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Steps for FFT Analysis of Analog Input and Graph Display (1/5)

Overview

This explains the steps from FFT analysis of periodic data such as vibration using a high-speed analog input unit (NX-HAD???) to graph display on an NA series HMI.

FFT graph of analyzed analog data displayed on the NA HMI
FFT graph NA HMI

It then explains the steps for outputting the analog input data and FFT analysis data to an SD card as csv.

Preparation

Measurement target

The measurement target is a periodic waveform
The Fourier transform decomposes a periodic waveform into multiple simple sine waves, and generally a fixed period (a few milliseconds to a few seconds) of the periodic waveform is cut out for calculation. A periodic waveform is, for example, the humming, buzzing or whining sound or vibration of a motor rotating at a constant speed, or the sound or vibration when an object is struck with a hammer. Note that if the motor speed changes, or the object is struck several times like knocking, within the period cut out for calculation, the frequencies in the result will be scattered.

Frequency

Roughly decide the frequency you want to measure. Within the audible range, use sounds like these as a guide.

  • 30Hz
  • 50Hz
  • 100Hz
  • 440Hz International standard pitch (the note A)
  • 10kHz TV test tone
  • 15kHz

Sampling frequency

The observable frequency depends on the sampling frequency (the period at which analog values are acquired). A faster sampling frequency allows higher frequencies to be observed, but the sampling frequency should stay below the performance of the connected sensor, such as a vibration sensor. In FFT calculation, half the sampling frequency is called the Nyquist frequency; data above it is aliased and is ignored

NOTE
A higher sampling frequency makes the FFT calculation take longer and lengthens the scan time, so measures such as lengthening the task period or running it in an event task are needed

Relationship between sampling frequency and observable frequency
Sampling frequency (Hz)Maximum frequency after FFT calculation (Hz)
1k500
2k1k
5k2.5k
10k5k
20k10k
100k50k

Number of data points

Making the number of data points for the Fourier transform 2 to the power of n enables calculation with the FFT (fast Fourier transform), which is fast.

NOTE
Increasing the number of sampled data points gives finer resolution but a longer collection time

Relationship between number of data points, collection time and resolution (sampling frequency = 10 kHz)
Number of data pointsCollection timeResolution
51251.2ms19.53Hz
1024102.4ms9.77Hz
2048204.8ms4.88Hz
4096409.6ms2.44Hz
8192819.2ms1.22Hz
163841638.4ms0.61Hz

From the next page,

we explain the steps for acquiring analog data and calculating the FFT

Download

If you want to download the project made here first,

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