Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage

This paper describes the measurement of straightness error motions (vertical straightness and horizontal straightness) and rotational error motions (pitch, yaw and roll) of a commercial precision linear air-bearing stage actuated by a linear motor. Each of the error motions was measured by two different methods for assurance of reliability. The stage was placed in the XY-plane and moved along the X-direction. The pitch error and yaw error, which were measured by an autocollimator and the angle measurement kit of a laser interferometer, were about 8.7 and 1.6 arc-s, respectively, over a travel of 150 mm with a moving speed of 10 mm/s. The roll error was measured by the autocollimator through scanning a flat mirror along the X-direction. The second method for roll error measurement was to scan two capacitance-type displacement probes along the flat surface placed in the XZ-plane. The two probes with their sensing axes in the Y-direction were aligned with a certain spacing along the Z-axis. The roll error can be obtained by dividing the difference of the outputs of the two probes by the spacing between the two probes. The roll error was measured to be approximately 11.8 arc-s over the 150 mm travel. The horizontal straightness error and the vertical straightness error (Y- and Z-straightness errors) were measured by using the straightness measurement kit of the laser interferometer. The second method for straightness measurement was to scan the flat surface with a capacitance-type displacement probe. The horizontal and vertical straightness errors of the stage over the 150 mm travel were measured to be approximately 207 and 660 nm, respectively.     

多圈光电轴角编码器在直线位移测量中的应用

多圈光电轴角编码器是一种适用于大量程轴角位移精密测量的光电数字测角仪,其测量范围可超过整周(360°)的几百倍,甚至上千倍.利用多圈光电轴角编码器具有分辨力高、精度高、体积小、量程大以及数字量输出等优点,设计了由高精度齿轮同步带传动机构与16位多圈编码器组合而成的直线位移测量系统,并对系统的测长精度进行了检定.实验结果表明,修正后的系统测长误差低于0.065 mm,可满足中低精度的工业测量要求.     

An evaluation of a modulated laser encoder

This paper introduces a new method of interpolation for sub-nanometer-resolution linear encoders. This method, called SPPE (scanning position probe encoder), uses high-order harmonics information obtained by a sinusoidal scanning pickup located on a periodic grating surface. The proposed encoder uses a current-modulated laser diode with diffractive grating optics. Since the electrical current changes the laser-diode wavelength, the interference light intensity is modulated as a sinusoidal scanning pickup on the scale grating. Phase-detection circuits can decode the position information in the pickup signal by using phase-locked loop techniques. The decoder achieves an interpolation rate of over 1/40,000 with interpolation errors of less than ±1 nm. A new interpolation-error measuring system was developed for the encoder. Finally, the evaluation results reveal that the presented encoder shows both high resolution and strong robustness.     

Performance evaluation of a new taut wire system for straightness measurement of machine tools

This paper describes evaluation of a method of measuring the straightness of motion of machine tool axes using a taut wire and an optical sensor head mounted at the tool point location. In contrast to commonly used taut wire instruments, straightedges or laser-based methods, this solution combines low cost, simplicity of setup and automated data capture while achieving state of the art accuracy suitable for application on precision machine tools. A series of tests are discussed which examine the performance of the new sensing head and different wires which highlight the suitability of the taut wire properties as a straightness reference. Experimental results obtained on a production machine tool are provided with respect to the accuracy and repeatability of both the proposed taut wire system and a laser interferometer operated under the same conditions. The reference errors of wires made of different materials are compared and the wire catenary is separated from the measurement results. The uncertainty budget for taut wire and laser systems is presented and expanded uncertainty of 4 μm obtained for both. During the experiment, the method showed excellent repeatability with two standard deviations of 1.5 μm over a measuring range of 1.5 m; this performance matches that of a commercial laser interferometer-based straightness reference to within 0.1 μm.     

Design and experimental validation of an ultra-precision Abbe-compliant linear encoder-based position measurement system

The design and development of an Abbe-compliant linear encoder-based measurement system for position measurement with a targeted 20 nm uncertainty (k = 2) in machine tools and CMMs is presented. It consists of a linear scale and a capacitive sensor, mounted in line on an interface which is guided in the scale's measurement direction and driven by a linear motor based on the output signal of the capacitive sensor. The capacitive sensor measures the displacement of a target surface on the workpiece table. The functional point, which is the center of a tool or touch probe, is always aligned with the scale and capacitive sensor such that this configuration is compliant with the Abbe principle. Thermal stability is achieved by the application of a thermal center between the scale and capacitive sensor at the tip of the latter, which prevents both components to drift apart. Based on this concept, a prototype of a one-DOF measurement system was developed for a measurement range of 120 mm, together with an experimental setup aimed at verifying the reproducibility of the system for changing ambient conditions of ±0.5 °C and ±5%rh and the repeatability during tracking of a target surface over a short period of time. These experiments have shown that the measurement uncertainty of the one-DOF system is below 29 nm with a 95% confidence level.     

