A thermal error model for large machine tools that considers environmental thermal hysteresis effects

Environmental temperature has an enormous influence on large machine tools with regards to thermal deformation, which is different from the effect on ordinary-sized machine tools. The thermal deformation has hysteresis effects due to environmental temperature, and the hysteresis time fluctuates with seasonal weather. This paper focused on the hysteresis nonlinear characteristic, analyzing the thermal effect caused by external heat sources. Fourier synthesis, time series analysis and the Newton cooling law were combined to build a time-varying analytical model between environmental temperature and the corresponding thermal error for a large machine tool. A multiple linear regression model based on the least squares principle was used to model the internal heat source effects simultaneously. The two models were united to make up a synthetic thermal error prediction model called the environmental temperature consideration prediction model (ETCP model). A series of experiments were performed using a large gantry type machine tool to verify the accuracy and efficiency of the predicted model under random environments, random times and random machining conditions throughout an entire year. The proposed model showed high robustness and universality, with over 85% thermal error, with up to 0.2 mm was predicted. The mathematical model was easily integrated into the NC system and could greatly reduce the thermal error of large machine tools under ordinary workshop conditions, especially for long-period cycle machining.     

A review on spindle thermal error compensation in machine tools

Thermal error caused by the thermal deformation is one of the most significant factors influencing the accuracy of the machine tool. Among all the heat sources which lead to the thermal distortions, the spindle is the main one. This paper presents an overview of the research about the compensation of the spindle thermal error. Thermal error compensation is considered as a more convenient, effective and cost-efficient way to reduce the thermal error compared with other thermal error control and reduction methods. Based on the analytical calculation, numerical analysis and experimental tests of the spindle thermal error, the thermal error models are established and then applied for implementing the thermal error compensation. Different kinds of methods adopted in testing, modeling and compensating are listed and discussed. In addition, because the thermal key points are vital to the temperature testing, thermal error modeling, and even influence the effectiveness of compensation, various approaches of selecting thermal key points are introduced as well. This paper aims to give a basic introduction of the whole process of the spindle thermal error compensation and presents a summary of methods applied on different topics of it.     

NURBS-based fast geometric error compensation for CNC machine tools

In this paper, a novel method for the compensation of geometric errors of CNC machine tools is presented. The key idea is to use the basis functions of the setting NURBS path to approximate its error compensation function and to generate a new compensated NURBS path. In this way, both the setting and the compensated NURBS path have the same NURBS form. More importantly, the control points of the error compensation function can be obtained by simply calculating the positioning deviations of the control points of the setting NURBS path using the error model. A high compensation accuracy can be achieved through the systematic insertion of new knots, which creates new control points and raises the flexibility of NURBS in representing the error compensation function. The real-time interpolation of the compensated NURBS path completes the error compensation automatically. Simulations and experiments have shown that the new method delivers the same positioning accuracy as a model-based real-time geometric error compensation method does, but without additional real-time CPU loading. The proposed method can also be implemented in the post-processor of a CAM system for off-line compensation.     

Thermal error measurement and modelling in machine tools. Part II. Hybrid Bayesian Network—support vector machine model

Prediction accuracy of machine tool thermal error significantly depends on the structure of the error model. Machine tool thermal error varies considerably depending upon the specific operating parameters adopted. Most error models developed thus far generally employ neural networks to map temperature data against thermal error. However, it is very important to account for the specific conditions as well within the model. This paper presents a hybrid Support Vector Machines (SVM)–Bayesian Network (BN) model that seeks to address this issue. The experimental data is first classified using a BN model with a rule-based system. Once the classification has been effected, the error is predicted using a SVM model. The hybrid thermal error model thus predicts the thermal error according to the specific operating conditions. This concept leads to a more generalised prediction model than the conventional method of directly mapping error and temperature irrespective of conditions. Such a model is especially useful in a production environment wherein the machine tools are subject to a variety of operating conditions.     

Simulation of thermal behavior of a CNC machine tool spindle

The thermal deformations of a CNC machine tool spindle are the major contributor of thermal error. It is very significant both theoretically and practically to study how to accurately simulate the thermal error of the spindle. Firstly, this paper proposes a method for computing the coefficient of convection heat transfer of the spindle surface by referencing the theory on computing the coefficient of convection heat transfer of a flat plate when air flows along it. Secondly, the temperature field and thermal errors of the spindle are dynamically simulated under the actions of thermal loads using the finite element method. Thirdly, the characteristics of heat flow and thermal deformation within the spindle are analyzed according to the simulation results. Fourthly, the selection principle of thermal key points, which are indispensable for building a robust thermal error model, is provided based on the thermal error sensitivity technology. At last, a verification experiment is implemented on a CNC turning center, and the results show the simulation results are satisfying to replace the experiment results for further studies.     

