Determination of Best Objective Function for Evaluating Geometric Deviations

Laser scanning equipment and coordinate measuring machines are used to sample points from manufactured surfaces for inspection purposes. The sampled points are then used to evaluate the geometric deviations associated with the surface. The evaluation of geometric deviations involves an optimisation step which fits a substitute surface to the measured points, while minimising the error between the substitute surface and the measured points. The geometric deviation is equal to the difference between the maximum and the minimum normal distances between the fitted surface and the measured surface points. The choice of the objective function used in fitting the substitute surface affects the accuracy by which the geometric deviations are estimated. This paper presents a procedure for determining the best fitting function. It considers the trade-off between the accuracy of the estimation and the susceptibility to measurements and sampling errors. The proposed procedure has been verified for a number of geometric deviation types. Those results show that adopting a generic form for the fitting objective function may lead to large estimation errors with some geometric deviations, and that the proposed procedure reduces these errors significantly.     

螺纹参数测量中工件定位误差分析和补偿

利用齐次坐标变换方法从理论上研究了单针扫描式螺纹测量仪的工件定位误差模型,并考虑探针尖头的几何形状,建立了更加精准的曲线方程。以该曲线作为最小二乘拟合曲线,根据数学模型的特点和参数的取值范围,采用改进的单纯形-模拟退火(SMSA)算法,通过对标准件的测量,求解模型参数,补偿对应误差,减小了简单直线拟合的模型误差。基于该方法,在自主研发的测针式螺纹测量仪上进行了实验验证,结果表明,所述模型更符合实际情况,能够有效地减小工件定位误差。     

在三坐标测量机上精确测量渐开线圆柱齿轮的齿形误差

针对传统齿形误差测量方法的测量误差来源多、测头与工件安装调整误差大等缺点,提出一种在三坐标测量机上利用扫描法实现渐开线圆柱齿轮齿形误差测量的新方法。该测量方法具有测量采集点精度高、齿形轮廓曲线拟合误差小、测量过程与误差处理过程人工干预少、测量精度高等特点。     

基于FLANN和最小二乘的磁梯度计误差校正

在基于偶极子磁场分量梯度的水下磁异常定位方法中,三轴磁力计自身误差及两磁场坐标系配准误差等是限制水下定位精度的主要因素,因此有必要对其进行校正,补偿磁场分量梯度计测量值。建立了磁场分量梯度计的测量误差模型,提出了基于函数链接型神经网络(functional link artificial neural network,FLANN)和最小二乘法的磁场分量梯度计误差校正方法,给出了误差参数辨识及校正算法,数值仿真和实测数据证明了校正算法具有良好的收敛性,能显著地抑制磁场分量梯度测量误差,该校正方法为提高磁场分量梯度计性能提供了一种可行途径。     

一种以测量关键特征拟合舱段位姿的方法

受工艺条件和产品性能限制，在舱段上无法事先加工用于测量其位姿的基准点。为此提出了一种以测量及拟合关键特征获取舱段位姿的方法。首先根据舱段结构特点提取舱段上满足装配精度要求的关键特征并利用激光跟踪仪测量。利用2σ准则剔除关键特征测量数据中粗差异常点，以改进基于经典测量平差理论中的最小二乘法在处理粗差时容错性较差的问题。然后利用处理后的关键特征数据拟合舱段坐标系原点及各坐标轴方向的单位向量，最终得到舱段的位姿参数。仿真试验结果表明：经改进的最小二乘法在拟合舱段位姿时能获得更高的精度；所提出的位姿拟合方法的实用性和通用性不仅能满足舱段位姿测量与计算需求，也能为其他刚体位姿求解提供参考。     

Modeling method for assembly variation propagation taking account of form error

The propagation of variations, such as fixture errors and datum errors resulting from assembly and machining processes, has been extensively studied. However, only a few studies that focus on form error propagation in assembly systems have been implemented. Machining errors, especially form errors, have great impact on assembly accuracy and accuracy stability of precision mechanical systems. With form errors being the research object, a method for calculating mating variation and specifying mating coordinate is proposed to improve the accuracy of the variation propagation model. Taking into account the form error of mating surfaces, the assembly variation propagation of a precision mechanical system is analyzed, and the brief derivation procedure of the variation propagation model is introduced afterwards. The variation propagation model involves a new concept of mating variation specified by the two mating surfaces. An innovative method, the difference surface search based method, is proposed to calculate the mating variation amongst the mating surfaces. The obtained mating variation is then utilized to specify the mating coordinate in the variation propagation model. Moreover, FEM is employed to simulate the contact state of the two mating surfaces to demonstrate effectiveness of the proposed method. Meanwhile, the mating variation and mating coordinate obtained are incorporated into the assembly variation propagation model, which is then verified by a following case study through a comparison between the calculated results and the experimental results. The comparing results indicate that the established model improves the prediction of assembly accuracy. The developed model enables the investigation of various fundamental issues in variation reduction, including variation analysis, process monitoring, accuracy prediction, and accuracy control.     

