High-accuracy roundness measurement by a new error separation method

This paper presents a new error separation method for accurate roundness measurement called the orthogonal mixed method. This method uses the information of one displacement probe and one angle probe to separate roundness error from spindle error. This method was developed from the mixed method, which uses the information of two displacement probes and one angle probe to carry out the error separation. In the present paper, the relationship between the characteristics of the mixed method and the probe arrangement is analyzed. Well-balanced harmonic response of the mixed method is verified to be obtainable for the case where the angular distance between the displacement probe and the angle probe is set at 90°. This orthogonal mixed method also had the simplest probe arrangement, because it requires only one displacement probe and one angle probe to realize the error separation. Optical probes were used to construct an experimental measurement system that employs the orthogonal mixed method. The displacement probe and the angle probe both use the principle of the critical angle method of total reflection, and they have stabilities of 1 nm and 0.01 in., respectively. The measurement results show that roundness measurement can be performed with a repeatability on the order of several nanometers.     

三点法中测头最佳角位置的确定方法

论述了三点法圆度及轴系运动误差测量系统中确定三个测头最佳角位置的方法。通过分析测头读数误差对圆度各次谐波测量精度的影响,提出了确定三个测头最佳角位置的优化策略,基于MonteCarlo思想和单纯形模式搜索方法编制了高效、高精度的寻优程序,优化得到三个测头的最佳角位置。研究表明：在误差分析的基础上对三个测头的角位置进行优化能很好地解决三点法圆度测量形状失真问题,随机模式搜索寻优是确定测头最佳角位置的有效手段。     

三点法中测头角位置的精密测量方法

研究了三点法圆度及轴系误差测量中测头角位置的精密测量方法。设计了能直接测量非接触电容传感器测头实测状态下的角位置的测角系统,提出了克服测头角位置测量误差及三个测头灵敏度标定误差影响的校正方法。实验表明：采用本文提出的“多刻线”法测角精度优于1′,测头角位置测量误差及三个测头灵敏度标定误差对测量精度的影响可降致最小。     

Uncertainty evaluation and reduction in three-probe roundness profile measurement based on the system transfer function

The three-probe method for separating the spindle rotation error and the specimen form error is extensively described in the literature. An attractive feature is its application in in-process measurement. However, the resulting uncertainty is studied far less extensively. In this paper, an evaluation and propagation method for the uncertainty, as well as for an uncertainty reduction, is given based on the system transfer function (S-function). First, utilizing the Laplace transform, the measurement system model is developed and expressed by an S-function. Second, the propagation laws of input uncertainties are analytically deduced by computing the partial derivatives of the S-function of roundness. Then, the laws are numerically validated by Monte Carlo simulations. The uncertainty propagation laws show that the uncertainties propagate with varying amplification over the harmonic domain, and moreover, they enable the quantification of both the harmonic and the total uncertainty of roundness. Taking the roundness uncertainty as a decisive parameter, three approaches are proposed for uncertainty reduction: (1) the hybrid 3-PM, where two roundness estimates are combined by taking individual harmonic estimate with the lowest uncertainty, (2) the fusion 3-PM, where the weighted average is taken over the harmonic domain, and (3) the angle optimization, which minimizes the total roundness uncertainty by properly arranging the sensor angles. The angle optimization is applied to the conventional 3-PM, as well as to the hybrid and the fusion 3-PMs. The genetic algorithm is adopted to speed up the optimization process. Finally, practical roundness measurements are performed.     

三点法圆度测量精度分析

详细分析了三点法中测头的读数及角位置误差对圆度测量精度的影响。从三点法的原理出发,根据误差理论,推导了测头及位置误差在圆度测量过程中的误差传播关系式。结果表明：三点法圆度测量结果失真的根本原因在于三个测头间的夹角选择不当,使测头读数误差在某些谐波上被大大放大。为提高三点法圆度测量精度,必须恰当选择三个测头间的夹角,以使读数误差对圆度各次谐波测量结果的影响都较小。     

Modeling and error analysis for assessing spindle radial error motions

The rotating accuracy of a machine tool spindle directly affects the roundness of machined parts. Commonly, a precision arbor and one or two probes are used to inspect the spindle axis error motion. When the spindle error motion is in the same order of magnitude as the accuracy of the reference arbor, it is desirable to separate the roundness error of the reference arbor from the spindle error. One of the methods used is the three-probe method. This paper presents an exact geometric model and error analysis for the conventional three-probe method. The exact model is used to show that there is an approximation error in the commonly used governing equations of the three-probe method. To reduce inaccuracy in the converted axis motion and arbor contour, the reference arbor accuracy should be at least ten times better than that of the axis motion. It is also shown that the mounting error of the probes should be less than one-fiftieth of the size of the axis motion and the arbor size. The exact geometric model developed in this paper can also be extended to analyze the accuracy of other spindle inspection or roundness measurement methods.     

