KEVOS® MAKEOS · Maintenance
Bearing Defect Frequency Check (BPFO, BPFI, Ball Spin, Cage, Match to a Measured Peak)
For this rolling bearing at this shaft speed, what are its outer race, inner race, ball spin and cage defect frequencies, and does the peak I measured in the vibration spectrum match one of them?
Characteristic defect frequencies of a rolling element bearing from its geometry and shaft speed: ball pass frequency of the outer race (BPFO) and inner race (BPFI), ball spin frequency (BSF) and fundamental train (cage) frequency (FTF), each in hertz, cycles per minute and orders of shaft speed, with their first three harmonics, compared with a measured spectrum peak within your tolerance to name the likely defect.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Shaft speed | rpm | Speed of the shaft carrying the rotating race, from a tachometer or the speed line in the spectrum. |
| Number of rolling elements | balls | Number of balls or rollers in one row, from the bearing maker’s data. |
| Rolling element diameter | mm | Diameter of one ball or roller, from the bearing maker’s data. |
| Pitch diameter | mm | Diameter of the circle through the ball centres (about the average of bore and outside diameter). |
| Contact angle | ° | Contact angle of the bearing (0° for a deep groove ball bearing under radial load). |
| Measured peak | ||
| Measured peak frequency | Hz | Frequency of the peak you want to identify, from the spectrum or envelope spectrum. |
| Matching tolerance | % | How close (as a share of the defect frequency) a peak must be to count as a match; allows for slip and speed error. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Shaft speed
- What it is
- The rotational speed of the shaft carrying the rotating race, which every defect frequency is proportional to.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1480 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All four defect frequencies rise in proportion to the shaft speed.
- Get it right
- Measure it at the time of the vibration reading; speeds on variable-speed drives change with load.
What this means: Number of rolling elements
- What it is
- The number of balls or rollers in one row of the bearing, which sets how many times per revolution a race defect is struck.
- Units and format
- Enter a number in balls: balls. The form accepts 3 balls to 200 balls. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9 balls as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The ball pass frequencies rise in proportion; the cage and ball spin frequencies do not change.
- Get it right
- Take it from the bearing maker’s data for the exact designation; it is not stamped on the bearing.
What this means: Rolling element diameter
- What it is
- The diameter of one ball or roller in the bearing, which with the pitch diameter sets the geometry ratio in every formula.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7.94 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger element lowers the outer race and cage frequencies and raises the inner race frequency.
- Get it right
- Use the maker’s value; measuring a ball from a used bearing is only an approximation.
What this means: Pitch diameter
- What it is
- The diameter of the circle through the centres of the balls or rollers, roughly midway between the bore and the outside diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 39.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the ratio d ÷ D that shifts every defect frequency.
- Get it right
- If the maker does not give it, the average of bore and outside diameter is a reasonable estimate.
What this means: Contact angle
- What it is
- The angle between the line of contact through a ball and the plane at right angles to the shaft, which reduces the effective geometry ratio.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 60°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger angle reduces the cosine term, moving the outer and inner race frequencies closer together.
- Get it right
- Deep groove ball bearings under radial load run close to zero; angular contact bearings are typically 15 to 40 degrees, from the maker’s data.
Measured peak
What this means: Measured peak frequency
- What it is
- The frequency of the spectrum peak you want to identify, read from the vibration spectrum or the envelope spectrum.
- Units and format
- Enter a number in Hz: hertz (cycles per second). The form accepts 0 Hz to 1000000 Hz. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 88.3 Hz as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only changes which defect, if any, is matched; the defect frequencies do not change.
- Get it right
- Read the peak from the envelope (demodulated) spectrum for early bearing faults; the raw spectrum often hides them.
What this means: Matching tolerance
- What it is
- How close the measured peak must be to a defect frequency or its harmonic, as a share of that frequency, to count as a match.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0.1% to 20%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider tolerance matches more peaks; the defect frequencies do not change.
- Get it right
- Allow a little for slip and speed error; too wide a band matches peaks that are not bearing faults.
Method and formulas
- Shaft frequency f_r = rpm ÷ 60; ratio r = (d ÷ D) cos φ.
- BPFO = (n f_r ÷ 2)(1 − r); BPFI = (n f_r ÷ 2)(1 + r); FTF = (f_r ÷ 2)(1 − r); BSF = (D f_r ÷ 2d)(1 − r²) (rolling element bearing kinematics, as given by MathWorks and Randall and Antoni).
- The measured peak matches a defect if it lies within the tolerance of any of the first three harmonics of that defect frequency.
- Example: BPFO 88.425 Hz, BPFI 133.58 Hz; the 88.3 Hz peak matches a defect frequency.
Limitations
- Kinematic frequencies assume no slip; real bearings slip by 1 to 2 %, so measured peaks sit slightly off the calculated values.
- A matching frequency suggests, but does not prove, a defect: confirm with the envelope spectrum, sidebands, trend and inspection.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Identify which part of a bearing a vibration peak points to
- Set alarm bands for a bearing in a monitoring system
- Check whether a peak is a bearing frequency or something else
Who it is for
- Vibration analysts
- Reliability and maintenance engineers
- Condition monitoring technicians
What you get
- BPFO, BPFI, BSF and FTF in Hz, cpm and orders
- First three harmonics
- Which defect frequency, if any, the measured peak matches
Interpreting the result
- Inner race defects usually show sidebands at shaft speed because the defect rotates in and out of the load zone; outer race defects on a stationary race usually do not.
References
- MathWorks, Rolling Element Bearing Fault Diagnosis (Predictive Maintenance Toolbox documentation) — https://www.mathworks.com/help/predmaint/ug/Rolling-Element-Bearing-Fault-Diagnosis.html
- Randall R. B. and Antoni J., Rolling element bearing diagnostics — A tutorial, Mechanical Systems and Signal Processing 25 (2), 485–520 (2011).
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Vibration checks in service
In Whirling Shafts by the Numbers
What it covers: Reading a rotating machine's vibration: levels, trends and spectra, what 1×, 2× and other peaks point to, bearing defect frequencies, and the wrong bearing geometry that hid a failing race.
Useful alongside · Library collection
Maintenance that prevents breakdowns: choosing a strategy for each machine in a small factory
In Lean, Maintenance and Continuous Improvement
What it covers: Running equipment until it breaks feels cheap until the breakdown comes at the worst time. How to rank machines, match maintenance to each, involve operators and learn from repeat failures.
Useful alongside · Library collection
Selecting bearings and lubrication for reliable machines: types, life, fits, sealing and failure causes
In Machine Elements and Mechanical Design
What it covers: Most bearings fail from contamination, poor lubrication or bad fitting, not fatigue. How to choose bearing types, size them for life, fit, seal and lubricate them, and diagnose failures.
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