Monday, 25 October 2010

Belt Me !

While I was in the middle of designing the y-axis for the cnc router, I came across some reasonable offers for timing belts (vee belts) and matching pulleys. I was very tempted as the speed-power profile is much better suited to my needs than the threaded rods.

After some pondering, spreadsheeting and paper sccribbling, I took the plunge and ordered 3 metre of T5 16mm Kevlar & Urethane open belt and two matching T5 16mm 15 tooth pulleys from AusXmods, the same shop I bought the steppers and PSU from.

The only issue/fear I have is to judge if 16mm or 10mm belts would be more suitable. AusXmods unfortunately didn't have any technical specifications, so it's trial and error. I tried to predict what I'm getting by referring to the product catalogue from Gates Mectrol.

Remember, my steppers have 2.7Nm nominal holding torque, so let's make some assumptions...
  • Holding torque: 2.7Nm
  • Low speed torque: 80% of 2.7Nm = 2.16Nm
  • Top speed: 5,000 full-steps per second
  • High speed torque: 20% of 2.7Nm = 0.54Nm
  • Let's ignore belt and threaded rod friction for now.

Option 1: M12 threaded Rod
Rod Pitch: 1.75mm
Top linear speed: 5000/200x1.75mm/s = 43.75mm/s
Force at low speed: 2.16Nm * 1000 * 2 * PI / 1.75mm = 7755N = 790kgf
Force at high speed: 0.54Nm * 1000 * 2 * PI / 1.75mm = 1938N = 197kgf
Micro-step length: 1.75mm/2000 = 0.000875mm

Clearly, precision and force are way too high, and movemement is slow.

Option 2: T5 10mm belt with 10-tooth pulley
Top linear speed: 5000/200*10*5mm= 1250mm/s
pulley radius: 5*10/2/PI=7.95mm
Force at low speed: 2.16Nm*1000/7.95=271N=27.7kgf
Force at high speed: 0.54Nm*1000/7.95=68N=6.9kgf
Micro-step length: 5mm*10/2000 = 0.025mm

Top speed is obviously theoretical, but precision is good.

Option 3: T5 16mm belt with 15-tooth pulley (no 10-tooth is available)
Top linear speed: 5000/200*15*5mm= 1875mm/s
pulley radius: 5*15/2/PI=11.93mm
Force at low speed: 2.16Nm*1000/11.93=181N=18kgf
Force at high speed: 0.54Nm*1000/11.93=45N=4.6kgf
Micro-step length: 5mm*15/2000 = 0.0375mm

Top speed is again theoretical, precision is not as good, but still acceptable.

As a comparison, the maximum belt tension for a Gates Mectrol T5 10mm Kevlar belt is 320N, and for the 16mm belt it is 512N. In option 2, the stepper exerts 271N on the belt, which is a bit close to 320N, in particular considering shock when things come to a sudden stop etc. Option 3 seems a better match with the stepper exerting 181N and the belt accepting 512N.

In terms of acceleration, the gantry might weigh up to 20kg. Assuming a linear bearing friction coefficient of 0.1, we lose 2kgf, and maybe another 2kgf for the cutting force. So, we would have 18-4=14kgf remaining for acceleration at low speed, and about 2.6kg (excluding cutting force) at top speed.

To summarise all that maths in everyday language: My top speed with the threaded rod is around 44mm/s which is not much at all. With the belts, I have a chance to move rapids somewhat more rapidly, and if I get to move them at 300mm/s, I'd be very proud. So, after some plain theoretical maths, I ordered the 16mm belt. It's experimental, and if it doesn't work, I'll revert to using the threaded rods.

And I hope it's all true...

(Corrections and suggestions to my layman's physics equations are most welcome)
And I need some idlers now !

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