Experimental investigation into the effects of exciter motions on the primary calibration of single-ended accelerometer

It is widely known that in the primary calibration of accelerometers by using a laser interferometer, a device under test (DUT) and the laser interferometer should measure vibration at the same reference position. However, this is not applicable to single-ended accelerometers because of the limitation of their design. One way of overcoming this limitation is to measure the vibration at several positions on the exciter table surface which connects DUT to a vibration exciter. However this can present the effects of rocking motions of the exciter. Although the motions of vibration exciters are presented in several studied, the different model of exciters might have different characteristics. This paper aims to study the motions of an air-bearing exciter (model 2911) used at National Institute of Metrology (Thailand) in order to expose their characteristics, their effects on the calibration results and the measurement errors due to these effects. The motions of the exciter are shown in terms of magnitude and phase shift distributions of sensitivities. These can be obtained by measuring the magnitudes and phase shifts at several positions on the exciter surface. The effects of exciter motions are measured in terms of how much the magnitudes and phase shifts at each measured positions deviate from the average values. To illustrate these effects, parametric studies were conducted. The influences of four parameters, i.e. the angular positions of the laser points, the distance of the laser positions from the centre of the exciter surface, the number of measured positions to be averaged and the mass loading effect, were examined experimentally. The frequency of interest is between 10 Hz and 15 kHz.     

On the calibration of surface plates

Calibration of large surface plates could be performed using different measuring systems. In this investigation an autocollimator system, a laser system and a coordinate measuring machine have been investigated. A comparison among these methods of calibration has been carried out. An Elcomat 3000 autocollimator of resolution 0.05 arcsecond, an Agilent 5529A laser interferometer system of resolution 0.05 arcsecond and a Prismo/Zeiss Computerized Numerically Controlled Coordinate Measuring Machine (CNC–CMM) respectively are used. Large reflecting mirror, angular retro reflector and sensitive probe are used with autocollimator, laser systems and CNC–CMM respectively to identify heights at each position on the tested surface plate. Repeated results from the different methods are carried out and presented in the paper. Uncertainties associated with the measurement results of each method have been estimated using the GUM procedures and given in the paper. The paper discusses the difficults and ease as well as accuracies associated with each method.     

激光跟踪视觉导引测量系统的全局校准方法

针对柔性装配中现有激光跟踪测量系统存在效率低、成本高、自动化程度低等问题,提出用单目视觉系统联合激光跟踪仪实现大尺寸组合式自主导引测量.为实现该系统的全局校准,提出了一种新的基于平面的全局校准方法,该方法通过获取靶标平面分别在视觉系统和激光跟踪仪坐标系中的平面方程,求解两坐标系间转换矩阵,完成系统全局校准.建立了数学模型,进行了算法仿真和全局校准实验.实验中测量30个不同位姿的平面靶标,并进行全局校准.结果表明,该方法操作简单,稳定性强,有实际应用价值,校准后平面法向量夹角、原点到平面距离的RMS误差分别为0.13°和1.50 mm.     

Effects of number of digits in large-scale multilateration

Since many years ago, multilateration has been used in precision engineering notably in machine tool and coordinate measuring machine calibration. This technique needs, first, the use of laser trackers or tracking interferometers, and second, the use of nonlinear optimization algorithms to determine point coordinates. Research works have shown the influence of the experimental configuration on measure precision in multilateration. However, the impact of floating-point precision in computations on large-scale multilateration precision has not been addressed. In this work, the effects of numerical errors (rounding and cancellation effects) due to floating-point precision (number of digits) were studied. In order to evaluate these effects in large-scale multilateration, a multilateration measurement system was simulated. This protocol is illustrated with a case study where large distances (≤20 m) between pairs of target points were simulated. The results show that the use of multi-precision libraries is recommended to control the propagation of uncertainties during the multilateration computation.     

