The bearing life formula is only as accurate as the load you put into it. And the load that a bearing actually sees is almost never just the weight of the shaft assembly. Belt tension, gear mesh forces, impeller thrust, coupling misalignment, and thermal growth all contribute. Miss one of these and your life calculation is wrong, your bearing selection is wrong, and you wonder why the bearing failed early.
This guide covers how to determine the equivalent dynamic load P for bearing life calculations, including the loads that people commonly forget.
Where Bearing Loads Come From
Radial load acts perpendicular to the shaft. Sources include: the weight of the shaft, coupling, and rotating components; belt or chain tension (often the largest single radial force on a shaft); gear mesh separating force; impeller hydraulic radial force on pumps; and external forces from the driven process.
Axial (thrust) load acts parallel to the shaft. Sources include: helical gear mesh thrust component; impeller thrust on pumps and fans; thermal growth of the shaft pushing against a fixed bearing; coupling misalignment creating a cyclic thrust; and gravity on vertical shafts.
The most commonly forgotten loads are: belt tension on the drive side (adds 2 to 3 times the transmitted torque as a radial force), helical gear thrust (typically 30 to 60 percent of the tangential gear force), and the weight of the shaft and coupling (small but not zero, especially on vertical applications).
Equivalent Dynamic Load Calculator
Calculate equivalent dynamic bearing load P from radial and axial forces. Supports deep groove, angular contact, cylindrical roller, self-aligning, and spherical roller bearings with correct X and Y factors.
X and Y Factors: Combining Radial and Axial Loads
When a bearing carries both radial and axial loads simultaneously, the equivalent dynamic load P combines them using weighting factors X and Y: P = X · Fr + Y · Fa. The factors depend on the bearing type, the contact angle, and the ratio of axial to radial load (Fa/Fr) relative to a threshold value called e.
For deep groove ball bearings, if Fa/Fr is less than e, the axial load has no effect and P simply equals Fr. This is the most common case for general industrial applications where the axial load is small relative to the radial load. Only when Fa/Fr exceeds e does the axial load start to reduce bearing life.
For angular contact bearings and tapered roller bearings, Y depends on the contact angle. A 15-degree angular contact bearing has a higher Y (more sensitive to axial load) than a 40-degree bearing. Tapered roller bearings have Y values specific to the cone angle of each series.
If Fa/Fr ≤ e: P = Fr
If Fa/Fr > e: P = X · Fr + Y · Fa
Typical values for deep groove ball (Fa/Fr > e):
X = 0.56, Y = 1.0 to 2.3 (depends on Fa/C0)
For angular contact 25°:
X = 0.68, Y = 0.41, e = 0.68
Equivalent Dynamic Load Calculator
Calculate equivalent dynamic bearing load P from radial and axial forces. Supports deep groove, angular contact, cylindrical roller, self-aligning, and spherical roller bearings with correct X and Y factors.
Variable Loads: The Cubic Mean Approach
Most real equipment does not run at constant load. A crusher bearing sees heavy impact loads during operation and near-zero load during idle periods. A pump bearing sees different loads at different flow rates. The L10 formula assumes constant load, so variable loads must be converted to a constant equivalent load.
The standard approach is the cubic mean load for ball bearings (or the 10/3 mean for roller bearings). Divide the duty cycle into segments where the load is approximately constant. For each segment, record the load and the fraction of total time at that load. The equivalent load is the weighted root-mean-cube of the individual loads.
The practical consequence: peak loads dominate the calculation. A bearing that runs at 50% of rated load for 90% of the time and 100% of rated load for 10% of the time has an equivalent load much higher than the simple average. The cubic weighting means that the high-load periods have an outsized impact on bearing life.
Pm = [q1·P1³ + q2·P2³ + ... + qn·Pn³]1/3
q = fraction of time at each load
P = load during each period
Using peak load instead of cubic mean overestimates the equivalent load and leads to oversized bearings.