Construction of an error map of rotary axes on a five-axis machining center by static R-test

This paper proposes an efficient and automated scheme to calibrate error motions of rotary axes on a five-axis machining center by using the R-test. During a five-axis measurement cycle, the R-test probing system measures the three-dimensional displacement of a sphere attached to the spindle in relative to the machine table. Location errors, defined in ISO 230-7, of rotary axes are the most fundamental error factors in the five-axis kinematics. A larger class of error motions can be modeled as geometric errors that vary depending on the angular position of a rotary axis. The objective of this paper is to present an algorithm to identify not only location errors, but also such position-dependent geometric errors, or “error map,” of rotary axes. Its experimental demonstration is presented.     

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.     

Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement

The geometric errors of rotary axes are the fundamental errors of a five-axis machine tool. They directly affect the machining accuracy, and require periodical measurement, identification and compensation. In this paper, a precise calibration and compensation method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The automated measurement is realized by using an on-the-machine touch-trigger technology and an artifact. A calibration algorithm is proposed to calibrate geometric errors of rotary axes based on the relative displacement of the measured reference point. The geometric errors are individually separated and the coupling effect of the geometric errors of two rotary axes can be avoided. The geometry error of the artifact as well as its setup error has little influence on geometric error calibration results. Then a geometric error compensation algorithm is developed by modifying the numeric control (NC) source file. All the geometric errors of the rotary errors are compensated to improve the machining accuracy. The algorithm can be conveniently integrated into the post process. At last, an experiment on a five-axis machine tool with table A-axis and head B-axis structure validates the feasibility of the proposed method.     

Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool

This paper proposes an efficient and automated scheme to predict and identify the position and motion errors of rotary axes on a non-orthogonal five-axis machining centre using the double ball bar (DBB) system. Based on the Denavit-Hartenberg theory, a motion deviations model for the tilting rotary axis B and rotary C of a non-orthogonal five-axis NC machine tool is established, which considers tilting rotary axis B and rotary C static deviations and dynamic deviations that total 24. After analysing the mathematical expression of the motion deviations model, the QC20 double ball bar (DBB) from the Renishaw Company is used to measure and identify the motion errors of rotary axes B and C, and a measurement scheme is designed. With the measured results, the 24 geometric deviations of rotary axes B and C can be identified intuitively and efficiently. This method provides a reference for the error identification of the non-orthogonal five-axis NC machine tool.     

Double ballbar test for the rotary axes of five-axis CNC machine tools

In this paper a new method that uses the double ballbar to inspect motion errors of the rotary axes of five-axis CNC machine tools is presented. The new method uses a particular circular test path that only causes the two rotary axes to move simultaneously and keeps the other three linear axes stationary. Therefore, only motion errors of the two rotary axes will be measured during the ballbar test. The theoretical trace patterns of various error origins, including servo mismatch and backlash, are established. Consequently, the error origins in the rotary block can be diagnosed by examining whether similar patterns appear in the motion error trace. The method developed was verified by practical tests, and the servo mismatch of the rotary axes was successfully detected.     

5轴加工奇异区域非线性误差控制方法

5轴数控机床在加工奇异区域时,由于旋转轴的剧烈变化导致产生较大的非线性误差,加工质量下降。针对这个问题,以A-C双转台机床为例,分析机床产生奇异现象的原因,提出检测5轴加工奇异区域的方案,通过对奇异区域相邻刀轴矢量之间进行插值处理,减小相邻刀轴的角度变化,使相邻刀位点之间的最大非线性误差小于机床允许的最大非线性误差。用MATLAB对比插值前后5轴机床转角和非线性误差的变化,证明该方法可以降低C轴的过大转角同时减小非线性误差。     

Analysis of circular trajectory equivalent to cone-frustum milling in five-axis machining centers using motion simulator

The present paper describes the effect of the half apex angle of the cone-frustum on the motion trajectory under simultaneous five-axis motion and the effect of the sensitive direction of the ball bar when the motion trajectory is measured along the three-dimensional circular conical path. In the present paper, simulation of the measurement by means of a ball bar instrument is mainly conducted using a motion simulator developed previously. In particular, a precise mathematical model was developed to express the pitch errors of the axes of rotation of the five-axis machining center having a tilting rotary table driven by worm gears. In the experiment and simulation, primarily the center position and half apex angle of the cone-frustum were varied. In addition, two sensitive directions of the ball bar were investigated. The motion simulator incorporating the pitch error model can express the detailed trajectories obtained by the ball bar, even if the half apex angle and center position of the cone-frustum and the sensitive direction of the ball bar were changed. Then, the influence of the frictional force of the linear axes of motion, and the backlash and pitch error of the axes of rotation on the circular trajectories were analyzed. In particular, for the case of a half apex angle of 45°, the trajectory due to the errors of the axis of rotation is strongly affected by the sensitive direction of the ball bar.     

