Bearing Rolling Life

Notes & Use

Calculates design values related to lifetime for rolling element bearings when the following is true:

  • The bearing operation is not characterized as an occilating motion; the spinning object tends to make full rotations at a roughly constant speed.
  • The RPM shall be approximated as an average RPM over the lifetime of the bearing.
  • The radial and thrust loads have been converted to an equivalent load as per the bearing manufacturer’s reccomendations.

This calculator does not calculate for:

  • Equivalent load
  • Tapered roller bearings.

Terms

$C$ = Basic dynamic load rating, pounds force or Newtons

$C_{0}$ = Basic static load rating, pounds force or Newtons

$L$ = Load on bearing, pounds force or Newtons

$S_{0}$ = Safety factor for static loads, unitless

$C_{x}$ = Rated lifetime hours, revolutions

$n$ = Average rotations per minute of bearing at load L.

$r$ = Revolutions

$h$ = Operating hours

$x$ = bearing type factor, from table:

Type factor
Ball Bearing 3
Roller Bearing (10 / 3)

$a_{1}$ = Rotation factor, from table:

Rotating member factor
Inner Ring 1
Outer Ring 1.2

$a_{2}$ = Reliability factor, from table:

Reliability factor
90% 1
95% 0.62
96% 0.53
97% 0.44
98% 0.33
99% 0.21

$a_{3}$ = Application factor, generally 1.0.

$a_{3}$ = 1.0 under ideal lubrication condition, when rolling element and track surface are completely isolated by oil film and surface failure can be ignored.

$a_{3}$ < 1 for poor lubrication conditions (such as low viscocity, minimal or dirty lubrication), extremely slow speeds, shock loading, vibration, or extreme temperatures. Value should not fall below 0.5.

$a_{3}$ > 1 for supremely excellent conditions.

Equations:

Calculate for “Lifetime”:

Safety factor: $$ S_{0} = \frac { C_{0} } {L} $$

Revolutions: $$ r = \left( \frac {C}{ L \, a_{1}} \right)^x \, C_{x} \, a_{2} \, a_{3} $$

Hours: $$ h = \frac {r}{60 \, n} $$

Calculate for “Bearing Rating”:

Basic static load: $$ C_{0} = S_{0} \, L $$

Revolutions: $$ r = 60 \, h \, n $$

Basic dynamic load:

$$ C = L \, a_{1} \left( \frac {r} {C_{x} \, a_{2} \, a_{3}} \right)^ \frac{1}{x} $$

Calculate for “Load”:

Safety factor: $$ S_{0} = \frac { C_{0} } {L} $$

Revolutions: $$ r = 60 \, h \, n $$

Load: $$ L = \frac {C} { a_{1} \, \left( \frac {r} {C_{x} \, a_{2} \, a_{3}} \right)^ \frac{1}{x} } $$

Calculate for “RPM”:

Safety factor: $$ S_{0} = \frac { C_{0} } {L} $$

Revolutions: $$ r = \left( \frac {C} {L \, a_{1}}\right)^x \, C_{x} \, a_{2} \, a_{3} $$

RPM: $$ n = \frac{r}{60 \, h} $$

Sources