Viscosity Temperature relationship of lubricants? 3

[jmw]

I have come up against a problem in another thread where there is serious disagreement between two calculation methods for viscosity.

I have always believed that a lubricant's viscosity temperature relationship can be described by the ASTM D341 equation....

Log₁₀.log₁₀( [ν]+0.7)=A-B.log₁₀(T+273.15)
where [ν] is the kinematic viscosity at temperature T[°]C.

I'd be interested to learn if this is the case or not.

Does anyone know of any alternative equations? I came across the Castrol Blend 42 equation once, which I seem to recall was for viscosity temperature, has anyone heard of this or know what the formula is?

JMW

http://www.ViscoAnalyser.com

 

[electricpete]

Does the problem go below 2 cSt?

According to the Appendix of the ASTM docmument, the form of the equation gets more and more complicated as we extend to lower viscosity ranges:

log10 (log10 Z) = A - B log10 T(K)
where Z is given by:
Z = (v + 0.7) from 2E7 to 2.00 cSt
Z = (v + 0.7 + C) 2E7 to 1.65 cSt
Z = (v + 0.7 + C ? D) 2E7 to 0.90 cSt
Z = (v + 0.7 + C ? D + E) 2E7 to 0.30 cSt
Z = (v + 0.7 + C ? D + E ? F + G) 2E7 to 0.24 cSt
Z = (v + 0.7 + C ? D + E ? F + G ? H) 2E7 to 0.21 cSt

The additional constants are:
C = exp (?1.14883 ? 2.65868v),
D = exp (?0.0038138 ? 12.5645v),
E = exp (5.46491 ? 37.6289v),
F = exp (13.0458 ? 74.6851v),
G = exp (37.4619 ? 192.643v),
H = exp (80.4945 ? 400.468v)..

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(2B)+(2B)' ?

 

[jmw]

According to tribology-abc.com ASTM D341 does describe the temperature viscosity relationship.....

http://www.tribology-abc.com/calculators/iso_3348.htm

But there is an interesting (I'll have to study this for a while) paper here which seemingly contests the use of the Uberholde Walther equation (ASTM D341):

http://www.riemschneider.org/uploads/essays/viscosity.pdf

????

JMW

http://www.ViscoAnalyser.com

 

[jmw]

Thanks for your reply EP,
The question has arisen from a poster looking for viscosity data on SAE 30 oil so we are well within the range of the simplified ASTM D341 equation and the discrepancies are not small ones.

Now, while I appreciate that a relationship is at best an approximation of the real world, and though ASTM D341 has proven a very practical and workable equation, it is not an exact description and has limitations as to how it may be interpolated or extrapolated.
So it has its limitations, as Riemschneider and others point out.
Now I have always used it as a very good model when used with care.

My problem is that in reply to a post in the Pipeline forum, a poster has suggested the spreadsheet downloaded here:

http://www.xlrotor.com/resources/files.shtml

I fully expect that extrapolation will give problems, especially when extrapolating to lower temperatures, but when I compare the results of this spreadsheet to the ASTM D341 spreadsheet I produced (and to the results from other ASTM D341 spreadsheets, so it isn't my spreadsheet in particular), about the only points they agree is on is at the two temperatures I selected from the Xlrotor spreadsheet (100

http://www.xlrotor.com/resources/files.shtml

and 220[°]F) and everywhere else the disagreement is major, not just a bit one might expect from two different models of the same data.
I could have used Va and Vb of course, but I don't think that would make any difference.

This gives me pause to ask "do lubricants not obey the same relationship as other hydrocarbons?"... which I find hard to believe.
None the less, I have to consider if the conditions under which I use the ASTM D341 equation (for purely practical reasons), are perhaps almost special cases which minimise the effects of measurement and calculation errors (which is of course true, but surely not to this extent?), and that maybe my experience of ASTM D341 is like a stopped clock... right twice a day i.e. right only under the conditions at which I use it.

But if I am wrong then so too are a number of others such as Tribology-abc.com and others who all seem to use ASTM D341.

xlrotor uses the expression:
V_s=V_a*EXP(LN(V_b/V_a)*(T_s-T_a)/(T_b-T_a))
Where V_s is the viscosity at T_s
and V_a is the viscosity at T_a
and V_b is the viscosity at T_b
Viscosity is cSt and temperature is [°]F

I might accept that other models might be more suitable for extrapolation into low temperatures but between the two reference temperature viscosities I would hope to see some correlation and this is lacking.

So.....? Well either the xlrotor calculation is wrong (not just in the extrapolation but interpolation also) or it describes lubricants better than ASTM D341.....Is there another option?

JMW

http://www.ViscoAnalyser.com

 

[electricpete]

I haven't read the paper in detail.

fwiw, my inclincation when faced between contradiction between approved industry standard and uncited worksheet (with no references for calc method) would be to favor the ASTM standard.

Another factor that leads me in that same direction is the fact that the xlrotor equation is a simpler functional form than either the ASTM equation or the equations referenced in the German Professor's paper. If there was a much simpler underlying releationship, I would think those other guys would have found it rather than finding some more complicated relationship.

