Compensation for five DOF motion errors of hydrostatic feed table by utilizing actively controlled capillaries

Five DOF motion errors of a hydrostatic bearing table driven by a coreless type linear motor were compensated by utilizing actively controlled capillaries in the present research. The motion errors of horizontal translation and yaw were compensated simultaneously with the two actively controlled capillaries, and those of vertical translation, pitch and roll were compensated simultaneously with the three actively controlled capillaries. The actively controlled capillaries were designed and their gains were adjusted by conducting micro step response tests. The five DOF motion errors were measured ultra-precisely by combining three measuring methods as follows. The yaw and pitch errors were measured with a laser interferometer, and the roll error was measured by the reversal method. Then, the translational motion errors in the horizontal and vertical directions were measured by the sequential two-point method, where influence of the angular motion errors on the translational measurement was compensated by utilizing the measured angular motion errors. By utilizing the developed capillaries and the combined measuring methods and by applying the iterative control, the motion errors of the horizontal translation, the vertical translation, the yaw, the pitch and the roll were compensated simultaneously and reduced significantly from 0.16 μm, 0.18 μm, 1.96 arcsec, 2.26 arcsec and 0.14 arcsec to 0.02 μm, 0.03 μm, 0.03 arcsec, 0.07 arcsec and 0.02 arcsec, respectively. The remaining motion errors were less than the measuring repeatabilities which were ±0.02 μm for the translational motion errors and ±0.05 arcsec for the angular motion errors. The results show that the present method is not only practical but also effective to realize the ultra-precision feed motion whose accuracy is equal to the currently reachable measuring accuracy.     

圆柱滚子轴承滚道圆度误差对旋转精度的影响

在圆度误差评定算法研究的基础上,探讨了圆柱滚子轴承内圈滚道圆度误差对旋转精度的影响,根据轴承零件的几何关系建立数学模型,详细阐述了算法原理及步骤,利用Visual C++编制相应的程序,对圆柱滚子轴承的运动状态进行数值仿真和模拟,分析不同的滚道圆度误差对其旋转精度的影响规律。     

机器人用四点接触球轴承旋转精度影响因素

针对机器人用四点接触球轴承旋转精度难以预测和控制的问题,提出了同时考虑轴承内圈沟道和外圈沟道圆度误差的轴承旋转精度数值计算方法。根据轴承内部元件运动学和几何学关系建立轴承旋转精度数值计算模型。使用MATLAB编写轴承旋转精度求解程序,得到内圈沟道圆度误差幅值和谐波阶次、外圈沟道圆度误差幅值和谐波阶次、钢球直径偏差及钢球个数对轴承旋转精度的影响规律。进行了轴承旋转精度试验,验证了仿真结果的正确性。轴承旋转精度涉及很多指标,所研究的四点接触球轴承旋转精度衡量指标指轴承外圈径向跳动。结果表明:轴承外圈径向跳动随着内外沟道圆度误差幅值的增大先平稳后快速增大,随着内圈外沟道圆度误差谐波阶次的增大呈现周期性变化,随着钢球直径偏差的增大呈线性减小,随着轴承内部钢球个数的增大呈指数减小。所建模型解决了四点接触球轴承旋转精度难以进行理论求解的问题,能够准确预测轴承的旋转精度,为四点接触球轴承的精度设计提供了理论基础。     

A 6-degree-of-freedom measurement system for the accuracy of X-Y stages

A precision 6-degree-of-freedom measurement system has been developed for simultaneous on-line measurements of six motion errors of an X-Y stage. The system employs four laser Doppler scales and two quadrant photo detectors to detect the positions and the rotations of an optical reflection device mounted on the top of the X-Y stage. Compared to the HP5528A system, the linear positioning accuracy of the developed measurement system is better than ±0.1 μm to the range of 200 mm and the vertical straightness error is within ±1.5 μm for the measuring range of ±0.1 mm. The yaw and pitch errors are about ±1 arcsec, and the roll error is about ±3 arcsec within the range of ±50 arcsec.     

