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。     

A note on the three-point method for roundness measurement

This technical note presents two enhancements to three-point method for roundness measurement. They enable measuring a larger bandwidth and also present a logical progression from two-point profile to three-point roundness measurement using the combined method. Simulated profiles with and without step variations are used to demonstrate these improvements.     

An improved three-point method based on a difference algorithm

The reason for the rounding error in a measurement system under the condition of a limited sampling period is analysed, and a three-point method based on the difference algorithm (D3P method) is proposed. The effect of the rounding error is reduced by differential approximation of the roundness error and reconstruction of the transfer function. The generalized three-point method (G3P method), the three-point method based on the first-order difference algorithm (I-D3P method) and the three-point method based on the second-order difference algorithm (II-D3P method) are compared and analysed by simulation. The results show that the accuracy of the D3P method is greatly improved compared with that of the G3P method under the restricted sampling period and that the D3P method retains high precision in the case of failed error separation of the G3P method. An experimental system was constructed to realize error separation, and the experimental results show that the D3P method has higher accuracy than the G3P method over a small sampling period.     

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.     

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。     

基于误差分离技术的圆度误差在位测量

总结了现有用于在位圆度误差测量的误差分离技术,并对经典频域三点法、时域三点法、频域三点法的近似实现方法和频域三点法的改进实现方法的测量特点进行了评述。针对球度误差没有实现在位测量的问题,将圆度误差分离技术引伸到球度误差分离技术,并在理论上进行了探讨。     

圆柱度的三点法测量技术

本文针对圆柱度误差的精密测量,提出了一种可分离截面圆度误差、截面半径差和截面最小二乘圆心初始位置并重构出被测圆柱形貌的方法,即三点法圆柱度误差分离与重构技术。据此方法,只要拾取3个传感器在各测量截面上的输出信号,就可以获得各截面上的测点在绝对坐标系内的位置,实现圆柱度的精密测量。同时还可以得到回转轴的纯回转运动误差和测量架的直行运动误差。     

A Spindleless Instrument for the Roundness Measurement of Precision Spheres

This paper presents an automated instrument for high-precision roundness measurement of spheres. Instead of a rotating spindle, the surface of the sphere itself is used as a geometrical reference. The measurement method is based on the well-established three-point method. In our design, two points are realized as mechanical contacting points and one as a capacitive gauge that directly faces the surface of the sphere. By this simple design—without any moving parts involved in the probing process—we measured the roundness of 1-inch steel spheres with nanometer resolution. After a short introduction into the basic mathematics of the three-point method, the design of the instrument is presented, including the automation of the measuring process and the means used to minimize environmental effects in an industrial environment. Results are presented that prove the outstanding repeatability and accuracy of the instrument. In a comparison with conventional methods, the advantages and limitation of the method are discussed.     

激光 ICF 聚变靶丸轮廓测量系统标定方法

针对激光惯性约束聚变靶丸轮廓高精度测量系统的溯源标定问题,提出一种基于激光差动共焦测量原理的标定溯源方法。该方法基于激光差动共焦靶丸测量系统轴向响应曲线过零点精确对应测量系统焦点的性质,首先利用激光差动共焦靶丸测量系统测量经中国计量科学研究院计量检定的标准椭圆块的圆度,其次通过比对测量值和标准椭圆块圆度计量值,得出该系统测量传递系数为1.03,最后通过多次检定验证测量的方法,完成系统的高精度标定。实验结果显示,利用标定完成的系统进行激光聚变靶金属球比对测量,其标准差为37 nm,该标定方法的测量重复性为17 nm,其为靶丸表面轮廓的高精度测量奠定了坚实基础。     

