Module 1 · 2.5 hours
FFT & Vibration Analysis
A vibration signature tells you which bearing is failing, which gear is damaged, and whether a joint is in resonance. This module teaches you to read a spectrum and calculate bearing defect frequencies.
Learning Objectives
- Explain the FFT transformation and its limitations (windowing, leakage)
- Calculate BPFO, BPFI, BSF, and FTF from bearing geometry
- Identify gear mesh frequencies and their sidebands
- Distinguish resonance from forced vibration
From time-series to spectrum
The FFT takes a time window and tells you how much energy is at each frequency. Short windows trade frequency resolution for time resolution.
Use a Hann window for most bearing work. Rectangular windows cause leakage that smears peaks across bins.
Sampling rate sets your upper frequency limit (Nyquist = Fs/2). For bearing defect work, sample at 10–20× the highest defect frequency you expect.
Bearing defect frequencies
BPFO (outer race): (n/2)(1 − (d/D)cosφ) × shaft speed
BPFI (inner race): (n/2)(1 + (d/D)cosφ) × shaft speed
BSF (ball): (D/2d)(1 − ((d/D)cosφ)²) × shaft speed
FTF (cage): (1/2)(1 − (d/D)cosφ) × shaft speed
Where n = number of rolling elements, d = ball diameter, D = pitch diameter, φ = contact angle. You will memorize these for the exam.
Field shortcut
Most modern BLDC actuators use a known bearing family. The platform definition in TechMedix contains the pre-computed BPFO/BPFI values for each joint — check there before calculating from scratch.
Resonance vs forced vibration
A resonant peak shifts frequency when you change the operating speed; a forced vibration peak stays at the driving frequency.
Treat resonance by modifying the structure (stiffening, damping). Treat forced vibration by fixing the source (balance, alignment, bearing).