viscosity conversion for temperature 1

[electricpete]

Does anyone have a formula for viscosity as a function of temperature, viscosity grade and viscosity index.

For example if I have VG32 with VI=1.0 at 80C, what is the viscosity?

Notes
1 - I have seen some charts, but most apply to VI=0.95
2 - note I am referring to kinematic viscosity in cSt

I have seen this can be done graphically using ASTM D2270 to determine the 100C viscosity from 40C viscosity grade and viscosity index, and then using special graph paper per ASTM D341 which allows a straight line connecting the two points.

Is there an easier way?


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[Skogsgurra]

I had this discussion with Shell a few months ago. They say that synthetic oils have a better "temperature index" (I think that they meant "viscosity index") so that viscosity of synthetic oils doesn't change with temperature as much as it does in a mineral oil.

There are data sheets for their oils on the web. Some give viscosity for different temperatures. I do not think that there is a general formula for it.

Gunnar Englund

http://www.gke.org

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[romke]

the socalled Walther equation describes the temperature-viscosity relationship of Newtonian fluids. If you know the viscosity of a Newtonian fluid at two different temperatures the equation can be solved and kinematic viscosities at other temperatures can be calculated. For non-Newtonian fluids this type of calculation is less accurate, especially at lower temperatures. Oils with a lot of VI-improver usually exhibit this type of behaviour at low temperatures (ATF, multigrade engine oils).

The ISO viscosity grades just define a certain viscosity range at 40 degrees C.(nominal value plus or minus 10%). Because no viscosity index is defined, the viscosity at other temperatures then at 40 degrees C can differ quite considerably for the same ISO VG grade. There is no possibility to calculate those viscosities on the basis of the ISO VG value alone.

The VI is calculated based on a standard ISO/ASTM method by comparing the oil with two reference oils. It is therefore a relative measure. If you look up the standard you will find that there is an appendix that gives information how you can calculate the viscosity index when the viscosity at 40 and 100 degrees C are known. The calculation can easily be done in a spreadsheet.

You can buy specialized graphing paper where you can plot two known viscosities and then draw a straight line that gives you the viscosities at other temperatures. This specialized graphing paper is based on the Walther equation: the vertical scale is the loglog(viscosity), the horizontal scale log(absolute temperature). Because of the "difficult" scaling, you can not plot this type of graph in a spreadsheet. You can buy an alternative plotting program however that makes this possible.

Visual Xsel is an example of such a program, see

http://www.crgraph.com/

You can either buy a simple version or a full version. The graphing is already possible with the simple version which is much cheaper then the full version. The programme can be downloaded for evaluation, the only restriction being that you will not be able to print the results or include graphs generated in other documents.

 

[25362]

Electricpete,

I assume your VI values should be multiplied by 100.
By definition, an ISO VG 32 grade should have a mid-point KV = 32 cS at 40^oC (min. = 28.8 cS; max.= 35.2 cS).

 

[electricpete]

yes, obviously

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[Skogsgurra]

Thanks, romke!

I had - as I said - this discussion with Shell. I got the impression that viscosity could not be calculated for a given temperature. So I am glad to learn about the Walther equation. My reason to dig into this is that the oil film in a ball bearing is very viscosity dependent (and speed dependent) and I have measured a break-down voltage temperature dependence that needs to be explained.

Re the graphing: MatLab and similar programs can plot with any function for the independent ("x") axis. There is a freeware (scilab) available at

http://www.scilab.org/

Gunnar Englund

http://www.gke.org

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[Skogsgurra]

I googled "Walther equation" and my first hit was thread483-145624 . A good discussion.

This is not the first time Eng-Tips has the best answer to a specific question. I begin to think that we are a good bunch of people

Gunnar Englund

http://www.gke.org

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[romke]

in a ball bearing there is usually socalled "elasto-hydrodynamic lubrication", meaning that the lubricating oil wedge (the carrying layer of lubricant)is formed due to both the movement of the balls in the groove and the small deformation that takes place in the ball and less in the raceway. that means that in the lubricating film very high pressures can be temporarily reached (of several hundreds of bars and maybe even more) and due to that high pressure the viscosity of the fluid may change. normally a fluid is thought to be non-compressible, but under very high pressure applications that no longer is the case. the fluid may temporarily thicken or even solidify. the change in viscosity due to high pressure can be calculated with the socalled Barus equation which correlates the viscosity to changes in pressure. However, there is much less knowledge about the viscosity-pressure relationship then about the viscosity-temperature relationship. One thing is sure though: the increase in viscosity due to high pressure stemming from deformation in EHD-contacts usually is the rescue of the engineer/designer - without it a rolling bearing or a "hot" camshaft problably would not have a long service life.

 

[electricpete]

I looked at jmw's spreadsheet. I don't see any calculation for the values A and B in there (it looks like they were solved in some other program for specific oils and dumped into this spreadsheet). Also he mentioned he used celsius temperature and the equation does require Kelvin ( checked and that makes a big difference). But I like his approach to forget about the straight line. I think the special graph giving the characteristics as a straight line was more important in the old days when numerical calcs were tough, but it is just an unnecessary complication these days when we have spreadsheets.

