Analysis of geometric errors associated with five-axis machining centre in improving the quality of cam profile

A five-axis machine is presently one of the most versatile machine tools available and they are becoming increasingly common. To increase the accuracy capabilities of such machines, it is crucial to be able to study the geometric errors of the components and its effect on the quality of machined products. In five-axis machine tools, all linear axes are theoretically perpendicular (dot product, cos 90°=0) to each other and directed along or around the X, Y and Z of the cartesian coordinate system; but in working machines, the axes are nearly perpendicular (cos89.90°≠0) because of manufacturing error and assembly error or quasi-static error. The present paper discusses the development of a generalised error model for the effects of geometric errors of the components of the kinematic chain of a machine in the workspace and the results obtained by this model have been verified experimentally. The effect of geometric error has been studied further for cam profile generation using a five-axis machining centre and an improvement in the profile has been obtained.     

三轴数控机床加工精度可靠性分析

机床作为机械制造业的基础,几何误差、热误差、装配误差等都会影响数控机床的加工精度,数控机床加工精度的高低直接决定产品的生产质量。为保证数控机床对产品的加工质量,需要对数控机床的加工误差数据处理,求得数控机床加工精度可靠性,而一次二阶矩法和蒙特卡罗法是常用的可靠性分析方法。以三轴数控机床为研究对象,针对给定的误差数据,运用一次二阶矩法和蒙特卡罗法分析出数控机床加工精度可靠性。此分析对提高数控机床加工精度及保证使用寿命具有重要指导意义和参考价值。     

Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement

The geometric errors of rotary axes are the fundamental errors of a five-axis machine tool. They directly affect the machining accuracy, and require periodical measurement, identification and compensation. In this paper, a precise calibration and compensation method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The automated measurement is realized by using an on-the-machine touch-trigger technology and an artifact. A calibration algorithm is proposed to calibrate geometric errors of rotary axes based on the relative displacement of the measured reference point. The geometric errors are individually separated and the coupling effect of the geometric errors of two rotary axes can be avoided. The geometry error of the artifact as well as its setup error has little influence on geometric error calibration results. Then a geometric error compensation algorithm is developed by modifying the numeric control (NC) source file. All the geometric errors of the rotary errors are compensated to improve the machining accuracy. The algorithm can be conveniently integrated into the post process. At last, an experiment on a five-axis machine tool with table A-axis and head B-axis structure validates the feasibility of the proposed method.     

Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

A Unified Error Model for Tolerance Design, Assembly and Error Compensation of 3-DOF Parallel Kinematic Machines with Parallelogram Struts

This paper presents a unified geometric error model that enables the tolerance design, assembly and calibration of a class of 3-DOF parallel kinematic machines with parallelogram struts to be integrated into a comprehensive framework. The error mapping function is formulated with a goal that enables the source errors affecting the uncompensatable pose error to be found. This is followed by the investigation into the influences of source errors on the pose accuracy with the aid of sensitivity analysis. The assembly process that enables to effectively reduce the uncompensatable pose error is also proposed.     

立式加工中心关键几何误差判定与量化验证

针对现阶段机床空间误差模型不完整且传统灵敏度分析存在局限性,导致其关键几何误差溯源不准确,以及关键几何误差判定结果难以量化验证的问题,以某立式加工中心为研究对象,提出一种机床关键几何误差判定与量化验证方法。以旋量理论为基础,研究某立式加工中心空间误差建模,以输出机床完整空间误差模型;在此基础上,以基于传统局部灵敏度分析为基础,利用误差贡献度因子判定机床关键几何误差;借助数值模拟实验对判定结果进行量化验证。结果表明：相较于传统灵敏度分析结果,利用误差贡献度因子判定关键几何误差的结果更准确;基于误差贡献度因子的判定结果,不仅能量化几何误差相对机床空间误差的影响程度,同时可为机床部件制造精度设计提供理论参考。     

基于激光跟踪仪的数控机床空间误差测量及补偿

为了改变机床空间误差综合性的测量手段和补偿技术在国内机床制造和生产中应用较少的现状和研究数控机床空间精度提升方法，介绍数控机床平动轴的21项误差和激光跟踪仪的空间误差测试原理，阐述测量与辨识机床空间误差的步骤和方法。在桥式五轴加工中心上进行空间误差测试，给出数控机床空间误差结果，并生成误差补偿文件，通过西门子的VCS功能进行了误差补偿。并对比分析了补偿前后的21项误差，对补偿前后数据的差异进行原因分析，并通过对机床空间体对角线的测量验证了空间误差测量与补偿的实际效果，补偿后误差缩小为原来的11.2%,应用该技术能够大大提高机床的空间精度。     

Accuracy enhancement of five-axis machine tool based on differential motion matrix: Geometric error modeling,identification and compensation

