A ball bearing supports relative rotation through balls running between inner and outer raceways. Follow their motion in the animation and compare how a single elastic contact patch grows with load. The calculator scales an assumed reference ellipse; bearing load ratings and fatigue life require a separate calculation using data for the selected bearing.
Ball Bearings Interactive Calculator
Scale a single contact ellipse from a supplied reference load and length. The animation shows rolling and a magnified contact patch, not a specific bearing product rating.
Equation Used
For fixed local curvature and elastic material properties, Hertz contact lengths scale with the cube root of the normal contact load. Doubling that local load increases the modeled length by about 26%. The supplied reference ellipse is a hypothetical comparison, not a product specification.
- Same local curvature and material in the reference and comparison.
- Load refers to one contact, not the total radial bearing load.
- Ellipse full width is assumed 40% of its full length.
- Reference dimensions are hypothetical; obtain appropriate local contact data before applying the comparison to a bearing.
Cube-root contact-length scaling requires a local normal load. The mean-pressure index is force divided by the assumed ellipse area; peak Hertz pressure and whole-bearing load distribution are not calculated.
Rolling motion and local contact
The inner and outer rings provide raceways that guide the balls. Rotation of one ring makes the balls spin and travel around the bearing. The front-view animation holds the outer ring stationary and omits the cage so the motion is visible.
Each loaded ball contacts both raceways. Elastic deformation spreads a nominal point contact into a small patch, often approximated as an ellipse. Its size depends on local load, curvature and elastic properties. The bearing’s total applied radial load is distributed among loaded rolling elements; it is not automatically the normal load on every ball contact.
Main parts
- Rings and raceways: transmit loads between the shaft, rolling elements and housing.
- Balls: roll and spin as the rings move relative to one another.
- Cage: separates and guides the balls; its forces and motion matter in real operation.
- Lubricant: supports the rolling contact and affects friction and temperature.
- Seals or shields, when fitted: help retain lubricant and limit contamination.
Real bearing friction includes rolling, sliding, seals and lubricant drag. The ideal rolling animation does not represent all of these losses or predict operating temperature.
Choosing a bearing for an application
Ball bearings support shafts and rotating components in motors, machine tools, gearboxes, rollers and many small mechanisms. Different arrangements serve different loads: deep-groove, angular-contact and self-aligning ball bearings are not interchangeable merely because their bore diameters match.
Selection considers radial and axial load, speed, stiffness, accuracy, operating clearance or preload, lubrication, fits, sealing and environment. There is no universal friction reduction, clearance class or guaranteed service life that applies to every ball bearing.
Mounting and service details should come from the equipment and bearing documentation. A larger rating alone does not prove that a replacement bearing has suitable dimensions, speed capability or operating conditions.
Contact scaling and bearing life are different calculations
What this calculator evaluates
Let F be one local normal contact load, Fref its reference load and Lref the reference full ellipse length. The calculated full length is L = Lref(F/Fref)1/3.
The assumed full width is 0.4L. Thus the semi-axes are L/2 and 0.2L, and area A = π(L/2)(0.2L) = 0.1πL². Mean pressure index = F/A in N/mm² when force is in N and length in mm. This area-average quantity is not peak Hertz pressure or an allowable stress.
The inputs use a positive numerical floor of 0.001. A zero-load limit is therefore not represented exactly. The cube-root relationship assumes the same local geometry and elastic properties; it is not a plastic-deformation or damage model.
A separate bearing-life equation
For ball bearings, basic rating life L10 = (C/P)³ in millions of revolutions. At constant speed n in rpm, L10h = 106(C/P)³/(60n) hours. C is the catalog basic dynamic load rating and P the equivalent dynamic bearing load, in matching units. P is not necessarily the local contact load used above.
L10 is a statistical basic rating at 90% reliability under its defined conditions. It does not guarantee when an individual bearing will fail, predict grease or seal life, or set a maintenance interval. The interactive tool on this page does not evaluate this life equation.
Worked examples with explicitly different loads
Contact-patch comparison
Take a hypothetical reference contact load of 1000 N with full ellipse length 0.8 mm. At that same load the assumed area is 0.20106 mm² and the mean pressure index is 4973.59 N/mm². These reference dimensions are examples, not measurements or ratings for a particular bearing.
At 500 N the load ratio is 0.5, length becomes 0.63496 mm, area 0.12666 mm² and index 3947.54 N/mm². At 2000 N the ratio is 2, length is 1.00794 mm, area 0.31917 mm² and index 6266.33 N/mm².
Doubling load increases area by about 58.7%, so the mean index rises by about 26%, rather than doubling. These numbers describe the assumed elastic scaling, not a permissible operating range.
Independent life-arithmetic example
For hypothetical catalog and operating values C = 42,300 N, P = 4500 N and n = 180 rpm, C/P = 9.4. Its cube is 830.584, giving L10h ≈ 76,906 hours. Halving P multiplies that basic rating by eight; doubling P divides it by eight.
This is not a documented factory installation or a guaranteed replacement interval. Contamination, lubrication, mounting and operating conditions can make actual service life very different.
Match the calculation to the question
| Question | Information needed | What this tool supplies |
|---|---|---|
| How does one contact patch change? | Local normal load and an appropriate reference for the same curvature and material. | Cube-root length scaling with a fixed assumed aspect ratio. |
| How long might a bearing resist fatigue? | Catalog rating, equivalent load, speed and appropriate life conditions. | No life output; a separate basic equation is explained above. |
| How much friction or heat occurs? | Bearing geometry, load, lubricant, seals, speed and temperature. | No friction or thermal model. |
| Which fit or clearance is appropriate? | Loads, shaft and housing, fits, temperature differences and manufacturer guidance. | No mounting recommendation. |
Ball-bearing questions
No. It is the normal load at one local ball-race contact. Whole-bearing load distribution must be established separately.
For fixed elastic contact geometry, its linear dimensions scale with the cube root of load. With the assumed fixed shape, area scales with load to the two-thirds power.
No. It is force divided by the assumed contact ellipse area. It is not the peak contact pressure, an allowable material stress or a fatigue-life result.
No. The reference load and ellipse dimensions are hypothetical. Real contact dimensions require the specific geometry, materials and local load.
No. It is a statistical fatigue rating under defined conditions, not a guarantee for one bearing. Lubrication, contamination and mounting also affect service life.
No. Unusual noise needs assessment under the equipment’s service procedure. Running a damaged bearing is not a general repair for indentations or false brinelling.
Apply the force to the ring being fitted, using the appropriate fitting method. Do not transmit installation force through the rolling elements. Follow the bearing manufacturer’s instructions rather than a universal heating temperature or shaft fit.
No. Required operating clearance or preload depends on the bearing arrangement, fits, temperatures and duty. Use the specific design requirements.
Bearing references
- SKF: Rolling bearings, basic rating life: definitions of L10, equivalent load and conversion to operating hours.
- SKF: Using a friction model as an engineering tool: separate rolling, sliding, seal and drag contributions.
- SKF Bearing Maintenance Handbook: application-specific mounting and maintenance guidance.
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