基于指数函数的机床主轴热误差补偿模型

在对机床主轴进行热特性分析的基础上,建立了基于指数函数的机床主轴轴向热误差补偿模型。该热误差补偿模型建模时间短、资金成本低,能够方便快捷地应用到工厂生产环境中。通过实验获得不同转速下的主轴轴向热变形数据。使用回归分析和最小二乘法建立了稳定状态下主轴轴向变形量和时间常数的估计方程,进而建立了基于指数函数的热误差补偿模型。该模型可以预测不同转速下主轴的轴向变形量。通过实验证明了该热补偿模型在机床主轴恒速运转和变速运转两种工况下均具有较高的精度。     

基于OE-CM算法的机床主轴热误差建模与补偿分析

针对机床热误差建模过程中,误差信息不透明、数据特性不全面等不利因素,根据机床主轴热误差实验数据,分别采用GM(1,n) 模型和最小二乘支持向量机(LS-SVM)模型建立主轴热误差预测模型并进行线性叠加,然后采用预测有效度算法调整模型加权系数,建立了最优有效度复合预测模型（OE-CM）以获取最佳预测效果。在VXC-560型三轴数控机床上进行在线实验建模,实验结果表明：OE-CM具有预测精度高、鲁棒性好等特点,整体预测效果优于灰色GM(1,n)模型和LS-SVM模型,适合在复杂工况条件下对机床主轴热误差进行预测和补偿,为提高机床热误差补偿精度建立了理论模型。为了验证该预测模型的有效性,对所研究的机床主轴进行热误差在线补偿,机床主轴Z向最大误差从23.8μm减小到8μm,减幅达到66.4%,较好地提高了机床精度,具有一定的工程化推广前景。     

基于刀具偏转的机床主轴径向热误差的建模预测方法

为了有效地解决刀具实际加工位置对机床主轴径向误差的影响,提出了一种基于刀具偏转的机床主轴径向热误差建模预测方法。以立式加工中心HNC715主轴为研究对象,利用主轴分析仪对主轴径向热误差进行了数据采集,在分析了机床主轴径向热误差的数据后进行了线性回归分析,构建了不同转速下检测棒上下端径向热误差模型。通过对刀具偏转原理与检测棒上下端径向热误差模型进行分析,提出了机床主轴径向热误差综合建模方法,并对该方法进行了实验验证。验证结果表明:该机床主轴径向热误差综合建模方法有效且预测精度高。     

变工况下基于迁移学习融合域内对齐的机床主轴热误差模型

热误差建模和补偿是提高机床加工精度的重要手段。 将得到的热误差模型应用到类似或相近任务中,对减少模型构建 和数据收集的成本具有重要意义。 本文提出了一种简易迁移学习(EasyTL)融合域内对齐的主轴热误差建模方法,以实现不同 工况下误差模型的迁移复用。 建立基于域内对齐和距离矩阵全组合择优的热误差迁移模型参数选取方法,获得最优组合。 进 一步分析不同类型的域内对齐和距离矩阵各自对模型迁移性能的影响。 最后,将迁移模型与 kNN 典型机器学习模型和卷积神 经网络深度模型进行比较验证,分别预测不同工况下主轴 Z 向和 Y 向的热误差。 此外,根据预测的主轴热误差进行工件补偿 加工实验。 该方法为热误差建模及补偿提供了一种新思路。     

基于状态空间模型的数控机床热误差建模

为了减小机床运行参数变化导致的机床热误差变化对模型预测精度的影响,提出了状态空间建模算法,该算法可根据机床运行参数的变化而自动调整模型,从而使模型对机床运行参数的变化具有良好的自适应性。通过实验比较了模型对机床处于不同条件下的热误差预测精度,并基于状态空间模型在Leaderway V-450型数控机床上进行了平面切削的热误差补偿实验。实验结果表明：与传统热误差建模算法相比较,所提算法的预测精度提高了58.12%,稳健性也得到了有效提升,且实际热误差补偿效果显著。     

基于粒子群优化灰色神经网络的机床主轴热误差建模

主轴热误差是影响机床精度的主要因素,建立准确的主轴热误差模型是进行机床误差补偿的关键。研究了温度测点优化和神经网络建模的方法,给出了粒子群优化灰色神经网络建模的流程。开展了主轴热误差热特性试验,得到了主轴热变形随主轴转速的变化规律。基于粒子群优化灰色神经网络建立了主轴轴向伸长和俯仰角热误差模型,并与灰色神经网络和BP网络的预测性能进行了对比,结果表明该模型可有效提高网络模型的收敛性和预测精度。     

数控机床热误差补偿模型稳健性比较分析

数学模型的精度特性和稳健性特性对数控机床热误差补偿技术在实际中的实施性影响不容忽视。对数控加工中心关键点的温度和主轴z向的热变形量采用多种算法建立了预测模型,对不同算法拟合精度进行分析。同时进行全年热误差跟踪试验,获得了机床在不同环境温度和不同主轴转速的试验条件下的敏感点温度和热误差值。以此为基础,对各种预测模型的预测精度进行比较验证不同模型的稳健性。结果表明,多元线性回归算法的最小一乘、最小二乘估计模型以及分布滞后模型在改变试验条件时预测精度下降,而基于支持向量回归机原理的热误差补偿模型仍能保持较好的预测精度,稳健性强。这为数控机床热误差补偿模型的选择提供了具有实用价值的参考,具有很好工程应用性。     

