Thinking CNC – Bootstrapping, Costing

 

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I’m starting this project with nothing more than an inexpensive drill press, a wood router, a Black and Decker RTX-1 and a few hand tools. This severely limits the precision of any metalforming work I can do.   This means that I’ll need to rely on precision made parts – bearings, primarily, and a ball screw and nut – and use those to create a reasonably true frame with bearing rails for a hand-cranked, single-axis feed table.

Commonly available aluminum extrusions used for door frames are typically hollow and thin walled, and readily twist and bend along their length. They may be suitable for framing in shorter lengths, if properly fastened to a rigid base and if care is taken to neutralize bending and torsion moments.

Also, bearing surfaces will need to be attached to the aluminum frame, to carry normal loads transferred from a workpiece holding plate via roller bearings (balls or rollers). Thankfully, there are a couple of metal suppliers nearby who sell hardened Type 304 and 316 stainless steel round and rectangular rods. I can have short lengths of these cut and milled by a nearby machine shop for use as rails, each as long as this big (80 cm square), fused ceramic tile I use for a tabletop.  The other linear dimensions for these rails need to be chosen to limit material cost – it’s surprising to find prices jump for each millimeter increase in slab thickness or shaft diameter.

This brings me to the material dimensions calculations. To start with, we’ll have to assume that the material specs (composition, and finish) given by our metal suppliers are correct. The idea is to be able to head over to a supplier, find out what stock is available or orderable, fill in the figures, and select the best-priced raw stock based on our requirements. What we’ll do is build a spreadsheet calculator into which we’ll input

  • Material composition name,
  • Material dimensions,
  • Bending modulus,
  • Strain modulus,
  • Beam length,
  • Loads (moments and normal forces),
  • Distortion (strain, torsion) limits, and
  • Cost per unit length, and a budget limit.

OpenOffice Calc will serve as the prototyping engine for this costing tool.

Calculator in hand, and working in typically ass-backwards fashion, I now need to think in greater detail about the design of the workholding platform.

This platform is going to be subject to substantial normal and torsional loads. The maximum normal load (at which the drill point or router mill needs to be held against the work piece to have cutting action) will depend on the hardness of the workpiece, cutting edge angle, and spindle rotation speed.

 

Plates and beams and aluminum seams…

Here’s some raw stock and tooling material that’s known to be readily available:

  • 1.2 cm steel plate.
  • Fused ceramic tile
  • Type 304 stainless steel (austenitic – nonmagnetic, corrosion resistant) round bar of various diameters.
  • Door framing aluminum sections – “push bars” (rectangular round bars with hemispheric short edge cross section), various thin walled open and closed sections with orthogonal edges.
  • High-speed tool steel blanks for lathe cutting bits.
  • Turned lead screws.
  • Roller bearings.

Now the precision machined parts we’ll use are these:

  • Set of three: ball screw 500mm, 400mm and 200mm travel; nut; and end-thrust bearings. I’m not futzing with n-bar mechanisms or chain drives, thanks. Did I mention nobody manufactures and distributes these, here?  We probably manufacture them at some export processing zone, but nobody stocks these, nobody sells these locally. WTF?  Go visit United Bearing Industrial, they supply NSK, SKF, THK linear motion components.  
  • A set of four, flat linear rails with high Z axis moment rigidity, for the X axis.
  • Up to 12.7mm / 1/2″ milled steel base plate, to flatness within 1 mil.

The ball screws will need to be mounted to resist axial stress only, and they’ll be sized to reduce axial strain below a fraction of the desired precision (well below 1 mil); bending moments in ball screws’ axial plane must be borne by the spindle carrier and gantry rails…

But I get ahead of myself just a bit. I need to pick a place to start. Eeps. That means going to Wikipedia, Google, and my old textbooks.

Since I’ll definitely be using stepper motors for this first table, and I’ve no experience using these, I’ll get these first. Hurst Motors sells a 1.8° / step motor that offers 5% positional accuracy, from their Series H23S hybrids. Their spec sheet shows (for the H23S030476 motor) torque ratings at a minimum pulse rate of 500/second (2.5 revs/second, or about 180 rpm), that peaks at about 750/sec (3.75 revs/s or 225 rpm). A ball screw shaft with 5mm lead would advance at  1.87 cm/sec, or 1.125 meters/minute at the motor’s peak torque of  1.13 Nm.  At this driving speed, the table would exert a force of 2πTv/l  = 1,419 v N, where v is the screw efficiency, T is the motor torque, and l is screw lead. Check your units! A 90% efficient ball screw would yield roughly 1,277 N force (about 130 kgF, barely enough to lift me off my seat at constant velocity).  Intuitively, that ought to suffice to drive a router through some thin FR4 PCB, don’t you think?

Must think some more.