Numerical Investigation of Thermal Behavior of CNC Machine Tool and Its Effects on Dimensional Accuracy of Machined Parts

The dimensional accuracy of machined parts is strongly influenced by the thermal behavior of machine tools (MT). Minimizing this influence represents a key objective for any modern manufacturing industry. Thermally induced positioning error compensation remains the most effective and practical method in this context. However, the efficiency of the compensation process depends on the quality of the model used to predict the thermal errors. The model should consistently reflect the relationships between temperature distribution in the MT structure and thermally induced positioning errors. A judicious choice of the number and location of temperature sensitive points to represent heat distribution is a key factor for robust thermal error modeling. Therefore, in this paper, the temperature sensitive points are selected following a structured thermomechanical analysis carried out to evaluate the effects of various temperature gradients on MT structure deformation intensity. The MT thermal behavior is first modeled using finite element method and validated by various experimentally measured temperature fields using temperature sensors and thermal imaging. MT Thermal behavior validation shows a maximum error of less than 10% when comparing the numerical estimations with the experimental results even under changing operation conditions. The numerical model is used through several series of simulations carried out using varied working condition to explore possible relationships between temperature distribution and thermal deformation characteristics to select the most appropriate temperature sensitive points that will be considered for building an empirical prediction model for thermal errors as function of MT thermal state. Validation tests achieved using an artificial neural network based simplified model confirmed the efficiency of the proposed temperature sensitive points allowing the prediction of the thermally induced errors with an accuracy greater than 90%.

Thermal Error Compensation for Telescopic Spindle of CNC Machine Tool Based on SIEMENS 840D System

In this paper, eddy current sensors and thermocouple sensors were employed to measure the thermal field and thermal deformation of a spindle of a telescopic CNC boring-milling machine tool, respectively. A linear regression method was proposed to establish the thermal error model. Furthermore, two compensation methods were implemented based on the SIEMENS 840D system by using the feed shaft of z direction and telescopic spindle respectively. Experimental results showed that the thermal error could be reduced by 73.79% when using the second compensation method, and the thermal error could be eliminated by using the two compensation methods effectively.

IMPROVING ACCURACY OF CNC MACHINE TOOLS THROUGH COMPENSATION FOR THERMAL ERRORS

A method for improving accuracy of CNC machine tools through compensation for the thermal errors is studied. The thermal errors are obtained by 1 D ball array and characterized by an auto regressive model based on spindle rotation speed. By revising the workpiece NC machining program, the thermal errors can be compensated before machining. The experiments on a vertical machining center show that the effectiveness of compensation is good.

Temperature Variable Optimization for Precision Machine Tool Thermal Error Compensation on Optimal Threshold

Machine tool thermal error is an important reason for poor machining accuracy. Thermal error compensation is a primary technology in accuracy control. To build thermal error model, temperature variables are needed to be divided into several groups on an appropriate threshold. Currently, group threshold value is mainly determined by researchers experience. Few studies focus on group threshold in temperature variable grouping. Since the threshold is important in error compensation, this paper arms to find out an optimal threshold to realize temperature variable optimization in thermal error modeling. Firstly, correlation coefficient is used to express membership grade of temperature variables, and the theory of fuzzy transitive closure is applied to obtain relational matrix of temperature variables. Concepts as compact degree and separable degree are introduced. Then evaluation model of temperature variable clustering is built. The optimal threshold and the best temperature variable clustering can be obtained by setting the maximum value of evaluation model as the objective. Finally, correlation coefficients between temperature variables and thermal error are calculated in order to find out optimum temperature variables for thermal error modeling. An experiment is conducted on a precise horizontal machining center. In experiment, three displacement sensors are used to measure spindle thermal error and twenty-nine temperature sensors are utilized to detect the machining center temperature. Experimental result shows that the new method of temperature variable optimization on optimal threshold successfully worked out a best threshold value interval and chose seven temperature variables from twenty-nine temperature measuring points. The model residual of z direction is within 3 μm. Obviously, the proposed new variable optimization method has simple computing process and good modeling accuracy, which is quite fit for thermal error compensation.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accu- racy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA（grey relational analysis） method is introduced into the selection of tem- perature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN （artificial neural network） model is presented, and ABC（artificial bee colony） algorithm is introduced to train the link weights of ANN, a new ABC- NN（Artificial bee colony-based neural network） modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR （least squares regression）, ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 pm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.

