数控机床误差测量、建模及网络群控实时补偿系统研究
|
摘要
误差补偿技术是提高数控机床加工精度的重要技术手段之一，与之密切相关的研究方向主要有：误差的测量与辨识、误差模型的建立以及误差补偿的实施方法。本课题在“国家科技重大专项”、“国家自然科学基金”和“全国高等学校博士学科点专项科研基金”等项目的资助和支持下，以沈阳机床有限公司生产的双转台式五轴加工中心和上海航天设备制造总厂使用的两台三轴立式加工中心为研究对象，进行了机床误差高效测量、精密建模和实时补偿的相关研究，并研发了基于网络群控的数控机床误差实时补偿系统，可以对一台或多台机床同时进行补偿，从而改善机床在不同温度条件下的运动精度。
本文的主要研究内容有：
（1）结合不同类型五轴机床的结构特点，建立了基于齐次坐标变换方法的通用运动学模型。通过配置不同的模型参数，可以描述在不同结构的机床中从刀具坐标系到工件坐标系的运动链传递关系。然后分析机床主要部件在运动过程中可能引入的误差元素，根据刚体运动理论和小角度误差假设，将其代入到通用运动学模型中，从而得到五轴机床通用综合误差模型。利用该模型可以计算出机床在运动过程中的空间误差补偿值。为了满足误差补偿的实时性要求，可以对综合误差模型进行简化处理，根据各项误差元素的实际分布规律，提出了综合误差模型的简化策略，从而在满足补偿精度要求的前提下提高模型计算速度。
（2）根据旋转轴的运动特点，提出了基于球杆仪的误差测量和辨识方法。通过MATLAB误差仿真试验，可以了解不同误差元素对球杆仪测量轨迹造成的影响。在一台五轴机床上实际进行的球杆仪测量试验结果表明：该方法可以高效、精确地对旋转轴引入的其中五项误差元素进行辨识。通过对不同温度条件下的误差测量结果进行分析，建立了基于自然指数的旋转轴热误差模型，可用于热误差的预测和补偿。
（3）无论是传统的三轴数控机床，还是引入了旋转轴的多轴数控机床，平动轴都是最重要的运动部件，平动轴引入的各项误差元素也是最重要的误差来源。本文用激光干涉仪测量了在不同温度条件下的平动轴定位误差和直线度误差，测量结果表明：定位精度受温度变化影响明显，而且环境温度及丝杠螺母温度对其影响最为显著，因此可以建立基于自然指数的误差预测模型，该模型不仅描述了机床热误差和温度变量之间的非线性变化规律，而且和多元回归分析模型相比具有温度变量少、预测精度高的优点；而对于直线度误差来说，其数值相对较小，且基本不受温度变化的影响，可以将其简化视为几何误差，并建立以机床坐标为自变量的多项式误差预测模型。
（4）机床主轴在高速旋转过程中会产生大量热量，所以由主轴热变形而导致的主轴热误差也是影响加工精度的重要因素。本文结合灰色理论和神经网络各自对数据处理的优点，提出三种不同结构的灰色神经网络热误差预测模型，即：串联型、并联型和嵌入型灰色神经网络。在串联型灰色神经网络中，首先使用灰色模型对机床关键测点的温度数据和热误差数据进行预处理，得到近似一阶动态微分模型，然后把多个不同灰色模型的预测结果输入到BP神经网络进行非线性拟合优化，利用BP神经网络误差反向传播的学习方法对模型进行训练，调节网络节点的权值和阈值，从而得到最终的预测模型；在并联型灰色神经网络中，先由灰色模型和神经网络分别对主轴热误差进行预测，然后采用一定的加权组合方式，按照目标预测精度优化模型的加权系数，从而得到最终的预测结果；而嵌入型灰色神经网络则是借鉴了灰色理论对数据处理的思想，在神经网络输入层前增加灰化层，在输出层后增加白化层，通过对神经网络拓扑结构的改进，达到弱化原始数据随机性、提高预测模型鲁棒性和容错能力的目标。通过与传统灰色模型和神经网络进行试验结果对比表明：上述三种结构的灰色神经网络模型均提高了预测精度，且具有对原始数据要求低、计算简便、鲁棒性强等优点，可用于复杂工况下的机床主轴热误差实时预测和补偿。
（5）介绍了基于外部机械原点偏移功能的误差补偿实施基本原理，并结合生产线上多台机床同时需要误差补偿的需求，研发了基于网络群控的机床误差实时补偿系统。从整体架构上，可将该补偿系统分为两大部分：主控中心PC和各机床PMC（Programmable Machine Controller）控制单元。前者的运算能力强，存储空间大，因此主要负责各机床空间误差补偿值的计算；后者和CNC（Computer Numerical Control）系统紧密相连，具有很高的数据交互实时性，因此主要负责查询机床当前坐标位置和查表调用各进给轴当前所需补偿值。网络群控误差补偿系统的主从结构充分利用了各自在运算能力方面的特点，不仅适于进行复杂的模型计算，而且满足误差补偿的实时性要求。此外，主控中心PC和数控机床PMC之间通过以太网通讯协议及Fanuc提供的FOCAS（Fanuc Open CNC API Specifications）动态链接函数进行数据交互，具有硬件端口占用资源少、数据传输速度快、可靠性高、功能模块连接简便和易于扩展的特点。
（6）结合本文提出的误差测量方法、建模方法和基于网络群控的机床误差实时补偿系统设计了两类试验。第一类试验是对单台五轴加工中心进行误差补偿试验，首先用激光干涉仪、球杆仪等测量仪器对机床平动轴和旋转轴引入的误差元素进行测量，并建立适用于不同温度条件的误差元素模型，将其代入到综合误差模型中计算出在机床空间范围内施加给各进给轴的误差补偿值，最后通过补偿系统将补偿值送给数控系统完成误差补偿步骤，试验结果表明，通过补偿可以大幅提高该机床的空间运动精度；第二类试验是同时对多台（两台及以上）数控机床进行补偿试验，在得到各机床误差模型的基础上，通过网络群控实时补偿系统和各机床间的数据交互，完成误差补偿步骤，试验结果表明，该系统可以实现对多台机床进行同时补偿，批量提高群控网络内所有机床的运动精度，和传统误差补偿模式相比，具有较高的补偿效率。通过以上两类试验可以发现：无论在何种应用场合中，基于网络群控的机床误差实时补偿系统均可大幅提高机床性能，而且工作稳定可靠，具有较高的实用价值和推广意义。
Error compensation technology is one of the most crucial methods to improve themachining accuracy of computer numerical control (CNC) machine tools, with which threeresearch directions related are: error measurement and identification, error modelingmethodology, and error compensation implementation method. This thesis is sponsored byChinese National Science and Technology Key Special Project, the National ScienceFoundation Project, and the Specialized Research Fund for the Doctoral Program of HigherEducation. Some experiments were carried out on a five-axis machining center and twothree-axis vertical machining centers, in order to conduct the research on efficient errormeasurement, accurate error modeling, and real-time error compensation. In addition, areal-time error compensation system based on Ethernet distributed control method isdeveloped to compensate for multiple machine tools simultaneously in order to improvethe machine performance under different temperature conditions.
The main contents of this thesis are described as follows:
(1) According to the structural kinematic features of different kinds of five-axis machinetools, a universal kinematic model is established based on the homogenous transformationmatrix method so as to describe the kinematic chain transfer from the tool coordinatesystem to the workpiece coordinate system. Furthermore, a universal volumetric errormodel can be obtained based on the analysis of error components possibly induced by themain machine links and the using of rigid motion theory. Then the volumetric errorcompensation values can be calculated within the machine working volume. In order tomeet the requirement of real-time compensation, a data processing strategy, in whichdifferent error components are classified and modeled with different methodologiesaccording their regularity of distribution, is proposed to simplify the volumetric errormodel aiming at increasing the calculation speed.
(2) An error measurement and identification method based on the double ball-bar (DBB) instrument is proposed according to the moving characteristic and error distribution of therotary axis. Through the MATLAB simulation experiment, different error’s influence onthe DBB measuring patterns can be obtained. A real DBB measuring experiment wasconducted on a five-axis machine tool, the results of which showed that the proposedmeasuring method is able to measure five error components simultaneously with highefficiency and accuracy. Moreover, this measuring method could be carried out underdifferent working conditions to obtain the error variations with temperature. A thermalerror modeling method based on the natural exponential model is developed to predict andcompensate for the thermal errors of the rotary axis.
(3) Either on three-axis or five-axis machine tools, translational axes are the mostimportant links, of which the error components are the crucial sources of machineinaccuracy. The laser interferometer can be employed to measure the positioning error andthe straightness error of translational axes. The measurement results show that thepositioning error is obviously affected by the temperature field, especially by the variationsof the ambient temperature and screw nut temperature. Based on the analysis of positioningerrors under different temperature conditions, a natural exponential model is established todescribe the non-linear relationship between the thermal term in the positioning error andthe temperature variables. Compared with a multiple regression analysis model, theproposed modeling method performs better in terms of prediction accuracy and robustness.As to the straightness error, it has relatively small value compared with the positioningerror. In addition, it is almost independent from the temperature variations. Therefore, itcan be regarded as the pure geometric error and modeled by a polynomial with the positioncoordinate.
