多轴数控机床几何误差的软件补偿技术

论述了在“华中Ｉ型”数控系统中开发的数控机床几何误差的软件补偿技术。分析了各轴的误差元通过运动链传播的建摸问题和其对切削刀具在机床工作空间中的姿态误差的影响;建立了机床结构的每个误差元和切削刀具相对工件位置误差相联系的通用数学模型;采用激光干涉仪直接测量的方法来获取误差模型中各个误差元参数,提出了一种测量机床运动部件滚摆角的新方法;测量点的误差参数被存储在计算机内,在测量点之间采用线性插值来获得补偿点的误差参数。数控系统每８ｍｓ中断一次,读取与补偿点相关的位移和转动误差参数以及刀具的参数,利用误差模型计算刀具相对工件的误差在各个运动轴上的误差分量,该误差分量被数控系统叠加到各运动轴的指令位移上,使各个运动轴产生附加的运动,从而实现数控机床几何误差的软件补偿。对比试验表明该补偿技术能使数控机床的几何误差减小７０％。     

数控机床误差的多项式预报与补偿

建立了数控机床空间误差预报的多项式模型，该模型把机床的空间误差表示为机床运动坐标的多项式函数；提出了用激光球杆仪直接测量机床空间误差的方法；由机床工作空间有限定位点误差的测量数据，利用最小二乘法来决定误差预报模型的系数。在XK713数控加工中心上进行了误差的多项式建模和补偿实验，结果表明本误差预报和补偿方法省时，效果显著。     

[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。     

HexaM并联机床的误差分析及补偿

以丰田工机公司制造的并联机床HexaM为模型,阐述了并联机床的运动学逆解析和顺解析方法、误差建模和补偿方法。提出了根据并联机床刀具运动误差求解机床制造误差的方法。通过机床运动的仿真,证实了用求出的机床误差进行误差补偿,能够有效地减小机床运动误差,从而为提高并联机床运动精度提供了一种解决方案。     

多轴机床空间误差的一般模型

本文提出了多轴机床空间误差的一般模型，该模型把刀具相对工件的误差表达为机床各相连组件之间误差的线性组合。适用于任意结构的机床以及坐标测量机和测量仪器。利用这个模型进行软件误差补偿，在不提高成本的情况下，可大幅度提高加工精度或测量精度。     

基于商空间的五轴数控机床几何误差标定与补偿算法

提出了一种基于商空间和指数积的五轴数控机床几何误差标定与补偿算法。首先,利用提出的机床几何误差标定模型可以快速、准确识别出机床各运动轴的实际旋量坐标,采用商空间法去除伴随变换冗余参数,避免了旋量坐标重复正交化和归一化。其次,采用基于微分法的雅克比矩阵补偿算法,可以在不求取机床运动学逆解的情况下,对机床几何误差进行补偿。最后,通过MATLAB仿真对误差标定模型和补偿算法模型进行验证。     

数控机床误差补偿技术及应用——几何误差补偿技术

利用多体系统运动学理论,通过分析低序体阵列、变换矩阵和运动方程,在相邻体之间引入位置误差和位移误差,建立了机床空间定位误差通用计算模型。基于激光测量提出机床的２１项几何误差参数辨识模型。在ＸＨ７１５加工中心上,对机床的空间几何误差进行理论计算,并进行补偿前后的对比实验,结果表明机床空间定位误差减小５０％以上,同时也表明利用误差补偿技术提高机床加工精度是有效的。     

数控插齿机的误差建模与误差补偿解耦

为提高数控插齿加工精度,需对其误差进行补偿。通过分析插齿机床的运动特点,建立了插齿机运动模型;基于机床误差运动学原理,推导出用齐次变换矩阵描述的刀具相对于工件的误差模型;基于小误差补偿运动假设和微分变换原理,对各轴运动副的误差补偿量与刀具相对于工件的位置及方向误差模型间存在的耦合关系进行了解耦,获得了影响插齿加工精度的各运动副位置或方向误差补偿量。     

数控机床径向运动误差的形成机理及补偿方法研究

研究数控机床圆周插补运动径向误差的形成机理,并提出一种误差软件补偿方法。分别用圆轨迹运动误差测试仪和圆度仪测出数控机床圆周插补运动的径向误差,对该误差建立计算机误差补偿模型,应用该模型进行软件补偿实验研究。实验结果验证了误差形成机理的分析,同时表明提出的误差软件补偿方法能有效地提高数控机床的圆轨迹精度。     

四轴数控机床误差综合建模原理及分析

详细分析了机床运动副的误差运动，利用基于齐次坐标变换的方法分析并给出了一台既包含移动副又包含转动副的四轴数控机床的误差综合数学模型，此模型中不仅包含了机床的几何误差且包含了热误差共计46个误差元素。本数学模型的建立方法可为其它类型的四轴及各种五轴数控机床的误差综合建模分析及误差补偿提供参考。     

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.     

