[可靠性建模及试验技术]基于元动作模块的多轴数控机床精度分析

为充分发挥多轴数控机床大数据的价值,降低运动精度的预测难度,提出了基于元动作模块的精度分析方法。采用多体模型描述机床运动系统的结构和运动关系,利用旋量理论和微分方法推导了用于运动精度评价的坐标误差模型;规划了多轴数控机床大数据驱动的精度分析的结构框架,并重点论述了以元动作模块为基本组成单元的分布式元动作数据库的构建方法,该方法充分发挥历史大数据和实时动态数据的价值,保证了机床运动系统的仿真和精度预测的稳定性与准确性。通过对五轴联动加工中心的刀具运动系统的实例分析,验证了精度分析方法的简便性和适用性。     

Anisotropic force ellipsoid based multi-axis motion optimization of machine tools

The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C++. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.     

基于激光干涉仪的数控机床运动误差识别与补偿

提出了数控机床运动误差的软件补偿方法。采用刚体运动假设和齐次坐标变换建立了多轴机床空间运动误差的通用模型。该模型把刀具相对于工件的空间误差表示为机床各结构件之间运动误差的位置函数。给出了全部运动误差参数的激光干扰仪识别方法，提出了一种新的roll误差测量措施，在立式加工中心上进行了运动误差的补偿实验，结果证明所提出的运动误差软件联动补偿效果显著。     

Geometric error calibration of multi-axis machines using an auto-alignment laser interferometer

This work will report the development and application of an auto-alignment laser interferometer system for the geometric error calibration of CNC multi-axis machines. The system is capable of a diagonal displacement measurement, where multiple machine axes are moved simultaneously, with automatic optic alignment. This capability provides a solution for quick evaluation of the overall volumetric error of a multi-axis machine tool. One application of the system is that the 21 geometric errors of a 3-axis machine can be quickly estimated from the displacement measurements of some determined diagonal lines in the working volume. Compared with a time of several days using a conventional laser interferometer system, it takes only 1 hour for the proposed system to complete the geometry calibration of a 3-axis machine. A method for the roll calibration of a vertical axis is also proposed and demonstrated in this work.     

[可靠性建模及试验技术]面向数控机床可靠性试验的多维力随动加载装置

面向五轴联动数控机床的可靠性试验提出多维力随动加载方法,对五轴联动进给主轴施加多维力载荷,形成复杂进给抗力,部分模拟主轴复杂切削力环境。基于6-PUS并联机构研制多维力随动加载装置,采用模糊PID控制器建立显式力控制系统,比例和积分增益可随加载误差自适应调节。在五轴联动数控机床上开展多维力随动加载实验,结果表明,加载装置能够跟随机床主轴的单轴、三轴联动和五轴联动进给运动,根据期望值对主轴施加三维力,加载误差小于3.2%,在机床执行多种加工轨迹时形成有效进给抗力,为后续引入动态加载模拟复杂切削力提供理论和装备支撑。研究成果可为数控机床可靠性试验提供低成本、可循环的加载方式,有利于测试的规模化和标准化发展,也可为精度保持性、超载试验、跑合试验等机床性能测试提供新的负载模拟思路。     

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.     

弧齿线圆柱齿轮全修形齿面的CNC修形加工方法

针对弧齿线圆柱齿轮全修形齿面的修形控制问题,提出一种在展成加工的同时对齿廓和齿线两个方向进行修形控制的加工方法。通过调整直刃刀盘的展成运动回转半径,实现齿面齿廓方向的修形量控制;通过调整刀倾角,实现齿面齿线方向的修形量控制。基于空间运动学原理,利用矢量旋转公式,在具有倾角的数控机床上与普通多轴联动数控机床上展成加工齿面时,保持刀具和工件的相对位置和相对运动相同,进行两类机床之间的运动转换,建立机床运动控制方程,从而实现弧齿线圆柱齿轮在普通多轴联动数控机床上的修形加工。并通过试件的切削试验和齿面接触分析试验,证明所提出的修形加工方法和分析的加工运动方程的正确性。与弧齿线圆柱齿轮传统的加工方法相比,这种加工方法效率高,运动关系简单,便于推广应用。     

A manufacturing model of helical groove on rotary burr and a universal post processing method

