激光跟踪仪多边测量的不确定度评定

激光跟踪仪多边测量是大型高端装备制造现场溯源的重要手段,正确评定其不确定度是确保制造过程量值统一、结果可靠的关键。本文提出了一种准确、快速的激光跟踪仪多边测量的不确定度评定方法。从仪器误差、环境干扰及靶球制造误差等方面分析激光跟踪仪多边测量的不确定度来源。针对多边测量的输出量为多维向量的特点,重点研究基于多维不确定度传播律(GUM法)的不确定度合成方法,同步评定目标点坐标和跟踪仪站位的不确定度。最后,介绍了点到点长度的不确定度计算方法。实验表明:GUM法评定的不确定度结果与蒙特卡洛法(MCM法)的结果相比,坐标不确定度偏差小于0.000 2 mm,相关系数偏差小于0.01,满足数值容差,且GUM法用时仅为MCM法的0.08%;点到点长度测试的En值均小于1。因此,基于GUM法评定激光跟踪仪多边测量的不确定度具有可行性及高效性,且评定结果正确、可靠。     

The detection of rotary axis of NC machine tool based on multi-station and time-sharing measurement

At present, the detection of rotary axis is a difficult problem in the errors measurement of NC machine tool. In the paper, a method with laser tracker on the basis of multi-station and time-sharing measurement principle is proposed, and this method can rapidly and accurately detect the rotary axis. Taking the turntable measurement for example, the motion of turntable is measured by laser tracker at different base stations. The redundant equations can be established based on the large amount of measured data concerning the distance or distance variation between measuring point and base station. The coordinates of each measuring point during turntable rotation can be accurately determined by solving the equations with least square method. Then according to the error model of rotary axis, the motion error equations of each measuring point can be established, and each error of turntable can be identified. The algorithm of multi-station and time-sharing measurement is derived, and the error separation algorithm is also deduced and proved feasible by simulations. Results of experiment show that a laser tracker completes the accuracy detection of the turntable of gear grinding machine within 3 h, and each error of the turntable are identified. The simulations and experiments have verified the feasibility and accuracy of this method, and the method can satisfy the rapid and accurate detecting requirements for rotary axis of multi-axis NC machine tool.     

Algorithm for detecting volumetric geometric accuracy of NC machine tool by laser tracker

Quick and accurate detecting the error of NC machine tool and performing the error compensation are important to improve the machining accuracy of NC machine tool.Currently,there are many methods for detecting the geometric accuracy of NC machine tool.However,these methods have deficiencies in detection efficiency and accuracy as well as in versatility.In the paper,a method with laser tracker based on the multi-station and time-sharing measurement principle is proposed,and this method can rapidly and accurately detect the geometric accuracy of NC machine tool.The machine tool is controlled to move in the preset path in a 3D space or 2D plane,and a laser tracker is used to measure the same motion trajectory of the machine tool successively at different base stations.The original algorithm for multi-station and time-sharing measurement is improved.The space coordinates of the measuring point obtained by the laser tracker are taken as parameter values,and the initial position of each base point can be determined.The redundant equation concerning the base point calibration can be established by the distance information of the laser tracker,and the position of each base point is further determined by solving the equation with least squares method,then the space coordinates of each measuring point can be calibrated.The singular matrix does not occur in calculation with the improved algorithm,which overcomes the limitations of the original algorithm,that the motion trajectory of machine tool is in a 3D space and there exits height difference between the base stations.Adopting the improved algorithm can expand the application of multi-station and time-sharing measurement,and can meet the quick and accurate detecting requirements for different types of NC machine tool.     

Station-transfer measurement accuracy improvement of laser tracker based on photogrammetry

Laser tracker has been used in a diverse range of applications due to its high accuracy and efficient, specifically as measuring the coordinates of points or scanning shape of objects. In real applications, we often need to measure common points on multi-stations by using this technology if objects are large scale. To ensure every common point within the range of laser tracker, common points are usually placed far from the laser tracker. However, the long distance between common points and laser tracker will decrease the accuracy of the result. In this research, we proposed a new method where photogrammetry and laser tracker are integrally used to measure common points to reduce measurement error. With the help of photogrammetry, we first constructed the geometric constraints of common points. Then, by using graphic correction method, the coordinates of common points on laser tracker will be corrected. Both of the theoretical and experimental study results indicated the great success of improving the measurement accuracy of laser tracker. We consider that this method we reported can highly increase the accuracy of measurement on laser tracker station-transfer.     

