Technical Report: Degree Ratio Analysis and Tracking Analysis 2

The order ratio analysis described in the previous section uses rotational pulses from a rotating body as the sampling clock for an FFT analyzer, and normalizes the horizontal axis by rotational order instead of frequency. This is displayed as shown in Figure a below. The constant ratio tracking analysis, a type of rotation-tracking analysis, is a tracking analysis that tracks the level change of the order component according to the rotational speed by specifying an arbitrary component from the order components obtained by this order ratio analysis and changing the rotational speed as shown in the rotational speed-spectral diagram in Figure b below. The display is as shown in Figure c.

When performing tracking analysis, measurements are taken while increasing or decreasing the rotational speed. However, if the change in rotational speed is too rapid relative to the analysis calculation time, the spectral waveform will be distorted, and accurate analysis will not be possible. Figure 9 below shows the results of spectral analysis due to differences in the rate of rotation change when performing order analysis during rotational speed increase. Figure 9-a shows the case where the rate of rotation change is small and the analysis is performed appropriately. Figure 9-b shows the case where the rate of rotation change is large, and the spectral peak is shifted to a lower order from the position of the original order. Figure 9-c shows the case where the rate of rotation change is very large, and the tail of the peak spreads in the direction of lower orders. It is important to operate at the rotational speed change planned for the test and confirm that the order ratio analysis and frequency analysis data are as shown in Figure a before conducting the actual test.

Stoichiometric order tracking is an analytical technique that uses rotational pulses obtained from a rotating body as an external sampling clock to perform order ratio analysis. It plots the change in the spectral level of the order component of interest in correspondence with the change in the rotational speed of the rotating body.

Constant-width order tracking performs frequency analysis using an internal sampling clock. For each change in rotational speed, it calculates the frequency of the order of interest based on the frequency range and the current rotational speed, and plots the change in the spectral level of the corresponding frequency component in relation to the change in rotational speed.

In constant-ratio tracking analysis and order ratio analysis, the maximum analytical order and order resolution (order bandwidth) remain constant regardless of rotational speed when viewed on the order axis. However, when viewed on the frequency axis, as shown on the left of Figure 10, the frequency of the maximum order and the frequency bandwidth of the order resolution change with the change in rotational speed. This effect means that, for example, when analyzing a random signal with constant amplitude, the level of the order component increases as the rotational speed increases. This tendency is particularly pronounced in overall analysis as the frequency range widens. The right side of Figure 10 shows the results of analyzing a random signal.

In constant-width order tracking analysis and frequency analysis, the maximum frequency and frequency resolution (frequency bandwidth) remain constant across the frequency range, regardless of the rotational speed, when viewed on the frequency axis. This is illustrated in Figure 11 in comparison to Figure 10. The fact that the frequency bandwidth of the frequency corresponding to the order and the overall frequency range remain constant even when the rotational speed changes means that, when viewed on the order axis, the order bandwidth is wide at low rotational speeds and narrows as the rotational speed increases. In other words, compared to constant-ratio tracking analysis, constant-width order tracking analysis tends to show a decrease in the level of the order component as the rotational speed increases.

It's a bit complicated, but there's a seemingly contradictory relationship between order ratio analysis and frequency analysis, and it's necessary to understand the characteristics of each and use them appropriately.

The 100th frequency f at 3000 r/min is:

The Δorder = first-order frequency Δf at 3000 r/min is:

At Δf = 5 HzSimilarly, at 9000 r/min, Δorder = approximately 0.033.

The following are points to note regarding constant ratio-order tracking and constant width-order tracking.

Stoichiometric order tracking	Fixed-width order tracking
The order of resolution is constant regardless of the rotational speed. In the case of random noise-like signals where the order components do not have clear peaks, higher rotation speeds tend to result in wider frequency bandwidth (resolution), thus increasing the spectral values.	The frequency resolution is constant regardless of the rotational speed. At lower frequency ranges, the rate of rotational increase cannot be as high as with constant-ratio order tracking. The maximum frequency must be determined beforehand, and then the analysis order must be set (because setting the frequency range limits the upper frequency).