# Viscosity index

The viscosity index (VI) is an arbitrary, unitless measure of the change of viscosity with temperature, mostly used to characterize the viscosity-temperature behavior of lubricating oils. The lower the VI, the more the viscosity is affected by changes in temperature. The VI was originally measured on a scale from 0 to 100; however, advancements in lubrication science have led to the development of oils with much higher VIs.

The viscosity of a lubricant is closely related to its ability to reduce friction in solid body contacts. Generally, the least viscous lubricant which still forces the two moving surfaces apart to achieve "fluid bearing" conditions is desired. If the lubricant is too viscous, it will require a large amount of energy to move (as in honey); if it is too thin, the surfaces will come in contact and friction will increase.

## Relevance

Many lubricant applications require the lubricant to perform across a wide range of conditions, for example, automotive lubricants are required to reduce friction between engine components when the engine is started from cold (relative to the engine's operating temperatures) up to 200 °C or 392 °F when it is running. The best oils with the highest VI will remain stable and not vary much in viscosity over the temperature range. This allows for consistent engine performance within the normal working conditions. Historically, there were two different oil types, recommended for usage in different weather conditions. For winter use, the engines required motor oil with the viscosity rating 5, while for warm and hot season it had to be changed to oil with 30-40 viscosity rating. Later on, there appeared multi-grade motor oils, which contained polymers that made the oil film thinner at higher temperatures without thickening the oil.[citation needed]

## Classification

The VI scale was set up by the Society of Automotive Engineers (SAE). The temperatures chosen arbitrarily for reference are 100 and 210 °F (38 and 99 °C). The scale was originally interpolated between 0 for a naphthenic Texas Gulf crude and 100 for a paraffinnic Pennsylvania crude. Since the inception of the scale better oils have also been produced, leading to VIs greater than 100 (see below).[1]

VI improving additives and higher quality base oils are widely used nowadays which increase the VIs attainable beyond the value of 100. The Viscosity Index of synthetic oils ranges from 80 to over 400.[citation needed]

Viscosity index Classification
Under 35 Low
35 to 80 Medium
80 to 110 High
Above 110 Very high

## Calculation

The viscosity index can be calculated using the following formula:[citation needed]

${\displaystyle \mathrm {VI} =100{\frac {L-U}{L-H}}}$

where U is the oil's kinematic viscosity at 40 °C (104 °F), and L and H are values based on the oil's kinematic viscosity at 100 °C (212 °F). L and H are the values of viscosity at 40°C for oils of VI 0 and 100 respectively, having the same viscosity at 100°C as the oil whose VI we are trying to determine. These L and H values can be found in ASTM D2270.[2]

## References

1. ^ "Viscosity Index". UK: Anton Paar. Retrieved 29 August 2018.
2. ^ Stachowiak, Gwidon W.; Batchelor, Andrew W. (2001). Engineering Tribology (2nd ed.). Boston: Butterworth-Heinemann.