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.     

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.     

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.     

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。     

A new approach to thermally induced volumetric error compensation

A traditional model for thermally induced volumetric error of a three-axis machine tool requires measurement of 21 geometric error components and their variation data at different temperatures. Collecting these data is difficult and time consuming. This paper describes the development of a new model for calculating thermally induced volumetric error based on the variation of three error components only. The considered error components are the three axial positioning errors of a machine tool. They are modelled as functions of ball-screw nut temperature and travel distance to predict positioning errors when the thermal condition of the machine tool has changed due to continuous usage. It is assumed that the other 18 error components remain identical to the pre-calibrated cold start values. This assumption is justified by the fact that the machine tool’s thermal status significantly affects three axial positioning errors that dominate machining errors for a machine tool after its continuous use. To demonstrate the effectiveness of the proposed model two types of machining jobs, milling and drilling, on a three-axis horizontal CNC machining centre are simulated and the machined part profiles are predicted. The results show that the thermally induced volumetric error was reduced from 115.40 to 45.37?μm for the milled surface, and the maximum distance error between drilled holes for the drilling operation was reduced from 38.69 to ?0.14?μm after compensation.     

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 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.     

双转台五轴机床空间误差补偿技术研究

几何误差、热误差和切削力误差占到了机床总误差的75%,对这3项误差进行控制是提高机床加工精度的关键所在。以双转台五轴机床的空间误差作为研究对象,通过对加工位置、主要热源及电动机电流等相关因素进行分析,确定空间误差建模所需的位移变量、温度变量和切削力变量。以现有的多种误差建模方法为基础,通过对信息融合技术进行研究,提出一种机床空间误差的多模型融合预测方法,建立综合反映几何误差、热误差和切削力误差的最优空间误差模型。最后以DSP为核心,设计空间误差补偿器,实施空间误差补偿,验证补偿效果。结果显示,建立的模型预测精度较高,残差小于2μm,而实施空间误差补偿后,加工零件的轮廓误差也由15μm降到了5μm,补偿效果明显。     

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.     

Simple and simultaneous measurement of five-degrees-of-freedom error motions of high-speed microspindle: Error analysis

We have developed a simple and low-cost optical measurement system for the simultaneous measurement of the five-degrees-of-freedom error motions of high-speed microspindles. We demonstrated the usefulness of the system by using it to measure actual spindle rotation errors, and analyzed the major error factors. First, the measurement error due to the form error of the lens was analyzed by ray tracing. Second, we analyzed the measurement error due to a displacement of an irradiation laser point on a 3 mm diameter ball lens. Furthermore, we investigated the effect of the centrifugal force and the crosstalk problem of multiple laser beams. The results indicated that a form error of the rod lens significantly affected the measurement accuracy and that a change in the laser beam irradiation point of the ball lens due to a radial displacement had no significant effect on the measurement accuracy. Finally, we confirmed that, owing to the centrifugal force, the measurement accuracy decreased as the speed of rotation increased, and that there was no crosstalk that the reflected and transmitted laser beams in the X direction were detected by the photodiode in the Y direction for displacements within −10 to 10 μm.     

‘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.     

基于虚拟立体视觉的气液两相流三维测量系统的标定

研究了基于虚拟立体视觉的气液两相流三维测量系统的标定技术。首先,基于单台高速摄像机和两组反射镜组构建虚拟立体视觉测量系统,建立高速摄像机透视投影变换模型以及虚拟立体视觉三维测量模型,对虚拟立体视觉系统中摄像机及虚拟立体视觉传感器进行标定。用靶标基准球模拟气泡在水中的分布,以其空间距离作为测量评价指标,比较了不同标定方法对三维重建精度的影响。实验结果表明,将标定参照物置于水箱内,并且分别对左、右虚拟摄像机及传感器进行标定,三维重建精度最高,测量空间距离绝对误差优于0.13 mm,相对误差优于0.49%。实验认为,对基于虚拟立体视觉的气液两相流三维测量系统进行标定时,必须充分考虑折光分光光路以及管壁折射对三维重建所带来的影响。     

齿轮误差三维评定方法

研究了齿轮误差三维评定方法,以消除测量仪器定位误差对齿轮误差评定的影响,提高齿轮测量仪器的测量精度。分析了传统齿轮二维评定方法的弊端,提出将齿轮误差评定从二维评定模式转变为三维评定模式。该评定模式不再要求齿轮各项误差测量点位于特征面内,实现了三维空间内的齿轮误差测量与评定。为提高齿轮三维误差评定算法的效率,通过螺旋降维方法将三维数据降至二维数据,再对二维测量数据进行各项误差的评定。以特大型齿轮激光跟踪在位测量系统作为实验对象,对4级标准齿轮的齿廓误差进行了测量,并与传统的齿轮二维误差评定方法以及德国ZEISS公司InvolutePro软件的评定结果进行了对比。结果表明:传统齿轮二维误差评定方法有较大误差,三维齿廓评定方法与德国ZEISS公司InvolutePro软件评定结果一致,精度达到0.1μm,证明了提出的齿廓误差三维评定方法完全正确,可以消除仪器定位误差对测量结果的影响,提高了测量仪器的测量精度。     

激光位移传感器在自由曲面测量中的应用

以点激光位移传感器(HL-C211BE)为对象,研究它在自由曲面测量中的应用。针对激光位移传感器因测点倾角代入的测量误差,提出了一个可以量化的倾角误差模型。基于直射式点激光三角法原理,分析了激光光路的几何关系,从会聚光斑光能质心发生的偏移推导出倾角误差模型。随后,用高精度激光干涉仪和正弦规对激光位移传感器进行校对实验,并用误差模型对测量结果进行补偿。结果显示,补偿后激光位移传感器的测量精度得到明显提高。对一非球面凸透镜进行了实验测量,得到了自由曲面测点倾角的计算方法,并用倾角误差模型修正了测量数据。实验结果表明,量化的倾角误差模型可以将激光位移传感器的测量误差控制到小于10μm,满足激光位移传感器在自由曲面测量中应用的要求。     

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.     

