ANALYSIS AND MEASUREMENT FOR THE DYNAMIC ERRORS OF COORDINATE MEASURING MACHINES

The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.

CAD Model-Based Intelligent Inspection Planning for Coordinate Measuring Machines

As the market competition among enterprises grows intensively and the demand for high quality products increases rapidly, product quality inspection and control has become one of the most important issues of manufacturing, and improving the efficiency and accuracy of inspection is also one of problems which enterprises must solve. It is particularly important to establish rational inspection planning for parts before inspecting product quality correctly. The traditional inspection methods have been difficult to satisfy the requirements on the speed and accuracy of modern manufacturing, so CAD-based computer-aided inspection planning （CAIP） system with the coordinate measuring machines （CMM） came into being. In this paper, an algorithm for adaptive sampling and collision-free inspection path generation is proposed, aiming at the CAD model-based inspection planning for coordinate measuring machines （CMM）. Firstly, using the method of step adaptive subdivision and iteration , the sampling points for the specified number with even distribution will be generated automatically. Then, it generates the initial path by planning the inspection sequence of measurement points according to the values of each point＇s weight sum of parameters, and detects collision by constructing section lines between the probe swept-volume surfaces and the part surfaces, with axis-aligned bounding box （AABB） filtering to improve the detection efficiency. For collided path segments, it implements collision avoidance firstly aiming at the possible outer-circle features, and then at other collisions, for which the obstacle-avoiding movements are planned with the heuristic rules, and combined with a designed expanded AABB to set the obstacle-avoiding points. The computer experimental results show that the presented algorithm can plan sampling points＇ locations with strong adaptability for different complexity of general surfaces, and generate efficient optimum path in a short time and avoid collision effectively.

Multiple Measurement Models of Articulated Arm Coordinate Measuring Machines

The existing articulated arm coordinate measuring machines（AACMM） with one measurement model are easy to cause low measurement accuracy because the whole sampling space is much bigger than the result in the unstable calibration parameters. To compensate for the deficiency of one measurement model, the multiple measurement models are built by the Denavit-Hartenberg＇s notation, the homemade standard rod components are used as a calibration tool and the Levenberg-Marquardt calibration algorithm is applied to solve the structural parameters in the measurement models. During the tests of multiple measurement models, the sample areas are selected in two situations. It is found that the measurement errors＇ sigma value（0.083 4 ram） dealt with one measurement model is nearly two times larger than that of the multiple measurement models（0.043 1 ram） in the same sample area. While in the different sample area, the measurement errors＇ sigma value（0.054 0 ram） dealt with the multiple measurement models is about 40% of one measurement model（0.137 3 mm）. The preliminary results suggest that the measurement accuracy of AACMM dealt with multiple measurement models is superior to the accuracy of the existing machine with one measurement model. This paper proposes the multiple measurement models to improve the measurement accuracy of AACMM without increasing any hardware cost.

ERROR COMPENSATION OF COORDINATE MEASURING MACHINES WITH LOW STIFFNESS

A technique for compensating the errors of coordinate measuring machines (CMMs) with low stiffness is proposed. Some additional items related with the force deformation are introduced to the error compensation aquations. The research was carried on a moving colunm horizontal arm CMM. Experimental results show that both the effects of systematic components of error motions and force deformations are greatly reduced, which shows the effectiveness of proposed technique.

Flexible Scanning Method by Integrating Laser Line Sensors with Articulated Arm Coordinate Measuring Machines

