五轴数控机床几何误差建模方法研究

五轴数控机床是实现工件复杂表面精密加工的重要设备,而机床本身精度是保证加工精度的重要前提。以一台大型五轴数控加工机床为研究对象,分析各项误差,应用多体系统运动学理论,建立移动轴与旋转轴的几何误差数学模型,推导出刀具相对工件坐标系的位置与姿态误差表达式,为误差补偿提供精确数学模型,提高机床加工精度。     

Tool path optimization in postprocessor of five-axis machine tools

Generally, tool path is generated in a computer-aided manufacturing software considering only the geometry of machining parts. It is converted into numerical control (NC) codes in the postprocessor based on the particular machine kinematics. For some special types of five-axis machine tools, e.g., non-orthogonal five-axis machine tools, the generated NC codes may produce unqualified parts because of the existence of the non-linear error. Conventional commercialized postprocessors usually do not have the function of non-linear error checking. Observing that the tool path is a non-smooth trajectory full of corners and a series of connected line segments, cubic spline interpolation is applied to smooth the tool path at regular points in this study. The cutter tip center points are computed by the cubic spine interpolation, while the cutter posture vectors are obtained via linear interpolation. At the splines (for regular points) and the line segments (feature points), more points are chosen to be converted into NC codes to reduce the non-linear error, which is called data densification. Using the cubic spline to smooth the tool path and the data densification to reduce the non-linear error, a novel tool path optimization algorithm in postprocessor is proposed. Experiments were carried out on an inclined rotary spindle axis non-orthogonal five-axis machine tool. It shows that the proposed tool path optimization provides improved accuracy and surface quality.     

Application of ACO-BPN to thermal error modeling of NC machine tool

Thermal errors are the major contributor to the dimensional errors of a workpiece in precision machining. Error compensation technique is a cost-effective way to reduce thermal errors. Accurate modeling of errors is a prerequisite of error compensation. In this paper, four key temperature points of a NC machine tool were obtained based on clustering method. A thermal error model based on the four key temperature points was proposed by using ant colony algorithm-based back propagation neural network (ACO-BPN). The ACO-BPN method improves the prediction accuracy of thermal deformation in the NC machine tool. A thermal error compensation system was developed based on the proposed model, and which has been applied to the NC machine tool in daily production. The results show that the thermal drift in workpiece diameter has been reduced from 33 to 8 μm from its center of tolerance.     

机械制造业数控机床几何误差自动控制

为了降低数控机床几何误差,提升加工精度,提出机械制造业数控机床几何误差自动控制方法。通过激光跟踪仪辨识机械制造业数控机床的几何误差,采用快速定位补偿算法与圆弧插补补偿算法相结合的方法补偿数控机床几何误差。利用计算机辅助制造软件生成刀位文件,依据刀位文件生成数控机床加工程序,通过补偿控制器生成数控机床各轴运动的控制指令,数控机床伺服系统接收控制指令后,自动控制数控机床各轴运动,以达到数控机床几何误差自动控制的目的。实验结果表明,采用该方法自动控制数控机床几何误差后,方向与角度的几何误差分别低于0.03 mm与0.1°,实际应用效果较好。     

双转台五轴机床空间误差补偿技术研究

几何误差、热误差和切削力误差占到了机床总误差的75%,对这3项误差进行控制是提高机床加工精度的关键所在。以双转台五轴机床的空间误差作为研究对象,通过对加工位置、主要热源及电动机电流等相关因素进行分析,确定空间误差建模所需的位移变量、温度变量和切削力变量。以现有的多种误差建模方法为基础,通过对信息融合技术进行研究,提出一种机床空间误差的多模型融合预测方法,建立综合反映几何误差、热误差和切削力误差的最优空间误差模型。最后以DSP为核心,设计空间误差补偿器,实施空间误差补偿,验证补偿效果。结果显示,建立的模型预测精度较高,残差小于2μm,而实施空间误差补偿后,加工零件的轮廓误差也由15μm降到了5μm,补偿效果明显。     

Geometric error compensation software system for CNC machine tools based on NC program reconstructing

It has been proved that error compensation is an effective approach to improve machining accuracy of a machine tool cost efficiently. In this paper, the framework of an error compensation software system, which can realize software error compensation via numerical control (NC) programs reconstructing, is investigated. And the algorithms relating to error prediction are discussed in detail, such as positioning movement error compensation, linear interpolation movement, and circular interpolation movement error compensation. To realize the error compensation, NC program is reconstructed according to the predicted errors during virtual machining before it is fed to the actual machining. Two controlled machining experiments were carried out. The results show that error compensation methods via reconstructing NC programs can improve the movement accuracy of a computer numerical control CNC machine tool obviously.     

