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.     

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。     

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.     

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.     

Spindle thermal drift measurement using the laser ball bar

Thermally induced errors are major contributors to the overall accuracy of machine tools. An important component of thermally induced errors is the error associated with spindle thermal drifts. In this paper, a novel method is developed to measure spindle thermal drifts in machine tools using a laser ball bar (LBB) as the calibration instrument. The method is implemented on a two-axis CNC turning center. The LBB is used to measure the coordinates of the spindle center and the direction cosines of the spindle axis at various thermal states. The axial, radial, and tilt thermal drifts of the spindle are then computed from the changes in these coordinates. The new method is verified by comparing the spindle drifts measured with the LBB to those measured by capacitance gauges. The results obtained by the new method show good agreement with the capacitance gauge technique. The primary advantage of the new method is the ability to measure the spatial coordinates of the spindle center and direction cosines of the spindle axis with the same instrument used for measurement of the geometric errors of the machine axes.     

Laser vibrometry measurements of an optically smooth rotating spindle

Laser doppler vibrometry (LDV) is a well-established non-contact method, commonly used for vibration measurements on static objects. However, the method has limitations when applied to rotating objects. The LDV signal will contain periodically repeated speckle noise and a mix of vibration velocity components.In this paper, the crosstalk between vibration velocity components in laser vibrometry measurements of a rotating dummy tool in a milling machine spindle is studied. The spindle is excited by an active magnetic bearing (AMB) and the response is measured by LDV in one direction and inductive displacement sensors in two orthogonal directions simultaneously. The work shows how the LDV crosstalk problem can be avoided if the measurement surface is optically smooth, hence the LDV technique can be used when measuring spindle dynamics.     

Pitch deviation measurement of an involute spur gear by a rotary profiling system

This paper presents surface-profiling based gear pitch deviation measurement for an involute spur gear. A rotary profiling system, which consists of an air-bearing spindle and a displacement sensor with a diamond stylus, is employed to measure gear pitch deviation. In measurement of gear pitch deviation, an eccentric error between a gear axis and a motion axis of the rotary stage in the profiling system would affect accuracy of gear profile measurement. In this paper, at first, the influence of the eccentric error on measurement of gear pitch deviation is estimated in computer simulation based on a geometric model of the profiling system. After that, a new scanning method named “opposite-direction dual scanning method” is proposed so that a steep profile of gear flank surface with a local slope of up to 90° can be measured by the developed rotary profiling system. For compensating distortions in the measured gear tooth profile, which are induced not only by the eccentric error but also by a probe offset introduced by the proposed scanning method, a self-calibration and compensation method is applied. To verify the feasibility of the proposed method, measurement of gear pitch deviation of a master involute spur gear with a certificate data is carried out. Measurement uncertainty of the proposed method is also analyzed.     

磁梯度张量系统传感器阵列的快速旋转校准

为有效消除磁梯度张量系统传感器阵列间非对准误差和传感器系统误差对测量精度造成的影响,提出了一种只需绕系统任意轴旋转一周便可理论上实现所有磁传感器与参考平台正交系间精确校准方法。利用两组无数学简化的非线性转换构建传感器系统误差线性校正模型,仅需同一旋转周期的10组测量数据便能得到参考平台与各传感器的理想正交输出。通过构建磁传感器三轴横倾、俯仰、方位转换的旋转矩阵,得到传感器空间任意姿态的非对准误差校正模型并对旋转角进行最小二乘估计,仅需同一旋转周期的3组测量数据便能对准张量系统。仿真和实测结果表明:在理想情况下仿真参数估计准确率接近100%,实验校正后各传感器输出具有较高重合与同轴性,张量分量RMSE(均方根误差)小于30nT/m。能以较简单步骤和较少采样数据高效提高差分法磁梯度张量系统测量精度。     

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。     

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。     

Position and orientation detection of capsule endoscopes in spiral motion

In this paper, a position and orientation detection method for the capsule endoscopes devised to move through the human digestive organs in spiral motion, is introduced. The capsule is equipped with internal magnets and flexible threads on their outer shell. It is forced to rotate by an external rotating magnetic field that produces a spiral motion. As the external magnetic field is generated by rotating a permanent magnet, the 3-axes Cartesian coordinate position and 3-axes orientation of the capsule endoscopes can be measured by using only 3 hall-effect sensors orthogonally installed inside the capsule. However, in this study, an additional hall-effect sensor is employed along the rotating axis at a symmetrical position inside the capsule body to enhance measurement accuracy. In this way, the largest position detection error appearing along the rotating axis of the permanent magnet could be reduced to less than 15mm, when the relative position of the capsule endoscope to the permanent magnet is changed from 0mm to 50mm in the X-direction, from −50mm to +50mm in the Y-direction and from 200mm to 300mm in the Z-direction. The maximum error of the orientation detection appearing in the pitching direction ranged between −4° and +15°.     

Simultaneous geometric error identification of rotary axis and tool setting in an ultra-precision 5-axis machine tool using on-machine measurement

This paper presents a method to identify the position independent geometric errors of rotary axis and tool setting simultaneously using on-machine measurement. Reducing geometric errors of an ultra-precision five-axis machine tool is a key to improve machining accuracy. Five-axis machines are more complicated and less rigid than three axis machine tools, which leads to inevitable geometric errors of the rotary axis. Position deviation in the process of installing a tool on the rotary axis magnifies the machining error. Moreover, an ultra-precision machine tool, which is capable of machining part within sub-micrometer accuracy, is relatively more sensitive to the errors than a conventional machine tool. To improve machining performance, the error components must be identified and compensated. While previous approaches have only measured and identified the geometric errors on the rotary axis without considering errors induced in tool setting, this study identifies the geometric errors of the rotary axis and tool setting. The error components are calculated from a geometric error model. The model presents the error components in a function of tool position and angle of the rotary axis. An approach using on-machine measurement is proposed to measure the tool position in the range of 10 s nm. Simulation is conducted to check the sensitivity of the method to noise. The model is validated through experiments. Uncertainty analysis is also presented to validate the confidence of the error identification.     