(4) Much heat is produced during the high-speed rotation of the spindle, so the thermalerror caused by the thermal deformation is one of the major sources of machine inaccuracy.This thesis combines the advantages of both grey model (GM) and artificial neural networkin terms of data processing to propose a novel error prediction model, namely grey neuralnetwork (GNN). According to the structure of the prediction model, three types of GNNare introduced and analyzed in this thesis: serial grey neural network (SGNN), parallelgrey neural network (PGNN), and inlaid grey neural network (IGNN). In SGNN, somegrey models with different length of data sequence firstly play an important role inpreprocessing the original thermal errors and temperature data, establishing a first-orderdifferential equation. Then, the neural network receives the predicted thermal errors fromdifferent grey models to make the nonlinear optimization by adjusting the weight and threshold of the network neurons based on the back propagation (BP) training algorithm.After these two steps, a complete error model is established to predict the final thermalerror of the machine tool spindle. In PGNN, one GM and one BP network are utilized topredict the thermal error, respectively. Then an effective combination algorithm combinesthe results of GM with BP to output the final data as the thermal error compensation value.In IGNN, the topological structure of the BP network is optimized by adding a grey layerbefore the input layer and a white layer after the output layer, in order to reduce therandomness of the original data and enhance the robustness and the fault-tolerant ability.Compared with the traditional GM and BP network, these three types of GNN prove betterin terms of prediction accuracy, calculation convenience and robustness. What’s more, theyrequire less to the original data. Thus, the new proposed models are properly applied todifferent working conditions to compensate for the spindle thermal error of machine tools.
(5) A real-time error compensation system based on Ethernet distributed control methodis developed to compensate for multiple machine tools simultaneously, in which theexternal machine zero point shift (EMZPS) function is utilized as the implementationinterface between the compensation system and the CNC machine tools. From the overallarchitecture, the compensation system is composed of two main parts: the PC controlcenter and the programmable machine controller (PMC). The former one has fastcomputation speed and large data storage, so it is responsible for calculating the volumetricerror compensation values of different machine tools. The latter one is directly connectedwith CNC system, so it is responsible for the real-time data processing parts, i.e. inquiringthe machine position coordinate and looking up the corresponding compensation value inthe data table stored in PMC. The proposed Ethernet distributed error compensation systemcan make full use of the data computation characteristic of both PC and PMC. It is not onlycapable for the complex mathematical model calculation, but also meets the requirement ofreal-time error compensation. In addition, the PC control center and the machine tool PMCis connected through the Ethernet cable under the Fanuc Open CNC API Specifications(FOCAS) protocol, which is featured by high data transmission speed, strong reliability,easy hardware connection, and convenient module expansion.
(6) Two kinds of error compensation experiment were conducted by utilizing the errormeasuring method, modeling methodology, and error compensation implementationtechnique proposed in this thesis. The first kind of experiment was conducted on afive-axis machining center with a rotary table. Firstly, a laser interferometer and a DBBinstrument were employed to conduct the error measurement on translational and rotary axes. Then, error component models were established under different temperatureconditions. The error compensation value applied to each feed axis could be obtainedthrough the volumetric error model, which includes the main error components of themachine. At last, the error compensation was implemented through the developedcompensation system. Experimental results showed that the volumetric accuracy wasimproved significantly after error compensation. The second kind of experiment wasconducted on multiple CNC machine tools. Error models for each machine tool should beobtained firstly, and then different machine tools could be compensated through theEthernet distributed control system. Experimental results showed that the proposed errorcompensation system could be utilized to improve the accuracy of multiple machine tools.It has much higher compensation efficiency compared with the traditional errorcompensation methods. Both the above experiments proved that the proposed errormeasuring method, error-modeling methodology, and the Ethernet distributed errorcompensation system were of significant use to improve the machine tool performanceunder different temperature conditions. This compensation system can work stability;therefore, it has high practical value and significance for popularization.
本文的主要研究内容有：
（1）结合不同类型五轴机床的结构特点，建立了基于齐次坐标变换方法的通用运动学模型。通过配置不同的模型参数，可以描述在不同结构的机床中从刀具坐标系到工件坐标系的运动链传递关系。然后分析机床主要部件在运动过程中可能引入的误差元素，根据刚体运动理论和小角度误差假设，将其代入到通用运动学模型中，从而得到五轴机床通用综合误差模型。利用该模型可以计算出机床在运动过程中的空间误差补偿值。为了满足误差补偿的实时性要求，可以对综合误差模型进行简化处理，根据各项误差元素的实际分布规律，提出了综合误差模型的简化策略，从而在满足补偿精度要求的前提下提高模型计算速度。
（2）根据旋转轴的运动特点，提出了基于球杆仪的误差测量和辨识方法。通过MATLAB误差仿真试验，可以了解不同误差元素对球杆仪测量轨迹造成的影响。在一台五轴机床上实际进行的球杆仪测量试验结果表明：该方法可以高效、精确地对旋转轴引入的其中五项误差元素进行辨识。通过对不同温度条件下的误差测量结果进行分析，建立了基于自然指数的旋转轴热误差模型，可用于热误差的预测和补偿。
（3）无论是传统的三轴数控机床，还是引入了旋转轴的多轴数控机床，平动轴都是最重要的运动部件，平动轴引入的各项误差元素也是最重要的误差来源。本文用激光干涉仪测量了在不同温度条件下的平动轴定位误差和直线度误差，测量结果表明：定位精度受温度变化影响明显，而且环境温度及丝杠螺母温度对其影响最为显著，因此可以建立基于自然指数的误差预测模型，该模型不仅描述了机床热误差和温度变量之间的非线性变化规律，而且和多元回归分析模型相比具有温度变量少、预测精度高的优点；而对于直线度误差来说，其数值相对较小，且基本不受温度变化的影响，可以将其简化视为几何误差，并建立以机床坐标为自变量的多项式误差预测模型。
（4）机床主轴在高速旋转过程中会产生大量热量，所以由主轴热变形而导致的主轴热误差也是影响加工精度的重要因素。本文结合灰色理论和神经网络各自对数据处理的优点，提出三种不同结构的灰色神经网络热误差预测模型，即：串联型、并联型和嵌入型灰色神经网络。在串联型灰色神经网络中，首先使用灰色模型对机床关键测点的温度数据和热误差数据进行预处理，得到近似一阶动态微分模型，然后把多个不同灰色模型的预测结果输入到BP神经网络进行非线性拟合优化，利用BP神经网络误差反向传播的学习方法对模型进行训练，调节网络节点的权值和阈值，从而得到最终的预测模型；在并联型灰色神经网络中，先由灰色模型和神经网络分别对主轴热误差进行预测，然后采用一定的加权组合方式，按照目标预测精度优化模型的加权系数，从而得到最终的预测结果；而嵌入型灰色神经网络则是借鉴了灰色理论对数据处理的思想，在神经网络输入层前增加灰化层，在输出层后增加白化层，通过对神经网络拓扑结构的改进，达到弱化原始数据随机性、提高预测模型鲁棒性和容错能力的目标。通过与传统灰色模型和神经网络进行试验结果对比表明：上述三种结构的灰色神经网络模型均提高了预测精度，且具有对原始数据要求低、计算简便、鲁棒性强等优点，可用于复杂工况下的机床主轴热误差实时预测和补偿。
（5）介绍了基于外部机械原点偏移功能的误差补偿实施基本原理，并结合生产线上多台机床同时需要误差补偿的需求，研发了基于网络群控的机床误差实时补偿系统。从整体架构上，可将该补偿系统分为两大部分：主控中心PC和各机床PMC（Programmable Machine Controller）控制单元。前者的运算能力强，存储空间大，因此主要负责各机床空间误差补偿值的计算；后者和CNC（Computer Numerical Control）系统紧密相连，具有很高的数据交互实时性，因此主要负责查询机床当前坐标位置和查表调用各进给轴当前所需补偿值。网络群控误差补偿系统的主从结构充分利用了各自在运算能力方面的特点，不仅适于进行复杂的模型计算，而且满足误差补偿的实时性要求。此外，主控中心PC和数控机床PMC之间通过以太网通讯协议及Fanuc提供的FOCAS（Fanuc Open CNC API Specifications）动态链接函数进行数据交互，具有硬件端口占用资源少、数据传输速度快、可靠性高、功能模块连接简便和易于扩展的特点。
（6）结合本文提出的误差测量方法、建模方法和基于网络群控的机床误差实时补偿系统设计了两类试验。第一类试验是对单台五轴加工中心进行误差补偿试验，首先用激光干涉仪、球杆仪等测量仪器对机床平动轴和旋转轴引入的误差元素进行测量，并建立适用于不同温度条件的误差元素模型，将其代入到综合误差模型中计算出在机床空间范围内施加给各进给轴的误差补偿值，最后通过补偿系统将补偿值送给数控系统完成误差补偿步骤，试验结果表明，通过补偿可以大幅提高该机床的空间运动精度；第二类试验是同时对多台（两台及以上）数控机床进行补偿试验，在得到各机床误差模型的基础上，通过网络群控实时补偿系统和各机床间的数据交互，完成误差补偿步骤，试验结果表明，该系统可以实现对多台机床进行同时补偿，批量提高群控网络内所有机床的运动精度，和传统误差补偿模式相比，具有较高的补偿效率。通过以上两类试验可以发现：无论在何种应用场合中，基于网络群控的机床误差实时补偿系统均可大幅提高机床性能，而且工作稳定可靠，具有较高的实用价值和推广意义。
Error compensation technology is one of the most crucial methods to improve themachining accuracy of computer numerical control (CNC) machine tools, with which threeresearch directions related are: error measurement and identification, error modelingmethodology, and error compensation implementation method. This thesis is sponsored byChinese National Science and Technology Key Special Project, the National ScienceFoundation Project, and the Specialized Research Fund for the Doctoral Program of HigherEducation. Some experiments were carried out on a five-axis machining center and twothree-axis vertical machining centers, in order to conduct the research on efficient errormeasurement, accurate error modeling, and real-time error compensation. In addition, areal-time error compensation system based on Ethernet distributed control method isdeveloped to compensate for multiple machine tools simultaneously in order to improvethe machine performance under different temperature conditions.
