micro Stress vs Strain Machine

Spec!

The goal here is to design and build a machine, which can be fabricated in $250k size fab labs, that can generate stress-strain curves for a wide set of materials as well as perform hardness testing.

To ballpark, I'd like to see 100mm diameter plates having a total travel from 0mm separation -> 500mm, this leaves enough room for fixturing etc.

Generating kN

We want lots of force, with very fine control of position. This means a nice linear transmission. To estimate the forces we might want to see, I wrote a quick table of forces required to rip apart ~ 3mm square (0.001mm^2) samples of a few materials.

Brinell hardness tests range from 10N through to 30kN (for steel and cast iron) but non-ferrous materials normally see 5kN only.

So, a ballpark of ~ 10kN would be ideal - this is a big number - off the bat I'm going to estimate that 5kN will be a more reasonable target. 1kN is enough for a complete set of plastics, but that's only allowing for a realtively small sample.

To generate the force required, we're going to need some motor / transmission oomph. Here's a list of typical NEMA size motors, and the torques they can generate. The atkstepper can supply enough current to power any of these.

Racks and Pinions

We'll be using two linear stages (one on either side of the platform), so, from our N34 156mm motor with 13Nm of torque we'll need 26, 5.2 and 2.6mm lever arms respectively for 1, 5 and 10kN total force.

Considering practical limits on pinion diameter (with a shaft of 14mm, and 19 3mm-pitch teeth, we'll have an 18mm diameter pinion - 9mm lever arm) we will only realistically achieve 1.44kN of linear force per motor with direct-drive rack and pinion on a Nema 34 size motor. This makes a 3kN machine, but to add some safety factor we're at at 2kN goal with this approach.

The next step would be to check against tooth shear stress for 3mm pitch.

From reasonable WEDM (time) and Waterjet (washout) limits, I expect the thickness of any fabricated pinion to have a limit around 12mm. To make this all simple, I'll say 10mm. For the waterjet, this is a bit of a stretch (get it?)...

To guess at resolutions, we'll take our sample above in aluminium having a length of 100mm - with elongation at break being 12%, we're interested in a 12mm 'long' stress / strain curve. For 1000 pts on this curve, we're interested in a step size of 12 microns.

From our 18mm diameter pinion having a circumference of 56mm, this means 4667 counts per revolution. In a 200-step motor, we would need 32 microsteps per revolution - most drivers will go to 256 - but microstepping isn't exactly linear. To do this really well, we will want to finish work on closed loop stepper driving, where we can use a 14-bit encoder to control around ~ 4096 counts reliably.

All in, a direct rack and pinion drive can land us at a 2kN machine with some desired resolution, but we're at or near most of the limits here.

Ball or Leadscrews

Racks aside, a ballscrew is the obvious way to do this. Ballscrews can be had for less than hundereds of dollars. Besides transmitting motion smoothly, their ratios are favourable. For example, with a 5mm pitch ballscrew having an efficiency of 85%, we can drive 14kN with our 13Nm motor - so 28kN for the machine.

For the same ballscrew, to achieve 12 micron resolution we'll only need 416 steps in each rotation - this is easy to get.

Step Two: Force Measurement

For load measurement, Sam has worked through a great loadcell design.

Fixturing

! important