿研究.[哈尔滨工业大学工学博士学位论文].2003:13-15
[102]王茂华,于俊一,张永亮.电流变技术在机床颤振控制中应用的研究.机械工程学报,2000,36(11):94-97