Monday, 29 March 2010

Feel the Energy !

Energized by the Australian Grand Prix here in Melbourne, it's time to calculate motor requirements...

Roton provides some good formulas, as well as a nice introductory discussion on screw threads. Of particular interest is the list of friction coefficients (eg, steel on steel dry - 0.80; steel on steel lubricated 0.16), as well as the maximum allowed rotation speed of a screw thread resulting from the way it is mounted (Type of end fixity versus critical speed factor).

On mycncuk, irving2008 made a nice post including an Excel spreadsheet to calculate needed stepper motor size. The spreadsheet is pretty ok, though I had to adapt it to compare a list of motors in a single step, and I believe he got the calculation of the rotor torque wrong.

My gantry will have around 28kg and it will sit on linear ball bearing, so friction is low. Cutting primarily wood, and maybe aluminium, I would need a cutting speed of maybe 1,000mm/min to 1,500mm/min.

I'll be using M12 (12mm) screw threads, with an x-axis length of 1,000mm. I intend to mount the screw threads in fixed-supported mode. Screw pitch is 1.75mm. I assume screw efficiency is "lousy", ie, 25%, though with lubrication this may go up. It'll be an interesting test to see if nut-heating is going to be an issue. I also assume a cutting force of 20N.

Putting it all together, I would need to 0.55Nm at 2,400 steps/second for cutting, and 0.3Nm at 4,300 steps/second for rapid movement (if the motor and driver can handle that speed). Taking a safety margin of 3 means I need a motor of around 1.6Nm or better. I'd like to give it an additional buffer to allow for future growth (meaning, router version 2), so 1.6Nm to 3Nm would suit my needs.

Now, the ideal voltages for eBay-available stepper motors with 1.5Nm or more ranges from 50 to 80 Volts. So, in order to get good performance from these motors and considering that my 1.75mm screw thread requires high speed, I will be looking at a 48V power supply. 24V is too low, 80V makes it more expensive for the driver and more limited on stepper choice.

So, in summary:
  • Stepper motor: 1.6Nm to 3Nm, ideal voltage near 48V.
  • Power Supply: 48V 

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