I went back to the ASTM standard / Walther equation and did it in a way which doesn’t seek to plot a straight line

from ASTM D341 :
log (log(v + 0.7)) = A - B log T <eq1>
where v is kinematic viscosity in cSt, T is temperature in K, log is base 10 log, and A and B are unknown constants which can be solved from two data points (v1,T1), (v2,T2)
Plug the data from the first ppoint v1,T1 into eq1:
log (log(v1 + 0.7)) = A - B log T1 <eq2>
solve eq2 for A
A = log(log(v1+0.7)) + B*log(T1) <eq3>
plug the data from the second point v2,T2 int eq1
log (log(v2 + 0.7)) = A - B log T2 <eq4>
substitute into eq4 the value A from eq3
log (log(v2 + 0.7)) = [log(log(v1+0.7)) + B*log(T1)] - B log T2 <eq5>
solve eq5 for B
B = {log (log(v2 + 0.7)) - log(log(v1+0.7)) } / (logT1-logT2) <eq6>
solve equation 4 for A
A = log (log(v2 + 0.7)) + B log T2 <eq7>
solve eq 1 for v
v = 10^(10^(A-B*LOG(T)))-0.7 <eq8>
equation 8 using values of A from eq7 and B from eq6 give us v as a function of T.

I have implemented this in a spreadsheet. Enter in the green the pairs (v1,T1), (v2,T2) in units cSt and deg C. Then enter the target temperautre T3 and it computes v3 as well as a curve based on the two points.

http://home.houston.rr.com/electricpete/eng-tips/ViscosityVsTemperatureCalculator.xls

Regarding the role of p-v. The rolling bearing manfuacturer’s give instructions for selecting oil based on minimum viscosity as a function of temperature (for example SKF, MRC). As you point out, variation of viscosity with pressure is a huge factor. What I have heard is that the variation with pressure does not change widely among non-synthetic oils, so this approach is valid for non-synth oils. For synth oils, perhaps we should use a limti curve which explicitly accounts for both pressure and temperature variation of viscosity.


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[Skogsgurra]

Wonderful! This might be the explanation to what I have seen.

Measuring break-down voltage vs temperature in a DGBB shows that mineral oil has a better withstand voltage than a synthetic oil has. From 20 C to 80 C. This is something Shell representatives deny - probably because they didn't send the right people. Salespersons and not lab guys. I shall certainly keep this in mind!

Gunnar Englund

http://www.gke.org

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[25362]

Engineering Tribology by Stachowiak and Batchelor, 24 of the Tribology Series, Elsevier, stresses the view that although the Walther equation is used as basis of the ASTM viscosity-temperature chart, the Vogel equation is more accurate and useful in engineering calculations to determine the dynamic viscosity [&eta;] [Pa.s]:

[&eta;] = ae^b/(T-c)​

a,b,c are three constants that can be calculated from three viscosity measurements for a specified oil at three temperatures.
T is absolute temperature [K]

The above-mentioned book provides a computer program that enables calculating the viscosity at any temperature and viceversa, using the Vogel equation.

 

[romke]

i fully agree that the dynamic viscosity is more suited for engineering calculations. the problem is that usually the kinematic viscosity is measured. ofcourse if you know also the density at the temperatures that the viscosities are known, you can convert the kinematic viscosity into the dynamic viscosity and then you can solve the Vogel equation.

 

[electricpete]

Thanks 25362. I have that book, but I didn't notice the appendices. I'll have to take a closer look at those. When I look at the program "viscosity" in Appendix A2, it looks like it requires 3 input points (viscosity at three temperatures).

Typically from the manufacturer we only get two. One is viscosity at 40C (VG). The other is either the viscosity at 100C or the viscosity index which can be used to calculate viscosity at 100C from viscosity at 40C (using ASTM D2270.. no other way that I know of).

I have more of a comfort level in being able to recreate the curve from an ASTM standard. I checked my spreadsheet again the ASTM D341 special graph paper and it works. That's good enough for me for the time being, but always interested to hear about other ways which may be better.

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[electricpete]

http://home.houston.rr.com/electricpete/eng-tips/ViscosityVsTemperatureCalculator1.xls

Above is revised spreadsheet. I added a new tab ValidationTestCase with the ASTM special graph paper.

Using an example VG32 (32cSt at 40C).
VI=100 => Viscosity at 100C is 5.4cSt (based on reverse table lookup in ASTM D2270... is there any easier way to determine the 100C viscosity from the 40cSt viscosity and the viscosity index?).

The graph shows
60C => viscosity = 15.2
80C => viscosity = 8.5
(to within a tenth or two).

This is the same thing that my spreadsheet shows.


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[romke]

no there isn't i'm afraid. be aware of the definition of the viscosity index. it is a relative value based on the vk40 and vk100 of an oil compared with two standard reference oils with an arbitrary VI of 100 and 0, being the best and the worst (in terms of viscosity/temperature sensitivity) that were available when the standard was defined (way back in 1916 or so). for any oil that you want to calculate the viscosity on the basis of one viscosity and the viscosityindex you need to compare it with the two relevant test oils. this can either be done by solving one of the formulae given in the appendix of the standard or by looking up the values in the reference tables published by ASTM.

 

[25362]

I wonder whether for simple estimations one can consider that the kVs of 100 VI oils on an ASTM chart rest on practically parallel lines. Thus having drawn that for one 100 VI oil, would enable to draw a parallel knowing just one viscosity of another oil with the same VI=100. Any comments ?

 

[romke]

unfortunately they run not exactly parallel. thinner oils with the same vi as more viscous oils have a somewhat greater slope. i think the reason for that is that two different sets of reference oils are used and that the vi of the oil to be drawn in the diagram is a relative measure (relative to the reference oils employed that is). although the difference in slope is not large, the error you make can be quite considerable, given the fact that the vertical scale is of the LOGLOG-type. you can check it for yourself if you take data from an oilsupplier (for example a range of hydraulic oils) and draw the diagrams yourself.