<VV> Fan Belt Tension (Reverse Coefficient of Thermal Expansion?)

[RoboMan91324 at aol.com]

Hi Jim,
 
That is a very interesting link but it was not written well  and can be a 
bit misleading.  The sentence from the link, "Unlike other  solids, stretched 
elastic polymers shrink upon heating." gives a clue as to what  is really 
means.  The word "stretched" is the focus of the  discussion.  It should be 
"pre stretched."
 
It has been many years since I taught Engineering Materials  (among other 
subjects) as a TA in my University days so please forgive any minor  errors.
 
Polymers are made up of many (poly) molecules which are linked  together in 
a somewhat random fashion.  The atoms within the molecules  themselves are 
linked at angles as well.  When you stretch a polymer like  rubber, those 
linked molecules stretch and become straighter but resist the  deformation and 
want to return to their natural state.  (Think of a  multitude of randomly 
formed springs held in a matrix that can be stretched  but want to return to 
their initial shape.)  The more you pull, the  straighter they become.  As 
they grow in length, they also draw closer  together which is why a rubber 
band gets thinner as you stretch it.  In the  manufacturing process they can 
stretch the polymer before it sets (cures)  permanently.  This process 
leaves the molecules somewhat aligned in one  direction after the curing is done. 
 They are pre stressed.  When the  polymer is heated, the molecules are 
more free to return to their original  unstressed state which is more random.  
This allows them to contract.   However, since they are cured in a certain 
configuration, they return to the  stretched/stressed state when they cool.
 
Overall, the pre stressed polymer will still expand as  temperature rises 
but only one dimension will shrink.  The other two  dimensions will expand 
due to the coefficient of thermal expansion plus the  volume by which the 
first dimension shrinks.  The total volume changes very  little if at all.
 
Yes, you qualified your posting with the word "stretched" in  your text but 
this does not apply to the stretching that occurs when you mount  the belt 
on the pulleys and then adjust it.  It applies to the pre  stretching that 
may or may not occur in manufacturing.  I am sure the  designers of fan belts 
are well aware of this phenomenon but I do not know if  they use it in 
their designs.  Since the thermal expansion of the belt is  negligible, they may 
not need to apply the Gough‐Joule effect briefly described  in your link.
 
Doc
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
In a message dated 4/13/2012 6:04:12 P.M. Pacific Daylight Time,  
virtualvairs-request at corvair.org writes:

Message:  2
Date: Fri, 13 Apr 2012 15:25:00 -0400
From: Jim Simpson  <simpsonj at verizon.net>
Subject: Re: <VV> Fan Belt  Tension
To: Virtual Vairs  <virtualvairs at corvair.org>
Message-ID:
<CAAeLaHsA6g98gnvvGGL8ZQ_Twf60Gh1ak4FeGp1j97e0joox=g at mail.gmail.com>
Content-Type:  text/plain; charset=ISO-8859-1

Actually, fan belts tighten as they get  hot.  Sort of mind-boggling, but 
stretched elastic polymers (i.e. rubber)  shrink as they are heated.  This 
has been known since at least 1805 --  here's a good reference if you want to 
look into the  phenomena:
http://tpt.aapt.org/resource/1/phteah/v48/i7/p444_s1?bypassSSO=1

By  the way, the shop manual has a tension spec for the fan belt.  In my  
opinion, it's way to high.  I have a fan belt tension measuring device  and 
if I actually tighten a fan belt to the shop manual spec, it's almost like  a 
violin string.  I, like most other Corvair owners, subscribe to the  "just 
tight enough so you can move the alternator" approach.  That's  worked for 
me for several decades.  I suppose it works because as the fan  belt is run, 
the flexing and friction heat it up and tighten it.

Jim  Simpson
Group Corvair