Measuring and reconstructing the shape of workpieces have been considered as a fundamental step in both reverse engineering and product quality control.Owing to increasing structural complexity of recent products,measurements from multiple directions are typically required in current scanning techniques.Specifically,the plane structured light can be applied to measure one area of a part at a time,with an additional algorithm required to merge the collected data of each area.Alternatively,the line structured light sensor integrated on CNC machines or CMMs could also realize multi-view measurement.However,the system needs to be repeatedly calibrated at each new direction.This paper presents a flexible scanning method by integrating laser line sensors with articulated arm coordinate measuring machines(AACMM).Since the output of the laser line sensor is 2D raw data in the laser plane,our system model introduces an explicit transformation from the 2D sensor coordinate frame to the 3D base coordinate frame of the AACMM(i.e.,the translation and rotation the of the 2D sensor coordinate in the sixth coordinate system of AACMM).To solve the model,the“conjugate pairs”are proposed and identified by measuring a fixed point(e.g.,a sphere center).Moreover,a search algorithm is adopted to find the optimal solution,which noticeably boosts the model accuracy.The experimental results show that the error of the system is about 0.2 mm,which is caused by the error of the AACMM,the sensor error and the calibration error.By measuring a complicated part,the proposed system is proved to be flexible and facilitate,with the ability to measure a part expediently from any necessary direction.Furthermore,the proposed calibration method can also be used for robot hand-eye relationship calibration.

COORDINATE MEASURING MACHINE PROBING ACCESSIBILITY

The accessibility of coordinate measuring machines (CMMs) in dimensional inspection is studied. The problem of computing the global accessibility cone is solved using a method of angle representation. Otherwise, the length and volume of probe are considered sufficiently so that all the feasible probe orientations could be determined for the inspection of a workpiece when a touch trigger probe is used and the shortcoming of abstracting a probe as an infinite half line could be overcome completely. In the end, an example is given to explain the method.

Helical angle measurement of worm by a coordinate measuring machine and its uncertainty evaluation

The purpose of the study concerns the measurement of worm's helical angle by a coordinate measurement machine in the ambient industrial environment. The novel measurement method and sampling strategy were described firstly. This method used the coordinate measurement machine to measure both of the worm gear's left and right surfaces. The worm surface was reconstructed based on the measured data of all the sampling points. Then a middle cylinder was established to truncate the fitted worm surfaces, and the truncated spiral lines were straightened to calculate the helical angle. The measurement uncertainty of worm's helical angle was evaluated by taking the difference of calculated helical angles along the truncated spiral lines on both the left and right side surfaces of the worm. Twenty-four measurement experiments show that the maximum measurement error of the proposed method is 0.105, and the measurement error ratios are all less than 3.5%. The result means that the measurement method can realize the precision measurement of worm's helical angle and can be employed in the generally industrial application.

Determination of the workspace of a new coordinate-measuring machine using parallel-link mechanism

Presents the detailed algorithm established for determination of workspace for a 3-DOF coordinate measuring machine using parallel link mechanism by constructing the inverse kinematic model first and then reviewing the physical and kinematical constraints from the structural characteristics of the parallel link mechanism, and discusses the actual geometries of workspace and the factors having effect on workspace through computer simulation thereby providing necessary theoretical basis for the research and development of coordinate measuring machines using parallel link mechanism.

Cylindrical coordinate measuring machines: probe offset and workpiece clamping error

A cylindrical coordinate measuring machine for the detection of large-size rotational parts is introduced. The measuring machine can simultaneously measure the geometrical dimensions, form and position errors of the inner and outer surfaces. Since the maximum length of the workpiece can reach 2 000 mm , it is difficult to be clamped and adjusted and easy to produce clamping error. The eccentricity can be up to 1.5 mm, which has an interaction effect with the probe mounting offset. We mainly study the probe offset of the measuring machine and the influence of the workpiece clamping error on the measurement. A method of controlling the offset of the measuring probe is proposed. The effect of the clamping error is eliminated through the space coordinate transformation of the workpiece axis, and the axis is fitted by the least square method. Finally, a common fixture can be realized to meet the clamping requirements of the workpiece.

Theoretical analysis and verification of uncertainty of measurement on a cantilever coordinate measuring machine

A cantilever coordinate measuring machine(CCMM)is proposed according to the in-situ measurement requirement of workpieces with complex structures limited by the finite space of the5-axes computerized numerical control(CNC)processing site.Factors affecting uncertainty of measurement(UM)are classified and analyzed on the basis of uncertainty evaluation criteria,and the estimation technique of UM for measuring systems is presented.UM of the CCMM is estimated from the factors such as temperature,error motions as well as the mechanism deformations.Measurement results show that the actual measurement error is smaller than that of measurement requirement.

