Measurement and compensation of error motions of a diamond turning machine

This paper describes the measurement and compensation of error motions of a diamond turning machine for nanofabrication of large sinusoidal metrology grids. The diamond turning machine has a T-base design, which consists of a spindle with its rotation axis along the Z-direction and a cross-slide with its movement direction along the X-direction. A fast-tool-servo (FTS) unit is mounted on the X-slide to generate sinusoidal microstructures on a flat workpiece surface mounted on the spindle. The error motions of the X-slide and the spindle, which introduce Z-directional profile errors (out-of-flatness) on the grid surface, are measured and compensated. The out-of-straightness of the X-slide is measured to be approximately 60 nm over a travel of 80 mm by using the reversal method. It is also confirmed that the out-of-straightness of the X-slide has a 10-nm periodic component with a period of 11 mm corresponding to the diameter of the needles used in the roller bearing of the X-slide. The angular motion of the spindle is measured to be approximately 0.3″ by using an autocollimator, which can cause a 73-nm out-of-flatness over a workpiece 100 mm in diameter. The axial motion of the spindle is measured to be approximately 5 nm, which is the smallest error motion. The out-of-flatness of the workpiece is reduced from 0.27 to 0.12 μm through compensating for the error motions by utilizing the FTS unit based on the measurement results of error motions.     

Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy

This paper describes a multi-probe scanning system comprising three laser interferometers and one autocollimator to measure a flat bar mirror profile with nanometer accuracy. The laser interferometers probe the surface of the flat bar mirror that is fixed on top of a scanning stage, while the autocollimator simultaneously measures the yaw error of the scanning stage. The flat bar mirror profile and horizontal straightness motion error are reconstructed by an application of simultaneous linear equations and least-squares method. Measurement uncertainties of the flat bar mirror profile were numerically evaluated for different installation distances between the laser interferometers. The average measurement uncertainty was found to be only 10 nm with installation distances of 10 and 21 mm between the first and second, and first and third interferometers, respectively. To validate the simulation results, a prototype system was built using an X–Y linear stage driven by a stepper motor with steps of 1 mm along the X direction. Experiments were conducted with fixed interferometers distances of 10 and 21 mm, as in the simulation, on a flat bar mirror with a profile known to an accuracy of λ = 632.8 nm. The average value of two standard deviations (95%) of the profile calculated over ten experiments was approximately 10 nm. Other results from the experiment showed that the system can also measure the yaw and horizontal straightness motion errors successfully at a high horizontal resolution. Comparing with the results measured by ZYGO's interferometer, our measured data excluding some edge points showed agreement to within approximately 10 nm. Therefore, we concluded that our measurement profile has an accuracy in the nanometer range.     

Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness

This paper presents a two-degree-of-freedom (two-DOF) linear encoder which can measure the position along the moving axis (X-axis) and the straightness along the axis vertical to the moving axis (Z-axis) of a precision linear stage simultaneously. The two-DOF linear encoder is composed of a reflective-type scale grating and an optical sensor head. A reference grating, which is identical to the scale grating except the scale length, is employed in the optical sensor head. Positive and negative first-order diffracted beams from the two gratings are superposed with each other in the optical sensor head to generate interference signals. The optical configuration is arranged in such a way that the direction of displacement in each axis can also be detected. A prototype two-DOF linear encoder is designed and constructed. The size of the optical sensor head is about 50 mm (X) × 50 mm (Y) × 30 mm (Z) and the pitch of the grating is 1.6 μm. It has been confirmed that the prototype two-DOF linear encoder has sub-nanometer resolutions in both the X- and Z-axes.     

A linear air bearing stage with active magnetic preloads for ultraprecise straight motion

In this paper, we propose a linear motion stage designed with magnetically preloaded air bearings. The magnetic actuators for preloading air bearings were combined with permanent magnets and coils to adjust the air bearing clearance by actively controlling the magnetic force. The system was designed to achieve a simplified configuration of air bearing stage while providing ultraprecise straight motion by actively compensating for the motion errors. The porous aerostatic bearings and magnetic preload actuators were designed and analyzed numerically for a single-axis prototype linear stage driven by a coreless linear motor. A magnetic circuit model was derived for the magnetic actuators. The static stiffness and load capacity of the air bearing stage in the vertical (magnetically preloaded) direction were experimentally measured and compared with the results from the numerical analysis. Motion control laws for three degrees of freedom (i.e., vertical, pitch, and roll motions) were obtained with a high linearity and independence for each axis. The active compensation of three motion errors, the vertical, pitch and roll motion errors were performed through curve-fitting the three errors measured with combination of capacitive gap sensors and a laser interferometer. The errors were reduced from 1.09 to 0.11 μm for the vertical straightness error, from 9.42 to 0.18 arcsec for the pitch motion, and from 2.42 to 0.18 arcsec for the roll motion as level of measured repeatability.     

Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration

This paper performs a comprehensive analysis and calibration on the geometric error of the ultra-precision drum roll lathe with dual-spindle symmetrical structure and cross slider layout. Firstly, the volumetric error model which contains all geometric errors of the dual-spindle ultra-precision drum roll lathe (DSUPDRL) is developed based on the combination of the homogenous transfer matrix (HTM) and multi-body system (MBS) theory. Secondly, sensitivity analysis for the volumetric error model is conducted to identify the sensitive geometric error components of the DSUPDRL using an improved Sobol method based on the quasi-Monte Carlo algorithm. The result of sensitivity analysis laid the foundation for the subsequent geometric error calibration. Then, some sensitive error components along the X and Z directions are calibrated using a laser interferometer and a pair of inductance displacement probes. Besides the volumetric error model, the concentricity error caused by dual-spindle symmetrical structure is proposed and calibrated by the on-machine measurement using a classic reversal method. Finally, a large-scale roller mold with a diameter of 250 mm and a length of 600 mm is machined using the DSUPDRL after calibration. The experimental result shows that 1.4 μm/600 mm generatrix accuracy is obtained, which validate the effectiveness of the geometric error analysis and calibration.     

五角棱镜扫描系统中调整误差及制造角差的影响分析-

五角棱镜扫描系统可以实现高精度测量光学表面面形,为了全面分析五角棱镜扫描系统中的调整误差及制造角差对指向误差和测角仪测量误差的影响。根据旋转变换矩阵和光线矢量追迹理论,运用MATLAB编写通用的五角棱镜扫描系统的光线矢量追迹函数及相关分析程序。同时通过二维二次多项式拟合推导出,在一定角度范围内,用于计算指向误差和测角仪测量值的二阶近似公式。分析结果表明：在扫描测量过程中,测角仪的俯仰角和五角棱镜的制造角差对沿扫描方向指向误差和测角仪垂直方向测量值的影响是常量,五角棱镜扫描过程中的偏摆角和滚动角与其成二次函数关系;五角棱镜的偏摆角和滚动角、测角仪的偏摆角与垂直扫描方向指向误差和测角仪水平方向测量值均成线性关系。当导轨误差滚动10"、偏摆10",系统的各项调整误差为±3"时,沿扫描方向最大测角误差为0.0010666"。     

基于激光干涉仪的直线度误差测量

机床导轨直线度误差的测量方法有很多种,其中最常用的是水平仪法、自准直仪法和平尺法。主要介绍的是用激光干涉仪测量直线度误差的方法、原理及误差分析,并提出为减少测量误差在测量过程中应注意的几个问题。     

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.     

High accuracy error separation technique for on-machine measuring straightness

A novel time-domain method, which can reconstruct straightness profile of workpiece exactly for on-machine measurement, has successfully been developed. The proposed method is based on difference measurement and can use two or three displacement probes. It possesses the following characteristics: (i) adapting to long or short workpiece, (ii) assuming no prior knowledge, (iii) employing large shears, (iv) needing no accurate zero-adjustment of probes, and (v) reconstructing various surfaces including smooth, non-smooth, periodic, and non-periodic profile with no theoretical error. The theoretical analysis and simulation justify the effectiveness of this method. Finally, the measurement system consisting of an autocollimator and two non-contact capacitive probes is built and evaluated experimentally on a diamond turning machine. This system can remove both pitching and translational error motion of the scanning stage.     

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.     

A 6-degree-of-freedom measurement system for the accuracy of X-Y stages

A precision 6-degree-of-freedom measurement system has been developed for simultaneous on-line measurements of six motion errors of an X-Y stage. The system employs four laser Doppler scales and two quadrant photo detectors to detect the positions and the rotations of an optical reflection device mounted on the top of the X-Y stage. Compared to the HP5528A system, the linear positioning accuracy of the developed measurement system is better than ±0.1 μm to the range of 200 mm and the vertical straightness error is within ±1.5 μm for the measuring range of ±0.1 mm. The yaw and pitch errors are about ±1 arcsec, and the roll error is about ±3 arcsec within the range of ±50 arcsec.     