Bayesian networks modeling for thermal error of numerical control machine tools

The interaction between the heat source location, its intensity, thermal expansion coefficient, the machine system configuration and the running environment creates complex thermal behavior of a machine tool, and also makes thermal error prediction difficult. To address this issue, a novel prediction method for machine tool thermal error based on Bayesian networks (BNs) was presented. The method described causal relationships of factors inducing thermal deformation by graph theory and estimated the thermal error by Bayesian statistical techniques. Due to the effective combination of domain knowledge and sampled data, the BN method could adapt to the change of running state of machine, and obtain satisfactory prediction accuracy. Ex- periments on spindle thermal deformation were conducted to evaluate the modeling performance. Experimental results indicate that the BN method performs far better than the least squares (LS) analysis in terms of modeling estimation accuracy.

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 fore- casting accuracy resulted from the volatility of tempera- ture-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 modelingindependent variable in the application of thermal error compensation of CNC machine tools.

STUDY ON THE FEEDFORWARD COMPENSATION OF THE MOTIONERRORS OF NC MACHINE TOOLS

A feedforward compensation naethod of the motion errors of NC machine tools imple- mented with software is proposed , with which the motion errors can be compensated whithout changing the original computer control systems of the NC machine tools. The experimental results show that the circular interpolation profile machining errors decrease by a factor of 2/3 after com- pensated.

Modeling Approach of Regression Orthogonal Experiment Design for Thermal Error Compensation of CNC Turning Center

The thermal induced errors can account for as much as 70% of the dimensional errors on a workpiece. Accurate modeling of errors is an essential part of error compensation. Base on analyzing the existing approaches of the thermal error modeling for machine tools, a new approach of regression orthogonal design is proposed, which combines the statistic theory with machine structures, surrounding condition, engineering judgements, and experience in modeling. A whole computation and analysis procedure is given. Therefore, the model got from this method are more robust and practical than those got from the present method that depends on the modeling data completely. At last more than 100 applications of CNC turning center with only one thermal error model are given. The cutting diameter variation reduces from more than 35 μm to about 12 μm with the orthogonal regression modeling and compensation of thermal error.

Identification of the key thermal points on machine tools by grouping and optimizing variables

The grouping and optimization approach to identify the key thermal points on machine tools is studied.To solve the difficulty in grouping because of the high correlated variables from distinct groups,the variables grouping technique is improved.Temperature variables are sorted according to their relativities with the thermal errors.The representative temperature variables are determined by analyzing the variable correlation in sort order and removing the other variables in the same group.Considering the diverse effect of importing the different variables on thermal error model,the method of variable combination optimization is improved.Regression models made up of different combination of representative temperature variables are evaluated by the index of both the determined coefficient and the average residual squares to select the combination of the temperature variables.For the machine tools with complicated structures which need more initial temperature measuring points the improvement is demanded.The improved approach is applied to a precision horizontal machining center to identify the key thermal points.Experimental results show that the proposed approach is capable of avoiding the high correlation among the different groups' variables,effectively reducing the number of the key thermal points without depressing the prediction accuracy of the thermal error model for machine tools.

Error compensation for precision machine tools

As one of the ways to improve the machining accuracy of machine tools, error compensation is reviewed from different view points, and the main barriers to further improvement of efficiency of error compensation are analyzed in detail and the vista of the error compensation in precision and ultra precision machines is discussed.