The main contents of this thesis are described as follows:
(1) According to the structural kinematic features of different kinds of five-axis machinetools, a universal kinematic model is established based on the homogenous transformationmatrix method so as to describe the kinematic chain transfer from the tool coordinatesystem to the workpiece coordinate system. Furthermore, a universal volumetric errormodel can be obtained based on the analysis of error components possibly induced by themain machine links and the using of rigid motion theory. Then the volumetric errorcompensation values can be calculated within the machine working volume. In order tomeet the requirement of real-time compensation, a data processing strategy, in whichdifferent error components are classified and modeled with different methodologiesaccording their regularity of distribution, is proposed to simplify the volumetric errormodel aiming at increasing the calculation speed.
(2) An error measurement and identification method based on the double ball-bar (DBB) instrument is proposed according to the moving characteristic and error distribution of therotary axis. Through the MATLAB simulation experiment, different error’s influence onthe DBB measuring patterns can be obtained. A real DBB measuring experiment wasconducted on a five-axis machine tool, the results of which showed that the proposedmeasuring method is able to measure five error components simultaneously with highefficiency and accuracy. Moreover, this measuring method could be carried out underdifferent working conditions to obtain the error variations with temperature. A thermalerror modeling method based on the natural exponential model is developed to predict andcompensate for the thermal errors of the rotary axis.
(3) Either on three-axis or five-axis machine tools, translational axes are the mostimportant links, of which the error components are the crucial sources of machineinaccuracy. The laser interferometer can be employed to measure the positioning error andthe straightness error of translational axes. The measurement results show that thepositioning error is obviously affected by the temperature field, especially by the variationsof the ambient temperature and screw nut temperature. Based on the analysis of positioningerrors under different temperature conditions, a natural exponential model is established todescribe the non-linear relationship between the thermal term in the positioning error andthe temperature variables. Compared with a multiple regression analysis model, theproposed modeling method performs better in terms of prediction accuracy and robustness.As to the straightness error, it has relatively small value compared with the positioningerror. In addition, it is almost independent from the temperature variations. Therefore, itcan be regarded as the pure geometric error and modeled by a polynomial with the positioncoordinate.
(4) Much heat is produced during the high-speed rotation of the spindle, so the thermalerror caused by the thermal deformation is one of the major sources of machine inaccuracy.This thesis combines the advantages of both grey model (GM) and artificial neural networkin terms of data processing to propose a novel error prediction model, namely grey neuralnetwork (GNN). According to the structure of the prediction model, three types of GNNare introduced and analyzed in this thesis: serial grey neural network (SGNN), parallelgrey neural network (PGNN), and inlaid grey neural network (IGNN). In SGNN, somegrey models with different length of data sequence firstly play an important role inpreprocessing the original thermal errors and temperature data, establishing a first-orderdifferential equation. Then, the neural network receives the predicted thermal errors fromdifferent grey models to make the nonlinear optimization by adjusting the weight and threshold of the network neurons based on the back propagation (BP) training algorithm.After these two steps, a complete error model is established to predict the final thermalerror of the machine tool spindle. In PGNN, one GM and one BP network are utilized topredict the thermal error, respectively. Then an effective combination algorithm combinesthe results of GM with BP to output the final data as the thermal error compensation value.In IGNN, the topological structure of the BP network is optimized by adding a grey layerbefore the input layer and a white layer after the output layer, in order to reduce therandomness of the original data and enhance the robustness and the fault-tolerant ability.Compared with the traditional GM and BP network, these three types of GNN prove betterin terms of prediction accuracy, calculation convenience and robustness. What’s more, theyrequire less to the original data. Thus, the new proposed models are properly applied todifferent working conditions to compensate for the spindle thermal error of machine tools.
(5) A real-time error compensation system based on Ethernet distributed control methodis developed to compensate for multiple machine tools simultaneously, in which theexternal machine zero point shift (EMZPS) function is utilized as the implementationinterface between the compensation system and the CNC machine tools. From the overallarchitecture, the compensation system is composed of two main parts: the PC controlcenter and the programmable machine controller (PMC). The former one has fastcomputation speed and large data storage, so it is responsible for calculating the volumetricerror compensation values of different machine tools. The latter one is directly connectedwith CNC system, so it is responsible for the real-time data processing parts, i.e. inquiringthe machine position coordinate and looking up the corresponding compensation value inthe data table stored in PMC. The proposed Ethernet distributed error compensation systemcan make full use of the data computation characteristic of both PC and PMC. It is not onlycapable for the complex mathematical model calculation, but also meets the requirement ofreal-time error compensation. In addition, the PC control center and the machine tool PMCis connected through the Ethernet cable under the Fanuc Open CNC API Specifications(FOCAS) protocol, which is featured by high data transmission speed, strong reliability,easy hardware connection, and convenient module expansion.
(6) Two kinds of error compensation experiment were conducted by utilizing the errormeasuring method, modeling methodology, and error compensation implementationtechnique proposed in this thesis. The first kind of experiment was conducted on afive-axis machining center with a rotary table. Firstly, a laser interferometer and a DBBinstrument were employed to conduct the error measurement on translational and rotary axes. Then, error component models were established under different temperatureconditions. The error compensation value applied to each feed axis could be obtainedthrough the volumetric error model, which includes the main error components of themachine. At last, the error compensation was implemented through the developedcompensation system. Experimental results showed that the volumetric accuracy wasimproved significantly after error compensation. The second kind of experiment wasconducted on multiple CNC machine tools. Error models for each machine tool should beobtained firstly, and then different machine tools could be compensated through theEthernet distributed control system. Experimental results showed that the proposed errorcompensation system could be utilized to improve the accuracy of multiple machine tools.It has much higher compensation efficiency compared with the traditional errorcompensation methods. Both the above experiments proved that the proposed errormeasuring method, error-modeling methodology, and the Ethernet distributed errorcompensation system were of significant use to improve the machine tool performanceunder different temperature conditions. This compensation system can work stability;therefore, it has high practical value and significance for popularization.
引文
[1]李圣怡.精密和超精密机床精度建模技术[M].国防科技大学出版社:2007.
[2]盛伯浩,唐华.数控机床误差的综合动态补偿技术[J].制造技术与机床.1997,(6):19-21.
[3]赵昌龙.高速加工中心主轴及刀具系统热误差综合补偿技术[D].博士学位论文,吉林大学.2010.
[4] Pahk, H., Lee, S. Thermal error measurement and real time compensation systemfor the CNC machine tools incorporating the spindle thermal error and the feed axisthermal error[J]. The International Journal of Advanced Manufacturing Technology.2002,20(7):487-494.
[5] Bryan, J. International status of thermal error research[J]. CIRP Annals-Manufacturing Technology.1990,39(2):645-656.
[6] Schwenke, H., Knapp, W., Haitjema, H., etc. Geometric error measurement andcompensation of machines--An update[J]. CIRP Annals-ManufacturingTechnology.2008,57(2):660-675.
[7] ISO230-2: Test code for machine tools-Part2: Determination of accuracy andrepeatability of positioning numerically controlled axes[S],2006
[8] GB/T17421.2:机床检验通则-第2部分：数控轴线的定位精度和重复定位精度的确定[S],2000
[9] Zhang, G., Zang, Y. A method for machine geometry calibration using1-D ballarray[J]. CIRP Annals-Manufacturing Technology.1991,40(1):519-522.
[10] GB/T17421.1:机床检验通则-第1部分：在无负荷或精加工条件下机床的几何精度[S],1998
[11]赵东升,贾敏强,孙会庆,等.激光干涉仪测量直线度误差因素分析[J].计量技术.2010,(3):32-35.
[12]张立新,黄玉美,乔雁龙.并联轴直线运动直线度的检测与误差补偿[J].机械工程学报.2008,44(9):220-224.
[13] Chen, Q., Lin, D., Wu, J., etc. Straightness/coaxiality measurement system withtransverse Zeeman dual-frequency laser[J]. Measurement Science and Technology.2005,162030.
[14] Sartori, S., Zhang, G. Geometric error measurement and compensation ofmachines[J]. CIRP Annals-Manufacturing Technology.1995,44(2):599-609.
[15] Bryan, J., Carter, D., Thompson, S. Angle interferometer cross-axis errors[J]. CIRPAnnals-Manufacturing Technology.1994,43(1):453-456.
[16] ISO230-1: Test code for machine tools-Part1: Geometric accuracy of machinesoperating under no-load or finishing conditiongs[S],1996
[17] Ibaraki, S., Knapp, W. Indirect measurement of volumetric accuracy for rhree-axisand five-axis machine tools: A Review[J]. International Journal of AutomationTechnology.2012,6(2):110-124.
[18] Kunzmann, H., Trapet, E., W ldele, F. A uniform concept for calibration,acceptance test, and periodic inspection of coordinate measuring machines usingreference objects[J]. CIRP Annals-Manufacturing Technology.1990,39(1):561-564.
[19] Trapet, E., Aguilar Martín, J.J., Yagüe, J.A., etc. Self-centering probes with parallelkinematics to verify machine-tools[J]. Precision Engineering.2006,30(2):165-179.
[20] Van Chung, N., Bohez, E., Belforte, G., etc. A new conceptual approach forsystematic error correction in CNC machine tools minimizing worst case predictionerror[J]. The International Journal of Advanced Manufacturing Technology.2012,60(1):211-224.
