Precision evaluation of surface form error of a large-scale roll workpiece on a drum roll lathe

This paper presents on-machine evaluation of surface form error components of a large-scale roll workpiece, including the out-of-roundness, the out-of-straightness, the taper angle and the diameter deviation, on a drum roll lathe. A pair of capacitive-type displacement probes is mounted on the carriage slide to target the two sides of the roll workpiece mounted on the spindle, which has a length of 2000 mm, a diameter of 320 mm and a mass of 350 kg. The outputs of the probes are employed to accurately evaluate the surface form error components through separating the influences of the motion errors of the spindle and the carriage slide of the lathe. It has been difficult to apply the reversal error-separation method for measurement of the out-of-roundness component of such a large workpiece because it is difficult to reverse the workpiece with respect to the spindle on the lathe due to its large size and heavy mass. An improved reversal operation technique, in which the spindle is rotated with respect to the stationary roll workpiece being held by a crane, is therefore proposed to solve this problem. Measurement uncertainty analysis is carried out to verify the reliability of the new technique for on-machine evaluation of the out-of-roundness component. The out-of-straightness component and the taper angle component of the roll workpiece are then evaluated by using a previously developed method. A simple and effective algorithm for evaluation of the diameter deviation component is also presented.     

Prioritization analysis and compensation of geometric errors for ultra-precision lathe based on the random forest methodology

Geometric errors remarkably affect the dimensional accuracy of parts manufactured by ultra-precision machining. It is vital to consider the workpiece shape for the identification of crucial error types. This research investigates the prioritization analysis of geometric errors for arbitrary curved surfaces by using random forest. By utilizing multi-body system (MBS) theory, a volumetric error model is initially established to calculate tool position errors. An error dataset, which contains information of 21 geometric errors, workpiece shape, and dimensional errors, is then constructed by discretizing the workpiece surface along the tool path. The problem of identifying crucial geometric errors is translated into another problem of feature selection by applying random forest on the error dataset. Moreover, the influence extent of each geometric error on the dimensional accuracy of four typical curved surfaces is analyzed through numerical simulation, and crucial geometric errors are identified based on the proposed method. Then, an iterative method of error compensation is proposed to verify the reasonability of the determined crucial geometric errors by specifically compensating them. Finally, under compensated and uncompensated conditions, two sinusoidal grid surfaces are machined on an ultra-precision lathe to validate the prioritization analysis method. Findings show that the machining accuracy of the sinusoidal grid surface with crucial geometric error compensation is better than that without compensation.     

Plane kinematic calibration method for industrial robot based on dynamic measurement of double ball bar

A new calibration method is proposed to improve the circular plane kinematic accuracy of industrial robot by using dynamic measurement of double ball bar (DBB). The kinematic model of robot is established by the MDH (Modified Denavit-Hartenberg) method. The error mapping relationship between the motion error of end-effector and the kinematic parameter error of each axis is calculated through the Jacobian iterative method. In order to identify the validity of the MDH parameter errors, distance errors and angle errors of each joint axis were simulated by three orders of magnitude respectively. After multiple iterations, the average value of kinematic error modulus of end-effector was reduced to nanometer range. Experiments were conducted on an industrial robot (EPSON C4 A901) in the working space of 180 mm × 490 mm. Due to the measuring radius of DBB, the working space was divided into 30 sub-planes to measure the roundness error before and after compensation. The average roundness error calibrated by the proposed method at multi-planes decreased about 21.4%, from 0.4637 mm to 0.3644 mm, while the standard deviation of roundness error was reduced from 0.0720 mm to 0.0656 mm. In addition, by comparing the results of positioning error measured by the laser interferometer before and after calibration, the range values of motion errors of end-effector were decreasing by 0.1033 mm and 0.0730 mm on the X and Y axes, respectively.     

Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool

The five-axis machine tools are increasingly popular for meeting the demand of machining the workpiece with growing geometric complexity and high accuracy. This paper studies the volumetric error modeling and its sensitivity analysis for the purpose of machine design. The volumetric error model of a five-axis machine tool with the configuration of RTTTR is established based on rigid body kinematics and homogeneous transformation matrix, in which 37 error components are involved. The sensitivity analysis of volumetric error regarding 37 error components is carried out respectively. The analysis results are successfully used for the accuracy design and manufacture of a five-axis ultra-precision machine tool. The preliminary experiment of machining sine grid surface testifies the high accuracy and effectiveness of the designed five-axis machine tool.     

