Mechanical Rigidity

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Mechanical Rigidity

This page goes into the basics, with illustrations, on how to ensure that a design is mechanically rigid, and also what to look for if buying an existing 3D printer. The key elements are:

  • Rigidity must be achieved in all six degrees of freedom: Rotation ("twisting" or "screwing") about each of X, Y and Z, and Movement in X, Y and Z (shearing or "parallelogramming").
  • The simplest rigid open structure is a triangle.
  • Solid materials (plates, bars, extrusions, rods etc.) have rigidity that is proportional to their thickness (or length). Rods (or bars) in particular have lateral flex that is proportional to the square of their length.
  • A "lever" effect on the way that two frame parts are connected together is critical to take into account. The further the distance the more critical the material strength of the parts (and their method of connection) becomes.

Thus, a quick guide to analysing an existing frame design is:

  • If it is a cube design, is there support in all six faces of some kind? Either plates (polycarbonate, acrylic, plywood or hardboard at least 2.5mm thick) filling each face, diagonal struts that go fully to corners creating complete triangles, or even suitably strong (i.e. with no flex) very high-tension wires (again creating complete triangles to all vertices)
  • If it is a Mendel style design, these are not rigid at all in their base, and rely completely on being on a flat surface, with gravity assisting to keep them down. This tends in practice to be ok, but it is not the only issue to watch out for.
  • If it is an "open design" without triangles (or plates), is the frame of sufficient thickness for the size (3020 for a 200x200 printer, to 8020 extrusion for a 300x300 or greater) and are the frame struts sufficiently strongly connected together?
  • 3D-printed plastic, if used at corners as the sole method to join frame parts together, should be definitively considered a "red flag" that warrants full investigation and a thorough analysis.
  • If you are concerned at all about rigidity affecting build quality, avoid Kossel (delta printers) entirely.

A quick guide to printbeds:

  • Mendel style printbeds are fine: just watch out for the plate under the printbed being made of sufficiently rigid material (see printbed section for details)
  • Cantilevered printbeds should have linear rails or V-rollers, and if rods are in use they should be at least 10mm preferably 12mm. Most cantilevered designs are severely problematic, and they all rely on the mechanical properties (amount of bend) of the materials used.
  • With dual z-screws (centrally-cantilevered printbed), look for four linear bearings/blocks (two per rod/rail) or twin V-rollers per rail, to ensure that the bed cannot wobble about (rotate). Ensure that there is a rigid cross-bar (plate or other assembly) to which all four bearings / blocks / V-rollers are mounted.
  • Kossel (delta) printer beds are fixed (and so are fine): it's the print-head rods that require micro-millimetre accuracy and are a huge headache to calibrate.
  • The best (vertically-moving) printbed arrangement is by far and above triple (or greater) lead screws and dual (or greater) rails/rods (even if the rods - if rods are used - are only 8mm and only have one bearing/block/roller per rod/rail).

Frame Examples

Mendel (Early Prusa) inadequate design characteristics

The very early Mendels (some of which are still copied and sold, particularly in China) are classic examples of significantly non-rigid design. Here is a photo:

Example early Mendel (Prusa) design

  • Firstly: the base. The base is a rectangle, having no diagonal bracing. This makes it possible for the entire base to be deformed into a parallelogram shape.
  • Second: the left and right sides are triangles: this is the (only) good part about this frame.
  • Third: the front and back faces (this is a toblerone-style frame) are again rectangles, with absolutely no diagonal bracing. The entire uprights can therefore wobble side-to-side, which will happen as the X-carriage moves.
  • Fourth: the base relies on gravity to keep it down. Lifting one corner will result in the entire frame twisting. This design is particularly bad as one corner may be lifted a whopping 10mm (1cm) off the ground!

Although it is historically a classic and iconic design, the original Mendel has a huge number of design flaws. It was an interesting learning experience for everyone.

Mendel90 (by nophead) - significant improvements

Chris Palmer (aka nophead) is an experienced engineer who inspired significant design improvements to the original Mendel design that are still copied and in use today: MendelMax is a Western variant and Chinese (acrylic-based) clones such as by Anycubic and others are commonplace.

Mendel90 - greatly improved rigidity

  • The base on the Mendel90 is a single flat piece. This provides sturdy mounting points as well as preventing "parallelogramming".
  • The Y-rods attached to the base on the top, along with two aluminum box section tubes on the bottom of the base, help stiffen the base and reduce bending.
  • The uprights are made from three pieces: an upside-down U-shape braced with rectangles behind it. There is thus no possibility of sideways "parallelogramming", nor can the uprights move backwards or forwards.
  • However as with all the Mendel designs, due to them being like a "toblerone", one of the base's corners can be lifted up whilst the others remain still on the ground.

The only way to "fix" the reliance on gravity would be to change the design to a cube, as any efforts to provide triangular bracing of the "toblerone" and still maintain that "toblerone" shape would need to go through the actual build area, which would be unacceptable to most operators.

