Vibration Analysis Workbench

REI Vibration Analysis Workbench

The REI Vibration Analysis Workbench is an end-to-end workspace for industrial machinery condition monitoring and rotor balancing.

Accelerometer / Proximity Probe
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Sensor Calibration (mV/g, Bias Voltage)
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High-Pass Regularized Integration (Acceleration → Velocity mm/s → Displacement μm)
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Time-Domain Statistics (RMS, Peak, Crest Factor, Kurtosis)
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FFT / 1X-10X Harmonic Order Spectrum / Hilbert Envelope Spectrum
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Bearing Defect Frequencies (FTF, BPFO, BPFI, BSF)
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Single-Plane Complex Vector Rotor Balancing
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Rule-Based Fault Classifier & Automated Vibration Diagnostic Report

📐 Kinematic Bearing Fault Formulas

For shaft frequency $f_{\text{shaft}} = \mathrm{RPM}/60$, ball diameter $d$, pitch diameter $D$, roller count $N$, and contact angle $\phi$:

$$\text{BPFO} = \frac{N}{2} \cdot f_{\text{shaft}} \cdot \left(1 - \frac{d}{D}\cos\phi\right)$$

$$\text{BPFI} = \frac{N}{2} \cdot f_{\text{shaft}} \cdot \left(1 + \frac{d}{D}\cos\phi\right)$$

$$\text{BSF} = \frac{D}{2d} \cdot f_{\text{shaft}} \cdot \left(1 - \left(\frac{d}{D}\cos\phi\right)^2\right)$$

$$\text{FTF} = \frac{1}{2} \cdot f_{\text{shaft}} \cdot \left(1 - \frac{d}{D}\cos\phi\right)$$

⚖️ Single-Plane Complex Vector Rotor Balancing

$$\vec{\alpha} = \frac{\vec{V}_1 - \vec{V}_0}{\vec{W}_{\text{trial}}}, \quad \vec{W}_{\text{correction}} = -\frac{\vec{V}_0}{\vec{\alpha}}$$