Life exponent

For life calculation of bearings, the two are life exponent s

${\displaystyle p=3}$for ball bearings

${\displaystyle p=10/3}$ for roller bearings

used.

origin

These exponents come from experiments by Palmgren and Lundberg on the service life of rolling bearings .

Derivation

When calculating the rolling bearing life, a distinction is made between point and line contact. While with ball bearings there is point contact between the rolling elements and the inner or outer ring of the rolling bearing, rolling elements and rings with roller bearings touch along a line. Taking this distinction into account, the DIN ISO 281 standard specifies two formulas for bearing service life: for point contact and for line contact . ${\displaystyle L_{10}=\left({\frac {C_{x}}{P_{x}}}\right)^{\frac {c-h+2}{3\cdot e_{1}}}}$ ${\displaystyle L_{10}=\left({\frac {C_{x}}{P_{x}}}\right)^{\frac {c-h+1}{2\cdot e_{2}}}}$

The following applies here:

${\displaystyle L_{10}}$ = Nominal bearing life (applies to 90% of all bearings in a batch)

${\displaystyle C_{x}}$ = Dynamic load rating, where x = r is set for radial and x = a for axial dynamic load rating

${\displaystyle P_{x}}$ = Bearing load, where x = r for radial and x = a for axial load.

${\displaystyle c}$ = Exponent of stress in relation to stress-life span (determined experimentally)

${\displaystyle h}$ = Exponent of the depth of the maximum shear stress (determined experimentally)

${\displaystyle e_{1},e_{2}}$= Slope of the Weibull straight line for the probability distribution of the service life (scatter), where for point contact and for line contact ${\displaystyle e_{1}}$ ${\displaystyle e_{2}}$

The constants and are specified with and . The slope of the Weibull straight line is specified for point contact with and for line contact with . ${\displaystyle c}$ ${\displaystyle h}$ ${\displaystyle c={\frac {31}{3}}}$ ${\displaystyle h={\frac {7}{3}}}$ ${\displaystyle e_{1}={\frac {10}{9}}}$ ${\displaystyle e_{2}={\frac {9}{8}}}$

Inserted in the above formulas for the service life one finally obtains:

${\displaystyle L_{10}=\left({\frac {C_{x}}{P_{x}}}\right)^{3}}$ for point contact

${\displaystyle L_{10}=\left({\frac {C_{x}}{P_{x}}}\right)^{4}}$ for line contact

Practical calculation

The practical life calculation of rolling bearings is based on the following equations:

${\displaystyle L_{10}=\left({\frac {C_{x}}{P_{x}}}\right)^{3}}$ for ball bearings

${\displaystyle L_{10}=\left({\frac {C_{x}}{P_{x}}}\right)^{\frac {10}{3}}}$ for roller bearings.

In contrast to the exponents calculated in the derivation , however, the exponent is used when the line is touched . This can be explained by the fact that under real conditions the line contact can change into a point contact and the service life would therefore be assessed too optimistically. The formulas used in practice thus represent a compromise in order to cover computational imponderables. ${\displaystyle p=3}$ ${\displaystyle p={\frac {10}{3}}}$

With ISO / TS 16281, a standardized numerical method is now available with which the contact relationships can be calculated in detail and which can therefore dispense with these safeguards.

Individual evidence

1. ↑ DIN ISO 281 supplement 2 , 1994-09, p. 9.
2. ↑ DIN ISO 281 supplement 2 , 1994-09, p. 39.
3. ↑ Lundberg, G., Palmgren, A .: Dynamic Capacity of Rolling Bearings. , Acta Polytechnica, Mechanical Engineering Series, Vol. 1, No. 3, The Royal Swedish Academy of Engineering Sciences, 1947.