五轴联动数控机床非线性误差的研究

五坐标插补过程中,旋转轴运动的影响使实际刀位运动偏离编程直线,产生了非线性误差。在深入分析双摆头五坐标机床运动原理和非线性误差的产生机理的基础上,介绍了一种集成RTCP(旋转刀具中心点)功能的插补算法。RTCP功能可使数控系统自动对旋转轴的运动进行实时线性补偿,从而保证插补点始终位于编程轨迹上。通过MATLAB仿真计算验证了该算法可以有效减小非线性误差。     

一种旋转折弯成形的数值模拟方法及实验验证

旋转折弯成形是板料的一种特殊的自由折弯成形方法,准确预测其回弹误差是控制旋转折弯角精度的前提.鉴于Dynaform软件无法直接实现旋转折弯成形的模拟,在分析Dynaform前处理器所生成的DYN文件的基础上,通过定义旋转动模的惯性张量参考坐标系、惯性张量、旋转坐标轴、自由度和旋转运动曲线等参数值,提出了一种旋转折弯成形...     

Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar

In this study, position-independent geometric errors, including offset errors and squareness errors of rotary axes of a five-axis machine tool are measured using a double ball-bar and are verified through compensation. In addition, standard uncertainties of measurement results are calculated to establish their confidence intervals. This requires two measurement paths for each rotary axis, which are involving control of single rotary axis during measurement. So, the measurement paths simplify the measurement process, and reduce measurement cost including less operator effort and measurement time. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants. Their effects on the measurement results are investigated to improve the accuracy of the measurement result. A novel fixture consisting of flexure hinges and two pairs of bolts is used to minimize set-up error by adjusting the ball's position located at the tool nose. Simulation is performed to check the validation of measurement and to analyze the standard uncertainties of the measurement results. Finally, the position-independent geometric errors of the five-axis machine tool (involving a rotary axis and a trunnion axis) are measured using proposed method.     

螺距误差补偿在提高数控转台定位精度中的应用

本文介绍了回转轴的螺距误差补偿原理和基于激光干涉仪的螺距误差测量系统,并讨论了这种螺距误差补偿方法在提高数控转台定位精度时所出现的问题和解决方案。     

Ballbar dynamic tests for rotary axes of five-axis CNC machine tools

This paper proposes a new ball bar test method for the inspection of dynamic errors of rotary axes in five-axis CNC machine tools. The test circle is defined in a workpiece coordinate system and the ball bar test is performed by simultaneously driving of linear–rotary axis couple. The effects of the center position and the radius on the setting values, rotational range and measurement sensitivity of the rotary axis were investigated. The proposed ball bar test is performed in two steps: the circular positioning and the circular tracking with a continuous feed. Axial dynamic errors are obtained by subtracting the measured tracking errors from the positioning errors. A ball bar test system (BBTS) was developed to plan the tool path and the tool orientation, to communicate with the five-axis CNC controller and to process the measured data. Error patterns were simulated regarding the gain mismatch, backlash and tracking direction to help a fast diagnosis of the error sources. Simulations and experimental results prove the effectiveness of the new test method.     

基于虚拟中心距加工原理的新型平面二次包络环面蜗杆数控磨床设计及关键技术研究

针对新型平面二次包络环面蜗杆数控磨床研发中的难题,在蜗杆齿面的成形原理及传统磨削方法的基础上分析了齿面的虚拟中心距磨削原理及关键技术,论证了四轴四联动磨削方法的可行性并提出了新型磨床的结构布局及总体设计方案;针对产形面到摆头回转工作台中心轴线距离过大以及砂轮产形面上的磨削点到联动回转工作台中心轴线距离过大的两类难题,在结构布局上提出了砂轮倾角式磨头设计匹配磨头内藏式的设计方案,对于砂轮的修整及补偿方式提出了主轴平移修砂的设计方案,解决了在磨削过程中,因联动回转工作台回转误差所造成的砂轮磨削区域形位超差的问题并完成了机床虚拟样机的设计。     

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.     

Identification and compensation of systematic deviations particular to 5-axis machining centers

This paper presents an algorithm for identifying particular deviations such as angular deviations around linear axes relating to rotary axes in 5-axis machining centers. In this study, three kinds of simultaneous three-axis control motions are designed for each rotary axis to identify the deviations. In the measurement, two translational axes and one rotary axis are simultaneously controlled keeping the distance between a tool and a worktable constant. Telescoping ball bar is an effective instrument for measuring the relative displacement to the reference length in the work volume because its attitude is freely changed. In these three-axis control motions, the sensitive direction of the ball bar is kept constant. In order to determine the deviations, we derive eight equations from the relationship between the eccentricities obtained from the measured circular trajectories and the approximations derived from the mathematical model based on the simulation. In the simulation, a mathematical model considering the particular deviations is developed and then the characteristic diagrams are prepared for every deviation and every three-axis control motion. Based on the results, we propose a procedure for identifying the particular deviations in 5-axis machining centers and its procedure has been applied to identify the deviations actually. From both the simulation and the experiment, it has been confirmed that the proposed method gives precision results and is able to apply to the measurement of 5-axis machining center which is a tilting rotary table type.     