Simultaneous geometric error identification of rotary axis and tool setting in an ultra-precision 5-axis machine tool using on-machine measurement

This paper presents a method to identify the position independent geometric errors of rotary axis and tool setting simultaneously using on-machine measurement. Reducing geometric errors of an ultra-precision five-axis machine tool is a key to improve machining accuracy. Five-axis machines are more complicated and less rigid than three axis machine tools, which leads to inevitable geometric errors of the rotary axis. Position deviation in the process of installing a tool on the rotary axis magnifies the machining error. Moreover, an ultra-precision machine tool, which is capable of machining part within sub-micrometer accuracy, is relatively more sensitive to the errors than a conventional machine tool. To improve machining performance, the error components must be identified and compensated. While previous approaches have only measured and identified the geometric errors on the rotary axis without considering errors induced in tool setting, this study identifies the geometric errors of the rotary axis and tool setting. The error components are calculated from a geometric error model. The model presents the error components in a function of tool position and angle of the rotary axis. An approach using on-machine measurement is proposed to measure the tool position in the range of 10 s nm. Simulation is conducted to check the sensitivity of the method to noise. The model is validated through experiments. Uncertainty analysis is also presented to validate the confidence of the error identification.     

Liquid low-flow calibration rig using syringe pump and weighing tank system

A calibration rig consisting of a syringe pump and a weighing tank system that can operate in the flow rate range of 0.02–60 L/h was developed in this study. This paper discusses the design considerations of the calibration methods, the development of the rig, the calibration results, and the uncertainty analysis conducted on the rig. A weighing tank system that minimizes the effects of outlet tube contact and evaporation was developed. The syringe pump system was designed using a servomotor, a precise ball screw, and a linear encoder, and it was calibrated using the developed weighing tank system via the standing start and stop method over the target range of flow rates with light oil and industrial gasoline. Several flowmeters were calibrated using the syringe pump via the flying start and finish method. During the flowmeter calibration stage, the effect of the evaporation error was eliminated because the calibration rig can form a closed pipeline system. The influence of dissolved gas and the position dependence of the syringe pulse factor on the calibration accuracy were investigated experimentally. As a result, all obtained syringe pulse factors were found to be within ±0.02% of each other. The preliminary expanded uncertainties (k=2) of the calibration rig were estimated to be 0.066% and 0.070% for mass and volumetric flows, respectively.     

Diamond machining using a prototype ultra-precision lathe

This paper describes the generation of mirror surfaces and, to this end, a personal computer controlled prototype ultra-precision lathe has been built. In addition, the cutting theory (derived from dislocation theory) capable of explaining the ultra-precision cutting mechanism, has been studied.The machined surface roughness achieved with aluminium was R_max = 0.01 μm using the new lathe, and a flatness of 0.1 μm/ø50 mm was achieved. The shearing stress computed, based on dislocation theory, closely coincided with that obtained from macroscopic machining experiments. The personal computer controlled ultra-precision lathe capable of these results has successfully been constructed on an experimental basis.     

辊筒模具超精密机床系统设计与工艺

为了提高国内大尺寸光学微结构薄膜的光学级模具制造水平,打破国外在辊筒模具超精密加工装备的垄断,完成了国内首台套大尺寸光学微结构辊筒模具超精密机床的设计、集成以及典型微结构工艺的研究工作。首先,根据辊筒模具表面微结构加工工艺的特点,分析了辊筒模具超精密机床的关键技术并完成了机床结构与运动控制系统设计。在机床系统集成后,完成了运动控制系统的调试。直线轴执行阶梯运动完成了直线轴运动分辨率的测试。其次,通过准直仪和激光干涉仪完成了机床关键轴系的直线度及定位精度的测试和补偿。最后,采用多步切削法切削实验,以降低毛刺高度为目标,完成了V槽阵列的加工工艺参数优化。经测试,该超精密加工机床的直线运动分辨可达到5nm,直线轴的双向定位精度均优于1μm/1 100mm;采用多步切削法加工V槽阵列,最后一次切削深度建议在1~2μm,可以获得合格的V槽阵列。     

Geometric error calibration of multi-axis machines using an auto-alignment laser interferometer

This work will report the development and application of an auto-alignment laser interferometer system for the geometric error calibration of CNC multi-axis machines. The system is capable of a diagonal displacement measurement, where multiple machine axes are moved simultaneously, with automatic optic alignment. This capability provides a solution for quick evaluation of the overall volumetric error of a multi-axis machine tool. One application of the system is that the 21 geometric errors of a 3-axis machine can be quickly estimated from the displacement measurements of some determined diagonal lines in the working volume. Compared with a time of several days using a conventional laser interferometer system, it takes only 1 hour for the proposed system to complete the geometry calibration of a 3-axis machine. A method for the roll calibration of a vertical axis is also proposed and demonstrated in this work.     

