We receive inquiries such as, "When performing rotational tracking analysis, data is sometimes missed at low rotational speeds (e.g., every 50 revolutions). Are there any solutions?"
This time, we'll consider the reasons why missed portions occur at low rotational speeds.
While rotational tracking (constant-width tracking) also occurs in frequency analysis, rotational speed has a significant impact on rotational tracking (constant-ratio tracking) in order analysis. For more information on order analysis and tracking analysis, please refer to the technical report below (link).
Degree ratio analysis and tracking analysis
Degree analysis analyzes how many changes occurred during one rotation.
(* Frequency analysis analyzes how many changes occurred in 1 second. The unit is Hz.)
The magnitude of a phenomenon that repeats once per rotation is the magnitude of the first-order component of the rotation.
If the vibrations caused by gear meshing occur 49 times per revolution, then it's a 49th-order component. If the vibrations caused by combustion (expansion) in a 4-cylinder engine occur once every two revolutions, then it's a 0.5th-order component.
If you want to examine order components up to the 25th order using FFT, you will need more than twice the number of samples (per revolution), exceeding the 50th order, similar to frequency analysis.
In Ono Sokki 's FFT analysis, samples are acquired at 2.56 times the normal rate, so the number of samples per revolution is 25 x 2.56 => 64 samples.
If there are 64 samples per rotation, then to perform an FFT on 1024 points, you would need 1024 ÷ 64 = 16
In other words, you will need data for 16 rotations.
(*Frequency analysis: If the range is 25 Hz, then 2.56 times is 64 Hz, 64 samples in 1 s, 1024 points FFT)
(Then, that will be 16 seconds of data.)
The time required to capture data for 16 rotations varies depending on the rotation speed at that time.
At 120 r/min (120 ÷ 60, which is 2 revolutions per second), the rotation time is a long 16 / (120/60) = 8 seconds. At 1200 r/min, it becomes a short 0.8 seconds.
As shown above, the time required to acquire 1024 data points varies depending on the rotation speed. Lower rotation speeds require longer acquisition times. If the rotation speed increases rapidly, the rotation speed will increase during 16 rotations, causing the average rotation speed for those 16 rotations to shift upwards. For example, acquiring data every 50 r/min might end up happening every 100 r/min.
Thus, when the rotation speed increases at a constant rate, at low frequencies, the rotation speed increases while data is being acquired, making it impossible to track at fine rotation intervals.
To obtain tracking data in the shortest possible time, the ideal approach is to slow down the ascent speed at low rotational speeds and increase it at high rotational speeds.
The graph below shows the rotation speed and duration when the maximum analysis order is 25th and the number of sample points is 1024. With a maximum analysis order of 25th, 64 samples are required per rotation, and for a 1024-point FFT, data from 16 rotations is required.
Time = (Number of sample points / Number of samples per rotation) / Rotation speed (Hz)
This is a rectangular hyperbola with the equation y = a/X (a > 0).
y = (1024/64) / (rotational speed/60)
(Excerpt from the email newsletter issued on November 20, 2018)
