I am not aware whether a analytical estimate with suitable accuracy exists. If so, I wonder whether that is of use anyway. What you want in the end is a situation where sufficient viscosity of the lubricant is available for lubrication the mating gears and a bulk oil temperature that is sufficiently low to avoid fast oxidation of the lubricant to prevent the need for a frequent oilchange.
You should end with a temperature range between 80 to 110 degrees Centigrade of the bulk oil with the gears under the load anticipated. The allowable temperature depends on the circumstances the lubricant has to operate (viscosity, viscosity index, type of base oil used, total amount of oil available, amount of oil sprayed onto the mating surfaces and the amount of heat that can be dissipated through the gear casing into the surrounding atmosphere).
The easiest way to get insight in what happens is to measure the bulk oil temperature with the oil volume, spray rate and viscosity as parameters. In stead of standard mineral gear oils, lubricants based on poly-alpha-olefins, esters or poly-alkylene-glycols may help to reduce operating temperature, energy losses and also increase oil change intervals.
let's say for 18MW High speed gearbox running at 90 m/s of plv, the oil flow to the gear mesh is "X" litres/minute. How to know, whether I can reduce 10% or 20% or 30% of X flow, so that the tooth the temperature is within the allowable and scuffing risk is low. oil is the mineral oil (ISO)(I cann't change the oil type). I would like to know the how the gear/pinion tooth temperature changes with gear mesh oil flow rate.
How to arrive at the optimum oil flow to gear mesh?
if oil flow is only towards outmesh, how much is sufficient for lubrication and how much is sufficient for cooling?
