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ASSESSMENT OF GEAR DAMAGE MONITORING

TECHNIQUES USING VIBRATION MEASUREMENTS

基于振动测量的齿轮故障诊断评估

Each gear damage monitoring technique has its merits and limitations.

This paper experimentally investigates the sensitivity and robustness of the currently well-accepted techniques: phase and amplitude demo- dulation, beta kurtosis and wavelet transform. Four gear test cases were used: healthy gears, cracked, filed and chipped gears. The vibration signal was measured on the gearbox housing and processed, online, under three filtering conditions: general signal average, overall residual and dominant meshing frequency residual. Test results show that beta kurtosis is a very reliable time-domain diagnostic technique. Phase modulation is very sensitive to gear imperfections, but other information should be used to confirm its diagnostic results. Continuous wavelet transform provides a good visual inspection especially when residual signals are used. The diagnosis based only on dominant meshing frequency residual, however, should not be used in- dependently for gear health condition monitoring, it may give false alarms.

每一项齿轮故障诊断技术都有其优缺点。这篇文章用实验研究了当前被广泛应用的技术灵敏性和鲁棒性，采用了幅值和相位解调，beta;函数峭度和小波变换等方法。在实验中，用到四组齿轮作为对照试验：完好的，带有裂纹的，锉刀锉过的和有明显缺口的齿轮。在线测试齿轮箱的振动信号，并在整体的信号平均，全部的残差和主要的啮合频率三种条件下进行滤波。试验结果表示beta;函数峭度法是一种十分可靠有效的时域诊断技术。相位调制法对齿轮的残缺检测的灵敏度很高，但是不能确定为何种缺陷，还需要其他信息来确定齿轮的诊断结果。

当利用残差信号进行分析时，采用连续的小波变换可以呈现出非常醒目的效果。诊断必须在主要的啮合频率下进行，并且不能对非独立的设备的健康状态进行监测，否则，它可能会给出错误的警报。

1. INTRODUCTION

Typical applications of gearboxes include electric utilities, auto- motive industry, ships and helicopters. A practical and robust monitoring system is critically needed to provide the earliest warning of damage or malfunction in order to avoid sudden failures. Currently, there are three types of approaches to the detection of faults in geared systems: acoustic signal analysis, debris monitoring and vibration analysis. The vibration- based diagnosis has been the most popular monitoring technique because of ease of measurement. When vibration features of a component are obtained, its health condition can be determined by comparing these patterns with those corresponding to its normal and failure conditions. This pattern classification process can be conducted by visual inspection or by inference approaches[1.2].

1.引文

齿轮箱被广泛应用于电力设施，汽车工业，船舶和直升飞机上。

现在工厂迫切地需要实用性强并且稳定好的监测系统提供早期的危险或故障警报以避免突发性的故障发生。目前有三种典型的方法来探测齿轮箱里的故障：声波信号分析，油液监测和振动分析。基于振动信号故障分析的技术已经成为最流行的监测技术，因为它比较容易测量。当获得一个零件的振动信号时，它的健康状况可以由它正常时和被破坏时的振动信号的差异来决定。这种模式分类过程能够通过目测或是根据推理来引导。

There are many vibration-based monitoring techniques currently available for the detection of gear faults. According to the analysis domain, they can be classified into frequency/cepstrum analysis, time/- statistical analysis and time-frequency analysis. A brief review of each is given below.

目前有许多基于振动信号监测的技术来探测齿轮的故障。根据领域分析，可以分为频谱/倒频谱分析，时间/统计分析和时域分析。下面给出每种方法简短的介绍。

• 1. FREQUENCY/CEPSTRUM ANALYSIS

Spectral analysis is the classical gear diagnostic technique. By com- paring the spectrum of a damaged gearbox with its reference spectrum in the healthy condition, some gear faults could be detected [3]. For example, for a gearbox containing only a few pairs of gears, it is possible to identify a tooth damage by inspecting the modulation side- bands around the gear meshing frequency and its harmonics. Cepstrum is the inverse Fourier transform of the logarithmic power spectrum. It highlights periodicity in the spectrum, therefore, a periodic sig- nature in the spectrum caused by a gear fault could be recognised [4, 5]. For com- plicated gear systems, however, it is difficult to identify faults from the spectrum or the cepstrum because of the large number of components involved.

1.1 频谱/倒频谱分析

频谱分析是一种典型的齿轮诊断技术。完好齿轮箱的频谱作为参考谱，把有故障的齿轮箱的频谱与之进行比较，就可以探测出一些齿轮故障。举个例子，在一个只有几对啮合齿轮的齿轮箱中,可以通过检查齿轮啮合频率的调制边频带和谐波来鉴定毁坏的齿。倒频谱是对数功率谱的反傅里叶变换。它强调频谱的周期性，因此，故障齿轮在频谱中产生的周期性的信号能被识别出来。对于复杂的齿轮传动系统，由于有许多零部件，很难从频谱和倒频谱中找出故障。

• 1. TIME/STATISTICAL ANALYSIS

Time synchronous average (TSA) is a signal averaging process over a large number of cycles, synchronous with the running speed of a speci-

fic shaft in the gearbox. It can remove not only the background noise but also periodic events that are not exactly synchronous with the gear being monitored. The use of interpolation and resampling techniques can reduce the effect of shaft speed fluctuation and eliminate the need of phase- locked frequency multipliers [6]. Advanced gear tooth damage can often be identified readily by the direct inspection of the TSA trace. McFadden [7] suggested the use of phase and amplitude demodulation of the do- minant meshing frequency residual for tooth crack detection, which has proved to be a very successful technique in a number of cases. In addition, kurtosis of the phase modulation as well as its derivatives can also be used for gear fault diagnosis[7, 8]. Ismail et al. [9] used kurtosis of beta function to emphasise transients generated by a tooth crack. They also proposed a statistical index to assess gear damage. Golnaraghiet al. [10] introduced a new idea from chaotic dynamics and non-linear time series analysis to detect global changes in system dynamics. Further, Lin et al. [11] investigated the effects that a gear tooth crack has on the correlation dimension of a gearbox vibration signal. The experimental evidence in [10, 11], however, was limited and further research was recommended in both works.

1.2 时间/统计分析

时间同步平均是一种在大周期中的信号平均过程，同步过程与齿轮箱中特定轴的转速一样快。它不仅能去除背景噪声还能去除那些不与被监测齿轮同步的周期性的信号。插值法和重新采样技术的应用能够减少轴转速波动的影响，还可以减少使用锁相倍频器。老化的轮齿的损坏经常很容易通过时间同步平均法检查出来。麦克法登指出：在相当多的例子中，对主要啮合频率残差采用相位和振幅解耦的方法来进行齿裂纹检测是一种非常成功的技术。另外，相位调制峰度和它的一些衍生物也能够被用来进行齿轮诊断。伊斯梅尔等人利用beta;函数的峰度来描述轮齿

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