Spatial Expression of Assembly Geometric Errors for Multi-axis Machine Tool Based on Kinematic Jacobian-Torsor Model

Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool.And it cannot be eliminated due to the error propagation of components in the assembly process,which is generally non-uniformly distributed in the whole working space.A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice.However,the expression ranges based on the standard quasistatic expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool.To address this issue,a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors.Firstly,an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies,respectively.Furthermore,based on the proposed kinematic Jacobian-Torsor model,a spatial expression of geometric errors for the multi-axis machine tool is given.And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools.The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors.

Monte Carlo Method for the Uncertainty Evaluation of Spatial Straightness Error Based on New Generation Geometrical Product Specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.

STUDY ON NEW METHOD OF IDENTIFYING GEOMETRIC ERROR PARAMETERS FOR NC MACHINE TOOLS

The methods of identifying geometric error parameters for NC machine tools are introduced. According to analyzing and comparing the different methods, a new method-displacement method with 9 lines is developed based on the theories of the movement errors of multibody system (MBS). A lot of experiments are also made to obtain 21 terms geometric error parameters by using the error identification software based on the new method.

Geometric Approximation Searching Algorithm for Spatial Straightness Error Evaluation

Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to the minimum condition principle of form error evaluation, the mathematic model and optimization objective of the GASA are given. The algorithm avoids the optimization and linearization, and can be fulfilled in three steps. First construct two parallel quadrates based on the preset two reference points of the spatial line respectively;second construct centerlines by connecting one quadrate each vertices to another quadrate each vertices;after that, calculate the distances between measured points and the constructed centerlines. The minimum zone straightness error is obtained by repeating comparing and reconstructing quadrates. The principle and steps of the algorithm to evaluate spatial straightness error is described in detail, and the mathematical formula and program flowchart are given also. Results show that this algorithm can evaluate spatial straightness error more effectively and exactly.

Modeling, identification and compensation for geometric errors of laser annealing table

In order to improve the process precision of an XY laser annealing table, a geometric error modeling, and an identification and compensation method were proposed. Based on multi-body system theory, a geometric error model for the laser annealing table was established. It supports the identification of 7 geometric errors affecting the annealing accuracy. An original identification method was presented to recognize these geometric errors. Positioning errors of 5 lines in the workspace were measured by a laser interferometer, and the 7 geometric errors were identified by the proposed algorithm. Finally, a software-based error compensation method was adopted, and a compensation mechanism was developed in a postprocessor based on LabVIEW. The identified geometric errors can be compensated by converting ideal NC codes to actual NC codes. A validation experiment has been conducted on the laser annealing table, and the results indicate that positioning errors of two validation lines decreased from ±37 μm and ±33 μm to ±5 μm and ±4.5 μm, respectively. The geometric error modeling, identification and compensation method presented in this work can be straightforwardly extended to any configurations of 2-dimensional worktable.

Development of analysis model for geometric error in turning processes

A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed.In the first analyzing step,the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge.Also,the deformation of a workpiece was estimated in the second step using the ANSYS.The deformation was analyzed for a 150 mm-long workpiece at three different measuring points,such as 10,70 and 130 mm from a reference point,and the amounts of the deformation were compared through experiments.In the results of the comparison and analysis,the values obtained from these comparison and analysis represent similar tendencies.Also,it is verified that their geometric errors increase with the increase in temperature.In addition,regarding the factors that affect the deformation of a workpiece,it can be seen that the geometric error in the lathe is about 15%,the error caused by the cutting force is about 10%,and the deformation caused by the heat is about 75%.

Geometric error measuring,modeling,and compensation for CNC machine tools:A review

Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining quality of manufactured parts,it has been a popular topic for academic and industrial research for many years.A great deal of research work has been carried out since the 1970s for solving the problem and improving the machining accuracy.Researchers have studied how to measure,detect,model,identify,reduce,and compensate the geometric errors.This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors.Recent advances in measuring the geometrical errors of machine tools are summarized,and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively.Besides,volumetric geometric error modeling,tracing,and compensation techniques for five-axis machine tools are emphatically introduced.Finally,research challenges in order to improve the volumetric accuracy of machine tools are also highlighted.

A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.