激光跟踪仪测角误差的现场评价

激光跟踪仪是基于角度传感和测长技术相结合的球坐标测量系统,其长度测量采用激光干涉测长方法,可直接溯源至激光波长,因此,激光跟踪仪的长度测量精度远高于角度测量精度,相对而言,测角误差就成为评价跟踪仪测量精度的重要指标。为了对现场测量激光跟踪仪的测角误差进行快速有效地评价,采用跟踪仪多站位对空间中测量区域内若干个被测点进行测量,与传统基于角度交汇原理的多站位冗余测量不同,利用各站位所观测的高精度测长值建立误差方程,并通过测长方向的矢量位移对跟踪仪测长误差进行约束,获得被测点三维坐标在跟踪仪水平角和垂直角方向上的改正值,以此来评价激光跟踪仪的测角误差。通过Leica激光跟踪仪AT901-LR进行了多站位测角误差评价实验,在现场测量条件下,跟踪仪水平和垂直方向测角误差约为0.003 mm/m(1σ),符合跟踪仪的测量误差特性。     

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.     

Modelling,kinematic parameter identification and sensitivity analysis of a Laser Tracker having the beam source in the rotating head

This paper presents a new kinematic model, a parameter identification procedure and a sensitivity analysis of a laser tracker having the beam source in the rotating head. This model obtains the kinematic parameters by the coordinate transformation between successive reference systems following the Denavit–Hartenberg method. One of the disadvantages of laser tracker systems is that the end-user cannot know when the laser tracker is working in a suitable way or when it needs an error correction. The ASME B89.4.19 Standard provides some ranging tests to evaluate the laser tracker performance but these tests take a lot of time and require specialized equipment. Another problem is that the end-user cannot apply the manufacturer’s model because he cannot measure physical errors. In this paper, first the laser tracker kinematic model has been developed and validated with a generator of synthetic measurements using different meshes with synthetic reflector coordinates and known error parameters. Second, the laser tracker has been calibrated with experimental data using the measurements obtained by a coordinate measuring machine as nominal values for different strategies, increasing considerably the laser tracker accuracy. Finally, a sensitivity analysis of the length measurement system tests is presented to recommend the more suitable positions to perform the calibration procedure.     

Estimation of three-dimensional volumetric errors of machining centers by a tracking interferometer

A tracking interferometer is a laser interferometer with the mechanism to steer the laser direction to automatically follow a target retroreflector. This paper experimentally investigates the performance of the tracking interferometer prototype, developed by a part of the authors, in estimating the volumetric accuracy of a machining center based on the multilateration principle. Then, the prototype's technical issues are discussed based on the measurement uncertainty analysis. This paper briefly reviews the direct algorithm to calculate the three-dimensional position of the target, as well as the indirect algorithm to estimate geometric error parameters of the machine's kinematic model. Their comparison is also presented based on the uncertainty analysis.     

Three-point method for measuring the geometric error components of linear and rotary axes based on sequential multilateration

The linear and rotary axes are fundamental parts of multi-axis machine tools. The geometric error components of the axes must be measured for motion error compensation to improve the accuracy of the machine tools. In this paper, a simple method named the three-point method is proposed to measure the geometric error of the linear and rotary axes of the machine tools using a laser tracker. A sequential multilateration method, where uncertainty is verified through simulation, is applied to measure the 3D coordinates. Three non-collinear points fixed on the stage of each axis are selected. The coordinates of these points are simultaneously measured using a laser tracker to obtain their volumetric errors by comparing these coordinates with ideal values. Numerous equations can be established using the geometric error models of each axis. The geometric error components can be obtained by solving these equations. The validity of the proposed method is verified through a series of experiments. The results indicate that the proposed method can measure the geometric error of the axes to compensate for the errors in multi-axis machine tools.     

