渐开线齿轮运动误差模型

讨论了齿轮运动误差与模拟齿轮加工过程的关系 ;分析了齿坯几何偏心和变形对齿轮运动误差的影响 ;建立了左右齿廓形误差模型。通过将左右齿廓形误差展开成傅立叶级数的形式 ,论述了模型参数的概率分布规律 ,比较了Г分布、威布尔分布和瑞利分布 ,并计算出分布的特征数值。内齿加工试验与所得运动误差模型的结果一致 ,表明该模型可以模拟齿轮的生产和控制过程     

光栅式单啮仪误差分离与修正技术的研究

应用时序分析方法研究单啮仪的误差分离与修正。提出了误差修正的数学模型，通过多位测量法分离系统误差，采用傅里叶级数逼近法和非线性最小二乘法将随机误差从测量结果中分离出来，建立了描述随机误差的自回归模型，并采用预报技术修正随机误差。验证结果表明，数学模型正确，误差分离与修正方法有效，可使仪器测量精度提高一级。     

齿面误差激励对二级齿轮系统脱啮行为的影响

在考虑齿轮时变啮合刚度、阻尼、齿轮误差及齿侧间隙的情况下,建立了具有5自由度的二级齿轮传动系统的动力学模型。为了便于用算法分解算法求解,用多项式拟合齿侧间隙,而将啮合刚度、齿轮综合误差用Fourier级数表示。利用Adomian分解算法的思想,用AOM得到了系统对齿轮啮合误差激励的动力学响应。仿真结果表明,在研究的转速范围内,齿面误差激励会导致强烈振动;在低速齿轮对中,可能同时伴随脱齿对象,并导致较大的动载荷。当脱啮现象发生时,响应频谱变得复杂起来,并导致系统产生准周期运动。     

型面3维误差分离理论与应用

针对3维型面采用误差矩阵和误差矢量表示方法，建立3维误差模型。对傅立叶变换的分频特性进行了理论分析，采用傅立嚅变换方法对3维误差进行分析，并进行了实践验证，实现对3维误差模型的频率分离，获得周期误差的幅一频信息，采用2维滤波与滤波器处理技术进行频率误差信息提取，从而实现有用信息的提取，为误差的可补偿研究提供补偿依据。     

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.     

REFERENCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION FOR OUTPUT-ONLY MODAL ANALYSIS

When performing vibration tests on civil engineering structures, it is often unpractical and expensive to use artificial excitation (shakers, drop weights). Ambient excitation on the contrary is freely available (traffic, wind), but it causes other challenges. The ambient input remains unknown and the system identification algorithms have to deal with output-only measurements. For instance, realisation algorithms can be used: originally formulated for impulse responses they were easily extended to output covariances. More recently, data-driven stochastic subspace algorithms which avoid the computation of the output covariances were developed. The key element of these algorithms is the projection of the row space of the future outputs into the row space of the past outputs. Also typical for ambient testing of large structures is that not all degrees of freedom can be measured at once but that they are divided into several set-ups with overlapping reference sensors. These reference sensors are needed to obtain global mode shapes. In this paper, a novel approach of stochastic subspace identification is presented that incorporates the idea of the reference sensors already in the identification step: the row space of future outputs is projected into the row space of past reference outputs. The algorithm is validated with real vibration data from a steel mast excited by wind load. The price paid for the important gain concerning computational efficiency in the new approach is that the prediction errors for the non-reference channels are higher. The estimates of the eigenfrequencies and damping ratios do not suffer from this fact.     

平面十字磁梯度张量系统的两步线性校正

磁梯度张量系统的测量精度受限于磁传感器的零漂、灵敏度差异和三轴非正交性等系统误差以及各传感器轴系间的非对准误差。构建了平面十字磁梯度张量系统的误差参数线性模型,提出了两步线性校正法。利用两个非线性变量转换构建单磁传感器系统误差的线性方程组,对误差参数进行最小二乘估计,将传感器实际输出校正为各自理想正交输出;利用旋转矩阵构建各传感器理想正交轴间非对准误差的线性方程组并求出最小二乘解,将各传感器输出校正到参考平台框架正交坐标系上。两步校正过程均无数学简化。仿真与实验表明,相比忽略二阶及以上高阶小量的常规线性校正,提出的张量系统两步线性校正法更为精确,误差参数仿真估计准确率高于93%,实测校正后总场强度均方根误差小于13 n T,张量分量均方根误差小于90 n T/m。     