Inverse determination of Johnson–Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search

In this paper, a systematic approach on how to predict kinematic errors based on tolerance of machine tools’ guideways is introduced. Firstly, the truncated Fourier series function is applied to fit curve of guideways surface. Since geometric profile errors are regarded as a bridge between tolerance and kinematic errors of machine tools’ guideways, the mapping relationship between tolerance and geometric profile errors of machine tools’ guideways is formulated, and the mapping relationship between geometric profile errors and kinematic errors of guideways is established. Then, kinematic errors prediction model based on tolerance of guideways is subsequently proposed. Finally, simulation verification is conducted with this method. Simulation results show the range of the predicted kinematic errors (positioning error, y direction and z direction straightness error, roll error, pitch error, and yaw error) is 17.12 μm, 56.57 μm, 70.71 μm, 28.28 μrad, 141.42 μrad, and 113.14 μrad, respectively. In order to verify the feasibility and effectiveness of the presented method, a measuring experiment is carried out on guideways of a gantry-type five-axis milling machine tools by using a dual-frequency laser interferometer. The measured and identified discrete data can be fitted precisely by Fourier curve fitting method. The fitting results show the range of the measured kinematic errors is 16.96 μm, 59.43 μm, 68.63 μm, 28.65 μrad, 135.40 μrad, and 111.58 μrad, respectively. The maximum residual errors between the predicted and measured values of kinematic errors are 1.67 μm, 5.19 μm, 5.50 μm, 1.87 μrad, 9.81 μrad, and 7.07μrad, respectively. Comparing with the measured results of kinematic errors, residual errors are considerably small and can be neglected. Therefore, there is no doubt that this method is effective enough for predicting kinematic errors and can be used to replace the measurement of kinematic errors. In the design stage of machine tools, this approach is convenient for engineers to derive the distribution of kinematic errors. And its basic idea can be applied to other type of machine tools’ guideways.     

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.     

基于立体视觉的旋翼共锥度动态测量系统精度分析

为了提高基于立体视觉的直升机旋翼共锥度动态测量系统的精度和可操作性,全面分析了其测量误差。首先,介绍了测量系统模型及误差来源;其次,分析了双目立体视觉静态三维测量的误差;再次,针对旋翼共锥度的多目标动态测量特点,分析了系统安装误差对共锥度解算精度的影响;最后,利用原理样机进行了6 058次静态测量重复实验,通过统计分析可知静态测量误差小于1.4 mm。对动态测量误差进行了仿真实验分析,给出了各参数对精度影响的量化结果,为实际共锥度测量的误差控制提供了理论依据。在标记点安装精度小于10 mm的情况下,动态测量误差小于3.5 mm,合成产生的总测量误差小于4.9 mm,能满足旋翼共锥度动态测量精度要求。     

Volumetric phase-measuring interferometer for three-dimensional coordinate metrology

We present a volumetric interferometer that has been specially designed to improve the measurement accuracy of the three-dimensional coordinate metrology by reducing excessive Abbe offsets. The interferometer is composed of two main parts; one is a three-dimensionally movable target and the other is a stationary two-dimensional array of photo-detectors. The target made of point diffraction sources emanates two spherical wavefronts, of which interference intensity is monitored by the photo-detectors. Applying phase shifting allows the phases of the photo-detectors to be precisely obtained, and the measured phases are fitted to a geometric model of multilateration so as to determine the xyz-location of the target by minimizing least square errors. A prototype built on a CMM demonstrates that the proposed interferometer is capable of measuring the xyz-coordinates of the probe with a volumetric uncertainty of less than 1.0 μm.     

用于三维变形测量的数字图像相关系统

针对材料力学实验中的三维变形测量,提出并实现了一种基于双目立体视觉、摄影测量术和数字图像相关法的便携式三维变形测量系统。研究了该系统涉及的双目摄像机标定,图像相关算法,三维重建,以及三维位移、应变计算等关键技术。提出了一种基于摄影测量术的摄像机标定算法,该算法采用10参数镜头畸变模型,不需要高精度标定板即可实现摄像机的高精度标定。利用最小二乘非线性优化算法实现了数字图像的高精度匹配,针对非线性优化初值难求的问题,提出了一种基于种子点的初值计算方法,为非线性优化提供了可靠的初值。最后,介绍了三维重建以及计算三维位移、三维应变的方法。实验结果表明,标定结果的重投影误差为0.03 pixel,图像匹配的误差约为0.02 pixel,静态外形及位移的测量精度为0.05%,应变的测量精度优于0.5%。与传统的测量方法相比,本文提出的系统可以更准确、全面、直观地实现对位移场、应变场的测量。