Theoretically predicting how long a bearing will last when designing a machine is a critical step for the reliability of the entire mechanical project. As we know, this prediction is made worldwide using the widely accepted L10 basic rating life formula: L10 = (C / P)^p. While the Dynamic Load Rating (C) in this equation is readily taken from the manufacturer's catalog, the most important variable that the machine designer must correctly determine is the Equivalent Dynamic Load (P).
In the real world, the forces acting on a bearing while a shaft is rotating are never simple and unidirectional. The bearing is simultaneously stressed by both lateral pushes (radial) originating from gears and forward-backward pushes (axial) originating from propellers or helical gears. The "P" value is the art of converting these complex forces in different directions into a single virtual (equivalent) load that the formula can understand. In this article, we will examine the logic of the Equivalent Dynamic Load (P) concept, how it is calculated, and its direct impact on bearing life. Once you have determined your P value correctly, you can use our Bearing L10 Life Calculator to get the result in seconds.
What is the Equivalent Dynamic Load Concept?
Bearing manufacturers (SKF, FAG, etc.) assume specific standard conditions when publishing the endurance limits (C values) of their bearings in catalogs. For radial bearings (e.g., deep groove ball or cylindrical roller bearings), the C value is tested assuming that a purely radial (perpendicular) force is applied to the bearing. For thrust (axial) bearings, the condition is tested as a purely axial (parallel to the shaft) force.
However, in 90% of industrial applications, the situation is different. For example, a bearing operating in a helical gearbox or the wheel hub of a car is not only subjected to downward pressure (radial) but also to a push along the shaft (axial). This is called a "combined load."
The L10 formula cannot accept two differently directed forces simultaneously; it needs a single force 'P' to be entered into the equation. The Equivalent Dynamic Load (P) is a hypothetical, unidirectional (radial or axial) load that would create the exact same fatigue impact on the bearing's life as the combined (radial + axial) loads actually present. Simply put, it answers the question: "This bearing is being subjected to X and Y forces from both the side and the top. The rate at which these two forces wear out the bearing would be the same if we applied a single force of how many kN from a single direction?" That answer is the 'P' value.
Combination of Radial and Axial Loads (The Formula)
To convert combined loads into a single P value, a general formula defined by ISO standards is used. For a standard radial bearing, the Equivalent Dynamic Load formula is as follows:
P = (X * Fr) + (Y * Fa)
Let's identify the variables in this formula:
- Fr (Radial Load): The actual force (kN) acting perpendicular to the shaft, coming from above/below or the sides.
- Fa (Axial Load): The actual force (kN) pushing forward or backward, parallel to the shaft axis.
- X (Radial Load Factor): A coefficient taken from the catalog that adjusts the impact of Fr, depending on the bearing type and its internal clearance.
- Y (Axial Load Factor): A coefficient also taken from the catalog that adjusts the impact of Fa, which varies depending on the contact angle of the bearing.
How is it applied?
First, the designer calculates the Fa (axial) and Fr (radial) loads in their system by drawing a mechanical free-body diagram. Then, they find the ratio (Fa/Fr). In every bearing's catalog, there is a limit value denoted by "e".
- If Fa/Fr <= e; the effect of the axial load is small enough to be neglected in the life calculation (usually X=1, Y=0 is assumed, and directly P = Fr).
- If Fa/Fr > e; the axial load must be taken seriously, and the formula (P = XFr + YFa) is calculated using the respective X and Y coefficients obtained from the catalog table.
For example: In a deep groove ball bearing, the X and Y values are relatively fixed (e.g., X=0.56, Y=1.5). In angular contact ball or tapered roller bearings, the Y value varies greatly depending on the contact angle of the bearing. A bearing with a high contact angle will "absorb" axial loads more easily, so its Y coefficient will be lower, preventing P from increasing unnecessarily.
The Impact of P on L10 Life and Practical Calculation
The P (Equivalent Dynamic Load) value is located directly in the denominator of the L10 = (C / P)^p formula. Mathematically, an increase in the denominator means a decrease in the result obtained (life in million revolutions). However, the truly critical point is the logarithmic exponent 'p' in the formula (3 for ball, 10/3 for roller).
What happens if you incorrectly calculate the vibrations, shock factors, or axial loads in your mechanical system and assume the P value is just 20% lower (1.2 times smaller) than what it actually is? For a ball bearing, the L10 life shrinks by a factor of (1.2)^3 = 1.728, meaning a 42% reduction! (Wait, let's correct that mathematical perspective: True Life = Theoretical Life / 1.728, which means the life drops to about 57% of what you expected). A 1000-hour life expectation results in the bearing disintegrating in the field at 578 hours due to an underestimated P value. The machine stops, production halts.
Therefore, carefully determining the P value (based on Fr and Fa) is an engineer's greatest responsibility. Once you have determined your "P" value (whether it's a simple radial load or a complex equivalent load calculated with X and Y factors) and your "C" value taken from the catalog, there is absolutely no need for you to manually perform the remaining logarithmic operations and conversions from revolutions to operating hours.
To obtain an error-free and instant result, you can use our Bearing L10 Life Calculator. Simply enter your "C" capacity, your determined "P" load, operating speed (rpm), and bearing type into the tool's interface. The system will calculate the L10 life in accordance with ISO 281 standards in both million revolutions and hours (L10h) and display it on the screen in seconds. Correct planning means uninterrupted production.
