Geometric characterisation and simulation of position independent geometric errors of five-axis machine tools using a double ball bar

A double ball bar (DBB) is extensively used to evaluate the geometric and dynamic performance of three-axis machine tools by means of the XY, YZ and XZ planar circular tests. Errors can be estimated by comparing them with known error profiles. However, such geometric interpretation of error plots of five-axis machine tools is limited. In this paper, a five-axis machine tool model is established with Homogeneous Transformation Matrices (HTMs), laying the foundation for characterising particular geometric shapes induced by various Position Independent Geometric Errors (PIGEs) of all five axes. A testing scheme is proposed to evaluate the target five-axis machine tool in two major steps: testing the rotary axes individually and testing the linear-rotary axes couples. In the first step, each rotary axis is tested with two substeps, with and without the extension bar on the DBB. The second step requires each linear and rotary axes combination to move simultaneously. Both approaches are performed with only one setup, thus simplifying the setup procedure and reduce the machine down time. To show the validity of the method, PIGEs for each axis are simulated with the given machine tool model. Several DBB trajectories are simulated using the machine tool model. Compared with the actual testing plots, the simulated DBB error plots are helpful to diagnose the PIGEs of linear and rotary axes based on their particular geometric shapes. The results suggest that the proposed method along with the given error characteristics can be used as a fast indication of a five-axis machine tool’s performance.     

Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools

A machining test of cone frustum, described in NAS (National Aerospace Standard) 979, is widely accepted by machine tool builders to evaluate the machining performance of five-axis machine tools. This paper discusses the influence of various error motions of rotary axes on a five-axis machine tool on the machining geometric accuracy of cone frustum machined by this test. Position-independent geometric errors, or location errors, associated with rotary axes, such as the squareness error of a rotary axis and a linear axis, can be seen as the most fundamental errors in five-axis kinematics. More complex errors, such as the deformation caused by the gravity, the pure radial error motion of a rotary axis, the angular positioning error of a rotary axis, can be modeled as position-dependent geometric errors of a rotary axis. This paper first describes a kinematic model of a five-axis machine tool under position-independent and position-dependent geometric errors associated with rotary axes. The influence of each error on machining geometric accuracy of a cone frustum is simulated by using this model. From these simulations, we show that some critical errors associated with a rotary axis impose no or negligibly small effect on the machining error. An experimental case study is presented to demonstrate the application of R-test to measure the enlargement of a periodic radial error motion of C-axis with B-axis rotation, which is shown by present numerical simulations to be among potentially critical error factors for cone frustum machining test.     

五轴机床旋转轴误差的在机测量与模糊径向基神经网络建模

考虑五轴机床中的旋转轴误差会影响加工精度和在机测量结果,本文研究了旋转轴误差的在机测量与建模方法。介绍了基于标准球和机床在机测量系统的旋转轴综合误差测量方法,采用随机Hammersely序列分组规划旋转轴的测量角位置,通过自由安放策略确定标准球初始安装位置。然后,引入模糊减法聚类和模糊C-均值聚类(Fuzzy C-means,FCM)建立旋转轴误差的径向基(Radial basis function,RBF)神经网络预测模型。最后,进行数学透明解析,从而为误差的精确解析建模提供新途径。利用曲面的在机测量实例验证了提出的旋转轴误差测量与建模方法。结果表明:利用所建模型计算的预测位置与实测位置的距离偏差平均值为9.6μm,最大值不超过15μm;利用所建模型补偿工件的在机测量结果后,其平均值由32.5μm减小到13.6μm,最大误差也由62.3μm减小到18.6μm。结果显示,提出的测量方法操作简单,自动化程度高;模糊RBF神经网络的学习速度快、适应能力强、鲁棒性好,能满足高度非线性、强耦合的旋转轴误差建模要求。     

Position-dependent geometric errors measurement and identification for rotary axis of multi-axis machine tools based on optimization method using double ball bar

Geometric errors measurement and identification for rotary table are important. However, precisely adjustment for the setup position of a double ball bar in each measurement pattern is inconvenient. This study proposes a novel optimization identification method using a double ball bar to recognize the position-dependent geometric errors (PDGEs) of rotary axis. A mathematical model for ball bar measurement is firstly constructed to map the relationship between measurement direction and position of the double ball bar. And then, the setup positions of the double ball bar for PDGEs identification are analyzed. According to analysis for setup positions of the double ball bar, simplified measurement patterns would be conducted by adjusting only two setup positions for the ball bar and thus reduce the procedure of accurate adjustment for the ball bar. The PDGEs can be fitted as an nth B-spline curve, on the account of its being smooth and continuous. To identify the PDGEs, an optimization method, by computing the suitable value of control points of nth B-spline curve of errors to minimize the optimal value of the target function between the actual measured value and the value derived from a theoretical measurement model, is proposed. Moreover, in order to obtain the accurate value of control points of the error curve, the sensitivity analysis is conducted to acquire the sensitivity matrix with respect to control points of errors. The PDGEs are able to be identified simultaneously after calculating the appropriate values of control points of errors. The proposed identification method is validated by simulation and experiment. The results prove the effectiveness of the proposed method.     

