五轴联动立式磨床几何误差灵敏度研究

以一台五轴联动立式磨床为例,提出了一种分析几何误差灵敏度的方法。基于多体系统理论和齐次坐标变换建立了五轴联动立式磨床的33项几何误差模型,利用求导的方式给出了几何误差灵敏度分析的数学模型。并根据该模型找出了关键几何误差,研究了关键几何误差的灵敏度系数随平移轴运动的变化规律,研究结果为精密机床改进设计和误差的实时补偿提供了理论依据。     

提高轮廓加工误差联机检测精度的研究

在数控机床或加工中心上采用联机检测轮廓加工误差的方法，不用价格昂贵的坐标测量机，具有简单、省时、经济的特点。文章分析了数控机床或加工中心的直线运动误差对联机检测轮廓加工误差精度的影响，并测量出了加工中心的几何运动误差，提出了消除机床几何运动误差影响，提高轮廓加工误差联机检测精度的方法。实验结果表明，所采用的方法可以明显提高轮廓加工误差联机检测精度。     

Uncertainty analysis in geometric best fit

In computing geometric tolerances using point data from a coordinate measuring machine (CMM), a best fit process is needed to match the measurement data to the substitute geometry. Since the measurement data does not precisely conform to the substitute geometry, the best fit result always contains uncertainties resulting from surface deviations, different point locations, and various sample size. Because the best fit uncertainties reduce accuracy of the evaluated tolerances, it is important to estimate and control the best fit uncertainties. In this paper, a theoretical model is presented to predict the uncertainty zones of the best fit parameters. Supported by simulations and experiments, the proposed model is proved to be effective in determining the best fit uncertainties. To explore factors that affect uncertainty variations, relationships between geometric variables and uncertainties are investigated. Then, to understand the effect of point location on the best fit uncertainty, an optimization scheme which minimizes the total uncertainties is used to find the best measurement locations. Simulations also show that the best fit uncertainty is inversely proportional to the squared root of the number of measurement points. This result can be used to estimate the CMM sample size that can control the best fit uncertainty under specified tolerances.     

Uncertainty analysis and variation reduction of three dimensional coordinate metrology. Part 1: geometric error decomposition

In this paper our study focuses on the uncertainty analysis and variation reduction of coordinate system estimation using discrete measurement data and is associated with the applications that deal with parts produced by end-milling processes and having complex geometry. This paper consists of three parts. Since the uncertainty of the estimated coordinate transformation arises from the geometric errors on a part surface, Part 1 is devoted to the study of surface geometric errors. In this study, according to the characteristics of end-milling processes the sampled geometric error is divided into two components, and a decomposition procedure is developed for geometric error decomposition. The results of surface geometric error decomposition will be used in Part 2 for uncertainty analysis and in Part 3 for variation reduction.     

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.     

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。     

The effect of sampling in circular substitute geometries evaluation

Coordinate Measuring Machines (CMMs) are widely used in dimensional metrology applications of the manufacturing industry. CMMs perform the dimensional control of machined parts by measuring a set of points of the manufactured part and by fitting a substitute geometry, which is a geometric element with known analytical representation (line, plane, circle, etc.). The substitute geometry is then used to determine position, dimension and form of the element and the accordance of the manufactured part with the design tolerances. Therefore, the precision of the substitute geometry estimate is the basis for a reliable and accurate dimensional measurement. Two important factors that affect the precision of the estimate are the number and the position of measured (or sampled) points. The present work is addressed to the definition of the relationship between the number and position of sampled points and the errors of the estimate of radius and position of the centre of circular profiles (holes or shafts) with the Least Squares Method. A new approach to the problem is proposed and the analytical solution of the problem is presented. Using the identified equations it is possible to evaluate the distributions of the estimate errors and therefore to determine their confidence limits. As will be discussed, as the number of sampled points increases the confidence limits of the errors may increase or decrease, depending on the spectra of the machined profiles. The problem of the definition of the optimal number and angular position of the sampled points is analysed and a solution is proposed. Finally, the last part of the present work is an application of these equations to a real case of turning operation of steel.     

Integrated post-processor for 5-axis machine tools with geometric errors compensation

Geometric errors of 5-axis machine tools introduce great deviation in real workpiece manufacture and on-machine measurement like touch-trigger probe measurement. Compensation of those errors by toolpath modification is an effective and distinguished method considering the machine calibration costs and productivity. Development of kinematic transformation model is involved in this paper to clarify the negative influences caused by those errors at first. The deviation of the designed toolpath and the real implemented toolpath in workpiece coordinate system is calculated by this model. An iterative compensation algorithm is then developed through NC code modification. The differential relationship between the NC code and the corresponding real toolpath can be expressed by Jacobi matrix. The optimal linear approximation of the compensated NC code is calculated by utilizing the Newton method. Iteratively applying this approximation progress until the deviation between the nominal and real toolpath satisfies the given tolerance. The variations of the geometric errors at different positions are also taken into account. To this end, the nominal toolpath and the geometric errors of the specific 5-axis machine tool are considered as the input. The new compensated NC code is generated as the output. The methodology can be directly utilized as the post-processor. Experimental results demonstrate the sensibility and effectiveness of the compensation method established in this study.     