Precision measurement of cylinder straightness using a scanning multi-probe system

This paper describes a scanning multi-probe system for measuring straightness profiles of cylinder workpieces. The system consists of two probe-units, each having three displacement probes. The two probe-units, which are placed on the two sides of the test cylinder, are moved by a scanning stage to scan the two opposed straightness profiles of the cylinder simultaneously. A differential output calculated from the probe outputs in each probe-unit cancels the influence of error motions of the scanning stage, and a double integration of the differential output gives the straightness profile. It is verified that the difference between the unknown zero-values of the probes in each probe-unit (zero-difference) will introduce a parabolic error term in the profile evaluation result, which is the largest error source for straightness measurement of long cylinders. To make zero-adjustment accurately, the cylinder is rotated 180° and scanned by the probe-units again after the first scanning. The zero-differences of the probe-units, as well as the straightness profiles of the cylinder, can be accurately evaluated from the output data of the two measurements. The effectiveness of this method is confirmed by theoretical analysis and experimental results. An improved method, which can measure the variation of the zero-difference during the scanning, is also presented.     

An international length comparison at an industrial level using a photoelectric incremental encoder as transfer standard

A Japanese–German interlaboratory comparison of length measurements was conducted. A photoelectric incremental encoder with a measurement length of 270 mm was used as transfer standard. An agreement of better than 27 nm over the entire length was ascertained, and the “short-range” deviations within a length interval of approximately 10 mm could be characterized with a standard deviation of σ=0.8 nm. The results attained are considered as consistent with the estimated uncertainties of measurement. Since the measurements performed are directly traceable to the SI unit of the “metre”, the comparison supports ideas currently being discussed by some National Metrology Institutes and dealing with the question of how foundations can be laid for a generally accepted application of this method of traceability.     

Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage

In this study, a laser linear encoder with three degrees of freedom (3-DOFs) based on diffraction and interference was developed to measure the linear displacement and two angular errors of a linear moving stage. Parts of the linear motion errors induced from the two angular errors can be calculated by this prototype 3-DOF laser encoder. It was an effective method for online error calculation and compensation to improve precision stage performance. This new function was superior to other laser encoders. The verification results showed that the resolution is 20 nm. It detected displacements relative to an external grating scale with accuracy of about +/-150 nm for a measuring range of +/-1 mm, and detected the angular errors with related accuracy of about +/-1 arc sec for a measuring range of +/-100 arc sec.     

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.     

小型编码器动态精度检测的安装误差控制

研究了小型编码器动态检测过程中由编码器与基准编码器轴系中心线不完全重合产生的偏角导入的安装误差,以便提高编码器检测装置的准确性和可靠性。分析了安装误差对被检编码器检测精度的影响,推导出了存在安装偏角时引入的安装误差公式及其控制范围公式。为了使编码器的动态检测能准确地反映编码器的实际精度,给出了最大偏角值α_(max)及高度差D_(max)的允许范围。使用现有21位检测装置对15位被检编码器进行了检测实验,分别对安装良好、小偏角和大偏角情况下的测量结果和安装误差曲线进行了比较和分析。结果表明:检测15位编码器时,将安装偏角值控制在0.36°以下可满足动态精度检测要求。本文提出的误差公式及控制方法可以运用在不同类型、不同精度的编码器检测过程中,对提高小型光电编码器动态检测的精度和可靠性很有意义。     

光电编码器误差检测转台的动态精度标定

由于光电编码器动态检测转台的分辨率、精度和转速都比较高,传统检测手段很难精确标定该类转台的动态精度,故本文开展了转台动态精度标定方法的研究。首先,分析动态转台工作原理,指出了影响转台动态精度的主要因素。然后,研究了动态误差的主要特性,提出了一种基于动态重复性的转台动态精度标定方法。最后,设计了FPGA+USB的数据采集电路,实现了对转台动态精度的标定。对自行研制的转台进行了动态精度标定。标定结果显示:提出的动态精度标定方法能够实现对转台的标定,验证了该转台能够实现对被检编码器的动态检测,解决了研制动态转台时缺少动态检测精度标定方法的难题。     

A novel Fourier-Eight-Sensor (F8S) method for separating straightness,yawing and rolling motion errors of a linear slide

A novel method called the Fourier-Eight-Sensor (F8S) method is proposed for the separation of the straightness, yawing and rolling motion errors as well as the profiles of a linear slide. Eight distance sensors are positioned on a vertical stage in two lines parallel to the target profiles with five sensors in the lower row and the other three in the upper row. The outputs of the sensors are fused together at different times to eliminate the dependence of motion errors. The method adopts a two-stage approach. First, the profile faced by the lower row sensors is represented by Fourier series the coefficients of which are obtained by matrix inversion. Then, another Fourier series is used to represent the difference between the two target profiles. By fusing the outputs of the three sensors in the upper row and their corresponding counterparts in the lower row, the coefficients of the Fourier series are determined by the Fourier series based error separation technique. In this way, different error components can be successfully separated from the sensor outputs. The effectiveness of the method is validated by simulation and experiment.     

A fast and simple algorithm for evaluation of minimum zone straightness error from coordinate data

Various methods have been suggested in the past to determine the minimum zone straightness error, but suffer from various drawbacks. A new, fast and simple algorithm is proposed to calculate the straightness error from planar coordinate data. It guarantees the minimum zone solution. An example and test data are provided. Results of simulation experiments to establish the time computational complexity of the algorithm are also presented.     

