Construction of an error map of rotary axes on a five-axis machining center by static R-test

This paper proposes an efficient and automated scheme to calibrate error motions of rotary axes on a five-axis machining center by using the R-test. During a five-axis measurement cycle, the R-test probing system measures the three-dimensional displacement of a sphere attached to the spindle in relative to the machine table. Location errors, defined in ISO 230-7, of rotary axes are the most fundamental error factors in the five-axis kinematics. A larger class of error motions can be modeled as geometric errors that vary depending on the angular position of a rotary axis. The objective of this paper is to present an algorithm to identify not only location errors, but also such position-dependent geometric errors, or “error map,” of rotary axes. Its experimental demonstration is presented.     

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.     

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.     

Error map construction for rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe

Position-dependent geometric errors, or “error map,” of a rotary axis represent how position and orientation of the axis of rotation change with its rotation. This paper proposes a scheme to calibrate the error map of rotary axes by on-the-machine measurement of test pieces by using a contact-type touch-trigger probe installed on the machine's spindle. The present scheme enables more efficient and automated error calibration, which is crucial to implement periodic check of rotary axes error map or periodic update of its numerical compensation for five-axis machine tools. The uncertainty analysis of the error calibration is also presented with a particular interest in the influence of error motions of linear axes. The experimental demonstration is presented.     

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

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.     

Double ballbar test for the rotary axes of five-axis CNC machine tools

In this paper a new method that uses the double ballbar to inspect motion errors of the rotary axes of five-axis CNC machine tools is presented. The new method uses a particular circular test path that only causes the two rotary axes to move simultaneously and keeps the other three linear axes stationary. Therefore, only motion errors of the two rotary axes will be measured during the ballbar test. The theoretical trace patterns of various error origins, including servo mismatch and backlash, are established. Consequently, the error origins in the rotary block can be diagnosed by examining whether similar patterns appear in the motion error trace. The method developed was verified by practical tests, and the servo mismatch of the rotary axes was successfully detected.     

带标准分度转台的激光角度干涉仪的不准直误差模型

为了探讨带标准分度转台的激光角度干涉仪在测量过程中的安装不准直误差对测量结果的影响,在分析回转轴转角误差测量原理的基础上,根据测量光路的几何特征变化规律,提出测量系统的不准直误差模型。研究不准直误差变化对转角误差测量结果的影响,明确了为保证最终测量结果的精度在±1″内宜采取的误差控制措施。通过与自准直仪配合高精度多面棱体方法进行比对实验,并利用不准直误差模型对测量结果进行修正后,可以将测量结果的最大差值减小为-0.52″。结果表明所建立的误差模型的正确性,在准确评估和提高测量系统的精度上有一定的推广价值。     

Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool

This paper proposes an efficient and automated scheme to predict and identify the position and motion errors of rotary axes on a non-orthogonal five-axis machining centre using the double ball bar (DBB) system. Based on the Denavit-Hartenberg theory, a motion deviations model for the tilting rotary axis B and rotary C of a non-orthogonal five-axis NC machine tool is established, which considers tilting rotary axis B and rotary C static deviations and dynamic deviations that total 24. After analysing the mathematical expression of the motion deviations model, the QC20 double ball bar (DBB) from the Renishaw Company is used to measure and identify the motion errors of rotary axes B and C, and a measurement scheme is designed. With the measured results, the 24 geometric deviations of rotary axes B and C can be identified intuitively and efficiently. This method provides a reference for the error identification of the non-orthogonal five-axis NC machine tool.     

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.     

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.     

Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part II: errors estimation

To improve the accuracy of CNC machine tools, error sources and its effects on the overall position and orientation errors must be known. Most motional errors in the error model of five-axis machine tool can be measured with modern laser interferometer devices, but there are still some not measurable geometric errors. These not measurable errors include constant, inaccurate link errors of components such as rotary axes block, main spindle block and tool holder. After setting all measured errors in the error model, a reduced error model is defined, which describes the influence of each unknown and not measurable link error on the overall position errors of the five-axis machine tool. On the other hand, the newly developed probe-ball device can measure the overall position errors of five-axis machine tools directly. Based on the reduced model and the overall position errors, the link errors can be estimated very accurately with the least square estimation method. The error model is then fully known and can be used for advanced purposes such as error prediction and compensation.     