Electromagnetic impulse calibration of high strength sheet metal structures

This study focused on using electromagnetically generated impulses to correct dimensional errors resulting from springback on two different geometric features. Modification or correction of a corner feature is considered first. A simple linear actuator is used to correct springback on a simply bent high strength aluminum alloy (AA 5754) and a high strength steel alloy (DP 600). It is shown to be possible to fully correct for springback using a net-shape die with both materials with higher electromagnetic discharge energies being required for the steel. The second geometric feature considered is a sidewall curl ‘defect’ that is the result of bending and unbending U-Channel drawing. A serpentine actuator and net-shape die were shown effective at correcting for this defect in both DP 600 and TRIP 700 high strength steels. A somewhat higher forming energy is required for effective shape correction in the higher strength TRIP 700 alloy. A detailed mechanistic understanding of springback correction remains elusive, but these results are consistent with several other studies in the literature that show this is an effective means to control springback.     

Tool path accuracy enhancement through geometrical error compensation

Kinematic and geometric errors of CNC machine tools, introduce large deviations in the real path traveled by the cutting tool. Tool path deviation reduces geometrical and dimensional accuracy of the machined features of the component. Tool path modification is an effective strategy to increase accuracy of the machined features. An improved error estimation model based on kinematic transformation concepts has been developed and used to calculate the volumetric overall error. These calculations are applicable for each arbitrary target positions of the machine's work space. Also a NC Program editor software has been developed in order to manage the calculations, modifications and to generate the new compensated NC program. The compensation procedure includes: fragmentation of nominal tool path to small linear elements, translating nominal position of elements to real positions using the Kinematics error model, finding compensated positions using the error compensation algorithm, converting newly generated elements to new tool paths using the packing algorithms and finally editing old NC program using NC code generator algorithm. Experimental tests showed 4-8 times accuracy improvement for linear, and S-pline tool paths deviations.     

基于多体系统理论的数控机床加工精度几何误差预测模型

针对多轴联动数控机床加工精度误差补偿问题,从分析数控机床误差产生机制和建立精度误差补偿模型的角度,提出基于多体系统理论的数控机床加工精度几何误差预测模型。分析B-A摆头五轴龙门数控机床的拓扑结构关系、低序体阵列、各典型体坐标变换,推导出B-A摆头五轴龙门数控机床的精度几何误差预测函数模型。采用平动轴十二线法误差参数辨识算法,计算出B-A摆头五轴数控机床21项空间几何误差,为精度几何误差预测函数提供有效的误差参数。该精度误差参数建模方法,对不同结构和运动关系的数控机床具有通用性,为后续数控机床误差动态实时补偿提高切削加工精度提供了理论基础。     

型砂水分测量若干关键技术研究

分析了型砂水分测量3种主流电测方法的原理和特点,针对传统测量方法固有的缺陷,提出了改进设计的思想和测量应用系统。其中,电阻测量采用测频测周电路转换后可以克服对测量范围的限制和测量信号远传质量问题;传统的高频电容测量存在较低的测量水分上限,采用超高频电容方法可以实现全量程测量;基于微波的型砂水分测量与被测型砂的温度、体密度等密切相关,为提高测量精度和测量适应性,采用双参量测量方法。3种改进方法都可以实现型砂水分的实时在线高精度测量。     

Geometric error measurement and identification for rotary table of multi-axis machine tool using double ballbar

In this paper, comprehensive geometric errors, including linkage errors and volumetric errors, of a rotary table are measured totally by employing a double ballbar and obtained by a two-step identification procedure. The derivations of the center of the ball installed on the table are measured in the error sensitive directions with newly developed serial of two axes controlled circular paths. Hence, there are nine results measured from three mounting positions of the ball at the same rotation angle. These results are used to form the identification model based on the homogeneous transformation. Moreover, a sensitivity analysis method is applied to select the optimum installation parameters of the ballbar to diminish the influence of the inaccuracy of the measurement parameters. As the mounting position errors of the socket on the table are inevitable during the installation of the balls, a new correction procedure is developed as well. Finally, an experiment is conducted on the four-axis machining center. The comparison results between the predicted errors and the measured results are shown to verify the proposed method.     

An analysis of the effect of datum-establishment methods on the geometric errors of machined features

With the advent of probing systems and their integration with machining centers, coordinate metrology-based datum establishment is eliminating the need for precision hard-contact locators in many machining applications. Unfortunately, the coordinate data collected by these systems are often subject to noise in the form of random and biased errors of the workpiece datum features and measurement system. Consequently it is important to use datum-establishment algorithms that are insensitive to noise and that lead to the least measurable machined-feature error.This paper describes a simulation analysis that was carried out to evaluate the performance of three datum-establishment methods: 3–2–1, sequential least-squares (SQLS) and simultaneous least-squares (SMLS). The analysis involved the simulated drilling of three holes in a two set-up process. Simulated coordinate data were obtained from three planar, nominally orthogonal surfaces subject to perpendicularity errors and random roughness errors. Workpiece datum reference frames were fitted to this data using the three methods, the holes were drilled relative to these reference frames, and their position errors were computed relative to an ANSI-Y14.5M-defined reference frame.This analysis demonstrated that the SMLS method results in significantly less hole-position error [0.0173 mm average, 0.0146 mm standard deviation (SD)] than either the 3–2–1 method (0.0943 mm average, 0.0143 mm SD) or the SQLS method (0.0904 mm average, 0.0245 mm SD). This is despite the fact that the datum reference planes (ANSI Y14.5M) used to define these errors are defined sequentially relative to the extrema of the datum features, whereas the SMLS method defines the datum reference planes simultaneously with the purpose of minimizing fitting error.     