面向任务的CMM圆度测量不确定度建模与优化

精密仪器正趋向于智能化以及功能多样化发展,评估精密仪器的测量不确定度因此也变得更加复杂。以CMM中的圆度测量为例,以面向任务的不确定度评定方法,实现快速、可靠地评估出CMM测量任务的不确定度。根据误差传播的实际情况,结合计算机模拟的蒙特卡洛方法,提出了一种误差分布多状态下的不确定度代数和合成方法。针对测量不确定度初次评定存在过量估计的问题,提出了优化评估方案。给出圆度测量任务的不确定度评定与优化实例,验证评定模型和优化方法的可行性与有效性。系统性解决CMM面向任务的不确定度评定难题,对于解决其他高精度仪器测量结果的不确定度评估、提高仪器的实际使用价值,均具有重要参考意义。

Application of NURBS for Obtaining Free Form Curves and Surfaces in Spur and Helical Gears by Using CMM （Coordinate Measurement Machine）

Currently, engineering processes require reduced manufacturing time and low cost, in addition to the growing demand for workpieces with high accuracy. Workpieces with complex geometries and free forms has been a common practice in industries from different sectors such as： automotive, aeronautics, bioengineering among others. One way to satisfy the market requirements satisfactorily is making measurements more efficient to make the production process faster, in other words, it is necessary to make the inspection system more accurate and flexible. The coordinate measuring evolved over the past three decades and today it is the technology that best meets the requirements of modem manufacturing through CMMs （coordinate measurement machines）. The CMMs are important tool for design, fabrication and inspection of manufactured products, also used in the application of reverse engineering. These machines are also used by engineers in order to produce an accurate digital model in a virtual space for later use in CAD （computer-aided design）/CAM （computer-aided manufacturing）. It is worth mentioning that the accuracy of the modeling process of given piece depends on the number of control points that are captured on the workpiece surface. Consequently, the laser inspection systems are the best tools for use in reverse engineering, but more expensive when compared to contact measurement systems that use the TTP （touch trigger probe）, also used by CMMs. In this case, this paper aims to present an approach based on NURBS （non-uniform rational B-splines） to obtain free form curves and surfaces from a group of points obtained by using a contact sensor, the touch trigger probe. NURBS is an important mathematical tool and consists of generalizations of Bezier curves and surfaces and B-splines. The approach proposed in this paper can be applied for obtaining free form curves and surfaces in spur and helical gears. Experimental results obtained by measuring spur gears showed that the NURBS technique contributes for application of CMMs with touch trigger probe in reverse engineering.

ASSESSING THE DYNAMIC ERRORS OF COORDINATE MEASURING MACHINES

The main factors affecting the dynamic errors of coordinate measuring machines are analyzed. It is pointed out that there are two main contributors to the dynamic errors: One is the rotation of the elements around the joints connected with air bearings and the other is the bending of the elements caused by the dynamic inertial forces. A method for obtaining the displacement errors at the probe position from dynamic rotational errors is presented. The dynamic rotational errors are measured with inductive position sensors and a laser interferometer. The theoretical and experimental results both show that during the process of fast probing, due to the dynamic inertial forces, there are not only large rotation of the elements around the joints connected with air bearings but also large bending of the weak elements themselves.

Error separation in CMM coordinate metrology

Form error measurement is a critical exercise in providing measures for the quality control in the precision manufacturing industry.Coordinate measuring machine （CMM） is one of the automated systems used in the accurate and precise dimensional measurements and geometrical form.This paper aims to study the effect of dynamic original unforeseeable errors at different undulations per revolution （UPR） of standard artifact measurement using selected two types of CMM touchtriggering stylus.Stylus-type and stylus-speed parameters were adopted and utilized throughout the course of experiment.The results are analyzed using fast Fourier transformation to obtain foreseeable geometrical errors due to CMM machine structure and stylus scanning speeds.The results of experiment successfully indicate that the number of UPR plays an important role in determining the CMM accuracy level of the roundness measurement result.Some specific error equations for stylus system and machine structure responses have been postulated and analysed to empirically predict the accuracy of PRISMOBridge-CMM-type at National Institute for Standards （NIS） in egypt.

