一种圆柱度测量基准的误差分离方法

通过对主轴回转误差运动的分析，结合三点法圆度误差分离技术，提出了一种完全分离圆柱度测量基准误差的分离方法，即利用主轴回转轴线平均线、测量传感器及直行导轨之间的空间位置关系，建立相应的坐标系，在分离出被测截面圆度误差、最小二乘圆心初始坐标的基础上，完整地分离出影响圆柱度精密测量的径向回转运动误差和导轨的直行运动误差。该技术不仅可以消除测量基准误差对圆柱度测量精度的影响，还可以实现主轴回转误差、导轨直线度以及导轨对主轴平行度误差的精密测量，对高精度误差补偿加工和机床的精度检验也具有重要意义。     

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.     

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.     

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.     

立式加工中心空间几何误差辨识解析及定位误差补偿研究

为大幅提升立式加工中心加工精度,满足当代数控机床对高精度的需求,针对立式加工中心3个运动轴,深入分析了其轴向运动空间几何误差,提出了可有效辨识运动轴轴向运动空间6项几何误差的辨识方法.建立了空间6项几何误差辨识模型,并针对关联轴联动垂直度误差进行了有效分析,建立了垂直度误差辨识解析模型.同时,针对3个独立运动轴轴向定位...     

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.     

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。     

单圈非重复性主轴回转精度评价

与工件圆度的误差评价相比,实现对不具有单圈重复性的主轴回转精度的评价较为困难.在分析主轴轴线定义及理想轴心可观测性的基础上,建立单圈非重复性主轴回转精度评价的数学模型,针对该数学模型,进行主轴回转误差的集合转换,使得转换后的集合能够适应于计算机处理的误差评价方法.然后利用极差极小化的原理,建立最小区域法的误差评定统一准则和作用表面的统一判别准则.利用这两个评判准则,可以顺利实现对主轴回转误差的最小区域法评价、最小外切圆法评价和最大内接圆法评价,从而提高单圈非重复性主轴回转误差的评价精度,同时也提高误差评价的效率.     

A new method for characterizing axis of rotation radial error motion: Part 1. Two-dimensional radial error motion theory

In the current standards of spindle metrology, the fundamental component of radial probe measurement is considered radial throw (eccentricity) of the installed test artifact and the fundamental radial error motion is treated as non-existent. The goals of this paper are: (1) to make evident the fact that fundamental radial error motion can actually exist; (2) to present a new two-dimensional (2D) method to analyze spindle radial error motion measurement; (3) to discuss the limitations of current spindle motion analysis methods. In the 2D framework, the radial error motion is an application-independent geometric property and thus separate from the consequence of radial error motion in spindle applications. The 2D method can not only determine the axis of rotation radial error motion, but also the consequence of error motion in all classes of spindle applications, including a new class of spindle applications with two radial sensitive directions. In comparison, the radial error motion values specified in current standards give the consequence of radial error motion in two classes of spindle applications, but do not represent radial error motion itself. The new method is presented in two parts. Part 1 focuses on the theory and illustration of the 2D method. Part 2 presents the experimental results of a ball bearing spindle and an aerostatic bearing spindle.     

Evaluation method to determine radial accuracy of high-precision rotating spindle units

In this paper, the authors present a new technique, called the vector indication method, which computes and illustrates the radial error motion of a rotating spindle as the instantaneous vectors on a plane normal to a spindle axis. The radial error motion is measured by two sensors located perpendicularly to each other. A new algorithm is developed to obtain the instantaneous vectors of spindle axis displacement by digital processing. It is revealed that the behavior of displacement of spindle axis can be more precisely known by the vector indication method than by “the Lissajous' figure,” which is one of the conventional methods.     

<Emphasis Type="Bold">Roundness Error Prediction with a Volumetric Error Model Including Spindle Error Motions of a Machine Tool</Emphasis>

This paper proposes a modified volumetric error model that includes spindle error motions as well as geometric errors. The model is constructed using rigid-body kinematics and homogeneous transformation matrices and an additional error matrix describing spindle error motions is included. The suggested model predicts the positioning errors at a given axis position as a function of both the axis position and the engaged spindle rotation angle. Two circular interpolation tests (inner and outer circle of the same radius) are simulated and the machined part profiles are predicted. To verify the simulation results, machining tests are performed according to the ISO 10791-7 standard. The error model with spindle errors shows a better agreement, between the simulated and measured roundness errors, than the simple geometric model. It can be seen that the geometric errors determine the basic part profiles and the spindle errors change the basic profiles according to the magnitude of the errors and the spindle rotation angle.     

