## Saturday, 11 August 2007

### Thermals

I need to knock up a controller for the extruder. This will take commands from the main controller via an I²C bus and control the motor speed and heater temperature. It may also need to control a fan to cool the workpiece and monitor a filament out detector.

I decided to drive the extruder with bench power supplies to see if it works first and get an idea of its parameters and hence the requirements for the controller. Here is my test setup :-

As you can see I have plenty of meters. I have been hoarding them for years but it is not often I get to use more than two at a time. Here I am measuring extruder voltage and current, temperature and thermistor resistance. I have another three or four about somewhere but I doubt I will ever need to measure 8 parameters!

The bench power supplies are ancient, I think the big one has valves in it and I built the small one when I was a child. I had a near perfect memory then so I never saw a need to label anything. I have several other items of equipment from that era, including an oscilloscope, with no labels on anything.

Here is the raw data I measured :-

 Power Temperature Resistance 0 W 23 C 2108 R 0.77 W 48 C 897 R 1.36 W 64 C 533 R 2.13 W 87 C 280 R 3.06 W 114 C 145 R 4.17 W 145 C 73 R 5.44 W 173 C 42 R 6.89 W 207 C 21.9 R 8.5 W 243 C 12.2 R

I plotted a graph of temperature against power. I expected it to be a straight line because the rate of heat loss is proportional to the temperature difference between the nozzle and its surroundings and at equilibrium that must equal the input power.

As you can see it is a bent line with a change of gradient at 150°C which I can't explain. I measured the temperature with a thermocouple inside the barrel. It is rated for use up to 250°C but the strange thing is that if I plot a graph of the temperature indicated by the thermistor then the graph is much straighter. I calculated the thermistor parameters from the thermocouple data ignoring the last three points.

So I am not sure what to make of it. I may have to repeat the experiment with my IR thermometer. As long as the thermistor measurements are repeatable I don't suppose absolute accuracy is necessary, other than to swap setting with other RepRappers.

The thermistor resistance is a extremely non linear. Its is approximated by a negative exponential of the reciprocal of absolute temperature.

Ro is resistance at known temperature To, in my case room temperature, expressed in Kelvin. Beta is a second parameter of the thermistor which can be calculated if you know the resistance at two different temperatures. I calculated it for each of the first six power levels and then took an average. It's probably not a very accurate value because the thermistor, being on the outside of the barrel, was probably at a significantly lower temperature than the thermocouple on the inside. However, it is the inside temperature I am interested in so I probably get a value of beta that sort of compensates for that.

Here is the graph of resistance against temperature :-

I plan to measure this with the analogue to digital converter in the MSP430 micros I am using. The problem is to cover such a large resistance range would end up with very little accuracy at the high temperature end where the machine will operate.

I had an idea that putting a fixed resistor in parallel would close up the bottom end without affecting the top much. Indeed it does, here is a graph of the combined resistance against temperature with a 100 Ohm resistor in parallel. You can see it is not far off being a straight line, much easier to digitise accurately.