[21] Bringmann, B., Küng, A., Knapp, W. A measuring artefact for true3D machinetesting and calibration[J]. CIRP Annals-Manufacturing Technology.2005,54(1):471-474.
[22] Hong, C., Ibaraki, S., Matsubara, A. Influence of position-dependent geometricerrors of rotary axes on a machining test of cone frustum by five-axis machinetools[J]. Precision Engineering.2011,35(1):1-11.
[23] Ibaraki, S., Sawada, M., Matsubara, A., etc. Machining tests to identify kinematicerrors on five-axis machine tools[J]. Precision Engineering.2010,34(3):387-398.
[24] Bryan, J. A simple method for testing measuring machines and machine tools Part1:Principles and applications[J]. Precision Engineering.1982,4(2):61-69.
[25] Bryan, J. A simple method for testing measuring machines and machine tools. Part2: Construction details[J]. Precision Engineering.1982,4(3):125-138.
[26] Florussen, G., Delbressine, F., Van de Molengraft, M., etc. Assessing geometricalerrors of multi-axis machines by three-dimensional length measurements[J].Measurement.2001,30(4):241-255.
[27] Tsutsumi, M., Saito, A. Identification of angular and positional deviations inherentto5-axis machining centers with a tilting-rotary table by simultaneous four-axiscontrol movements[J]. International Journal of Machine Tools and Manufacture.2004,44(12-13):1333-1342.
[28] Lei, W.T., Sung, M.P., Liu, W.L., etc. Double ballbar test for the rotary axes offive-axis CNC machine tools[J]. International Journal of Machine Tools andManufacture.2007,47(2):273-285.
[29] Lei, W.T., Paung, I.M., Yu, C.C. Total ballbar dynamic tests for five-axis CNCmachine tools[J]. International Journal of Machine Tools and Manufacture.2009,49(6):488-499.
[30] Zargarbashi, S.H.H., Mayer, J.R.R. Assessment of machine tool trunnion axismotion error, using magnetic double ball bar[J]. International Journal of MachineTools and Manufacture.2006,46(14):1823-1834.
[31] Khan, A.W., Chen, W. A methodology for error characterization and quantificationin rotary joints of multi-axis machine tools[J]. The International Journal ofAdvanced Manufacturing Technology.2010,51(9):1009-1022.
[32]张大卫,商鹏,田延岭,等.五轴数控机床转动轴误差元素的球杆仪检测方法[J].中国机械工程.2008,19(022):2737-2741.
[33]王民,胡建忠,昝涛,等.五轴数控机床运动误差建模与测试技术[J].北京工业大学学报.2010,(004):433-439.
[34] Zhu, S., Ding, G., Qin, S., etc. Integrated geometric error modeling, identificationand compensation of CNC machine tools[J]. International Journal of Machine Toolsand Manufacture.2012,52(1):24-29.
[35]商鹏.基于球杆仪的高速五轴数控机床综合误差建模与检测方法[D].博士学位论文,天津大学.2008.
[36]商鹏.基于球杆仪测量技术的三轴数控机床综合误差检测[D].硕士学位论文,天津大学2006.
[37] Weikert, S. R-Test, a new device for accuracy measurements on five axis machinetools[J]. CIRP Annals-Manufacturing Technology.2004,53(1):429-432.
[38] Du, Z., Zhang, S., Hong, M. Development of a multi-step measuring method formotion accuracy of NC machine tools based on cross grid encoder[J]. InternationalJournal of Machine Tools and Manufacture.2010,50(3):270-280.
[39] ISO230-6: Test code for machine tools-Part6: Determination of lineardisplacement accuracy on body and face diagonals[S],2002
[40] Shen, J., Zhang, H., Cao, H.T., etc. Volumetric positioning errors of CNCmachining tools and laser sequential step diagonal measurement[J]. KeyEngineering Materials.2006,31598-102.
[41]曹洪涛,沈金华,张宏韬,等.三维空间定位精度的高效测量与补偿及校验[J].现代制造工程.2006,(1):17-20.
[42]王正平.用激光向量测量技术测量和补偿体积定位误差[J].计量技术.2001,1010-13.
[43]王正平,杨建国.加工中心三维体积定位误差的理论及其激光测量[J].世界制造技术与装备市场.2006,(5):91-95.
[44] Chapman, M.A.V. Limitations of laser diagonal measurements[J]. PrecisionEngineering.2003,27(4):401-406.
[45] Svoboda, O. Testing the diagonal measuring technique[J]. Precision Engineering.2006,30(2):132-144.
[46] Bossmanns, B., Tu, J.F. A power flow model for high speed motorizedspindles—heat generation characterization[J]. Journal of Manufacturing Scienceand Engineering.2001,123494.
[47] Min, X., Shuyun, J., Ying, C. An improved thermal model for machine toolbearings[J]. International Journal of Machine Tools and Manufacture.2007,47(1):53-62.
[48] Min, X., Jiang, S. A thermal model of a ball screw feed drive system for a machinetool[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal ofMechanical Engineering Science.2011,225(1):186-193.
[49] Lo, C. H. Real-time error compensation on machine tools through optimalthermal error modeling[D]. Ph.D., the University of Michigan1994.
[50] Yang, J., Yuan, J., Ni, J. Thermal error mode analysis and robust modeling for errorcompensation on a CNC turning center[J]. International Journal of Machine Toolsand Manufacture.1999,39(9):1367-1381.
[51] Zhao, H., Yang, J., Shen, J. Simulation of thermal behavior of a CNC machine toolspindle[J]. International Journal of Machine Tools and Manufacture.2007,47(6):1003-1010.
[52] Zhu, J., Ni, J., Shih, A. J. Robust machine tool thermal error modeling throughthermal mode concept[J]. Journal of Manufacturing Science and Engineering.2008,(130)061006.
[53] Fraser, S. Control-oriented modeling of thermal deformation of machine toolsbased on inverse solution of time-variant thermal loads with delayed response[J].Journal of Manufacturing Science and Engineering.2004,126286.
[54]张琨,张毅,侯广锋,等.基于热模态分析的热误差温度测点优化选择[J].机床与液压.2012,40(7):1-3.
[55] Ni, J. CNC machine accuracy enhancement through real-time errorcompensation[J]. Journal of Manufacturing Science and Engineering.1997,119717-725.
[56] Yuan, J., Ni, J., Wu, S. Real-time compensation for time-variant volumetric error ona machining center[J]. ASME Journal of Engineering for Industry.1993,114472-479.
[57] Yang, J., Ren, Y., Du, Z. An application of real-time error compensation on an NCtwin-spindle lathe[J]. Journal of Materials Processing Technology.2002,129(1):474-479.
[58] Tseng, P.C., Ho, J.L. A study of high-precision CNC lathe thermal errors andcompensation[J]. The International Journal of Advanced Manufacturing Technology.2002,19(11):850-858.
[59]沈金华,李永祥,鲁志政,等.数控车床几何和热误差综合实时补偿方法应用[J].四川大学学报:工程科学版.2008,40(1):163-166.
[60]王维,杨建国,姚晓栋,等.数控机床几何误差与热误差综合建模及其实时补偿[J].机械工程学报.2012,(07):165-170+179.
[61] Chen, J.S., Yuan, J.X., Ni, J., etc. Real-time compensation for time-variantvolumetric errors on a maching center[J]. J Eng Ind Trans ASME.1993,115(4):472-479.
[62] Chen, J. S., Yuan, J., Ni, J., etc. Real time compensation of time-variant volumetricerror on a machining center[J]. Sens Cont Qual Iss Manufact ASME.1991,241-253.
[63] Ramesh, R., Mannan, M. A.. Poo, A. N. Error compensation in machine tools-areview: Part II: thermal errors[J]. International Journal of Machine Tools andManufacture.2000,40(9):1257-1284.
[64] Chen, J. S., Ling, C.C. Improving the machine accuracy through machine toolmetrology and error correction[J]. The International Journal of AdvancedManufacturing Technology.1996,11(3):198-205.
[65] Yang, H., Ni, J. Dynamic neural network modeling for nonlinear, nonstationarymachine tool thermally induced error[J]. International Journal of Machine Toolsand Manufacture.2005,45(4-5):455-465.
[66] Shen, J.H., Yang, J.G. Application of partial least squares neural network in thermalerror modeling for CNC machine tool[J]. Key Engineering Materials.2009,39230-34.
[67] Mize, C.D., Ziegert, J.C. Neural network thermal error compensation of amachining center[J]. Precision Engineering.2000,24(4):338-346.
[68] Yang, S., Yuan, J., Ni, J. The improvement of thermal error modeling andcompensation on machine tools by CMAC neural network[J]. International Journalof Machine Tools and Manufacture.1996,36(4):527-537.
[69]张宏韬,杨建国. RBF网络在线建模方法在热误差实时补偿技术中的应用[J].上海交通大学学报.2009,(005):807-810.
[70] Li, X. Real-time prediction of workpiece errors for a CNC turning centre, Part2.Modelling and estimation of thermally induced errors[J]. The International Journalof Advanced Manufacturing Technology.2001,17(9):654-658.
[71] Tseng, P.C., Chen, S.L. The neural-fuzzy thermal error compensation controller onCNC machining center[J]. JSME International Journal Series C.2002,45(2):470-478.
[72]邓聚龙.灰理论基础[M].华中科技大学出版社:2002.
[73] Deng, J.L. The basis of grey theory[J]. Huazhong Science&Technology.2002,
[74] Deng, J.L. Introduction to grey system theory[J]. The Journal of Grey System.1989,1(1):1-24.
[75]李永祥,杨建国.灰色系统模型在机床热误差建模中的应用[J].中国机械工程.2007,17(23):2439-2442.