Measurements of dimensional standards and etalons with feature size from tens of micrometres to millimetres by using sensor strengthened nanomeasuring machine

A laser focus sensor and a contact inductive sensor have been coupled to an ultra high precision positioning stage, referred to as a nanomeasuring machine (NMM), for measurements of dimensional standards with a large measurement volume of 25 mm × 25 mm × 5 mm. Control and measurement software have been designed and complemented. The measurement uncertainty of strengthened NMM has been analyzed and discussed. Groove depth and step height standards with feature heights of tens of micrometres to millimetres as well as aspherical surface etalons are calibrated by nanomeasuring machine. The paper also introduces a method for characterising the measured aspheric surface by least square fitting the measured data to a quadratic paraboloid function. The obtained quadratic coefficients are compared to that measured by a conventional coordinate measuring machine (CMM) and a stylus profiler, showing a good agreement.     

多边法激光三维坐标测量系统及其跟踪机构设计

为实现对空间目标三维坐标的测量,研究出一种基于多边法的激光三维坐标测量系统。系统使用了四路激光跟踪干涉仪,通过冗余设计使系统具有许多独到的功能特点。由于跟踪机构的性能对整个测量系统的影响大,为此设计了一种独立式跟踪机构。介绍了系统的工作原理和主要功能特点,论述了跟踪机构的工作原理、结构及其误差。对有关实验的方法、结果做了简要论述。     

Standardised Reference Data Sets Generation for Coordinate Measuring Machine (CMM) Software Assessment

Rapid and accurate in-process measurement has recently become more common in product cycles, especially for producing parts having 3D contoured shapes. As a result, the ability to analyse large quantities of dimensional data requires today’s coordinate measuring machines (CMM) to employ their extreme functionality. With the increasing demand for performance of the software supplied for a CMM, the testing methods for these software packages must be rigorous, stable, and efficient. Motivated by the aforementioned demand, this work is intended to design and develop an algorithm and computer code to generate the reference data sets representing the coordinates of Gaussian associated features for CMM measured parts. These reference data sets can be used to test the CMM software submitted for approval to the National Institute of Standards and Technology (NIST). A generic algorithm for the development of the data sets is proposed and the program code is designed and developed by employing object oriented concepts. Dynamic errors during measurement are also accounted for, using Fourier harmonics representing the form errors and noise in the measured data. The data sets, being an integral part of the proposed International Standard – ISO 10360, will become a significant step towards the standardisation of software testing procedures for coordinate measuring machines.     

Nanomeasuring and nanopositioning engineering

The paper describes traceable nanometrology based on a nanopositioning machine with integrated nanoprobes. The operation of a high-precision long range three-dimensional nanopositioning and nanomeasuring machine (NPM-Machine) having a resolution of 0.1 nm over the positioning and measuring range of 25 mm × 25 mm × 5 mm is explained. An Abbe offset-free design of three miniature plan mirror interferometers and applying a new concept for compensating systematic errors resulting from mechanical guide systems provide very small uncertainties of measurement. The NPM-Machine has been developed by the Institute of Process Measurement and Sensor Technology of the Technische Universität Ilmenau and manufactured by the SIOS Messtechnik GmbH Ilmenau. The machines are operating successfully in several German and foreign research institutes including the Physikalisch-Technische Bundesanstalt (PTB), Germany.     

Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of XY linear stage

Today, with the development of microsystem technologies, demands for three-dimensional (3D) metrologies for microsystem components have increased. High-accuracy micro-coordinate measuring machines (micro-CMMs) have been developed to satisfy these demands. A high-precision micro-CMM (M-CMM) is currently under development at the National Metrology Institute of Japan in the National Institute of Advanced Industrial Science and Technology (AIST), in collaboration with the University of Tokyo. The moving volume of the M-CMM is 160 mm × 160 mm × 100 mm (XYZ), and our aim is to achieve 50-nm measurement uncertainty with a measuring volume of 30 mm × 30 mm × 10 mm (XYZ). The M-CMM configuration comprises three main parts: a cross XY-axis, a separate Z-axis, and a changeable probe unit. We have designed a multi-probe measurement system to evaluate the motion accuracy of each stage of the M-CMM. In the measurement system, one autocollimator measures the yaw error of the moving stage, while two laser interferometers simultaneously probe the surface of a reference bar mirror that is fixed on top of an XY linear stage. The straightness motion error and the reference bar mirror profile are reconstructed by the application of simultaneous linear equations and least-squares methods. In this paper, we have discussed the simulation results of the uncertainty value of the multi-probe measurement method using different intervals and standard deviations of the laser interferometers. We also conducted pre-experiments of the multi-probe measurement method for evaluating the motion errors of the XY linear stage based on a stepper motor system. The results from the pre-experiment verify that the multi-probe measurement method performs the yaw and straightness motion error measurement extremely well. Comparisons with the simulation results demonstrate that the multi-probe measurement method can also measure the reference bar mirror profile with a small standard deviation of 10 nm.     

Calibration of a 3D-ball plate

The presented 3D-ball plate is used for testing machine tools with a workspace of 500 mm × 500 mm × 320 mm. The artefact consists of a 2D-ball plate which is either located by a kinematic correct coupling on a base plate or on a spacer. The spacers are placed between the base plate and the ball plate and are also kinematic coupled to the other elements of the artefact. The kinematic couplings provide a high repeatability of the measurement setup. Because of the specific application the known calibration procedures for 2D-ball plates are not applicable.A calibration method for the pseudo-3D-artefact on a coordinate measuring machine (CMM) is presented, with the aim to minimise the influence of geometric CMM errors. Therefore a computer simulation is used to analyse the effects of these disturbing errors on the calibration of the ball plate and the spacers. Using a reversal method, the plate is measured at four different horizontal positions after rotating the ball plate around its vertical axis. A couple of the CMM errors, e.g., a squareness error C0Y between the X- and Y-axis of the CMM, can be eliminated by that method—others have to be determined with additional measurements, e.g., the positioning errors EXX or EYY of the X- and Y-axis, respectively. The paper also contains a measurement uncertainty estimation for the calibration by use of experiments, tolerances and Monte Carlo-simulations. The achieved uncertainty for ball positions in the working volume is less than 2.1 μm (coverage factor k = 2).     

Calibration and analysis of eccentric error of the laser rotary-scanning measurement system

A laser rotary-scanning measurement system was developed for the reverse engineering of 360° objects. The system is constructed by an optical head and a rotary indexing. The optical head is composed of a laser diode strip-light projector and dual CCD cameras. Based on the principle of structured-light triangulation, a laser line is projected onto the object upon which the distorted line is captured by dual CCD cameras from left and right simultaneously. By processing a series of line fittings from the discrete angular positions of an object, the entire 3D profile can be reconstructed. Since the actual space coordinates of the object are computed according to the geometric relationship between the coordinate of optical head system and the coordinate of the rotary indexing systems, if these two coordinate systems are not in good alignment, errors in the computed coordinates will be introduced.This paper describes the influences of the alignment and eccentricity errors of the laser rotary-scanning measurement system on the computed geometrical profile. Calibration procedures are then proposed to adjust the alignment to avoid image distortions and thus enhance the system accuracy. Experimental results show that this easy-to-use calibration procedure can significantly improve the accuracy of the system.     

Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments

We present a virtual experiment for the accuracy assessment of the sub-aperture interferometric measurement of a synchrotron mirror involving several thousand sub-aperture topographies. The virtual experiment simulates the measurement process and accounts for the influence of positioning device errors, interferometer errors, non-perfect calibration of machine geometry as well as errors in the interferometer reference. Two principles are considered for reconstructing the form of a test specimen from the conducted sub-aperture topographies, a stitching procedure and a direct measurement method. The virtual experiments are applied to the task of absolute form measurement (including its radius of curvature) of a synchrotron mirror with a length of 30 cm, a width of 4 cm, a maximum curvature of about 44 mm⁻¹ and a peak-to-valley of 5 mm. As a result, reconstruction accuracies can be expected to be in the range of 100 nm when the stitching method is applied, which outperforms the direct measurement method by a factor of about 3.     

