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。     

五轴数控机床摆动轴几何误差的测量与辨识

提出一种基于球杆仪的摆动轴几何误差测量和辨识的新方法。通过圆弧测量轨迹测量球杆仪球心在回转工作台上3个安装位置的球心偏差,并利用齐次坐标变换理论建立其几何误差的辨识模型,分两步从球杆仪测量结果中辨识出4项轴线位置误差和6项运动误差。在转摆台式五轴数控机床上采用球杆仪进行实验验证,通过比较误差补偿前后球杆仪的测量值来验证辨识方法的有效性。     

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。     

五轴联动数控机床旋转轴几何误差测量与分离方法

提出一种基于球杆仪的新颖、快速的五轴联动数控机床旋转轴几何误差测量与分离方法,它选择径向和轴向安装测试路径,采用单旋转袖运动或1个旋转轴和2个直线轴联动方式,进行圆度误差测试,给出了旋转轴几何误差与各测试路径的关联图谱.并深入研究了球杆仪虚拟安装偏心技术.简化了旋转轴误差与球杆仪测试值的数学关联模型,并对影响测试结果的因素进行分析,提出采用球杆仪二次测量方法,对直线轴径向耦合误差进行解耦,实现了旋转轴几何误差的辨识和精确测量.     

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。     

基于球杆仪单轴运动测量的旋转轴几何误差辨识

为避免非辨识轴几何误差、伺服控制误差等干扰源对测量结果的负面影响,降低辨识模型复杂度,提出了一种基于球杆仪单轴运动测量的旋转轴几何误差辨识方法。以单轴运动模式代替传统的多轴联动测量模式,首先基于齐次坐标变换理论建立了旋转工作台在位置相关几何误差影响下的杆长变化量(ΔL)的数学模型;然后通过分析球杆仪的安装参数,基于列满秩辨识矩阵构建误差辨识模型,并据此设计了一种包含9次独立测量试验的辨识方案。该方案通过提高测量试验次数,减少了单次试验中较大测量误差可能造成的系统辨识精度损失,具有较高的方法鲁棒性。在辨识实验中,通过迭代调整的方式对刀具球进行精确安装,并排除了工件球安装误差和工作台位置无关几何误差的影响。最后,进行了ΔL的预测分析和误差补偿实验,补偿后工作台一圈内ΔL的最大绝对值由0.010 3 mm减少至0.002 0 mm,验证了该辨识方法的有效性。     

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。     

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。     

虚拟观测法在球杆仪估算机床平动轴 几何误差中的应用

在利用球杆仪辨识数控机床平动轴的几何误差过程中,由于建立的辨识模型中任意位置的参数矢量矩阵为病态矩阵, 致使在求解辨识模型时存在不精确解或者无解的现象。 针对上述问题,提出了一种基于虚拟观测法的岭估计求解辨识模型解 的方法。 以机床的平动轴为研究对象,基于球杆仪测量的杆长数据,将其代入所建立的误差元素与球杆仪杆长变化量之间的映 射关系,并基于虚拟观测法求解出几何误差项的多项式系数。 该方法从病态矩阵的病因来改善辨识矩阵的病态性,进而实现对 各轴相关误差元素的辨识。 仿真以及实验结果验证了辨识方法的正确性,并改善了辨识矩阵的病态性,研究结果为准确辨识机 床几何误差提供了理论依据。     

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。     

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.     

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.     

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。     

[误差建模及精度保证方法]双五轴数控铣削机床旋转轴误差辨识方法

为了快速、系统地辨识双五轴数控铣削机床旋转轴几何误差,提出了一种基于R-test的误差测量辨识方法。根据R-test误差模型研究误差测量值与各项误差参数的关系,辨识旋转轴各个几何误差项以得到旋转轴的安装误差和运动误差;利用最小二乘法原理平面圆拟合和直线拟合的方法分别辨识出2项位移误差和2项垂直度误差;基于多体系统理论及齐次坐标变换方法建立刀具坐标系与工件坐标系的齐次坐标变换模型,并辨识出3项移动误差和3项转动误差;最后,根据所得辨识值对X向和Y向位移误差进行补偿。实验结果表明,补偿后X向和Y向位移误差明显减小,误差补偿结果验证了测量、辨识的准确性和有效性。     

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.     

<Emphasis Type="Bold">Roundness Error Prediction with a Volumetric Error Model Including Spindle Error Motions of a Machine Tool</Emphasis>

This paper proposes a modified volumetric error model that includes spindle error motions as well as geometric errors. The model is constructed using rigid-body kinematics and homogeneous transformation matrices and an additional error matrix describing spindle error motions is included. The suggested model predicts the positioning errors at a given axis position as a function of both the axis position and the engaged spindle rotation angle. Two circular interpolation tests (inner and outer circle of the same radius) are simulated and the machined part profiles are predicted. To verify the simulation results, machining tests are performed according to the ISO 10791-7 standard. The error model with spindle errors shows a better agreement, between the simulated and measured roundness errors, than the simple geometric model. It can be seen that the geometric errors determine the basic part profiles and the spindle errors change the basic profiles according to the magnitude of the errors and the spindle rotation angle.     

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。     

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。     

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。