Power loss prediction in ball bearings

Synopsis The determination of power losses and traction forces in modern ball bearings typical of aerospace applications is a complex task. The high rotational speeds commonly experienced by such bearings cause inertia effects to be important, and this inturn loads the balls heavily against the outer raceway of the bearing. The resulting disparity in contact angle tends to introduce a spin component to the motion of the inner raceway/ball contacts on top of the usual sliding and rolling motion. A complete analysis of the contacts would have to include the elastohydrodynamic analysis of heavily loaded contacts, and conjunctions with continuously variable surface velocities. The iterative solution required for such conditions, despite the use of powerful, modern numerical methods, still requires many tens of minutes processing on a large mainframe computer. The computations required for a bearing having 20–30 rolling elements (40–60 contacts) is therefore unreasonable, and even if this were possible its incorporation into the overall dynamic analysis of the bearing would again introduce many more levels of difficulty. For many years the design of bearings for aerospace applications has been based on knowledge gained experimentally, but with the slow introduction of various theoretical work to aid the designer in such calculations as minimum lubricant film thickness. The ever increasing cost of experimental work and the need to make the initial design the best possible, however, provide a requirement for much improved theoretical methods, and hence the need for developments of the type described in this paper. The purpose of the work has been to unite an analysis of bearing dynamics with realistic elastohydrodynamic pressure and film thickness profiles, and then to calculate realistic values for power loss and power transfer within the bearing together with the provision of information on the contact traction forces. A well tried analysis was adopted for calculation of the bearing dynamics, and the use of a simple extrapolation allowed existing solutions to the elastohydrodynamic lubrication problem to be introduced. Calculations of power loss and traction force were then undertaken with the fluid assumed to be either Newtonian or Non-Newtonian, firstly for a single contact and secondly for the whole of an example bearing. The results obtained were then compared with other computations for the same bearing which were known to agree well with the available experimental evidence, and finaly the sensitivity of the analysis to various lubricant parameters was examined. The conclusions drawn from the work were that realistic power loss calculations could be made with a Non-Newtonian fluid model, and that the most important lubricant parameters were the pressure-viscosity coefficient and the limiting-shear-stress-pressure