Automated measurement and compensation of thermally induced error maps in machine tools

In this paper, a direct method of machine tool calibration is adopted to model and predict thermally induced errors in machine tools. This method uses a laser ball bar (LBB) as the calibration instrument and is implemented on a two-axis computerized numerical control turning center (CNC). Rather than individually measuring the parametric errors to build the error model of the machine, the total positioning errors at the cutting tool and spindle thermal drifts are rapidly measured using the LBB within the same experimental setup. Unlike conventional approaches, the spindle thermal drifts are derived from the true spindle position and orientation measured by the LBB. A neural network is used to build a machine model in an incremental fashion by correlating the measured errors with temperature gradients of the various heat sources during a regular thermal duty cycle. The machine model developed by the neural network is further tested using random thermal duty cycles. The performance of the system is also evaluated through cutting tests under various thermal conditions. A substantial improvement in the overall accuracy was obtained.     

五轴联动数控机床中高速电主轴的热误差研究

建立了高速电主轴的一维简化模型,利用传热学中的傅里叶定律以及主轴的两个边界条件,推得主轴热源与主轴轴向热形变之间的关系。通过机器人学中的齐次坐标变换原理,建立各个运动副坐标系之间的变换矩阵,并求得数控机床各个误差量与五个联动轴补偿量之间的关系,利用该关系式即可对高速电主轴中的热误差进行补偿。     

主轴热误差的数值建模分析

数控机床逐渐向高精度、高速度、精密化、智能化方向发展。机床的精度直接影响了工件的加工精度。以测量加工中心主轴系统的温度场和热误差数据为基础,采用五点法测量了加工中心主轴系统的温度场和热误差数据,用偏最小二乘回归方法建立了两者的多元线性回归模型,并对各个测温点的温度变化与主轴热误差之间的量化关系进行了定性研究。经研究分析,该模型具有较强的预测能力和较为理想的精度,可以满足加工中心热误差实时补偿的需要,也可作为机床设计和制造的参考依据。     

Thermal influence of the Couette flow in a hydrostatic spindle on the machining precision

Hydrostatic spindles are increasingly used in precision machine tools. Thermal error is the key factor affecting the machining accuracy of the spindle, and research has focused on spindle thermal errors through examination of the influence of the temperature distribution, thermal deformation and spindle mode. However, seldom has any research investigated the thermal effects of the associated Couette flow. To study the heat transfer mechanism in spindle systems, the criterion of the heat transfer direction according to the temperature distribution of the Couette flow at different temperatures is deduced. The method is able to deal accurately with the significant phenomena occurring at every place where thermal energy flowed in such a spindle system. The variation of the motion error induced by thermal effects on a machine work-table during machining is predicated by establishing the thermo-mechanical error model of the hydrostatic spindle for a high precision machine tool. The flow state and thermal behavior of a hydrostatic spindle is analyzed with the evaluated heat power and the coefficients of the convective heat transfer over outer surface of the spindle are calculated, and the thermal influence on the oil film stiffness is evaluated. Thermal drift of the spindle nose is measured with an inductance micrometer, the thermal deformation data 1.35 μm after running for 4 h is consistent with the value predicted by the finite element analysis's simulated result 1.28 μm, and this demonstrates that the simulation method is feasible. The thermal effects on the processing accuracy from the flow characteristics of the fluid inside the spindle are analyzed for the first time.     

Modified Elman network for thermal deformation compensation modeling in machine tools

Thermal deformation is one of the most significant causes of machining errors in machine tools. One effective method is to build a compensation system to offset the thermal errors. Therefore, an accurate model is the key part of the compensation system. This study proposed a modified Elman network (EN) to improve the prediction accuracy of the compensation model in machine tools. And the improved EN can be regarded as a feed-forward neural network with feedback from hidden layer and output layer as an additional set of inputs. The structure of this network determines its dynamic characteristic with memory function. On the other hand, thermal deformation of the spindle contributes the largest part of total thermal errors in precision machining. Then a precise finite element model of machine tool spindle was established. And a new method for calculating the heat transfer convection coefficient on the surface of the spindle was proposed in this paper. The improved EN was used to map the nonlinear relationship between temperature field and thermal errors of the spindle. At last, a verification experiment was implemented on a CNC center and some satisfying results were achieved.     