[76]闫嘉钰,杨建国.灰色GM(X, N)模型在数控机床热误差建模中的应用[J].中国机械工程.2009,(011):1297-1300.
[77]李永祥,杨建国,郭前建,等.数控机床热误差的混合预测模型及应用[J].上海交通大学学报.2006,40(012):2030-2033.
[78] Wang, K.C. The grey-based artificial intelligence modeling of thermal error formachine tools[J]. Journal of Grey System.2010,22(4):353-366.
[79] Wang, K.C., Tseng, P.C., Lin, K.M. Thermal error modeling of a machining centerusing grey system theory and adaptive network-based fuzzy inference system[J].JSME International Journal Series C.2006,49(4):1179-1187.
[80] Li, Y.X., Yang, J.G., Gelvis, T., etc. Optimization of measuring points for machinetool thermal error based on grey system theory[J]. The International Journal ofAdvanced Manufacturing Technology.2008,35(7):745-750.
[81] Yan, J., Yang, J. Application of synthetic grey correlation theory on thermal pointoptimization for machine tool thermal error compensation[J]. The InternationalJournal of Advanced Manufacturing Technology.2009,43(11):1124-1132.
[82]林伟青,傅建中,陈子辰,等.数控机床热误差的动态自适应加权最小二乘支持矢量机建模方法[J].机械工程学报.2009,45(003):178-182.
[83] Ramesh, R., Mannan, M., Poo, A., etc. Thermal error measurement and modellingin machine tools. Part II. Hybrid Bayesian Network--support vector machinemodel[J]. International Journal of Machine Tools and Manufacture.2003,43(4):405-419.
[84] Ramesh, R., Mannan, M., Poo, A. Thermal error measurement and modelling inmachine tools.:: Part I. Influence of varying operating conditions[J]. InternationalJournal of Machine Tools and Manufacture.2003,43(4):391-404.
[85] Hartenberg, R., Denavit, J. A kinematic notation for lower pair mechanisms basedon matrices[J]. Journal of Applied Mechanics.1955,77(2):215–221.
[86] Paul, R. P. Robot manipulators: mathematics, programming, and control[M]. MITPress:1981.
[87] Suh, S. H., Lee, J.J. Five-axis part machining with three-axis CNC machine andindexing table[J]. Journal of Manufacturing Science and Engineering.1998,120120.
[88] Kiridena, V., Ferreira, P. Mapping the effects of positioning errors on the volumetricaccuracy of five-axis CNC machine tools[J]. International Journal of Machine Toolsand Manufacture.1993,33(3):417-437.
[89] Mahbubur, R., Heikkala, J., Lappalainen, K., etc. Positioning accuracyimprovement in five-axis milling by post processing[J]. International Journal ofMachine Tools and Manufacture.1997,37(2):223-236.
[90] Bohez, E.L.J. Compensating for systematic errors in5-axis NC machining[J].Computer-Aided Design.2002,34(5):PII S0010-4485(01)00111-7.
[91] Srivastava, A.K., Veldhuis, S.C., Elbestawit, M.A. Modelling geometric andthermal errors in a five-axis CNC machine tool[J]. International Journal of MachineTools and Manufacture.1995,35(9):1321-1337.
[92]任永强,杨建国.五轴数控机床综合误差补偿解耦研究[J].机械工程学报.2004,40(2):55-59.
[93] Hsu, Y.Y., Wang, S.S. A new compensation method for geometry errors of five-axismachine tools[J]. International Journal of Machine Tools and Manufacture.2007,47(2):352-360.
[94]张宏韬,杨建国,姜辉,等.双转台五轴数控机床误差实时补偿[J].机械工程学报.2010,(021):143-148.
[95] Khan, A. W., Chen, W. A methodology for systematic geometric error compensationin five-axis machine tools[J]. The International Journal of Advanced ManufacturingTechnology.2011,53615-628.
[96] Ekinci, T., Mayer, J. Relationships between straightness and angular kinematicerrors in machines[J]. International Journal of Machine Tools and Manufacture.2007,47(12-13):1997-2004.
[97]张兆瑞.精密丝杠车床校正尺的修理工艺[J].机械工艺师.1983,(11):20-21.
[98]李林山.螺丝磨床丝杠延寿法(MM582螺丝磨床顶针移动扶架)[J].机床与工具.1958,(11):43.
[99]徐时金.提高滚齿机凸轮摆杆机构校正精度的方法[J].四川机械.1981,(05):1-8+65.
[100]吴丹,谢晓丹,王先逵.快速刀具伺服机构研究进展[J].中国机械工程.2008,19(011):1379-1385.
[101] Sze-Wei, G., Han-Seok, L., Rahman, M., etc. A fine tool servo system for globalposition error compensation for a miniature ultra-precision lathe[J]. InternationalJournal of Machine Tools and Manufacture.2007,47(7-8):1302-1310.
[102] Okazaki, Y. A micro-positioning tool post using a piezoelectric actuator fordiamond turning machines[J]. Precision Engineering.1990,12(3):151-156.
[103] Patterson, S., Magrab, E. Design and testing of a fast tool servo for diamondturning[J]. Precision Engineering.1985,7(3):123-128.
[104] Zhu, W.H., Jun, M.B., Altintas, Y. A fast tool servo design for precision turning ofshafts on conventional CNC lathes[J]. International Journal of Machine Tools andManufacture.2001,41(7):953-965.
[105] Kim, H.S., Kim, E.J. Feed-forward control of fast tool servo for real-timecorrection of spindle error in diamond turning of flat surfaces[J]. InternationalJournal of Machine Tools and Manufacture.2003,43(12):1177-1183.
[106] Sze-Wei, G., Han-Seok, L., Rahman, M., etc. A fine tool servo system for globalposition error compensation for a miniature ultra-precision lathe[J]. InternationalJournal of Machine Tools and Manufacture.2007,47(7):1302-1310.
[107] Gao, W., Tano, M., Araki, T., etc. Measurement and compensation of error motionsof a diamond turning machine[J]. Precision Engineering.2007,31(3):310-316.
[108]张冲,张东升,陶涛,等.西门子840D/810D几何误差补偿研究[J].机械工程师.2011,(1):32-34.
[109]刘朝华,戴怡,石秀敏,等.西门子840D数控系统温度误差补偿的研究与应用[J].机床与液压.2009,37(009):12-13.
[110]刘志兵.西门子840D系统温度补偿功能在数控机床上的开发应用[J].机床电器.2005,32(4):19-21.
[111] Yee, K., Gavin, R. Implementing Fast Part Probing and Error Compensation onMachine Tools[R].1990;
[112]张虎,周云飞,唐小琦,等.数控加工中心误差G代码补偿技术[J].华中科技大学学报(自然科学版).2002,30(2):
[113]吴宇刚,王炯槐.卧式加工中心机床HMC1000按ISO230—6标准检测和G代码补偿[J].数控机床市场.2010,(004):75-83.
[114] Cui, G., Lu, Y., Li, J., etc. Geometric error compensation software system for CNCmachine tools based on NC program reconstructing[J]. The International Journal ofAdvanced Manufacturing Technology.2012,1-12.
[115] Shen, H., Fu, J., He, Y., etc. On-line asynchronous compensation methods forstatic/quasi-static error implemented on CNC machine tools[J]. InternationalJournal of Machine Tools and Manufacture.2012,60(0):14-26.
[116] Eskandari, S., Arezoo, B.. Abdullah, A. Positional, geometrical, and thermal errorscompensation by tool path modification using three methods of regression, neuralnetworks, and fuzzy logic[J]. The International Journal of Advanced ManufacturingTechnology.2012,1-15.
[117]杨建国,张宏韬,童恒超,等.数控机床热误差实时补偿应用[J].上海交通大学学报.2005,39(009):1389-1392.
[118]姜辉,孙翰英,范嘉桢,等.基于FANUC0i系统外部坐标原点偏移功能的数控机床误差补偿研究[J].机械制造.2009,47(7):73-76.
[119]张宏韬.双转台五轴数控机床误差的动态实时补偿研究[D].博士学位论文,上海交通大学.2011.
[120] Wang, W., Zhang, Y., Yang, J.G. Modeling of compound errors for CNC machinetools[J]. Advanced Materials Research.2012,4721796-1799.
[121] Cui, G., Lu, Y., Gao, D., etc. A novel error compensation implementing strategy andrealizing on Siemens840D CNC systems[J]. The International Journal of AdvancedManufacturing Technology.2011,1-14.
[122] Chen, F. On the structural configuration synthesis and geometry of machiningcentres[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journalof Mechanical Engineering Science.2001,215(6):641-652.
[123] ISO841: Industrial automation systems and integration-Numerical control ofmachines-Coordinate system and motion nomenclature[S],2001
[124] Creighton, E., Honegger, A., Tulsian, A., etc. Analysis of thermal errors in ahigh-speed micro-milling spindle[J]. International Journal of Machine Tools andManufacture.2010,50(4):386-393.
[125]李永祥,童恒超,曹洪涛,等.数控机床热误差的时序分析法建模及其应用[J].四川大学学报:工程科学版.2006,38(002):74-78.
[126] Lai, J. M., Liao, J. S., Chieng, W. H. Modeling and analysis of nonlinear guidewayfor double-ball bar (DBB) measurement and diagnosis[J]. International Journal ofMachine Tools and Manufacture.1997,37(5):687-707.
[127]任永强.数控机床误差高效测量,建模及补偿应用研究[D].博士学位论文,上海交通大学.2004.