An Improved Fourier Five-Sensor (IF5S) method for separating straightness and yawing errors of a linear slide based on multiple sensor parameter sets and least square regression technique

In this paper, an Improved Fourier Five-Sensor (IF5S) measurement method is proposed for separating the straightness and yawing motion errors as well as determining the profile of a linear slide. The previous F5S method [3] used the constant parameters initially to estimate the profile function based on three sensor equations for different angle ranges. The profile estimation and error separation are implemented via an iterative method which can only yield acceptably accurate results with tremendous computational efforts. Here, the improved F5S method applies the least square regression technique instead of the iterative method to estimate the profile functions by using three distinct sets of parameters and different fused sensor data according to the travel of the linear slide. Various errors can then be separated based on the calculated profile function. Simulation results confirm that the IF5S method provides better performance and effectiveness as compared to the previous F5S method.     

防抖动易更换高炉位置编码器固定装置

高炉编码器固定装置是随高炉炉顶设备订货的,在现场应用中,出现了编码器固定不牢,出现故障后更换不方便等弊端。针对这些弊端,设计了防抖动、易更换的编码器固定装置,提高编码器测量精度,使得高炉布料过程和布料质量得到控制。     

航天级光电编码器的信号处理系统设计

为了实现航天级光电编码器的小型化,减小航天设备的体积、重量并满足其冷备份要求,设计了具有双读数系统的航天级光电编码器信号处理系统。首先,介绍了双读数系统航天级光电编码器的精码和粗码信号处理方法以及信号处理系统的小型化和可靠性设计;然后,从光电编码器误差产生的原因及空间分布特征出发,对双读数系统航天级光电编码器进行了精度分析;最后,采用比较法,以23位高精度光电编码器作为角度基准,对该光电编码器进行了精度检测。实验结果表明:应用该信号处理系统的双读数系统光电编码器的分辨力为20″,精度σ≤30″。该系统已在工程项目中得到应用,实践表明系统的设计满足航天设备的技术要求。     

Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine

This paper describes the surface profile measurement of a XY-grid workpiece with sinusoidal microstructures using an atomic force microscope (AFM) on a diamond turning machine. The sinusoidal micro-structures, which are fabricated on an aluminum plate by fast tool servo-assisted diamond turning, are a superposition of periodic sine-waves along the X- and Y-directions (wavelength (XY): 150 μm, amplitude (Z): 0.25 μm). A linear encoder with a resolution of 0.5 nm is integrated into the AFM-head for accurate measurement of the Z-directional profile height in the presence of noise associated with the diamond turning machine. The spindle and the X-slide of the machine are employed to spirally scan the AFM-head over the sinusoidal grid workpiece. Experiments fabricating and measuring the sinusoidal grid workpiece are carried out after accurate alignment of the AFM cantilever tip with the spindle centerline.     

双读数系统的航天级绝对式光电编码器设计

为了有效地减小航天相机的体积,减轻其重量并满足冷备份要求,设计了双读数系统的航天级绝对式光电编码器.根据航天相机的要求,对绝对式光学码盘进行了小型化设计;根据码盘的特点,研制了双读数狭缝盘及读数系统;最后,对设计的双读数系统的航天级绝对式光电编码器进行了精度检测.实验结果表明:双读数系统的航天级绝对式光电编码器外形尺寸为50 mm×32 mm、重量为150 g、分辨力为20″、精度σ≤30″.本编码器具有读数系统冷备份功能,且体积小、重量轻、抗干扰能力强,可满足航天相机的要求.     

基于51单片机的光电编码器接口装置设计

光电编码器以其分辨率高、测量精度高、形式多样等优点,被广泛运用于现代工业、航天航空领域。在工程中对光电编码器信号的采集一般使用专用PCI卡,这无形中增加了工程的成本,本文介绍了一种基于AT89S52单片机的绝对式光电编码器的接口装置及软件设计,该装置使用LCM12684作为显示模块,实现了对绝对式光电编码器的数据采集、处理及输出。     

Multi-probe method for straightness profile measurement based on least uncertainty propagation (1st report): Two-point method considering cross-axis translational motion and sensor's random error

In the straightness profile measurement of a mechanical workpiece, hardware datums have been the traditional standard. However, error separation techniques of the surface profile from parasitic motions have been developed. These are known as software datums, which separate the surface profile from the parasitic motions using multiple sensors and/or multiple orientations and realize higher accuracy than that of the hardware datum. However, the conventional software datum cannot measure a large-scale workpiece because the large sampling number causes random error amplification. Furthermore, the conventional software datum assumes that sensor's random noise is small enough in comparison with the parasitic motions. But, the accuracy of the hardware datum has become high. Then, the accuracy of the sensor's random noise is not so small, relatively. In this paper, a next-generation software datum, the two-point method based on the least uncertainty propagation, is proposed. The proposed two-point method consists of weighting and inverse filtering, resulting in the least uncertainty of the estimated surface profile by choosing suitable weighting.