基于实时反馈的机床热误差在线补偿模型

为建立一种能够适应机床不同工况且具有准确预测能力的热误差补偿模型,提出一种基于限定记忆递推最小二乘法辨识热误差模型参数的机床热误差预测建模方法。该方法随着机床工作状况的改变,根据实时反馈的温度和热误差数据,采用递推方法对模型参数进行即时修正,使热误差模型能够及时跟踪机床系统的热特性变化,实现以较高的预测精度对机床热误差进行补偿。通过数控车床主轴轴向热误差辨识建模及补偿实验可以看出,限定记忆递推最小二乘法比一步最小二乘法辨识精度有较大提高,最大残差值减小了52.3%,标准差减小了67%。实验结果表明,利用该方法进行机床热误差模型参数辨识具有较高的预测精度和鲁棒性,有效可行。       

精密数控车床主轴热误差建模

开展了精密数控车床主轴系统热误差补偿的实验与建模方法的研究。建立了精密数控车床主轴系统轴向与径向偏转热误差补偿模型以增强其误差补偿能力,并提高机床加工精度。构建了主轴系统热误差测试平台,应用五点法测试主轴系统热误差,使用热电偶与红外热像仪测量主轴系统温升关键点温度变化数据,应用灰色综合关联分析法实现温度敏感测点辨识。构建了基于粒子滤波重采样粒子群算法的热误差预测模型,对模型预测效果进行评价。结果表明:基于粒子滤波重采样粒子群热误差补偿模型得到的轴向热误差预测残差为-1.29μm~1.55μm,建模精度为95.04%;y向热偏转误差预测残差为-4.68×10~(-6°)~9.66×10~(-6°),建模精度为91.26%;z向热偏转误差预测残差为-5.83×10~(-6°)~8.59×10~(-6°),建模精度为93.24%。实验结果证明该热误差补偿模型具有较高的预测精度,具有较强的工程应用价值。     

多变量电主轴热误差预测模型与补偿实验研究

为解决加工中心电主轴的热误差补偿问题,建立适用性更强的电主轴热误差预测模型,实验测试了不同转速下加工中心电主轴的温升和热伸长,建立了基于指数函数的电机温升、主轴转速及时间的三变量轴向热误差预测模型。随后取两种转速进行实验,对补偿效果进行了验证;并与主轴转速、时间双变量热误差预测模型进行了对比。结果表明,三变量模型补偿效果优于双变量模型,为加工中心电主轴热误差补偿并实用化提供了新的思路。     

精密数控机床主轴热伸长补偿技术研究

针对目前精密数控机床热误差补偿问题,在基于主轴热误差测量系统的基础上,提出一种基于FCM聚类、多元线性回归的热误差补偿模型。通过对某卧式加工中心主轴恒定转速和变速工况下进行温敏点测量,建立关键温敏点与机床主轴热伸长的几何关系,通过补偿结果和切削试验表明该方法可以有效地降低主轴热伸长误差,提升零件的加工精度。     

Robustness of thermal error compensation modeling models of CNC machine tools

In order to achieve effective control of thermal error compensation of computer numerical control (CNC) machine tools, the prediction accuracy and robustness of the compensation model is particularly important. In this paper, the temperature of sensitive points and thermal error of the spindle in Z direction are measured. Using a combination of fuzzy clustering analysis and gray correlation method to select temperature-sensitive points and then using multiple linear regression of least squares and least absolute estimation methods, distributed lag model, and support vector regression machine to establish prediction models of the relationship between temperature of sensitive points and the thermal error. Also, the temperature values of sensitive points and the thermal error in the experimental conditions of different ambient temperatures and different spindle speeds are measured. By comparing the prediction accuracy of various prediction models under different experimental conditions verify the robustness of the models. Experimental results show that when the modeling data are less, the prediction accuracy of multiple linear regression of least squares and least absolute estimation methods and distributed lag model is declined, and their robustness are poor, while support vector regression model has good prediction accuracy and its robustness remains strong when changing the experimental conditions. However, when modeling data are rich, the prediction accuracy of various algorithms is improved, but the robustness of support vector regression model is volatile. The robustness analysis of different models provides a useful reference for the thermal error compensation model, selection of CNC machine tools, and has good engineering applications.     