数控机床误差检测及其误差补偿技术研究

使用Renishaw激光干涉仪和高精度位移传感器实现了机床线性定位误差和主轴热误差的测量。通过补偿机床螺距和丝杠间隙误差,实现了机床线性定位误差的补偿。同时,使用PMAC控制卡对数控系统的G代码指令进行了实时修改,实现了机床主轴热误差的实时补偿。分析补偿后的机床,发现机床的加工精度得到了很大提高,表明该补偿效果明显。     

Three-point method for measuring the geometric error components of linear and rotary axes based on sequential multilateration

The linear and rotary axes are fundamental parts of multi-axis machine tools. The geometric error components of the axes must be measured for motion error compensation to improve the accuracy of the machine tools. In this paper, a simple method named the three-point method is proposed to measure the geometric error of the linear and rotary axes of the machine tools using a laser tracker. A sequential multilateration method, where uncertainty is verified through simulation, is applied to measure the 3D coordinates. Three non-collinear points fixed on the stage of each axis are selected. The coordinates of these points are simultaneously measured using a laser tracker to obtain their volumetric errors by comparing these coordinates with ideal values. Numerous equations can be established using the geometric error models of each axis. The geometric error components can be obtained by solving these equations. The validity of the proposed method is verified through a series of experiments. The results indicate that the proposed method can measure the geometric error of the axes to compensate for the errors in multi-axis machine tools.     

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。     

Premachining Computer Numerical Control Contour Validation

The current procedure followed to manufacture a new part by computer numerical control (CNC) machining is to write the part program, machine a test part, and measure the test part for conformance to the required dimensions and tolerances. If the test part dimensions are incorrect, the part program is modified, and the process is repeated until a successful part is machined. In many applications, such as the aerospace industry, where material cost and machining time are high, this iterative process becomes economically unacceptable. Research has been conducted to test the feasibility of using the laser ball bar (LBB), a spatial coordinate measuring device, to measure dynamic continuous path contours of CNC part programs to micrometer accuracy before machining. In this way, a virtual test part can be measured and compared to the design drawings to validate the CNC part program. This reduces or eliminates the costly and time-consuming steps involved in the machining of physical test parts. This paper outlines the testing method and results acquired using one LBB to measure dynamic part paths employing sequential trilateration. A circular contour was measured using an encoder trigger for data capture. The radial error motions of the spindle used to generate the circular contour were also measured using a capacitance probe nest to verify the LBB results. Comparable error waveforms between the LBB and cap probe measurements verified the possibility of using the LBB to measure dynamic continuous path contours. Future work using three LBBs simultaneously is also outlined.     

Thermal error reduction based on thermodynamics structure optimization method for an ultra-precision machine tool

Thermal error is one of the main errors in ultra-precision machine tools. This paper presents a thermodynamics-based structure optimization method to reduce the thermal displacements of machine tools during operation. The method makes use of the thermal–structure coupled model to analyze the thermal behavior considering the thermal contact resistance and the temperature rise of the oil film in hydrostatic spindle. The structure of the motor link, spindle, and headstock of grinder are optimized by setting appropriate gaps in the contact region of two neighboring parts to change the heat transfer distribution and minimize the thermal displacement of the spindle center position. The proposed method is validated by an equivalent thermal conductivity-based simulation method and experiment on an ultra-precision grinding machine tool. Experimental results show that the proposed method can provide an important instruction on how to reduce the thermal error for the design of the precision machine tools, especially for those with key parts placed near the heat sources.     