CMM面向任务的多测量策略测量不确定度评定

基于产品几何技术规范GPS,研究了常规测量、替代测量及补偿测量三种测量策略下的CMM面向尺寸测量任务的测量不确定度评定技术。对各测量策略下的测量不确定度影响来源进行分析和不确定度评定建模,给出具体的评定方法。通过孔径测量实例,给出应用这三种测量策略进行不确定度评定的过程,并比较评定结果,总结出这三种测量策略的优缺点及适用场合,为测量机用户根据实际需求评定面向尺寸测量任务的测量不确定度提供应用参考。

等高法叶片型面CMM测量数据处理算法研究

三坐标测量机对叶片进行测量是保证叶片加工质量的必要手段。但是其型面测量数据处理非常复杂。在分析不同叶片型面公差的基础上,提出了恒值轮廓度、变值轮廓度、正轮廓度和负轮廓度公差带的建立方法。针对叶片等高法测量,在数据处理时采用最小区域原则对测量点和理论截面轮廓线进行匹配以分离叶片叶型误差、扭转误差和弯曲变形误差,并提出了基于公差带的匹配目标函数、匹配方法和有约束的匹配原则。针对叶片叶型参数计算,提出了叶片前后缘圆弧拟合方法和最大厚度计算方法。最后通过实例表明该算法对叶型参数和误差计算的正确性。

高能光源磁铁的三坐标标定技术

针对高能同步辐射光源需要进行大批量磁铁的中心引出标定,提出了一种基于三坐标测量机的磁铁机械中心标定方案,确定了编写自动测量程序的流程和方法 ,参与完成了加速器中多种类型磁铁的标定。对176块储存环六极铁的三坐标机测量数据进行分析,结果表明:每块磁铁进行两遍机械中心标定,获得准直基准点的标定重复性在0.01 mm之内;极缝间距离的实测值与设计值标准偏差均在0.015 mm之内;标定效率相较激光跟踪仪提高了2倍。这种借助三坐标测量机的磁铁标定方法可以提高标定精度,降低人力成本,提高工作效率,能为加速器工程中磁铁中心的引出标定工作提供参考,保证加速器装置的安装顺利,满足加速器准直测量的工程进度要求。

基于三维CAD和CMM的计算机辅助检测规划系统的研究与实现

对基于三维CAD和三坐标测量机的计算机辅助检测规划(CAIP)系统的各项关键技术进行研究,给出了相关的实现算法、原理及解决思路,着重解决采样及路径规划中的相关问题。对于采样规划,指出了决定采样点数量及分布的相关因素,并提出了一种以规则采样为基础的步长自适应再分采样方法;对于路径规划,先对测量点采用按参数加权和大小排序的方法进行检测顺序规划以形成初始路径,再以碰撞检查及规避对其进行改进,生成无碰撞的检测路径。采用Microsoft Visual C++开发环境开发了CAIP系统,计算机试验验证了相关算法的可行性,结果表明该系统能高效率、智能化地完成常见零件的自动检测工作。

智能CMM检测系统中摄像机的内参数标定方法研究

集成化的ＣＭＭ智能检测系统研究的目标是利用ＣＭＭ和机器视觉系统各自的优势，实现对已知或未知ＣＡＤ模型的产品的自动检测．其中关键的一步是如何确定物体的空间尺寸与所成图象的对应关系，即高质量地完成对摄像机的参数标定工作．本文提出在实际工业现场中实现对摄像机内参数的快速、准确的测定和估计算法，并以实例证明算法的有效性．