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Kinematic replenishment/starvation reduction factor

For oil-air, oil jet, low level oil bath lubrication (i.e. oil level H lower than the centre of the lowest rolling element) and grease lubrication methods, continuous over-rolling displaces excess lubricant from the raceways. In applications where viscosity or speeds are high, the lubricant may not have sufficient time to replenish the raceways, causing a "kinematic starvation" effect. Kinematic starvation reduces the thickness of the hydrodynamic film (decreasing κ value, refer to Viscosity ratio κ) and rolling friction.
For the type of lubrication methods described above, the kinematic replenishment/starvation reduction factor can be estimated using

Φrs Kinematic replensihment-starvation reduction factor

φrs =kinematic replenishment/starvation reduction factor

base of natural logarithm 


Krs =

replenishment/starvation constant: 

= 3 x 10-8 for low level oil bath and oil jet lubrication 

= 6 x 10-8 for grease and oil-air lubrication

Kz =bearing type related geometric constant (table 1)
ν =kinematic viscosity at operating temperature of the oil or the base oil viscosity of the grease [mm2/s]
=rotational speed [r/min]
=bearing bore diameter [mm]
=bearing outside diameter [mm]
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