Diagnostics of rotating components are a maturing field and the tachometer plays an important role in the quality of vibration based diagnostics. Various studies have disclosed a number of analysis techniques, such as synchronous analyses (primarily for shafts and gears) and non-synchronous analyses (primarily for bearings). Synchronous analyses are typically based on the time synchronous average (TSA) so as to eliminate signal components that are not synchronous with the rate of rotation of the shaft or gear, whereas non-synchronous analysis generally uses some type of demodulation and enveloping, returning energy associated with the fault frequency of the item under analysis (e.g., bearing).
Synchronous analyses of vibration signals relating to rotating equipment have used the Fourier transform or the Fast Fourier transform (FFT) (the latter being more typically employed for processing efficiencies) to provide vibration based diagnostics by measuring the magnitude and phase of vibration of components under observation (such as shafts, gears or bearings), which can be indicative of wear and failure. When using the FFT, typically one assumes that the signal under analysis is infinite in time; however, this assumption fails for real signals and a common mitigation technique is the use of a window function, such as the Hamming window (general form:
                    w        ⁡                  (          n          )                    =              α        -                  β          ⁢                                          ⁢                      cos            ⁡                          (                                                2                  ⁢                  π                  ⁢                                                                          ⁢                  n                                                  N                  -                  1                                            )                                            )    .Another common assumption is that the vibration signal is stationary; however, as all rotating machines vary in their rotational rate due to changing load conditions and the limits of the feedback control bandwidth, this assumption of stationarity also commonly fails.
In practice, the lack of stationarity results in “spectral smearing” of energy associated with a shaft, which in turn results in inaccurate measuring of the energy associated with a particular fault frequency. To improve the performance of vibration analysis using the FFT, Time Synchronous Averaging (the TSA, for shaft/gear analysis) and Time Synchronous Resampling (TSR) have been developed. Examples of TSA and TSR systems are shown in FIG. 1.
At a high level, the TSA resamples the vibration associated with a shaft or gear in the spatial domain such that vibration associated with each shaft order in the Fourier domain represents one frequency bin. For example, the gear mesh energy of a 37 tooth gear on a given shaft is found in the Fourier domain to be bin 38, and the second harmonic of that gear would be in bin 75 (37×2+1, (bin 1 is the DC energy)). The TSA also reduces non-synchronous vibration by 1√(rev), where rev is the total number of shaft revolutions that constructed the TSA.
The TSR resamples (e.g., upsamples) the vibration to correct for variation in shaft speed. The apparent sample rate is the ratio of the total resampled time domain, i.e., vibration data set length divided by original data set length, multiplied by the original sample rate.
TSA and TSR typically use a tachometer signal to calculate the time over which a shaft completes one revolution. As is generally known, the time taken for any shaft to complete a rotation can be calculated even if the tachometer is not associated with a given shaft. This can be calculated, for example, by taking into account the shaft ratio between the shaft with a tachometer to the shaft under analysis, then interpolating based on the known tachometer signal.
The type of tachometer signal is dependent on the sensor type. Types of sensors typically used include, but are not limited to: 1) a Hall sensor, where there is a rising voltage associated with the passing of a ferrous target (such as a gear tooth) in front of the sensor; 2) an inductive sensor, where there is a rising voltage associated with the passing of any metallic target (such as an aluminum shaft coupling); 3) an optical sensor, where there is a rising voltage associated with the receiving of light from a reflective target on the shaft; or 4) a generator or variable reluctance sensor, where the frequency and amplitude of a sinusoidal signal is proportional to target (usually a gear) RPM, and the time of the zero crossing is taken at the transition of the sinusoid from negative to positive voltage.
An incorrect tachometer signal reduces the effectiveness of the TSA and TSR to reduce spectral smearing, which negatively affects the ability of the vibration analysis to detect component faults. While important to all frequency signatures, the impacts are more apparent to higher frequency signatures and higher harmonics, which are often present with a fault.
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