A new multiprobe method of roundness measurements

This paper presents a new multiprobe method for roundness measurements called the mixed method. In this method, displacements at two points on a cylindrical workpiece and an angle at one of the two points are simultaneously monitored by two probes. The differential output of the probes cancels the effect of the spindle error, and deconvolving the differential data yields the correct roundness error. The mixed method is compared to the traditional 3-point method with respect to the transfer function and resolution. Unlike the 3-point method, the mixed method can completely separate the roundness error and the spindle error, and can measure high-frequency components regardless of the probe distance. Resolution can also be improved throughout the entire frequency domain by increasing angular separation of the probes. An optical sensor specifically suited to the mixed method is designed and used to make roundness measurements. A fiber coupler and single-mode fibers are used in the sensor to divide a light beam from a laser diode into two beams, resulting in a compact sensor with good thermal drift characteristics. The displacement meter of the sensor is based on the imaging system principle and has a resolution of 0.1 μm. The angle meter is based on the principle of autocollimation and has a resolution of 0.5 in. A measurement system is constructed to realize measurements of roundness by using the optical sensor. Experimental results confirming the effectiveness of the mixed method for roundness measurements are also presented in this paper.     

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。     

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.     

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。     

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。     

极大熵法在几何量测量不确定度评定中的应用

为提高新一代GPS标准体系中几何量测量不确定度的评定精度,提出了一种基于极大熵检验的曲线拟合方法.该方法根据极大熵原理,将极大熵函数法应用到几何量测量要素操作的拟合中,把曲线拟合转化为光滑函数优化问题进行求解.最后以圆度为例,利用极大熵法和最小二乘法对测量数据进行了处理.对比结果表明,该方法简单易行,精度高,符合新一代GPS标准的要求.     

New analytical method for V-block three-point method

The V-block method is a widely accepted method for measuring the roundness of a cylindrical workpiece. However, the complexity of conventional analysis schemes, based on Fourier transformation, makes it difficult to develop specific software programs for analyzing the measured data. Here, a new algorithm developed for the three-point method using inverse matrix calculations is extended to the analysis of the V-block method. The results are compared with the conventional analytical algorithm and the validity of the new method is confirmed.     

圆度、圆柱度和同轴度的测量原理及数据处理的解析方法

在形位公差国标的贯彻中,形位误差的精确测量是一项很重要的工作。目前,测量圆度的仪器主要有圆度仪,而测量圆柱度和同轴度还没有专用的测量设备,配有电子计算机进行数据处理的也很少见。本文的目的是提供一种圆度、圆柱度和同轴度的测量原理和用于电子计算机的线性数据处理的解析方法为设计新的专用测量设备用的。这样,与通用测量设备相比可以进一步提高测量的精度和效率。由于圆度测量及数据处理是上述三种项目测量的基础,因此本文以圆度的测量及数据处理的解析方法作为重点加以介绍,同时对被测零件的安装精度提出了要求。     

Application of Monte Carlo simulation for estimation of uncertainty of four-point roundness measurements of rolls

Large-scale rotors in the paper and steel industry are called rolls. Rolls are reground at regular intervals and roundness measurements are made throughout the machining process. Measurement systems for roundness and diameter variation of large rolls (diameter <2000 mm) are available on the market, and generally use two to four sensors and a roundness measurement algorithm. These methods are intended to separate roundness of the rotor from its movement. The hybrid four-point method has improved accuracy, even for harmonic component amplitudes. For reliable measurement results, every measurement should be traceable with an estimation of measurement uncertainty. In this paper, the Monte-Carlo method is used for uncertainty evaluation of the harmonic components of the measured roundness profile under typical industrial conditions. According to the evaluation, the standard uncertainties for the harmonic amplitudes with the hybrid method are below 0.5 μm for the even harmonics and from 1.5 μm to 2.5 μm for the odd harmonics, when the standard uncertainty for the four probes is 0.3 μm each. The standard uncertainty for roundness deviation is 3.3 μm.     

基于蒙特卡罗方法的圆度测量不确定度评定

利用蒙特卡罗方法对圆度测量的不确定度进行评定。首先,根据最小二乘法得到圆度的误差模型;然后采用蒙特卡罗仿真方法对测量值进行模拟仿真,从而得到圆度误差的不确定度;最后将评定结果与传统评定方法的结果进行比较。结果表明该方法是可行的,且计算更为简便。     

PLC在圆度测量上的应用

为提高外圆圆度的测量精度，介绍了采集实际轮廓圆的逐点数值的方法。与基准圆进行比较、使用可编程控制器对数据进行最小二乘法处理后，得到的测量数据，比常用测量方法更精确，同时大大提高了圆度测量仪的测量速度。