Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement.We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control(CNC)machine tools.This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method.We consider a three-axis gantry-type CNC machine tool,and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain.The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle.A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg-Marquardt nonlinear least squares method,and the geometric error is solved using Taylor’s first-order linearization iteration.The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer.For a volume of 800 mm×1000 mm×350 mm,the maximum differences of the linear,angular,and spatial position errors were 2.0μm,2.7μrad,and 12.0μm,respectively,which verifies the accuracy of the proposed algorithm.This research proposes a modeling method for the precise measurement of errors in machine tools,and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

INSTRUMENT FOR MEASURING GEOMETRIC ERRORS OF GUIDE RAIL OF ELEVATOR

A new instrument for checking the quality of elevator guide rails is introduced.With this instrument,the general geometric errors such as straightness,flatness,squareness,twist,thickness and height can be measured automatically,simultaneously in a short time with high accuracy.It is very useful for elevator guide rail factories to improve their work efficiency and the quality of their products.

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.

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. /n 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 workpiecc, 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 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.

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.

Design, Development and Geometric Error Analysis of an Aerostatic Rotary Table

Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of several configurations for manufacturing or inspection of parts with complex geometries. The demand for high accuracy, high efficiency and fewer errors in the positioning of the part in precision machines increases every day, thus ensuring their high confidence and the use of aerostatic bearings enable constructive innovations to the equipment. In this context, this work presents the mechanical design, the development and error analysis of a prototype of an aerostatic rotary table. This study emphasizes the analysis of a prototype that uses the air as a working principle for reducing friction between moving parts, increasing the mechanical efficiency, and its influence of motion error is also discussed based on the experimental results. For the geometrical errors analysis, experimental tests were realized in laboratory using a DBB （Double Ballbar）. The tests are performed with only one axis moving, observing the behavior of the system for different feedrate at the C-axis.

Complex geometric modeling and tooth contact analysis of a helical face gear pair with arc-tooth

A complex geometric modeling method of a helical face gear pair with arc-tooth generated by an arc-profile cutting(APC)disc is proposed,and its tooth contact characteristics are analyzed.Firstly,the spatial coordinate system of an APC face gear pair is established based on meshing theory.Combining the coordinate transformation matrix and the tooth profile of the cutter,the equations of the curve envelope of the APC face gear pair are obtained.Then the surface equations are solved to extract the point clouds data by programming in MATLAB,which contains the work surface and the fillet surface of the APC face gear pair.And the complex geometric model of the APC face gear pair is built by fitting its point clouds.At last,through the analysis of the tooth surface contact,the sensitivity of the APC face gear to the different types of mounting errors is obtained.The results show that the APC face gear pair is the most sensitive to mounting errors in the tooth thickness direction,and it should be strictly controlled in the actual application.

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].

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.

Load-induced error identification of hydrostatic turntable and its influence on machining accuracy

In heavy duty machine tools, hydrostatic turntable is often used as a means for providing rotational motion and supporting workpiece, so the accuracy of turntable is crucial for part machining. In order to analyze the influence of load-indcued errors on machining accuracy, an identification model of load-induced errors based on the deformation caused by applied load of hydrostatic turntable of computerized numerical control(CNC) gantry milling heavy machine is proposed. Based on multi-body system theory and screw theory, the space machining accuracy model of heavy duty machine tool is established with consideration of identified load-induced errors. And then, the influence of load-induced errors on space machining accuracy and the roundness error of a milled hole is analyzed. The analysis results show that load-induced errors have a big influence on the roundness error of machined hole, especially when the center of the milled hole is far from that of hydrostatic turntable.

A general framework for progressive point-sampled geometry

Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic properties of the pro- gressive point-sampled geometry are characterized. Another distinct feature of the proposed framework is its compatibility with most previously proposed surface inference engines. Given the proposed framework, the performances of four representative well-reputed engines are studied and compared.

The Quantification of Intra-Fractional Tumour Motion Errors in Lung Stereotactic Ablative Radiotherapy Patients

This work aims at quantifying intra-fractional motion errors and evaluating the appropriateness of a Planning Target Volume (PTV) margin for Queen Elizabeth (QE) Hospital’s patients. Intra-fractional motion errors were quantified for 29 patients who underwent lung Stereotactic Ablative Radiotherapy (SABR) treatment at the cancer centre of QE Hospital. One hundred thirty post-Cone Beam Computed Tomography (CBCT) scans were collected to calculate these errors. In terms of the adequacy of a PTV margin, the intra-fractional motion errors that were calculated are combined with other geometric errors which were taken from historical audit studies. Then, the combined outcome was compared with the common PTV margin that is delineated by most United Kingdom (UK) oncology centres. The findings of this study showed that the systematic component of intra-fractional motion error is equal to 0.08, 0.08 and 0.08 cm in right/left, superior/anterior and anterior/posterior directions, respectively, While the random component of this error is equal to 0.11, 0.13 and 0.14 cm. In addition to that, a PTV margin of 0.5 cm is the appropriate margin for QE Hospital’s patients and this volume is compatible with the common PTV margin that is delineated by the most UK oncology centres. This work concluded that A PTV margin of 0.5 cm is the suitable volume for lung SABR patients at QE Hospital.

Embedded sensor system for five-degree-of-freedom error detection on machine tools

Any linear stage of machine tool has inherent six-degree-of-freedom(6-DOF)geometric errors.Its motion control system,however,has only the position feedback.Moreover,the feedback point is not the commanded cutting point.This is the main reason why the positioning error along each axis and the volumetric error in the working space are inevitable.This paper presents a compact 5-DOF sensor system that can be embedded in each axis of motion as additional feedback sensors of the machine tool for the detection of three angular errors and two straightness errors.Using the derived volumetric error model,the feedback point can be transferred to the cutting point.The design principle of the developed 5-DOF sensor system is described.An in-depth study of systematic error compensation due to crosstalk of straightness error and angular error is analyzed.A prototype has been built into a three-axis NC milling machine.The results of a series of the comparison experiments demonstrate the feasibility of the developed sensor system.

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。

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。

高速接触网静/动态几何参数及误差特性

接触网几何状态是决定高铁供电安全与弓网受流质量的关键因素。根据接触网静/动态属性,明确接触网静/动态几何参数与静/动态检测涵义。针对接触网动态检测时车辆姿态变化、轨面弹性变形、接触线动态抬升与环境扰动问题,开展动力激扰下接触网几何动态检测复合误差形成机理与补偿方法研究。通过轨道、车辆、接触网系统动力耦合及环境扰动作用下复合误差分解、溯源与辨识,分析车辆姿态误差特性及其表征模型,结合轨面弹性变形、接触线动态抬升、风载动态响应,阐述轮轨、弓网、风场多重耦合下接触网几何动态检测误差补偿方法。旨在揭示动力激扰作用下接触网几何动态检测误差产生、传播、复合与演变过程,形成面向高速接触网几何动态检测的复合误差控制基础理论方法,为提高我国接触网检测水平和保障接触网高品质维修起到科学有效的促进作用。

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。