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Hi Jeffturbo,

I may be wrong but I am guessing that you are after the minimum viscosity required to give adequate lubrication at a specific temperature for bearing application.
Such calculations can be found in the SKF "General Catalogue" which has a series of tables. You probably can get a copy by contacting your local SKF branch or maybe try the website www.skf.com
SKF refer to the Kappa value (K) and calculations & tables on rated viscosity versus actual operating viscosities are given. It's under the chapter "Selection of Bearing Size" - Lubricant conditions - the viscosity ratio K.
I hope this helps.
Unfortunately, you do need the catalogue as the calculations refer to a number of tables in the book.

There are snapshots of the graphs on the website. If you type in "kappa values" in the search tab on the website, a return on "Lubrication" comes up, click on it. A file called 516327.pdf comes up, you should be able to save this file.

Go to page 29 of 45, there are two tables, one the required viscosity the other operating viscosity. If you have the bearing bore diameter "d" in mm, the outside "D" in mm, also the operating speed. Use the little formula below the graph given on the page dm=0.5(d+D)with the corresponding r/min in red line. This gives the minimum rated viscosity. Once you have this value, then work out the operating temp. Use the second graph, for example if required viscosity works out to 11mm2/s for the first graph and the operating temp is 70C, then from the second graph, the closest actual viscosity required is ISO VG 32 at 40C.

Most OEMs would have given the information in the various manuals as to what ISO VG rating the lubricant required at the given operating temps.

I also did the Noria course "How to grease a Motor Bearing" online which was very useful with references to tables and sample calculations.
Many years ago, my coach gave me a formula that was used to calculate viscosity as a Kosntant K times the inverse of the square root of the speed.

THis is Visc in Cst = K x 1/Velocity (high 1/2)

If we consider speed as = medium diameter (Dm x 3.14 x RPM, in a 100 mm Dm bearing and 3000 RPM, speed is 942 m/min; square root is 30.7; its inverse is 0.0326 times a K of lets say 4000 equals 130 cSt oil.

The issue stays to determine the constant K that is defined by the type of bearing, temperature, load, and other conditions of the tribologic system that can not be determined easily.

FAG has more serious work done in determiation of viscosity based on testing and practical experience. ALl this was done some 20 years ago, I still have the charts and calculations somewhere, that are available to you. In the meantime machines are heavier loaded, bearings are smaller and cheaper, and you can not relay on that dated information.

Doctors and Professors and studious may have a formula. Contact the STLE for that information. I am sure there is no easy formulation. Calculating the viscosity for securing a HDL film remains a science called Tribology.
As well as knowing the physical bearing parameters (diameter, etc) and operating speeds and temps, you will also need to know the viscosity/pressure coefficient of the lubricant you are using. You can vary the oil film thickness by using different lubricants with PAO synthetics tending to give better film thicknesses than mineral.
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