Application of the continuous wavelet transform in periodic error compensation

This paper introduces a new discrete time continuous wavelet transform (DTCWT)-based algorithm, which can be implemented in real time to quantify and compensate periodic error for constant and non-constant velocity motion in heterodyne displacement measuring interferometry. It identifies the periodic error by measuring the phase and amplitude information at different orders (the periodic error is modeled as a summation of pure sine signals), reconstructs the periodic error by combining the magnitudes for all orders, and compensates the periodic error by subtracting the reconstructed error from the displacement signal measured by the interferometer. The algorithm is validated by comparing the compensated results with a traditional frequency domain approach for constant velocity motion. The algorithm demonstrates successful reduction of the first order periodic error amplitude from 4 nm to 0.24 nm (a 94% decrease) and a reduction of the second order periodic error from 2.5 nm to 0.3 nm (an 88% decrease). The algorithm also reduces periodic errors for non-constant velocity motion overcoming limitations of existing methods.     

基于角域平均和倒阶次谱分析的齿轮箱故障诊断

本文研究旋转机械非稳态信号的分析方法。对等时间间隔采样的齿轮箱振动信号,利用插值算法实现角域重采样。为了抑制与工频无关的噪声信号以提高信噪比,对重采样信号进行了角域平均。将倒频分析引入阶次分析中,以检测出功率谱中难以辨识的周期性。以上方法成功地识别了齿根裂纹故障,说明了对旋转机械非稳态信号进行角域平均和倒阶次谱分析的可行性和有效性。     

Real-time FPGA-based Kalman filter for constant and non-constant velocity periodic error correction

Displacement measuring interferometry has high resolution and high dynamic range, which is widely used in displacement metrology and sensor calibration. Due to beam leakage in the interferometer, imperfect polarization components, and ghost reflections, the displacement measurement suffers from periodic error, whose pitch is multiple harmonics of the Doppler frequency. In dynamic measurements, periodic error is usually on the order of nanometers, which impacts the dynamic measurement accuracy. This paper presents an approach to estimate and correct periodic error in real time based on an extended Kalman filter, which has the capability to deal with both constant and non-constant velocity motions. This algorithm is implemented on an application-specific hardware architecture in an FPGA, which has advantages in throughput and resource usage compared with conventional implementations. The measurement validation shows that this approach can effectively eliminate the periodic error for both constant and non-constant velocity motion, and the residual error reaches to the level of the background noise of the interferometer.     

基于现代信号处理方法的动态测量误差分析

动态测量误差信号是包含多分量的非平稳信号,成分的复杂性决定了对动态测量误差的分析和处理需要结合多种信号处理方法.如傅里叶变换、小波变换和神经网络等.分析了各种信号处理方法的原理及其在非平稳信号处理中的应用,建立了一个动态测量误差分析仿真系统,对系统输出的动态测量误差进行分析,将总误差进行分解,找出引起此总误差的各组成单元带来的单项误差,为进一步更精确的进行动态精度评定、动态误差诊断与控制,提供了科学的理论依据.     

阶次包络谱在轴承故障诊断中的应用

旋转机械的升降速过程包含丰富的状态信息,因而旋转机械的升降速过程对于旋转机械的故障诊断具有独特的价值.将常规的阶次分析技术与包络谱相结合,提出基于阶次包络谱的齿轮箱故障诊断方法.首先对齿轮箱升降速瞬态信号进行时域采样,再对时域信号实行等角度重采样,转化为角域平稳信号,最后对角域重采样信号进行包络谱分析,就可提取轴承的故障特征.通过对轴承内圈、外圈故障实验信号的分析,表明该方法能有效诊断轴承的故障.     

基于改进Bussgang算法的多机组故障诊断仿真和试验

针对非平稳信号改进Bussgang算法,借助参考噪声抵消包含在混合信号中的噪声,最小化输出信息的广义能量来获得最好的消噪效果;通过计算机仿真确定适合的非线性函数,仿真结果发现随着延迟系数的增大,收敛误差函数值减小,收敛性能增强;试验模拟了两个故障和三个故障的情况,分离结果与基于ICA、Bussgang算法的结果比较,验证改进算法对多机组含噪非平稳信号分离的有效性。     

超声彩色血流成像中基于动态区域划分抑制杂波的方法

为提高超声彩色血流成像质量,提出了一种基于动态区域划分的杂波抑制方法。先根据超声回波信号的幅度对血流与组织区域作出初步的划分,再根据杂波运动的非平稳性对组织区域作进一步的调整,最后对各区域用特征向量滤波器进行杂波抑制。将本方法用于计算机仿真血流信号和人体实测血流数据,结果表明:本方法在有效抑制非平稳杂波的同时,能较好地保持血流流速剖面的完整性,解决了传统均匀分段特征向量滤波器选取区间长度时的矛盾,有望成为超声彩色血流成像中一种有效的杂波抑制方法。     