One possibility would be to add a plate (or Ultimaker2-style frame) right across the full height and width of the back, then another board across the top, creating an enclosed space. This would create a rigid cube area out of the back half of the Mendel90, with the front half protruding out. As the front half of the base is supported by the Y-rods (and the aluminium box-section) the whole assembly would be totally rigid in all six degrees of freedom.

In practice, without this design enhancement, despite the Mendel90 needing to be operated on a flat, rigid surface this 3D printer design is actually really good: all of the issues except the reliance on gravity when compared to the original Mendel are solved. Its designer regularly operated it at up to 150mm/s and speeds of 200mm/s have been reported without significant degradation of print quality when using a 0.4mm nozzle.

Cube design needing improvement

Here is a design where some advice was asked here http://forums.reprap.org/read.php?177,722199:

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).

Ultimaker 2: no improvement needed

The Ultimaker 2 is an excellent example of a completely rigid cube design:

Excellent Cube Design: Ultimaker 2

This design is superb. Every single one of the six faces is filled with panels that provide the full required set of rigidity for all six degrees of freedom.

  • The top is a panel that looks to be a 40mm "picture frame" that is at least 4mm thick. If the hole gave a border less than 40mm then the panel could potentially start to flex and bow, thus defeating the purpose of it being present.
  • The sides except the front (and probably the bottom as well) are entirely solid, providing excellent rigidity
  • The front is again a panel that has an access hole, but the border is sufficiently large so as to not result in flexing.
  • There are lots of attachment points between the panels, particularly in the corners, but also in the middle (to stop the panels bowing outwards).

Interestingly there are no internal struts: no extruded aluminium. The cube is entirely made from its panels. With this technique, as long as the assemblies within the cube are securely attached to all three panel faces then the assemblies are also constrained in all six degrees of freedom. If the assemblies themselves are also rigid then the assemblies, if placed in each corner, would double up as corner bracing for the panels.

Overall, this frame is a superb piece of engineering design.

Kossel Delta Printers

The Kossel is an innovative design that is unfortunately completely lacking in rigidity:

Kossel design: completely lacking in rigidity

Essentially its frame is a toblerone, however as can be seen each rectangular face has absolutely no bracing whatsoever. Twisting is therefore extremely easy to do about the Z-axis, and there will also be significant shearing in both X and Y. An original Kossel Delta printer should, for this reason alone, be avoided.

Properly fixing a Kossel's toblerone frame, by adding diagonal bracing from corner-to-corner across all three of the rectangular faces, would unfortunately impinge significantly onto the build area.

The typical use of plastic parts for the corners in Kossel designs is also a major factor in the lack of rigidity. However efforts to replace these with metal, or to brace the twin base with external panels, really does not help because the uprights are so long in a Delta printer that the flexibility of the uprights themselves becomes significant.

Add to that the fact that Delta printers require extreme micro-millimetre-accurate lengths of rods and require extremely complex calibration and they're just not worth the hassle.

Proposed (Hexagon) Kossel Delta Frame

A much better design would be to start from a hexagonal base (and top), with at least three consecutive sides completely filled in with panels, from top to bottom, with smaller panels on the remaining sides of height at least 50mm on the top and bottom hexagons, in order to ensure that the hexagons themselves are rigidly supported. The three full panels, by being at an angle of 60 degrees to each other, would provide self-supporting rigidity of the four uprights that they were attached to, but would transfer any "twisting" to an unsupported base (and top) hexagon. The smaller panels top and bottom would prevent such twisting effects.

The advantage of a hexagonal base would be rigidity without significantly reducing the build area. Panels with cutouts (similar to the Ultimaker 2 front) could also be considered, although the long height of a Delta design could result in twisting of any open (holed) panel that would need to be supported on the outside (with a 300 degree brace) so as not to interfere with the operation of the printer.

Bracing on Folgertech Kossel designs

An attempt to improve the Kossel has been made, to brace the uprights:

Bracing on the Folgertech 2020 uprights

This design has significant triangular bracing on all three uprights, which successfully alleviates the "parallelogramming" inherent in a toblerone-style frame. In this particular modification the bracing (which is at the top) is done in such a way so as to not interfere with the operation of the printhead.

However, what this bracing does is simply rely on the structural strength (rigidity) of the 20x20 extrusion, which as it is particularly long on Delta 3D printers, becomes a bit of a problem. If however the 2020 uprights were replaced with 30x30 or even 40x40 then this would no longer be a problem. Note that the horizontal parts would also need to be replaced, because the load from each triangle is transferred to the middle of each horizontal part, without that point then being braced vertically. One way to fix that would be to have a second set of horizontal parts at the top, filling the three gaps with panels... or to just use 8020 extrusion instead.

Voxel Ox: 8020 frame parts

In this thread the use of 8020 frame parts is demonstrated: http://forums.reprap.org/read.php?177,702346,702528#msg-702528

Effectiveness of 8020 extrusion

This design has a number of improvements over the basic Mendel:

  • The base is made from four 8020 extrusions that are joined together with double 20x20 triangles per corner.
  • The base also appears to be braced across the middle, preventing parallelogramming.
  • The uprights, by also being 8020 and being attached on both sides, will also not rotate about the X-Axis.
  • The top support for the Z motor will therefore not rotate about the Z-axis
  • The build plate is again mounted on 8020 extrusion, which should not be going anywhere: it appears to be fixed with double 20x20 triangles in at least three points, with one being a (green) 3D-printed part.