Relationship between geometric errors of thrust plates and error motions of hydrostatic thrust bearings under quasi-static condition

A new model using approximate formulas is established to predict the error motions of hydrostatic thrust bearings. Three different types of geometric errors of thrust plates are listed in this paper including tilt errors, saddle shaped errors and petal shaped errors. The influences of them on lateral tilt error motion, longitudinal tilt error motion and axial error motion are discussed. Definitions of averaging coefficients are made based on the approximate formulas. It is found that the time-varying tilt errors are the main reason for the error motions of hydrostatic thrust bearings. The thrust bearings with six pairs of recesses have priority over the thrust bearings with four and three pairs of recesses in the view of rotation accuracy. Experiments are done using a hydrostatic rotary table with an outer diameter of 2 m. It is found that the second harmonic errors are the main component of the radial run-out and the results agree well with the results calculated from the approximate formulas.     

A comparison of techniques for identifying the configuration state of statically indeterminate rotor bearing systems

Turbomachinery rotors are frequently supported on several hydrodynamic bearings and so are statically indeterminate. In such cases, the relative locations of the bearing centres (viz. the system configuration state) affect the bearing reaction forces and hence their stiffness and damping properties, thereby significantly influencing the vibration behaviour of the rotor bearing system. Since this configuration state may differ from its value at time of installation, due to thermal effects and/or foundation settlement, it would be useful to identify its value under operating conditions. This paper illustrates how this can be done in principle, regardless of the unbalance, by measuring the locations of the rotor journals relative to their respective bearing housings at any speed at which the system has reached steady state operating conditions, provided one has good models of the rotor and the foundation. Two identification procedures are compared. Both methods rely, to varying degrees, on using the Reynolds equation for hydrodynamic lubrication to obtain the bearing reaction forces. The first procedure uses the Reynolds equation to evaluate both the magnitudes and directions of the forces (the ‘magnitude and direction’ or MAD method), whereas the second procedure uses the Reynolds equation to evaluate only the directions of the forces (the ‘direction only’ or DO method). Numerical experiments on a flexibly supported statically indeterminate four bearing flexible rotor prove that both the MAD and DO identification procedures are sound in principle, being able to identify the locations of the two inboard bearings relative to the two outboard bearings to within 0.1 μm assuming seven-digit accuracy in journal orbit eccentricity measurements. On the other hand, three-digit measurement accuracy, felt to be the best accuracy practically achievable, restricts identification of the bearing locations to within 10 μm, with somewhat better identification being achieved with the MAD procedure. Such identification accuracy presupposes that the Reynolds equation correctly predicts the bearing reaction forces and could be in error owing to the temperature dependence of the bearing clearance, the assumption of a mean lubricant viscosity and the uncertainty of the cavitation boundaries. It is shown that error in lubricant viscosity may introduce significant errors into the identification achievable with the MAD procedure, but has no effect on that achievable with the DO procedure; and error in clearance introduces more error into the identification achievable with the MAD procedure than the DO procedure. Identification errors due to assumed cavitation conditions still need to be addressed.     

Estimation of sphericity by means of statistical processing for roundness of spherical parts

In the industrial standard of “balls for rolling bearings,” deviation from spherical form (sphericity) is defined as follows. It is usually determined by numerically evaluating the ball profiles, in two or three equatorial planes at 90° to each other, and recording them on a polar chart. Furthermore, the standard indicates that the minimum circumscribed circle method is relatively simple and generally satisfactory for ball profiles, and the method is also based on the assumption that two or three equatorial profiles at 90° to each other are a good indication of the deviation from spherical form. The measurement method for three-dimensional (3-D) spherical profiles is two-dimensional (2-D), because a practical (3-D) measuring system for spherical forms remains to be developed. This is another important problem. Using the method recommended in the standard, the deviation value is significantly underestimated, because the major part of the 3-D surface is not measured. Verification of the above-mentioned assumption is also difficult in general. If numerous measurements of 2-D profiles are performed, the degree of underestimation decreases. However, this requires much time and labor. In this study, a 3-D deviation value from spherical form is calculated from a few 2-D roundness values obtained using a general roundness measuring system with a statistical technique. Furthermore, an appropriate number of measuring cross sections necessary to estimate the sphericity with high reliability are presented.     

