Mechanical Rigidity/Cube Example

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Cube design needing improvement

Here is a design where some advice was asked here,722199:

Example Cube Design

Analysing each face:

  • The base is fantastic, it is entirely rigid (in the X-Y directions only). The bottom face therefore cannot "shear" (become a parallelogram).
  • The top face is also excellent: the aluminium plate, despite having a hole for the X-Y assembly, is of sufficient thickness and the hole is not so large (close to the outer extent of the plate) so as to reduce the rigidity of the aluminium plate as a frame. Thus it provides complete rigidity in the top (in the X-Y directions only).
  • However the open sides mean that the entire assembly may be "twisted" or "sheared": any one of the four sides may become a parallelogram, resulting in the entire frame being completely flexible.
  • Any parallelogramming caused by the sides will end up flexing and buckling both the base plate and the top face.

Note that there are no corner braces in this design, on any of the uprights, so there is absolutely nothing to stop the twisting and shearing. "Twisting" may be demonstrated by securing the four feet of the cube to the floor, then taking the top and trying to "unscrew" the whole assembly as you would a jar's lid. With this type of cube design if any one side is left open, then like a cardboard box where the top is open, all efforts spent on rigidity of the other five cube sides are entirely wasted: it is essential that all six sides are made rigid.

To illustrate this further: it is worth noting that the aluminium top plate, whilst being rigid in X and Y and may not be "parallelogrammed", relies fully on the other five sides for its rigidity to keep it fully in the same plane, i.e. not "twist" out of a flat shape. This applies to all six sides of a cube and is one of a cube's unique defining characteristics.

So as described in the forum thread, fixing this design to make it rigid may be achieved by:

  • Filling in all four remaining sides with some form of panel. Although acrylic or lexan provides internal visibility, even 3mm hardboard or MDF is sufficient for this purpose, and even 1.5mm plywood would suffice if, along the actual frame, the plywood is doubled up so as to spread the load of the bolts (with thin plywood, washers would be inadequate), and there are attachment points at least every 80-100mm on every single piece of the frame. Particular attention needs to be paid to ensure that there is good friction between the frame and the panel.
  • If however there are large holes to be put in the panels (so as to provide visibility or access) then thin materials such as hardboard, MDF or plywood are not sufficient, not least because these cheaper materials are subject to expansion under different temperatures and humidity. Better materials would be aluminium or other metal, lexan, acrylic and so on. The required thickness of the panel with a large access hole will depend on the size of the printer. For a 200x200 printer a minimum of 5mm material should be considered and a minimum of 40mm border, with more than that at corners. A good example is the Ultimaker 2 (see below).
  • Adding diagonal struts from corner to corner in all four faces, ensuring that the struts do actually go into the corners instead of some distance along one of the other frame pieces. Attaching the diagonals to both the horizontal and upright parts of the frame is best.
  • Replacing the upright struts with much thicker extrusion (30x30, 40x40) and then ensuring that they are braced properly in the corners. This means using beefy triangular braces (40x40mm or greater) or drilling sideways through the extrusion and using an allen keyed hex bolt to attach it to the centre hole of the piece that it is to be attached to. For this particular trick to work the ends of the extrusions must be absolutely dead flat.
  • Bolting on beefy aluminium (or other metal) triangular plates on the outsides at the corners, attached in multiple places. Attachments in at least two places per strut (preferably three) is a must, and using a minimum of M4 bolts is also a must, to prevent slippage or threading of the bolts. The size of the plate should be at least 50mm preferably 80mm. Basically it substitutes for needing to use a panel, and thus must go in the corner of each face. Four per side. However even with this size of corner-plate 20x20 extrusion is still not really adequate, not even for a 200x200 build area (because the frame will be a minimum of a 300x300 or greater size), so 30x30 or 40x40 would still need to be considered for the uprights.
  • Any combination of the above, in any order, as long as all four upright sides are covered and may no longer "parallelogram".

It is actually quite complex, involving a significant number of bolts, regardless of whether panels, plates or triangular bracing is used, to create a properly rigid cube frame, which is why Ultimaker took a different approach and threw out the extrusion entirely (see below).