谐波与圆度误差分析的范数理论

在测量圆度误差和分析谐波时,为了从测量信号中提取测量对象的真实信息,测量系统的偏心滤波就成为一个很重要的问题.目前,经常采用的方法有最小二乘法、卡尔曼滤波法和三传感器法等.此处研究这些方法的缺陷.研究表明,这些方法有较大的非线性误差和干扰误差.为了解决这些问题,使用范数理论,提出一种谐波与圆度误差分析的新方法.这种新方法对各种类型误差的衰减能力很强,相对圆度误差真值的收敛性很好,参数估计误差很小.     

圆度与谐波评价的误差分析

揭示了圆度谐波评价中产生误差的原因及参数估计与谐波分量提取的结果失真性，这种误差可以表征为数学模型的近似，非线性取舍误差；安装偏心与一阶谐波的混合，评价准则与标准公差定义的最小条件准则的差异，还给出了消除误差的相应方法。附图２幅。     

圆度误差分离的三点法及其演化形式与精度分析

论述了圆度误差分离的三点法及其演化形式一二点法和四点法的基本原理,并对它们各自特点和测量精度进行了分析、讨论。指出应针对具体情况选择适当的圆度误差分离方法。     

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。     

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.     

基于误差分离技术的圆度自动检测的研究

通过对圆度测试过程中的位置误差—圆度检测截面几何中心与圆度检测时的回转中心之偏心误差—引起的附加圆度测量误差的分析,指出了虽然附加误差的影响将随传感器分辨率的提高而减小,但在工业生产现场传感器分辨率的提高常受成本等因素限制,为此需在圆度测试过程中实施位置误差分离和补偿的措施。在此基础上,阐述了基于误差分离技术的圆度自动检测系统的工作原理,进而介绍了圆度评定系统的组成与测试实例,从而说明误差分离后的测试精度得到了明显的提高。     

圆度、直线度误差分离方法之比较

分析了圆度误差分离技术和直线度误差分离技术的异同点，通过实验算例，进一步验证了精确的频域三点法直线误差分离技术的理论正确性。     

基于两步法超精密圆度仪误差分离系统

基于两步法误差分离原理的圆度仪误差分离系统,克服了传统的“多步法”分离过程中存在的“谐波抑制问题”,缩短了分离时间,有效地抑制了分离过程中引入的测量噪声及系统漂移的影响。该装置不仅可以使圆度仪主轴回转误差从被测工件测量结果中可靠分离,而且整个测量过程实现了全自动无人操作,提高了系统的抗干扰能力及可靠性。     

基于几何动态模型的圆度误差分离模拟

针对精密加工过程中影响圆度误差分离精度的问题,提出了一种基于几何动态模型的圆度误差分离模拟方法。在主轴空间运动规律的基础上,通过回转体轴心的自转和公转关系建立工件截面的几何模拟动态模型。结合三点法圆度误差分离技术实现了动态条件下的圆度误差准确表示,并分析研究了传感器安装角度与干扰误差对圆度误差分离精度的影响。数值实验分析表明,建立的几何模型分析有利于研究回转加工中圆度误差分离结果的正确性,达到了提高误差分离精度及抑制误差对加工精度影响的目的。     

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.     

曲轴连杆颈圆度误差的测量与评定方法研究

曲轴轴颈圆度是评价曲轴合格性和加工精度的一项重要指标。针对曲轴综合测量过程中连杆轴颈沿主轴颈公转运动,导致连杆轴颈的检测数据无法直接用于圆度误差评定的问题,建立基于运动坐标系的圆度误差检测模型,实现了连杆轴颈检测数据转换处理。同时,深入分析用于圆度误差评定的3种最小二乘法的适用条件,结合采样数据的特点实现了连杆轴颈圆度误差的高精度检测。以某型号发动机曲轴为例进行大样本误差检测试验,并与最小区域评定结果进行对比,偏差在1μm以内。数据分析表明了所提出的曲轴连杆轴颈圆度误差检测方法理论上的正确性及工程实践的可行性。     

圆度仪的调平和圆柱度误差评定

从圆柱度误差的测量要求和圆柱度误差评定搜索算法两个方面研究了提高测量精度的方法。为了减小圆柱度误差测量中的工件倾斜误差,设计并分析了两点垂直布局的调平方法;根据工件轴线的方向余弦,计算得到了两点调整的高度值,克服了手动调整存在的问题,实现了工件快速精确调平并提高了工件圆柱度的测量精度。由于圆柱度误差评定是对满足最小条件的圆柱轴线的搜索,文中针对Nelder-Mead单纯形法的收敛精度依赖于初始解和收敛速度较慢,提出了拟牛顿法和Nelder-Mead单纯形法相结合的联合算法来实现全局最优解的快速准确搜索。对经典测试函数的Matlab仿真及实际测量数据的应用表明,该联合算法能有效地提高收敛速度和收敛精度,其收敛速度提高了50%,收敛精度提高了1倍,从而提高了工件圆柱度误差的测量精度。     

电磁式电流互感器谐波比值误差实验与分析

电磁式电流互感器谐波传变特性复杂多变,传变误差难以估计。设计了铁磁性材料磁滞回线的观测实验,分析了磁滞回线形状对电流互感器谐波传变误差的影响。针对谐波误差检测精度要求高的难点,研制了高精度的电流互感器谐波误差检测系统,并通过实验分析了频率、负载、基波电流、谐波相角、直流分量对电流互感器谐波传变误差的影响。     

两点法在曲轴圆度误差测量中的应用

采用误差分离技术,将经典三点法演化为两点法,对曲轴轴颈圆度误差进行实时在位精确测量。实现曲轴轴颈圆度误差和工件主轴回转运动误差的有效分离,去除了工件主轴回转运动误差对圆度误差的影响,对系统的测量精度及测量误差做了详细分析。     

转台定位误差谐波函数计算方法研究

为了保障转台定位误差谐波补偿准确性,针对一种谐波误差函数计算方法开展研究.首先分析了转台定位误差谐波补偿方法,阐述了基于坐标旋转数字计算方法(CORDIC)的谐波误差函数计算原理可行性;针对算法原理误差进行分析,分别建立了与迭代次数n、数据位宽b的量化模型,明确了算法在谐波补偿值计算过程的总量化误差;根据计算精度要求对...     

A hybrid three-probe method for measuring the roundness error and the spindle error

The three-probe method is the most widely used technique for separating the artifact roundness error from the spindle error, with the superiority available for in situ measurement. For further improving the measurement accuracy of the three-probe method, in this paper, the harmonic measurement errors are investigated analytically and experimentally. To achieve this aim, firstly, according to the transfer matrices W(k), the harmonics are classified into two types: the suppressed harmonics with zero W(k) and the unsuppressed harmonics with no-zero W(k). Then, on one hand, through mathematical deduction, the formulation for determining the suppressed harmonics is derived; on the other hand, the measurement errors to the unsuppressed harmonics are experimentally acquired, and the experimental results demonstrate that the measurement errors to the unsuppressed harmonics are greatly related to the determinant of the transfer matrix |W(k)|, but not rigorously in inverse proportion to |W(k)|. Based on the conclusions drawn from the investigations, a hybrid three-probe method is constructed, where several conventional three-probe measurements are performed for optimizing individual harmonic coefficients. Experiments verify that the hybrid three-probe method is more robust to the error sources than the conventional method.     

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.     

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.     

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.