This paper presents the precision enhancement of five-axis machine tools according to differential motion matrix, including geometric error modeling, identification and compensation. Differential motion matrix describes the relationship between transforming differential changes of coordinate frames. Firstly, differential motion matrix of each axis relative to tool is established based on homogenous transformation matrix of tool relative to each axis. Secondly, the influences of errors of each axis on accuracy of tool are calculated with error vector of each axis. The sum of these influences is integration of error components of machine tool in coordinate system of tool. It endows the error modeling clear physical meaning. Moreover, integrated error components are transformed to coordinate frame of working table for integrated error transformation matrix of machine tools. Thirdly, constructed Jacobian is established using differential motion matrix of each axis without extra calculation to compensate the integrated error components of tool. It makes compensation easy and convenient with reuse of intermediate. Fourthly, six-circle method of ballbar is developed based on differential motion matrix to identify all ten error components of each rotary axis. Finally, the experiments are carried out on SmartCNC500 five-axis machine tool to testify the effectiveness of proposed accuracy enhancement with differential motion matrix.     

A new compensation method for geometry errors of five-axis machine tools

The present study aims to establish a new compensation method for geometry errors of five-axis machine tools. In the kinematic coordinate translation of five-axis machine tools, the tool orientation is determined by the motion position of machine rotation axes, whereas the tool tip position is determined by both machine linear axes and rotation axes together. Furthermore, as a nonlinear relationship exists between the workpiece coordinates and the machine axes coordinates, errors in the workpiece coordinate system are not directly related to those of the machine axes coordinate system. Consequently, the present study develops a new compensation method, the decouple method, for geometry errors of five-axis machine tools. The method proposed is based on a model that considers the tool orientation error only related to motion of machine rotation axes, and it further calculates the error compensations for rotation axes and linear axes separately, in contrast to the conventional method of calculating them simultaneously, i.e. determines the compensation of machine rotation axes first, and then calculates the compensation associated with the machine linear axes. Finally, the compensation mechanism is applied in the postprocessor of a CAM system and the effectiveness of error compensation is evaluated in real machine cutting using compensated NC code. In comparison with previous methods, the present compensation method has attributes of being simple, straightforward and without any singularity point in the model. The results indicate that the accuracy of positioning was improved by a factor of 8–10. Hence, the new compensation mechanism proposed in this study can effectively compensate geometry errors of five-axis machine tools.     

立式加工中心空间误差验证及补偿

为提高某立式加工中心整机加工精度,借助旋量理论建立完备立式加工中心空间误差模型,在此基础上实现机床空间误差有效补偿.以旋量理论为基础推导并建立机床刀具运动链与工件运动链运动学正解,分析机床21项几何误差原理,在考虑21项几何误差的基础上建立该立式加工中心完备空间误差模型;利用九线法完成各项几何误差辨识;基于旋量运动学正解求解机床运动学逆解后得出运动轴实际运动路径,并通过体对角线实验对比补偿前后的效果.结果表明:所提补偿方法补偿效果显著,验证了机床空间误差模型的准确性,实现了提高机床加工精度的目的.     

Integrated Inspection and Machining for Maximum Conformance to Design Tolerances

Designers' intent for the form, fit and function of products is expressed by design tolerances the conformance to which is the main objective of manufacturing processes. A methodology for maximizing the adherence to the specified tolerances using an integrated machining and inspection system is presented. Considering the desired tolerance envelope of the part, an error decomposition technique is developed to model machining errors caused by the systematic and non-systematic errors in the machine tool. The model is used to adaptively plan the final machining cuts, based on inspection feedback, to enhance the geometric accuracy of the final product and is illustrated by an example. This approach reduces scrap and rework and their associated costs.     

基于多体系统理论的车铣中心空间误差模型分析

数控机床的误差建模是进行机床运动设计、精度分析和误差补偿的关键技术,也是保证机床加工精度的重要环节.本文利用多体系统理论来构建超精密数控机床的几何误差模型,该模型简便、明确,不受机床结构和运动复杂程度的限制,为计算机床误差、实现误差补偿和修正控制指令提供了理论依据.在机床实际应用中,可以利用由精密机床误差建模所推导出的几何位置误差来修正理想加工指令,控制机床的实际运动,从而实现几何误差补偿,提高机床加工精度.     

高精密数控机床的非线性误差分析、控制及补偿

误差控制及补偿是提高数控机床精度的重要手段,因此误差模型的建立与分析显得至关重要.本文详细阐述了数控机床几何误差、热误差、切削力误差和控制误差的基本概念、起因、建模及参数辨识,综述了误差研究现状,并对今后的研究方向进行了展望.对减小误差的控制策略和误差综合软件补偿两个方面进行了探讨.为提高数控机床的加工精度提出了可行的思路.     

Relationships between straightness and angular kinematic errors in machines

The software compensation approach for the improvement of machine tool and coordinate measuring machine accuracy depend to some extent on machine error modelling and measurement methodologies. The currently established methodology is based on the derivation of tool position error (for machine tools) or stylus tip position error (for coordinate measuring machines) by the combination of individual axis joint kinematic error parameters. The purpose of this paper is to propose a machine error analysis based on error classification. This taxonomic approach forms a conceptual basis for an analysis of machine errors with a deeper understanding of error mechanisms at more fundamental levels. The relevance of this approach is investigated through the case study of the coupling mechanism between joint kinematic angular and straightness errors of machine linear axes. The limitations of the joint kinematic straightness and angular error modelling based on purely abstract mathematical dependence principles are explored through simulations and experiments.     