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.     

Assessing geometrical errors of multi-axis machines by three-dimensional length measurements

In this paper a method is presented for assessing geometrical errors of multi-axis machines based on volumetric three-dimensional length measurements. A universal machine error model is proposed since a large variety of machine configurations exists. Such models can be used for software error compensation techniques in order to improve the machine’s positioning behaviour as well as for diagnostic purposes. Length measurements are chosen for the measurement of the positioning errors of a multi-axis machine because these measurements can be executed in a short period of time in a relatively simple way combined with a high accuracy. In order to get comparable results for the geometrical errors as measured with conventional techniques, i.e., laser interferometry, the design of the measurement setup as well as the formulation of the machine error model (including parameter correlation effects) appeared to be of major importance and are subject of this paper.     

数控机床误差的激光干涉仪自动瞄准测量及补偿技术研究

开发了用于数控机床空间误差测量的激光干涉仪自动瞄准系统。该系统实现了机床多轴联动、而激光束的方向发生连续改变时空间曲线轨迹定位误差的测量。提出了通过一次对光实现数控机床整个空间定位误差的直接测量方法。采用网格方法储存测量误差,用有限元法实现补偿误差的预报。在立式数控加工中心上进行了误差的测量和补偿试验,结果表明所提出的误差测量方法精度高、速度快,误差补偿效果明显。     

Modelling thermomechanical behaviour of multi-axis machine tools

This paper describes a method to measure and model the thermally induced positioning errors of multi-axis machines. These errors result from changes in temperature distribution of such a machine. To achieve a reduction of the machine's tool positioning errors a generally applicable model has been developed. First the temperature distribution of a machine tool is computed from a limited number of sensors. Using this calculated temperature distribution and a deformation model based on the machine's structural loop and rigid body kinematics the tool positioning error is computed. To validate the developed thermomechanical model a new measuring method based on three-dimensional length measurements has been used.     

Geometric error compensation for multi-axis CNC machines based on differential transformation

As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path.     

数控机床空间误差球杆仪识别和补偿

提出了多轴机床空间误差的球杆仪识别方法和补偿技术。建立了机床刀尖相对工件的空间误差的误差参数模型;给出了在机床工作空间中三个互相垂直的平面内,用球杆仪测量圆周运动的半径误差结合机床的空间误差模型识别定位、直线度、角度、垂直度和反向间隙等误差参数的方法。补偿试验结果证明该误差识别与补偿方法省时有效。     

Modeling and compensation of geometric errors in simultaneous cutting using a multi-spindle machine tool

A volumetric error compensation method for a machining center that has multiple cutting tools operating simultaneously has been developed. Due to axis sharing, the geometric errors of multi-spindle, concurrent cutting processes are characterized by a significant coupling of error components in each cutting tool. As a result, it is not possible to achieve exact volumetric error compensation for all axes. To minimize the overall volumetric error in simultaneous cutting, a method to determine compensation amount using weighted least squares has been proposed. This method also allows tolerance distribution of machining accuracy for different surfaces of a workpiece. A geometric error model has been developed using an arch-type, multi-spindle machine tool, and the error compensation simulation results based on this model are presented. The simulation results demonstrated effectiveness of the proposed error compensation algorithm for use with multi-spindle simultaneous cutting applications.     

Thermally induced volumetric error modeling based on thermal drift and its compensation in Z-axis

Traditional thermally induced volumetric error modeling requires 21 geometric error components at different temperatures. Taking thermal drift errors into account, 30 geometric errors are described to model volumetric error in this paper. The main sources of thermally induced volumetric error are positioning errors of each axis and thermal drift errors. An experiment on milling and boring machine is carried out, which shows that volumetric error in Z-axis is affected significantly. To compensate volumetric error of Z-axis, a model of positioning error is proposed based on nut temperature. A finite elements analysis of headstock thermal characteristic is carried out, and error chain is established, which shows the main source of thermal drift of Z-axis is ram expansion. Thermal drift compensation system of Z-axis is developed based on Invar metal and thermal error compensation module of Siemens CNC system. Therefore, the positioning error and thermal drift of Z-axis are compensated. The thermally induced volumetric error in Z-axis is reduced by 80 % after compensation.