提取磨削主轴型转子轴承系统在加速度期间振动信号的特征研究外文文献翻译、中英文翻译

1、附录Proceedings of the 7th ICFDM2006 International Conference on Frontiers of Design and Manufacturing June 19-22, 2006, Guangzhou, China Pages 255-260 A STUDY ON VIBRATION SIGNAL-BASED FEATURE EXTRACTION FOR GRINDING SPINDLE-TYPED ROTOR-BEARING SYSTEM DURING ACCELERATIONJong-Kweon Park , Bong-Suk Kim

2、 , Soo-Hun Lee and Jun-Yeob Song Intelligence and Precision Machinery Research Division, KIMM, 305 343, Rep. of KoreaSchool of Mechanical Engineering, Ajou University, 443 749, Rep. of KoreaAbstract: The goal of system monitoring is to minimize economic loss, to increase reliability, to maximize pro

3、ductivity, and to maintain product quality in manufacturing. Since vibration signals sufficiently contain the abundant running information of the real system and the hidden fault symptoms, the feature extraction through those signals is widely applied for performance evaluation fault diagnostics of

4、rotating machineries. This paper shows feature extraction from vibration signals gathered in the grinding spindle-typed rotor-bearing system during acceleration in order to monitor an abnormal condition of current system like shaft crack by using various kinds of signal processing methods such as th

5、e Fast Fourier Transform, Short-Time Fourier Transform, Wigner-Ville Distribution, and Discrete Wavelet Transform. As well, the result of feature extraction in shaft crack condition was compared with that in normal condition. Keywords: Feature extraction, Grinding spindle-typed rotor-bearing system,

6、 Non-stationary signal processing method, Accelerating process, Wavelet transform1. Introduction The condition monitoring or fault diagnosis in rotating machineries and machining process is a crucial requirement in order to maintain reliability, safety, and product quality and to prevent failures or

7、 damages .Compared with other machining methods, high- performance grinding process is one of the most complicated and important cutting processes as final machining stage; consequently, the monitoring of grinding process and machine is much more necessary in order to supervise the process and machi

8、ne and also detect abnormalities . Among various kinds of approaches, vibration signal analysis method for feature extraction and nondestructive damage identification has been widely utilized due to capability to carry the abundant dynamic information and to indicate detailed motion of mechanical sy

9、stems and to describe simultaneously when a fault occurs or what is its frequency . However, since most of the vibration signals sampled on mechanical systems are non-stationary or transient signals which sufficiently contain additional information or abnormal symptom, which can not be revealed from

10、 stationary signal, it is the key how to accurately draw dominant feature components from vibration signals because non-stationary signal is more complex than stationary signal. Up to date, for feature extraction of rotating machinery, many kinds of research results have mainly been focused on the s

11、tationary signal process; on the other hand, little research has been accomplished for the non-stationary signal process such as speed-up process; especially, there is almost no feature extraction using vibration signal of speed-up condition in the field of grinding process. .This paper was about a

12、study to extract the dominant features from vibration signals acquired in a laboratory grinding spindle-typed rotor-bearing system during acceleration by using several signal processing methods such as Time Domain Analysis (TDA), Frequency Domain Analysis (FDA), and the Time-Frequency Analysis Metho

13、d (TFAM). Modal testing, which detects dynamic characteristics of the system like natural frequency, was performed for the purpose of determining operating range for acceleration in test setup. Vibration data from the bearing housing passing through the distinctive resonance frequencies and frequenc

14、y band in speed-up process were gathered through the experiments with normal and crack shaft condition. To get prominent signals of abnormality from acquired time data as a fundamental stage for diagnosis or monitoring technology, the Fast Fourier Transform (FFT), Short-Time Fourier Transform (STFT)

15、, Wigner-Ville distribution (WVD), and Wavelet Transform (WT) using commercial software were carried out and compared with each result 2. Theoretical Background 2.1. Review of Signal Analysis Methods There are two major types of signal in the first natural division category: the stationary signal an

16、d non-stationary signal. Stationary signals are constant in their statistical parameters over time. Moreover, stationary signals are further divided into deterministic and random signals. Random signals are unpredictable in their frequency content and their amplitude level, but they still have relat

17、ively uniform statistical characteristics over time.On the other hand, non-stationary signals are divided into continuous and transient types. Transient signals are defined as signals which start and end at zero level and last a finite amount of time. In the stationary signal analyses, there are the

18、 RMS, Peak Value, Average/Distribution, and dynamic time models such as AR model and ARMA model in time domain analysis as well as the Fourier Transform (FT) in frequency domain analysis. However, most signals of mechanical system like vibrations, noises, and sounds, generate non-stationary signals

19、that data are intricate and irregular, so it is certainly necessary to use non-stationary signal processing methods to extract valid information from those signals. The FT is mainly used in frequency analysis of stationary signals, while frequency analysis tends to accompany errors with regard to no