Accuracy improvement of miniaturized machine tool: Geometric error modeling and compensation

A novel capacitance–sensor based multi-degree-of-freedom (DOF) measurement system has been developed for measuring geometric errors of a miniaturized machine tool (mMT) overcoming the size limitations. In the present work five geometric error components of a three-axis mMT are measured simultaneously along each axis and the squareness errors are determined by the slopes of straightness error profiles. Least-squares fitting method is used to represent the analytical models of geometric errors. A kinematic chain consisting of various structural members of mMT is introduced to establish the positional relationships among its coordinate frames. Based on this kinematic chain a general volumetric error model has been developed to synthesize all geometric error components of a miniaturized machine tool. Then, a recursive compensation method is proposed to achieve error compensation efficiently. Test results show that the positioning accuracy of miniaturized machine tool has been improved with compensation.     

Validation of volumetric error compensation for a five-axis machine using surface mismatch producing tests and on-machine touch probing

In order to validate volumetric error compensation methods for five-axis machine tools, the machining of test parts has been proposed. For such tests, a coordinate measuring machine (CMM) or other external measurement, outside of the machine tool, is required to measure the accuracy of the machined part. In this paper, a series of machining tests are proposed to validate a compensation strategy and compare the machining accuracy before and after the compensation using only on-machine measurements. The basis of the tests is to machine slots, each completed using two different rotary axes indexations of the CNC machine tool. Using directional derivatives of the volumetric errors, it is possible to verify that a surface mismatch is produced between the two halves of the same slot in the presence of specific machine geometric errors. The mismatch at the both sides of the slot, which materializes the machine volumetric errors is measured using touch probing by the erroneous machine itself and with high accuracy since the measurement of both slot halves can be conducted using a single set of rotary axes indexation and in a volumetric region of a few millimetres. The effect of a compensation strategy is then validated by comparing the surface mismatch value for compensated and uncompensated slots.     

数控机床在线检测系统的定位误差补偿实验研究

为了提高数控机床在线检测精度,研究机床各个轴的定位误差对数控机床在线检测精度的影响。针对数控机床误差补偿进行实验研究,采用激光干涉仪在数控机床上测量出各个轴的定位误差,将各个轴的定位误差依次进行补偿;并以Visual C++6. 0为工具,编写了三次样条曲线的算法程序,将测量的数据点拟合成一条曲线,达到可以预测机床任意点误差的效果;进行标准块检测实验。结果表明:在数控机床在线检测系统中实施误差补偿,效果较为明显,利用补偿软件可以实现对数控机床任意点进行补偿。     

Kinematical calibration of a hybrid machine tool with Regularization method

The hybrid machine tools, combining the advantages of serial and parallel type machine tools, provide more and more application opportunities for less-freedom parallel mechanism. Accuracy performance is still an important index of hybrid machine tool for industry application. In this study, configuration of a 3-P(4R)S-XY hybrid machine tool is first introduced. The 3-P(4R)S parallel mechanism can be simplified to a 3-PRS mechanism on kinematical calibration. Based on that, error model and error kinematics are derived to introduce all possible manufacturing and assembling errors into calibration. Then, identification matrix is derived by differentiating kinematical equations. Combining the advantages of calibration schemes based on both inverse and forward kinematics model, a new measurement scheme is put forward, in which not all freedoms of motions needs to be measured and error identification could be efficiently accomplished in one time measurement. In order to solve the ill-posed problem in error identification, practical Regularization methods are adopted. Finally, the kinematical calibration experiment of the prototype machine tool is performed with a combined measuring tool. The results of RTCP accuracy test reveal that the positioning accuracy is less than 0.05 mm in the 30° cone workspace. Calibration experiments for the prototype verify feasibility and effectivity of the more precise kinematical error model, the low-cost measurement scheme, and the error identification solution with Regularization method.     

Accuracy enhancement of five-axis CNC machines through real-time error compensation

Although error modeling and compensation have given significant results for three-axis CNC machine tools, a few barriers have prevented this promising technique from being applied in five-axis CNC machine tools. One crucial barrier is the difficulty of measuring or identifying link errors in the rotary block of five-axis CNC machine tools. The error model is thus not fully known. To overcome this, the 3D probe-ball and spherical test method are successfully developed to measure and estimate these unknown link errors. Based on the identified error model, real-time error compensation methods for the five-axis CNC machine tool are investigated. The proposed model-based error compensation method is simple enough to implement in real time. Problems associated with the error compensation in singular position of the five-axis machine tool are also discussed. Experimental results show that the overall position accuracy of the five-axis CNC machine tool can be improved dramatically.