An Improved Fourier Five-Sensor (IF5S) method for separating straightness and yawing errors of a linear slide based on multiple sensor parameter sets and least square regression technique

In this paper, an Improved Fourier Five-Sensor (IF5S) measurement method is proposed for separating the straightness and yawing motion errors as well as determining the profile of a linear slide. The previous F5S method [3] used the constant parameters initially to estimate the profile function based on three sensor equations for different angle ranges. The profile estimation and error separation are implemented via an iterative method which can only yield acceptably accurate results with tremendous computational efforts. Here, the improved F5S method applies the least square regression technique instead of the iterative method to estimate the profile functions by using three distinct sets of parameters and different fused sensor data according to the travel of the linear slide. Various errors can then be separated based on the calculated profile function. Simulation results confirm that the IF5S method provides better performance and effectiveness as compared to the previous F5S method.     

圆光栅角度传感器的误差补偿及参数辨识

基于正弦函数和粒子群算法提出了一种误差补偿及参数辨识方法,用于提高圆光栅角度传感器的测量精度。使用光电自准直仪和金属多面体对圆光栅角度传感器的测量误差进行了离散标定,通过对标定数据的频谱分析,发现传感器测量误差主要由几种不同频率的正弦函数信号组成,由此提出了一种基于正弦函数的圆光栅角度传感器误差补偿模型。补偿模型中包含7个待定常量,本文采用粒子群算法求解这7个待定常量以克服最小二乘法无法收敛的问题。以待定常量为粒子位置坐标,以平均误差为适值函数,建立了一种基于粒子群算法的参数辨识模型,并根据参数辨识模型求出最优的待定常量。应用补偿模型对关节臂式坐标测量机的6个圆光栅角度传感器测量误差进行了补偿,结果表明:补偿后各角度传感器的平均测量误差减小了约398～1102.5倍,大大地提高了传感器的测量精度。     

Development of integrated acceleration/deceleration look-ahead interpolation technique for multi-blocks NURBS curves

Modern motion control adopts acceleration/deceleration before interpolation (ADBI) motion planning to eliminate path command errors. However, the individual velocity profiles might not be continuous at the junction of the blocks. Acceleration/deceleration after interpolation (ADAI) method may provide an alternative for solving the discontinuous problems, but it causes path command errors. In this paper, an integrated acceleration/deceleration interpolation (IAD) scheme which integrates the ADBI and ADAI modules is proposed. The ADBI provides a look-ahead function which plans the feedrate profiles based on chord errors, command errors, curvatures, and acceleration limits. Within the look-ahead function, the command error equation is utilized to determine the feedrate at the junction of adjacent blocks. Then the ADBI performs non-uniform rational B-spline (NURBS) interpolation using the planned feedrate profile and outputs the position points to the ADAI module. The ADAI module processes the points by a digital convolution technique such that the continuity of the block junction velocity is ensured. Finally, the IAD is applied to the multi-block NURBS interpolation to validate its effectiveness. Simulations and experiments are conducted to demonstrate the IAD scheme. It is shown that the IAD scheme can reduce the acceleration significantly at the junctions of the blocks under the given tolerance of the command error. Furthermore, the proposed algorithm can improve tracking and contour accuracies as compared to the hybrid multi-blocks look-ahead approach.     

CCD的非线性效应对改进型傅里叶变换轮廓术的影响

在傅里叶变换轮廓术中 ,由于 CCD探测器光电响应的非线性 ,将在测量中引入高次项 ,从而对相位的求解造成较大误差 ,通过理论的推导定性地解释了误差的来由 ,并用计算机进行了模拟计算 ,最后提出了减小误差的方法     

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.     

Estimation method for errors of an aerostatic planar XY stage based on measured profiles errors

This paper describes a method for estimating the geometric errors of an aerostatic planar XY stage. The method calculates two-dimensional (2D) position errors and flatness based on measured guideway profiles. Profile measurements, estimates of motion error, and geometric error models are considered to estimate the 2D position and flatness errors along the X- and Y-axes. A three-probe system is used to measure the guideway profiles for the X- and Y-axes. The motion errors, which are used as input data for geometric error models, are calculated from the force equilibrium of aerostatic bearings along the measured guideway profiles and compared with laser interferometer measurements. Geometric error models were derived to calculate the 2D position and flatness errors of the stage. The measured results and estimates for the 2D position error and flatness differed by 0.5 and 0.6 μm, respectively. Therefore, the proposed estimation method for 2D position and flatness errors of an aerostatic planar XY stage will be a useful tool during the machining and assembly of guideways.     