[128] Jung, J.H., Choi, J.P., Lee, S.J. Machining accuracy enhancement by compensatingfor volumetric errors of a machine tool and on-machine measurement[J]. Journal ofMaterials Processing Technology.2006,174(1):56-66.
[129] Lee, E. S., Suh, S. H., Shon, J.W. A comprehensive method for calibration ofvolumetric positioning accuracy of CNC-machines[J]. The International Journal ofAdvanced Manufacturing Technology.1998,14(1):43-49.
[130] Lee, D.M., Zhu, Z., Lee, K.I., etc. Identification and measurement of geometricerrors for a five-axis machine tool with a tilting head using a double ball-bar[J].International Journal of Precision Engineering and Manufacturing.2011,12(2):337-343.
[131] Wang, M., Hu, J.Z., Zan, T., etc. Research on modeling and measurement techniqueof kinematic error particular to5-axis NC machining tool[J]. Journal of BeijingUniversity of Technology.2010,(4):433-439.
[132] Uddin, M.S., Ibaraki, S., Matsubara, A., etc. Prediction and compensation ofmachining geometric errors of five-axis machining centers with kinematic errors[J].Precision Engineering.2009,33(2):194-201.
[133] Dassanayake, M., Yamamoto, K., Tsutsumi, M., etc. Simultaneous five-axis motionfor identifying geometric deviations through simulation in machining centers with adouble pivot head[J]. Journal of Advanced Mechanical Design, Systems, andManufacturing.2008,2(1):47-58.
[134] Dassanayake, K.M.M., Tsutsumi, M., Saito, A. A strategy for identifying staticdeviations in universal spindle head type multi-axis machining centers[J].International Journal of Machine Tools and Manufacture.2006,46(10):1097-1106.
[135] Mayr, J., Jedrzejewski, J., Uhlmann, E., etc. Thermal issues in machine tools[J].CIRP Annals-Manufacturing Technology.2012, http://dx.doi.org/10.1016/j.cirp.2012.05.008
[136] ISO230-3: Test code for machine tools-Part3: Determination of thermal effects[S],2007
[137]刘思峰,郭天榜,党耀国.灰色系统理论及其应用[M].科学出版社,1999.
[138]阳红,方辉,刘立新,等.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.
[139] Fines, J. M., Agah, A. Machine tool positioning error compensation using artificialneural networks[J]. Engineering Applications of Artificial Intelligence.2008,21(7):1013-1026.
[140]王明涛.确定组合预测权系数最优近似解的方法研究[J].系统工程理论与实践.2000,20(3):104-109.
[141]杨建国.数控机床误差综合补偿技术及应用[D].博士学位论文,上海交通大学.1998.
[142]周文彬.基于FANUC0i MC的数控机床补偿研究[J].制造技术与机床.2010,(03):115-117.
[143]张琨. CK6430数控车床几何与热误差实时补偿研究[D].硕士学位论文,上海交通大学.2012.
[144]陈禹. FANUC系统窗口功能在数控曲轴磨床中的应用[J].精密制造与自动化.2010,(001):44-46.
[145]陈辉,奚叶敏. FANUC PMC窗口功能的应用[J].精密制造与自动化.2008,210-15.
[146]陈贤国. FANUC Ladder窗口功能等的使用[J].制造技术与机床.2005,(008):135-137.
[2]盛伯浩,唐华.数控机床误差的综合动态补偿技术[J].制造技术与机床.1997,(6):19-21.
[3]赵昌龙.高速加工中心主轴及刀具系统热误差综合补偿技术[D].博士学位论文,吉林大学.2010.
[4] Pahk, H., Lee, S. Thermal error measurement and real time compensation systemfor the CNC machine tools incorporating the spindle thermal error and the feed axisthermal error[J]. The International Journal of Advanced Manufacturing Technology.2002,20(7):487-494.
[5] Bryan, J. International status of thermal error research[J]. CIRP Annals-Manufacturing Technology.1990,39(2):645-656.
[6] Schwenke, H., Knapp, W., Haitjema, H., etc. Geometric error measurement andcompensation of machines--An update[J]. CIRP Annals-ManufacturingTechnology.2008,57(2):660-675.
[7] ISO230-2: Test code for machine tools-Part2: Determination of accuracy andrepeatability of positioning numerically controlled axes[S],2006
[8] GB/T17421.2:机床检验通则-第2部分：数控轴线的定位精度和重复定位精度的确定[S],2000
[9] Zhang, G., Zang, Y. A method for machine geometry calibration using1-D ballarray[J]. CIRP Annals-Manufacturing Technology.1991,40(1):519-522.
[10] GB/T17421.1:机床检验通则-第1部分：在无负荷或精加工条件下机床的几何精度[S],1998
[11]赵东升,贾敏强,孙会庆,等.激光干涉仪测量直线度误差因素分析[J].计量技术.2010,(3):32-35.
[12]张立新,黄玉美,乔雁龙.并联轴直线运动直线度的检测与误差补偿[J].机械工程学报.2008,44(9):220-224.
[13] Chen, Q., Lin, D., Wu, J., etc. Straightness/coaxiality measurement system withtransverse Zeeman dual-frequency laser[J]. Measurement Science and Technology.2005,162030.
[14] Sartori, S., Zhang, G. Geometric error measurement and compensation ofmachines[J]. CIRP Annals-Manufacturing Technology.1995,44(2):599-609.
[15] Bryan, J., Carter, D., Thompson, S. Angle interferometer cross-axis errors[J]. CIRPAnnals-Manufacturing Technology.1994,43(1):453-456.
[16] ISO230-1: Test code for machine tools-Part1: Geometric accuracy of machinesoperating under no-load or finishing conditiongs[S],1996
[17] Ibaraki, S., Knapp, W. Indirect measurement of volumetric accuracy for rhree-axisand five-axis machine tools: A Review[J]. International Journal of AutomationTechnology.2012,6(2):110-124.
[18] Kunzmann, H., Trapet, E., W ldele, F. A uniform concept for calibration,acceptance test, and periodic inspection of coordinate measuring machines usingreference objects[J]. CIRP Annals-Manufacturing Technology.1990,39(1):561-564.
[19] Trapet, E., Aguilar Martín, J.J., Yagüe, J.A., etc. Self-centering probes with parallelkinematics to verify machine-tools[J]. Precision Engineering.2006,30(2):165-179.
[20] Van Chung, N., Bohez, E., Belforte, G., etc. A new conceptual approach forsystematic error correction in CNC machine tools minimizing worst case predictionerror[J]. The International Journal of Advanced Manufacturing Technology.2012,60(1):211-224.
[21] Bringmann, B., Küng, A., Knapp, W. A measuring artefact for true3D machinetesting and calibration[J]. CIRP Annals-Manufacturing Technology.2005,54(1):471-474.
[22] Hong, C., Ibaraki, S., Matsubara, A. Influence of position-dependent geometricerrors of rotary axes on a machining test of cone frustum by five-axis machinetools[J]. Precision Engineering.2011,35(1):1-11.
[23] Ibaraki, S., Sawada, M., Matsubara, A., etc. Machining tests to identify kinematicerrors on five-axis machine tools[J]. Precision Engineering.2010,34(3):387-398.
[24] Bryan, J. A simple method for testing measuring machines and machine tools Part1:Principles and applications[J]. Precision Engineering.1982,4(2):61-69.
[25] Bryan, J. A simple method for testing measuring machines and machine tools. Part2: Construction details[J]. Precision Engineering.1982,4(3):125-138.
[26] Florussen, G., Delbressine, F., Van de Molengraft, M., etc. Assessing geometricalerrors of multi-axis machines by three-dimensional length measurements[J].Measurement.2001,30(4):241-255.
[27] Tsutsumi, M., Saito, A. Identification of angular and positional deviations inherentto5-axis machining centers with a tilting-rotary table by simultaneous four-axiscontrol movements[J]. International Journal of Machine Tools and Manufacture.2004,44(12-13):1333-1342.
[28] Lei, W.T., Sung, M.P., Liu, W.L., etc. Double ballbar test for the rotary axes offive-axis CNC machine tools[J]. International Journal of Machine Tools andManufacture.2007,47(2):273-285.
[29] Lei, W.T., Paung, I.M., Yu, C.C. Total ballbar dynamic tests for five-axis CNCmachine tools[J]. International Journal of Machine Tools and Manufacture.2009,49(6):488-499.
[30] Zargarbashi, S.H.H., Mayer, J.R.R. Assessment of machine tool trunnion axismotion error, using magnetic double ball bar[J]. International Journal of MachineTools and Manufacture.2006,46(14):1823-1834.
[31] Khan, A.W., Chen, W. A methodology for error characterization and quantificationin rotary joints of multi-axis machine tools[J]. The International Journal ofAdvanced Manufacturing Technology.2010,51(9):1009-1022.
[32]张大卫,商鹏,田延岭,等.五轴数控机床转动轴误差元素的球杆仪检测方法[J].中国机械工程.2008,19(022):2737-2741.
[33]王民,胡建忠,昝涛,等.五轴数控机床运动误差建模与测试技术[J].北京工业大学学报.2010,(004):433-439.
[34] Zhu, S., Ding, G., Qin, S., etc. Integrated geometric error modeling, identificationand compensation of CNC machine tools[J]. International Journal of Machine Toolsand Manufacture.2012,52(1):24-29.
[35]商鹏.基于球杆仪的高速五轴数控机床综合误差建模与检测方法[D].博士学位论文,天津大学.2008.
[36]商鹏.基于球杆仪测量技术的三轴数控机床综合误差检测[D].硕士学位论文,天津大学2006.
[37] Weikert, S. R-Test, a new device for accuracy measurements on five axis machinetools[J]. CIRP Annals-Manufacturing Technology.2004,53(1):429-432.
