【作者】 张毅；

【导师】 杨建国；

【作者基本信息】 上海交通大学 ， 机械工程， 2013， 博士

【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。更多还原

【Abstract】 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.更多还原