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。     

圆度误差测量及误差分析

介绍了圆度误差的最小二乘法及其数学模型的建立 ,并分析了影响圆度误差测量的几种误差因素。     

A new method for characterizing axis of rotation radial error motion: Part 2. Experimental results

In the current standards of spindle metrology, the fundamental component of radial probe measurement is considered radial throw (eccentricity) of the installed test artifact and the fundamental radial error motion is treated. The goals of this paper are: (1) to make evident the fact that fundamental radial error motion can actually exist; (2) to present a new two-dimensional (2D) method to analyze spindle radial error motion measurement; (3) to discuss the limitations of current spindle motion analysis methods. In the 2D framework, the radial error motion is an application-independent geometric property and thus separate from the consequence of radial error motion in spindle applications. The 2D method can not only determine the axis of rotation radial error motion, but also the consequence of error motion in all classes of spindle applications, including a new class of spindle applications with two radial sensitive directions. In comparison, the radial error motion values specified in current standards give the consequence of radial error motion in two classes of spindle applications, but do not represent radial error motion itself. The new method is presented in two parts. Part 1 focuses on the theory and illustration of the 2D method. Part 2 presents the experimental results of a ball bearing spindle and an aerostatic bearing spindle.     

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.     

回转一次直线误差对车削表面影响的精确分析

用数学方法,分析并验证在车削加工中,当主轴回转轴线作一次简谐直线运动时,对应加工工件轮廓曲线的"最小区域中心"位置及其运动轨迹,得出正确的圆度误差和偏心误差值;以及以上圆度误差值与误差运动方向无关的结论.     

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。     

转台-摆头式五轴机床几何误差测量及辨识

为降低转动轴几何误差对转台-摆头式五轴机床精度的影响,提出了基于球杆仪的位置无关几何误差测量和辨识方法。基于多体系统理论及齐次坐标变换方法建立了转台-摆头式五轴机床位置无关几何误差模型,依据旋转轴不同运动状态下的几何误差影响因素建立基于圆轨迹的四种测量模式,并实现10项位置无关几何误差的辨识。利用所建立的几何误差模型进行数值模拟,确定转动轴的10项位置无关几何误差对测量轨迹的影响。最后,采用误差补偿的形式实验验证所提出的测量及辨识方法的有效性,将位置无关几何误差补偿前后的测量轨迹进行比较。误差补偿后10项位置无关几何误差的平均补偿率为70.4%,最大补偿率达到88.4%,实验结果表明所提出的建模和辨识方法可用于转台-摆头式五轴机床转动轴精度检测,同时可为机床精度评价及几何精度提升提供依据。     

轴颈形状误差对液体静压主轴回转精度的影响

液体静压主轴是精密、超精密机床的核心功能部件,已在工程领域广泛应用,但轴颈形状误差作为静压主轴形成回转误差的主要因素,其对回转误差的定量影响规律并不明确。通过分析和简化主轴轴颈的形状误差特征,运用CFD动网格技术定量计算了形状误差作用下主轴在轴承油膜中的平衡位置,模拟了主轴旋转时轴颈形状误差凹、凸部位依次通过最小油膜厚度位置的轴心轨迹,发现了轴颈圆度误差使主轴形成回转误差,其大小与轴颈圆度频次和幅值有关,揭示出轴颈圆度误差对液体静压主轴回转精度的作用机制。通过对比理论计算和试验测试轴颈圆度误差作用下的回转精度,理论计算值约为试验测试值的75.2%。理论计算结果和所提出的研究方法具有重要的理论意义和工程参考价值。     

考虑热误差的双转台机床工艺误差谱预测方法

五轴数控机床的几何误差和热误差是影响工件加工精度的两个重要因素,对这些误差因素进行分析可以有效提高薄壁件工件的加工精度。本文首先基于齐次坐标变换法,建立了双转台五轴数控机床的旋转轴几何误差模型;然后基于对标准球进行在机接触测量,辩识得出两旋转轴的12项几何误差,这些误差考虑了两旋转轴之间的相互影响和其热误差的影响;最后分析五轴数控机床加工空间的几何误差场,在该加工空间内几何误差从中心到外侧逐渐增加,当A轴旋转角度增加时,误差的最大值也随之增加。与其它位置误差辨识方法相比,本方法的测量精度符合加工要求,测量时间只需要30 min。