测头读数及定位误差对三点法圆度测量精度的影响

研究三点法测量圆度时测头的读数及角位置误差对圆度测量精度的影响。从三点法的原理出发对测量过程进行误差分析,导出了圆度测量误差方程,并通过计算机仿真详细研究了测头的读数及角位置误差对圆度测量精度的影响。圆度测量精度主要决定于读数误差;如果３个测头间的夹角选择不当,将使测头读数误差在某些谐波上被大大放大。必须恰当选择３个测头间的夹角,使读数误差对圆度各次谐波测量结果的影响都较小。     

Rotation error measurement technology and experimentation research of high-precision hydrostatic spindle

The hydrostatic spindle is widely applied in the field of high-precision machine tools, which has some advantages such as high stiffness, high rotary precision, and the high damping shock absorption. The spindle rotation error is an important index to measure the machining accuracy of machine tools. Due to the installing eccentric error of the test bar, conventional method based on the standard test bar to measure the rotation error indirectly is applied to the precision machine tools and common machine tools whose rotation error is greater than 1 μm only. In order to eliminate the installing eccentric error of the standard test bar, it presents a self-reference approach that takes the online finish turning test bar, rather than that of the standard test bar, as the measuring datum. Using the capacitive micro-displacement sensor and the LMS data acquisition equipment as the test platform, it designs a set of spindle rotation error measurement system. Then it studies the frequency domain three-point method and has the rotation error and roundness error of high-precision hydrostatic spindle separated. Experimental study shows that the rotation error and the roundness error of the spindle are 0.9 and 0.3 μm, respectively, under the circumstance of conventional standard test bar as the measuring datum. However, if it takes the online finish turning test bar as the measuring datum, the rotation error and the roundness error of the spindle are only 0.3 and 0.1 μm, respectively. The self-reference method is able to eliminate the installing eccentric error of standard test bar directly, and the measurement system has realized the accurate measurements of the rotation error and roundness error of the high-precision hydrostatic spindle.     

基于主轴回转运动误差在线检测的二次相移三点法

提出了一种基于数据重组和反滤波的二次相移三点法圆度误差分离技术,可以先行分离出主轴的回转运动误差,从而能够实现运动误差的在线检测.通过对三个传感器的测量数据按照二次相移原则进行数据重组,可以在数据处理的首次操作时消除圆度形状误差的影响,从而在二次操作时先行得到运动误差.权函数的对比分析表明该方法与圆度三点法在本质上的同源性和统一性.仿真与实验结果均表明:该方法可以先后分离出运动误差和形状误差,具有良好的分离效果.     

CMM touch trigger probes testing using a reference axis

A new method of testing of touch trigger probes for coordinate measuring machines (CMM) has been proposed. The concept is based on measurements of the distance between reference and triggering points in various directions. The reference points are established by the rotation axis of a precise rotary table. The advantage of this method relies on easy realisation with application of a commercial device for roundness error measurement. The accuracy of the presented method is much higher in comparison with the existing procedures of CMM probes calibration.The mathematical principle of the method has been presented and used for evaluation of its uncertainty. The validity of the method was experimentally confirmed by means of one- and two-stage type probes.     

五点法测量机床主轴轴向及倾角的运动误差

提出了测量机床主轴的轴向及倾角运动误差的端面五点法。在轴端面绕轴心的某一圆周上,垂直于轴端面,按通过误差分析优化确定的位置,布置五个测头,在主轴回转一圈中同时测得主轴的轴向及倾角运动误差以及端面基准的形状误差,并将测头的读数及定位误差的影响降至最低程度。本方法可用于机床主轴回转精度的实时测量,试验表明其测量精度可达亚微米级。     

Uncertainty estimation for multiposition form error metrology

We analyze a general multiposition comparator measurement procedure that leads to partial removal of artifact error for a class of problems including roundness metrology, measurement of radial error motions of precision spindles, and figure error metrology of high-accuracy optical components. Using spindle radial error motion as an explicit example, we present a detailed analysis of a complete test with N orientations of a test ball with respect to the spindle. In particular, we show that (1) all components of the ball roundness error average to zero except those with frequencies of kN cycles/revolution, where k is a positive integer; and (2) the combined standard uncertainty of the measurement is proportional to 1/√N. We then show how a complete set of measurements for an N-position test can be synthesized from only two measurements, and we derive a general expression for the combined standard uncertainty as a function of the number of positions n (2 ≤ n ≤ N) actually measured in an N-position test. This uncertainty can serve as a useful guide to measurement design, involving trade-offs between multiple setup cost and complexity and required levels of angular harmonic resolution and combined standard measurement uncertainty.     

