An exact algorithm for self-calibration of two-dimensional precision metrology stages

We describe an algorithm that can achieve exact self-calibration for high-precision two-dimensional (2-D) metrology stages. Previous attempts to solve this problem have often given nonexact or impractical solutions. Self-calibration is the procedure of calibrating a metrology stage by an artifact plate whose mark positions are not precisely known. By assuming rigidness of the artifact plate, this algorithm extracts the stage error map from comparison of three different measurement views of the plate. The algorithm employs the orthogonal Fourier series to expand the stage error map, which allows fast numerical computation. When there is no random measurement noise, this algorithm exactly calibrates the stage error at those sites sampled by the mark array. In the presence of random measurement noise, the algorithm introduces a calibration error of about the same size as the random measurement noise itself, which is the limit to be achieved by any self-calibration algorithm. The algorithm has been verified by computer simulation with and without random measurement noise. Other possible applications of this algorithm are also discussed.     

Influence of measurement noise and laser arrangement on measurement uncertainty of laser tracker multilateration in machine tool volumetric verification

This paper aims to present different techniques and factors that affect the measurement accuracy of a commercial laser tracker responsible for capturing checkpoints used in machine tool volumetric verification. This study was conducted to uncover various sources of error affecting the measurement uncertainty of the laser tracker, additional sources of error that further contributed to the uncertainty, and the factors influencing these techniques. We also define several noise reduction techniques for the measurements.The improvement in the accuracy of captured points focuses on a multilateration technique and its various resolution methods both analytically and geometrically. Similarly, we present trilateration and least squares techniques that can be used for laser tracker self-calibration, which is an essential parameter in multilateration.This paper presents the influence of the spatial distribution of laser trackers (LTs) in measurement noise reduction by multilateration, which produces an improvement in volumetric error machine tool reduction. A study of the spatial angle between LTs, the distance and the visibility of the point to be measured are presented using a synthetic test. All of these factors limit the scope of multilateration. Similarly, a comparison of self-calibration techniques using the least squares and trilateration methods with which to determine the relative position of the laser tracker employees is presented. We also present the influence of the relationship between the radial and angular measurement noise self-calibration processes as it relates to the volumetric error reduction achieved by the machine tool with multilateration. All studies were performed using synthetic tests generated using a synthetic data parametric generator.     

Dynamic characterization of multi-axis dynamometers

In this paper, we present a comprehensive technique for accurate determination of three-dimensional (3D) dynamic force measurement characteristics of multi-axis dynamometers within a broad range of frequencies. Many research and development efforts in machining science and technology rely upon being able to make precise measurements of machining forces. In micromachining and high-speed machining, cutting forces include components at frequencies significantly higher than the bandwidth of force dynamometers. Further, the machining forces are three-dimensional in nature. This paper presents a new experimental technique to determine the three-dimensional force-measurement characteristics of multi-axis dynamometers. A custom-designed artifact is used to facilitate applying impulsive forces to the dynamometer at different positions in three dimensions. Repeatable and high-quality impulse excitations are provided from a novel impact excitation system with a bandwidth above 25 kHz. The force measurement characteristics are presented within 25 kHz bandwidth using 3 × 3 force-to-force frequency response functions (F2F-FRFs), which capture both direct and dynamic cross-talk components to enable fully three-dimensional characterization. The presented approach is used to characterize the dynamic behavior of a three-axis miniature dynamometer. The effects of force-application position, artifact geometry, and dynamometer-fixturing conditions are explored. Moreover, the relationship between the force-measurement characteristics and structural dynamics of the dynamometer assembly is analyzed. It is concluded that the presented technique is effective in determining the force-measurement characteristics of multi-axis dynamometers. The changes in dynamometer assembly that affect its structural dynamics, including artifact (workpiece) geometry and especially the fixturing conditions, were seen to have a significant effect on force-measurement characteristics. Furthermore, the force-measurement characteristics were seen to change substantially with the force-application position. The presented technique provides a foundation for future compensation efforts to enable measuring forces within a broad range of frequencies.     

An on-site approach for the self-calibration of terrestrial laser scanner

Two approaches available for performing self-calibration are: (1) point-based and (2) feature-based. The reliance on planes in the feature-based approach is a restriction to the aim of finding a suitable approach for on-site calibration. Also, the requirement for a strong network configuration in point-based self-calibration has made it difficult to implement on-site. The aim of this study was to investigate the suitability of lowering the network station and target configuration requirements. Investigations of minimum network configurations were carried out by analysing three important elements: (1) the minimum number of scan stations; (2) the minimum number of real-world planes on which targets are distributed; and (3) the minimum number of point targets per plane. Also, experiments were carried to determine the effects of the choice of datum constraints. The results show that a minimum configuration of two scan stations, two planes and 16 targets for point-based self-calibration is suitable for on-site calibration and the datum choice has little effect for minimum configuration.     