复杂曲面零件在线检测与误差补偿方法

复杂曲面零件的高精度加工与精密检测一直是数字化制造领域的研究热点。为提高复杂曲面零件的加工精度、检测精度,提出一种集数控机床在线检测、加工误差分解与补偿加工为一体的集成化方法。介绍集成化在线检测方法及补偿系统的基本原理,分析数控加工后曲面零件测点数据的误差组成,提出一种基于空间统计分析的加工误差分解方法,在建立基于B样条曲面的确定性曲面回归模型的基础上,对回归模型残差进行空间独立性分析,分解出系统误差和随机误差,进而通过数控代码的修改,实现零件加工过程的系统误差补偿。列举一个曲面零件的加工与检测实例,进行方法有效性验证。通过加工工件的在线检测、误差分解、代码修改及补偿加工等环节,实例零件的加工精度有了大幅提高,而该系统的检测精度也通过与三坐标测量机(Coordinate measuring machine, CMM)检验结果的对比,得到了有效验证。     

便携式坐标测量仪的最佳测量位姿研究

提出了一种利用现有五自由度便携式坐标测量仪提高工件测量精度的测量方法。该方法在已知设备关节转角随机误差量及测量点的情况下,通过反求各关节处可能的角度值,并在相应的各关节转角组合下,加入转角的随机误差量,重构相应姿态下的测头坐标,然后与已知测量点比较得出该姿势下受角度随机误差影响的最大值,不同的位姿对应不同的最大值,把最小的一个最大值对应的位姿作为最优测量位姿。文中通过引入两球模型和间接球法,大大的减少了反求角度过程中的计算量。     

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.     

[误差建模及精度保证方法]双五轴数控铣削机床旋转轴误差辨识方法

为了快速、系统地辨识双五轴数控铣削机床旋转轴几何误差,提出了一种基于R-test的误差测量辨识方法。根据R-test误差模型研究误差测量值与各项误差参数的关系,辨识旋转轴各个几何误差项以得到旋转轴的安装误差和运动误差;利用最小二乘法原理平面圆拟合和直线拟合的方法分别辨识出2项位移误差和2项垂直度误差;基于多体系统理论及齐次坐标变换方法建立刀具坐标系与工件坐标系的齐次坐标变换模型,并辨识出3项移动误差和3项转动误差;最后,根据所得辨识值对X向和Y向位移误差进行补偿。实验结果表明,补偿后X向和Y向位移误差明显减小,误差补偿结果验证了测量、辨识的准确性和有效性。     

基于自适应采样的曲面加工误差 在机测量方法

基于模具在机测量的自适应采样结果,提出一种新的获取自由曲面加工误差的方法。该方法首先基于自适应采样获取加工曲面上少量测点的坐标数据,利用NURBS曲面重构来拟合加工曲面;然后基于广义牛顿法计算重构的实际曲面和理论曲面的法向距离,获得自由曲面的加工误差,并对实验加工的模具模型曲面的轮廓度误差进行分析。实验结果表明,基于自适应采样的加工曲面重构方法能够在机测量且有效地获得自由曲面加工误差。     

Calibration of laser beam direction for optical coordinate measuring system

For the purpose of measuring free form surfaces of some key parts in the aviation field accurately and effectively, such as blades, a non-contact optical coordinate measuring system is set up in the paper. A laser displacement sensor is mounted on the Z axis of a CMM via a turntable and adjusted to the suitable orientation according to the shape of the target surface. The combination of optical sensor and CMM can reach the full potential of them both. To enable the laser sensor to perform measurement in every direction, a calibration method used to determine the laser beam direction based on a standard sphere is proposed, the principle of which is analyzed in detail in the paper. In the calibration procedure, the sensor moves at an equal step along X, Y and Z axes respectively and then equation sets are established to calculate the unit direction vector of the line which the laser beam is on. In the process of solving the unknown quantities, a new parameter substitution method is applied. Finally, a gauging block and a sphere with known size are used to verify the method. As the experimental results show, the measuring errors in several directions are all smaller than 0.05 mm, which manifests that the calibration method proposed can meet the requirements of reverse engineering.     

A Hole-Plate Artifact Design for the Volumetric Error Calibration of CMM

To measure the volumetric error of coordinate measuring machines (CMMs), a hole-plate artifact method was studied. Example designs of the hole-plate are shown using titanium and ceramic materials. The deflection by its own weight of the designed hole-plate is analysed using the finite element method. The hole distances moved by the deflection are shown in different hole-plate set-up cases, for vertical and horizontal positions. The influence of inside hole roundness as a measuring standard is also studied. Eccentric errors for different hole roundness are simulated. The hole-plate set-up errors are also discussed. A method for obtaining the parametric errors of a CMM is shown using the hole-plate as a measuring artifact for CMM positioning error. In addition, a method for measuring 2D and 3D length errors using the hole-plate data is introduced.     

Least squares evaluations for form and profile errors of ellipse using coordinate data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.     