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。     

Identification of two different geometric error definitions for the rotary axis of the 5-axis machine tools

Geometric errors are clearly among the critical error sources in 5-axis machine tools and directly contribute to the machining inaccuracies. According to the definition of geometric errors of the rotary axis, different understandings have been exist in published studies. It is extremely dangerous as it makes the comprehension of the geometric errors ambiguous and may make the geometric error identification and compensation less effective. This phenomenon has not been noticed so far. In this paper, two different commonly used geometric error definition and modeling methods are firstly identified and analyzed, named as “Rotary axis component shift” and “Rotary axis line shift”. The features and relationships of these two error modeling methods are analyzed. After a detailed comparison, “Rotary axis component shift” is more suitable to definite the geometric errors of rotary axis. An experiment has been conducted on a 5-axis machine tool to show the correctness of our work. The results show that the identified geometric errors of rotary axis based on the two error models are greatly different and need to be concerned.     

非球面数控磨床的误差建模与补偿研究

以实验室自主研发的非球面数控磨床为研究对象,系统分析了该磨床几何误差元素,基于齐次变换原理和多体系统理论,建立了该磨床包含所有几何误差源的综合误差模型。基于双频激光干涉测量仪,应用9线误差辨识法和回转误差辨识法建立了以磨床单项误差为变量的组合方程,并求取了磨床的各误差分量。针对非球面数控磨床定位误差的特性,提出了增量式误差补偿原理。研究表明:该误差建模及补偿原理可以有效地提升非球面数控磨床的定位精度。     

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.     

Identification and compensation of systematic deviations particular to 5-axis machining centers

This paper presents an algorithm for identifying particular deviations such as angular deviations around linear axes relating to rotary axes in 5-axis machining centers. In this study, three kinds of simultaneous three-axis control motions are designed for each rotary axis to identify the deviations. In the measurement, two translational axes and one rotary axis are simultaneously controlled keeping the distance between a tool and a worktable constant. Telescoping ball bar is an effective instrument for measuring the relative displacement to the reference length in the work volume because its attitude is freely changed. In these three-axis control motions, the sensitive direction of the ball bar is kept constant. In order to determine the deviations, we derive eight equations from the relationship between the eccentricities obtained from the measured circular trajectories and the approximations derived from the mathematical model based on the simulation. In the simulation, a mathematical model considering the particular deviations is developed and then the characteristic diagrams are prepared for every deviation and every three-axis control motion. Based on the results, we propose a procedure for identifying the particular deviations in 5-axis machining centers and its procedure has been applied to identify the deviations actually. From both the simulation and the experiment, it has been confirmed that the proposed method gives precision results and is able to apply to the measurement of 5-axis machining center which is a tilting rotary table type.     

精密卧式加工中心空间误差的建模、测量与补偿技术

采用空间误差补偿技术,可有效提高数控机床的空间定位精度。以一台精密卧式加工中心为对象,系统阐述其几何误差补偿中的关键问题及解决方案。通过三维误差建模与分析,得到该机床的21项几何误差中有17项需要测量和补偿,另外4项误差对机床定位精度的影响甚微。以此为依据,设计误差测量及补偿方案,并给出误差的具体测量方法和补偿结果。结果表明:经过一次系统地误差测量与补偿,精密卧式加工中心的空间定位精度可以提高50%～70%;合理规划和实施空间误差测量,可大幅提高测量效率。     

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.     

A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar

Ensuring that a five-axis machine tool is operating within tolerance is critical. However, there are few simple and fast methods to identify whether the machine is in a “usable” condition. This paper investigates the use of the double ball bar (DBB) to identify and characterise the position independent geometric errors (PIGEs) in rotary axes of a five-axis machine tool by establishing new testing paths. The proposed method consists of four tests for two rotary axes; the A-axis tests with and without an extension bar and the C-axis tests with and without an extension bar. For the tests without an extension bar, position errors embedded in the A- and C-axes are measured first. Then these position errors can be used in the tests with an extension bar, to obtain the orientation errors in the A- and C-axes based on the given geometric model. All tests are performed with only one axis moving, thus simplifying the error analysis. The proposed method is implemented on a Hermle C600U five-axis machine tool to validate the approach. The results of the DBB tests show that the new method is a good approach to obtaining the geometric errors in rotary axes, thus can be applied to practical use in assembling processes, maintenance and regular checking of multi-axis CNC machine tools.