Fatigue Life of Roller Bearings
Original article date: March 1998
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 is based on empirical research carried out in the 1940s and 1950s by Lundberg and Palmgren. It 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 106revolutions |
| For roller bearings | L10= (C/P)10/3 | x 106revolutions |
where:
An extension to this theory was later adopted by ISO with additional factors. Lna= a1.a2.a3.L10wher e 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. Now NSK claims to 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 The life adjustment factor for environment a4is a function of the oil film parameter ((gronch) and P/C and can be classified into seven zones ranging from zero contamination (no influence due to debris) to contaminated completely (intrusion by an extremely large quantity of debris). As the cleanliness of bearing steel has improved considerably over recent years data has been collated and analysed enabling the fatigue limit to be assessed. The life adjustment factor a5is based on the fatigue limit of the bearing material and is a function of P/C. 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 well understood. The equation offers the advantage of being familiar as it 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 with a high degree of confidence in their suitability thus reducing costs. The example in Fig 4 shows how a comparison can be made between life predicted by the new and existing theories. The graph shows the use of the NSK new life equation for a standard 6306 bearing charged with a popular NSK grease running at 2000rpm under a radial load of 4000N. * Condition 1 assumes no contamination of the bearing and an operating temperature of 40degC to give an NSK L10life of about 15 times the ISO L10life.* Condition 2 assumes a large influence due to debris in the bearing and an operating temperature of 100degC to give an NSK L10life of about 15% of the ISO L10life.
March 1998
L10represents the rating fatigue life with a reliability of 90%
C is the basic dynamic load rating – the load which will give a life of 1million revolutions – which can be found in bearing catalogues.
P is the dynamic equivalent load applied to the bearing.
a1= the life adjustment factor for reliability
a2= life adjustment factor for special bearing properties
a3= life adjustment factor for operating conditions
a4:
L ife adjustment factor for environment
a5:
Life adjustment factor for fatigue limit
p:
Exponent to load (3 for ball bearings 10 for roller bearings)