Those interested, i cleaned up my temperature prediction spreadsheet 
and if you want to play with it, let me know.
The math is crude, it might even have small errors.

The spreadsheet is prepopulated in column E with data from an calculated RC
network with source (green area), that you can erase, or use it to play with 
base data.
The data is rounded to a settable  number of digits.
Best performance at time sampling of  tau/50 and 2 digits minimum
of resolution of the temperature ( x.xx  degrees).
At 3 digits the prediction is spectacular.

Accuracy won't impact the results. It's the resolution that counts.
With 1 digit of resolution the results are not very usable in terms
of calculation, however your experienced engineers eye may draw conclusions 
anyway.

After an arbitrary number of samples, the sheet calculates the final temperature
tau , end of test time and creates a graph.






Regards,

Ing. Gert Gremmen
Approvals manager
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From: John Allen [mailto:jral...@productsafetyinc.com] 
Sent: Monday 9 January 2017 05:19
To: EMC-PSTC@LISTSERV.IEEE.ORG
Subject: Re: [PSES] Thermal equilibrium - 10% rule

The subject itself can easily be a presentation at ISPCE.  Doug, what you and 
Gert have done should be a formal paper.  Please consider collaborating and 
making it happen.

John



________________________________________
From: Pete Perkins <00000061f3f32d0c-dmarc-requ...@ieee.org>
Sent: Sunday, January 8, 2017 9:33 PM
To: EMC-PSTC@LISTSERV.IEEE.ORG
Subject: Re: [PSES] Thermal equilibrium - 10% rule 
 
Doug,
 
               A great approach; it would make for an interesting ISPCE/PSES 
presentation and a paper.   Go for it.  
 
:>)     br,      Pete
 
Peter E Perkins, PE
Principal Product Safety & Regulatory Affairs Consultant
PO Box 23427
Tigard, ORe  97281-3427
 
503/452-1201
 
p.perk...@ieee.org
 
From: Doug Powell [mailto:doug...@gmail.com] 
Sent: Sunday, January 8, 2017 10:39 AM
To: EMC-PSTC@LISTSERV.IEEE.ORG
Subject: Re: [PSES] Thermal equilibrium - 10% rule
 
Richard,
 
I have tried a number of approaches in the past.  Given that most products are 
quite complex with regard to all the potential heat sources/sinks and 
interfaces I decided that anything along the lines of FEA is impractical.  
 
I also tried the time constants idea which is analogous to RC time constants.  
I found this works well enough if you have a good amount of history with the 
product itself.  Otherwise, due to the non-linear nature of the problem, it is 
difficult to predict end time or temperature until 3 to 4 time constants have 
already passed.
 
I tried using the slope of ΔT to estimate when the end of the test is pending.
 
The next attempt was to dig in a little following the equations V = Voe-(t/RC) 
and V = Vo[1-e-(t/RC)] where I substitute V for the the various temperatures 
(Vo = the absolute value of the temperature delta from start to end), C is 
analogous to product mass and R is the Rtheta of the product. With a little 
testing history, you can assume the composition of the product is similar for 
other products designed by the same company (copper, steel, plastics, air, 
liquids, etc), I solved for RC and then rearranged the algebra to solve for t 
which is time.  There are a couple of problems in that I am still unable to 
come up with a general purpose solution.  First this is a simultaneous solution 
of several unknowns which is not conducive to quick on the fly solutions.  This 
is especially true when you are in the early stages of a temperature run when 
things are still moving quickly.  As you know extrapolating outside an existing 
dataset is risky, especially when nonlinearities are invo!
 lved.  
 
I am now going back to basics.  Q = Cp * m * abs(T2-T1)
 
q = heat energy in Joules
m = mass of the product
Cp = specific heat of the product
T1 = The initial temperature of the product at the start
T2 = The final temperature of the product
abs() is used to correct for heating or cooling
 
With the start/final temperatures and mass taken from prior tests I can extract 
a Cp for a particular product. Understanding one watt is Joules/second you can 
factor into the equation time.    My thought is that the composition of a 
product from the same engineering group with have similar ratios of copper, 
iron, plastics, etc.  And then I may be able to solve for total test time or 
final temperature.  Not forgetting that the air mass and equipment of the 
environmental chamber is part of the big picture.
 
I have not fully tested this method yet, but so far I remain hopeful.  If this 
works, I plan to build a small database of product Cp values.  I would be 
interested to know if anyone else gives this a go and how as yet undiscovered 
problems are overcome.
 
 
-Doug
 
 
Douglas E Powell
Laporte, Colorado USA
doug...@gmail.com
http://www.linkedin.com/in/dougp01
 
 
 
 
 
 
 
 
On Sat, Jan 7, 2017 at 12:51 PM, Richard Nute <ri...@ieee.org> wrote:
> We have to consider that the temperatures sought are not of
> metrological value, but to
> to establish a safe/non-safe result.

Yes!

> The mathematical limit of an exponential rise is easy to
> estimate, once a few timed samples are available,

I haven't been able to come up with an equation, even though I have tried and 
sought help from folks who are more knowledgeable than me in the field of 
thermodynamics.  Please tell us your methodology.

Best wishes for the New Year!
Rich
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-- 
 
Douglas E Powell

doug...@gmail.com
http://www.linkedin.com/in/dougp01
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