A systematic machining theory and precision method to determine cutter location in a grinding system is presented for rotary burr. First, the helical cutting edge on various kinds of revolving surfaces is built. Then, based on the geometry model of the helical cutting edge, the smooth spiral rake surface with constant normal rake angle and flank surface can been formed during the one-pass grinding process by this method. No interference between the grinding wheel and workpiece happens by the wheel special rotation. The method has the characteristic of detaching the grinding wheel path solution from specified machining conditions. The grinding wheel path is suitable for different NC machine tools through post processing. Meanwhile, a mechanism kinematic model of the NC machine tool is built, and a generalized algorithm for post-processing of multi-axis NC machine tools is presented. This model is applied to arbitrary configuration of NC machine tool, and the motion value for each axis will be generated by the inputting structure and motion parameters of the machine tool. The model, together with the machining method mentioned in this paper, make the calculation and generation of the grinding wheel path simpler and universal. At last, the validity of the method given in the paper is identified by an example of grinding.     

A control strategy with motion smoothness and machining precision for multi-axis coordinated motion CNC machine tools

The advanced manufacture technology requires that multi-axis coordinated motion computer numerical control (CNC) machine tools have the capability of high smoothness and high precision. At present, the study of the motion smoothness mainly concentrates on the acceleration and deceleration control method and the look-ahead process of velocity planning in the interpolation stage. The control strategy of the contouring error mainly focuses on tracking error control, cross-coupling control, and optimal control. In order to improve the motion smoothness and contouring precision for multi-axis high-speed CNC machine tools, a multi-axis modified generalized predictive control approach was presented in this paper. In the control strategy, the estimation models of tracking error, contouring error, velocity error, and acceleration error were structured separately. A new improved quadratic performance index was proposed to guarantee the minimum of these errors. Generalize predictive control was also introduced, a multi-axis generalized predictive control model was deduced for motion smoothness and machining precision for multi-axis coordinated motion CNC system, and an approved multi-axis generalized predictive controller based on the model was designed in this paper. The proposed predicted control approach was evaluated by simulation and experiment of circular, noncircular, and space line trajectories, respectively. These simulative and experimental results demonstrated that the proposed control strategy can significantly improve the motion smoothness and contouring precision. Therefore, the new position control method can be used for the servo control system of multi-axis coordinated motion CNC system, which increases motion smoothness and machining precision of CNC machine tools.     

基于误差模型的三轴联动加工轨迹预补偿方法

为了减小由于进给系统动态特性造成的多轴联动加工轮廓误差,提出了一种基于轮廓误差模型的三轴联动加工轨迹预补偿方法。首先建立了关于轨迹曲率、加工速率及进给系统动态特性参数的轮廓误差模型;然后根据读取的插补数据,利用轮廓误差模型实时预测三轴联动加工过程中的轮廓误差补偿向量并对加工轨迹指令进行补偿;最后通过对圆、变曲率和螺旋线轨迹的MATLAB仿真和机床加工实验,证明该补偿方法将轮廓误差减小了85%以上,可显著提高数控机床加工精度。     

Three-dimensional tool radius compensation for multi-axis peripheral milling

Few function about 3D tool radius compensation is applied to generating executable motion control commands in the existing computer numerical control (CNC) systems. Once the tool radius is changed, especially in the case of tool size changing with tool wear in machining, a new NC program has to be recreated. A generic 3D tool radius compensation method for multi-axis peripheral milling in CNC systems is presented. The offset path is calculated by offsetting the tool path along the direction of the offset vector with a given distance. The offset vector is perpendicular to both the tangent vector of the tool path and the orientation vector of the tool axis relative to the workpiece. The orientation vector equations of the tool axis relative to the workpiece are obtained through homogeneous coordinate transformation matrix and forward kinematics of generalized kinematics model of multi-axis machine tools. To avoid cutting into the corner formed by the two adjacent tool paths, the coordinates of offset path at the intersection point have been calculated according to the transition type that is determined by the angle between the two tool path tangent vectors at the corner. Through the verification by the solid cutting simulation software VERICUTwith different tool radiuses on a table-tilting type five-axis machine tool, and by the real machining experiment of machining a soup spoon on a five-axis machine tool with the developed CNC system, the effectiveness of the proposed 3D tool radius compensation method is confirmed. The proposed compensation method can be suitable for all kinds of threeto five-axis machine tools as a general form.     