高速立式加工中心主轴箱热态分析

高速立式加工中心在加工过程中产生的热效应对机床加工精度的影响日益凸显.XH714B高速立式加工中心在高速加工过程中会出现主轴轴线热偏转现象,机床行业俗称为“闷头”,影响了机械加工表面的完整性,降低了粗糙度.主轴箱作为加工中心的重要热源,为了解决立式加工中心出现“闷头”现象的主要原因,对主轴箱的热态分析就显得尤为重要,采用有限元方法建立了XH714B高速立式加工中心主轴箱热态特性分析模型,分析计算了主轴箱在额定转速下的稳态热特性.与传统观点“滚动轴承为主轴主要热源”不同,提出主轴电动机的热损耗是导致机床主轴轴线在y-z平面内发生偏转的主要原因.     

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。     

Thermal Error Measurement and Real Time Compensation System for the CNC Machine Tools Incorporating the Spindle Thermal Error and the Feed Axis Thermal Error

Thermally induced errors have been significant factors affecting machine tool accuracy. In this paper, the thermal spindle error and thermal feed axis error have been considered, and a measurement/compensation system for thermal error is introduced. Several modelling techniques for thermal errors are also implemented for the thermal error prediction; i.e. multiple linear regression, neural network, and the system identification methods, etc. The performances of the thermal error modelling techniques are evaluated and compared, showing that the system identification method is the optimum model having the least deviation. The thermal error model for the feed axis is composed of geometric terms and thermal terms. The volumetric errors are calculated, combining the spindle thermal error and feed axis thermal error. In order to compensate for the thermal error in real-time, the coordinates of the CNC controller are modified in the PMC program. After real-time compensation, the machine tool accuracy improved about 4–5 times. ID="A1" Correspondence and offprint requests to: Dr H. J. Pahk, School of Mechanical and Aerospace Engineering, Seoul National University, San 56–1, Shinlim-Dong, Kwanak-Ku, Seoul 151–742, Korea. E-mail: hjpahk@plaza.snu.ac.kr     

龙门数控机床主轴热误差及其改善措施

依据ISO和ASME标准建立龙门数控(Numerical control,NC)机床热误差测试条件,通过主轴恒转速和变转速热误差试验分析主轴箱温度场分布及其对主轴热误差的影响趋势。建立龙门机床误差元素模型,分析影响机床各坐标轴加工精度的主轴热误差分量。研究发现,主轴热误差和主轴箱温度存在单调对应关系,温度对主轴轴向的热伸长误差的影响要远大于主轴径向的热漂移误差,但温度变化相对各坐标变形存在热延迟和热惯性等特性。对主轴径向精度影响最大的热误差分量是由机床生热产生的同方向的偏移误差和与之垂直的偏转误差;对轴向精度影响最大的则是轴向的偏移误差。针对热误差特点和分布规律,提出结构优化、热平衡、误差补偿建模等3种减小热误差的措施,并对其各自优点进行了分析。     

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.     

The laser ball bar: a new instrument for machine tool metrology

Current techniques for mapping the volumetric positioning errors of machine tools are time and labor intensive. To address these shortcomings, a linear displacement measuring device is introduced to rapidly and easily determine tool positions via trilateration. The laser ball bar (LBB) consists of a laser interferometer aligned within a telescoping ball bar. The design of the device is discussed and an error budget is developed to estimate its predicted accuracy. Results of repeatability and linear accuracy test of the assembled prototype LBB are given. The LBB is used to map the volumetric errors of a two-axis turning center. Comparison of the LBB error map and the error map obtained through parametric error measurements shows the LBB can accurately map the machine errors in a timely manner.     

IMPROVING ACCURACY OF CNC MACHINE TOOLS THROUGH COMPENSATION FOR THERMAL ERRORS

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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。       

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

Aiming at the problem of low machining accuracy 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 temperature 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 ABCNN(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 lm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.     

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。