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The order analysis tools in the NI Sound and Vibration Measurement Suite provide two methods for performing order analysis: the Gabor transform method and the resampling method.

Gabor Transform

You can use the Gabor transform method to perform order analysis by analyzing sound and vibration signals in both time and frequency domains.

Traditional Fast Fourier Transform (FFT) analysis provides only frequency domain information. When the rotational speed changes over time, FFT analysis is unable to reflect this variation. Thus the FFT analysis is ineffective at analyzing sound and vibration signals with changing rotational speed. Joint time-frequency analysis (JTFA), which provides both time and frequency domain information, can overcome the limitation of FFT analysis. The basic JTFA method is Short-Time Fourier Transform (STFT) analysis. When applying STFT analysis to a signal, you can identify the order components in the time-frequency domain even if the speed is variable.

Suppose the rotational speed of a machine increases from approximately 1,400 RPM to 3,700 RPM during a run-up test. You can apply STFT analysis to the vibration signal and use a colormap to display the result, as shown in the following front panel.

The red lines in the Colormap represent significant vibration amplitudes. Notice that this plot contains several red curves. These curves correspond to the order components. The order component frequencies increase over time as the speed increases.

The Gabor transform is a special type of time-frequency analysis. Like STFT analysis, the Gabor transform can help you identify the order components in the time-frequency domain when the speed is variable. The Gabor transform also is a type of invertible joint time-frequency transform. With invertible joint time-frequency transforms, you can recover any time-domain input signal or an approximation of the signal by applying an inverse transform to the transform of the signal. The inverse Gabor transform is known as the Gabor expansion. You can recover the time-domain signal from a Gabor transform by using the Gabor expansion, but you cannot recover the time-domain signal from general STFT analysis. The results of the Gabor transform are Gabor coefficients.

The ability to recover time-domain signals is a feature of Gabor transforms and Gabor expansions. Gabor transforms and expansions enable you to extract signal components related to rotational speed from the Gabor coefficients, or from the time-frequency representation. With the Gabor technique, you can extract the signal components associated with any particular orders.

Resampling

When applying an FFT to even-time-spaced samples, or a time waveform, you can calculate the frequency components that are periodic in time. Order components, however, take place n times per revolution and are periodic in rotational angle. Signals that are evenly-spaced in rotation angle are even-angle signals. You can think of even-angle signals as those acquired when a machine rotates over a constant angle. If sound or vibration samples are evenly-spaced in rotation angle, you can apply an FFT to the even-angle-spaced samples to calculate the order components that are periodic in rotational angle. You can use standard FFT methods to perform order analysis with an even-angle signal.

In order to acquire even-angle samples, you must adjust the sampling rate of your DAQ device according to the rotational speed. The adjusted sampling rate is a synchronous sampling rate. In practice, you need complex additional hardware to set a variable sampling rate to acquire samples with a synchronous sampling rate. Applying anti-alias filtering also is difficult when the sampling rate is variable. The Sound and Vibration Measurement Suite provides order analysis tools for software resampling that can avoid the challenges of hardware implementation. You can acquire a sound and vibration signal with a fixed sampling rate and then use software to resample the signal with a synchronous sampling rate.

The following illustration shows the effect of resampling on a simulated vibration signal in a run-up test.

Each point on the two shafts represents a sampling position. The left-hand shaft illustrates even-time-spaced sampling. As the shaft rotates faster, the intervals between adjacent samples become greater. Accordingly, the period of the signal gets smaller, and the frequency span becomes wider. With so many elements changing, identifying the characteristic components is difficult. After resampling, however, all the samples appear with constant angle intervals, as you can see from the right-hand shaft. The period of the even-angle signal is constant, and you then can identify the order components.

Comparing Order Analysis Methods

The Gabor transform order analysis method can generate order waveforms that are not available with the resampling method. You can use the generated order waveform to evaluate the sound quality aspects of order-related tones by listening to the tone or subtracting the tone from the overall signal. National Instruments does not recommend applying the Gabor transform order analysis method in online applications because of the computational complexity.

The resampling order analysis method typically provides higher order resolution than the Gabor transform order analysis method. The resampling method works for both machine condition monitoring applications and noise, vibration, and harshness testing. You can use the resampling order analysis method for multi-channel online processing applications in both run-up and run-down tests and in constant-speed situations.