Correcting capacitive displacement measurements in metrology applications with cylindrical artifacts

Metrology applications commonly require non-contact, capacitive sensors for displacement measurements due to their nanometer resolution. In some metrology applications, for example, the measurement of roundness and spindle error motion, the displacements of stationary and rotating cylindrical artifacts are measured. Error from using a conventionally calibrated sensor with a non-flat (e.g., cylindrical) target is typically neglected, but these errors cannot be ignored for nanometer-level accuracy. The capacitance between a sensor and a cylindrical target is less than that of a sensor with a flat target, which causes four effects. As the diameter of the target shrinks, the sensitivity of the sensor increases, the sensing range decreases, the sensing range shifts towards the target, and the nonlinearity increases. These errors can be greatly reduced by either calibrating sensors with the correct target surface or by determining corrections for post-processing data. This paper quantifies and experimentally verifies these errors for a commonly used sensor, and a simulation of a nanometer-level measurement of out-of-roundness and spindle error motion demonstrates that measurement accuracy is improved with corrected sensitivities.     

平行三点法圆度误差分离技术的精度分析

阐述了一种能临床测量与分离工件圆度误差和主轴系统回转误差的新方法——平行三点法误差分离技术的测量原理 ,定量分析了测量装置的结构参数、传感器初始调零误差、传感器随机误差和标定误差对圆度测量精度的影响 ,给出了误差传播方程。并讨论了一些消除或减小上述误差的方法。     

机床导轨对主轴回转轴线平行度的精密测量

机床导轨与主轴回转轴线之间的平行度是影响机床加工精度的重要因素．也是影响测量圆柱度测量精度的主要因素。提出了一种完全分离机床导轨与回转轴线平行度的新方法。即以主轴平均回转轴线为坐标轴所建立的绝对坐标系内，利用三点法圆度误差分离技术。通过分离各截面的圆度误差及回转误差，结合绝对坐标系与各截面测量坐标系的关系。计算出在绝对坐标系的两个坐标平面内直行导轨上对应点与主轴平均回转轴线的关系。从而实现导轨与回转轴线平行度的精密测量。     

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.     

A comprehensive technique for measuring the three-dimensional positioning accuracy of a rotating object

A method for measuring the accuracy of rotating objects was studied. Rotating axis errors are significant; such as the spindle error of a machine tool which results in increased surface roughness of machined work pieces. Three capacitance-type displacement sensors were used to measure the position of a rotating master ball. The sensors were mounted at the three orthogonal points on the spindle axis. The measurement data were analysed for rotating spindle accuracy, not only for the average roundness error but also for the spindle volumetric positional error during rotation. This method is simple and economical for industrial field use for regular inspection of spindles using portable equipment. The time taken for measurement and analysis using this method is only about two hours. This method can also measure microscopic amplitudes in 3-D directions of vibrating objects.     

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.     

噪声环境下圆度误差分离的统一方法

提出了一种噪声环境下圆度误差分离的统一方法。这种方法利用频域测量矩阵直接给出了圆度形状误差和回转误差的最小二乘解或最小均方误差解。频域测量矩阵的范数反映了噪声对误差分离结果的影响程度。介绍了圆度误差分离中的频域最小范数混合解，这种混合解比最小二乘解和最小均方误差解具有更好的噪声抑制效果。     

车床主轴回转精度测量系统的研制

车床作为制造业的基础设备,零件加工精度受到诸多因素制约,其中主轴回转误差是主要的影响因素之一.该车床主轴回转精度计算机测量系统由光电编码器、电涡流传感器、微机、变送器、数据采集卡及辅助工具构成.在测量车床主轴回转精度的同时,可获得与主轴角位置对应的径向跳动、端面跳动和角度摆动误差,使用数理统计法误差分离技术编制LabV...