Thermal error mode analysis and robust modeling for error compensation on a CNC turning center

In this paper a novel concept of thermal error mode analysis is proposed in order to develop a better understanding of the thermal deformation on a turning center. The thermal error of the machine can be treated as the superposition of a series of thermal error modes with corresponding mode shapes and time constants. The selection of sensor location can then be improved based on the thermal error mode analysis. A robust modeling approach is also proposed to minimize the errors due to temperature measuring noise and the adverse effect of environmental changes. Through the use of thermal error mode analysis and the robust modeling approach, the number of thermal sensors has been reduced from 16 to four. The thermal error compensation system has been applied to a turning center in daily production for more than two years and it has kept year-round accuracy. The thermal drift in workpiece diameter on the turning center has been reduced from 35 μm to 6 μm from its center of tolerance.     

基于球杆仪的数控机床误差识别与补偿

论述了数控机床几何误差的球杆仪识别及软件补偿技术。提出了从Renishaw球杆仪测量数控机床的联动误差数据中识别反向间隙、直线度、垂直度、定位误差的一种方法;建立了机床结构的每个误差元和切削刀具相对工件位置误差相联系的通用数学模型;用球杆仪在数控机床上进行补偿前后加工轨迹的测量实验表明该方法效率高、效果显著。     

Design optimization and development of CNC lathe headstock to minimize thermal deformation

This paper has investigated an approach to reduce and compensate thermal displacement for high accuracy NC lathes. An efficient design and optimization method is proposed for a headstock structure design of NC lathes to minimize the thermal displacement of the spindle center position. Compared to the existing empirical methods, this method saves development time and cost. The Taguchi method and FEA method are used to identify the optimal headstock structure. The proposed method is verified by evaluating the spindle center transition of the headstock according to the optimization results.     

A general approach for error modeling of machine tools

This paper presents a general and systematic approach for geometric error modeling of machine tools due to the geometric errors arising from manufacturing and assembly. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within machine tool kinematic chains using homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the error intensities of a machine tool; (3) combination of these two models for error separation. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the machine tool to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement by suitable measures, i.e. component tolerancing in design, manufacturing and assembly processes, and error compensation. Two typical multi-axis machine tools are taken as examples to illustrate the generality and effectiveness of this approach.     

A new technique for volumetric error assessment of CNC machine tools incorporating ball bar measurement and 3D volumetric error model

This paper presents a useful technique for assessing the volumetric errors in multiaxis machine tools using a kinematic double ball bar. This system has been developed based on a volumetric error model which describes the three-dimensional errors of machine tools. The developed system requires input of the measured radial data performed on the three orthogonal planes, and analyzes parametric errors such as positional, straightness, angular, squareness, and backlash errors. The developed system can also assess the dynamic performance of machine tools such as errors due to the servo gain mismatch. The developed system has been tested using an actual machine tool, showing high potential for error assessment of multiaxis machine tools.     

五轴联动机床的误差补偿与优化研究

以五轴联动精密卧式加工中心为研究对象,首先阐述了五轴联动机床的圆度测试过程,对可能出现的测试结果给出分析与解决方法;从而得到具体的检测步骤以及相应的机床数据;最后讨论了同步龙门轴的调整问题.实验结果表明了所述方法的有效性.     

Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools

In order to investigate the effect of thermal expansion on the ball screw feed drive system of a precision boring machine tool, theoretical modeling of and experimental study on thermally induced error along with heat generation characteristics are focused in this paper. A series of thermal experiments are conducted on the machine tool to measure and collect the thermodynamic data with the feed drive system operating at different speeds. Based on the heat generation and transfer analysis of ball screw system, thermal expansion of screw shaft in the axial direction is modeled mathematically. Relationships between the thermal error and axial elongation are established to characterize the thermal error distribution considering the thermal expansion coefficient as a temperature-variant parameter. It turns out that the thermal error varies with different working positions through the ball screw length and working time nonlinearly, and there definitely exists certain transform from the thermal expansion to the thermal error obtained by measurement. In addition, regression analysis is employed to carry out the theoretical modeling of thermal error with the temperature data of the critical heat generation points. The relations between temperature rise and thermal error are formulated directly while taking the thermal expansion as an implicit variable. Experiments under a different condition are preformed and the proposed methods for thermal error modeling prove to be effective and accurate enough to be used in the machining process as well.     

A machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test

This paper proposes a machining test to parameterize error motions, or position-dependent geometric errors, of rotary axes in a five-axis machine tool. At the given set of angular positions of rotary axes, a square-shaped step is machined by a straight end mill. By measuring geometric errors of the finished test piece, the position and the orientation of rotary axis average lines (location errors), as well as position-dependent geometric errors of rotary axes, can be numerically identified based on the machine׳s kinematic model. Furthermore, by consequently performing the proposed machining test, one can quantitatively observe how error motions of rotary axes change due to thermal deformation induced mainly by spindle rotation. Experimental demonstration is presented.     

Thermal error measurement and modelling in machine tools.: Part I. Influence of varying operating conditions

Thermal error in machine tools has been observed to be closely linked to the temperature of critical elements of the machine. It was found, in the experiments conducted herein, that there was a significant increase in the axis positioning error on account of an increase in the temperature of the machine elements due to continuous operation. However, it was also observed that the specific operating parameters of the test cycles carried out also significantly affected the positioning error. Different sets of operating parameters generated significantly different error values even though the temperature of the machine elements generated by those operating conditions was similar. As such, this observation forms a very important consideration in the development of a generic thermal error compensation system. It appears to indicate that such a system needs to be capable of evaluating the compensation depending upon the temperature values of the machine elements as well as account for the effect that different operating parameters induce upon the positioning error under the same thermal condition of the machine. This paper attempts to analyse the thermal behaviour of a three-axis vertical machining centre under the influence of various operating parameters and, through the experimental results obtained, point out and explain the effect of these parameters on the axis positioning error. This behaviour forms the basis of an improved modelling methodology that is presented separately in Part II of this paper.     

数控插齿机热误差模块化稳健性预测模型建立

针对数控插齿机固有的主轴进给系统结构带来的传动间隙引起波动性热变形建模预测精度不高的问题,提出一种基于均值平滑处理波动的模块化建模方法。利用模糊聚类结合灰色关联度方法和多元线性回归对该机床主轴x、y向分别建立热误差补偿模型,并计算预测残余值在不同分布范围的概率。结果表明：与传统热误差建模方法相比,模块化预测残余值在不同范围的分布较均匀,稳健性得到了有效提升,为热误差模块化建模方法提供了参考。     

Thermal analysis for the feed drive system of a CNC machine center

A high-speed drive system generates more heat through friction at contact areas, such as the ballscrew and the nut, thereby causing thermal expansion which adversely affects machining accuracy. Therefore, the thermal deformation of a ballscrew is one of the most important objects to consider for high-accuracy and high-speed machine tools. The objective of this work was to analyze the temperature increase and the thermal deformation of a ballscrew feed drive system. The temperature increase was measured using thermocouples, while a laser interferometer and a capacitance probe were applied to measure the thermal error of the ballscrew. Finite element method was used to analyze the thermal behavior of a ballscrew. The measured data were compared with numerical simulation results. Inverse analysis was applied to estimate the strength of the heat source from the measured temperature profile. The generated heat sources for different feed rates were investigated.     

数控机床热误差的模型预报补偿

阐述了数控机床热误差补偿技术的基本概念，提出了一种基于人工神经网络的数控机床热误差模型预报补偿系统，介绍了该方法的原理，并对该系统的建立及相关技术进行了讨论。     

Verification and evaluation method for volumetric and positional errors of CNC machine tools

This paper provides a testing device and an automatic sampling technique for fast checking of volumetric errors of CNC machine tools. With the proposed automatic sampling technique, the verification work is carried out automatically and reliably. Furthermore, the analyzed result obtained via the traditional least-squares method is not the minimum zone solution, and may overestimate the volumetric error. Thus, genetic algorithms (GAs) are employed to obtain the minimum zone solution in this paper. Experimental test results show that the proposed method is superior to the least-squares method.     

数控机床定位误差的激光干涉法检测与补偿

用激光干涉法测量误差的原理,通过计算机控制的误差补偿系统对数控机床不的定位误差进行补偿,实验结果表明这种方法可以大幅度提高数控机床的定位精度。     

Modification of a neural network utilizing hybrid filters for the compensation of thermal deformation in machine tools

This study proposes a modified method that combines feed-forward neural network (FNN) and hybrid filters to improve the accuracy and reduce computation times for the prediction of thermal deformation in a machine tool. The hybrid filter consists of the linear regression (LR), moving average (MA) and autoregression (AR). Their outputs serve as input of FNN, which are estimated by the static and dynamic relationships between the temperature distributions and thermal deformations. This modified method enables the propagation accuracy between input and output layers of a static FNN to be improved and the learning time to be reduced. Furthermore, the modified method is compared with other three ones, which are traditional ARMA, FNN, and FNN combined with LR by numerical analysis and practical experiments. In analysis, the error margins of various approaches are compared using a finite element model that is determined for the relationships between thermal deformation and temperature distribution. Also, practical experiments of these approaches for a grinding machine are realized to compare the deformation predications according to temperature measurements.