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March 10, 2011

A Little Dryer Trouble

Well there's your problem!

Well there's your problem!

   Last night I noticed it was taking a really long time to dry a couple of towels I had bleached clean.  After inspecting the dryer, I found it was not producing any heat.  Today, I decided to look into this issue.  Like a kid with a big toy and tool, I started to remove screws to see what was inside.
   When my washer had died a couple months back, I pretty much gave up before looking into the problem too deeply.  I was fairly sure it was either the drive motor or the gear box, and I didn't want to replace either.  The dryer, on the other hand, isn't nearly as complex.  No heat only results from a few issues.  My guess was a thermocouple was bad, and it was just a matter of finding it. 
   I started by trying to take the back off the dryer, but that wasn't possible.  So I took off the top.  I could see nothing wrong with the basic control panel: no wires had fallen off, no smell of cooked electronics, ext.  But I needed at the heater.  Turns out the only way to get at this item was to remove the front of the dryer, and then remove the drum—no small task.  But I'm good at taking things apart—it's putting them back together that is more tricky.
   After I had the device in pieces (pictured) I broke out the shopvac and cleaned the lint off everything so I could see what I was working with.  There is a metal duct that contains heating elements, on which are two thermocouples.  A wiring diagram showed that there are, in fact, three thermocouples.  One is an operating thermostat, which I assume is located on the blower.  An other is a high temperature limit, which I believe to be on the heater duct.  An the last thermocouple is a high temperature fuse, also on the heater duct.  I got out the multimeter and found one of the thermocouples did not conduct, and it was my guess this was the problem.  After removing it, I found it was a 360 degree F thermal fuse—now clearly blown.
   To be sure, I decided to by-pass the fuse (there are two other thermocouples so this should be alright for a temporary test) by moving the wire from the dead fuse to the next thermocouple.  Then it was back to reassembling the dryer.  Other then having to look up how to reconnect the belt, I did pretty good—everything went back together.  In fact, it went together better—I found two springs that had once helped the door to close.  They had fallen off, so I reconnected them.  And my test: it worked.  The dryer has heat again. 
   So I will order a new thermal fuse, and my dryer will continue to serve.
   I would like to note how much I like the fact appliances like washers and dryers contain electrical schematics.  I could repair a lot more things if more companies included schematics.  So thank you manufacturers who do this.

March 08, 2011

Exp( pi * i )

Diff. Eq. Homework

Diff. Eq. Homework

   I wanted to share some of my differential equation homework.  My instructions were to express an equation in terms of sine and cosine.  This section uses complex numbers, which I hear is extremely useful in the engineering field, but we hardly ever touch them in my math classes.  (I know, lame, right?)  The conversion process involves expending the Taylor series for the function, and after some separation work, out pops the series for sine and cosine.  It took my professor most of the class the prove this, so I'm not going to try and explain the process (although I really do love Taylor series).  But after all the work, we ended up with a general function that took this form:
  e(λ + i μ ) = eλ(cos μ + i sin μ)
   Where i = √-1 and λ and μ are variables.  Then what appeared as a rather uneventful question was this:
eπ i
    This expression is classic and known as Euler's Identity.  Without going through the Taylor series, let's just use the general formula above to translate this expression.   There is no λ, so λ=0, and μ = π.  Thus:
e(0 + i π) = e0(cos π + i sin π)
   We can reduce: anything to the power of 0 is 1 (including 0—crazy, hu?) so e0 = 1.  1 times anything is just the other quantity, so basically the e0 goes away.  The sine of π is 0, so i, which is √-1, times 0 is just 0—imaginary or not, it too goes away.  And the cosine of π is -1, which by now is the only thing left.  So after the reduction, we have:
eπ i = -1
Or
eπ i + 1 = 0
    How cool is that?  Two irrational constants e (Euler's number) and π, and an imaginary number coming out to an integer number.  It was even cool enough for xkcd.  The equation is considered the "most beautiful theorem in mathematics."  And there it was, problem number 3 of the homework, like it was just an other exercise.  No wonder people people don't appreciate math!
   I guess I find this exciting because I now understand why it happens, pretty much completely.  With this knowledge, I can do other things with the equation (like my homework!).  This gives me hope that one day I really will understand one of my big goals in mathematics: working the Fourier transform.
   The Red-Dragon took a dive a month or two ago.  I think what happened was that Ubuntu was in the middle of an update when the computer turned itself off.  After that, it refused to get on the network and refused to fix itself.  Rather then care too much and look into fixing the problem, I just installed Ubuntu 10.10.  The only thing the Red-Dragon does that isn't right out of the box is mount a 1 TB hard drive and share it.  I have some back up scripts on the Blue-Dragon that will archive my graphics and web site to the Red-Dragon.  And backup are a good thing!
Cari

Cari

   Took a trip to Madison today and watched UW's production of Rocky Horror.  Their set was amazing, and so was their lighting.  Having worked on Rocky Horror myself for UW-Rock, it was a rather humbling experiences.