‘Open-loop’ tracking interferometer for machine tool volumetric error measurement—Two-dimensional case

The tracking interferometer, or the laser tracker, is a laser interferometer with a steering mechanism to regulate the laser beam direction to follow a retroreflector (“target”). Applying the multilateration principle, it measures the target's three-dimensional position at an arbitrary location in the workspace. Its application to the volumetric accuracy measurement for coordinate measurement machines or machine tools has been long studied. In this paper, we propose the ‘open-loop’ tracking interferometer, where the laser beam is regulated toward the command target position. This eliminates the automated tracking mechanism and thus may significantly reduce the manufacturing cost of conventional tracking interferometers. The objective of this paper is to validate this ‘open-loop’ tracking interferometer concept by investigating its measurement uncertainty both experimentally and analytically. To simplify the problem, this paper focuses on the measurement of the target's two-dimensional position by using a single-axis ‘open-loop’ tracking interferometer prototype.     

面向对象的大尺寸测量不确定度分析

测量结果必须说明不确定度。常规尺寸的解析法和标准比对法难以适用于评价大尺寸测量不确定度,尤其是特定拟合任务结果的不确定度。针对大尺寸测量的特殊性,研究基于蒙特卡罗的评价方法评价大尺寸特定测量对象的不确定度,并用计算机可视化直观表示离散点云。利用离线仿真评价测量不确定度,用于设计最优采样策略。以激光跟踪仪测量大型圆形截面工件分析为例,给出测点对称、均匀分布和半径约束等优化测量思想。最后应用于激光跟踪仪测量隧道构件的实例当中。仿真和实际实验表明,蒙特卡罗评价和离散点云表示法可准确、直观评价大尺寸测量特定测量对象的不确定度,制定的最优采样策略可提高测量精度。     

The laser ball bar: a new instrument for machine tool metrology

Current techniques for mapping the volumetric positioning errors of machine tools are time and labor intensive. To address these shortcomings, a linear displacement measuring device is introduced to rapidly and easily determine tool positions via trilateration. The laser ball bar (LBB) consists of a laser interferometer aligned within a telescoping ball bar. The design of the device is discussed and an error budget is developed to estimate its predicted accuracy. Results of repeatability and linear accuracy test of the assembled prototype LBB are given. The LBB is used to map the volumetric errors of a two-axis turning center. Comparison of the LBB error map and the error map obtained through parametric error measurements shows the LBB can accurately map the machine errors in a timely manner.     

Laser tracker performance quantification for the measurement of involute profile and helix measurements

Standard-conforming measurements for a large involute gear were performed with a manually operated laser tracker system and the corresponding task-specific measurement uncertainties were estimated. Especially, readers using laser trackers for inspecting large involute gears will get information of a taskspecific measurement performance for the first time, which significantly differs from the laser tracker machine specification. To ensure unambiguous and repeatable measurement results, user-friendly auxiliary tools are used, which allows the operator to probe the measurement points according to existing guidelines and standards. Measurements were taken on a robust and highly accurate large involute gear measurement standard of the Physikalisch-Technische Bundesanstalt (PTB) under laboratory conditions. The size of this gear measurement standard complies with those gears used in wind power plants. The external gear materializes a left and a right hand gear as well as a spur gear. The obtained results of profile, helix and surface measurements are presented. These research activities were carried out at the PTB in the department of coordinate metrology.     

Impact of measurement procedure when error mapping and compensating a small CNC machine using a multilateration laser interferometer

This paper deals with the accuracy of compensation of machine tools using a tracking interferometer using the multilateration method. The measurement strategy and thermal drift compensation of the measurements are studied. It shows that most effects of temperature are accurately compensated by the laser tracking interferometer software. However, thermal drifts of accessories are not taken into account, and are therefore not corrected. To validate the robustness of procedures, the geometrical errors of the same machine tool were measured by five measurement strategies using the same equipment. Each strategy is devised and carried out independently by a different person from several institutions. For each strategy, the geometrical compensations were applied to a set of nominal tool path points. The difference, between the nominal points and the compensated or uncompensated points was calculated. This criterion was used to discuss the procedures employed by the participants.     