Structural scheme and theory behind feedback compensation of new parallel machine tools

Analyses the errors of new parallel machine tools and presents a structural scheme for feedback compensation of machine tools to eliminate these errors, the theory behind and the relation between direction consine of normal vector of the workpiece surface and the rotation angles α,β,γ of the cutter head.

Geometric error measuring,modeling,and compensation for CNC machine tools:A review

Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining quality of manufactured parts,it has been a popular topic for academic and industrial research for many years.A great deal of research work has been carried out since the 1970s for solving the problem and improving the machining accuracy.Researchers have studied how to measure,detect,model,identify,reduce,and compensate the geometric errors.This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors.Recent advances in measuring the geometrical errors of machine tools are summarized,and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively.Besides,volumetric geometric error modeling,tracing,and compensation techniques for five-axis machine tools are emphatically introduced.Finally,research challenges in order to improve the volumetric accuracy of machine tools are also highlighted.

Study on the thermally induced spindle angular errors of a five-axis CNC machine tool

Thermally induced spindle angular errors of a machine tool are important factors that affect the machining accuracy of parts.It is critical to develop models with good generalization abilities to control these angular thermal errors.However,the current studies mainly focus on the modeling of linear thermal errors,and an angular thermal error model applicable to different working conditions has rarely been investigated.Furthermore,the formation mechanism of the angular thermal error remains to be studied.In this study,an analytical modeling method was proposed by analyzing the formation and propagation chain of the spindle angular thermal errors of a five-axis computer numerical control(CNC)machine tool.The effects of the machine tool structure and position were considered in the modeling process.The angular thermal error equations were obtained by analyzing the spatial thermoelastic deformation states.An analytical model of the spindle angular thermal error was established based on the geometric relation between thermal deformations.The model parameters were identified using the trust region least squares method.The results showed that the proposed analytical model exhibited good generalization ability in predicting spindle pitch angular thermal errors under different working conditions with variable spindle rotational speeds,spindle positions,and environmental temperatures in different seasons.The average mean absolute error(MAE),root mean square error(RMSE)and R2 in twelve different experiments were 4.7μrad,5.6μrad and 0.95,respectively.This study provides an effective method for revealing the formation mechanism and controlling the spindle angular thermal errors of a CNC machine tool.

基于热图像的GWOA-BiLSTM机床主轴热误差预测

热误差是影响高精密数控机床加工精度的重要因素。为了提高机床加工精度和性能,减少机床运行中产生的热误差,文章提出一种基于热图像的灰狼优化算法(grey wolf optimization algorithm,GWOA)和双向长短期记忆神经网络(bidirectional long short-term memory,BiLSTM)混合的热误差预测模型。首先,采用热成像仪获取机床主轴区域的温度场信息;其次,利用DBSCAN聚类(density-based spatial clustering of applications with noise)算法和相关系数法筛选出温度敏感点;然后,通过模拟灰狼群体捕食行为,在参数空间中进行搜索以找到BiLSTM所需的最优参数;最后,使用获得的机床温度敏感点和热位移数据进行热误差预测,并在试验机床上进行验证。实验结果表明,使用GWOA优化BiLSTM神经网络的预测模型相比BiLSTM神经网络预测模型的均方根误差(root mean square error,RMSE)和平均绝对误差(mean absolute error,MAE)分别减小了约0.5180、0.3823μm,决定系数R^(2)提升了0.0578。与BiLSTM神经网络模型相比,利用GWOA优化后的模型具有更加优良的预测性能。

数字孪生下基于DACS-MFAC的数控机床热误差自适应预测方法

基于现代控制理论的经验建模法,在针对数控机床不同生产工况时,难以建立一种共性的热误差解决方案。探索了在数字孪生框架下以无模型驱动方式实现数控机床热误差自适应预测的研究。首先,建立了机床“热传感-映射-融合与优化-驱动”数字孪生框架,实现热特征信息在数字孪生体中的存储与融合。然后,基于MISO系统的假设条件和动态线性化几何释义,提出了一种不受被控系统任何结构数据影响的热误差无模型自适应控制(MFAC)方法。进一步,基于动态发现概率和自适应步长的DACS-MFAC算法按照一定的周期更新系统参数,实现数字孪生系统下热误差预测值的动态优化。实验结果表明,DACS-MFAC方法具有适应强、精度高、收敛性好等优点。

