Ball bearings. Calculations Life duration

This article and the  [BM 5 371] explains how to check the mechanical strength of ball bearings subjected to any static loading, and how to calculate the friction torque to be expected. More specifically, this article presents life calculations for ball bearings. They are based on two theories :

• the theory developed by Lundberg and Palmgren from probability theory using Weibull's Law of Fatigue Strength of Materials, first published in 1947 ;

• the theory of hydrodynamic lubrication, which enables us to calculate the thickness of the oil film that forms between the ball and the raceway, and which determines the formation of wear debris, which plays a decisive role in service life.

When the oil film is thick enough, the formation of wear debris is greatly slowed down. The first lubrication theory, published in 1977, calculated the thickness of the oil film and introduced a lubrication factor. Subsequently, other corrective factors have been proposed by bearing manufacturers and researchers, based on theoretical and empirical approaches. Most of these advances are due to Swedish manufacturer SKF. In february 2007, the bearing life calculation standard NF EN 281 was revised and reissued. It enables a much better prediction of service life, as it takes into account new parame-ters such as fatigue limit load and contamination factor. The fatigue limit load is the radial load that generates a Hertz pressure of 1 500 MPa. Experience has shown that below this threshold, the service life becomes unlimited, provided that the speed and viscosity of the oil are high enough to separate the surfaces in the ball/track contact. To do this, one calculates the viscosity ratio and check that it is greater than 0.1. The contamination factor takes into account operating cleanli-ness conditions. If solid particles of high hardness mix with the lubricant, they may cause indentations on the balls and raceways, degrading service life.

This article presents the calculations in accordance with this standard, as well as additional calculations not covered by the standard, such as :

• in the case of any combination load ;

• variable loading over time ;

• calculation of the dynamic load capacity of a ball bearing of any internal geometry (the standard only...