Calculator
Example data table
| RPM | Elements | Element diameter | Pitch diameter | Angle | FTF (Hz) | BPFO (Hz) | BPFI (Hz) | BSF (Hz) |
|---|---|---|---|---|---|---|---|---|
| 1800 | 8 | 10 | 50 | 0° | 12 | 96 | 144 | 72 |
The sample uses consistent diameter units; only the ratio matters.
Formulas used
First convert shaft speed to shaft frequency: fr = RPM / 60.
Let n be rolling elements, d element diameter, D pitch diameter, and θ contact angle. Use k = (d / D) · cos(θ).
| Fault | Frequency |
|---|---|
| FTF (cage) | 0.5 · fr · (1 − k) |
| BPFO (outer race) | 0.5 · n · fr · (1 − k) |
| BPFI (inner race) | 0.5 · n · fr · (1 + k) |
| BSF (rolling element) | (D / (2d)) · fr · (1 − k²) |
Outputs can be shown in Hz, CPM (Hz × 60), or order (Hz / fr).
How to use this calculator
- Enter shaft speed in RPM.
- Fill bearing geometry: n, d, and D.
- Set contact angle if the bearing is angular.
- Select output unit and number of harmonics.
- Press Calculate to see results above the form.
- Use CSV or PDF to save and share results.
Article
1. What defect frequencies represent
Defect frequencies are repeating impact rates created when a damaged surface is struck during rotation. A vibration spectrum often shows these rates as peaks, sometimes surrounded by sidebands from speed changes. This calculator predicts the main bearing-related peak locations so you can search the right bands first.
2. Inputs that control the result
The model uses shaft speed, rolling element count, pitch diameter, element diameter, and contact angle. Only the diameter ratio matters, so you can enter millimeters or inches as long as both diameters share the same unit. Contact angle changes the cosine term and shifts every predicted defect line.
3. Reading BPFO and BPFI
BPFO is the outer race impact rate and commonly appears as a stable, narrow peak because the outer ring is stationary. BPFI is the inner race impact rate and often shows stronger modulation because the defect rotates relative to the sensor. Comparing both helps separate stationary versus rotating fault sources.
4. Understanding BSF and FTF
BSF is the rolling element spin rate and can appear with multiple harmonics because the element may slip. FTF is the cage rate and is usually much lower than 1X speed, making it easier to miss if the spectrum starts too high. Including low-frequency ranges improves early fault detection.
5. Why harmonics matter
Real machines rarely show only one clean line. Surface damage, load direction, and looseness can create 2X, 3X, or higher harmonics. The harmonics table lists multiples up to 20X, helping you match clustered peaks and avoid confusing them with gearmesh or electrical components.
6. Unit choices: Hz, CPM, and orders
Hz is standard for spectra. CPM is helpful when your instrument reports cycles per minute. Orders normalize by shaft frequency, so 1.0 order equals 1X speed. Orders make comparisons easier when RPM drifts, because predicted lines remain near constant order values.
7. Practical measurement tips
Use consistent sensor mounting and record RPM during the same capture window. If speed varies, consider averaging or using order tracking. Confirm geometry values from bearing catalogs, not assumptions, because small diameter errors shift predictions. Finally, use the exported report to document baseline readings and follow changes over time.
FAQs
1) What if I only know the bearing number?
Look up rolling element count, pitch diameter, element diameter, and contact angle from the bearing catalog or datasheet. Enter those values with your measured RPM. The calculator needs geometry, not just the part number, to predict accurate frequencies.
2) Do diameters need a specific unit?
No. Use any unit you like, but keep element diameter and pitch diameter in the same unit. The formulas use the ratio d/D, so consistent units keep the ratio correct and the predicted frequencies unchanged.
3) Why do I see sidebands around defect peaks?
Sidebands often come from amplitude modulation caused by load changes, misalignment, looseness, or speed variation. You may see peaks spaced by 1X speed around BPFO or BPFI. Use the order output to compare patterns across different RPM values.
4) What contact angle should I enter?
Use the catalog contact angle for angular contact or thrust bearings. For many deep-groove bearings under light axial load, using 0 degrees is a practical approximation. If axial load is high, the real angle can increase and shift predictions.
5) Which frequency usually appears first in early faults?
It depends on where damage starts. Outer race faults often show stable BPFO lines early. Inner race faults can show BPFI with stronger modulation. Cage and ball defects may appear later, but low-frequency FTF can be visible if the measurement includes that range.
6) Why can BSF be harder to confirm?
Rolling elements can slip, changing the true spin rate and smearing BSF peaks. BSF may appear with multiple harmonics and interact with modulation from race faults. Using a longer record length and good signal-to-noise helps identify stable BSF-related patterns.