Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors

Kinematic errors due to geometric inaccuracies in five-axis machining centers cause deviations in tool positions and orientation from commanded values, which consequently affect geometric accuracy of the machined surface. As is well known in the machine tool industry, machining of a cone frustum as specified in NAS979 standard is a widely accepted final performance test for five-axis machining centers. A critical issue with this machining test is, however, that the influence of the machine's error sources on the geometric accuracy of the machined cone frustum is not fully understood by machine tool builders and thus it is difficult to find causes of machining errors. To address this issue, this paper presents a simulator of machining geometric errors in five-axis machining by considering the effect of kinematic errors on the three-dimensional interference of the tool and the workpiece. Kinematic errors of a five-axis machining center with tilting rotary table type are first identified by a DBB method. Using an error model of the machining center with identified kinematic errors and considering location and geometry of the workpiece, machining geometric error with respect to the nominal geometry of the workpiece is predicted and evaluated. In an aim to improve geometric accuracy of the machined surface, an error compensation for tool position and orientation is also presented. Finally, as an example, the machining of a cone frustum by using a straight end mill, as described in the standard NAS979, is considered in case studies to experimentally verify the prediction and the compensation of machining geometric errors in five-axis machining.     

五轴数控机床几何误差建模方法研究

五轴数控机床是实现工件复杂表面精密加工的重要设备,而机床本身精度是保证加工精度的重要前提。以一台大型五轴数控加工机床为研究对象,分析各项误差,应用多体系统运动学理论,建立移动轴与旋转轴的几何误差数学模型,推导出刀具相对工件坐标系的位置与姿态误差表达式,为误差补偿提供精确数学模型,提高机床加工精度。     

[误差建模及精度保证方法]几何误差贡献值影响下五轴数控机床运动轴误差灵敏度分析方法

针对现有误差元素灵敏度分析与后续误差补偿关联性不强的问题,建立运动轴几何误差贡献值模型并提出运动轴几何误差灵敏度分析方法,以获得本身几何误差对机床精度有很大影响的关键运动轴。结合指数积理论和坐标系微分运动理论建立基于误差敏感矩阵的运动轴几何误差贡献值模型,各运动轴几何误差贡献值相加得到机床综合误差模型;计算各运动轴误差权重分量和误差综合权重实现运动轴误差灵敏度分析,选择误差综合权重平均值最大的运动轴为机床关键运动轴,并对关键运动轴的误差补偿方法进行分析讨论。最后,在北京精雕集团的五轴加工中心上进行仿真实验验证。研究结果表明：所建立模型和所提出分析方法是有效的,且只补偿关键运动轴的几何误差贡献值能有效地提高五轴机床加工精度。     

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.     

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。     

五轴加工中心旋转轴几何误差元素区别建模辨识技术

构建五轴加工中心空间误差模型的关键环节在于准确辨识旋转轴位置相关几何误差元素(PDGE)和位置无关几何误差元素(PIGE).以某五轴加工中心为研究对象,提出了一种面向旋转轴PDGE和PIGE的区别建模辨识方法.以多体系统理论和齐次坐标变换为基础,以两运动链末端所构空间向量欧氏范数的演变规律为依据,推导建立旋转轴PDGE...     

五轴数控机床旋转轴几何误差测量与建模

利用球杆仪对五轴数控机床旋转轴的几何误差进行了测量及建模。在测试中,五轴数控机床采用两个平动轴和一个旋转轴同步运动,球杆仪采用径向、切向和轴向三种测试路径,并在此基础上对其进行几何误差建模。     

考虑热误差的双转台机床工艺误差谱预测方法

五轴数控机床的几何误差和热误差是影响工件加工精度的两个重要因素,对这些误差因素进行分析可以有效提高薄壁件工件的加工精度。本文首先基于齐次坐标变换法,建立了双转台五轴数控机床的旋转轴几何误差模型;然后基于对标准球进行在机接触测量,辩识得出两旋转轴的12项几何误差,这些误差考虑了两旋转轴之间的相互影响和其热误差的影响;最后分析五轴数控机床加工空间的几何误差场,在该加工空间内几何误差从中心到外侧逐渐增加,当A轴旋转角度增加时,误差的最大值也随之增加。与其它位置误差辨识方法相比,本方法的测量精度符合加工要求,测量时间只需要30 min。     

Axis geometrical errors analysis through a performance test to evaluate kinematic error in a five axis tilting-rotary table machine tool

Geometrical work piece errors in milling process are commonly generated by different error sources. Axis geometrical errors, such as the straightness error for linear axis and the offset location error of the origin of rotary axis, introduce kinematic error in the tool path. Direct measurement of kinematic error requires special devices such as laser interferometers, grid plate encoders or double ball bars, which impose production stop and specialized staff. These problems could be analyzed using indirect measurements obtained by means of a cutting performance test that is already a standard for three axis machine tools. Because of the different architectures of five-axis milling machines these tests are hardly standardizable, therefore this paper proposes a devised easy-to-use and time efficient cutting performance test to identify and quantify axis geometrical errors for a five axis tilting-rotary table machine tool. This test can be performed as a periodical checkup or, in case of production, as a re-start test. The main goal of this study is to develop a kinematic analytical model capable of correlating the work-piece geometrical errors to the axis geometrical errors of the machine tool. The model has been implemented on a multi-body software in order to simulate the axes motion sequence of the performance test and validated to decouple the kinematic error into the geometrical axis errors. The developed models have demonstrated to be capable of correcting a generic five axis tool path by predicting the tool-path error displacement. The overall validation of this approach has been carried out by comparing the simulated and experimentally measured profile of the NAS 979 standard five axis contouring cone frustum profile.     

