As we pour the lubricant in the cup when the balls interact whether regime is boundary lubrication or in hydrodynamic lubrication
The conditions of hydrodynamic lubrication is rather unavailable on Four Ball Test Rig becouse of too small load capacity (high unit pressure and too small friction surfaces). The regimes of friction in 4 Ball Tester include mixed and boundary friction. It's very hard to idicate a kind of friction becouse the condiitions of friction are changable (continuous wear, changable friction surface). I think hydrodynamic lubrication is possible with very, very small load (or without) but it depends on liquid viscosity also.
Boundary and mixed lubrication
EHD lubrication is not likely to occur because of the severe operating conditions (full sliding motion, high contact pressure, high temperature elevation)
This test device was originally designed to test additives (antiwear for instance)
Boundary, mixed, EHD lubrication. It depends on the level of wear of the ball.
Is there any theoretical calculation to find which lubrication regime take place between
contact of four ball? And also, how much wear can take place according to lubrication regime?
The increase in wear of the balls increases the contact area. The composition of the lubricant and the testing regime determines the smoothness of the spot of wear. Of course, I mean long-term tests on four-ball tester. This effect does not need to be considered when short-term standard four-ball tests of lubricants.
There is a way to find the lubrication regime, there are models for that, if you know the roughness and the applied conditions. You can take a look here, for example: http://link.springer.com/article/10.1007/s11249-015-0536-z. A a little bit simpler model, that you can readily apply can be found here (Matlab code with GUI): http://tribonet.org/cmdownloads/friction-calculation-mixed-lubrication/.
BL in EP testing
EHL in no load case
Remaining all conditions it will be mixed regime.
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