A cross-target-based accurate calibration method of binocular stereo systems with large-scale field-of-view

This paper presents an accurate calibration method of binocular 3D measurement systems for industrial on-site inspection, which uses a cross target with ring coded points. The cross target can be used to calibrate large-scale field-of-view stereo measurement systems and obtain higher measurement precision conveniently. The world coordinates of these ring coded points are not required. All we need is the distance of two ring coded points as a scale. A new calibration model with 10 distortion parameters for each camera is proposed. The calibration initial values are computed using the relative orientation method and the Direct Linear Transform (DLT) method of photogrammetry. The bundle adjustment algorithm is used to optimize the calibration parameters as well as the 3D coordinates of the ring coded points. Experiment results show that the RMS error of the reprojection in our method is less than 0.05 pixels and the measurement error is 0.011 mm compared with the Coordinate Measuring Machine (CMM).     

利用弹性网络算法求解大型三坐标测量机几何误差的方法

为提高大型三坐标测量机(CMM)的精度,修正空间几何误差,研究利用激光追踪仪多站位测量技术取代实物基准,提出了基于弹性网络算法求解CMM几何误差的方法。基于激光追踪仪多站位测量技术,结合L-M算法,实现CMM空间规划点体积误差的高精度测量,有效提高测量效率。利用弹性网络算法解算CMM准刚体模型,解决模型求解存在多重共线的难题,实现CMM几何误差的求解;将方程组中部分系数为0的项结合体积误差与单轴几何误差的关系模型来求解几何误差。实验搭建了激光追踪多站位测量系统,测量了CMM的空间待测点体积误差。实验结果表明,提出的方法可以有效求解大型CMM的几何误差。     

Laser interferometric system for six-axis motion measurement

This article presents the development of a precision laser interferometric system, which is designed to achieve six-axis motion measurement for real-time applications. By combining the advantage of the interferometer with a retroreflector and that of the interferometer with a plane mirror reflector, the system is capable of simultaneously measuring large transverse motions along and large rotational motions about three orthogonal axes. Based on optical path analysis along with the designed kinematics of the system, a closed form relationship between the six-axis motion parameters of the object being measured and the readings of the six laser interferometers is established. It can be employed as a real-time motion sensor for various six-axis motion control stages. A prototype is implemented and integrated with a six-axis magnetic levitation stage to illustrate its resolution and measurement range.     

Uncertainty analysis of a laser calibration system for evaluating the positioning accuracy of a numerically controlled axis of coordinate measuring machines and machine tools

This paper presents an uncertainty analysis of a Positional Error Calibrator based on a laser interferometer system. This laser calibration system is capable of evaluating the positioning accuracy of a numerically controlled axis of machine tools and coordinate measuring machines (CMM) under dynamic conditions. In order to assess the measurement uncertainty of this calibrator, an analysis of the uncertainty components that make up the uncertainty budget of this calibrator has been carried out. These uncertainty components can be classified into three categories as follows: (1) uncertainties intrinsic to the laser system; (2) uncertainties due to environmental effects; (3) measuring uncertainties due to the installation. The procedure for evaluating the uncertainty of this calibrator follows GUM (“Guide to the Expression of Uncertainty in Measurement”). This uncertainty analysis was carried out when this calibrator was used to assess the positional errors of the “X” axis of a moving bridge type CMM.     

