On extrusions speeds

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I have been losing a fight with my latest extuder/hotend combination. It works ok as far as I do not want it to work too fast. I want to keep the PG35L motor not too hot or it will break. So I am powering at 500mA, which seems to be well beyond its maximum rated current, so it gets hot. But I've added a passive cooler to it so won't get dangerously hot. Should I used a higher current, as someone suggested, maybe my mileage might vary, but at the expense of needing a fan blowing directly to keep the motor from frying itself.

One of the things that was bothering me was the maximum printing speed I could use with this new setup on my Prusa i3. Extrusion speed on Pronterface software (the host I use) is user selectable but measured in millimeters per minute, while travel speed is usually configured in the slicing software in millimeters per second. But doing the apparently simple math of dividing by 60 will not help here, among other things because the extrusion speed is the 3mm filament input speed.

As the hotend nozzle is much thinner than the 3mm stock filament, a much longer distance is expected at the output of the nozzle. A simple calculation can be done (assuming the volume is preserved through the extrusion process). If we consider that both input and output filaments are cylinder shaped, then, for a 0.5 mm output nozzle I can measure a 0.6mm diameter for my extruded filament output. Each millimiter that enters the hotend is 7.07 cubic millimeters of plastic, that for a 0.6 mm output diameter will turn into 25 mm of length (yes, that's right, every input millimeter turns into 25 mm of filament at the output).

Equipped with this data, we can finally do the math. For example, if the maximum speed you can get an steady flow of plastic is 180 mm/min, then that means you can lay output filament (without stretching it) at 180 * 25 / 60 = 75 mm / sec.

Of course this calculation needs to be adapted whenever input or output diameters of filament differ from these above. Please let me know if I am getting the facts wrong.

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