MODIFIED CLOSED-FORM NUMERICAL ALGORITHM FOR PERIODIC VIBRATION RESPONSE OF MECHANICAL TRANSMISSIONS

A closed-form numerical algorithm (CFNA) is analyzed in detail. CFNA is widely used in mechanical dynamics for periodic solution of second-order original differential equations (SODE) with periodic time-variant coefficients. The principle of the algorithm is to discretize the motion period into many short time intervals, so the coefficient matrices of the equation set are regarded as constant in a time interval. Defects are found in the original algorithm in treating the modal coordinates at the two end-nodes and important modifications to the defects is made for the algorithm. The modified algorithm is finally used to solve the dynamic problem of a three-ring planetary gear transmission.     

基于阶次跟踪和经验模态分解的滚动轴承包络解调分析

针对齿轮箱升降速过程中振动信号非平稳的特点,将计算阶次跟踪方法与经验模态分解技术相结合,提出一种研究旋转机械瞬态信号故障诊断的分析方法。首先对齿轮箱启动时测得的振动信号进行时域采样,再对时域信号进行等角度重采样,将其转化为角域准平稳信号,然后对角域里的信号进行经验模态分解得到多个固有模态函数分量,最后对包含轴承故障信息的高频固有模态分量进行包络解调分析。结果显示：阶次跟踪技术能够有效地避免传统频谱方法所无法解决的“频率模糊”现象,将非平稳信号转化为准平稳信号;经验模态分解方法能够提取包含故障信息的固有模态分量,将两种方法相结合是对传统频谱分析法的有力补充,具有很广阔的应用前景。     

Determination of the averaging time for precision calibration of a build-up system in a deadweight force machine

This paper describes the determination of the optimal averaging time for the precision calibration of a build-up system. When a build-up system is calibrated using a deadweight machine, the oscillating signal components of force transducers in the build-up system are strongly related to the motion of the deadweight. We propose a model based on the analysis of oscillating signals of force transducers to measure the deadweight oscillation. In this paper, we have investigated the behavior of deadweight motion for a deadweight force machine of 498 kN using the proposed model, and also determined the optimal averaging time for the output signals of force transducers in a build-up system. It revealed that the deadweight force machine has a periodic oscillation of frequencies of about 0.23 and 0.8-1.5 Hz in which the 0.23 Hz component comes from the pendulum motion of the deadweights and the 0.8-1.5 Hz comes from the bounce-mode oscillations of weights. If the length of the rectangular window can be set equal to the period of the deadweight oscillation in a build-up system, the error due to the deadweight oscillation diminishes, regardless of the initial phase of signal fluctuation and the initial time of measurement.     

First and second order periodic error measurement for non-constant velocity motions

This paper describes a digital algorithm that can be applied in real time to measure and compensate first and second order periodic error in heterodyne displacement measuring interferometers. Comparisons are made between the new algorithm and the traditional frequency domain measurement approach, where the error signal is Fourier transformed into the frequency domain to identify periodic error magnitudes. Experimental results are provided for both constant velocity and non-constant velocity conditions.     

Gear fault detection and diagnosis under speed-up condition based on order cepstrum and radial basis function neural network

Varying speed machinery condition detection and fault diagnosis are more difficult due to non-stationary machine dynamics and vibration. Therefore, most conventional signal processing methods based on time invariant carried out in constant time interval are frequently unable to provide meaningful results. In this paper, a study is presented to apply order cepstrum and radial basis function (RBF) artificial neural network (ANN) for gear fault detection during speedup process. This method combines computed order tracking, cepstrum analysis with ANN. First, the vibration signal during speed-up process of the gearbox is sampled at constant time increments and then is re-sampled at constant angle increments. Second, the re-sampled signals are processed by cepstrum analysis. The order cepstrum with normal, wear and crack fault are processed for feature extracting. In the end, the extracted features are used as inputs to RBF for recognition. The RBF is trained with a subset of the experimental data for known machine conditions. The ANN is tested by using the remaining set of data. The procedure is illustrated with the experimental vibration data of a gearbox. The results show the effectiveness of order cepstrum and RBF in detection and diagnosis of the gear condition.     

