Hi, I am in the process of designing a machine to make overwrapped musical instrument strings. I need to size the drive motors, and determine how fast the machine can wrap the wire on. To do this I need to work out the torque required to bend the overwrap wire onto the core.

The machine will tension the core wire and rotate it in order to wrap on the over-winding which will be fed in under tension. So the motor that drives the core rotation must do work to deform the wrap wire onto the core. The size and spacings of the wire are both variable, so I'd need to work out the formula.

The winding wire will vary in proportion to the core from about 1/10th dia to a similar diameter, so the deformation in some cases is quite severe. The wire I'll be using will be a soft and ductile brass wire or pure copper wire for the wrap. The core is 60:40 hard drawn brass wire.

I probably only need a ball park figure for the torque required, enough to choose a motor size and any gearing. Unfortunately I am not a mechanical engineer - my skills are in Radio electronics engineering and instrument making though I ought to be able to follow some equations and concepts

Google has let me down here, and I need some guidance - thanks for any thoughts!

 

@GarethW I clicked your link but it errors. So I guess i'm in the wilderness then I can suck it and see, but I'd be upset to buy a NEMA23 motor when a NEMA 17 was overkill ..

 

Thanks. I applied to join. In the meantime some more detail:

• The core wire will be tensioned between two spindles. The spindles are then coupled to a single shaft with synchronous belt drives with the shaft driven from a stepper motor. The core wire is hard drawn brass at typ. 80% breaking strain, so about 10kg for a typ. 0.44mm dia core.
• The overwrap wire is drawn onto the core by rotating the core by turning the spindles. The over wrap is fed through an eye connected to a traverse gantry driven by a second stepper motor and leadscrew. The traverse rate relative to the spindle sets the wrap spacing from continuous to about 5:1. Wrap dia can be 0.19mm to 0.56mm and is soft annealed brass wire or possible soft copper.
• The overwrap wire will be fed from the reel and tensioned by hand. The machine is for small batches so no need to construct a complicated tensioner.

I started think about how to solve this. If you consider the overwrap, which is bent from straight into a tight circle, the inside of the wire will be compressed and the outside stretched. There will be a neutral axis in the centre. What would be required is a double integral across the wire cross section and along the stress strain curve to calculate the energy of plastic deformation per turn of the wire. The circular cross section makes it complex.

I fear a closed form solution will be difficult (at least for me) but it might be possible to compute numerically. Does this sound tractable?

 

You don't need an exact answer, you need an approximate answer that is ideally conservative. You are trying to size a motor. Too small bad, big enought with margin, great. 10 times too large bad, 3 times too large probably okay.
Assume material behaves as elastic/perfect plastic. ie stress strain curve is linear and then perfectly horizontal. Figure out how much force it takes to get the entire cross section to yield stress. Done.