A SCR method for uncertainty estimation in geodesy non-linear error propagation: Comparisons and applications

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC(Monte Carlo), SUT(scaled unscented transformation), and SI(sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time, namely, SCR(spherical cubature rule), which is no need for setting parameters. By theoretical derivation, we prove that the precision of uncertainty obtained by SCR can reach second-order. We conduct four synthetic experiments, for the first two experiments, the results obtained by SCR are consistent with the other three methods with optimal setting parameters, but SCR is easier to operate than other three methods, which verifies the superiority of SCR in calculating the uncertainty. For the third experiment, real-time calculation is required, so the MC is hardly feasible. For the forth experiment, the SCR is applied to the inversion of seismic fault parameter which is a common problem in geophysics, and we study the sensitivity of surface displacements to fault parameters with errors. Our results show that the uncertainty of the surface displacements is the magnitude of ±10 mm when the fault length contains a variance of 0.01 km^(2).

Geometric Properties of AR(q) Nonlinear Regression Models

This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].

标准钢卷尺计量比对关键技术研究

标准钢卷尺是线纹计量器具检定系统中的三等线纹标准,用于我国大量钢卷尺等带状工作线纹尺的量值传递。为了保障我国标准钢卷尺的量值一致性,并科学评估我国计量机构标准钢卷尺的测量校准能力(CMC),中国计量科学研究院主导组织了首次全国标准钢卷尺计量比对(项目编号2019-B-05)。介绍了比对的基本情况、方案及比对结果,分析了比对结果及参比装置,研究了标准钢卷尺校准中关键技术问题及主要误差来源,提出了解决问题的方法,以推动标准钢卷尺量值校准能力的提升。

舵类结构件几何量误差视觉检测方法及误差评定

针对现有接触式测量方法装夹定位后只能测量一种或两种参数、检测效率低等问题,提出一种舵类结构件几何量误差和装配误差视觉检测方法。首先,利用计算机视觉系统获取舵轴和舵面区域图像,利用图像预处理技术去除图像畸变和噪声,为了更有效地提取舵类结构件边缘,分别采用Sobel算子、Scharr算子、Laplace算子和Canny算子对图像进行边缘检测以确定轮廓,实验对比发现Scharr算子处理后的舵轴图像边缘更清晰且无间断,Canny算子处理后的摇臂图像边缘比较清晰,因此选用Scharr算子提取舵轴图像边缘、Canny算子提取摇臂图像边缘。结合被测要素特点,采用霍夫直线和霍夫圆检测方法提取舵面边缘线特征、舵轴母线特征、摇臂圆轮廓特征;确定了舵芯对称度、舵轴垂直度、摇臂夹角的基准要素,构建了几何量误差检测目标函数,运用自适应遗传算法计算最优解;结合相机标定的内外参矩阵,得到舵芯对称度、舵轴垂直度、摇臂夹角的测量值。最后,研发了舵类结构件几何量误差和装配误差视觉检测软件,搭建了视觉检测实验平台,实现了几何量误差及装配角度误差快速检测功能。经过多次重复测量实验,对称度检测精度达到0.055 mm,垂直度检测精度达到0.225 mm,装配角度检测精度达到0.772°,完成单次检测耗时7 s。该方法不仅提高了几何量误差检测精度和检测效率,同时有助于提高舵类结构件成型-制造-在机检测的自动化和智能化水平。

精密镗床旋转轴几何误差完备性测量与辨识

针对四轴卧式镗床旋转轴需测几何误差的数目不统一与完备性缺失的问题,提出了基于形状创成函数的四轴卧式镗床旋转轴PIGEs形成机理分析方法与旋转轴完备几何误差测量辨识方法。基于形状创成机理构建了卧式镗床几何误差创成函数,确定了旋转轴可通过误差补偿进行调整的最少与位置无关的几何误差(Position-independent geometric error, PIGEs)数目。建立了卧式镗床旋转轴4项PIGEs、6项与位置有关的几何误差(Position-dependent geometric error, PDGEs)、6项安装误差(Setup error, SEs)与球杆仪(Double ball bar, DBB)测量轨迹半径之间的完备性函数模型,设计了基于DBB的四轴联动Viviani曲线测量轨迹,构建了旋转轴6项PDGEs的NURBS表征与PIGEs、SEs辨识方法。开展了误差补偿对比实验验证,结果表明,利用几何误差完备性测量与辨识结果进行误差补偿,较仅单一补偿6项PDGEs可提升圆轨迹测量精度40.69%。

五轴数控机床旋转轴综合误差测量与辨识

针对五轴数控机床旋转轴的运动误差和几何误差的综合评估问题,在不考虑直线轴运动误差影响的情况下,提出了一种采用R-test测量仪的测量及其辨识方法。首先,测量过程按照参考球的两种不同高度设置进行,仅移动旋转轴,而不移动直线轴。其次,利用R-test测量仪对旋转轴的运动精度进行了测量。此外,假设旋转轴位置几何误差和工作台上参考球的设置误差是影响测量结果的因素,并通过最小二乘法对这些因素进行分离。采用IBS公司的R-test测量仪,对米克朗公司UCP800Duro立式五轴加工中心C轴的运动误差和几何误差进行了测量实验。研究结果表明,该方法能够正确识别旋转轴的运动误差和几何误差,可以有效地综合评估旋转轴的运动精度,并有助于进一步提高旋转工作台的精度。