Calibration of laser beam direction for optical coordinate measuring system

For the purpose of measuring free form surfaces of some key parts in the aviation field accurately and effectively, such as blades, a non-contact optical coordinate measuring system is set up in the paper. A laser displacement sensor is mounted on the Z axis of a CMM via a turntable and adjusted to the suitable orientation according to the shape of the target surface. The combination of optical sensor and CMM can reach the full potential of them both. To enable the laser sensor to perform measurement in every direction, a calibration method used to determine the laser beam direction based on a standard sphere is proposed, the principle of which is analyzed in detail in the paper. In the calibration procedure, the sensor moves at an equal step along X, Y and Z axes respectively and then equation sets are established to calculate the unit direction vector of the line which the laser beam is on. In the process of solving the unknown quantities, a new parameter substitution method is applied. Finally, a gauging block and a sphere with known size are used to verify the method. As the experimental results show, the measuring errors in several directions are all smaller than 0.05 mm, which manifests that the calibration method proposed can meet the requirements of reverse engineering.     

A high performance one-dimensional homodyne encoder and the proof of principle of a novel two-dimensional homodyne encoder

Displacement laser interferometers and interferometric encoders currently are the dominating solutions to the displacement measurement applications which require measurement uncertainties in the order of a few nanometers over hundreds of millimeters of measurement range. But, in comparison with interferometric encoders, to achieve nanometer order or even lower measurement uncertainties, displacement laser interferometers require much stricter environmental control if not vacuum, which will increase their Total Cost of Ownership (TCO). Therefore interferometric encoders are getting more and more preferable. Furthermore, for some applications, the measurement of the out-of-plane displacement is required as well. Therefore, in this work, a one-dimensional interferometric encoder was built and investigated, a novel two-dimensional (one is in-plane, the other one is out-of-plane) interferometric encoder was devised and its principle was proven experimentally. For the one-dimensional encoder, a periodic nonlinearity of ±50 pm with HEIDENHAIN EIB 741 and a periodic nonlinearity of less than ±10 pm with a home built phase meter and off-line Heydemann correction were identified through a comparison measurement with a differential heterodyne interferometer. In addition, this one-dimensional encoder was identified to have a better measurement stability compared to the differential heterodyne interferometer.     

NON-CONTACT MEASUREMENT OF SCULPTURED SURFACE OF ROTATION

A method for measuring the sculptured surface of rotation by using coordinate measuring machine (CMM) and rotary table is proposed. The measurement is realized during the continuous rotation of the workpiece mounted on the rotary table while the probe moves along the generatrix of the surface step by step. This method possesses lots of advantages such as simplicity of probe motion, high reliability and efficiency. Some key techniques including calibration of the effective radius of the probing system, determination of the position of axis of rotation, auto-centering of the workpiece, data processing algorithm, are discussed. Approaches for determining the coordinates on measured surface, establishing workpiece coordinate system and surface fitting are presented in detail. The method can be used with contact or non-contact probes. Some fragile ceramic and plaster parts are measured by using the system consisting of a CMM, rotary table, motorized head and non-contact laser triangulation probe. The measurin     

激光制导测量机器人运动系统设计

激光跟踪测量系统是目前最新型的便携式空间大尺寸坐标测量系统,但在测量大型被测对象时,人工布点及测量过程繁杂,测量效率低,并造成被测对象几何形状变形,严重影响其测量精度。为解决以上问题,提出了新型的“光束运动—光靶跟踪”激光跟踪测量方法,建立了新型激光跟踪测量方法论,并在此理论基础上,研制开发了一种能够在水平和垂直被测对象表面上运动小型轮臂复合式激光制导测量机器人。该机器人机构融合轮式机构、爬行臂式结构和真空吸附式机构优点,并且具有重量轻、体积小、运动灵活和反应快速等特点,可以根据不同的被测对象表面特征变换测量模式,利用轮式结构实现机器人在水平被测表面上高速远距离运动,利用爬行臂式和真空吸附式机构实现机器人在倾斜光滑表面上灵活地爬行和转向。对其运动特性进行了详细的分析。最后利用激光跟踪仪和三坐标测量机对研制激光制导测量机器人进行了性能测试,试验结果证明了该机器人能跟踪激光束自动高效地完成被测对象实体测量。