[38] Du, Z., Zhang, S., Hong, M. Development of a multi-step measuring method formotion accuracy of NC machine tools based on cross grid encoder[J]. InternationalJournal of Machine Tools and Manufacture.2010,50(3):270-280.
[39] ISO230-6: Test code for machine tools-Part6: Determination of lineardisplacement accuracy on body and face diagonals[S],2002
[40] Shen, J., Zhang, H., Cao, H.T., etc. Volumetric positioning errors of CNCmachining tools and laser sequential step diagonal measurement[J]. KeyEngineering Materials.2006,31598-102.
[41]曹洪涛,沈金华,张宏韬,等.三维空间定位精度的高效测量与补偿及校验[J].现代制造工程.2006,(1):17-20.
[42]王正平.用激光向量测量技术测量和补偿体积定位误差[J].计量技术.2001,1010-13.
[43]王正平,杨建国.加工中心三维体积定位误差的理论及其激光测量[J].世界制造技术与装备市场.2006,(5):91-95.
[44] Chapman, M.A.V. Limitations of laser diagonal measurements[J]. PrecisionEngineering.2003,27(4):401-406.
[45] Svoboda, O. Testing the diagonal measuring technique[J]. Precision Engineering.2006,30(2):132-144.
[46] Bossmanns, B., Tu, J.F. A power flow model for high speed motorizedspindles—heat generation characterization[J]. Journal of Manufacturing Scienceand Engineering.2001,123494.
[47] Min, X., Shuyun, J., Ying, C. An improved thermal model for machine toolbearings[J]. International Journal of Machine Tools and Manufacture.2007,47(1):53-62.
[48] Min, X., Jiang, S. A thermal model of a ball screw feed drive system for a machinetool[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal ofMechanical Engineering Science.2011,225(1):186-193.
[49] Lo, C. H. Real-time error compensation on machine tools through optimalthermal error modeling[D]. Ph.D., the University of Michigan1994.
[50] Yang, J., Yuan, J., Ni, J. Thermal error mode analysis and robust modeling for errorcompensation on a CNC turning center[J]. International Journal of Machine Toolsand Manufacture.1999,39(9):1367-1381.
[51] Zhao, H., Yang, J., Shen, J. Simulation of thermal behavior of a CNC machine toolspindle[J]. International Journal of Machine Tools and Manufacture.2007,47(6):1003-1010.
[52] Zhu, J., Ni, J., Shih, A. J. Robust machine tool thermal error modeling throughthermal mode concept[J]. Journal of Manufacturing Science and Engineering.2008,(130)061006.
[53] Fraser, S. Control-oriented modeling of thermal deformation of machine toolsbased on inverse solution of time-variant thermal loads with delayed response[J].Journal of Manufacturing Science and Engineering.2004,126286.
[54]张琨,张毅,侯广锋,等.基于热模态分析的热误差温度测点优化选择[J].机床与液压.2012,40(7):1-3.
[55] Ni, J. CNC machine accuracy enhancement through real-time errorcompensation[J]. Journal of Manufacturing Science and Engineering.1997,119717-725.
[56] Yuan, J., Ni, J., Wu, S. Real-time compensation for time-variant volumetric error ona machining center[J]. ASME Journal of Engineering for Industry.1993,114472-479.
[57] Yang, J., Ren, Y., Du, Z. An application of real-time error compensation on an NCtwin-spindle lathe[J]. Journal of Materials Processing Technology.2002,129(1):474-479.
[58] Tseng, P.C., Ho, J.L. A study of high-precision CNC lathe thermal errors andcompensation[J]. The International Journal of Advanced Manufacturing Technology.2002,19(11):850-858.
[59]沈金华,李永祥,鲁志政,等.数控车床几何和热误差综合实时补偿方法应用[J].四川大学学报:工程科学版.2008,40(1):163-166.
[60]王维,杨建国,姚晓栋,等.数控机床几何误差与热误差综合建模及其实时补偿[J].机械工程学报.2012,(07):165-170+179.
[61] Chen, J.S., Yuan, J.X., Ni, J., etc. Real-time compensation for time-variantvolumetric errors on a maching center[J]. J Eng Ind Trans ASME.1993,115(4):472-479.
[62] Chen, J. S., Yuan, J., Ni, J., etc. Real time compensation of time-variant volumetricerror on a machining center[J]. Sens Cont Qual Iss Manufact ASME.1991,241-253.
[63] Ramesh, R., Mannan, M. A.. Poo, A. N. Error compensation in machine tools-areview: Part II: thermal errors[J]. International Journal of Machine Tools andManufacture.2000,40(9):1257-1284.
[64] Chen, J. S., Ling, C.C. Improving the machine accuracy through machine toolmetrology and error correction[J]. The International Journal of AdvancedManufacturing Technology.1996,11(3):198-205.
[65] Yang, H., Ni, J. Dynamic neural network modeling for nonlinear, nonstationarymachine tool thermally induced error[J]. International Journal of Machine Toolsand Manufacture.2005,45(4-5):455-465.
[66] Shen, J.H., Yang, J.G. Application of partial least squares neural network in thermalerror modeling for CNC machine tool[J]. Key Engineering Materials.2009,39230-34.
[67] Mize, C.D., Ziegert, J.C. Neural network thermal error compensation of amachining center[J]. Precision Engineering.2000,24(4):338-346.
[68] Yang, S., Yuan, J., Ni, J. The improvement of thermal error modeling andcompensation on machine tools by CMAC neural network[J]. International Journalof Machine Tools and Manufacture.1996,36(4):527-537.
[69]张宏韬,杨建国. RBF网络在线建模方法在热误差实时补偿技术中的应用[J].上海交通大学学报.2009,(005):807-810.
[70] Li, X. Real-time prediction of workpiece errors for a CNC turning centre, Part2.Modelling and estimation of thermally induced errors[J]. The International Journalof Advanced Manufacturing Technology.2001,17(9):654-658.
[71] Tseng, P.C., Chen, S.L. The neural-fuzzy thermal error compensation controller onCNC machining center[J]. JSME International Journal Series C.2002,45(2):470-478.
[72]邓聚龙.灰理论基础[M].华中科技大学出版社:2002.
[73] Deng, J.L. The basis of grey theory[J]. Huazhong Science&Technology.2002,
[74] Deng, J.L. Introduction to grey system theory[J]. The Journal of Grey System.1989,1(1):1-24.
[75]李永祥,杨建国.灰色系统模型在机床热误差建模中的应用[J].中国机械工程.2007,17(23):2439-2442.
[76]闫嘉钰,杨建国.灰色GM(X, N)模型在数控机床热误差建模中的应用[J].中国机械工程.2009,(011):1297-1300.
[77]李永祥,杨建国,郭前建,等.数控机床热误差的混合预测模型及应用[J].上海交通大学学报.2006,40(012):2030-2033.
[78] Wang, K.C. The grey-based artificial intelligence modeling of thermal error formachine tools[J]. Journal of Grey System.2010,22(4):353-366.
[79] Wang, K.C., Tseng, P.C., Lin, K.M. Thermal error modeling of a machining centerusing grey system theory and adaptive network-based fuzzy inference system[J].JSME International Journal Series C.2006,49(4):1179-1187.
[80] Li, Y.X., Yang, J.G., Gelvis, T., etc. Optimization of measuring points for machinetool thermal error based on grey system theory[J]. The International Journal ofAdvanced Manufacturing Technology.2008,35(7):745-750.
[81] Yan, J., Yang, J. Application of synthetic grey correlation theory on thermal pointoptimization for machine tool thermal error compensation[J]. The InternationalJournal of Advanced Manufacturing Technology.2009,43(11):1124-1132.
[82]林伟青,傅建中,陈子辰,等.数控机床热误差的动态自适应加权最小二乘支持矢量机建模方法[J].机械工程学报.2009,45(003):178-182.
[83] Ramesh, R., Mannan, M., Poo, A., etc. Thermal error measurement and modellingin machine tools. Part II. Hybrid Bayesian Network--support vector machinemodel[J]. International Journal of Machine Tools and Manufacture.2003,43(4):405-419.
[84] Ramesh, R., Mannan, M., Poo, A. Thermal error measurement and modelling inmachine tools.:: Part I. Influence of varying operating conditions[J]. InternationalJournal of Machine Tools and Manufacture.2003,43(4):391-404.
[85] Hartenberg, R., Denavit, J. A kinematic notation for lower pair mechanisms basedon matrices[J]. Journal of Applied Mechanics.1955,77(2):215–221.
[86] Paul, R. P. Robot manipulators: mathematics, programming, and control[M]. MITPress:1981.
[87] Suh, S. H., Lee, J.J. Five-axis part machining with three-axis CNC machine andindexing table[J]. Journal of Manufacturing Science and Engineering.1998,120120.
[88] Kiridena, V., Ferreira, P. Mapping the effects of positioning errors on the volumetricaccuracy of five-axis CNC machine tools[J]. International Journal of Machine Toolsand Manufacture.1993,33(3):417-437.
[89] Mahbubur, R., Heikkala, J., Lappalainen, K., etc. Positioning accuracyimprovement in five-axis milling by post processing[J]. International Journal ofMachine Tools and Manufacture.1997,37(2):223-236.
[90] Bohez, E.L.J. Compensating for systematic errors in5-axis NC machining[J].Computer-Aided Design.2002,34(5):PII S0010-4485(01)00111-7.
[91] Srivastava, A.K., Veldhuis, S.C., Elbestawit, M.A. Modelling geometric andthermal errors in a five-axis CNC machine tool[J]. International Journal of MachineTools and Manufacture.1995,35(9):1321-1337.