基于参数化建模的球杆仪安装误差与直线轴几何误差分离方法

针对球杆仪圆测试中直线轴几何误差与球杆仪安装误差共同作用造成检测结果失真的问题,提出了基于参数化建模的球杆仪安装误差与直线轴几何误差分离方法.首先,通过齐次坐标变换建立了包含球杆仪安装误差与直线轴几何误差的杆长变化模型;其次,结合直线轴几何误差的位置相关特性对其进行参数化建模;接着,通过对直线度误差缺项建模,构建了可解的杆长变化参数化模型,实现直线轴几何误差与球杆仪安装误差的分离;最后,仿真验证了分离方法的正确性,并应用于实际的圆测试中,分离了数值为4.3 mm和18.7 mm的X向和Y向安装误差,X向与Y向综合几何误差分量变化范围由30.7 mm、27.9 mm减小为13.6 mm、11.4 mm,实现了球杆仪安装误差与直线轴几何误差的有效分离.     

五轴数控机床几何误差建模与分析

基于多体系统基本理论推导出相邻体理想坐标变换以及误差变换矩阵并通过拓扑方法拓展到任一体理想坐标及误差变化公式。进而应用到五轴机床对应的零部件进行机床几何误差建模。最后推导出刀具形成点与工件被加工点的空间位置误差模型。并结合实验探究五轴数控机床37项误差参数对实际运动中的刀具形成点的位置误差影响,为之后的误差补偿和机床精度预测奠定理论基础。     

Kinematic error separation on five-axis NC machine tool based on telescoping double ball bar

The theory and algorithm of the homogeneous transformation matrix (HTM) method are applied in establishing the kinematic error model of five-axis machining tool with two-axis turntable. Based on this model, a new method for the kinematic error separation in five-axis numerical control (NC) machining tool is proposed. In this study, three types 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 to keep a constant distance between the tool and the worktable. Telescoping double ball bar is used to measure the relative distance between the spindle and the worktable in the motion of NC machining tool. Finally, the value measured by telescoping double ball bar is substituted into the model to obtain kinematic error of NC machining tool. Comparison has confirmed that the proposed method is high precision and can be applied to effectively and conveniently measure the five-axis machining tool.     

转台-摆头式五轴机床几何误差测量及辨识

为降低转动轴几何误差对转台-摆头式五轴机床精度的影响,提出了基于球杆仪的位置无关几何误差测量和辨识方法。基于多体系统理论及齐次坐标变换方法建立了转台-摆头式五轴机床位置无关几何误差模型,依据旋转轴不同运动状态下的几何误差影响因素建立基于圆轨迹的四种测量模式,并实现10项位置无关几何误差的辨识。利用所建立的几何误差模型进行数值模拟,确定转动轴的10项位置无关几何误差对测量轨迹的影响。最后,采用误差补偿的形式实验验证所提出的测量及辨识方法的有效性,将位置无关几何误差补偿前后的测量轨迹进行比较。误差补偿后10项位置无关几何误差的平均补偿率为70.4%,最大补偿率达到88.4%,实验结果表明所提出的建模和辨识方法可用于转台-摆头式五轴机床转动轴精度检测,同时可为机床精度评价及几何精度提升提供依据。     

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.     

Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools

This study investigated the influence of the rotary axis of a 5-axis machine tool on the tool-workpiece compliance. The evaluation focused on the influence of the rotation angle and clamping condition of the B axis on the compliance variation. A method was determined to calculate the tool-workpiece compliance in an arbitrary direction from compliances measured using orthogonal triaxial excitations. Then, the tool-workpiece compliance of a 5-axis machine tool was evaluated and displayed using a color map. The compliance map showed that the magnitude of the compliance varied by up to 40% with changes in the B axis rotation angle and its clamping condition. A drastic change in the negative real part of the compliance was also detected in the compliance map. The results of an experimental modal analysis are used to discuss the cause of the compliance variation. The bending mode of the B axis is an important mode because the change in the bending direction due to B axis rotation has a great influence on the direction dependency of the compliance magnitude and the stability limit. A cutting experiment was conducted to verify the correspondence between the evaluated compliance and the vibrational amplitude in a real cutting process. The compliance variation in the compliance map corresponded to the amplitude variation of the vibration in an end milling process. The compliance map revealed that the vibration synchronized with the passing cycle of cutters was decreased by 80% by unclamping the B axis.     

