Basic Rating Life Formula
L10h (hours) = (10⁶ / 60n) × (C / P)^p
C = Basic dynamic load rating (from bearing catalogue, kN)
P = Equivalent dynamic bearing load (kN)
p = Life exponent: 3 for ball bearings; 10/3 for roller bearings
n = Rotational speed (RPM)
Equivalent Dynamic Load
When both radial and axial forces act on a bearing, the equivalent dynamic load P combines them:
Fr = Radial force (kN)
Fa = Axial force (kN)
X = Radial load factor (from bearing catalogue — depends on Fa/Fr ratio)
Y = Axial load factor (from bearing catalogue)
For purely radial loads with no significant axial component (Fa/Fr ≤ e, where e is a bearing-specific ratio): P = Fr. X and Y factors are tabulated in bearing manufacturer catalogues for each bearing series and load angle.
Worked Example
Deep groove ball bearing 6310 (from SKF catalogue: C = 61.8 kN) running at 1,450 RPM, radial load Fr = 5 kN, no axial load:
- Equivalent load: P = Fr = 5 kN (no axial component)
- L10 = (61.8 / 5)³ = 12.36³ = 1,886 million revolutions
- L10h = (10⁶ / (60 × 1,450)) × 1,886 = 11.49 × 1,886 = 21,680 hours
This means 90% of identical bearings under these conditions will survive beyond 21,680 hours (~2.5 years continuous operation).
Modified Rating Life (ISO 281)
The basic L10 life assumes ideal lubrication and contamination conditions. The modified life accounts for real operating conditions:
a1 = Reliability factor (1.0 = 90% survival; 0.62 = 95%; 0.53 = 96%; 0.44 = 97%; 0.33 = 98%; 0.21 = 99%)
aISO = Life modification factor for lubrication and contamination conditions
The aISO factor is determined from the viscosity ratio κ (actual viscosity / required viscosity at operating speed) and the contamination factor eC. When κ ≥ 1.0 (full lubricant film) and contamination is low, aISO can reach 5–50, meaning real bearing life far exceeds the basic L10. When κ < 0.5 (lubricant film breakdown), aISO < 1.0 and actual life is shorter than L10.
Factors That Reduce Bearing Life
| Factor | Effect on life | Notes |
|---|---|---|
| Contamination (particles in lubricant) | Can reduce life by 5–10× | ISO 4406 cleanliness code — target 17/15/12 or better |
| Misalignment (shaft deflection, housing bore) | Reduces life as edge loading increases | Spherical roller bearings tolerate misalignment; deep groove ball bearings do not |
| Inadequate lubrication (κ < 1) | Reduces life as metal-to-metal contact increases | Check viscosity grade vs. operating temperature and speed |
| Elevated temperature | Reduces lubricant viscosity; reduces grease base oil life | Every 15°C rise above 70°C roughly halves grease life |
| Overload (P > catalogue limits) | Cubic relationship — doubling load reduces life by 8× | Check C/P ratio; target C/P ≥ 5 for long life |
C/P Ratio as a Design Rule
A useful rule of thumb from the C/P ratio:
| C/P ratio | Expected relative life | Application suitability |
|---|---|---|
| < 2 | Very short — heavily loaded | Not recommended for continuous operation |
| 2–4 | Short life | Acceptable for slow-speed applications only |
| 4–6 | Moderate life | Acceptable for general industrial use |
| 6–10 | Good life | Recommended for most industrial applications |
| >10 | Long life | Optimal — bearing life likely exceeds machine life |
Use the C/P ratio to screen bearing selections quickly. Detailed L10h calculation is then used to confirm the selected bearing meets the design life requirement (typically 20,000–100,000 hours for industrial equipment).