20、n-stationary signals. Since the frequency analysis simply shows only frequency components when non-stationary transient signals occur, it is difficult to find the time information. However, the TFAMs such as the STFT, WVD, and WT, which perform frequency analysis at the time when failure occurs, com

21、pensate defects of time and frequency domain analysis, so that, it is considerably useful for applications to a number of fields.2.2. Fast Fourier Transform An infinite-range FT of a real-valued or a complex-valued record x(t) is defined by the complex-valued quantity. （2.1）Theoretically, as noted p

22、reviously, this transform X(f) will not exist for an x(t) that is a representative member of a stationary random process when the infinite limits are used. However, by restricting the limits to a finite time interval of x(t), say in the range (0,T), then the finite-range the FT will exist, as define

23、d by （2.2）Assume now that this x(t) is sampled at N equally t apart, where t has been spaced points a distance selected to produce a sufficiently high Nyquist frequency. As before, the sampling times are t=nt. However, it is convenient here to start with n=0 like Eq. (3). Let （2.3）Then, for arbitrar

24、y f, the discrete version of Eq. (2) is （2.4）The usual selection of discrete frequency values for the computation of X(f,T) is （2.5）At these frequencies, the transformed values give the Fourier components defined by （2.6）Where t has been included with X(f ) to have a scale kfactor of unity before th

25、e summation. Note that results are unique only out to k=N/2 since the Nyquist frequency occurs at this point. The function defined in Eq. (6) is often referred to as the Discrete Fourier Transform (DFT). A drawback in utilizing the DFT Eq. (6) for discrete signal processing is the time it takes to c

26、ompute the transform values at all frequencies for large arrays of discrete data. More efficient numerical algorithms were developed to improve computational speed, and this has resulted in numerous the FFT algorithms. 2.3. Short-time Fourier Transform The STFT is a Fourier Transform performed in su

27、ccessive time frames : （2.7）Where t is time, w is frequency, and h(u) is a temporal window function such as Rectangular, Gaussian, Blackman, Hanning, Hamming, etc. The STFT characterizes the temporal signal f(t) in both time and frequency domains. The main limitation of this TFAM is caused by the fi

28、xed temporal window applied, whose size (number of sampling points) defines the time and frequency resolutions; a large frame size improves the frequency resolution, while decreasing the time resolution and vice versa. Since fixed window is unable to adjust time and frequency resolution by signals,

29、time-frequency resolution about non-stationary signals analysis needs to make mutual balance. 2.4. Wigner-ville Distribution The WVD provides a relationship between time and frequency during the period of the time data window that is not present in standard Fourier Spectral Analysis. It is capable o

30、f displaying any phase and magnitude changes presented. The WVD can be defined in both the time and frequency domains. Due to computational efficiency and good time resolution, the time domain definition is used. The definition of the WVD is （2.8）Where x(t) is the time signal, conjugate, t is the ti

31、me domain variable, and frequency. Any real signal x(t) is not only contaminated by the noise, but also by the interference terms. Suppression of both of these requires a combination of time and frequency windowing with the WVD. This approach is called the Smoothed Pseudo-Wigner-Ville Distribution (

32、SPWVD), and expressed as follows: （2.9）In this Eq. (9), two independent windows exist. The function W() is a result of the application of a truncating window to the original time data, and determines the frequency resolution of the WVD. The g(t) is a smoothing window, which determine the times resol

33、ution. The independence of the two window functions enables them to be applied individually, or in combination, so that the desired degree of interference suppression can be achieved. Discrete smoothed version of the SPWVD can be expressed as （2.10）Where the n and m denote the time and frequency ind

34、ices, respectively, and S is analytic signal obtained form Hilbert transform of the original windowed signal. N is the half-size of the FFT window w(k) and Q is the half-size of the post smoothing window g(p). The SPWVD is achieved by convolving the WVD with smoothing window. 2.5. Wavelet Transform

35、The WT, a popular tool for studying intermittent and localized phenomena in various signals, is efficient signal processing method to obtain time information lost in the FT, partly irregular fluctuation, time change changing, and discontinuous point. Due to the multi-resolution ability of the WT, th

36、e noised signals can be separated into several approximation signals and detail signals. The WT of a signal f(t) is defined as the sum of all of the time of the signal f(t) multiplied by a scaled and shifted version of the wavelet function (t). The coefficients C(a,b) of the WT of the signal f(t) ca

37、n be expressed as follows （2.11）Where a and b are the scaling and shifting parameters in the WT. Basically, a small scaling parameter corresponds to a compressed wavelet function. As a result, the rapidly changing features in the signal f(t), i.e. high frequency components, can be obtained from the

38、WT by using a small scaling parameter. On the other hand, the low frequency features in the signal f(t) can be extracted by using a large scaling parameter with a stretched wavelet function. For the sampled signal, a digital signal, f(k), k=0, 1, 2, !-, the Discrete Wavelet Transform (DWT) should be

