OK...here's just a brief run down. Its been a while since I worked in instrumentation but here goes.
Inconel or ceramic is where the thermowell is concerned. This is a hollow tube that is blinded on the end that the thermocouple slides in to. They are made to protect the thermocouple and they will also dampen rapid temperature fluctuations. Some folks have experienced lower temperatures readings using a thermowell. This may be due to a number of reasons, one, the thermowell being the improper material for the application, it being too thick, or not being placed in the proper location in the furnace or material.
How thermocouples work is that they are two disimilar metals forming a "thermo-couple". Due to this "couple" being two different metals, a microvoltage is produced and this potential will be different at different temperatures. It is a non linear scale however will be different for each type of thermocouple used.
The upper range of a type K thermocouple is around 2400 degrees. Type K thermoucouples are made from chromel-alumel. Out of all of the thermocouples this type is probably the hardest to weld. If you ever look at a type K thermocouple at the weld it will look splattered somewhat. I have seen where a bad K thermocouple will open up at higher temperatures and close back up and appear to be good when checked cold.
Type R or type S thermouples are made from platinum-platinum/rhodium and are good up to about 2700 degrees. For what you pay for these they better last longer than a type K!
As far as controllers are concerned, a PID controller was mentioned. PID stands for proportional, integral, and derivative action. These controllers have to be tuned. Most controllers have an auto tune feature these days.
When purchasing a controller one of the first things you have to know is what sort of a "final control element" you are going to use. All that it means is wheather you are going to use a relay to turn electrical power on or off, use an SCR drive to pulse an heating element or use a positioning valve.
On/off control is about the sloppiest. That is what your kitchen oven uses. I would recommend using a time proportioning output. What this does is that it will still turn it off and on however it does it on cycles or pulses. The closer it is to the operating temperature or setpoint the less it is on. It is much more accurate control then just basic on/off control. This is used to drive a contact or relay output. In other words, don't drive a heating element directly with your controller, drive a relay with your controller and wire the "other side" of your relay to the element. You can also use this sort of output to drive a solenoid gas valve.
A current proportioning output usually puts outa standard 4-20 milliamps which drives some device such as an SCR drive that would drive a heating element or some other FCE or Final Control Element. What we do in industry is usually have what is called an I/P, or current to pressure transducer that converts or transduces this 4-20ma current to 3-15 psi to drive a valve. This is pretty common but expensive for the average person like you or me.
A position proportioning output is directly to a motor. Not very likely we'll use this either.
So all this gobble-de-goop to say this. For most of our needs other than a heat treat oven where fairly tight control is needed, we primarily need just a temperature indicator. Most any temperature controller or indicator will give you what you want.
Craig