Pre-deformation for assembly performance of machine centers

The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation, however, there are little researches focusing on the effect of machine center elastic deformations on workspace volume. Therefore, a method called pre-deformation for assembly performance is presented. This method is technically based on the characteristics of machine tool assembly and collaborative computer-aided engineering （CAE） analysis. The research goal is to enhance assembly performance, including straightness, positioning, and angular errors, to realize the precision of the machine tool design. A vertical machine center is taken as an example to illustrate the proposed method. The concept of travel error is defined to obtain the law of the guide surface. The machine center assembly performance is analyzed under cold condition and thermal balance condition to establish the function of pre-deformation. Then, the guide surface in normal direction is processed with the pre-deformation function, and the machine tool assembly performance is measured using a laser interferometer. The measuring results show that the straightness deviation of the Z component in the Y-direction is 158.9% of the allowable value primarily because of the gravity of the spindle head, and the straightness of the X and Y components is minimal. When the machine tool is processed in pre-deformation, the straightness of the Z axis moving component is reduced to 91.2%. This research proposes a pre-deformation machine center assembly method which has sufficient capacity to improving assembly accuracy of machine centers.     

A new vacuum interferometric comparator for calibrating the fine linear encoders and scales

A new one-dimensional laser interferometric comparator has been developed for the calibration of the fine linear encoders and scales up to 1600 mm. In the comparator, the interferometer is fully arranged in vacuum and the calibration objects are mounted under atmospheric conditions. The Abbe’s principle on the alignment of workpiece with the measuring beam is satisfied in the structure of a long measuring range. A travelling slide table, on which the calibration objects are mounted, is supported on guide rails by the air bearing and is driven through a recirculating ballscrew. The exhaust of the air bearing is guided to the exterior of the booth in which the comparator is placed. The travel of the table is measured by a reference interferometer with a beam path in vacuum shielded by an evacuated metal bellow, so that the effect of refractive index is eliminated. The laser beam is led by a polarization plane maintaining glass fiber from a self-designed stabilised He–Ne laser, which is placed in an adjacency room, to the beam inlet of the main unit. The measurement system can input the interferometer signal by the encoder signal or the scale signal, and input the encoder or scale data by the interferometer signal. The system resolution is approximately 0.8 nm and maximum travelling measurement speed is 20 mm/s at continuous measurement. The uncertainly (k=2) of measurement is approximately 30 nm in linear encoders of 500 mm length and, approximately 40 nm in scales of 500 mm, although it depends on the length and the characteristics of encoders and scales. It is successful such a high accuracy that the uncertainty of measurement system is smaller than 40 nm in encoders of 1 m length.     

Straightness evaluation using inclinometers with a pair of offset bars

To evaluate the straightness of large objects, the use of an inclinometer is advantageous because it requires neither straight shape references nor transferring mechanisms. Herein, we consider adopting it for precise (with greater accuracy than 1 mm) evaluation of the straightness of linear particle accelerators (linacs) that are several hundred meters long or longer. In this study, the straightness evaluation of a 206-m-long part of the KEK injector linac was demonstrated using inclinometers with a pair of cantilevers called offset bars. The offset bars were adopted to extend the evaluation length by avoiding obstacles that block the evaluation path. Errors caused by the offset bars can be eliminated by reversal measurement considering the slope angles of the offset bars. The derived straightness corresponded with those derived by an alignment telescope and a laser-based alignment system within several millimeters and partly within several hundred micrometers. The reproducibility of slope angles for an arbitrary measurement point was 15 μrad at standard deviation. This corresponds to a standard deviation of 0.47 mm for straightness, with a total evaluation length of 500 m and measurement intervals of 2 m. The results indicate that our newly devised method is applicable for evaluating the straightness.     

Measurement of lathe Z-slide straightness and parallelism using a flat land

A method is described to measure the straightness of travel of the carriage of a single-point diamond turning machine. The method also measures the slide parallelism to the workhead spindle. A cylindrical artifact was produced on the lathe and used as a straightedge. A flat land was cut in the artifact that was parallel to the workhead axis of rotation. The flat land was measured with a LVDT indicator. The method was demonstrated on a Moore Special Tool Co. M18 Aspheric Generator. The quality of measurements achieved were better than 0.1 μm.     