Implementation of the principal-axis method for machining of complex surfaces

In this paper a new strategy for 5-axis machining of complex surfaces is presented. The method uses curvature alignment and matching between the design surface and the cutting tool to improve surface finish and reduce machining time. The method is implemented on two configurations of 5-axis machines, and used to machine a test surface. The results of the tests show a considerable improvement over conventional 3-axis machining.     

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.     

空间自由曲面五轴联动数控加工

介绍了五轴数控机床的运动方式,阐述了空间自由曲面五轴联动数控加工中刀具路径规划的基本方法:参数线法、CC路径截面线法、CL路径截面线法、导动面法等。之后对五轴加工中刀具轴向规划进行了论述:垂直于表面方式、平行于表面方式、倾斜于表面方式。最后归纳总结了刀具干涉的检测与处理的方法,并分别说明了其优缺点和适应范围。     

Design of a five-axis ultra-precision micro-milling machine—UltraMill. Part 2: integrated dynamic modelling, design optimisation and analysis

Using computer models to predict the dynamic performance of ultra-precision machine tools can help manufacturers to substantially reduce the lead time and cost of developing new machines. However, the use of electronic drives on such machines is becoming widespread, the machine dynamic performance depending not only on the mechanical structure and components but also on the control system and electronic drives. Bench-top ultra-precision machine tools are highly desirable for the micro-manufacturing of high-accuracy micro-mechanical components. However, the development is still at the nascent stage and hence lacks standardised guidelines. Part 2 of this two-part paper proposes an integrated approach, which permits analysis and optimisation of the entire machine dynamic performance at the early design stage. Based on the proposed approach, the modelling and simulation process of a novel five-axis bench-top ultra-precision micro-milling machine tool—UltraMill—is presented. The modelling and simulation cover the dynamics of the machine structure, the moving components, the control system and the machining process and are used to predict the entire machine performance of two typical configurations.     

用于五轴联动数控机床的曲线插补控制策略

为实现复杂曲面零部件的高速高精数控加工,提出了一种用于五轴联动数控机床的曲线插补控制策略.实现该控制策略的数控机床控制器将控制任务分为非实时任务和实时任务两部分.非实时任务包括刀具路径信息中位置矢量的曲线插值计算和刀位矢量的曲线插值计算;实时任务包括位置矢量插值曲线和刀位矢量插值曲线的实时插补计算,以及插补点坐标的逆机床运动变换.加工实验表明,该插补加工方法町以用于五坐标数控机床的运动控制,具有良好的应用前景.     

任意结构多轴数控机床后置处理的全微分求解算法

针对目前多轴数控机床后置求解算法主要是面向某一结构机床的特点,提出适用于任意结构多轴数控机床的通用后置求解方法。根据多体运动学理论建立任意结构多轴数控机床通用运动学模型,通过使用全微分形式描述相邻刀位点空间关系,使复杂的运动学逆向求解转化为求解以各轴运动坐标增量为变量的线性方程组求解问题,求解快速精确。初始各轴运动坐标的求解采用数值方法和全微分法相结合的方法,确保后续点的求解精度。对特定结构的多轴数控机床采用全微分法、公式推导法和数值计算法进行后置求解,对比各算法的结果表明这种全微分后置求解方法具有通用性,算法精度很高,求解速度快。     

The mathematical models of the basic entities of multi-axis serial orthogonal machine tools using a modified Denavit–Hartenberg notation

The use of virtual techniques as a means of training operators and familiarizing them with the machine tools on which they work has become increasingly widespread throughout the manufacturing industry in recent years. To support the development and implementation of virtual machine tools, this paper constructs the generic mathematical models of the basic building links, joint types, and cutting tools of multi-axis serial orthogonal machine tools. The modeling methodology can support the synthesis of various machine tools with different configurations but similar functions and facilitates the processes of error analysis, numerical control data generation, parameter measurement, and cutting kinematics analysis. The validity of the modeling approach is demonstrated using a six-axis serial orthogonal machine tool for illustration purposes.     

活塞生产线中复合专机的结构布局形态方案创成

研究了概念设计阶段活塞生产线中复合专机的结构形态创成方法。先综合分析了活塞加工工艺路线，根据复合专机所实现的工序方案，确立了复合专机的基型机的运动及结构形态方案，然后根据生产线及工艺的需求，创成设计出复合专机的结构形态方案，为活塞加工生产线中复合专机的详细设计提供依据。