[92]任永强,杨建国.五轴数控机床综合误差补偿解耦研究[J].机械工程学报.2004,40(2):55-59.
[93] Hsu, Y.Y., Wang, S.S. A new compensation method for geometry errors of five-axismachine tools[J]. International Journal of Machine Tools and Manufacture.2007,47(2):352-360.
[94]张宏韬,杨建国,姜辉,等.双转台五轴数控机床误差实时补偿[J].机械工程学报.2010,(021):143-148.
[95] Khan, A. W., Chen, W. A methodology for systematic geometric error compensationin five-axis machine tools[J]. The International Journal of Advanced ManufacturingTechnology.2011,53615-628.
[96] Ekinci, T., Mayer, J. Relationships between straightness and angular kinematicerrors in machines[J]. International Journal of Machine Tools and Manufacture.2007,47(12-13):1997-2004.
[97]张兆瑞.精密丝杠车床校正尺的修理工艺[J].机械工艺师.1983,(11):20-21.
[98]李林山.螺丝磨床丝杠延寿法(MM582螺丝磨床顶针移动扶架)[J].机床与工具.1958,(11):43.
[99]徐时金.提高滚齿机凸轮摆杆机构校正精度的方法[J].四川机械.1981,(05):1-8+65.
[100]吴丹,谢晓丹,王先逵.快速刀具伺服机构研究进展[J].中国机械工程.2008,19(011):1379-1385.
[101] Sze-Wei, G., Han-Seok, L., Rahman, M., etc. A fine tool servo system for globalposition error compensation for a miniature ultra-precision lathe[J]. InternationalJournal of Machine Tools and Manufacture.2007,47(7-8):1302-1310.
[102] Okazaki, Y. A micro-positioning tool post using a piezoelectric actuator fordiamond turning machines[J]. Precision Engineering.1990,12(3):151-156.
[103] Patterson, S., Magrab, E. Design and testing of a fast tool servo for diamondturning[J]. Precision Engineering.1985,7(3):123-128.
[104] Zhu, W.H., Jun, M.B., Altintas, Y. A fast tool servo design for precision turning ofshafts on conventional CNC lathes[J]. International Journal of Machine Tools andManufacture.2001,41(7):953-965.
[105] Kim, H.S., Kim, E.J. Feed-forward control of fast tool servo for real-timecorrection of spindle error in diamond turning of flat surfaces[J]. InternationalJournal of Machine Tools and Manufacture.2003,43(12):1177-1183.
[106] Sze-Wei, G., Han-Seok, L., Rahman, M., etc. A fine tool servo system for globalposition error compensation for a miniature ultra-precision lathe[J]. InternationalJournal of Machine Tools and Manufacture.2007,47(7):1302-1310.
[107] Gao, W., Tano, M., Araki, T., etc. Measurement and compensation of error motionsof a diamond turning machine[J]. Precision Engineering.2007,31(3):310-316.
[108]张冲,张东升,陶涛,等.西门子840D/810D几何误差补偿研究[J].机械工程师.2011,(1):32-34.
[109]刘朝华,戴怡,石秀敏,等.西门子840D数控系统温度误差补偿的研究与应用[J].机床与液压.2009,37(009):12-13.
[110]刘志兵.西门子840D系统温度补偿功能在数控机床上的开发应用[J].机床电器.2005,32(4):19-21.
[111] Yee, K., Gavin, R. Implementing Fast Part Probing and Error Compensation onMachine Tools[R].1990;
[112]张虎,周云飞,唐小琦,等.数控加工中心误差G代码补偿技术[J].华中科技大学学报(自然科学版).2002,30(2):
[113]吴宇刚,王炯槐.卧式加工中心机床HMC1000按ISO230—6标准检测和G代码补偿[J].数控机床市场.2010,(004):75-83.
[114] Cui, G., Lu, Y., Li, J., etc. Geometric error compensation software system for CNCmachine tools based on NC program reconstructing[J]. The International Journal ofAdvanced Manufacturing Technology.2012,1-12.
[115] Shen, H., Fu, J., He, Y., etc. On-line asynchronous compensation methods forstatic/quasi-static error implemented on CNC machine tools[J]. InternationalJournal of Machine Tools and Manufacture.2012,60(0):14-26.
[116] Eskandari, S., Arezoo, B.. Abdullah, A. Positional, geometrical, and thermal errorscompensation by tool path modification using three methods of regression, neuralnetworks, and fuzzy logic[J]. The International Journal of Advanced ManufacturingTechnology.2012,1-15.
[117]杨建国,张宏韬,童恒超,等.数控机床热误差实时补偿应用[J].上海交通大学学报.2005,39(009):1389-1392.
[118]姜辉,孙翰英,范嘉桢,等.基于FANUC0i系统外部坐标原点偏移功能的数控机床误差补偿研究[J].机械制造.2009,47(7):73-76.
[119]张宏韬.双转台五轴数控机床误差的动态实时补偿研究[D].博士学位论文,上海交通大学.2011.
[120] Wang, W., Zhang, Y., Yang, J.G. Modeling of compound errors for CNC machinetools[J]. Advanced Materials Research.2012,4721796-1799.
[121] Cui, G., Lu, Y., Gao, D., etc. A novel error compensation implementing strategy andrealizing on Siemens840D CNC systems[J]. The International Journal of AdvancedManufacturing Technology.2011,1-14.
[122] Chen, F. On the structural configuration synthesis and geometry of machiningcentres[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journalof Mechanical Engineering Science.2001,215(6):641-652.
[123] ISO841: Industrial automation systems and integration-Numerical control ofmachines-Coordinate system and motion nomenclature[S],2001
[124] Creighton, E., Honegger, A., Tulsian, A., etc. Analysis of thermal errors in ahigh-speed micro-milling spindle[J]. International Journal of Machine Tools andManufacture.2010,50(4):386-393.
[125]李永祥,童恒超,曹洪涛,等.数控机床热误差的时序分析法建模及其应用[J].四川大学学报:工程科学版.2006,38(002):74-78.
[126] Lai, J. M., Liao, J. S., Chieng, W. H. Modeling and analysis of nonlinear guidewayfor double-ball bar (DBB) measurement and diagnosis[J]. International Journal ofMachine Tools and Manufacture.1997,37(5):687-707.
[127]任永强.数控机床误差高效测量,建模及补偿应用研究[D].博士学位论文,上海交通大学.2004.
[128] Jung, J.H., Choi, J.P., Lee, S.J. Machining accuracy enhancement by compensatingfor volumetric errors of a machine tool and on-machine measurement[J]. Journal ofMaterials Processing Technology.2006,174(1):56-66.
[129] Lee, E. S., Suh, S. H., Shon, J.W. A comprehensive method for calibration ofvolumetric positioning accuracy of CNC-machines[J]. The International Journal ofAdvanced Manufacturing Technology.1998,14(1):43-49.
[130] Lee, D.M., Zhu, Z., Lee, K.I., etc. Identification and measurement of geometricerrors for a five-axis machine tool with a tilting head using a double ball-bar[J].International Journal of Precision Engineering and Manufacturing.2011,12(2):337-343.
[131] Wang, M., Hu, J.Z., Zan, T., etc. Research on modeling and measurement techniqueof kinematic error particular to5-axis NC machining tool[J]. Journal of BeijingUniversity of Technology.2010,(4):433-439.
[132] Uddin, M.S., Ibaraki, S., Matsubara, A., etc. Prediction and compensation ofmachining geometric errors of five-axis machining centers with kinematic errors[J].Precision Engineering.2009,33(2):194-201.
[133] Dassanayake, M., Yamamoto, K., Tsutsumi, M., etc. Simultaneous five-axis motionfor identifying geometric deviations through simulation in machining centers with adouble pivot head[J]. Journal of Advanced Mechanical Design, Systems, andManufacturing.2008,2(1):47-58.
[134] Dassanayake, K.M.M., Tsutsumi, M., Saito, A. A strategy for identifying staticdeviations in universal spindle head type multi-axis machining centers[J].International Journal of Machine Tools and Manufacture.2006,46(10):1097-1106.
[135] Mayr, J., Jedrzejewski, J., Uhlmann, E., etc. Thermal issues in machine tools[J].CIRP Annals-Manufacturing Technology.2012, http://dx.doi.org/10.1016/j.cirp.2012.05.008
[136] ISO230-3: Test code for machine tools-Part3: Determination of thermal effects[S],2007
[137]刘思峰,郭天榜,党耀国.灰色系统理论及其应用[M].科学出版社,1999.
[138]阳红,方辉,刘立新,等.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.
[139] Fines, J. M., Agah, A. Machine tool positioning error compensation using artificialneural networks[J]. Engineering Applications of Artificial Intelligence.2008,21(7):1013-1026.
[140]王明涛.确定组合预测权系数最优近似解的方法研究[J].系统工程理论与实践.2000,20(3):104-109.
[141]杨建国.数控机床误差综合补偿技术及应用[D].博士学位论文,上海交通大学.1998.
[142]周文彬.基于FANUC0i MC的数控机床补偿研究[J].制造技术与机床.2010,(03):115-117.
[143]张琨. CK6430数控车床几何与热误差实时补偿研究[D].硕士学位论文,上海交通大学.2012.
[144]陈禹. FANUC系统窗口功能在数控曲轴磨床中的应用[J].精密制造与自动化.2010,(001):44-46.
[145]陈辉,奚叶敏. FANUC PMC窗口功能的应用[J].精密制造与自动化.2008,210-15.
[146]陈贤国. FANUC Ladder窗口功能等的使用[J].制造技术与机床.2005,(008):135-137.