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.     

基于激光干涉仪的数控机床运动误差识别与补偿

提出了数控机床运动误差的软件补偿方法。采用刚体运动假设和齐次坐标变换建立了多轴机床空间运动误差的通用模型。该模型把刀具相对于工件的空间误差表示为机床各结构件之间运动误差的位置函数。给出了全部运动误差参数的激光干扰仪识别方法，提出了一种新的roll误差测量措施，在立式加工中心上进行了运动误差的补偿实验，结果证明所提出的运动误差软件联动补偿效果显著。     

The detection of rotary axis of NC machine tool based on multi-station and time-sharing measurement

At present, the detection of rotary axis is a difficult problem in the errors measurement of NC machine tool. In the paper, a method with laser tracker on the basis of multi-station and time-sharing measurement principle is proposed, and this method can rapidly and accurately detect the rotary axis. Taking the turntable measurement for example, the motion of turntable is measured by laser tracker at different base stations. The redundant equations can be established based on the large amount of measured data concerning the distance or distance variation between measuring point and base station. The coordinates of each measuring point during turntable rotation can be accurately determined by solving the equations with least square method. Then according to the error model of rotary axis, the motion error equations of each measuring point can be established, and each error of turntable can be identified. The algorithm of multi-station and time-sharing measurement is derived, and the error separation algorithm is also deduced and proved feasible by simulations. Results of experiment show that a laser tracker completes the accuracy detection of the turntable of gear grinding machine within 3 h, and each error of the turntable are identified. The simulations and experiments have verified the feasibility and accuracy of this method, and the method can satisfy the rapid and accurate detecting requirements for rotary axis of multi-axis NC machine tool.     

Geometric error calibration of multi-axis machines using an auto-alignment laser interferometer

This work will report the development and application of an auto-alignment laser interferometer system for the geometric error calibration of CNC multi-axis machines. The system is capable of a diagonal displacement measurement, where multiple machine axes are moved simultaneously, with automatic optic alignment. This capability provides a solution for quick evaluation of the overall volumetric error of a multi-axis machine tool. One application of the system is that the 21 geometric errors of a 3-axis machine can be quickly estimated from the displacement measurements of some determined diagonal lines in the working volume. Compared with a time of several days using a conventional laser interferometer system, it takes only 1 hour for the proposed system to complete the geometry calibration of a 3-axis machine. A method for the roll calibration of a vertical axis is also proposed and demonstrated in this work.     

基于敏感度分析的机床关键性几何误差源识别方法

零部件几何误差耦合而成的机床空间误差是影响其加工精度的主要原因,如何确定各零部件几何误差对加工精度的影响程度从而经济合理地分配机床零部件的几何精度是目前机床设计所面临的一个难题。基于多体系统理论,在敏感度分析的基础上提出一种识别关键性几何误差源参数的新方法。以一台四轴精密卧式加工中心为例,基于多体系统理论构建加工中心的精度模型,并利用矩阵微分法建立四轴数控机床误差敏感度分析的数学模型,通过计算与分析误差敏感度系数,最终识别出影响机床加工精度的关键性几何误差。计算和试验分析表明,该方法可以有效地识别出对机床综合空间误差影响较大的主要零部件几何误差因素,从而为合理经济地提高机床的精度提供重要的理论依据。     

机械制造业数控机床几何误差自动控制

为了降低数控机床几何误差,提升加工精度,提出机械制造业数控机床几何误差自动控制方法。通过激光跟踪仪辨识机械制造业数控机床的几何误差,采用快速定位补偿算法与圆弧插补补偿算法相结合的方法补偿数控机床几何误差。利用计算机辅助制造软件生成刀位文件,依据刀位文件生成数控机床加工程序,通过补偿控制器生成数控机床各轴运动的控制指令,数控机床伺服系统接收控制指令后,自动控制数控机床各轴运动,以达到数控机床几何误差自动控制的目的。实验结果表明,采用该方法自动控制数控机床几何误差后,方向与角度的几何误差分别低于0.03 mm与0.1°,实际应用效果较好。     