激光跟踪仪测角误差补偿

由于激光跟踪仪的角度测量精度直接影响仪器的测量精度,本文提出了用自准直仪结合多面棱体对跟踪仪金属圆光栅测角误差进行离散标定的方法。研究了基于谐波分析的误差补偿方法,取金属柱面圆光栅测角误差中幅值较大且相位基本不变的谐波分量建立了补偿模型,避免了最小二乘法不收敛的问题。分析了标定测角误差的不确定度,结果显示：水平测角精度补偿前后分别为1.60"和0.90",俯仰测角精度补偿前后分别为4.89"和0.91",精度分别提高了44%和81%,从角秒级提高到了亚角秒级。结果表明,提出的方法可为激光跟踪仪水平和俯仰轴系提供测角误差补偿,对类似测角系统的误差补偿也有参考价值。     

光束平差在激光跟踪仪系统精度评定中的应用

对自主研制的激光跟踪仪的精度评定进行研究,以期解决大尺寸空间坐标测量系统的空间坐标精度难于评定的问题.考虑现场环境条件、仪器状态和操作者技能等因素对测量精度影响都很大,提出了基于光束平差原理对激光跟踪仪系统进行精度评定的方法.通过Matlab软件对激光跟踪仪的精度评定进行了仿真,仿真结果显示光束平差法能客观地反映激光跟踪仪的测量精度.另外,使用Faro生产的激光跟踪仪进行了实物实验,实验结果显示其水平角精度σH为1.97″,垂直角精度σV为2.61″,测距精度σD为3.75×10-6,对比Faro生产的激光跟踪仪精度(σH =2.0″;σV =2.0″;σD=4 μm)可证明采用光束平差法评定自主研发的激光跟踪仪测量精度是正确、可行的.该方法为探索激光跟踪仪新的应用技术、开展面向对象的测量不确定评定奠定了基础.     

数控机床误差的激光干涉仪自动瞄准测量及补偿技术研究

开发了用于数控机床空间误差测量的激光干涉仪自动瞄准系统。该系统实现了机床多轴联动、而激光束的方向发生连续改变时空间曲线轨迹定位误差的测量。提出了通过一次对光实现数控机床整个空间定位误差的直接测量方法。采用网格方法储存测量误差,用有限元法实现补偿误差的预报。在立式数控加工中心上进行了误差的测量和补偿试验,结果表明所提出的误差测量方法精度高、速度快,误差补偿效果明显。     

激光跟踪仪几何误差修正

本文推出了激光跟踪仪主要几何误差数学模型，给出了误差分离方法及修正方法，首次在激光跟踪仪全程35m范围内进行了比长实验和误差修正实验，得到了LTD500大范围空间测长精度，同时验证了误差修正的正确性和有效性。     

A new formulation of laser step-diagonal measurement—two-dimensional case

The laser step-diagonal measurement modifies the diagonal displacement measurement by executing a diagonal as a sequence of single-axis motions. It has been claimed that the step-diagonal test enables the identification of all the volumetric error components, including linear errors, straightness and squareness errors, in three-dimensional space. In this paper, we show that the conventional formulation of the step-diagonal measurement is valid only when implicit assumptions related to the configuration of laser and mirror setups are met, and that its inherent problem is that it is generally not possible to guarantee these conditions when volumetric errors of the machine is unknown. To address these issues, we propose a new formulation of the step-diagonal measurement, in order to accurately identify volumetric errors even under the existence of setup errors. To simplify the discussion, this paper only considers the two-dimensional version of laser step-diagonal measurement to estimate volumetric errors on the XY plane. The effectiveness of the proposed modified identification scheme is experimentally investigated by an application example of two-dimensional laser step diagonal measurement to a high-precision machine tool.     

Uncertainty assessment of a prototype of multilateration coordinate measurement system

Large Volume Metrology is essential to many high value industries to go towards the factory of the future, but also to many science facilities for fine alignment of large structures. In this context, we have developed a multilateration coordinate measurement system, traceable to SI metre, and suitable for outdoor measurements or industrial environments. It is based on a high accuracy absolute distance meter developed in-house and shared between several measurement heads by fibre-optic links. Thus, from these measurement stations, multiple distance measurements of several positions of a target can be performed. At the end, coordinates of the heads and of the different target locations are determined using a multilateration algorithm with self-calibration.In this paper, the uncertainty of this multilateration coordinate measurement system is determined with a consistent metrological approach. First, 13 different sources of errors are listed and quantified. Then, thanks to Monte Carlo simulations, the standard uncertainty on a single absolute distance measurement is assessed to 4.7 μm. This includes the uncertainty contribution of the telemetric system itself, but also the contributions of the mechanical designs of the measurement heads and the target. Lastly, measurements of three-dimensional coordinates of target positions are performed in a control environment, then in a large workshop without temperature control: these measurements validate the uncertainty assessment of the system.