Mechanical model of errors of probes for numerical controlled machine tools

CNC machine tool probes are not only used to set up the workpiece before machining and to control it after machining, but also to determine volumetric errors of the machine tool. That’s why there is a necessity not only for knowledge of the complete on-machine measurement system errors, but also for the knowledge about probe’s errors in separation from machine tools. This paper presents a theoretical model of errors of probes for CNC machine tools. It takes into account such unique features of the machine tool probes as the transducer with support on the whole circumference and as wireless communication. 3 probes: RMP60, MP700 and IRP32.00-MINI were tested using moving master artifact method, out of machine tool, to verify the model described. The triggering radius values obtained experimentally were compared with values calculated using theoretical model, resulting with a compliance up to 92%.     

Epicyclic Load Sharing Map — Development and validation

Under ideal conditions, every sun-planet-ring path in an epicyclic gear set transmits the same amount of torque. But, in the presence of certain manufacturing variations, equal load sharing is not achieved. In a companion paper, a physical explanation has been provided for the load sharing behavior observed in epicyclic gears. The explanation of the root cause led to the development of a load sharing formulation for 3, 4, 5, and 6 planet epicyclic systems. In this paper the same approach will be taken to develop the formulation for a seven planet epicyclic gear set. The developed expressions will then be used to develop the concept of an Epicyclic Load Sharing Map. This map describes the load sharing characteristics of every epicyclic gear set at any positional error and torque level. The developed expressions are then expanded to describe the general case when there are arbitrary errors on the position of every planet in the epicyclic gear set. Finally, the developed expressions will be validated by comparing the predicted load sharing behavior with the results from a validated system level computational model.     

双目立体视觉测量系统的标定

考虑传统的自标定方法虽然无需场景信息即可实现摄像机标定,但是标定精度较低,故本文提出了一种新的大视场双目视觉测量系统自标定方法。该方法无需高精度标定板或者标定物,仅需利用空间中常见的平行线和垂直线建立摄像机参数与特征线间的约束方程,即可实现摄像机的内参数与旋转矩阵标定;同时利用空间中距离已知的3个空间点即可线性标定两摄像机间的平移向量。通过标定实验对本文提出的方法进行了验证。结果表明:该方法标定精度能够达到0.51%,可以较高精度地标定双目测量系统。由于避免了大视场测量系统标定中大型标定物制造困难,以及摄像机自标定过程中算法冗杂,标定精度不高等问题,该方法操作简便,精度较好,适用于大视场双目测量系统的在线标定。     

基于主动视觉标定线结构光传感器中的光平面

提出了一种基于主动视觉的光平面标定方法实现对线结构光传感器的自动标定.与以往求取光平面上标定点后拟合平面的方法不同,该方法通过控制传感器做若干平移运动分两步完成标定.首先,经多次平移运动得到光平面中相互平行直线在摄像机中的投影,经计算消影点完成光平面法向的标定.然后,控制传感器沿设定的与光平面法向垂直的方向做2次平移运动,使其满足三点透视模型(P3P),完成摄像机坐标系原点到光平面距离信息的标定.实验结果表明:该标定方法具有较高的准确性,平均绝对测量偏差为0.015 4 mm,相对误差为0.183 0％.该方法本质上属于自标定方法,标定过程无需使用标靶,降低了标定成本,且操作灵活方便,适合现场标定.     

机器视觉测量中相机两步标定法的改进

在机器视觉中为了确定空间三维模型和图像模型之间的几何坐标关系,必须要建立相机的图像几何模型及其参数,这个过程被称为相机的标定。作为最广泛使用的标定方法之一,两步标定法使用了网格板来进行相机的标定。在标定中,相机的多数参数都是通过求解分析方程得到的,然后经过反复迭代得到其他标定参数,使用这种标定方法需要在多个位置拍摄多个图像。本文针对两步标定法进行改进。在改进的方法中,用到了一个呈直角的L形标定板,标定时得到一副包含两个垂直标定图像的图片,之后使用两步标定法进行必要的相机内、外部参数的计算。标定的结果显示误差低于0.7%,能满足要求。     

Self-calibration method for vision-guided cell micromanipulation systems

A new self-calibration method for a piezoelectric actuator-based vision-guided cell micromanipulation system is proposed. This method consolidates all the system parameters' uncertainties into a matrix instead of classifying into intrinsic and extrinsic. The position difference of the micromanipulator tip in the image plane between the measured and estimated output which is based on estimations of relevant parameters is assumed to be caused by the matrix. This matrix is estimated by means of collecting several pairs of known input and the corresponding output differences. Matrix standard deviation and gray-value based matching are applied to identify the output differences. Biological contamination is reduced since a calibration template is not required. This self-calibration is particularly suitable for cell micromanipulation systems where the micromanipulator is frequently dismounted and mounted.     