Postprocessor development of a five-axis machine tool with nutating head and table configuration

The postprocessor is an important interface that transforms cutter location data into machine control data, and in a five-axis machine tool is highly complex because the simultaneous linear and rotary motions occur. Since most works of the five-axis postprocessor method have dealt only with the orthogonal machine tool’s configuration, this study presents a postprocessor scheme for two types of five-axis machine tools, each with a nutating head and a table whose rotational axes are in an inclined plane. The benefit of such a configuration is that it allows switching from vertical to horizontal machining by a single machine. The general analytical equations of NC data are obtained from the forward and inverse kinematics and the homogeneous coordinate transformation matrix. The linearization algorithm for the postprocessor is developed to ensure the machining accuracy. The presented algorithm is implemented using a window-based five-axis postprocessor with nutating axes, and programmed in Borland C++ Builder and OpenGL. A simulation is performed using solid cutting software and a trial-cut experiment was conducted on a five-axis machine tool with a nutating table to elucidate the accuracy of the proposed scheme.     

基于数控系统底层通信的实时误差补偿及应用

为提高数控机床加工精度,设计开发基于CNC底层通信的实时误差补偿功能模块,该模块通过GSK-Link网络通信协议与CNC底层进行数据交互。实时补偿过程为：通过温度采集模块和数据通信模块实时采集机床温度及各坐标轴坐标,误差补偿器计算误差补偿值并将计算结果直接送往CNC实时误差补偿功能模块,以实现机床误差实时补偿。该补偿过程的最大优点是实时补偿器与CNC底层直接通信,而不是目前国际上惯用的先通过PLC再与CNC底层通信的方式,因此实时补偿的速度和效率更高,补偿效果更好。GSK 25i数控系统的实时补偿结果表明,实时误差补偿可有效提高机床精度,最大可提高91.7%。     

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.     

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accuracy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA(grey relational analysis) method is introduced into the selection of temperature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN(artificial neural network) model is presented, and ABC(artificial bee colony) algorithm is introduced to train the link weights of ANN, a new ABCNN(Artificial bee colony-based neural network) modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR(least squares regression), ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 lm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.     

[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。     

A methodology for error characterization and quantification in rotary joints of multi-axis machine tools

A novel methodology was developed and implemented for error characterization, evaluation, and its quantification in a rotary joint of multi-axis machine tools by using a calibrated double ball bar (DBB) system as a working standard. This methodology greatly simplified the measurement setup and accelerated the error quantification. Moreover, the methodology is observed to be highly economical by reducing the tooling and instrumentation. However, considerable time and little more efforts are required in measuring and computing the errors. The developed methodology is capable of evaluating the five degrees of freedom (DOF) errors including two radial errors, one axial error, and two tilt errors out of six DOF error components of rotary joints. A DBB system with point accessory was used for direct measurement by change of length at multi-points and various locations, whereas mathematical modeling technique was implemented, and equation solvers were exercised for error evaluation and its quantification. Validation and authentication of the methodology and results obtained were carried out by simulation process prior to implementing the methodology on rotary joints of a five-axis turbine blade grinding machine. The results obtained from “A” and “B” rotary joints of the turbine blade grinding machine were presented by applying cubic spline technique for error modeling and its further utilization. The methodology was found extremely pragmatic, quite simple, efficient, and easy to use for error characterization and its quantification in rotary joints of multi-axis machine tools.     

提高数控机床加工精度技术研究

基于多体系统理论，建立了多坐标数控机床误差模型。介绍了3坐标数控机床9线辨识方法，研究了回转坐标6项误差的辨识方法。在4坐标数控机床上实现了几何误差的软件补偿。试验结果说明误差模型的准确性和补偿方法的实用性。     

