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。     

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。     

球杆仪安装误差对测量误差的影响规律及其分离方法

通过齐次坐标变换理论建立了五轴数控机床摆动轴几何误差的辨识模型,深入分析了在误差测量过程中球杆仪磁性球座的安装误差对测量误差的影响规律,提出了一种球杆仪磁性球座安装误差的分离方法,并在五轴数控机床上进行了实验验证。结果表明,该方法可以有效分离出球杆仪磁性球座的安装误差,提高摆动轴几何误差的测量和辨识精度。     

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。     

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。     

球杆仪用于数控机床几何误差补偿的研究

介绍了利用球杆仪测试和辨识数控机床几何精度的方法,在精确掌握三坐标数控机床几何误差的基础上,通过建立三轴数控机床的几何误差模型,利用误差综合补偿软件进行了补偿实验.结果表明,机床的各项误差都有所降低.     

基于球杆仪的五轴机床空间圆弧误差建模及补偿方法

针对自主研发五轴数控机床进行空间圆弧误差的研究,建立了旋转轴和直线轴误差数学模型,依据该模型进行误差因素分析。采用球杆仪作为测量仪器,进行空间圆度的测量,并对建模的数学模型进行验证。分析误差项与误差因素之间的关系,针对反向越冲和伺服不匹配进行误差分析,基于五轴高端数控系统,指明了一种可以通用的机床误差项补偿方法。通过进行实验数据对比,验证该补偿方案效果良好。得出误差项间相互耦合的结论,并且发现调整误差项先后顺序会对总误差值产生影响。     

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。     

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。     

数控机床旋转轴误差的快速测量与辨识新方法

根据齐次变换理论推导出旋转轴基本几何误差辨识模型,在此基础上,提出了一种基于球杆仪的旋转轴基本几何误差快速测量和辨识新方法,将球杆仪一端的中心座分别安装在旋转工作台的3个不同位置,通过联动控制球杆仪另一端球心按圆形轨迹运动,分别测量旋转轴圆周每个离散位置点在X、Y、Z方向上的偏差,并根据所建立的辨识模型,辨识出旋转轴的6项基本几何误差。同时,提出了基于系数矩阵灵敏度分析的方法,用于指导测量点的合理分布,减少测量误差的影响,从而提高误差辨识精度。     

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.     

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。     

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。     

Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes

Synthesis modeling of a geometric error-based traditional method for large-scale grinding machine tools with six axes is too complicated to perform in a real-time compensator with a built-in position control system, and it is difficult to obtain all of the error elements corresponding to the model. This paper proposed a novel strategy in which a machine may be considered as translation axes and rotary axes, and geometric errors of the translation axes and rotary axis are modeled and the geometric error models of the machine are very simple for real-time error compensation. The volumetric errors of the translation axes are measured using spatial circular curve ball bar test, and every element of the rotary axis is also obtained by a series of considerate ball bar tests. According to the characteristics of a position controller used in the machine, a synthesis error compensation system based on the NUM numerical control system was developed. Error compensation experiments were carried out, and the results show that the accuracy of the machine is improved significantly.     

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与PIGE辨识基本方程,并借助球杆仪获取辨识基本方程求解所需参数;结合所建辨识基本方程揭示旋转轴PDGE与PIGE的耦合机制,提出了一种迭代方法以实现旋转轴PDGE和PIGE的准确分离与解耦。为验证上述辨识方法的有效性与准确性,提出一种基于虚拟样机的数值验证策略。仿真结果表明,所提辨识方法较好地解决了五轴加工中心旋转轴两类几何误差元素之间的耦合问题,可为建立加工中心空间模型提供准确的数据支撑。     

Interim check and practical accuracy improvement for machine tools with sequential measurements using a double ball-bar on a virtual regular tetrahedron

This study proposes a method for a quick, simple interim check and practical accuracy improvement of machine tools using just a double ball-bar. The double ball-bar is used to measure sequentially the length of the six sides of a virtual regular tetrahedron within the workspace of the machine tool. Then, the scale and squareness errors of and between the three linear axes are calculated from the length results, and the measured lengths and the calculated errors can be used as criteria for the interim check. The calculated errors can also be compensated for to improve the accuracy of experimented machine tools practically. A sample machine tool was subjected to experimental interim checks applying the proposed method; it showed primarily large length deviations for the six sides due to geometric errors mainly. To improve the geometric accuracy practically, the calculated errors were compensated for and the measurements were repeated, showing significantly improved length deviations for the six sides. The main advantage of the proposed method is that it requires only a double ball-bar and sequential measurements; thus, it is a simple procedure with a measuring time of ～5 min for a virtual regular tetrahedron. Additionally, the size of the virtual regular tetrahedron can be readily modified by changing the nominal length of the double ball-bar, increasing measurement flexibility. Thus, the proposed method is suitable for quick, simple, cost-effective daily and periodic interim checks, with practical improvement of machine tool accuracy.     

任意拓扑结构机床运动轴误差传递链建模方法

在对任意结构机床进行空间几何误差建模时,必须要获得该机床运动轴误差传递链,从而基于微分变换实现任意结构机床误差建模。通过运用多体系统理论,构建任意结构机床拓扑结构与低序体阵列,利用机床拓扑结构与低序体序列提出了机床运动轴连接支承件相对运动矩阵与机床支承件连接矩阵概念,建立了获取运动轴误差传递链的数学模型。该数学模型将描述机床拓扑结构的低序体序列与机床支承件相对运动关系结合起来,给出了获取任意机床运动轴误差传递链的建模方法。并且将利用此建模方法获得的运动轴误差传递链运用于基于微分变换的机床空间几何误差建模中,实现了对任意结构机床空间几何误差建模。最后以五轴立式加工中心为算例,验证了该运动轴误差传递链建模方法的有效性。     

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.     

Three-point method for measuring the geometric error components of linear and rotary axes based on sequential multilateration

The linear and rotary axes are fundamental parts of multi-axis machine tools. The geometric error components of the axes must be measured for motion error compensation to improve the accuracy of the machine tools. In this paper, a simple method named the three-point method is proposed to measure the geometric error of the linear and rotary axes of the machine tools using a laser tracker. A sequential multilateration method, where uncertainty is verified through simulation, is applied to measure the 3D coordinates. Three non-collinear points fixed on the stage of each axis are selected. The coordinates of these points are simultaneously measured using a laser tracker to obtain their volumetric errors by comparing these coordinates with ideal values. Numerous equations can be established using the geometric error models of each axis. The geometric error components can be obtained by solving these equations. The validity of the proposed method is verified through a series of experiments. The results indicate that the proposed method can measure the geometric error of the axes to compensate for the errors in multi-axis machine tools.