Optruss

Bearing Kinematic Vibration Fault Frequency Calculator

Compute BPFO, BPFI, BSF, and FTF defect frequencies based on internal bearing geometry and shaft rotational speed.

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ISO 10816 / VDI 2056KINEMATIC VIBRATION HARMONICSReal-Time Engineering Engine
INTERACTIVE SIMULATION WORKBENCH

Configure Parameters to Run Model

Shaft Running Speed (1X):24.67 Hz
BPFO (Outer Race)
88.1 Hz

3.57X Order

BPFI (Inner Race)
133.9 Hz

5.43X Order

BSF (Ball Spin)
57.3 Hz

2.32X Order

FTF (Cage / Train)
9.8 Hz

0.40X Order

These calculated kinematic frequencies are streamed into Optruss Edge Demodulation filters to automatically detect defects without dismantling the machine.
MATHEMATICAL FORMULATIONS & VARIABLES

Rigorous Engineering Formulations

Ball Pass Frequency Outer Race (BPFO)

BPFO = (n / 2) × (RPM / 60) × [1 - (d / D) × cos(β)]

Frequency of rolling elements impacting a defect on the fixed outer ring raceway.

Ball Pass Frequency Inner Race (BPFI)

BPFI = (n / 2) × (RPM / 60) × [1 + (d / D) × cos(β)]

Frequency of rolling elements impacting a defect on the rotating inner ring. Modulated by 1X shaft speed sidebands.

Ball Spin Frequency (BSF)

BSF = [D / (2d)] × (RPM / 60) × [1 - ((d / D) × cos(β))²]

Frequency of a damaged ball or roller striking both inner and outer raceways during each revolution.

Fundamental Train Frequency (FTF)

FTF = (1 / 2) × (RPM / 60) × [1 - (d / D) × cos(β)]

Rotational speed of the bearing separator cage assembly. Typically 0.38X to 0.44X of shaft speed.

WORLD-CLASS INDUSTRY BENCHMARKS

Comparative Performance Quartiles

Benchmark QuartileTarget Metric RangeOperational & Financial Implication
Stage 1 (Incipient)Acoustic Stress WavesUltrasonic emission detectable (>20 kHz). Zero increase in ISO velocity. Months of remaining life.
Stage 2 (Defect Exists)Envelope PeaksBPFO/BPFI visible in Hilbert envelope demodulation. Bearing natural frequencies excited.
Stage 3 (Severe)Sidebands & HarmonicsMultiple harmonics (2X, 3X BPFO) with 1X sidebands. Plan immediate turnaround replacement.
PRACTICAL OPTIMIZATION STRATEGIES

Actionable Engineering Best Practices

Hilbert Envelope Demodulation

Bandpass filter around bearing housing resonance (5-15 kHz) to amplify micro-impact peaks.

Lubrication Thickness Verification

High-frequency ultrasound detects micro-friction long before metal-to-metal spalling occurs.

AUTOMATED OPTRUSS TELEMETRY INTEGRATION

Stream Live Sensor Telemetry Directly into CMMS Metrics

Eliminate manual spreadsheet logging. Optruss connects directly to PLC/SCADA tags and vibration sensors to compute live MTBF, calculate real-time downtime loss, and dispatch predictive work orders before machines trip.

Automate ISO 10816 / VDI 2056 Calculations with Optruss AI

Eliminate manual data entry. Connect plant telemetry directly to Optruss to automate calculations and trigger proactive work orders.