基于参数化建模的旋转轴误差快速辨识方法

针对现有旋转轴几何误差辨识方法计算量大且无法避免异常值等问题,提出了一种基于参数化建模的旋转轴位置相关几何误差快速辨识方法。首先,分析了旋转轴位置相关几何误差的特性,建立了测量旋转轴时球杆仪杆长变化的综合模型,并基于约束条件进行化简;其次,使用四阶傅里叶级数对5项位置相关几何误差进行参数化建模,并基于5种测量模式得到位置相关误差的辨识模型;接着,分析了球杆仪安装误差对杆长变化及辨识结果的影响规律并消除其影响;最后,在小型五轴机床的旋转工作台上进行了实验,辨识出旋转轴的5项位置相关几何误差,并通过改变安装位置和安装角度的球杆仪杆长预测实验对辨识方法的正确性进行了验证。     

数控机床旋转轴误差辨识研究

以多体系统理论为基础建立了包含旋转轴几何误差的DMP60U型机床运动模型,并利用某公司的QC10球杆仪对DMP60U型的C轴和斜转轴B轴各4项位置误差分别进行测量和辨识。在对球杆仪测量点的在坐标系中的位置坐标表达分析后,得出了球杆仪测量圆的偏心率与位置误差间数学关系。通过运用机床RTCP功能控制多轴同步运动,设计进行不同高度下的4次测量,可辨识出这8项位置误差,快速高效。经实验验证,这种辨识方法测量结果精确,可用于五轴加工中心误差辨识。     

基于错位塔形工件的旋转轴几何误差辨识

旋转轴的几何误差直接影响五轴机床的加工精度，但由于其误差项多且高度耦合，因此辨识难度较大。提出了一种工件切削在机测量方法，用于辨识五轴机床旋转轴6项与位置相关的几何误差。设计并加工一种错位塔形工件，它由三层错位叠加的矩形块组成。在工件不同层级的底面与侧面布置测点并进行在机测量，基于空间误差模型推导出每项误差的辨识原理与解析解，并采用蒙特卡洛模拟进行不确定性分析。最后，通过与球杆仪误差辨识方法进行对比验证，线性误差E_XC,E_YC与E_ZC的辨识结果偏差最大为2.7,-1.7与-1.3μm；角度误差E_AC,E_BC与E_CC的辨识结果偏差最大为1.3″，-0.6″与-2.1″，两者辨识平均吻合度达95.4%。本方法通过工件切削与在机测量，每项误差的辨识原理与解析解形式简单，可辨识实际工况下的旋转轴6项位置相关的几何误差。     

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。     

五轴加工中心空间误差分析及补偿研究

加工中心精度是影响产品加工精度的最重要因素,误差补偿技术是提高加工中心精度的重要方式。通过分析五轴加工中心的空间误差及建模结果,以TTTRR五轴加工中心为例,建立了综合空间误差模型,为误差补偿打下理论基础;通过研究多种误差补偿技术,提出了一种可以基于建模结果的平动轴几何误差测量新方法,结合旋转轴几何误差的测量结果,最后通过在某台五轴加工中心上进行测量和补偿实验,验证了建模结果的正确性和新位移测量法的有效性。     

五轴数控机床旋转轴综合误差测量与辨识

针对五轴数控机床旋转轴的运动误差和几何误差的综合评估问题,在不考虑直线轴运动误差影响的情况下,提出了一种采用R-test测量仪的测量及其辨识方法。首先,测量过程按照参考球的两种不同高度设置进行,仅移动旋转轴,而不移动直线轴。其次,利用R-test测量仪对旋转轴的运动精度进行了测量。此外,假设旋转轴位置几何误差和工作台上参考球的设置误差是影响测量结果的因素,并通过最小二乘法对这些因素进行分离。采用IBS公司的R-test测量仪,对米克朗公司UCP800Duro立式五轴加工中心C轴的运动误差和几何误差进行了测量实验。研究结果表明,该方法能够正确识别旋转轴的运动误差和几何误差,可以有效地综合评估旋转轴的运动精度,并有助于进一步提高旋转工作台的精度。     

卧式加工中心关键几何误差元素甄别方法

以某卧式加工中心为研究对象,通过定义机床各部件局部坐标系间初始位置特征矩阵和初始位置误差特征矩阵,构建机床空间误差完备模型,解决传统建模方法中若干项几何误差元素缺失的问题。借助体对角线定位精度测量实验,对所建完备模型准确性进行验证,进而在此基础上提出几何误差元素实际参预度的概念及其计算方法,并由此形成基于空间误差完备模型和实际参预度的关键几何误差元素辨识新方法。分别根据计算所得实际参预度和灵敏度,对给定加工中心关键几何误差元素进行甄别。对比分析显示,相较于传统灵敏度分析,所提基于实际参预度的甄别方法具有更高的准确性。甄别结果表明,该加工中心关键几何误差元素有7项,且均与位置相关,与X轴进给相关的关键几何误差元素有4项,说明机床X轴运动组件制造精度可能存在较大缺陷。     

