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。     

基于模拟退火算法的数控机床热误差补偿方法

为提高数控机床的精度,基于模拟退火算法设计数控机床热误差补偿方法,分别建立机床内部零件沿X轴、Y轴、Z轴方向做平移与旋转运动时的变化矩阵,计算电动机与轴承的发热量,二者相加后就可以得到高速运动下机床发热量。基于模拟退火算法建立热误差偏移补偿模型,获得系统温度的状态参量,得到温度下降后求和单元的传递函数,计算偏移补偿模型内X轴、Y轴、Z轴上经过多次迭代后的位置。设计数控机床热误差补偿算法,得到数控机床热误差补偿结果。实验结果显示,该数控机床在Y轴上的热误差值较小,但是在X轴与Y轴上的热误差较大,经过误差补偿后,其热误差分别降低至1～2 m m和0～1 m m,可见该热误差补偿方法效果较好。     

[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。     

五轴数控机床综合误差补偿解耦研究

五轴数控机床具有3个移动副和2个转动副,能对复杂曲面实现高精度加工,然而其误差补偿运动却比较复杂,因为其各运动副的误差补偿运动量与刀具和工件间的误差值(位置及方向误差)间存在一定的耦合关系。通过分析五轴机床的运动特点,用齐次坐标变换的方法建立了各运动副坐标系间的变换矩阵。基于小误差补偿运动假设,分析了误差运动和补偿运动间的相互关系,对五轴机床各运动副的位置及方向误差补偿运动进行了解耦,建立了可以进行空间五个误差补偿量计算的数学模型,为五轴机床的误差实时补偿提供了理论基础。     

五轴数控机床轮廓误差预补偿技术研究

五轴数控机床在加工过程中不可避免会产生误差,为了进一步提高五轴数控机床的加工精度,本文提出了五轴数控机床轮廓误差的预补偿技术,首先分析了轮廓误差的产生原因和组成要素,然后提出了跟踪误差的预测方法并建立预测模型,接着对于轮廓误差的预测进行建模,最后根据五轴机床加工过程中给出的路径仿真得出了轮廓误差未补偿和补偿的对比,结果表明了经过轮廓误差的预补偿,能够很大程度上减小加工过程中出现的轮廓误差,进一步证明了本文方法的有效性。     

数控机床综合误差分析与建模研究

分析了影响机床精度的误差来源及运动副的误差运动学原理。以一台三轴数控机床为研究对象,利用低序体阵列描述多体系统拓扑结构,用特征矩阵表示多体系统中间体的相对位置和姿态,建立误差综合数学模型,模型中不仅包含了几何误差且包含了热误差和切削力误差,可为其他类型的机床误差综合建模及补偿提供参考。     

数控机床进给轴综合误差解耦建模与补偿研究

为建立高精度的数控机床综合误差补偿模型,提出一种针对机床定位误差的解耦分离建模方法。通过对数控机床温度场与定位误差进行测量,研究机床在不同工况下温度场与定位误差的变化规律,基于该规律定义机床定位误差敏感度的概念,采用灰色关联度算法建立定位误差敏感度矩阵并优化了测温点。根据机床定位误差变化规律,利用多元回归和GM(1,n)算法对机床几何基准误差和热误差进行解耦分离建模,并将上述模型进行线性叠加构建机床定位误差综合模型。在不同工况条件下对一台VXC-560型加工中心进行在线补偿,试验结果表明机床x轴在冷态条件下的定位误差从11.1μm降低到4.5μm,降幅为59.5%,在热态条件下的最大定位误差由34.9μm降低到8.2μm,降幅为76.5%,并验证了采用误差模型直接驱动机床硬件进行补偿的新思路,具有一定的工程应用前景。     

多功能复合五轴数控机床的综合误差建模研究

数控机床误差补偿是提高数控机床加工精度的有效方法,而建立快速准确的误差模型又是实施误差补偿的前提和基础。以多功能复合五轴数控机床为对象,阐述了五轴数控机床的综合误差建模过程,对传统建模过程中刀具、工件和参考坐标系之间的关系进行了优化处理,得到了包含方向误差在内的综合数学模型。     

基于多体系统理论的TTTR型四轴数控打磨机床空间误差分析及建模

根据多体系统理论,建立了机床空间坐标系,描述了机床部件的拓扑关系和相对运动方式,根据部件的运动形式分析了机床结构中的误差元素,最后用Denavit-Hartenberg齐次变换矩阵描述体间坐标变换矩阵。根据相邻体间变换矩阵得到了机床的空间综合误差模型,为数控机床的计算机仿真和误差补偿提供了理论依据。     

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。     

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.     