A study on accuracy of porous journal air bearing

In order to predict error motion of continuous porous journal air bearing, an accuracy model is established to reveal the relationship among error motion, roundness error and structure parameter under quasi-static conditions. Based on the model, averaging coefficient is defined to quantitatively characterize the error averaging ability. The study finds that whether the bush and shaft roundness errors match is the cause of error motion. The trilobal roundness error of shaft has a major impact on accuracy for a porous journal air bearing with an elliptical bush, while the elliptical roundness error of shaft has a major impact on accuracy for that with a trilobal bush. On the two-dimensional plane of bush wave numbers n₂ = 2~7 and shaft wave numbers n₁ = 2~15, the averaging coefficients are symmetrical along the line n₁ = n₂. The shaft wave numbers which equal integer multiples of prime numbers of bush wave number have no impact on accuracy, while the remaining shaft wave numbers have impact. Among them, those at points n₁ = n₂*i ± 1 are with obvious averaging coefficients and have a major impact on accuracy where i is a positive integer. The main peaks of averaging coefficients appear at the points n₁ = n₂ ± 1, which have the most important impact on accuracy. The theory has many potential applications such as prediction of error motion, structural optimization and selection of parts grinding method, which is of significant importance for design and testing of porous journal air bearings used widely in ultra-precision machine tools.     

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.     

Thermally induced volumetric error modeling based on thermal drift and its compensation in Z-axis

Traditional thermally induced volumetric error modeling requires 21 geometric error components at different temperatures. Taking thermal drift errors into account, 30 geometric errors are described to model volumetric error in this paper. The main sources of thermally induced volumetric error are positioning errors of each axis and thermal drift errors. An experiment on milling and boring machine is carried out, which shows that volumetric error in Z-axis is affected significantly. To compensate volumetric error of Z-axis, a model of positioning error is proposed based on nut temperature. A finite elements analysis of headstock thermal characteristic is carried out, and error chain is established, which shows the main source of thermal drift of Z-axis is ram expansion. Thermal drift compensation system of Z-axis is developed based on Invar metal and thermal error compensation module of Siemens CNC system. Therefore, the positioning error and thermal drift of Z-axis are compensated. The thermally induced volumetric error in Z-axis is reduced by 80 % after compensation.     

Simulation and experimental verification of a fuel calibration system based on metering cylinder

Simulation and experimental verification of a fuel calibration system based on hydraulic metering cylinder has been carried out in this paper. A novel hydraulic metering cylinder is designed for more accurate flow rate measurement. The calibration workbench with this cylinder is presented and mathematically modeled. Also, the calibration system is numerically simulated in AMESim. The simulation results show that the calibration system can work smoothly. In addition, the impact of given plunger speeds and calibration strokes on the accuracy of the calibration results is experimentally verified. It can be found that stroke of approximate 600 mm and a medium given speed are the most effective ways to reduce the measuring error under the experimental condition provided in this paper. Moreover, a calibration error less than 0.5% is achieved in the fuel calibration system.     

基于三轴测量机拓扑结构的单项几何误差模型

基于刚体模型和小角度假设,传统的几何误差模型采用传递矩阵建立几何误差与测量机空间误差的关系。但通过传递矩阵建立的几何误差模型难以清晰揭示各单项几何误差对空间误差的影响关系。为了更清楚地表达单项几何误差对空间误差的影响关系,基于三轴测量机拓扑结构建立了各单项几何误差模型,分析了测量机各项阿贝误差产生机制。利用所建立的单项几何误差模型分析各单项几何误差的影响权重,对自研测量机高权重几何误差进行辨识与补偿,结果表明,补偿后测量机测量直径150 mm平面与直径60 mm凹球面的PV值分别达到344.32 nm和161.74 nm,面形误差与波面干涉仪测量结果基本一致。单项几何误差模型有助于了解阿贝误差的产生机理;提出的几何误差权重计算方法有助于实现对测量机敏感误差的精确控制,指导高精度测量机结构设计与测量精度的提升。     