复杂曲面零件在线检测与误差补偿方法

复杂曲面零件的高精度加工与精密检测一直是数字化制造领域的研究热点。为提高复杂曲面零件的加工精度、检测精度,提出一种集数控机床在线检测、加工误差分解与补偿加工为一体的集成化方法。介绍集成化在线检测方法及补偿系统的基本原理,分析数控加工后曲面零件测点数据的误差组成,提出一种基于空间统计分析的加工误差分解方法,在建立基于B样条曲面的确定性曲面回归模型的基础上,对回归模型残差进行空间独立性分析,分解出系统误差和随机误差,进而通过数控代码的修改,实现零件加工过程的系统误差补偿。列举一个曲面零件的加工与检测实例,进行方法有效性验证。通过加工工件的在线检测、误差分解、代码修改及补偿加工等环节,实例零件的加工精度有了大幅提高,而该系统的检测精度也通过与三坐标测量机(Coordinate measuring machine, CMM)检验结果的对比,得到了有效验证。     

On the workpiece setup optimization for five-axis machining with RTCP function

Nonlinear errors in five-axis machining process are caused due to the nonlinear motions of the rotational axes, which are inevitable. For the RT-type machine tool, the workpiece setup location on the working table has a direct effect on the nonlinear errors, thus there must be an optimal setup position which can reduce the nonlinear errors. Today’s five-axis machine tools are mostly equipped the with the RTCP (rotational tool center point) function, with which the NC program becomes independent from the workpiece setup. In this paper, we have focused on finding the optimal workpiece setup for the RT-type machine tool with RTCP function, more specifically, the Mikron UCP 600 five-axis machine tool in our lab. The kinematics of the machine tool is briefly analyzed. Based on that, the nonlinear error evaluation method with RTCP interpolation is derived. With this method, nonlinear errors can actually be considered as a function of the workpiece setup position. Then, the particle swarm optimization (PSO) is applied to find the optimal workpiece setup, in which a mutation operation is used since PSO traps into local optimum easily. The proposed optimal workpiece setup method is implemented and tested. Example results show that the optimal setup with least nonlinear errors can be found. Some interesting results also show that the nonlinear errors are not sensitive with the z component of the workpiece setup vector. The proposed optimization is nearly zero-cost and easy to both understand and implement, yet has a potential to reduce the nonlinear errors and thus to improve the accuracy of five-axis machining.     

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。     

工件分特征下的五轴数控机床关键几何误差分析与补偿方法

提出了工件分特征下的五轴数控机床关键几何误差分析与补偿方法,将复杂工件进行特征分解,通过灵敏度分析辨识工件分特征下的关键几何误差并补偿,从而提高工件整体加工精度。以某一复杂工件为例,首先,将其分解为平面、斜面、圆柱和圆锥台四个典型特征;然后,基于灵敏度分析分别辨识出各典型特征对应的关键几何误差;最后,分特征地进行误差补偿。在AC双转台五轴数控机床上进行了实验验证,实验结果表明,辨识得到的关键几何误差灵敏度系数之和占比均大于90%,补偿后工件四个典型特征的加工精度提高了20%~30%。研究结果表明,所提方法能有效辨识不同工件分特征下的关键几何误差,从而提高复杂工件的加工精度。     

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.     

An accurate probe pre-travel error compensation model for five-axis on-machine inspection system

On a five-axis CNC machine tool, the pretravel errors of touch-trigger probes are severely affected by gravity and must be compensated to ensure the required measurement accuracy. The situation is more complex than that of the three-axis on-machine inspection system. This paper proposes a simple and accurate modeling and compensation method for the probe pretravel error of a five-axis on-machine inspection system. First, the pretravel error for the 5-axis CNC tool is decoupled into three parts, which are analyzed based on the probe's mechanical structure. Then, a new calibration point selection strategy is proposed to obtain the accurate reference sphere center. Finally, we carry out calibration tests to validate the proposed method. The compensation results show that the proposed compensation method for the probe pretravel error under the influence of gravity (PPEUG) can improve the accuracy considerably.     

薄壁件加工变形误差预估及补偿的集成

针对薄壁件数控加工过程中产生的力致变形误差,提出了一种将变形误差预测与误差补偿进行集成的方法。在提出高效的误差计算迭代算法基础上,采用APDL的方式开发了集迭代计算、刀具走刀、材料去除于一体的误差动态仿真程序,实现全过程加工误差的自动计算。借助UG二次开发工具UG/Open开发的应用程序实现了UG和ANSYS之间的数据通信,根据预测变形误差自动修正CAD模型,继而利用UG CAM生成考虑误差补偿因素的加工代码。研究了涉及误差离线预测及补偿的集成方法的多个关键技术。算例表明：误差预测值逼近实验值,精度可靠;集成软件能够自动生成误差补偿的加工代码,实现了误差离线预测和补偿全过程的CAD/CAE/CAM集成,集成程度高。