数控机床误差的激光干涉仪自动瞄准测量及补偿技术研究

开发了用于数控机床空间误差测量的激光干涉仪自动瞄准系统。该系统实现了机床多轴联动、而激光束的方向发生连续改变时空间曲线轨迹定位误差的测量。提出了通过一次对光实现数控机床整个空间定位误差的直接测量方法。采用网格方法储存测量误差,用有限元法实现补偿误差的预报。在立式数控加工中心上进行了误差的测量和补偿试验,结果表明所提出的误差测量方法精度高、速度快,误差补偿效果明显。     

Geometric error compensation for multi-axis CNC machines based on differential transformation

As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path.     

Product of exponential model for geometric error integration of multi-axis machine tools

This paper proposes a product of exponential (POE) model to integrate the geometric errors of multi-axis machine tools. Firstly, three twists are established to represent the six basic error components of each axis in an original way according to the geometric definition of the errors and twists. The three twists represent the basic errors in x, y, and z directions, respectively. One error POE model is established to integrate the three twists. This error POE formula is homogeneous and can express the geometric meaning of the basic errors, which is precise enough to improve the accuracy of the geometric error model. Secondly, squareness errors are taken into account using POE method to make the POE model of geometric errors more systematic. Two methods are proposed to obtain the POE models of squareness errors according to their geometric properties: The first method bases on the geometric definition of errors to obtain the twists directly; the other method uses the adjoint matrix through coordinate system transformation. Moreover, the topological structure of the machine tools is introduced into the POE method to make the POE model more reasonable and accurate. It can organize the obtained 14 twists and eight POE models of the three-axis machine tools. According to the order of these POE models multiplications, the integrated POE model of geometric errors is established. Finally, the experiments have been conducted on an MV-5A three-axis vertical machining center to verify the model. The results show that the integrated POE model is effective and precise enough. The error field of machine tool is obtained according to the error model, which is significant for the error prediction and compensation.     

Calibrating the volumetric errors of a precision machine by a laser tracker system

In this paper, a quick solution for measuring the volumetric errors of a precision machine is presented. It requires a laser tracker system and a plate including three caves on it. The laser tracker system can detect the coordinate of a sensor ball anywhere in the working space. The plate is fixed on the machine spindle. After installation, the spindle is moved toward the diagonal of the working space. The real movements are along the x, y, and z-axis directions, respectively; it will back to the diagonal line for one complete cycle motion. In each step movement, the spindle is stopped and the laser tracker detects the coordinates of the three caves by putting the target sensor ball into caves sequentially. By means of the coordinates, the volumetric errors at that position can be derived. The overall volumetric errors can be measured quickly by just one setup and many step movements with laser tracker detections.     

数控机床空间误差球杆仪识别和补偿

提出了多轴机床空间误差的球杆仪识别方法和补偿技术。建立了机床刀尖相对工件的空间误差的误差参数模型;给出了在机床工作空间中三个互相垂直的平面内,用球杆仪测量圆周运动的半径误差结合机床的空间误差模型识别定位、直线度、角度、垂直度和反向间隙等误差参数的方法。补偿试验结果证明该误差识别与补偿方法省时有效。     

Assessing geometrical errors of multi-axis machines by three-dimensional length measurements

In this paper a method is presented for assessing geometrical errors of multi-axis machines based on volumetric three-dimensional length measurements. A universal machine error model is proposed since a large variety of machine configurations exists. Such models can be used for software error compensation techniques in order to improve the machine’s positioning behaviour as well as for diagnostic purposes. Length measurements are chosen for the measurement of the positioning errors of a multi-axis machine because these measurements can be executed in a short period of time in a relatively simple way combined with a high accuracy. In order to get comparable results for the geometrical errors as measured with conventional techniques, i.e., laser interferometry, the design of the measurement setup as well as the formulation of the machine error model (including parameter correlation effects) appeared to be of major importance and are subject of this paper.     

