Markus Raabe explores bearing calculation methods.

Rolling element bearings are important components within transmissions. Usually, they are selected based on geometric restrictions, requirements on load directions and rating life.

Rating life is mostly calculated based on ISO 281 using an equivalent load and the dynamic load rating from the catalogue. Additional influence factors such as lubrication and cleanliness can be considered in a modified life rating. The life rating restricts the maximum load. Regarding minimum load, the bearing catalogues provide limitations in the range of 1-2% of the dynamic or static load rating as slippage can lead to wear or smearing. Using an equivalent load based on ISO 281, misalignment, moment load or bearing clearance is not considered.

A more detailed approach to calculate bearing rating life is provided by ISO/TS 16281. This cannot be evaluated manually as it is based on the load distribution within the bearing. By considering the load distribution additional effects can be included like misalignments, bearing clearance or fitting. Broadening this approach allows housing deformations to be considered, which will also affect the load distribution within the bearing.

Further evaluations can be done by using the load distribution based on a quasi-static equilibrium. For ball bearingsthe risk of truncation on high axial loads can be evaluated by comparing the extension of the contact ellipse with the height of the shoulder. The spin-to-roll ratio and circumferential ball advance are kinematic properties which are used to evaluate high-speed ball bearings. For high-speed applications, the minimum contact stress should be sufficient to avoid slipping. In addition to rating life the maximum contact stress can be evaluated, which some industries prefer. Calculation of the bearing load distribution will also provide bearing stiffness matrices which can be used to calculate deflections or rotor dynamics. For bearings with contact angles there will be a coupling between axial, radial deflections and tilting angles in the stiffness matrix.

For the calculation of the bearing load distribution and the resulting reference rating life according to ISO/TS 16281, there are several programs available, usually in combination with a shaft calculation so the misalignment can be captured.

For some further damage modes, transient calculations using a multi-body approach are necessary instead of a quasi-static equilibrium. Usually only bearing manufacturers do such evaluations, which consider local interactions between rolling elements and races or cage.

Case study

The current standards for bearing life calculation still have some shortcomings. Fig.1. shows an example of rating life of an angular contact bearing with variation of contact angle under constant pure axial load. For a contact angle of about 40° the reference rating life according to ISO/TS 16281 is almost twice the rating life according to ISO 281. For a contact angle above 45° the bearing is considered as thrust bearing and the reference rating life according to ISO/TS 16281 will be reduced by factor 2.6. If an additional misalignment from shaft deflections is considered for thrust bearings, the reference rating life according to ISO/TS 16281 will be smaller than the rating life according to ISO 281.