KEVOS® MAKEOS · Power Transmission
Roller Bearing Load Ratings from Geometry (Basic Dynamic and Static Ratings, L10 Life, Static Safety)
From a roller bearing’s geometry — rows, contact angle, number, diameter and effective length of the rollers — what are its basic dynamic and static load ratings, what L10 life does it give at my equivalent load and speed, and is the load within the range the rating formulas suit?
Basic load ratings of radial and thrust roller bearings (cylindrical, tapered, spherical and needle) by the AFBMA formulas the handbook gives: radial C = fc (i leff cos α)^(7/9) Z^(3/4) D^(29/27), with bearings in tandem by the 7/9 power; thrust Ca = fc leff^(7/9) Z^(3/4) D^(29/27) at 90° or fc (leff cos α)^(7/9) Z^(3/4) D^(29/27) tan α otherwise, with equal rows by formula (18); static ratings Co = 44 (1 − D cos α ÷ dm) i Z leff D cos α and Coa = 220 (1 − D cos α ÷ dm) Z leff D sin α; then L10 = (C ÷ P)^(10/3) in millions of revolutions and hours, the static safety and the handbook’s warnings for long rollers and heavy loads. The factor fc is read from the handbook table for D cos α ÷ dm, which the tool shows.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bearing type | choice | Radial roller bearings, or thrust roller bearings. |
| Rows of rollers i | rows | Number of rows of rollers (for a thrust bearing, rows carrying load in the same direction). |
| Nominal contact angle α | ° | Nominal contact angle: 0° for a cylindrical roller bearing, 90° for a pure thrust bearing. |
| Rollers per row Z | rollers | Number of rollers in each row. |
| Roller diameter D (mean for tapered, major for spherical) | mm | Roller diameter: the mean diameter of a tapered roller, the major diameter of a spherical roller. |
| Effective roller length leff | mm | Effective length of contact: roller length less chamfers or grinding undercuts where contact is shortest. |
| Pitch diameter of the roller set dm | mm | Pitch diameter of the roller set, used for the static rating and for reading fc. |
| Factor from the handbook tables | ||
| Dynamic factor fc (metric, for D cos α ÷ dm) | Dynamic rating factor read from the handbook table for the bearing type and D cos α ÷ dm (metric column). | |
| Similar bearings in tandem | bearings | Number of similar single-row bearings mounted in tandem and sharing the load. |
| Loads and requirements | ||
| Equivalent dynamic load P | N | Equivalent dynamic load, X Fr + Y Fa, from the bearing life tools. |
| Speed | rpm | Rotational speed of the bearing. |
| Life you require | h | Rating life the application needs. |
| Static equivalent load Po | N | Static equivalent load on the bearing. |
| Least static safety Co ÷ Po you accept | Least static safety factor you accept. | |
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: Bearing type
- What it is
- Whether the roller bearing carries mainly radial load or mainly thrust.
- Units and format
- Choose one of 2 options from the list: Radial roller; Thrust roller.
- Example
- The form opens with “Radial roller” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the rating formulas and the static rating.
- Get it right
- Angular contact bearings count as radial when the contact angle is below 90°.
What this means: Rows of rollers i
- What it is
- Number of rows of rollers in the bearing.
- Units and format
- Enter a number in rows: rows. The form accepts 1 rows to 8 rows. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 rows as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More rows raise the rating less than in proportion.
- Get it right
- For a thrust bearing, count only rows carrying load in the same direction.
What this means: Nominal contact angle α
- What it is
- Nominal contact angle between the load line and the plane square to the axis.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0° to 90°. 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 lowers the radial rating and raises the thrust rating.
- Get it right
- 0° for deep groove and cylindrical bearings, 90° for pure thrust bearings.
What this means: Rollers per row Z
- What it is
- Number of rollers carried in each row of the bearing.
- Units and format
- Enter a number in rollers: rollers. The form accepts 3 rollers to 500 rollers. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 14 rollers as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rating rises with a power of the number below one.
- Get it right
- Count them, or take the number from the bearing drawing.
What this means: Roller diameter D (mean for tapered, major for…
- What it is
- Diameter of the rollers: mean diameter of a tapered roller, major diameter of a spherical roller.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The dynamic rating rises with D^(29/27).
- Get it right
- Measure a roller or take it from the bearing drawing.