Simultaneous geometric error identification of rotary axis and tool setting in an ultra-precision 5-axis machine tool using on-machine measurement

This paper presents a method to identify the position independent geometric errors of rotary axis and tool setting simultaneously using on-machine measurement. Reducing geometric errors of an ultra-precision five-axis machine tool is a key to improve machining accuracy. Five-axis machines are more complicated and less rigid than three axis machine tools, which leads to inevitable geometric errors of the rotary axis. Position deviation in the process of installing a tool on the rotary axis magnifies the machining error. Moreover, an ultra-precision machine tool, which is capable of machining part within sub-micrometer accuracy, is relatively more sensitive to the errors than a conventional machine tool. To improve machining performance, the error components must be identified and compensated. While previous approaches have only measured and identified the geometric errors on the rotary axis without considering errors induced in tool setting, this study identifies the geometric errors of the rotary axis and tool setting. The error components are calculated from a geometric error model. The model presents the error components in a function of tool position and angle of the rotary axis. An approach using on-machine measurement is proposed to measure the tool position in the range of 10 s nm. Simulation is conducted to check the sensitivity of the method to noise. The model is validated through experiments. Uncertainty analysis is also presented to validate the confidence of the error identification.     

Applying bidirectional kinematics to assembly error analysis for five-axis machine tools with general orthogonal configuration

Since a five-axis machine tool has two more rotary axes and two more degrees of freedom than a three-axis machine tool, it can manufacture a complex surface more efficiently. However, there are more error terms due to the extra axes. Error sources for machine tools include structural error, dynamic error, and static error. The static error, which includes thermal and geometric errors, is the main source of machining inaccuracy in machine tools. Although a large number of studies have been made on geometric errors, the influence of individual error term on volumetric error is seldom discussed. This paper analyzes assembly error that belongs to the category of static error, and the analytic method can be applied to general orthogonal configurations. By adopting the machine tool form-shaping function, the effect of assembly errors on volumetric errors has been investigated. And the error terms that cannot be compensated by driving single control axis have been recognized and explored for general orthogonal configurations.     

Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes

Synthesis modeling of a geometric error-based traditional method for large-scale grinding machine tools with six axes is too complicated to perform in a real-time compensator with a built-in position control system, and it is difficult to obtain all of the error elements corresponding to the model. This paper proposed a novel strategy in which a machine may be considered as translation axes and rotary axes, and geometric errors of the translation axes and rotary axis are modeled and the geometric error models of the machine are very simple for real-time error compensation. The volumetric errors of the translation axes are measured using spatial circular curve ball bar test, and every element of the rotary axis is also obtained by a series of considerate ball bar tests. According to the characteristics of a position controller used in the machine, a synthesis error compensation system based on the NUM numerical control system was developed. Error compensation experiments were carried out, and the results show that the accuracy of the machine is improved significantly.     

大型数控龙门铣床几何误差补偿方法研究

针对大型数控龙门铣床几何误差的问题,建立了大型数控龙门铣床的几何误差模型,分析了大型数控龙门铣床的几何误差源;利用API(T3)激光跟踪仪高精度大尺寸的测量特点及数据处理能力,提出了X、Y、Z轴线位移误差、角位移误差及各轴间垂直度误差的辨识算法,通过激光测量与计算准确地辨识了大型数控龙门铣床的几何误差;建立了大型数控龙门铣床加工空间几何误差数学模型,采用基于对象的事件驱动机制的程序设计语言Visual Basic开发了几何误差补偿软件,实现了几何误差补偿;现场检测了大型数控龙门铣床空行程平面运动轨迹及工件的平面度。研究结果表明,该方法使平面加工精度提高了50.77%,并验证了几何误差模型的正确性及几何误差补偿方法的有效性。     

Modeling and compensation of geometric errors in simultaneous cutting using a multi-spindle machine tool

A volumetric error compensation method for a machining center that has multiple cutting tools operating simultaneously has been developed. Due to axis sharing, the geometric errors of multi-spindle, concurrent cutting processes are characterized by a significant coupling of error components in each cutting tool. As a result, it is not possible to achieve exact volumetric error compensation for all axes. To minimize the overall volumetric error in simultaneous cutting, a method to determine compensation amount using weighted least squares has been proposed. This method also allows tolerance distribution of machining accuracy for different surfaces of a workpiece. A geometric error model has been developed using an arch-type, multi-spindle machine tool, and the error compensation simulation results based on this model are presented. The simulation results demonstrated effectiveness of the proposed error compensation algorithm for use with multi-spindle simultaneous cutting applications.     