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.     

补偿运动误差新的诊断原理及系统

本文就补偿运动误差提出了新的诊断方法及系统。新方法将运动误差变换到被切轮齿法向进行考虑。新系统不需像传统方法一般采用精密元件组成基准系统而是可用被测机床精切后的工件测量元件,运用误差相关和误差分离原理,求解补偿运动误差和工件齿面波度误差,并捕捉二者误差的主源。文章给出了实例。     

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.     

大型望远镜测角系统误差的修正

由于大型望远镜转台轴系对测角精度要求较高,本文研究了测角数据系统的误差修正技术。分析了测角数据误差产生的原因,对测角元件误差、安装误差、被测轴系误差进行了讨论,指出轴系测角分系统的误差规律符合谐波方程,故提出采用谐波方程式来表达误差规律。针对工程应用,建立了基于傅里叶级数的简化谐波方程误差公式,用谐波方程算法和多项式拟合算法对系统误差进行修正。在一个望远镜垂直轴转台进行了试验验证,结果显示测角精度峰值由原来的3.81″提高到了1.06″。实验表明,基于傅里叶级数的修正算法,较好地符合误差分布规律;采用系统误差修正技术,可以对系统综合误差统一修正,能够有效提高系统测角精度。     

正交并联六轴力传感器耦合误差测量模型及实验分析

为解决并联六轴力传感器量程提升受限问题,设计了一种正交构型并联六轴力传感器。正交并联六轴力传感器是基于并联六轴力传感器的一种构型上的改进,具有承载能力强、解耦性能良好的优势,但同时该力传感器的耦合误差输出具有自身的特点。考虑该力传感器测量分支间摩擦以及正交结构自身特点引起的耦合误差输出,建立了正交并联六轴力传感器耦合误差测量模型。基于所建立的测量模型,通过数值算例分析探讨了传感器设计参数与两种耦合误差输出之间的影响关系,据此研制了一种正交并联六轴力传感器。最后对传感器样机进行了实验,得到其误差分布及检验测量精度。实验所得传感器各维力/力矩在各方向误差分别为0.43%/0.31%,0.18%/0.68%,0.80%/1.28%。     

基于耦合源误差分析的转子振动信号识别方法

转子振动信号实时监测是保障旋转机械健康运行的关键,转子圆度误差和电涡流位移传感器误差的耦合源误差在以往的研究和振动监测中很少考虑,使得转子振动信号有一定的失真,甚至会引起误判。以实际转子为例,提出了圆度误差测量表达式;测量和分析了两种常用电涡流位移传感器的误差,利用傅里叶拟合方法构建了圆度误差和电涡流位移传感器耦合源误差表达式,建立了耦合源误差与转子振动信号之间的映射关系。提出了点-点法、平均值法与最大值法3种转子振动信号识别方法,3种方法都能有效识别转子振动信号,其中点-点法最精确,识别误差占比约20%;平均值法计算简便,识别误差占比约10%;最大值法偏保守,但可有效避免误判,识别误差占比约32%。     

Nanopositioning and Nonlinearity Compensation for Step Imprint Lithography Tool

In this paper, the motion mode and nanopositioning accuracy in the step imprinting lithography process are presented, and the positioning errors different from the traditional errors, such as the gap error existing in the hinges of the stage structure and the random error produced during the process of the stage position adjustment, are analyzed. To avoid and eliminate these nonlinearity errors, radial basis function-proportional integral derivative and position control algorithms are introduced into the macro- and microdriving processes, respectively. The innovation of this driving method is that the motion locus is monotone, nonoscillatory, and a multistep approaching target, which eliminates the root of the random error by single direction driving mode and avoids the backlash error through preloading function. Driving experiments of different motion ranges prove that this nonlinearity compensation is very effective and the positioning accuracy during the step imprinting process can be improved up to 10-nm.