New look at new life

In most rolling element bearing applications there is a requirement to estimate the fatigue life of the bearings. The current ISO method of calculating bearing life based on empirical research by Lundberg and Palmgren is widely used as it gives a good benchmark for comparison of probable fatigue life between bearing sizes and designs.

{{The basic equations are:For ball bearings:L10 = (C/P)3 x 106 revolutionsFor roller bearings:L10 = (C/P)10/3 x 106 revolutions}}

where L10 represents the rating fatigue life with a reliability of 90%, C is the basic dynamic load rating (ie the load which will give a life of 1 million revolutions), which can be found in bearing catalogues. P is the dynamic equivalent load applied to the bearing.

An extension to this theory was later adopted by ISO, with additional factors.

Lna = a1.a2.a3.L10

where a1 = the life adjustment factor for reliability, a2 = life adjustment factor for special bearing properties and a3 = life adjustment factor for operating conditions.

The use of this theory is adequate for most applications. However, it does not take into account the vast improvements in steel quality and surface finish over recent years, or enable allowance to be made for the contamination of lubrication. It is further known that the actual bearing life, as determined in tests repeated under gradually decreased loads, shifts from the theoretical life to a longer life as shown in Figure 1.

NSK have developed a new life equation, as a method of estimating the fatigue life of rolling bearings under various conditions. The equation was derived from empirical data gathered over a wide range of applications over a number of years, and thus gives a more accurate estimate of the life of an NSK bearing than previous theories. The equation is based on the current ISO life equation and catalogue load ratings, with additional factors.

The equation takes the form: Lna = a1.a2.a3.a4.a5 (C/P)p

where a4 = Life adjustment factor for environment, a5 = Life adjustment factor for fatigue limit, p = exponent to load (3 for ball bearings, 10/3 for roller bearings).

The life adjustment factor for environment a4 is a function of the oil film parameter (L) and P/C, and can be classified into seven zones, ranging from zero contamination, to contaminated completely (Figure 2).

As the cleanliness of bearing steel has improved, data has been collated and analysed enabling the fatigue limit to be assessed. The life adjustment factor a5 is based on the fatigue limit of the bearing material and is a function of P/C, as shown in Figure 3.

The example in Figure 4 shows how a comparison can be made between life predicted by the new and existing theories. NSK’s new life theory enables greater accuracy in predicting equipment failure or required service intervals for applications where the operating and lubrication conditions are understood.

The equation closely resembles the format of the current ISO calculation equation, enabling engineers to compare and quantify life improvements. In some applications the theory enables the use of more compact bearings, thus reducing costs.

The graph shows an example of the use of the NSK new life equation for a standard 6306 bearing charged with an NSK grease running at 2000rpm under a radial load of 4000N.