数控机床主轴热变形伪滞后研究及主轴热漂移在机实时补偿

为研究数控机床热变形规律,实现数控机床误差在机实时补偿,进行数控机床主轴热变形理论及试验分析,结果表明,数控机床主轴热变形与主轴温变在距热源约1/3位置存在近似线性关系,即主轴热变形存在伪滞后现象,这一结果为数控机床测温点优化布置及热误差鲁棒建模提供理论依据。为验证机床热变形伪滞后现象,对VM850加工中心主轴热漂移误差在机实时检测并建模,通过自主研发数控机床误差在线实时补偿系统对主轴热漂移误差进行实时补偿,经补偿,机床主轴热漂移误差减少90%以上,有效提高了数控机床主轴精度。     

Analysis of CNC machining based on characteristics of thermal errors and optimal design of experimental programs during actual cutting process

The compensation of thermal errors plays a critical role in developing the machine tools of intelligent computer numerically controlled (CNC). According to the international standards, the testing, modeling, and compensation of thermal error of CNC machine tools are carried out only in a so-called idling state where the spindle is free running without any workload. However, in practical applications, machine tools are often applied in the actual cutting state with more influence factors, such as cutting parameters, cooling liquid, and cutting force. Subsequently, the thermal characteristics at idling state and actual cutting state are compared and analyzed in this paper. It was found that the thermal error compensation model under idling state is not precise enough to be applied in actual cutting state. Also, further research finds that different combinations of cutting parameters, such as spindle speed and feed rate, also have influences on the accuracy of prediction and robustness of thermal error model under actual cutting state. Therefore, the cutting parameters of spindle speed, feed rate, depth of cut, and ambient temperature are studied with the usage of the Taguchi method. Through calculating signal-to-noise ratio (SN) of each combination through residual standard deviation of thermal error model, the combination of optimal cutting parameters can be obtained. The resultant analysis shows that the thermal error model under the combination of optimal cutting parameters demonstrates higher accuracy of prediction and better robustness.     

Thermal Error Modeling Method with the Jamming of Temperature-Sensitive Points’ Volatility on CNC Machine Tools

Aiming at the deficiency of the robustness of thermal error compensation models of CNC machine tools, the mechanism of improving the models’ robustness is studied by regarding the Leaderway-V450 machining center as the object. Through the analysis of actual spindle air cutting experimental data on Leaderway-V450 machine, it is found that the temperature-sensitive points used for modeling is volatility, and this volatility directly leads to large changes on the collinear degree among modeling independent variables. Thus, the forecasting accuracy of multivariate regression model is severely affected, and the forecasting robustness becomes poor too. To overcome this effect, a modeling method of establishing thermal error models by using single temperature variable under the jamming of temperature-sensitive points’ volatility is put forward. According to the actual data of thermal error measured in different seasons, it is proved that the single temperature variable model can reduce the loss of forecasting accuracy resulted from the volatility of temperature-sensitive points, especially for the prediction of cross quarter data, the improvement of forecasting accuracy is about 5 μm or more. The purpose that improving the robustness of the thermal error models is realized, which can provide a reference for selecting the modeling independent variable in the application of thermal error compensation of CNC machine tools.     

数控机床工作台误差综合补偿方法研究

针对由几何误差与热误差引起的数控机床工作台与主轴之间相对位置变动的问题,通过试验分析其在不同温度状态下的误差数据,得到机床工作台平面度误差随热变形保持不变的规律,并提出了一种数控机床工作台平面度误差与主轴热误差的综合补偿方法。该方法通过分别建立工作台平面度误差模型和热误差模型,并运用叠加原理建立综合误差补偿模型,对传统固定单位置点建模补偿方法的原理性缺陷进行了改进。结合机床关键部件的实时温度值和刀具位置的实时坐标值,计算出了全工作台各区域各温度阶段的误差补偿值,进而实现了全工作台主轴轴向综合误差的实时补偿。检验及分析结果表明,相比于传统固定单位置点热误差建模补偿方法,该方法所建模型残余标准差减小约7μm,精度提高比例达到50%;单次最大补偿残差减小约11μm,精度提高比例达到60%,大幅度提高了机床的加工精度。     

IMPROVING ACCURACY OF CNC MACHINE TOOLS THROUGH COMPENSATION FOR THERMAL ERRORS

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150MD24Z7.5型电主轴动态误差和热变形实验研究

电主轴的动态误差和热变形是影响数控机床精度的重要指标,其对定位精度和工件表面加工质量的影响尤为显著。采用主轴误差分析仪,对150MD24Z7.5型主轴的各项动态误差及各方向的热变形量进行实验研究。通过试验结果数据分析,获得了主轴系统在不同转速下的同异步误差、热平衡时间及不同方向的热变形量等,为主轴动态误差补偿和热变形智能预测提供了准确的数据支撑。     

Orthogonal polynomials-based thermally induced spindle and geometric error modeling and compensation

The spindle error and geometric error are the main sources of inaccuracy in CNC machining. With the rising of the machine tool parts' temperature, the spindle error and geometric error increase continually, and the error curves have a nonlinear distribution. To analyze the thermal effects on spindle error and geometric error, an experiment is carried out. To improve the machining accuracy of a CNC machine, an error model is proposed based on orthogonal polynomials. With the application of the orthogonal polynomials, the polynomial regression can be transformed into multiple linear regressions which are easier to calculate. In order to implement the real-time error compensation for the thermally induced spindle error and geometric error, an error compensation method is proposed based on the external coordinate offset. The thermally induced spindle and geometric error are compensated by 90 % compared with no compensation.