基于球杆仪位姿的机床回转台几何误差辨识研究

针对误差测量中由移动轴联动引起的旋转轴与移动轴误差耦合现象,提出一种基于球杆仪实际位姿的误差辨识方法。以CFXYZA型五轴数控机床的回转台为测量对象,设计了球杆仪X向,Y向及Z向组合测量模式,通过改变球杆仪中心座的安装位置和高度,共测得6组杆长变化数据,再利用齐次变换理论推导几何误差参数与杆长变化量的关系式,以辨识出回转台6项几何误差。测量试验和辨识结果表明,使用该法不仅提高了辨识精度,而且可消除测量过程中耦合的移动轴误差,对同类型机床回转台的几何误差测量、辨识均具有参考意义。     

[误差建模及精度保证方法]卧式加工中心关键几何误差元素甄别方法

以某卧式加工中心为研究对象，通过定义机床各部件局部坐标系间初始位置特征矩阵和初始位置误差特征矩阵，构建机床空间误差完备模型，解决传统建模方法中若干项几何误差元素缺失的问题。借助体对角线定位精度测量实验，对所建完备模型准确性进行验证，进而在此基础上提出几何误差元素实际参预度的概念及其计算方法，并由此形成基于空间误差完备模型和实际参预度的关键几何误差元素辨识新方法。分别根据计算所得实际参预度和灵敏度，对给定加工中心关键几何误差元素进行甄别。对比分析显示，相较于传统灵敏度分析，所提基于实际参预度的甄别方法具有更高的准确性。甄别结果表明，该加工中心关键几何误差元素有7项，且均与位置相关，与X轴进给相关的关键几何误差元素有4项，说明机床X轴运动组件制造精度可能存在较大缺陷。     

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。     

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.     

Position error reduction of tool center point in multi-tasking machine tools through compensating influence of geometric deviations identified by ball bar measurements

A method to compensate the influence of geometric deviations on tool center point (TCP) for a multi-tasking machine tool is proposed in this paper. Some methods to compensate geometric deviations of a rotary axis in five-axis machining centers have been proposed. However, due to the special topological structure of multi-tasking machine tools, the identification and compensation methods for geometric deviations are different from those of the five-axis machining centers, which have been seldom researched until now. In this paper, the main attention is paid to analyze the eccentricities of the trajectories measured by a ball bar under simultaneous three-axis motions and to reduce the influence of the identified geometric deviations on the position error of TCP by the compensation method. It is divided into two sequential subtasks. At first, the geometric deviations are identified by using the eccentricities of measured trajectories. A simple and practical measuring procedure is proposed to identify geometric deviations of rotary axes existing in a multi-tasking machine tool. For the second step, a method is proposed by modifying the original NC code according to the kinematic chain model of the targeted machine tool to compensate the influence of the existing geometric deviations on TCP. An experiment is conducted on a multi-tasking machine tool with a swivel tool spindle head in the horizontal position. The repeatability of the measured eccentricities based on three experimental results is also investigated to reduce the influence of measuring error on the identified results. As a result, the corresponding values of geometric deviations after the compensation are less than 2.2 arcseconds or 2.4 μm. It is concluded that the influence of geometric deviations on TCP is compensated effectively, and the position error of TCP is reduced significantly.     

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.     

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.     

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.     

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.     

Geometric error measurement and compensation for the rotary table of five-axis machine tool with double ballbar

This paper proposes a novel measuring method for geometric error identification of the rotary table on five-axis machine tools by using double ballbar (DBB) as the measuring instrument. This measuring method greatly simplifies the measurement setup, for only a DBB system and a height-adjustable fixture are needed to evaluate simultaneously five errors including one axial error, two radial errors, and two tilt errors caused by the rotary table. Two DBB-measuring paths are designed in different horizontal planes so as to decouple the linear and angular errors. The theoretical measuring patterns caused by different errors are simulated on the basis of the error model. Finally, the proposed method is applied to a vertical five-axis machining center for error measurement and compensation. The experimental results show that this measuring method is quite convenient and effective to identify geometric errors caused by the rotary table on five-axis machine tools.     

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。