I can also imagine how the xlrotor equation might come about. Let's say someone remembers that the relationship is a straight line when plotted on a certain kind of paper. We both know it's the ASTM graph paper, but he thinks its log-log paper. He tries to plot a relationship where viscosity vs temperature is linear on log-log paper and what does he come up with? The xlrotor equation is one possible equation a person could come up with under that misguided approach.

If it is a big interest to you, you might try contact xlrotor at the link listed. They are pretty accessible people from my one encounter..... I emailed with a question about the demo version and Dr Murphy emailed me right back.

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(2B)+(2B)' ?

 

[electricpete]

He tries to plot a relationship where viscosity vs temperature is linear on log-log paper and what does he come up with? The xlrotor equation is one possible equation a person could come up with under that misguided approach.

Small correction.... it is not a straight line on a log log scale. I misread that the ln on RHS enclosed the temperature terms.

But it doesn't change the conclusion. This particular equation would be a straight line on a log-linear scale (log Viscosity, linear temperature).
ln(Vs/Va) = ln(Vb/Va)*(Ts-Ta)/(Tb-Ta)
ln(Vs) = ln(Va) - Ta/(Tb-Ta)*ln(Vb/Va)+Ts*ln(Vb/Va)/(Tb-Ta)

intercept is ln(Va) - Ta/(Tb-Ta)*ln(Vb/Va)
slope is ln(Vb/Va)/(Tb-Ta)

I am very sure if velocity vs temperature was a simple straight line on a log-lin scale as xlrotor equation suggests, ASTM would have seen that simple relationship instead of the more complex relationships that they came up with.

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(2B)+(2B)' ?

 

[jmw]

Thanks very much for the reality check ElectricPete, I have already emailed xlrotor for clarification and I am waiting for a reply.
Your logical approach of favouring the industry standard, especially if the alternative solution appears simplistic, is seductive but I had to get some feedback. Looking at the alternative methods there is some justification for the form of the xlrotor expression which is what really gave me pause.

I'll give feedback from xlrotor when I get it.

JMW

http://www.ViscoAnalyser.com

 

[jmw]

I have received a reply from Brian Murphy with which I am now entirely happy as it applies equally to the ASTM D341 equation.... it is good under certain conditions and poor under others:

The formula used to compute viscosity can be seen in the cells of the
viscosity column. I believe some refer to this formula as "Reynolds
viscosity equation" and it is often used in the analysis of journal bearings
because it is computationally convenient. It is of course based on giving
it two temperature/visc points as a baseline. It is entirely adequate for
the temperature ranges that bearing lubricants typically operate in.
Adequate results for Reynolds formulation can be obtained if the known
temperature/viscosity points are
chosen at the oil inlet temperature and below the maximum film temperature

my emphasis.

JMW

http://www.ViscoAnalyser.com

 

[electricpete]

Google did not lead me to anything resembling Reynold's equation for viscosity vs temeprature.

The reference below shows several formualtions, including one that may be vaguely similar to xlrotor:

http://books.google.com/books?id=ax...ds largely depends upon temperature."&f=false

From above:
Equation 2.16:
mu = mu0 * exp(-E/T)
ln(mu/mu0) = -E/T
Substitute: E = a + b*T + c*T^2
ln(mu/mu0) = -a/T – b - c*T [equation 1]

Contrast to xlrotor:
ln(Vs/Va) = ln(Vb/Va)*(Ts-Ta)/(Tb-Ta) [equation 2]

Equation 1 and 2 are not too far apart. We see the left hand side matches. The right hand side of [2] has term which varies linearly with Ts (similar to c*T in [1]) and term that is constant (similar to b in [1]). If the a/T term in 2 is small and if there is some negative sign to be found, then maybe those 2 expressions would act similarly.

Reference 4 is GROFF J. L. E.~ABC du Graissage. Edition Technip, 1961

Groff had some of his own complaints about the ASTM method at the link below, but they all seemed related to ease of use:

http://books.google.com/books?id=Wt...onepage&q=viscosity temperature groff&f=false

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(2B)+(2B)' ?

 

[electricpete]

if there is some negative sign to be found,

I found the negative sign.
the constant on RHS of 2 is:
ln(Vb/Va)*(Ts-Ta)/(Tb-Ta)
If Tb>Ta, then Vb<Va and the coefficients of the linear and constant terms in [equation 2] end up being negative.

=====================================
(2B)+(2B)' ?

 

[cloa]

http://www.eng-tips.com/viewthread.cfm?qid=293735&nx=1

This thread is useful for your discussion

 

[jmw]

Thanks Cloa, that's thee thread that started me off!
Brian has further stated:

The Reynolds formula is fine for its intended use, but using it outside that
temperature range one should not count on it without prior validation.

Lubricants used in industrial bearings typically do have their viscosity
drop significantly as they get hotter. The Reynolds formula is best used
between two known v/T points, and it assumes a linear variation in the
log(v) versus T. This assumption may or may not work well for other types
of fluids

There is a point here; if you want to take a viscosity measurement at two different temperatures and try to determine the viscosity at some temperature well away from from either, and especially a lower temperatures, you must expect significant errors whatever formula you use.

In some applications, if the calibration points are close enough to the measurement point and you have sufficient accuracy budget, you can use pretty much any relationship.

Thanks again for you valuable assistance ElectricPete.

JMW

http://www.ViscoAnalyser.com