飞秒激光跟踪仪光轴与竖轴同轴度的标定

考虑飞秒激光跟踪仪仪器轴系的几何误差会影响仪器的指向精度并最终影响坐标测量精度,本文研究了激光光轴与竖轴的几何误差对仪器测量精度的影响。提出了激光光轴与竖轴的同轴度标定方法,以降低其不重合带来的跟踪测量误差。首先,基于几何光学原理建立了光轴与竖轴的几何误差模型,分别分析了光轴与竖轴的倾斜与平移误差对仪器测角精度的影响。然后,针对设计的仪器提出了基于旋转成像原理的光轴与竖轴同轴度的检测方法,并设计了一套同轴度检测装置。最后,基于该检测装置,通过调节两组双光楔完成了激光光轴与竖轴的倾斜与平移误差的标定。结果显示,经标定校准后激光光轴与竖轴的角度误差为3.4″;平移误差为26.1μm,得到的结果为仪器后续建立误差补偿模型奠定了基础。     

A control strategy with motion smoothness and machining precision for multi-axis coordinated motion CNC machine tools

The advanced manufacture technology requires that multi-axis coordinated motion computer numerical control (CNC) machine tools have the capability of high smoothness and high precision. At present, the study of the motion smoothness mainly concentrates on the acceleration and deceleration control method and the look-ahead process of velocity planning in the interpolation stage. The control strategy of the contouring error mainly focuses on tracking error control, cross-coupling control, and optimal control. In order to improve the motion smoothness and contouring precision for multi-axis high-speed CNC machine tools, a multi-axis modified generalized predictive control approach was presented in this paper. In the control strategy, the estimation models of tracking error, contouring error, velocity error, and acceleration error were structured separately. A new improved quadratic performance index was proposed to guarantee the minimum of these errors. Generalize predictive control was also introduced, a multi-axis generalized predictive control model was deduced for motion smoothness and machining precision for multi-axis coordinated motion CNC system, and an approved multi-axis generalized predictive controller based on the model was designed in this paper. The proposed predicted control approach was evaluated by simulation and experiment of circular, noncircular, and space line trajectories, respectively. These simulative and experimental results demonstrated that the proposed control strategy can significantly improve the motion smoothness and contouring precision. Therefore, the new position control method can be used for the servo control system of multi-axis coordinated motion CNC system, which increases motion smoothness and machining precision of CNC machine tools.     

Identification and measurement of geometric errors for a five-axis machine tool with a tilting head using a double ball-bar

Geometric errors are one of the primary potential sources of error in a five-axis machine tool. There are two types of geometric errors: position-dependent geometric errors and position-independent geometric errors. A method is proposed to identify and measure the position-independent geometric errors of a five-axis machine tool with a tilting head by means of simultaneous multi-axis controlled movements using a double-ball bar (DBB). Techniques for identifying position-independent geometric errors have been proposed by other researchers. However, most of these are based on the assumption that position-dependent geometric errors (such as linear displacement, straightness, and angular errors) are eliminated by compensation, once the position-independent geometric errors have been identified. The approach suggested in this paper takes into account the effect of position-dependent geometric errors. The position-dependent geometric errors are first defined. Path generation for circle tests with two or three simultaneous control movements is then carried out to measure the position-independent geometric errors. Finally, simulations and experiments are conducted to confirm the validity of the proposed method. The simulation results show that the proposed method is sufficient to accurately identify position-independent geometric errors. The experimental results indicate that the technique can be used to identify the position-independent errors of a five-axis machine tool with a tilting head.