三坐标测量机动态误差的建模方法

为了提高三坐标测量机的测量速度,缩短测量周期,分析了影响给定的三坐标测量机动态误差的因素。对三坐标测量机的具体和了分析,用电感测微仪进行了动态偏转角的测量,并推导出由动态偏转误差得到测头处的动态位移误差的方法。同时,对由导轨的直线度造成的误差进行了讨论。指出动态误差主要是由各构件绕气浮导轨连接处的偏转和各运动构件本身的弯曲变形造成挫理论上可以证明,在气浮导轨力矩刚度和横梁弯曲刚度已知的情况下,只要     

Three-dimensional profile stitching measurement for large aspheric surface during grinding process with sub-micron accuracy

A novel measurement method is proposed to realize three-dimensional (3D) profile stitching for large aspheric surface. The proposed method is based on the multiple sub-regions stitching technology applying a four-axis fixture and a commercial small-range profiler. The partition of sub-regions is due to the effective profiler’s range and the characteristic parameters of aspheric surface, and the measurement for each sub-region within the profiler’s range is achieved through the fixture to translate and rotate the aspheric surface. Then a stitching algorithm including the multi-body theory, the invariability of curvature radiuses and the least square principle is established to reconstruct the full 3D profile. Simulations of multiple sub-regions stitching for different aspheric surfaces are performed to predict the stitching accuracy of proposed method and analyze the influence of alignment errors in Y direction caused by the rotation error along Z direction (Δβ_w,g). The stitching accuracy of proposed method is verified by measuring the 3D profile of an off-axis parabolic surface and an axisymmetric aspheric surface. The experimental standard deviations of stitching errors are 0.16 μm and 0.42 μm, which are less than the form errors of aspheric surface during grinding process. The results show that the proposed method achieves 3D profile stitching for large aspheric surface with sub-micron accuracy.     

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.     

Reliability of roughness measurements using contact stylus instruments with particular reference to results of recent research at the Physikalisch-Technische bundesanstalt

Even today international comparison measurements of surface roughness show differences of 40% and more, as they did more than 10 years ago. However, within the framework of the Deutscher Kalibrierdienst, differences occurring in comparison measurements do not exceed 5%. At the end of 1982, a project of the European Communities was started for the purpose of also carrying out comparison measurements yielding small differences. The prerequisites are the following: clearly defined surface roughness parameters including details of the measurement conditions required and calibration and testing of the contact stylus instruments before the comparison measurements are made.In recent years the contacting process, the interaction between stylus and surface, has been the subject of very thorough investigations at the Physikalisch-Technische Bundesanstalt. Elastic and plastic deformations of the surface were examined. The parameters of influence are the geometry of the stylus tip and of the surface under examination, the properties of the materials, the static and dynamic measuring forces and the rate of feed. Calculation methods for optimizing these parameters are stated in order to keep the resulting measurement errors as small as possible. A new contactless measuring method is described which is based on the evaluation of scanning electron microscopy stereo pairs. An error analysis makes precision measurements possible which up to now could not be carried out at all. Examples examined have shown that sometimes, particularly on finely ground surfaces, measurements with contact stylus instruments on surfaces with R_z values below 1 μm can be very significantly in error.     

Form Error Characterisation by an Optical Profiler

Form errors are deviations of the machined surface from the geometrical surface excluding position errors, waviness and roughness. From a functional point of view, as for surface roughness, form error characterisation is also important. In the present work, an optical profiler is used to measure and numerically characterise form errors such as roundness and cylindricity of cylindrical surfaces. A double orientation method using mean value analysis has been applied to separate the workpiece error from the spindle error during roundness measurement. Software is developed for data generation, fitting the reference data for assessing form errors in terms of statistical and functional parameters including new parameters. An optical profiler measures all the surface irregularities and hence can be used to study both micro and macro errors of the profile measured. A study of both roughness and roundness parameters along the circumferential direction is made for the unfiltered signal using different filter cut-off values. It is known that filtering greatly affects the value of the form error parameters measured. The form measurements obtained by the optical profiler are compared with the stylus profiler and the results are presented.     

Investigation of error separation for three dimensional profile rotary measuring system

High precision 3D profile rotary measuring systems for large diameter workpieces are urgently needed in precision engineering. Error separation is critical for improving the accuracy of the system. In order to obtain higher accuracy for 3D profile rotary measuring systems, the random and systematic errors are analyzed and separated in this paper. In the measuring system, roll and pitch caused by the probe tilt violate the Abbe principle. Roll is removed by using two probes and pitch is separated by the interferometer method. The radial run-out and the perpendicularity error between the probe and the spindle axis are compensated by a two-probe-two-step method carried out on a standard hemisphere artifact. As the form error of the artifact is mixed with the perpendicularity error, the least-squares method is applied to fit the hemisphere and work out the perpendicularity error and the profile error of the hemisphere. Finally, numerical validation is presented using Matlab program to demonstrate the effectiveness and correctness of the proposed method.