曲轴综合测量机几何误差建模及敏感性分析

为提高曲轴综合测量机测量精度,针对其几何误差元素多,逐一进行补偿工作量大、过程繁琐等问题,基于多体系统理论和齐次坐标变换建立曲轴综合测量机的几何误差模型,采用Sobol敏感性分析方法进行分析,识别出对测量精度影响较大的关键几何误差项。通过对曲轴综合测量机随动测板不同位置处的误差元素敏感性系数进行分析计算,从21项几何误差中识别出10项对曲轴综合测量机测量精度影响较大的关键项,为合理经济地提高曲轴综合测量机测量精度提供依据。

基于贝叶斯动态模型的激光干涉仪漂移误差预测

针对长时间测量时激光干涉仪产生的漂移问题,提出了一种基于贝叶斯动态模型的漂移误差预测方法。通过采集非测量阶段的漂移误差序列,分析了数据特征并据此建立了贝叶斯动态模型。然后,利用无信息先验分布法获取了递推所需的初始信息,运用贝叶斯递推算法训练并估计了模型状态参数。最后,基于实验室自制的迈克尔逊激光干涉仪对漂移误差预测效果进行了实验验证。结果表明:与常用的最小二乘拟合法和神经网络建模法相比,基于该方法预测补偿后的残余漂移误差的均方差分别减小了67.85%和99.08%;由重复实验的预测效果可知,残余漂移误差的均方差较补偿前都减小了82%以上。验证了提出的基于贝叶斯动态模型的漂移误差预测方法的有效性和稳健性。

数控机床几何误差单轴五次测量与辨识方法

针对数控机床几何误差项的准确测量与辨识问题,提出了一种基于激光干涉仪的机床空间几何误差单轴五次测量与辨识方法。首先,针对X、Y、Z轴分别设置了一条测量线,测量了3条划定线上除滚转误差外的其他15项几何误差,共计15次测量;然后,分析了转角误差对直线度误差以及直线度误差对定位误差的耦合影响,并建立了误差辨识方程组;最后,根据误差辨识方程组,得到了机床21项几何误差;并进行了单轴五次测量法的测量和辨识实验,并将所得结果与空间九线法测量辨识结果进行了对比分析。研究结果表明:单轴五次测量法与空间九线法测量辨识结果的空间误差向量最大偏差为1.93μm,平均偏差为0.58μm,该结果验证了单轴五次测量法是准确和有效的。该方法考虑了实际测量过程中的误差耦合情况,因此相比于空间九线法,该方法减少了测量线数与测量次数,简化了误差项的求解过程;同时,采用单轴运动方式可以有效避免其他轴对当前运动轴误差的影响。

几何变换在圆柱度评定优化算法中的研究

针对利用最小区域方法评定圆柱度时速度慢、算法复杂等问题,采用降维策略进行优化。在原有最小区域法几何模型的基础上利用最小二乘拟合轴线,建立了一种改进的圆柱度评定几何模型。通过对测量数据进行几何变换,将三维圆柱面转化为二维平面,根据最小条件原则将转换后的平面度误差,等效为原始测量数据的圆柱度误差值。经实验验证,在满足精度要求的前提下,圆柱度误差计算速度相较于现有最小区域法提升了约20%。实验结果表面,利用几何变换方法进行误差评定具有实用价值。

基于激光扫描仪的点云配准方法

针对激光扫描仪实际扫描得到的不完整点云配准困难问题,提出了一种基于对应点对的配准方法。通过激光扫描仪进行实验,得到被测工件的实测点云数据,基于Visual Studio软件配置Point Cloud Library环境,对实测模型与理想模型的点云配准进行研究。首先对实测点云数据进行体素滤波以及均匀下采样的预处理;其次通过对应点对的方式进行对齐为后续精细配准提供较好的变换初值,后基于ICP算法实现点云配准精配准;最终以均方根误差作为点云配准精度评价指标对配准结果进行评价。借助CloudCompare软件对配准结果进行直观展示分析可知,在实测工件本身存在不绝对光滑的情况下,配准的均方根误差可控制在0.62 mm,表明该方法对于不完整点云的配准效果较好。