What this means: Effective roller length leff
- What it is
- Effective length of roller contact.
- 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 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The dynamic rating rises with leff^(7/9); above 2.5 D the factor fc falls.
- Get it right
- The roller length less chamfers or grinding undercuts where contact is shortest.
What this means: Pitch diameter of the roller set dm
- What it is
- Pitch diameter of the roller set, from bearing centre to roller centre and back.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets D cos α ÷ dm, the value for reading the factors.
- Get it right
- About the mean of the bore and the outside diameter of the bearing.
Factor from the handbook tables
What this means: Dynamic factor fc (metric, for D cos α ÷ dm)
- What it is
- Dynamic rating factor from the handbook table for the bearing type.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 87.7 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The dynamic rating rises in proportion.
- Get it right
- Read the metric column at the D cos α ÷ dm the tool shows; interpolate between rows.
What this means: Similar bearings in tandem
- What it is
- Number of similar bearings mounted in tandem and sharing the load.
- Units and format
- Enter a number in bearings: bearings. The form accepts 1 bearings to 10 bearings. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 bearings as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The dynamic rating rises by a power below one; the static rating in proportion.
- Get it right
- Only when they are made and mounted to share the load equally.
Loads and requirements
What this means: Equivalent dynamic load P
- What it is
- Equivalent dynamic load on the bearing.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Life falls with the cube (ball) or the 10/3 power (roller) of the load.
- Get it right
- X Fr + Y Fa with the factors from the handbook tables, or from the bearing life tools.
What this means: Speed
- What it is
- Rotational speed of the bearing.
- 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 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Converts the life in revolutions to hours.
- Get it right
- Use the mean speed over the duty cycle.
What this means: Life you require
- What it is
- Rating life the application needs, in hours.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h to 10000000 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fails the bearing when its life is shorter.
- Get it right
- The handbook lists typical design lives for many machines.
What this means: Static equivalent load Po
- What it is
- Static equivalent load on the bearing at rest or turning slowly.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the static safety.
- Get it right
- The greater of Xo Fr + Yo Fa and Fr; 0 if there is no static load.
What this means: Least static safety Co ÷ Po you accept
- What it is
- Least static safety factor Co ÷ Po you accept.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fails the bearing when the static safety is lower.
- Get it right
- Take it from the bearing maker for the duty and the quietness you need.
Method and formulas
- Radial: C = fc (i leff cos α)^(7/9) Z^(3/4) D^(29/27); tandem bearings × n^(7/9).
- Thrust: Ca = fc leff^(7/9) Z^(3/4) D^(29/27) (α = 90°) or fc (leff cos α)^(7/9) Z^(3/4) D^(29/27) tan α; i equal rows or bearings in tandem × (i n)^(7/9) by formula (18).
- Static: Co = 44 (1 − D cos α ÷ dm) i Z leff D cos α; Coa = 220 (1 − D cos α ÷ dm) Z leff D sin α; × number of rows or bearings in tandem.
- L10 = (C ÷ P)^(10/3) million revolutions; hours = L10 × 10⁶ ÷ (60 n); static safety = Co ÷ Po.
- Example: the bearing’s dynamic rating is 45,128 N, giving 9,262.9 h at 6000 N and 1500 rpm.
Limitations
- Rollers longer than 2.5 D need a lower fc, which the bearing maker sets.
- Above a load of C/4 to C/2 the 10/3 exponent may not hold; consult the bearing maker.
- The rating life is for 90 % reliability; adjust it with the bearing life tools. Catalogue ratings take precedence over these estimates.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate the load rating of a special roller bearing or roller path from its geometry
- Compare roller lengths, numbers and diameters for a rating
- Find the L10 life and static safety at the design loads
Who it is for
- Machine designers
- Maintenance and reliability engineers
- Bearing application engineers
What you get
- D cos α ÷ dm for reading fc
- Basic dynamic load rating C or Ca
- Basic static load rating Co or Coa
- Rating life L10 in millions of revolutions and hours
- Static safety Co ÷ Po
- Checks for long rollers and heavy loads
Interpreting the result
- Roller length and number raise the rating less than in proportion (powers 7/9 and 3/4).
- Rollers running directly on a shaft or housing need a surface equal to a raceway to reach the rating.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2409–2413, 2416–2417. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
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.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.