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.     

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.     

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.     

Using a double ball bar to identify position-independent geometric errors on the rotary axes of five-axis machine tools

A measuring method using a double ball bar (DBB) is proposed for identifying the eight position-independent geometric errors (PIGE) on the rotary axes of five-axis machine tools. Three measuring patterns are used, in which the translational axes are kept stationary and only two rotary axes move to obtain a circular trajectory. In this way, the effects of translational axes are totally excluded, and the measurement accuracy is improved. Motion equations, describing how the A-axis and C-axis move simultaneously to realize a circular trajectory, are presented. The influence of each deviation on the measurement patterns is simulated, and analytical solutions for the eight PIGEs are demonstrated. Finally, the measuring method is verified in a five-axis CNC machine tool. Experimental results confirm that the method provides precision results for the eight PIGEs.     

五轴数控加工中旋转轴运动引起的非线性误差分析及控制

五轴数控(Computer numerical control,CNC)加工中,刀具路径规划阶段与实际加工阶段对旋转轴运动采用的插补方式存在差异,其中刀具路径规划阶段是根据零件的几何信息进行插补,而实际加工中则根据机床信息进行插补,这种差异将引起原理性加工误差。针对五轴数控加工中旋转轴的运动,分析采用线性插补方式控制两个旋转轴进行加工时刀具姿态变化引起的原理性误差,进一步研究不同加工情况下由此产生的在垂直于走刀方向的平面内的非线性误差。通过分析旋转轴运动过程中线性插补引起的刀轴偏差角,证明刀具在相邻两刀位点运动过程的中间时刻处刀轴偏差角取得最大值,并得到由该最大值的显式表达式,在此基础上分析最大偏差角的影响因素。提出通过限制相邻两刀位点间刀轴夹角来控制此非线性误差的方法,并给出实例验证。     

A/C轴双轴转台几何误差检测与补偿技术研究

A/C轴双轴转台是中、小规格五轴联动加工中心的核心功能部件。分析了A轴、C轴与工作台台面之间的五项几何误差,利用激光干涉仪与RX10回转基准分度器对A轴、C轴的分度误差进行检测与补偿,利用五轴数控系统对A轴轴线与C轴轴线之间的位置误差、A轴轴线与工作台台面之间的尺寸误差进行检测与补偿,并提出了一种即节省成本又能有效降低A轴轴线与C轴轴线之间角度误差的修正方法。     

A methodology for systematic geometric error compensation in five-axis machine tools

To enhance the accuracy, an efficient methodology was developed and described for systematic geometric error correction and their compensation in five-axis machine tools. The methodology is capable of compensating the overall effect of all position-dependent and position-independent errors which contribute to volumetric workspace. It was implemented on a five-axis grinding machine for error compensation and for the check of its effectiveness. Error compensation algorithm was designed, and a routine was written in Matlab software. The developed technique and software are based on an error table which interprets the function of axis through cubic spline technique and synthesis modeling of a machine tool. Recursive compensation methodology was used to remove the machine errors from the actual tool path and inverse technique was implemented to find the corrected positions of prismatic and rotary joints. Moreover, it can convert the corrected tool paths into practical compensated NC codes. The generated, corrected and modified NC codes directly fed to the controller of a five-axis machine tool. Validation of the technique was preceded by repeated experimentation of measurement and through machining of typical standard workpieces with some additional specific features. Experimental results exhibit effective compensation and remarkable improvement in the parametric and volumetric-workspace accuracy of the five-axis machine tool.     

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。     

数控机床转动轴进给系统轮廓误差分析

在五轴联动数控机床中,转动轴进给系统的动态精度对轮廓误差的影响是不可忽视的。采用不同空间位置上的外形轮廓,对五轴联动数控机床转动轴的联动运动产生的轮廓误差进行分析。在建立转动轴进给系统模型的基础上,利用刀具位置系统到加工系统的转换得到转动轴指令,通过进给系统动态误差模型得到仿真输出指令,再将输出指令从加工系统转换回刀具位置系统,比较刀具位置的偏差,从而得到轮廓误差。找出轮廓误差点与外形轮廓空间位置之间的对应关系,利用这种关系可快速通过轮廓误差来考察转动轴进给系统的动态性能,为机床快速调整和维修提供一种手段。     

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.     

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.