Error modelling and measurement for the rotary table of five-axis machine tools

Rotary tables are widely used with multi-axis machine tools as a means for providing rotational motions for the cutting tools on the three-axis machine tools used for five-axis machining operations. In this paper, we present a comprehensive procedure for the calibration of the rotary table including: geometric error model; error compensation method for the CNC controller; error measurement method; and verification of the error model and compensation algorithm with experimental apparatus. The methods developed were verified by various experiments, showing the validity and effectiveness of the presented methods, indicating they can be used for multi-axis machine tools as a means of calibration and precision enhancement of the rotary table.     

Machining tests for identification of location errors on five-axis machine tools with a tilting head

The International Journal of Advanced Manufacturing Technology - Location errors are considered as one of the fundamental errors of five-axis machine tools. For the improvement of machine accuracy,...     

基于球杆仪的直线轴位置相关误差辨识研究

针对多轴机床空间误差检测及辨识方法成本高、时间长等问题,提出一种新的基于球杆仪测试的直线轴位置相关几何误差辨识方法。分别建立各平面内轴运动误差模型,并采用多项式对误差元素预拟合,以常规的三平面圆弧轨迹测量获取误差数据,并基于最小二乘法求解拟合系数,替代直接对误差元素具体数值求解的传统方法,实现对各直线轴位置相关误差元素的辨识。通过实验验证了辨识结果的正确性和有效性,该方法对机床直线轴误差辨识、补偿具有参考价值。     

基于球杆仪的五轴数控机床误差快速检测方法

几何误差是五轴数控机床重要误差源,针对传统测量方法仪器昂贵、测量周期长问题,提出基于球杆仪的五轴数控机床几何误差快速检测方法。对于机床的平动轴误差,利用多体系统理论及齐次坐标变换法,建立平动轴空间误差模型,通过球杆仪在同一平面不同位置进行两次圆轨迹,辨识出4项平动轴关键线性误差;针对五轴机床的转台和摆动轴,设计基于球杆仪的多条空间测试轨迹,完整求解出旋转轴12项几何误差。实验结果显示,所提方法获得转角定位误差与激光干涉仪法最大误差为0.001 8°,利用检测结果进行机床空间误差补偿,测试轨迹偏差由16μm降至4μm,为补偿前的25%,验证了方法的有效性。提出的五轴机床几何误差检测方法方便、便捷,适用于工业现场。     

Study on the influence of geometric errors in rotary axes on cubic-machining test considering the workpiece coordinate system

Evaluating the influence of geometric errors in rotary axes is a common method used by a five-axis machine tool for improving the machining accuracy. In conventional geometric error models, the table coordinate system is considered as the final workpiece coordinate system. In this study, an additional workpiece coordinate transformation was proposed to identify the influence of geometric error. First, a cubic machining test was conducted. Second, the necessity of workpiece coordinate transformation was analyzed, and a method for coordinate transformation was proposed. In addition, both machining simulation and an actual machining experiment of the cubic machining test were conducted to verify the efficiency of the proposed method. The results indicate that the workpiece coordinate transformation is an essential part of the geometric error model for accurately simulating the geometric error influence. The method for identifying the geometric error influence considering the workpiece coordinate transformation is applicable in manufacturing.     

Parametric modeling and estimation of geometric errors for a rotary axis using double ball-bar

In this study, the geometric errors of the rotary axis of machine tools are modeled parametrically and estimated using a double ball-bar. To estimate the geometric errors from the measured data, they are defined as position-dependent/position-independent geometric errors. The position-dependent and position-independent geometric errors are modeled as nth-order polynomials with C ¹-continuity and constants, respectively. Additionally, the set-up errors which are inevitable during the installation of the double ball-bar are modeled as constants to increase the accuracy of the estimation process. The measurement paths are designed to increase the sensitivity of the geometric errors in the measured data. The position of the balls constituting the double ball-bar is calculated in the reference coordinate system using the homogeneous transform matrices. The ball-bar equation is applied to determine the relation between the measured data and geometric errors. The linearized relations between them are derived by eliminating the higher-order error terms. The parameters of the modeled geometric errors and set-up errors are calculated using the least squares method. Finally, the geometric errors are estimated using the calculated parameters. The validity of the proposed method is tested through simulations and it is used to estimate the geometric errors of the rotary axis of five-axis machine tools.