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.     

基于Sobol’法的机床关键几何误差元素辨识方法研究

针对机床几何误差元素多、误差测量与辨识过程繁琐等问题,利用Sobol’全局灵敏度分析方法对空间误差模型中的几何误差元素进行灵敏度分析,筛选出影响较大的几何误差元素,从而降低误差测量与辨识过程的复杂度,简化空间误差模型。以螺旋理论为建模基础,建立机床空间误差模型;对所有几何误差元素进行Sobol序列抽样并通过蒙特卡洛估计法求解灵敏度,计算各误差元素的一阶灵敏度值及全局灵敏度值,从21个误差项中筛选出对机床空间误差影响较大的12项;将简化模型与完备模型进行对比,空间误差元素简化率为48%,其预测精度大于80%,说明了误差元素筛选的有效性,为机床空间误差建模、误差元素辨识以及空间误差补偿工作的简化提供参考。     

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.     

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.     

Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar

In this study, position-independent geometric errors, including offset errors and squareness errors of rotary axes of a five-axis machine tool are measured using a double ball-bar and are verified through compensation. In addition, standard uncertainties of measurement results are calculated to establish their confidence intervals. This requires two measurement paths for each rotary axis, which are involving control of single rotary axis during measurement. So, the measurement paths simplify the measurement process, and reduce measurement cost including less operator effort and measurement time. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants. Their effects on the measurement results are investigated to improve the accuracy of the measurement result. A novel fixture consisting of flexure hinges and two pairs of bolts is used to minimize set-up error by adjusting the ball's position located at the tool nose. Simulation is performed to check the validation of measurement and to analyze the standard uncertainties of the measurement results. Finally, the position-independent geometric errors of the five-axis machine tool (involving a rotary axis and a trunnion axis) are measured using proposed method.     

基于敏感度分析的机床关键几何误差元素辨识与评定

为了正确识别和判定机床关键几何误差元素对机床精度设计的影响,以PCV-620立式加工中心为研究对象,采用多体系统理论建立机床空间误差模型,从而得到机床几何误差元素与机床精度之间的关联函数。对空间误差模型进行灵敏度分析,获得机床各运动方向的局部灵敏度系数,完成机床关键几何误差元素的初步辨识。以局部灵敏度系数为基础,提出一种与局部灵敏度系数和工作空间中任意位置处的几何误差元素值相关的全局灵敏度系数计算方法,将其作为机床关键几何误差元素的辨识和评定标准,分析得到PCV-620立式加工中心的关键几何误差元素包含3项定位误差、3项垂直度误差和5项直线度误差。     

Single setup estimation of a five-axis machine tool eight link errors by programmed end point constraint and on the fly measurement with Capball sensor

Five-axis machine tools can be programmed to keep a constant nominal tool end point position while exercising all five axes simultaneously. This kinematic capability allows the use of a 3D proximity sensing head mounted at the spindle to track the position changes of a precision steel ball mounted on the machine table effectively measuring the 3D Cartesian volumetric errors of the machine. The new sensing head uses capacitive sensors to gather data on the fly during a synchronized five-axis motion which lasts less than 2 min. Because the measured volumetric errors are strongly affected by the link geometric errors, they can be used to estimate the link errors through an iterative procedure based on an identification Jacobian matrix. The paper presents the new sensor, the identification model and the experimental validation. The approach allows all eight link errors i.e. the three squarenesses of linear axes and the four orientations and center lines offset of the rotary axes to be estimated with the proposed single setup test. The estimation approach is performed on a horizontal five-axis machine tool. Then, using the estimated link errors, the volumetric errors are predicted for axes combinations different from those used for the identification process. The estimated machine model correctly predicts 52–84% of the volumetric errors for the tested trajectories.     