五轴联动数控系统非线性误差的研究与控制

五轴联动数控机床由于两个旋转轴的存在使得插补后获得的刀具轨迹与理论编程轨迹不相等,存在非常大的非线性误差。通过对运动学坐标变换、双摆头五轴联动机床刀具运动原理和插补原理进行分析得出引起非线性误差的原因。介绍一种基于时间分割法的插补算法,通过MATLAB进行仿真实验及参数分析,其结果表明了该算法的有效性。     

激光干涉仪检测光路的快速校准方法

在使用激光干涉仪时,光路校准过程比较困难,需反复调整,耗时极长,严重依赖操作者的技术水平及经验,导致检测效率大大降低。通过对雷尼绍XL-80激光干涉仪检测的机床直线轴Y轴的光路进行分析,建立被测轴的齐次坐标变换误差模型,利用机床Y轴移动距离,再借助随着光点从光靶中心移动到光靶边缘的固定距离,求解与被测轴Y轴位置无关的激光发射器偏摆和俯仰角,以及间接得到激光器和反射镜位置偏移误差和光点在坐标系间变换的距离。通过建立的误差模型求解无法直接测量的分光镜与反射镜绕各自本身垂直底座轴线的偏摆误差,调整各部件,快速准确地完成光路校准。     

A new compensation method for geometry errors of five-axis machine tools

The present study aims to establish a new compensation method for geometry errors of five-axis machine tools. In the kinematic coordinate translation of five-axis machine tools, the tool orientation is determined by the motion position of machine rotation axes, whereas the tool tip position is determined by both machine linear axes and rotation axes together. Furthermore, as a nonlinear relationship exists between the workpiece coordinates and the machine axes coordinates, errors in the workpiece coordinate system are not directly related to those of the machine axes coordinate system. Consequently, the present study develops a new compensation method, the decouple method, for geometry errors of five-axis machine tools. The method proposed is based on a model that considers the tool orientation error only related to motion of machine rotation axes, and it further calculates the error compensations for rotation axes and linear axes separately, in contrast to the conventional method of calculating them simultaneously, i.e. determines the compensation of machine rotation axes first, and then calculates the compensation associated with the machine linear axes. Finally, the compensation mechanism is applied in the postprocessor of a CAM system and the effectiveness of error compensation is evaluated in real machine cutting using compensated NC code. In comparison with previous methods, the present compensation method has attributes of being simple, straightforward and without any singularity point in the model. The results indicate that the accuracy of positioning was improved by a factor of 8–10. Hence, the new compensation mechanism proposed in this study can effectively compensate geometry errors of five-axis machine tools.     

5轴卧式加工中心回转工作台设计与应用

大型5轴卧式加工中心机床回转工作台是机床在加工过程中驱动工件回转的部件,回转精度及可靠性直接影响机床的整体性能。针对5轴机床在联动切削过程中B轴移动的特点,选用大型可调间隙蜗轮蜗杆进行传动,传动机构配置有减速机构以增加驱动力矩,回转机构通过大型轴向径向组合轴承支撑,通过高精度光栅尺进行位置反馈,得到快速进给5 r/min、定位精度为3″、重复定位精度为1.5″的高精度回转工作台。     

A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar

Ensuring that a five-axis machine tool is operating within tolerance is critical. However, there are few simple and fast methods to identify whether the machine is in a “usable” condition. This paper investigates the use of the double ball bar (DBB) to identify and characterise the position independent geometric errors (PIGEs) in rotary axes of a five-axis machine tool by establishing new testing paths. The proposed method consists of four tests for two rotary axes; the A-axis tests with and without an extension bar and the C-axis tests with and without an extension bar. For the tests without an extension bar, position errors embedded in the A- and C-axes are measured first. Then these position errors can be used in the tests with an extension bar, to obtain the orientation errors in the A- and C-axes based on the given geometric model. All tests are performed with only one axis moving, thus simplifying the error analysis. The proposed method is implemented on a Hermle C600U five-axis machine tool to validate the approach. The results of the DBB tests show that the new method is a good approach to obtaining the geometric errors in rotary axes, thus can be applied to practical use in assembling processes, maintenance and regular checking of multi-axis CNC machine tools.