Volumetric error modelling of a stereo vision system for error correction in photogrammetric three-dimensional coordinate metrology

Optical three-dimensional coordinate measurement using stereo vision has systematic errors that affect measurement quality. This paper presents a scheme for measuring, modelling and correcting these errors. The position and orientation of a linear stage are measured with a laser interferometer while a stereo vision system tracks target points on the moving stage. With reference to the higher accuracy laser interferometer measurement, the displacement errors of the tracked points are evaluated. Regression using a neural network is used to generate a volumetric error model from the evaluated displacement errors. The regression model is shown to outperform other interpolation methods. The volumetric error model is validated by correcting the three-dimensional coordinates of the point cloud from a photogrammetry instrument that uses the stereo vision system. The corrected points from the measurement of a calibrated spherical artefact are shown to have size and form errors of less than 50 μm and 110 μm respectively. A reduction of up to 30% in the magnitude of the probing size error is observed after error correction is applied.     

超精密车床进给伺服系统的复合控制设计

超精密车床在非球曲面以及超光滑表面的加工中具有广泛应用.将超精密车床进给系统设计成为具有电流环、速度环和位置环的三环伺服系统结构,并根据实际伺服特性,在位置环上设计了具有速度/加速度前馈补偿的半闭环复合控制策略.通过实验数据的比较,显著提高了进给伺服系统的控制精度,减少了跟踪误差.     

Error analysis and compensation for the volumetric errors of a vertical machining centre using a hemispherical helix ball bar test

Machining accuracy is directly influenced by the quasi-static errors of a machine tool. Since machine errors have a direct effect upon both the surface finish and geometric shape of the finished workpiece, it is imperative to measure the machine errors and to compensate for them. A laser measurement system to identify geometric errors of a machine tool has disadvantages, such as a high cost, a long calibration time and the usage of a volumetric error synthesis model. In this study, we proposed a novel analysis of the geometric errors of a machine tool using a ball bar test without using a complicated error synthesis model. Also, a statistical analysis method was employed to derive geometric errors using a hemispherical helix ball bar test. According to the experimental result, we observed that geometric errors of the vertical machining centre were compensated by 88%.     

长度约束下双相机外参数不稳定定向

动态立体视觉测量技术在几何量测量特别是大视场测量中应用越来越广。在分析动态双相机立体视觉测量相对定向算法的基础上,提出了一种基于一定数量距离约束的相机不稳定定向算法。在测量场中固定放置一定数量的一维标定靶标,双相机获取标定靶标上点的中心坐标,由极线几何约束快速准确解算双相机外参数,每次测量根据标定靶重新定向相机,由靶标补偿相机在测量过程中的位置变动,保证在测量场中即使相机站位发生位置变化仍可精确测量。实验中对分布范围2.5 m×1.6 m×4.5 m测量场中90个自反射目标点进行测量,选用5对点间距离作为距离约束,并与V-STARS/S进行结果比对。结果表明在相机站位发生明显变动情况下,90个空间点三维重建位置误差小于0.160 mm,标准差小于0.042 mm。将该方法应用于合成孔径雷达测量,得到相近结果。     

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-based thermal error model for articulated arm coordinate measuring machines

The influence of thermal changes in the accuracy of articulated arm coordinate measuring machines (AACMMs) is one of their main error sources. Usually, the effects of this problem are minimized by using low thermal-expansion materials in the arm design or by implementing an empirical error correction model based on the outputs of several temperature sensors placed inside the arm. These models, inherited from temperature correction models for robot arms, are based on the empirical arm positioning error characterization of several temperatures inside its measuring range and by posterior corrections implemented using an average error approximation. Considering this approximation as a correction valid for all the temperature range violates the AACMM calibration conditions, which are defined by a kinematic parameter identification procedure at 20 °C. This implies that, by applying these models, the AACMM will work outside of calibration conditions and will not meet the nominal accuracy values obtained from the identification procedure. In this work a new empirical correction model for thermal errors is presented. This model keeps the calibration conditions established in the parameters identification procedure unaltered. This fact makes it possible to apply other correction models for geometric and non-geometric errors obtained at the calibration temperature after having applied the temperature correction. The algorithm and objective functions used, which are based on a new approach including terms regarding measurement accuracy and repeatability and using the measurements of a ball-beam gauge artifact are shown. The empirical correction model and the arm accuracy and repeatability results before and after correction are also explained, showing an important accuracy improvement in the arm performance for typical arm operation at temperatures different from 20 °C.