In physics, as it's often impossible to model something full scale, mathematical models are produced, which can predict
a) how a system behaves; and
b) how a model will behave when smaller than the machine to be designed.
A key tool in this modelling is "dimensionless numbers", which are ratios of parameters that end up not having a length, velocity, time, mass component.
Super simple example is a "scale" model. Take a 1:24 model, and it's dimensions are Length/Length (L/L cancells, and thus has no "dimension")...Multiplied by a length, it then gives the dimension to the length of the scale model.
Pretty simple, but when modelling complex systems, the dimensionless numbers start to take into effect other things, e.g. velocity has a length and time component, mass can come into it (density x length x length x length)...etc.
A commonly used dimensionless number in hydraulic systems is Reynolds Number, equal to
density X Velocity X Length/dynamic viscosity
It works for ducts, pumps, pipes, skin frictions, determining laminar and turbulent flow regimes...
As an example, if you wanted to do a scale model of say a pipe, running water at a constant temperature, if you halved the pipe size, doubled the velocity, you would get the same modeled behaviour when you scaled it up...you could also predict behaviour from empirical models on something that you haven't built.
Bearings use another number, Sommerfeld's Number...
So= (r/c)^2 X uN/P
r = shaft radius
c = diametrical clearance (r/c becomes dimensionless)
u = absolute viscosity (Units PaS, or (Force Seconds/Length^2)
N = rotational speed (Units Radians per second, radians being dimensionless, the units are 1/s)
P = projected bearing pressure (Force/length^2)
So the uN/P becomes also dimensionless...the number is dimensionless, and is used to model bearings.
What it tells you is that to change anything on a correctly designed bearing, you have to look at what has to change also to keep So the same.
Double the bearing load, and you can do any of the following to keep So the same :
* double bearing area (brings P back to the same);
* double the rotational speed;
* increase the journal size (note, this has to iteratively play back into the bearing width to balance P and r);
* reduce bearing radial clearance by 29.3%;
* double the viscosity; or
* similar to the journal size, manipulate all of the above to keep within safe parameters.
Study the number, and get a feel for what the variables do in bearing behaviour.
Which gets me back to the title, the dimensionless number that is Viscosity Index...it's a dimensionless number useful for comparisons for sure...for comparing the viscosity indices of oil.
It is NOT, however, one of those dimensionless numbers that can be used to predict anything whatsoever about lubricant behaviour, and any such analysis would be back to the basics of actual viscosity at the operating temperature being examined...
As such, IMO, VI is not one of the most important determinants in a lubricant.
a) how a system behaves; and
b) how a model will behave when smaller than the machine to be designed.
A key tool in this modelling is "dimensionless numbers", which are ratios of parameters that end up not having a length, velocity, time, mass component.
Super simple example is a "scale" model. Take a 1:24 model, and it's dimensions are Length/Length (L/L cancells, and thus has no "dimension")...Multiplied by a length, it then gives the dimension to the length of the scale model.
Pretty simple, but when modelling complex systems, the dimensionless numbers start to take into effect other things, e.g. velocity has a length and time component, mass can come into it (density x length x length x length)...etc.
A commonly used dimensionless number in hydraulic systems is Reynolds Number, equal to
density X Velocity X Length/dynamic viscosity
It works for ducts, pumps, pipes, skin frictions, determining laminar and turbulent flow regimes...
As an example, if you wanted to do a scale model of say a pipe, running water at a constant temperature, if you halved the pipe size, doubled the velocity, you would get the same modeled behaviour when you scaled it up...you could also predict behaviour from empirical models on something that you haven't built.
Bearings use another number, Sommerfeld's Number...
So= (r/c)^2 X uN/P
r = shaft radius
c = diametrical clearance (r/c becomes dimensionless)
u = absolute viscosity (Units PaS, or (Force Seconds/Length^2)
N = rotational speed (Units Radians per second, radians being dimensionless, the units are 1/s)
P = projected bearing pressure (Force/length^2)
So the uN/P becomes also dimensionless...the number is dimensionless, and is used to model bearings.
What it tells you is that to change anything on a correctly designed bearing, you have to look at what has to change also to keep So the same.
Double the bearing load, and you can do any of the following to keep So the same :
* double bearing area (brings P back to the same);
* double the rotational speed;
* increase the journal size (note, this has to iteratively play back into the bearing width to balance P and r);
* reduce bearing radial clearance by 29.3%;
* double the viscosity; or
* similar to the journal size, manipulate all of the above to keep within safe parameters.
Study the number, and get a feel for what the variables do in bearing behaviour.
Which gets me back to the title, the dimensionless number that is Viscosity Index...it's a dimensionless number useful for comparisons for sure...for comparing the viscosity indices of oil.
It is NOT, however, one of those dimensionless numbers that can be used to predict anything whatsoever about lubricant behaviour, and any such analysis would be back to the basics of actual viscosity at the operating temperature being examined...
As such, IMO, VI is not one of the most important determinants in a lubricant.