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技術レポート 次数比分析とトラッキング解析 2

Rotation - Tracking Analysis

2.1 Constant Ratio Type Tracking Analysis

Using the rotational pulses from a rotating body as the sampling clock for the FFT analyzer, and normalizing the horizontal axis by rotational order instead of frequency, this is the order ratio analysis explained in the previous section, displayed as shown in Figure a. Among the rotational-tracking analyses, the constant ratio type tracking analysis specifies any component of the order components determined by this order ratio analysis, and changes the rotational speed to track the level changes of that order component according to the rotational speed, as illustrated in the rotational speed - spectrum diagram in Figure b, with the display as shown in Figure c.

  • Figure 6

Figure 7 below is an example of noise analyzed through first, second, third, and fourth order constant ratio tracking.

  • Figure 7

Fixed-width Type Tracking Analysis

Figure 8 shows an example of fixed-width tracking analysis. By using the internal sampling clock of the FFT analyzer, frequency analysis is performed on a three-dimensional display, and arbitrary order components are extracted from the data and plotted to conduct tracking analysis.

  • Figure 8

2.3 Other Tracking Analysis

In addition to fixed ratio type and fixed width type tracking analysis, there are other types of tracking analysis. The analysis method is conducted in the same way as the fixed width type.

Fixed Width Frequency Tracking

This is a tracking analysis that utilizes an internal sampling clock to follow specified frequency components in accordance with the rotational speed. Please note that this is not a degree ratio analysis.

octave tracking

It is similar to fixed-width frequency tracking, but it is a tracking analysis that follows the specified band components of 1/3 and 1/1 octave band data according to the rotational speed.

2.4 About Tracking Analysis and Rotation Change Rate

When conducting tracking analysis, measurements are taken while increasing or decreasing the rotational speed. However, if the change in rotational speed is too rapid compared to the analysis computation time, it can cause shifts in the spectral waveform, leading to incorrect analysis. Figure 9 shows the results of spectral analysis based on different rates of rotational change during an increase in rotation. Figure 9-a represents a case with a small rate of change, where the analysis is appropriate. Figure 9-b shows a case with a large rate of change, where the spectral peaks shift towards lower positions than their original order. Figure 9-c illustrates a case with a very large rate of change, where the peaks spread towards lower order directions. It is important to operate under the planned rotational changes and confirm that the order ratio analysis and frequency analysis data resemble those in Figure a before conducting the main test.

in the case of a small rotation change rate

  • Figure 9-a

in cases where the rate of rotational change is large.

  • Figure 9-b

In cases where the rate of change of rotation is very large.

  • Figure 9-c

3. Summary

I have summarized the previously explained content by comparing constant ratio order tracking and constant width order tracking, which are the main methods of tracking analysis.

3.1 Constant Ratio Type Tracking and Constant Width Type Tracking

Constant ratio order tracking is a method that utilizes rotational pulses obtained from a rotating body as an external sampling clock to perform order ratio analysis. This analytical technique plots the changes in the spectral levels of the order components in correspondence with changes in the rotational speed of the rotating body.

Fixed-width order tracking performs frequency analysis using an internal sampling clock, calculating the frequency of interest based on the frequency range and the changing rotational speed. It then plots the changes in the spectral level of the corresponding frequency component in relation to the changes in rotational speed.

In order tracking analysis and order ratio analysis, when viewed on the order axis, the maximum analysis order and order resolution (order bandwidth) remain constant regardless of the rotational speed. 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 variations in rotational speed. This effect is evident, for example, when analyzing a random signal with a constant amplitude; the higher the rotational speed, the greater the level of the order components. This trend is particularly pronounced in the overall frequency range, as shown on the right of Figure 10, which illustrates the analysis of a random signal.

In fixed-width harmonic tracking analysis and frequency analysis, when viewed on the frequency axis, the maximum frequency and frequency resolution (frequency bandwidth) remain constant regardless of the rotational speed. This is illustrated in Figure 11, compared to Figure 10. Even if the rotational speed changes, the frequency bandwidth corresponding to the harmonic order and the overall frequency range remain constant. This means that when viewed on the harmonic order axis, at lower rotational speeds, the harmonic bandwidth is wider, and as the rotational speed increases, the harmonic bandwidth narrows. In other words, in fixed-width harmonic tracking analysis, there is a tendency for the levels of harmonic components to decrease as the rotational speed increases compared to ratio-type tracking analysis.

It has become somewhat complicated, but there are opposing relationships between degree ratio analysis and frequency analysis, and it is necessary to understand the characteristics of both constant ratio and constant width types and to use them appropriately.

Constant Ratio Type Frequency Tracking Analysis

  • Figure 10

The frequency f at 100 times when the speed is 600 r/min is;

The frequency bandwidth Δf of each order component is;

Similarly, at 1200 r/min,will become.

Fixed-width type frequency tracking analysis

  • Figure 11

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

The frequency change Δf at 3000 r/min is;

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

The points to note regarding constant ratio tracking and constant width tracking are as follows.

Constant Ratio Type Frequency Tracking Fixed-width type frequency tracking
  • The frequency decomposition ability is constant regardless of the rotational speed.
  • In the case of a random noise signal that does not have a clear peak in its frequency components, a higher rotation speed tends to result in a wider frequency bandwidth (resolution), leading to larger spectral values.
  • The frequency resolution is constant regardless of the rotational speed.
  • A low frequency range cannot achieve as large an increase in rotation rate as constant ratio order tracking.
  • You must set the maximum frequency in advance before determining the analysis order (as setting the frequency range restricts the upper limit of the frequency).