Key point selection in large-scale FBG temperature sensors for thermal error modeling of heavy-duty CNC machine tools

Thermal error is one of the main factors that influence the machining accuracy of computer numerical control(CNC)machine tools.It is usually reduced by thermal error compensation.Temperature field monitoring and key temperature measurement point(TMP)selection are the bases of thermal error modeling and compensation for CNC machine tools.Compared with small-and medium-sized CNC machine tools,heavy-duty CNC machine tools require the use of more temperature sensors to measure their temperature comprehensively because of their larger size and more complex heat sources.However,the presence of many TMPs counteracts the movement of CNC machine tools due to sensor cables,and too many temperature variables may adversely influence thermal error modeling.Novel temperature sensors based on fiber Bragg grating(FBG)are developed in this study.A total of 128 FBG temperature sensors that are connected in series through a thin optical fiber are mounted on a heavy-duty CNC machine tool to monitor its temperature field.Key TMPs are selected using these large-scale FBG temperature sensors by using the density-based spatial clustering of applications with noise algorithm to reduce the calculation workload and avoid problems in the coupling of TMPs for thermal error modeling.Back propagation neural network thermal error prediction models are established to verify the performance of the proposed TMP selection method.Results show that the number of TMPs is reduced from 128 to 5,and the developed model demonstrates good prediction effects and strong robustness under different working conditions of the heavy-duty CNC machine tool.

Apriori算法及神经网络在数控机床中应用研究

数控机床加工精度受到机床零部件、外部环境等因素的影响,从而需要添加适当的补偿参数确保加工精度的稳定性,另外,不同车床不同时刻的补偿参数实时变化。为此,提出一种基于关联规则及神经网络方法的智能误差补偿模型。以实际生产中产生的数据集为基础,通过Apriori算法对数据集进行筛选;对各个特征值与补偿参数进行归一化处理,以提高数据的收敛速度;利用神经网络模型为不同情形下的车床搜寻最佳补偿参数模型,从而构建起最佳的智能误差补偿模型;经过智能误差补偿后,对生产的物件进行图像识别,分析其是否符合精度要求。仿真测试结果表明:针对训练集数据和测试集数据,车床稳定性分别提高了0.695和0.713。实测结果显示:利用上述方法,对30个产品进行雕刻,精度均符合要求。因此,智能误差补偿模型能够提高车床加工稳定性,提升产品合格率。

复合加工机床空间误差补偿和精度提升

对特殊结构的复合加工机床采用D-H和H-M方法结合的系统主法进行了运动学建模,使激光跟踪仪测量的机床空间误差便于模型参数辨识,并列出了机床理论模型的正解和机床误差模型的识别参数。在机床运动学误差模型中,以验证点的理论空间位姿为基准,根据刀具点空间位姿相对于机床坐标轴的雅克比矩阵,使用分块矩阵结合L-M算法,计算得到了验证点的坐标轴补偿值,算法收敛速度快,相对于雅克比矩阵迭代法提高了计算效率,经过坐标轴补偿后机床的空间位置误差和姿态误差平均值分别为0.00422 mm和9.99×10-4 rad,比补偿前误差分别降低了82.5%和16.1%,表明复合加工机床的空间位姿精度得到大幅提升。

基于阿贝原则的机床主轴误差测量研究

机床测量是误差补偿的前提,分析主轴箱移动时产生的阿贝误差原因,给出主轴箱沿Z轴移动时X方向和Y方向的直线度误差,根据主轴箱直线度误差数据进行建模并给予补偿,结合具体的工程实例验证了阿贝误差补偿的有效性。