Hydrodynamic Load Calculation in Rolling Element Bearings

Abstract

ABSTRACTHydrodynamic effects are responsible for a dimensionless load increase ΔW (relative to the load WHertz calculated in a dry contact) calculated primarily as a function of the dimensionless rolling element–race geometrical interference Δ/Rx, dimensionless speed, and radii ratio. The final load (W = WHertz + ΔW) is therefore never nil, even in cases when the geometrical interference is negative or nil, which corresponds to a Hertzian load nil.The final load is calculated by solving the following dimensionless algebraic relationship: , where δ is the elastic deformation (function of the load and radii ratio) calculated using a Hertzian relationship and H is the dimensionless film thickness, again a function of the load and radii ratio but also dimensionless speed and material parameters, the latter being included in piezoviscous-rigid (PVR) and piezoviscous-elastic (PVE, also called elastohydrodynamic or EHD) film thickness relationships. Advanced new curve-fitted relationships are also suggested in this article for calculating miscellaneous Hertzian parameters, such as contact dimensions, maximum pressure, and deformation.A detailed survey of several film thickness relationships was conducted covering different lubrication regimes: isoviscous-rigid (IVR, found at low dimensionless load and speed), PVR, and EHD (high dimensionless load and low dimensionless speed). It has been shown that the IVR regime prevails when Δ/Rx is negative or nil and the radii ratio is large (as found in roller bearings); hence, an IVR approach can be suggested for numerically calculating ΔW.A powerful set of curve-fitted relationships is then suggested for easily calculating ΔW.A simplified approach based on a previously published analytical solution of ΔW applicable to line contact (LC) but used here in a sliced point contact (PC) was also tested after having demonstrated that LC results (for H and δ) can be used in slices for retrieving (within 10%) PC results on H and δ. This result is surprising given that the exponents used for calculating H and δ differ substantially in LC versus PC.In addition, a new IVR thermal correction factor was developed for better calculating the film thickness.Although very small, ΔW can be responsible for a moderate bearing preload and torque increase, calculated using previously published IVR hydrodynamic rolling forces when the dimensionless speed is high and the bearing clearance is small or nil.Hydrodynamic effects, both normal and tangential to the contact, also contribute to the roller speed decreases in the unloaded zone of a bearing, so there is no need to consider large drag force to explain this drop. Previously published roller drag force relationships may therefore overestimate these forces when calibrated versus tests by not considering the rolling element–race hydrodynamic effect described herein.