超精密级二维工作台的自标定

为了提高超精密级二维工作台的运动定位精度,提出了一种实现工作台系统误差分离的二维自标定算法.基于工作台测量误差模型,该算法利用辅助标记板的5个不同测量位姿,分别得到迭代模型和迭代初始值,最终建立完整的迭代二维自标定模型.应用该算法对系统误差为0.2 μm的二维工作台进行仿真,结果显示:当不存在随机测量噪声时,标定精度为0.33 nm;引入随机测量噪声时,标定精度与噪声同一量级.对x、y向给定测量精度分别为2.98 μm和3.22μm的二维工作台进行自标定,得到x、y向测量精度分别为2.59 μm和3.14 μm.提出的自标定算法对随机测量噪声有很好的鲁棒性,能够用于精密或超精密级二维工作台自标定.     

自标定重载并联四维测力台测量机理与标定试验

面向航空航天领域对重载大测力面积多维测力台研发的迫切需要,为克服现有多维力传感器研制后均需繁冗的加载标定,采用提出的多维力传感器“自标定”设计理念,通过构建机械解耦测力分支并辅以并联正交分布结构,提出一种新型弱耦合自标定重载并联正交四维测力台构型。基于滚动摩阻理论分析与论证其解耦测量机理与自标定原理。在此基础上,设计并研制了该自标定重载并联四维测力台及其标定加载系统,标定试验结果表明,该四维测力台最大测量误差为0.62%,最大耦合误差为0.56%,论证了其解耦及自标定特性,从而为该自标定重载并联四维测力台的实际应用奠定基础,也为研制大量程重载并联多维力传感器提供了新思路。     

基于灰色神经网络的传感器分段标定

针对大量程高精度传感器不能一次完成标定实验的情况,提出一种将优化灰色GM(1,1)模型与BP神经网络相结合来预测分段标定过程中特征值缺失的方法,从而实现传感器的分段标定。首先,根据实验数据建立传统灰色GM(1,1)模型,对待标定传感器和标准传感器的测量值进行缺失数据的预测;然后,为弱化传统灰色GM(1,1)模型序列变化的幅度,提高模型的预测精度,利用中心逼近的思想对传统的GM（1,1）模型进行优化;最后,利用BP神经网络对优化的灰色GM(1,1)残差序列进行修正,以较高的精度实现对分段标定过程中缺失特征值的预测。结果表明,待标定传感器和标准传感器组合预测模型的平均残差分别为0.023%和0.401%,证明了组合预测模型的有效性。所提出方法为解决大量程高精度传感器分段标定时静态特性曲线的拟合提供了一种新思路。     

Sensor design and evaluation for on-machine probing of extruded tool joints

This paper describes the design and evaluation of two contact probes used to measure the length and bore concentricity of cylindrical, extruded tool joints while clamped in a production lathe spindle. The probes consisted of an LVDT, a spring-preloaded shaft supported by linear bearings used to isolate the LVDT from side loads, and a hardened steel sphere to contact the rough surface. For bore concentricity measurements, a parallelogram leaf-type flexure and 45° surface was used to transfer radial deviations to the spindle/part/LVDT axis. The LVDT output was used in conjunction with the lathe turret position to determine the extruded part dimensions prior to machining. Experimental results are provided for measurements of multiple parts; variations in length, internal diameter, and bore concentricity are compared to the nominal dimensions. Additionally, a calibration artifact is described which enabled evaluation of the measurement accuracies for the two probes. Given the pre-machining part dimensions, it is shown how this information can be used to select from a pre-defined matrix of part programs to reduce cycle time and machining cost.     

