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.     

Statistical optimization and assessment of a thermal error model for CNC machine tools

The objective of a thermal error compensation system for CNC machine tools is improved machining accuracy through real time error compensation. The compensation capability depends on the accuracy of the thermal error model. A thermal error model can be obtained using an appropriate combination of temperature variables. In this study, the thermal error modeling is based on a correlation grouping and a successive linear regression analysis. During the successive regression analysis, the residual mean square is minimized using a judgement function, which, although simple, is effective in the selection of variables in the error model. When evaluating the proposed thermal error model, the multi-collinearity problem and computational time are both improved through the correlation grouping, and the linear model is more robust against measurement noises than the engineering judgement model, which includes variables with higher order terms. The modeling method used in this study can be effectively and practically applied to real-time error compensation because it includes the advantages of simple application, reduced computational time, sufficient model accuracy, and model robustnesss.     

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 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.     

A new method and instrument for measuring circular motion error of NC machine tools

A new method and instrument for measuring circular motion error of numerical control (NC) machine tools are described in this paper. The instrument consists of a linear displacement transducer bar with two balls at each end and a high accuracy rotary encoder. The radius variations are detected by the transducer and the rotation angle of the bar is measured by the rotary encoder while the machine is moving in a circular path. The measuring area is circular except for a small area around the center of the disc. The bar can be expanded and contracted along its axis for different application. The instrument has a compact structure and can be installed on a machine tool simply and quickly. It is shown by the experimental results that the instrument has good repeatability and high precision of measuring circular motion trajectories. The instrument can be widely used especially in the error-compensation and error-source project in the industrial application.     

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。     

五轴数控机床综合空间误差的多体系统运动学建模

基于多体系统运动学理论的基本原理，结合RRTTT型五轴立式数控机床，阐述了多体系统的拓扑结构和低序体阵列，提出了特征矩阵的基本概念和构建方法，分析了多体系统有误差运动的基本规律，研究了根据特征矩阵得到综合空间误差的算法。理论分析和实例建模都显示所述方法能很好地解决误差建模的正确性、速度、通用性和自动化问题，为五轴数控机床精度分析和误差补偿提供了一种理想的误差建模技术。     

基于补偿模糊神经网络的数控机床热误差预报模型

文章提出了一种基于补偿模糊神经网络的数控机床热误差预报模型,讨论了该模型的详细结构、模糊规则、训练算法及相关技术问题,并给出了智能预报结果和精度评价.     

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.     

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。     

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.     

A tool-path control scheme for five-axis machine tools

This paper presents a new servo control method for five-axis machining applications. The proposed method conducts a direct elimination of the deviation error, the orientation error, and the tracking-lag error that are the main concerns for five-axis tool-path control. To achieve this purpose, the proposed five-axis control system is based on a real-time transformation between the drive-coordinate basis, in which the five drives are operated, and the workpiece-coordinate basis, in which the deviation error etc., are defined.     

A displacement measurement approach for machine geometric error assessment

It is complicated and time-consuming to evaluate the performance of a machine tool. In this research, a displacement method is proposed to shorten the measurement time and to simplify the measurement. By measuring the positioning errors along the 15 lines in the machine work zone, a total of 21 geometric error components can be determined. Among the 15 lines, seven of them are mandated by the ANSI/ASME standard for the performance evaluation of CNC machining centers. Therefore, only eight additional positioning error measurements are necessary to evaluate the machine's performance. The results from the experimental tests show that the method is feasible and accurate. This method shortens the calibration time and is beneficial, particularly to the reconfigurable machining system, which needs frequent calibration.     

大型超精密机床数控系统的研制

文章以自行研制的大型非球面超精密数控机床数控系统为对象,介绍了其软、硬件构成和为其配套研制的自动编程系统.并分析了系统超精密定位和反馈检测性能,其能很好满足所装备的大型数控机床的超精密定位和位置跟踪指标,能进行大型非球面光学零件的超精密加工.     

Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error

This paper presents a new modeling methodology for nonstationary machine tool thermal errors. The method uses the dynamic neural network model to track nonlinear time-varying machine tool errors under various thermal conditions. To accommodate the nonstationary nature of the thermo-elastic process, an Integrated Recurrent Neural Network (IRNN) is introduced to identify the nonstationarity of the thermo-elastic process with a deterministic linear trend. Experiments on spindle thermal deformation are conducted to evaluate the model performance in terms of model estimation accuracy and robustness. The comparison indicates that the IRNN performs better than other modeling methods, such as, multi-variable regression analysis (MRA), multi-layer feedforward neural network (MFN), and recurrent neural network (RNN), in terms of model robustness under a variety of working conditions.     

An improved thermal model for machine tool bearings

Thermal model for machine tool spindle is of great importance to machine tool design. Traditionally, the thermal contact resistance between solid joints and the change of the heat generation power with the bearing temperature are often ignored when thermal characteristics of a machine tool spindle are analyzed. This has caused inaccuracies in the thermal model. With the heat source models and the heat transfer models from Bossmanns and Tu [Journal of Manufacturing Science and Engineering 123 (2001) 495–501, International Journal of Machine Tools & Manufacture 39 (1995) 1345–1366], a model including the thermal contact resistance at solid joints based on a fractal model and the change of the heat generation power, viz. the amount of the heat generation per second, with the bearing temperature increases is developed. The complete thermal model is used to simulate the temperature distribution in grinding machine housing with a conventional spindle bearing. Compared with experiment, it is shown that the completed model is much more accurate than the traditional model which ignores the two important factors above. The thermal expansion of the housing system is analyzed.     

Configuration analysis of five-axis machine tools using a generic kinematic model

Five-axis machine tools are designed in a large variety of kinematic configurations and structures. Regardless of the type of the intended analysis, a kinematic model of the machine tool has to be developed in order to determine the translational and rotational joint movements required to achieve a specified position and orientation of the cutting tool relative to the workpiece. A generic and unified model is developed in this study as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of five-axis machine tools: the spindle rotating, rotary table, and hybrid type. A numerical measure of total translational joint movement is proposed to evaluate the kinematic performance of a five-axis machine tool. The corresponding kinematic analyses have confirmed the advantages of the popular machine design that employs intersecting rotational axes and the common industrial practice during setup that minimizes the characteristic rotating arm length of the cutting tool and/or workpiece.     

Accuracy improvement of miniaturized machine tool: Geometric error modeling and compensation

A novel capacitance–sensor based multi-degree-of-freedom (DOF) measurement system has been developed for measuring geometric errors of a miniaturized machine tool (mMT) overcoming the size limitations. In the present work five geometric error components of a three-axis mMT are measured simultaneously along each axis and the squareness errors are determined by the slopes of straightness error profiles. Least-squares fitting method is used to represent the analytical models of geometric errors. A kinematic chain consisting of various structural members of mMT is introduced to establish the positional relationships among its coordinate frames. Based on this kinematic chain a general volumetric error model has been developed to synthesize all geometric error components of a miniaturized machine tool. Then, a recursive compensation method is proposed to achieve error compensation efficiently. Test results show that the positioning accuracy of miniaturized machine tool has been improved with compensation.     

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.     

Modeling and improvement of dynamic contour errors for five-axis machine tools under synchronous measuring paths

In this paper, a contour error model of the tool center point (TCP) for a five-axis machine tool is proposed to estimate dynamic contour errors on three types of measuring paths. A servo tuning approach to achieve five-axis dynamic matching is utilized to improve contouring performance of the cutting trajectory. The TCP control function is developed to generate measuring trajectories where five axes are controlled simultaneously to keep the TCP at a fixed point. The interpolation method of the rotary axes with S-shape acceleration/deceleration (ACC/DEC) is applied to plan smooth five-axis velocity profiles. The contour error model for five axes is derived by substituting five-axis motion commands into servo dynamics models. The steady state contour error (SSCE) model is demonstrated to illustrate three particular dynamic behaviors: the single-circle with amplitude modulation, double-circle effect and offset behavior. Furthermore, the model is also utilized to investigate the behaviors of dynamic contour errors change in 3D space. The factors that affect dynamic contour errors, including the initial setup position, feedrate and five-axis servo gains, are analyzed. With the developed servo tuning process under the measuring paths (CK1, CK2 and CK4), the contour errors caused by servo mismatch are reduced remarkably. Finally, experiments are conducted on a desktop five-axis engraving machine to verify the proposed methodology can improve dynamic contouring accuracy of the TCP significantly.