# - Predicting the Life of Rolling Element Bearings-

## A superb illustration of the statistical nature of fatigue

The prediction of the life of a rolling-element bearing (ball, roller, needle) is a statistical calculation of the FATIGUE properties of the bearing components, in which the specific parameters defining the operation of the bearing are taken into account. Those parameters include: load, rpm, lubrication viscosity, bearing material and cleanliness. The predicted ** life** is expressed as the number of ** hours** that a specified ** percentage** of a large population of the bearing being considered will survive under the specified **load** with the specified set of **operating conditions**.

The life of a given bearing is a nonlinear function of the applied load. For a ball bearing, it is related to load to the **3.00** power (i.e. *load x load x load*); For roller and needle bearings, it is the **3.33** power. That means that a relatively small increase in bearing load can cause a dramatic reduction in bearing life.

The *dynamic load rating***listed in bearing catalogs** is the load at which *90%* of a large population of *apparently-identical bearings* will survive *one million cycles*. when subjected to **idealized operating conditions** of lubrication and cleanliness. Notice that a bearing supporting a shaft turning at 6000 RPM will experience one million cycles in **2 hours and 46 minutes**. That's probably OK for a race car, but not exactly an aircraft-quality life expectancy.

The usual life rating for industrial applications is called "L-10" life. The L-10 lif is defined as the **number of hours** in service that ** 90%** of a large population of *apparently-identical bearings* will **survive** when subjected to the ** boundary conditions** (*load, speed, lubrication, material* and *cleanliness)* that are **specific to the application**. Stated another way, 10% of that population will have failed in the L-10 number of service hours under the specific operating conditions.

To achieve the 5% failure rate with a given set of boundary conditions requires 1.64 times greater bearing capacity (dynamic load rating); to achieve a 2% failure rate requires 3.0 times greater dynamic load rating.

Put another way, for a given L-10 life, the L-5 life of the same bearing at the same load and under the same conditions is 61% of the L-10 value, and the L-2 life is 33% of the L-10 value. We think that the L-5 life (5% predicted failure) criterion is a bare minimum requirement for aircraft design.

From that discussion, it should be clear that the prediction of the expected life of a rolling element bearing in a specific application involves a bit more analysis than simply plucking a load rating from a bearing catalog.

Most rolling element bearing manufacturers publish detailed life-load analysis procedures. The bearing life calculations which the manufacturers publish take into account factors including:

- the combined effect of applied radial and thrust loads,
- RPM,
- pitchline velocity,
- lubricant viscosity,
- contamination,
- bearing load ratings, and
- desired probability of survival (failure rate).

All of them are important, but the effects of *lubricant viscosity* and *cleanliness* are **huge**.

These calculations have been implemented in a computer program which EPI wrote several years ago for doing bearing life analysis. This program uses a user-defined LOAD MODEL of the expected service to evaluate bearing life in an actual application. The load model is a set of different operating loads and speeds which the actual machine is designed to handle, and an estimate of the % of service that each load and speed represents.

For example, the load model of an an aircraft propeller gearbox on a normally-aspirated engine might be described as 5% of the time at max power (takeoff), 10% at climb power, 70% at cruise power, and 15% in aerobatic maneuvers. Each one of those conditions impose significantly different loads and speeds on the gearbox bearings. The combination of those different conditions in a realistic load model allows for a more reasonable selection of bearings for an application.

Certain bearing manufacturers (SKF, for example, in late 2003) have made available, on their websites interactive programs for predicting "L-10" bearing life.

The SKF website provides a life-calculation program which produces THREE different values for an L-10 life rating:

- the original (old)
*Arvid Palmgren*method, which predicts a relatively short life, - the seasoned, proven "A
_{23}" method (the one implemented in the**EPI bearing program**), and - the new, SKF-"marketing-friendly" rating.

#### The rating you pick depends on how realistic you want to be.

Our bearing life calculation program matches the SKF-website values calculated for an L-10 life under the "A_{23}" method **for the same input values**. However, our program also includes the ability to calculate life ratings for complete load models (described above) as well as for survival probabilities more appropriate to aircraft applications (95, 96, 97, 98 and 99%).