3. The equivalent load: turning two forces into one
The life equation takes a single number P, but a real bearing sees a radial force and an axial force at once. The equivalent dynamic load is the pure radial load that would do the same damage:
P = X · Fr + Y · FaISO 281
The threshold e
Below a certain axial-to-radial ratio the axial load simply rides along inside the existing contact and does no extra damage. Above it, the load zone shifts and both components count:
| Condition | Equivalent load |
|---|---|
| Fa/Fr ≤ e | P = Fr |
| Fa/Fr > e | P = X·Fr + Y·Fa |
X, Y and e are inputs here, not built in. They belong to the specific
bearing series, and for a deep groove ball bearing they also depend on Fa/C₀ — the
catalogue gives a small table. Every source that could be reached publishes that table as an image,
so rather than transcribe numbers that could not be checked, BearingLab asks you for them. Read them
off the page for the bearing you are actually considering; that is how the calculation is done in
practice anyway.
A duty cycle that varies
A robot joint does not sit at one load. Because damage accumulates with Pp, the correct average is not the arithmetic mean but the equal-damage mean:
Pm = ( Σ fi ni PipΣ fi ni )1/p
Two blocks of equal duration at 2 kN and 6 kN give Pm = 4.82 kN, not 4 kN. The heavy block dominates, which is why a short, hard part of the cycle can decide the whole bearing.