Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
(OP)
Hello all,
There's been a few discussions on the Walther equation for plotting the viscosity/temperature relationship of lubricants. I'm trying to basically make my own plot...but I am having trouble understanding the vertical scale to use to get the linear relationship. I think I've puzzled out how to make a log scale. But, the log log needed for this equation isn't working out.
The ASTM d341 chart uses this scale. And while I could download the graph...that's not going to tell me how the vertical scale was created. I sure appreciate the help.
(the "why" is a much longer story)
Thanks,
Andy
There's been a few discussions on the Walther equation for plotting the viscosity/temperature relationship of lubricants. I'm trying to basically make my own plot...but I am having trouble understanding the vertical scale to use to get the linear relationship. I think I've puzzled out how to make a log scale. But, the log log needed for this equation isn't working out.
The ASTM d341 chart uses this scale. And while I could download the graph...that's not going to tell me how the vertical scale was created. I sure appreciate the help.
(the "why" is a much longer story)
Thanks,
Andy





RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
with standard spreadsheet software you will not be able to make a chart like that, because you will not be able to get the vertical scaling needed.
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
The Walther formula[1] is typically written in the form
log_{10}[\log_{10}(\nu+\lambda)] = A - B\,\log_{10}(T)
where λ is a shift constant, and A, B are empirical parameters.
http://en.wikipedia.org/wiki/Temperature_dependenc...
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
where:
a, b, c, d are constants
ν is the kinematic viscosity (m2/s)
T is the absolute temperature (K)
It has been found that if ν is in cS, then a ≅ 0.6. By taking d=10 and log twice one gets:
Although an incorrect derivation of the above equation, the ASTM viscosity-temperature chart ewhere the ordinate is log10log10(νcS +0.6) and the abscissa is log10T, is quite successful when used on oils (mineral and synthetic) under "normal" conditions.
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
You could build a table:
T, v, X, Y, X1, Y1.
T is the independent variable Ttemperature (in the correct units)
v = b*10^*(1/T) - 0.6
Y = log(log(v + 0.6)
X is log(logb + 1/T) (plug in whatever b is… I'm working from what is posted above).
Y1 = (log(v + 0.6)
X1 is (logb + 1/T) (plug in whatever b is… I'm working from what is posted above).
Then if you a simple excel linear plot Y vs X or log log excel plot based on Y1 vs X1 I think you would have a straight line on your graph (slope 1 on the linear plot). The only problem is the axes are not v and T. You could take out all auto-generated gridlines and tickmarks and build your own vertical gridlines using extra series with constant values of T and your own horizontal gridlines with constant values of v.
Labeling those gridlines would be the challenge. Two approaches:
1 - You could add labels manually (for example in powerpoint) and get a nice pretty chart.
2 - If you wanted excel to do it you might keep it a small number of gridlines to keep it manageable and label the gridlines using the normal series label feature. Then to read the scale you wouldn't look at each gridline and then at the legend to figure out the values associated with the gridlines. Easier for you to build but not as pretty when you're done.
=====================================
(2B)+(2B)' ?
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
=====================================
(2B)+(2B)' ?
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)
=====================================
(2B)+(2B)' ?
RE: Plotting Viscosity Data and making the ASTM D341 Graph (Logarithms)