First
The CF-7200 data palette, a new FFT analyzer, has arrived.
When it comes to understanding FFT analyzers, the basics remain the same even with new products. We've covered FFT before, but please bear with us again as we go over the "basics of FFT" this time.
Generally, complex waveforms are made up of superpositions of sine and cosine waveforms. Therefore, in sound vibration theory, it is said that "even complex waveforms are easier to understand if you first consider them as a single sine or cosine waveform." We will proceed with the discussion of FFT analyzers from this perspective. For theoretical details, please refer to "About FFT Analyzers."
I've arbitrarily decided which terms are commonly used, but I've enclosed them in brackets [] to highlight key points in the explanation.
1. Sinus wave (MP series electromagnetic detector)
Physical phenomena are measured directly or indirectly by sensors and observed as voltage signals.
For example, if we consider measuring rotational speed, there is the MP-9100 Electromagnetic Detector as a sensor. This detector is mounted close to the gear.
When a gear rotates, the change in magnetic flux strength caused by the gap difference between the peaks and valleys of the gear is used to detect a signal that corresponds to the number of teeth on the gear.
The output waveform is affected by the gear shape, but it is almost always a sine wave. Hereafter, we will refer to sine waves as "sin waves" and cosine waves as "cos waves".
A sine wave repeats the same waveform shape after a certain period of time. By shifting the time, the waveforms can be superimposed, and in mathematics, this is called a "periodic function."
The minimum elapsed time until the same waveform is produced (the time of one cycle) is called the period time (abbreviated as period), and the unit used is seconds (s).
It can also be expressed as frequency (in Hz) by taking the reciprocal of the period.
Frequency represents the number of cycles per second.
The signal from the MP series electromagnetic detector changes in frequency and amplitude as the rotational speed decreases. It exhibits a characteristic where the amplitude increases with higher rotational speeds, and this is represented as an output voltage characteristic graph with frequency on the x-axis and amplitude on the y-axis. Furthermore, because the amplitude increases with narrower gaps between the detector and gears, and is affected by cable length, measurement conditions are noted.
Examples of installation conditions and output voltage characteristics can be found at the following location.
[Rotational Speed (r/min)] When measuring the rotational speed, if you know the number of teeth P on the gear and the frequency F (Hz) of the MP-9100 signal...
Rotational speed (r/min) = F ÷ P × 60 (s) ... (1)
You can find it this way.
At the end of the experimental waveforms, the waveform and its amplitude spectrum are shown when rotating at a constant 2000 r/min. Amplitude spectra and power spectra are often confused and used interchangeably.
The power spectrum is represented by the square of the amplitude, and the amplitude spectrum is the Y-axis unit of the power vector displayed as amplitude. We will discuss this again later. Looking at the amplitude spectrum data, we can read the frequency and its amplitude (the maximum value of the sine wave).
Observed waveforms are displayed in the time domain, with the X-axis representing time, while spectra are displayed in the frequency domain, with the X-axis representing frequency.
In the time domain, we can read the period and its amplitude, and in the frequency domain, we can read the frequency and its amplitude; both represent a sine wave. From this, you can see that "both the observed waveform and the spectrum represent the same signal," or in other words, the same signal is observed from different perspectives in the time domain and the frequency domain.
A sine wave has amplitude A, period T, frequency f, and time t.
Asin2πft f＝1/T ・・・（2）
This is how it is expressed.
The MP-output voltage characteristic described above represents the relationship between f and A.
A sine wave with constant frequency and amplitude is often used as a reference signal for calibrating measuring instruments. In the case of sound vibration, for example, an acoustic calibrator might use a signal of 250 Hz and a sound pressure of 124 dB, or a vibration calibrator might use a signal of 159.2 Hz and an acceleration of 10 m/s².
As a side note, you may have noticed that the amplitude of the observed waveform changes even when the rotation speed is constant at 2000 r/min. This is because the change in the gap due to the eccentricity of the gear mounting manifests as a change in amplitude.
When installing gears in MP series electromagnetic detectors, please pay attention to eccentricity.
Key point: A sine wave can be represented by its amplitude and frequency.
(Excerpt from the email newsletter issued on December 21, 2006)