39、 considered. The most commonly used DWT is the scaling and shifting of parameters with powers of two. That is: （2.12） （2.13）Where j is the number of levels in the DWT. The coefficients C(a,b) of the DWT can be divided into two parts: that is, one is the approximation coefficients and the other is th

40、e detailed coefficients. The approximation coefficients are the high scale and the low frequency components of the signal f(t), while the detail coefficients are the low scale and the high frequency components of the signal f(t). The approximation of the DWT for the sampled signal f(t) at Coefficien

41、ts level j can be expressed as Eq. (14). （2.14）Where (n) is the scaling function associated with j,k (n). Similarly, the detail the wavelet function coefficients (D) of the DWT for the sampled signal f(t) at level j can be expressed as follows. 英文翻译中文提取磨削主轴型转子轴承系统在加速度期间振动信号的特征研究摘要: 目标监控系统，是为了最大限度地减少

42、经济损失, 以增加可靠性, 最大限度地提高工作效率，从而保持制造业产品质量。由于振动信号含有真实系统和故障患症状的相当丰富的运动信息的，因此这些信号被广泛应用于评价故障诊断旋转机械。本文主要讲述提取聚集在磨削转子系统加速度振动信号并监测异常的情况，目前可以利用各种方法对信号进行处理，如轴断裂的处理方法有傅立叶变换、短时傅里叶变换、魏格纳分布,以及离散小波变换，同时将常状态与轴断裂提取情况特征相比。关键词:特征提取 磨梭型转子系统 非平稳信号处理的方法 加速进程 小波变换1简介状态监测和故障诊断在旋转机械的加工过程中是一个重要要求，其目的为了保持可靠性和安全性，以及产品质量，防止故障或损坏。与其

43、他加工方法相比，高性能研磨过程是切削过程最复杂和最重要的最后加工阶段；因此，磨削加工工艺及设备，更需要利用监督过程发现机器异常。在各种方式中由于有能力进行丰富的动态查询，并进行详细的分析，机械系统在什么频率发生故障，振动信号分析方法的特征提取和无损鉴定已被广泛使用，不过，由于大部份的振动信号为非静态或暂态信号中含有大量的干扰或异常的症状，这些并不能显示平稳信号，它的关键是如何准确地绘制振动信号的主成分，因为非平稳信号较平稳的信号更复杂。截至目前为止，对于旋转机械特征提取，多种研究成果主要集中在平稳信号的研究过程。在另一方面，对加速进程非平稳信号研究却很少， 因此几乎没有任何研磨过程加速状态领域

44、的振动信号特征提取。本文是关于研究从动态信号中提炼的有用信号，利用一个实验室纺锤型转子系统在加速状态下振动，用几个信号处理方法如时间域分析(tda)和频域分析(FDA)、时间-频率分析法(tfam)测试模型，从而展现其中的动态系统的特性，在正常及裂纹轴条件下振动数据从轴承箱通过独特的共振频率和频段混合。取得异常段时间数据作为一个阶段的诊断或监测技术，用(快速傅立叶变换),短时傅里叶(Fourier),魏格纳分布(WVD), 和小波变换(WT)用商业软件进行比较每个结果。 2理论背景2.1回顾信号分析方法第一部自然分法中主要有两种类型的信号: 稳态信号和非平稳信号。 稳态信号在整个过程中是不变的

45、。此外，稳态信号又进一步分为确定性信号和随机信号，随机信号是意想不到的频率内容及其振幅的大小，但他们仍然有相对统一的统计特征随着时间变化。 在另一方面，非稳态信号分为连续型和瞬态型。暂态信号是指信号的开始和结束时为零级，只是持续在一定的时间内的信号。 对静态的信号分析量有有效值，峰值，平均值与动态的时间模式，如AR模型和ARMA模型在时间域分析以及傅立叶变换的频域分析。然而，大多数信号的机械系统，如振动、噪音和声音都生非平稳信号，数据是错综复杂和不规则的，因此绝对有必要使用非平稳信号处理方法，从这些信号提取有效信息。傅立叶变换主要用于稳态信号频率分析，虽然对非稳态信号频率分析往往伴随着错误,既

46、然率分析只是倾向于频率元件非稳态信号发生时间，其中很难找到时间相关信息。不过，时域分析如短时短时傅立叶分析、魏格纳分布、和小波分析其中推演出失效时频率分析，从而弥补缺陷，这是一个在很多领域都相当有用的方法。 2.2傅立叶变换一个实值或复值函数的无穷傅立叶变换由x(t)得到 （2.1）理论上,如前所述, 这个变换X(f)将不会存在,对于一个X(t)这是一个典型无限极限应用在固顶过程的例子。不过这里限制了极限一个有限的时间间隔的x(t)即(0,t), 然后在有限范围内的傅立叶变换是永远存在的，正如下面公式所示: （2.2）现在假定x(t)在同一个t时刻采样,这里t间隔被用于产生足够高的奈奎斯特频率。一如以往，采样时间为t=nt。 然而,在这里以N=0开始很方便，象