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I know TBN is the "Total Base Number" of the oil. And I know the higher the TBN, the better. But what exactly is the TBN a measurement of? And how is it measured? What factors directly affect the TBN number? Is there a formula to estimate TBN depletion?
As stated we are talking acids and bases here, not base oil. The base number indicates the reserve alkalinity of a lubricating fluid, in mg KOH. In an engine oil, we are of course talking about the ability of the oil to neutralize any acids formed via combustion or even condensation. These neutralizing agents, this reserve alkalinity, usually shows up in UOA's as Ca and Mg compounds.
The techniques to arrive to arrive at the TBN differ as there are two/three ASTM methods (D-2896, D-664, D-4739, and many hybrid and proprietary (mostly portability such as Dexsil's) methods. These methods can and do get different numbers depending on the water phase/solvent phase separation, the acid used for titration. For example, D-2896, uses a stronger Perchloric acid for the tritration and the solvent is Cholorobenzene and acetic acid and will titrate out all the detergent base, the dispersant base, salts, etc and yield a higher TBN.
A new oil could have an artificially high TBN by adding NaOH to just impress people (I guess) but be a terrible lubricant, so higher when new isn't better. On the other hand a well used oil may have a TBN of 0.5 (or even almost zero) and not mean the oil is eating the engine while the engine oil continues to do a great job of protecting and cooling, etc.
A simple pH test strip will not work in a non aqueous system.
Hope this helps.