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Abstract
In high-speed rolling element bearings the drag force generated by the motion of the balls in an air–oil mixture is frequently taken into account using the results for a sphere in an infinite medium. This approach is surprising because important interaction between the flows around the balls may occur. The drag coefficient value should be then adjusted to the configuration that is observed in a rolling element bearing (REB). In this article, a computational fluid dynamics code is applied to simulate three configurations: one single sphere, two spheres in tandem, and a set of spheres that are aligned along the air flow. It can be seen that both the flow pattern around one sphere and its drag coefficient are modified when placing another sphere in its vicinity. Furthermore, in REB configuration the drag coefficient value is far from the one observed when the obstacle is isolated and mainly depends on the space between the obstacles.
NOMENCLATURE
| D | = | Ball diameter (mm) |
| dFx | = | Infinitesimal effort exerted by the flow (N) |
| dm | = | Pitch diameter (mm) |
| k | = | Turbulent kinetic energy (m2.s−2) |
| L | = | Gap (mm) |
| N | = | Rotational speed (rpm) |
| p | = | Pressure (Pa) |
| T | = | Period (s) |
| t | = | Time (s) |
| tc | = | Cage thickness (mm) |
| Δt | = | Time step (s) |
| Δt* | = | Dimensionless time step |
| u | = | Velocity (m.s−1) |
| uτ | = | Wall friction velocity (m.s−1) |
| V | = | Velocity (m.s−1) |
| xi | = | Cartesian coordinate (m) |
| y+ | = | Dimensionless distance from wall parameter |
| α | = | Contact angle (°) |
| δij | = | Kronecker's symbol |
| μ | = | Dynamic viscosity (Pa.s) |
| μt | = | Turbulent viscosity (Pa.s) |
| ρ | = | Density (kg.m−3) |