T R I B O L O G Y & L U B R I C A T I O N T E C H N O L O G Y S E P T E M B E R 2 0 0 7 27

Lubrication Fundamentals

n the July TLT we reviewed themeasurement and classificationof viscosity. As we have said

many times, viscosity is the mostimportant property of a lubricant.And so it is important to understandthe concepts fully. In this article, we’lltake a look at viscosity index (VI).

VI is a means of expressing thelubricant’s variation in viscosity withrespect to temperature (see Figure 1).In general, this means the viscosityincreases with cold and decreaseswith heat. Each machine is designedwith an optimum lubricant viscosityrange to insure sufficient film thick-ness to reduce friction and preventwear. Clearly, the less a lubricantvaries with temperature, the more alubricant can be used in cold as wellas hotter environments.

This cuts two ways. When a lubri-

cant is too cold (not up to operatingtemperature), either because of theenvironment, as in winter, or justbecause we are just starting up amachine, the viscosity is too high,the lubricant doesn’t flow well andwear can ensue. Equally, if the lubri-cant is too hot because of the envi-

ronment or because we are overwork-ing a machine, the viscosity is toolow, and we don’t have sufficient filmthickness to prevent wear.

So if this is important, how do wedetermine the VI of a lubricant? VI iscalculated from the measured viscos-

By Dr. Robert M. Gresham

Contributing Editor

I

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The basics of viscosity indexThe basics of viscosity index

There are many factors to calculating the viscosity

of a lubricant. But understanding its temperature

in cold and hot environments is the first step.

Figure 1. Viscosity vs. Temperature

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28 S E P T E M B E R 2 0 0 7 T R I B O L O G Y & L U B R I C A T I O N T E C H N O L O G Y

ity at 40 C and 100 C using ASTMMethod D 2270. Unfortunately, themethod is a wee bit awkward andarcane, yet widely used. Its utility isin characterizing base oils or finishedlubricants and cannot be used asblending guidance (i.e., blending twooils 50-50, which have VIs of 80 and100 don’t necessarily provide oil witha VI of 90).

The idea of the method is tomeasure the viscosity of a test oil at100 C (called Y). Then, consulting ahuge chart in the ASTM method andusing the measured viscosity of thetest oil, the tester looks up values fortwo parameters called L and H. L isthe 40 C viscosity of some mythicaloil having the same viscosity of ourtest oil at 100 C, defined as having aVI of 0. H is also the 40 C viscosity ofanother mythical oil having the sameviscosity of our test oil at 100 C butdefined as having a VI of 100. High VIis defined as having less variationwith respect to temperature; thus L

is larger than H. The VI of the test oilis defined by the relationship of its40 C viscosity (called U) to theparameters L and H. Thus, the VI ofthe test oil becomes the percent ofthe way U is from L to H, as shown inthe formula below:

VI = 100 X (L – U) / (L – H)

This is pretty exciting stuff, right?Perhaps the example below will help.For an oil of 10.0 centistokes (cSt)viscosity at 100 C, the table in ASTMD 2270 provides L = 147.7 and H =82.87. If the test oil has a 40 C vis-cosity of 110 cSt, it would have a VI of58 using the formula above:

VI = 100 X (147.7 – 110) /(147.7 – 82.87) = 58

If this isn’t painful, awkward andarcane enough, if the VI is over 100,as many mineral oils and syntheticsnow are, we have to go to a com-pletely different calculation. As ofnow, when dealing with VIs of 100 ormore, U, the viscosity of the test oil

at 40 C, is less than H. For these oils,VI is defined by a new parameter, N,calculated from Y and H rather thanH and L as before. Thus, a new for-mula is shown below:

VI = 100 + 140 X ((antilog N) – 1),whereN = (log H – log U) / log Y)

We’re having fun now! So what’s apoor soul to do?

Probably the easiest and fastestthing to do is to call your supplier.Second, grind it out with ASTM D2270, ugh. Finally, you might find acomputer program that will calculateit all for you.

The point of all this is that viscos-ity index is an important parameterin characterizing base oils and lubri-cants. <<

You can reach Bob Gresham, STLE’s director of professional development, atrgresham@stle.org.

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