五轴机床旋转轴误差的在机测量与模糊径向基神经网络建模

考虑五轴机床中的旋转轴误差会影响加工精度和在机测量结果,本文研究了旋转轴误差的在机测量与建模方法。介绍了基于标准球和机床在机测量系统的旋转轴综合误差测量方法,采用随机Hammersely序列分组规划旋转轴的测量角位置,通过自由安放策略确定标准球初始安装位置。然后,引入模糊减法聚类和模糊C-均值聚类(Fuzzy C-means,FCM)建立旋转轴误差的径向基(Radial basis function,RBF)神经网络预测模型。最后,进行数学透明解析,从而为误差的精确解析建模提供新途径。利用曲面的在机测量实例验证了提出的旋转轴误差测量与建模方法。结果表明:利用所建模型计算的预测位置与实测位置的距离偏差平均值为9.6μm,最大值不超过15μm;利用所建模型补偿工件的在机测量结果后,其平均值由32.5μm减小到13.6μm,最大误差也由62.3μm减小到18.6μm。结果显示,提出的测量方法操作简单,自动化程度高;模糊RBF神经网络的学习速度快、适应能力强、鲁棒性好,能满足高度非线性、强耦合的旋转轴误差建模要求。     

Plane kinematic calibration method for industrial robot based on dynamic measurement of double ball bar

A new calibration method is proposed to improve the circular plane kinematic accuracy of industrial robot by using dynamic measurement of double ball bar (DBB). The kinematic model of robot is established by the MDH (Modified Denavit-Hartenberg) method. The error mapping relationship between the motion error of end-effector and the kinematic parameter error of each axis is calculated through the Jacobian iterative method. In order to identify the validity of the MDH parameter errors, distance errors and angle errors of each joint axis were simulated by three orders of magnitude respectively. After multiple iterations, the average value of kinematic error modulus of end-effector was reduced to nanometer range. Experiments were conducted on an industrial robot (EPSON C4 A901) in the working space of 180 mm × 490 mm. Due to the measuring radius of DBB, the working space was divided into 30 sub-planes to measure the roundness error before and after compensation. The average roundness error calibrated by the proposed method at multi-planes decreased about 21.4%, from 0.4637 mm to 0.3644 mm, while the standard deviation of roundness error was reduced from 0.0720 mm to 0.0656 mm. In addition, by comparing the results of positioning error measured by the laser interferometer before and after calibration, the range values of motion errors of end-effector were decreasing by 0.1033 mm and 0.0730 mm on the X and Y axes, respectively.     

基于激光三角法的圆度误差在线检测技术研究

提出了一种基于激光三角测距原理的圆度误差在线检测新方法。论述了检测系统的构成、测量原理和测量方法,讨论了主轴回转误差的分离,最后在普通车床上进行了实验验证,并用三坐标测量机作了对比测量,结果表明,两种测量方法的标准差均为0.75μm,两者间相对误差平均为4%。     

三面静压转台回转精度干涉测量与误差处理

介绍了激光干涉法测三面静压转台回转精度的原理及测量方法,分析了激光干涉仪在回转轴运动位置精度测量中的主要误差诱因;作出了角度测量中正弦近似误差特性曲线,并建立了该测量误差的数学模型,为机床的运动精度误差补偿提供了数据。经现场检验,该方案简便易行,成效显著。     

Prediction and compensation of motion accuracy in a linear motion bearing table

In the present research, a corrective machining algorithm is introduced to improve the motion accuracy of linear motion bearing tables. The algorithm commences with reverse analysis, in which the rail form error is estimated from the measured linear and angular motion errors. In the next step, the rail is remachined to reduce the estimated form error. Then, the motion errors are measured again, and the procedure is repeated until the measured errors are sufficiently small. A transfer function, which represents the bearing force variation of a bearing block with respect to the spatial frequency components of the rail form error, is used to describe the characteristics of the linear motion bearings. Computations are carried out via the Hertz contact theory. From the theoretical evaluation, it is evident that the magnitude of the normalized transfer function quantitatively represents the accuracy averaging effect at each spatial frequency and that motion errors are not affected by the preload and the stiffness of the bearings. It is also clear that the algorithm can be used to estimate the equivalent rail form error in terms of motion errors. As a practical application, the algorithm is utilized to improve the motion errors of an XY table with linear motion bearings. The experimental results show that the motion accuracy of a linear motion bearing table can be improved to about 1 μm of linear motion error and about 1-2 arcsec of angular motion error by applying the proposed algorithm.     