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。     

机器人单目视觉标定圆心靶标特征点几何求解

针对机器人单目视觉标定圆心靶标特征点求取问题,利用射影变化公切线不变性,建立圆心靶标的特征点几何求解模型,并进行了精确求解,该模型理论上不存在模型误差;为了检验几何求解模型的精确性和稳定性,分别对机器人单目视觉坐标系下的圆心靶标圆心点和棋盘格靶标角点进行了三维测量。实验结果表明:测量长度在300 mm内的最大相对误差小于1.5%,测量结果较精确;各点的距离平均绝对偏差均在0.2 mm左右,且无阶跃,该方法稳定。     

微型钻头钻芯尺寸测量的研究

微型钻头钻芯尺寸精度对钻头的寿命影响很大,准确地测量钻芯尺寸有利于钻头加工精度的评估.现行的测量方法精度差、效率低,且不能测量出钻芯对钻头柄轴线的偏心.三坐标测量机可以测出微型钻头排屑槽底部轮廓,通过该轮廓数据的拟合即可求出所有钻芯尺寸,但测量成本较高.本文在自制的四轴数控实验台上搭建一个测量系统,采用悬臂梁、电涡流传感器作为测量元件,针对每次测量时接触力不同引起的测量误差,通过悬臂梁位移补偿予以消除.实验证明,该测量系统实用且测量精度较高.     

Uncertainty analysis and variation reduction of three dimensional coordinate metrology. Part 3: variation reduction

In this part of the paper, the uncertainty analysis of coordinate estimation for the case in which the sampled geometric errors are dominated by the random component is investigated. In practice, the uncertainty analysis of coordinate estimation using high-precision datum surfaces often falls into this type. In this paper, a sensitivity matrix, which serves as the theoretical basis of the uncertainty analysis, is presented to establish a linearized relationship between the variations of the coordinate estimation and the geometric errors of the part surface at the measurement points. Based on the sensitivity matrix, quantitative measures are derived for the prediction of coordinate variation. Computer simulation and experiments are conducted to verify the theoretical predictions when the surface geometric errors are small and dominated by the random component.     

Quantitative circularity tolerance analysis and design for 2D precision assemblies

Circular, cylindrical, or spherical features are fundamental geometric features in engineering. As precision requirement becomes more stringent, it is not sufficient to consider only size tolerance of circular and cylindrical parts. However, currently there is no quantitative and systematic way of assigning circularity and cylindricity tolerances. This paper investigates how to specify circularity tolerance quantitatively for 2D assemblies. Statistical matrices to quantify positioning error of two perfectly circular mating parts subject to size tolerance for both clearance and transition fit conditions are first developed. The analysis is then extended to nonideal profiles whose profile errors are assumed to deviate from a best-fit circle according to a normal distribution. The assumption of the normal distribution is then removed for more general results via computer simulation. For this purpose, an experimentally verified profile model is used to generate realistic profiles as those produced by various machining processes. Numerous pairs of these realistic profiles are then assembled virtually using Monte Carlo simulation to quantify their positioning errors. The simulation results and the analytical results are compared for cross-checking. Finally, systematic design procedures are proposed to assign circularity tolerance by prescribing a fit condition with a desirable process capability. By the nature of circularity tolerance, this paper addresses a 2D assembly. The result of this 2D analysis can be a foundation for more complicated 3D problems, such as assigning cylindricity tolerance.     

Adaptive Monte Carlo applied to uncertainty estimation in five axis machine tool link errors identification with thermal disturbance

Knowledge of a machine tool axis to axis geometric location errors allows compensation and corrective actions to be taken to enhance its volumetric accuracy. Several procedures exist, involving either lengthy individual test for each geometric error or faster single tests to identify all errors at once.This study focuses on the closed kinematic chain method which uses a single setup test to identify the eight link errors of a five axis machine tool. The identification is based on volumetric error measurements for different poses with a non-contact Cartesian measuring instrument called CapBall, developed in house.In order to evaluate the uncertainty on each identified error, a multi-output Monte Carlo approach is implemented. Uncertainty sources in the measurement and identification chain – such as sensors output, machine drift and frame transformation uncertainties – can be included in the model and propagated to the identified errors. The estimated uncertainties are finally compared to experimental results to assess the method. It also reveals that the effect of the drift, a disturbance, must be simulated as a function of time in the Monte Carlo approach.Results shows that the machine drift is an important uncertainty source for the machine tested.