Calculation of the theoretical service life of ball bearings
The theoretical service life is only achieved in practice if the following conditions are met:
In more complex applications or cases of doubt, we recommend that you seek our technical advice.
We have used the formulas and theories of the ISO and AFBMA standards to calculate the load rating and theoretical service life of ball bearings.
1. Service life of radial and axial ball bearings
| Definitions: | |
| L10 | = Service life in millions of revolutions |
| C | = Dynamic load rating in N |
| P | = Dynamic equivalent load in N |
| C/P | = Load safety |
2. Service life in hours
| Definitions: | |
| L10 | = Service life in millions of revolutions |
| n | = Speed in 1/min |
Conversion of units
1 N = 1 kg m/s2
1 kgf (= 1kp) = 9.81 N
3. Definitions
| L10 | = service life in millions of revolutions or in |
| L10h |
= hours, which is achieved by 90 % of a larger number of identical ball bearings under the same conditions. 40 % of them achieve a five times longer service life.
|
| C |
= The basic dynamic load rating is a constant, unchanging load at which the bearing has a basic rating life of one million revolutions.
achieved. For radial bearings, the basic radial dynamic load rating Cr refers to the constantly unchanging load capacity.
radial load only. For axial bearings, the axial dynamic load rating Ca refers to the unchanging, only axial load acting in the bearing axis. For each bearing, the load ratings Cr and Ca are specified in the dimension tables, which depend on the bearing size, the number of rolling
body, the material and the bearing design.
are dependent on. The values of the load ratings were determined in accordance with the STN ISO 281 standard. These values are confirmed on the test benches and by the operating results.
|
The dynamic load rating is taken into account:
| P |
= Dynamic equivalent load. It is a fictitious load that includes axial and radial load components in such a way that the same values are determined when calculating the theoretical service life as if only a pure radial load (for radial bearings) or a pure axial load (for axial bearings) were acting.
|
| C0 | = Basic static load rating. In the case of radial bearings, this is a radial load and in the case of axial bearings an axially directed constant load, in which a permanent deformation of max. 0.1 promill of the rolling element diameter is achieved at the highest loaded contact point and the following operating conditions apply: ■ Standstill ■ Very slow swivel movements ■ Very low speeds |
| P0 | = statically equivalent load. |
4. Calculation of the dynamic equivalent load
4.1 Radial deep groove ball bearing, single row:
P = X – Fr + Y – Fa
| Definitions: | |
| P | = Dynamic equivalent load in N |
| Fr | = Radial component of the load in N |
| Fa | = Axial component of the load in N |
| X | = Radial factor of the bearing according to table below |
| Y | = Axial factor of the bearing according to table below |
4.2 Axial deep groove ball bearings:
P = Fa
5. Calculation of the static load rating
C0 = S0 – P0
| Definitions: | |
| C0 | = Basic static load rating in N |
| P0 | = Equivalent static load in N |
| S0 | = Static load safety factor |
| S0 | = 0.5 to 0.7 for low requirements and vibration-free operation |
| S0 | = 1.0 to 1.2 for normal requirements and vibration-free operation |
| S0 | = 1.5 to 2.0 for high requirements and impact loads |
6. Calculation of the equivalent static load
6.1 Radial deep groove ball bearing:
P0 = X0 – Fr + Y0 – Fa
| Definitions: | |
| P0 | = Equivalent static bearing load in N |
| Fr | = Radial component of the largest static load in N |
| Fa | = Axial component of the largest static load in N |
| X0 | = Radial load factor |
| Y0 | = Axial load factor |
If the statically equivalent bearing load P0 < Fr determined according to this formula is used, P0 = Fr must be calculated. Values for the factors X0 and Y0, X0 = 0.6 Y0 = 0.5
6.2 Axial deep groove ball bearings:
P0 = Fa
7. Duplex bearing
7.1 Duplex arrangement X or O
Basic dynamic load rating
| Definitions: | |
| Cd | = Basic dynamic load rating for a pair of ball bearings in N |
| αº | = Contact angle |
| C | = Basic dynamic load rating for a single ball bearing in N |
| L10 | = Service life in millions of revolutions |
| P | = Dynamic equivalent load in N |
Dynamic equivalent load
P = X – Fr + Y – Fa
| Definitions: | |
| P | = Dynamic equivalent load in N |
| Fr | = Radial component of the load in N |
| Fa | = Axial component of the load in N |
| X | = Radial factor for a pair of ball bearings according to page 34 |
| Y | = Axial factor for a ball bearing pair according to page 34 |
Duplex arrangement X or O with preload
Fa = 0.8 (Fap + Fa1)*
| Definitions: | |
| Fa | = Effective axial load in N |
| Fap | = Preload of the ball bearing pair in N |
| Fa1 | = External axial force acting on the pre-loaded ball bearing pair in N. |
* The ratio of preload Fap and axial force Fa1 must be selected so that no bearing is completely relaxed. Within the radial clearances and contact angles recommended by myonic, this condition is met if:
Fap ≥ 0.35 Fa1
Duplex arrangement X or O without preload or with low axial play
| Definitions: | |
| Z | = Number of balls |
| Dw | = Diamter of the balls in mm |
7.2 Tandem arrangement
Basic dynamic load rating
Ct = C – N0.7
| Definitions: | |
| Ct | = Dynamic load rating of the tandem arrangement in N |
| C | = Dynamic load rating of a single ball bearing in N |
| N | = Number of ball bearings |
The dynamic equivalent load and the rating life are calculated taking Ct into account, as for single bearings with a row of balls. The factors X, Y and e are in the table at the bottom of this page.
8. Calculation example
Example 1
Calculation of the theoretical rating life Lh of a radial deep groove ball bearing R 2570X for the following operating conditions:
| Radial load | Fr = 5.7 N |
| Axial load | Fa = 2.8 N |
| Speed | n = 8000 rpm |
| Radial clearance | 2 / 5 μm |
Values of X and Y for radial ball bearings
For detailed calculations, please contact myonic for further assistance.
