I can find L10 and L50 life of bearings on the bearing catalog and use that to find the life of bearing for a certain load 'F'. But I can't really find any references on how these companies find dynamic load rating, 'C0. Is there any statistics involved as well? If yes, would like to know the derivation for that as well.
Manufacturers of ball bearings typically publish Load Ratings for each bearing they produce. The methods used to calculate ratings can vary from manufacturer to manufacturer. However, both ABMA and ISO have published standards related to load ratings.
ABMA Std. 9 – Load Ratings and Fatigue Life for Ball Bearings ABMA Std. 12.1 and 12.2 – Instrument Ball Bearings ISO 76 – Static Load Ratings ISO 281 – Dynamic Load Ratings and Rating Life With regard to load ratings, one thing to remember is - static load ratings (Cor) and dynamic load ratings (Cr) are formulated on completely different premises and have no direct relationship to one another.
Dynamic load ratings are determined by bearing geometry, number and size of balls, bearing pitch diameter, and ring and ball material. This load rating is used in conjunction with the actual applied radial load to calculate bearing fatigue life.
The static load rating relates to limiting loads applied to non-rotating bearings. The static load rating depends on the maximum contact stress between the balls and either of the two raceways. It is affected by material, number and size of balls, raceway curvatures, raceway depths, and contact angles. It is also based on using clean, high quality bearing steel with typical hardness levels of 58-64 HRC for rings and 60-65 HRC for balls.