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。     

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。     

A sub-nanometre spindle error motion separation technique

This work designs and validates a spindle error motion separation technique having a sub-nanometre measurement uncertainty. This technique overcomes typical measurement error sources arising from sensor, indexing or the repositioning of the artifact. We compare and assess various known reversal and multiprobe techniques by means of a novel error analysis method. From this, we develop an improved implementation of the multiprobe technique, which by-passes accurate indexing of the artifact and sensor(s) during testing, as well as unequal sensor sensitivities, in case multiple sensors are used. This is achieved by measuring the error motion consecutively under three different orientations by rotating the stator of the spindle utilising a high-precision indexing table. These modifications result in a measurement uncertainty that is four times smaller than the conventional multiprobe technique. Furthermore, the suppression of the low-order harmonics is reduced by an optimisation of measurement angles. Finally, several experimental tests are performed to quantify the measurement uncertainty and the influence of the measurement angles on the error separation. Repeatability tests on the radial error motion of an aerostatic rotary table show a measurement uncertainty of 0.455 nm.     

Self-calibration and compensation of setting errors for surface profile measurement of a microstructured roll workpiece

Microstructured roll workpieces have been widely used as functional components in the precision industries. Current researches on quality control have focused on surface profile measurement of microstructured roll workpieces, and types of measurement systems and measurement methods have been developed. However, low measurement efficiency and low measurement accuracy caused by setting errors are the common disadvantages for surface profile measurement of microstructured roll workpieces. In order to shorten the measurement time and enhance the measurement accuracy, a method for self-calibration and compensation of setting errors is proposed for surface profile measurement of microstructured roll workpieces. A measurement system is constructed for the measurement, in which a precision spindle is employed to rotate the roll workpiece and an air-bearing displacement sensor with a micro-stylus probe is employed to scan the microstructured surface of the roll workpiece. The resolution of the displacement sensor is 0.14 nm and that of the rotary encoder of the spindle was 0.15r~. Geometrical and mathematical models are established for analyzing the influences of the setting errors of the roll workpiece and the displacement sensor with respect to the axis of the spindle, including the eccentric error of the roll workpiece, the offset error of the sensor axis and the zero point error of the sensor output. Measurement experiments are carded out on a roll workpiece on which periodic microstructures are a period of 133 i~m along the circumferential direction. Experimental results demonstrate the feasibility of the self-compensation method. The proposed method can be used to detect and compensate the setting errors without using any additional accurate artifact.     

主轴回转运动精度的计算机视觉测量系统

基于计算机视觉测量技术,建立了机床主轴回转运动精度测量系统。系统主要由CCD 摄像机、计算机和相应的图像处理软件组成。利用图像传感器记录靶标特征点运动轨迹,经过图像处理软件的数据处理,可直接测得主轴的回转运动。由于靶标特征点的提取直接影响系统的测量精度,因此提出了以圆形标记作为靶标图案,采用面积矩方法提取圆心来提高系统测量精度。在MATLAB 环境下编程实现图像处理和数据计算,采用最小区域圆法计算主轴回转误差。最后采用该系统对车床主轴进行了测量,试验证明,系统可以实现主轴回转运动精度的精确、快速测量,且精度达到微米级。     

未知相对位置条件下回转体厚度的双激光检测

为了实现对大型空心回转体厚度的测量,提出了一种基于双激光位移传感器的非接触扫描检测方法。在回转体与双激光位移传感器相对位置未知的条件下,分析了由回转体安装偏心以及传感器光轴与原点不共线时所引入的测量误差,建立了双传感器信号与被测位置厚度之间的数学模型。并借助于相关理论相位差计算法、牛顿迭代法以及循环平移方法,将实际厚度值从传感器信号中提取出来。对回转体厚度检测算法的仿真实验表明,当检测信号中干扰分量的幅值不大于0.3mm时,算法检测厚度的相对误差总体保持在0.5%以内,并将此作为调整旋转台转速的依据。分析实验测量数据发现,两路信号的最大相对平移量为4;通过对数据进行偏心补偿以及平移,本厚度检测算法的测量重复性误差不大于0.05mm,可以实现在随机位置状态下对回转体厚度的高精度检测。     

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.     

基于激光干涉仪的旋转轴误差快速检定方法

为了提升五轴数控机床各旋转轴精度,解决旋转轴几何误差难以测量的问题,提出了一种基于激光干涉仪的旋转轴几何精度快速测量方法。该方法针对AC双转台和BC摆头转台的结构特性,采用旋转轴与直线轴联动的测量技术,可以避免传统测量方法对旋转轴中心的依赖性,推导了测量中直线轴转角误差与直线度对旋转轴几何误差约束关系,在保证精度的同时减少了测量过程中的设备安装调试时间,实现了五轴机床旋转轴转角误差、重复转角误差以及反向间隙的快速测量和补偿。对实际五轴机床AC双转台几何精度进行检定,提高了旋转轴的几何精度,实验证明该测量方法具有很强的工程应用价值。