五轴龙门数控铣床转动轴联动中的动态轨迹误差仿真分析

针对刀具两摆的五轴龙门数控铣床,对一转动轴与一平动轴联动及两转动轴联动加工圆弧时的动态轨迹误差分别进行了分析。采用D-H(Denavit-Hartenberg)法对轴的输入的进给指令位置计算公式进行了推导,并将进给指令位置输入到由动态仿真工具Simulink构建的进给伺服系统仿真模型中,得到了圆弧上动态轨迹误差的分布曲线。通过对转动轴联动加工圆弧的动态轨迹误差分析,可为五轴龙门数控铣床转动轴动态误差的检测提供指导,使得机床的检测与调整更加快速和便捷。     

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。     

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.     

五轴数控机床加工误差动态修正方法研究

为修正五轴数控机床加工误差,提高五轴数控机床加工质量,提出一种新的五轴数控机床加工误差动态修正方法.构建五轴数控机床加工误差计算模型,获取五轴数控机床加工的刀心方位、刀轴方位轮廓误差;锁定误差方位后,通过五轴数控机床误差的动态实时补偿方法,实现五轴数控机床加工误差动态修正.研究结果表明:所提方法可实现全方位、高效率的五...     

Geometrical Error Analysis and Control for 5-axis Machining of Large sculptured surfaces

One of the important tasks in five-axis machining of large sculptured surfaces is to control and reduce the machined errors. This paper presents the methods to control geometrical errors based on the establishment of the link between geometrical errors and the parameters of tool path planning. Nonlinear errors, which are the majority of geometrical errors during five-axis machining, are is strictly analysed and formulated. An adaptive step length method is proposed to control effectively the cutter contact path error. The measures to reduce the scallop error in machining of the large sculptured surfaces are discussed also. With the combination of this research with CAM software, both large Kaplan and Francis hydroturbine blades have been successfully machined. It shows that the machined errors can be controlled effectively and the machining efficiency can be improved in the machining of the large sculptured surfaces by the proposed methods.     

Elasto-geometrical error modeling and compensation of a five-axis parallel machining robot

Parallel manipulators have the potentials of high efficiency and high precision in the field of machining and manufacturing. However, accuracy improvement of the parallel manipulator is still an essential and challenging issue, encountering two important problems. Firstly, the ignorance of elastic deformation caused by gravity or deviations of static stiffness model restricts further improvement of accuracy. To solve this problem, an elasto-geometrical error modeling method is proposed. The comprehensive effects of structural errors, elastic deformation under gravity and compliance parameter errors on pose deviations are disclosed. On this basis, the identification equation of actual structural errors and compliance parameter errors can be established. Secondly, the ill-conditioned identification matrix and the identification equation with anisotropic residual error can lead to inaccurate identification results. To solve this problem, a weighted regularization method is proposed. The identification equation with isotropic residual error is built, and accurate identification can be realized with the regularization method. Based on the proposed methods, the error compensation experiment is conducted on the prototype of a five-axis parallel machining robot using a laser tracker. Experiment results show that the accuracy of the machining robot is significantly improved after compensation. An M1_160 test piece and an S-shaped test piece are machined and measured to further validate the effectiveness of the proposed methods. The elasto-geometrical error modeling method and the weighted regularization method can be applied to other parallel manipulators’ accuracy improvement.     

Neural network-based modelling and error compensation of thermally-induced spindle errors

This research is concerned with enhancing the accuracy of a machining centre by compensating for thermally induced spindle errors in real-time. A neural network model was developed for on-line thermal error monitoring. A PC-based error compensation scheme was also developed to upgrade a commercial CNC controller for real-time thermal error compensation without any hardware modifications to the machine. The spindle thermal errors of a vertical machining centre were reduced by 70% after compensation.     

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.     

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。