A multi-orientation error separation technique for spindle metrology of miniature ultra-high-speed spindles

This paper presents a multi-orientation error separation technique to remove the artifact form error from the radial measurements to obtain the radial spindle error motions of miniature ultra-high-speed (UHS) spindles. Unlike the existing approaches, the present technique neither relies on high-accuracy fixtures, nor necessitates measurements from specific orientations of the artifact. Rather, the spindle error motions are measured from a set of arbitrary artifact orientations using laser Doppler vibrometry (LDV). The angle of each artifact-setup orientation with respect to the spindle is determined with high precision through reflectivity measurement of the marks made on both the artifact and the spindle using another LDV. Although the presented approach can be applied by using different sensors (e.g., capacitance probes), we demonstrate the approach using LDVs. With the displacement measurement direction fixed, measurements are conducted from both LDVs for multiple orientations of the artifact. Using the unique implementation scheme developed in this paper, data from these orientations are post-processed to compute the artifact form error and further remove it from the radial motion measurements to obtain the synchronous radial spindle error motions. A thorough experimental evaluation is presented to quantify both the repeatability of the measured artifact form errors as well as the bandwidth of error separation for various number of artifact orientations. The spindle error motions measured from both the sphere and stem portions of a custom fabricated sphere-on-stem artifact mounted on a typical miniature UHS spindle, are seen to be similar in shape and within 5 nm in magnitude across the revolution, thus demonstrating the effectiveness of the technique. Using this technique, spindle error motions at ultra-high speeds up to 150 krpm were successfully quantified. Although the implementation scheme is demonstrated for miniature UHS spindles, it is readily applicable for error separation on macro-scale spindles without the need for any high-precision fixtures and precise setting of angles.     

高精度无导轨位移平台误差分析

研究了基于补偿式柔性平行四杆机构的高精度位移平台的运动精度,对变形板尺寸误差、比例杆球心距误差和内外变形板装配夹角误差等误差源进行了分析计算.采用半梁模型分析了变形板,得到变形板行程与耦合位移量的关系,给出了平台直线度误差和耦合位移量误差关于平台位移和变形板尺寸的表达式.使用自准直仪和高精度微分测量头对平台直线度和耦合位移量进行了测量,结果表明:该补偿式结构的高精度无导轨位移平台在大行程(5 mm)工作时,仍具有较高的运动精度,直线度小于1.5″,耦合位移量小于13.7 μm,与理论分析吻合.     

测试设备位姿失调对自准直仪法测量圆分度误差的影响

为了提高圆分度仪器分度误差的测量精度,介绍了用多面棱体自准直仪测量分度误差的原理和方法,对影响测量结果的误差源进行了分析。根据测量原理建立了多面棱体和自准直仪坐标系,利用坐标变换分别建立了多面棱体工作面与受检仪器轴线的平行差、自准直仪光轴与多面棱体工作面不垂直度误差、自准直仪电十字竖线与受检仪器轴线的平行差对分度误差影响的精确模型。在实验室内,以单轴位置转台的定位精度为测试对象,设计了以上三种位姿失调误差模型的验证实验,实验结果与理论模型仿真结果具有很好的一致性,三种位姿失调引入的误差实测值与理论值的最大偏差小于0.9″,验证了位姿失调量引入测量误差模型的正确性,该模型及仿真结果可以准确指导圆分度误差测试。     

A new 3-DOF Z-tilts micropositioning system using electromagnetic actuators and air bearings

A new 3-DOF Z-tilts (z, pitch, and roll motion) micropositioning system has been developed. It uses electromagnetic actuators and air bearings. An electromagnetic actuator produces an attraction force between the air bearing and the base plate. An air bearing has the role of suspension and guidance, with a clearance of several tens of micrometers in the z-direction. Therefore, this system has design features of guiding 3-DOF XYθ motion without limiting the plane motion and playing the role of a z-directional position actuator. With the control of current, the equilibrium position between magnetic attraction force and air bearing thrust force can be controlled with inherently infinite resolutions. The theoretical background of an electromagnetic actuator is explained. Then, an air bearing is analyzed in the point of z-directional positioning mechanism. The air bearing can be modeled as a second-order system with parameter variation—stiffness and damping vary with respect to the z-directional displacement. Therefore, a simple robust control algorithm is applied to improve the control performance. With the aid of robust control, this system provides 25 nm positioning resolution over the total range of 40 μm along the z-direction and, accordingly, 0.29 μrad resolution over the total range of 460 μrad in pitch and roll motion.     

Large-scale accelerator alignment using an inclinometer

A precise inclinometer (Talyvel 4) was adopted for evaluating aligning straightness of the first 71 m of the KEK electron/positron injector linear accelerator (linac). The straightness could be evaluated with a standard deviation of less than 49 μm. It is in good agreement with those obtained using a conventional alignment telescope and our laser-based alignment system.Error estimation based on the rules of error propagation shows that shape evaluation with a standard deviation of 0.3 mm for a distance of 500 m can be achieved using the proposed method. It indicates that this method is suitable for evaluating straightness of several hundred meters of linacs with sub-millimeter of accuracy.