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。     

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.     

基于误差转换的汽车曲轴圆度及圆柱度误差评价数学模型构建研究

针对国内汽车曲轴轴颈圆度误差、圆柱度误差检测普遍存在的效率低、精度低等问题,建立基于误差转换的平面曲线和空间曲线误差数学模型,结合圆和圆柱的数学表达建立满足最小包容条件的圆度和圆柱度误差评定数学模型,并采用遗传优化算法计算出符合最小评定要求的曲轴轴颈形位误差,解决了理想包容要素位姿参数不精确的问题。同时,建立基于图像域的汽车曲轴轴颈形状误差检测试验台,针对测量过程中连杆轴颈沿主轴颈公转运动,从而导致连杆轴颈图像域检测数据存在坐标不归一问题,以曲轴法兰端特征孔为基准,通过模板匹配特征与孔边缘提取实现了连杆轴颈圆度和圆柱度测量数据空间坐标归一化处理。以某型号发动机曲轴为例进行大样本误差检测试验,并与三坐标测量机测得的结果进行对比,数据分析表明提出的曲轴轴颈形状误差检测方法的精度为1μm,且重复检测误差在0.1μm以内,证明了其理论上的正确性及实践操作的可行性。     

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.     

Geometric error measurement and compensation for the rotary table of five-axis machine tool with double ballbar

This paper proposes a novel measuring method for geometric error identification of the rotary table on five-axis machine tools by using double ballbar (DBB) as the measuring instrument. This measuring method greatly simplifies the measurement setup, for only a DBB system and a height-adjustable fixture are needed to evaluate simultaneously five errors including one axial error, two radial errors, and two tilt errors caused by the rotary table. Two DBB-measuring paths are designed in different horizontal planes so as to decouple the linear and angular errors. The theoretical measuring patterns caused by different errors are simulated on the basis of the error model. Finally, the proposed method is applied to a vertical five-axis machining center for error measurement and compensation. The experimental results show that this measuring method is quite convenient and effective to identify geometric errors caused by the rotary table on five-axis machine tools.     

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。     

一种圆度仪辅助测量工装的设计

转台式圆度仪是一种用于测量圆度、圆柱度、同轴度等参数的仪器。传统的使用圆度仪测量半径的方法由于操作繁琐、定位精度低,已不适用于大批量生产检测。提出了一种新的测量工装,具有结构简单、使用方便等特点。实践证明,使用新的工装辅助圆度仪进行内孔半径的测试,可以对工件进行较精确的定位,充分发挥圆度仪的精准性,有效避免了因定位误差导致需要重新调整工件位置的困扰,显著提高测量定位精度及工作效率。     

Development of an automatic cumulative-lead error measurement system for ballscrew nuts

Ballscrew is a precision mechanical component used to convert rotational motion to linear motion in the precision linear stage. The precision measuring system for the screw's cumulative-lead error is already well known. Up to now, however, there is no suitable measuring equipment for internal cumulative-lead error of the nut. For a matching pair, it is not reasonable to understand the quality of only one piece. This paper presents a developed automatic cumulative-lead error measuring system for ballscrew nuts. The nut is clamped by a rotational stage, in which the moving angle is detected by a rotary encoder. The probing ball is inserted into the nut and remains in contact with the thread groove of the nut. The probe arm is mounted on a linear slide so that when rotating the nut, the probing ball will be pushed by the groove wall and moved axially. A high-resolution diffraction scale is employed to detect the linear movement of the probe to nanometer resolution. Combining the angular and linear motions, the cumulative-lead error of the nut can be realized. In practice, however, the nut will cause typical spindle errors during rotating, including axial slip, radial run out, and tilt motions. These errors have to be compensated in order to guarantee the accuracy of measurement results. A multi-sensor error compensation system is thus developed. Experimental results show the applicability of this developed measuring system.