时栅传感器定距变换与误差频率扫描自标定法

时栅传感器在特殊恶劣环境中应用,面临安装偏差、电气参数偏移、外部导磁介质介入引起电磁场畸变等因素的影响,导致测量精度下降。现场又缺乏提供高精度参考基准的条件,无法实施在线标定。针对这一问题,本文提出利用两个相隔恒定间距测量值函数求解误差函数频谱的算式(定义为定距变换),并据此设计了一种基于定距变换的误差频率扫描自标定方法。该方法通过合理的间距组合,可对包含有限频率成分误差的时栅传感器实施误差频谱扫描,重构误差函数,在无参考标准器的前提下实现传感器的在线自标定。在此基础上,研制样机进行自标定和比对实验。实验结果表明:由于安装偏差和电气参数偏移引起±40″测量误差的时栅传感器,在实施误差频率扫描自标定后与参考标准器进行比对,二者差异小于0.7″。本研究为时栅传感器进一步提高测量精度以及在特殊环境的应用中保持精度提供了有效的解决方案和可靠的理论依据。     

A level-based optimization algorithm for complex part localization

An algorithm for the workpiece-balancing problem is proposed in this paper. The approach allows optimal part positioning in machine tools in order to ensure sufficient stock allowance during the machining process. For complex applications, where some material is found to be missing during the removal process, the balancing technique preferentially orients the lack of material in order to minimize the rework for the part. The technique refers to a best point alignment of the blank, which is represented through a dataset of points, with respect to a corresponding CAD representation of the nominal part. The constrained alignment is based on the optimization of an objective function that is specially developed to force each point to lie outside the solid model under a prescribed order of priority. This preferential optimization aims to orient any shortage of material to areas where the rework is made possible. Two objective functions, including a penalty term, are proposed and compared in terms of results and efficiency: a least-squares and a logarithmic formulation. The main scope of this paper is the development of those functions in such a way as to severely penalize any unsatisfied constraint related to specific part areas, which shall be protected from any shortage of material during machining. The complete development is presented for the logarithmic penalty function, and the behavior of both functions is presented and compared through application examples. The results show that the part alignment with the logarithmic formulation converges much faster than with the least-squares and is more appropriate to the material-balancing problem. The preferential optimization approach developed is found to work well for the balancing problem of blank parts through sparse datasets of points. This innovative approach is promising for any other application requiring a set of constraints to be satisfied based on a specific order of priority.     

加工中心时间定额的制定

结合VF-2加工中心时间定额制定特点,提出的时间定额制定方法和相关标准数据,此方法不但可以在其他类型加工中心使用,而且可以在其他数控切削设备工时定额制定中试用。     

ASSESSMENT OF MACHINING MODELS: PROGRESS REPORT

Progress in developing and assessing predictive modeling of machining processes has been hindered by the extremely localized nonlinear physical phenomena that occur in machining and the many different types of models ranging from theoretical to empirical. The difficulty in assessing models has been cited by industry as the major barrier to use of modern machining models. Current practice in industry is to machine and change tools conservatively, or to conduct costly empirical studies for a limited selection of tools and coolants. The Assessment of Machining Models project will assess the ability of modern machining models to predict the outputs of machining processes based upon a consistent, well measured calibration data set. The data set is nearly complete and is to be used in benchmarking the predictive capability of machining models in blind tests. This paper presents the project motivation, goals, and representative calibration data set results. The next steps in the effort include release of the calibration data, solicitation and collection of predictions, and evaluation and reporting of results.     

In Situ Measurement of Contact Area and Pressure Distribution in Machine Elements

In machine element design it is important to know the size and pressure distribution of the contacts between components. Ultrasound will reflect back from the interfaces between these machined parts. This phenomenon has been investigated with a view to determining its suitability for contact measurements. An ultrasonic transducer, which both emits and receives pulses, is scanned across the interface. The reflected pulses are recorded and used to build up a map of the contact. Experiments have been performed to produce these reflection maps for simple point contacts. An analytical model was used to determine the stiffness of the interface from these measurements and a calibration procedure performed to predict contact pressures. The resolution of the method is relatively coarse and this results in some finite blurring of Hertz-type contacts. Numerical deconvolution procedures have been used to improve the accuracy of measured data. Two applications of this technique are presented. Measurements of the contacts within a universal joint demonstrate that for small concentrated contacts it is difficult to obtain more than qualitative information. But, for the large interface between the bush and shaft in an interference fit, measurements of the interfacial pressure are much more feasible.     

Maximum Likelihood approach to calibrate hysteretic transducers

This paper deals with the calibration of hysteretic transducers. The limits of the traditional approach are explained and a new method based on the Maximum Likelihood algorithm is proposed, overcoming the mentioned limits. It is also shown that the features of the input to the transducer are important to determine in which situation the proposed method is needed. The harmonic and random cases are analysed, showing that different calibration strategies are required in the two different situations. The calibration of a hysteretic transducer is therefore much more complex than that of a non-hysteretic one. The analysis is carried out numerically, adopting a model to simulate the behaviour of hysteretic load cells and then a real case is analysed at the end of the paper.