基于阶次双谱的齿轮箱升降速过程故障诊断研究

针对齿轮箱升降速过程中振动信号非平稳的特点，将常规的阶次分析与双谱分析技术相结合，提出了基于阶次双谱的齿轮箱故障诊断方法。首先对齿轮箱升降速瞬态信号进行时域采样，再对时域信号进行等角度重采样，转化为角域平稳信号，最后对角域重采样信号进行双谱分析，就可提取轴承的故障特征。通过对轴承内圈故障实验信号的分析表明，该方法能有效地识别轴承的故障。     

多轴双光子聚合加工系统综合误差建模

针对所研制中的一台多轴双光子加工系统,通过齐次坐标变换建立了激光束焦斑中心与试件期望位置之间的综合误差模型。假定对各个运动轴误差及光路系统的误差服从非平稳概率分布,考察了各个运动轴误差及光路系统误差对综合误差的影响。为主动补偿多轴双光子聚合加工系统的综合误差、提升多轴双光子聚合加工系统的工作精度提供了依据。     

发电机组橡胶柱销联轴器异常振动噪声诊断

为诊断某型柴油发电机组产生的异常噪声故障,将经验模态分解方法(empirical mode decomposition,简称EMD)和Hilbert变换用于发电机主轴承的非平稳振动信号处理,有效提取了主轴承振动信号的时频特征,对机组振动噪声信号、发电机主轴承振动和轴系扭振信号进行了分析。诊断结果表明,由于柴油机激励下机组轴系扭振幅值过大,引起柱销联轴器橡胶件表面的相对运动,产生干摩擦作用力,导致机组轴系产生间歇性的异常振动噪声。该方法对旋转轴系部件摩擦引起的振动噪声故障诊断具有参考价值。     

渐开线齿轮加工过程中的大周期误差研究

基于齿轮误差理论,对渐开线齿轮大周期误差进行研究。大周期误差属于低频,主要包括滚齿加工中的几何偏心、运动偏心和它们的合成与补偿,以及在插齿加工中的插齿刀的偏心误差。研究表明,对于滚齿加工来说,几何偏心对左、右齿面产生的啮合线误差等于该齿面上的径向与切向之和;运动偏心对左右齿面产生了一个大小相等且方向相反的误差且误差曲线是正弦曲线;几何偏心而不是运动偏心对齿廓径向误差有影响;可以引入几何偏心去补偿运动偏心。     

运用阶次跟踪和奇异谱降噪诊断齿轮早期故障

针对齿轮箱升降速过程中振动信号非平稳的特点,将阶次跟踪分析与奇异谱降噪技术相结合,提出了一种针对齿轮早期故障的诊断方法。首先对齿轮箱加速时测得的瞬态信号进行时域采样,再对时域信号进行等角域重采样,转化为角域伪稳态信号;然后对角域信号进行奇异谱降噪处理,以减小背景噪声的影响;最后对降噪后的信号进行阶次谱分析。通过对齿轮箱早期故障信号的分析表明,该方法能准确地识别出齿轮的故障特征。     

Generalized proportional integral control for periodic signals under active disturbance rejection approach

Conventional repetitive control has proven to be an effective strategy to reject/track periodic signals with constant frequency; however, it shows poor performance in varying frequency applications. This paper proposes an active disturbance rejection methodology applied to a large class of uncertain flat systems for the tracking and rejection of periodic signals, in which the possibilities of the generalized proportional integral (GPI) observer-based control to address repetitive control problems are studied. In the proposed scheme, model uncertainties and external disturbances are lumped together in a general additive disturbance input that is estimated and rejected on-line. An illustrative case study of mechatronic nature is considered. Experimental results show that the proposed GPI observer-based control successfully rejects periodic disturbances even under varying speed conditions.     

一类单边刚性碰撞系统的分岔与混沌控制

研究了一类单自由度刚性碰撞系统的分岔和混沌运动。建立系统周期运动的Poincaré映射,通过数值仿真揭示了系统通过倍化分岔通向混沌的道路和系统的周期运动、混沌运动。最后运用外加恒定载荷控制方法对系统的混沌运动进行了有效的控制,使系统达到不同的周期轨道。     

Bias error due to windows for the Wigner–Ville distribution estimation

The Wigner–Ville distribution has been recognized as a useful method for time-frequency analysis of non-stationary signals. For mechanical signatures such as vibration and acoustic signals it has demonstrated a very good ability to reveal what actually happens, which is not the case if the signals are processed by conventional methods such as spectrum analysis and amplitude-time analysis. Because of these promising figures for the Wigner–Ville interpretation of mechanical signatures, the possible errors associated with estimation, which are mainly due to the finite record length, have not been analysed. In this paper, the error due to the time window which changes with respect to time, and the error associated with the smoothing process have been analysed theoretically. The error produced by employing a time window has been found to be proportional to the frequency of curvature of the Wigner–Ville distribution and that associated with smoothing has turned out to be proportional to even numbers of derivatives with respect to time and frequency.