数控机床平动轴误差辨识及补偿研究

为了大幅提升数控机床平动轴的运动精度,从而满足当代数控系统对其高精度的要求,针对机床平动轴的空间几何误差开展了深入研究,提出了可以有效辨识平动轴空间几何误差的便捷方法,并基于齐次坐标变换原理建立了平动轴空间几何误差的辨识模型;针对机床平动轴定位误差的特性,提出了可以实现有效补偿的增量式误差补偿原理,并建立了相应的误差补偿模型。经验证,所提出的平动轴误差辨识法和增量式误差补偿原理不仅理论正确,而且可以大幅地提高机床平动轴的定位精度。     

Parameter estimation and model verification of first order quasistatic error model for three-axis machining centers

Quasistatic error sources, which include thermal, mechanical loading and geometric error sources, are responsible for a very large proportion (typically, 70%) of the volumetric errors of a numerically controlled machine-tool. This paper, the first in a set of three, discusses the development of a very general model for the effects of geometric errors of the components of the kinematic chain (structural members and axes) of a machine on the volumetric errors in the work space. The effects of the other two sources are modeled as changes in the geometric error. The generality of the model arises from the fact that the errors along an axis of the machine can be characterized by any polynomial functions and the model is recursive in the order of these polynomials. This model can be used as the basis of a compensation scheme as well as in budgeting of errors on a machine-tool.     

基于多体系统理论的矫直机几何误差的建模与补偿

针对矫直机的几何误差建模和补偿技术进行研究。将矫直机床视为一个多体系统结构,完成对矫直机的拓扑结构描述,并进行压头、夹头和跨距调整等关键运动部件的误差分析。通过其次变换矩阵体系统推导机床几何误差模型,基于建立的误差模型,采用激光干涉仪识别机床运动轴的几何位置误差。提出矫直机的几何误差补偿方法并设计与开发补偿软件,对矫直机定位精度进行补偿。通过实验进行了误差补偿效果评价,实验结果证明误差模型的正确性以及软件补偿的可行性。     

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.     

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.     

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。     

A machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test

This paper proposes a machining test to parameterize error motions, or position-dependent geometric errors, of rotary axes in a five-axis machine tool. At the given set of angular positions of rotary axes, a square-shaped step is machined by a straight end mill. By measuring geometric errors of the finished test piece, the position and the orientation of rotary axis average lines (location errors), as well as position-dependent geometric errors of rotary axes, can be numerically identified based on the machine׳s kinematic model. Furthermore, by consequently performing the proposed machining test, one can quantitatively observe how error motions of rotary axes change due to thermal deformation induced mainly by spindle rotation. Experimental demonstration is presented.     

Evaluation of servo,geometric and dynamic error sources on five-axis high-speed machine tool

Many sources of errors exist in the manufacturing process of complex shapes. Some approximations occur at each step from the design geometry to the machined part.The aim of the paper is to present a method to evaluate the effect of high-speed and high dynamic load on volumetric errors at the tool center point.The interpolator output signals and the machine encoder signals are recorded and compared to evaluate the contouring errors resulting from each axis follow-up error. The machine encoder signals are also compared to the actual tool center point position as recorded with a non-contact measuring instrument called CapBall to evaluate the total geometric errors. The novelty of the work lies in the method that is proposed to decompose the geometric errors into two categories: the quasi-static geometric errors independent from the speed of the trajectory and the dynamic geometric errors, dependent on the programmed feed rate and resulting from the machine structure deflection during the acceleration of its axes.The evolution of the respective contributions for contouring errors, quasi-static geometric errors and dynamic geometric errors is experimentally evaluated and a relation between programmed feed rate and dynamic errors is highlighted.     

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.     

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.     

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。     

三轴数控机床静态精度设计研究进展

国内三轴数控机床存在精度低和可靠性差的问题,而机床精度和可靠性可通过合理的静态精度设计方法得以保证.机床静态精度设计方法包括加工精度稳健设计方法和静态几何精度设计方法,针对两种精度设计方法的衔接合理性和工程应用实用性低的问题,在深入调研机床静态精度设计研究成果的基础上,从机床空间误差建模、平动轴几何误差元素辨识、关键几何误差元素溯源和加工精度稳健设计以及静态几何精度设计这5个关键问题着手,分别给出具体的解决方法,并形成一套完整的三轴数控机床静态精度设计系统实施方案,为完善机床几何精度设计和静态几何精度设计提供了参考.     

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.