However despite the beefy use of 8020 extrusion there are still a couple of flaws:

  • The base can still be lifted at one corner whilst the other three remain on the ground. However in reality the amount by which this frame would actually twist should be absolutely minimal, but just to be safe it would be best operated on a rigid absolutely dead-flat surface.
  • The uprights may still "parallelogram" (shear sideways). However looking closely at the X-Carriage it appears to have rollers on a plate that is upright (and firmly attached to the two X-carriage extrusions) that might assist in reducing sideways shear, but potentially at the cost of damaging the rollers. In reality though this printer would have to be operated at extreme speeds (and the objects being printed very tall) for there to be any problems.

Fixing this latter problem would involve extending the uprights a good 75mm above the top horizontal assembly, then attaching two beefy aluminium triangular plates at each corner (minimum 75mm size). The reason for extending the uprights is because if triangular bracing was added underneath it would interfere with the maximum build height, as the sides of this particular design are used for running rollers. Alternatively the top extrusion could be extended outwards, and multiple 40x40 triangles on each upright utilised to achieve the same effect.

Overall however this is a really good design.

Printbed Examples

Mendel style printbeds

Mendel style printbeds have one significant advantage: they are flat, only move in one direction, and need only three bearings and two rods (see photos above of Mendel90). One thing to watch out for however, particularly on cheap-cost China clones, is the use of an inadequate thickness metal plate to which the bearings (and the Y-belt) are attached. Anything less than a 3mm aluminium plate, 6mm acrylic or 4mm dibond is going to be completely inadequately stiff, resulting in flexing of the plate (to which the printbed is attached), thus in turn adversely affecting build quality.

Print Bed Mounting: 3 or 4 points

Although it is considered unnecessary to have 4 mount points for bed levelling, one of the problems with printbeds is that sometimes they will be warped. Depending on the degree of warping, 4-point levelling allows the warping to be corrected, whereas if a triple-mounted printbed is warped it will need to be repaired or entirely replaced. Sourcing a triple-mounted printbed plate that is sufficiently thick and properly machined (and adequately packaged when shipping) is therefore critical.

Triple lead screws, dual rails

This type of design is discussed on the reprap forum here: http://forums.reprap.org/read.php?397,726304,766930 and the design files may be obtained here: https://www.youmagine.com/designs/2040-laser-cut-core-xy-v0-8

Note that this particular design's frame suffers from lack of rigidity (no side support, insufficient upright bracing - see above) however the bed support is excellent. Here is a photo highlighting the use of dual rails:

Highlighting dual rails on a triple leadscrew design

A six degrees of freedom analysis of this design is as follows:

  • Triple lead screws stop X and Y rotation of the printbed and control (allow) Z linear movement but do not prevent X or Y linear movement (sideways sliding) and do not prevent Z rotation of the printbed (not least, the Z-screws can bend).
  • Dual rails will stop X and Y linear movement, will permit the required Z linear movement, will stop Z rotation, and will stop EITHER X OR Y rotation (but not both). Specifically: without the lead screws, one rail could go up and the other could go down, causing the bed to rotate about the axis that's perpendicular to the two rails.

The COMBINATION of those two sets of constraints happens by a happy coincidence to provide the full set of required control over all six degrees of freedom.

Note that a single rail will not do the job, because the Z-screws can bend about the middle and the printbed could rotate around the centre of a single rail. Triple (or greater) rails would be redundant. Quadruple z-screws or greater would also be redundant.

For a moving bed like this, one or two lead screws are not sufficient: with only one or two lead screws the burden then falls onto the z-rails to prevent rotation in X Y and Z, and that places significant strain on the block.

One of the big, big advantages of the "triple lead, dual rails/rods" design is that there is no critical dependence on the mechanical rigidity (along the length) of the leads screws or rails or rods utilised. Cantilevered bed designs on the other hand tend to require 10mm or even 12mm rods in order to ensure that the weight of the bed (and object as it is printed) does not cause significant bending.

Laser-cut acrylic / wood, single lead screw, dual rods cantilevered design

There is an innovative upgrade to the Cupcake CNC which is based around laser-cutting of thick acrylic / wood:

Single lead-screw, dual 10/12mm rods

  • The use of sturdy (6-8mm thick) laser-cut panels means that no bending / flexing will occur
  • The rods look like they are either 10 or 12mm and there are two large bearings one under the other on one side
  • The printbed is supported underneath on three sides so will not flex.

All in all this is a surprisingly good design, despite the left-hand rod only having one bearing where the other side has two. Improvements to this design would involve creating a full "box" structure entirely surrounding the bearings, expanding the depth of the box so that there is at least 70mm separation betweeen the bearings, and using four bearings (two per rod) instead of just three. This would ensure that both rods are used to prevent rotation about the Y-axis of the entire assembly, whereas in its current incarnation the right-most rod with two bearings is exclusively responsible for preventing rotation.

Fusebox: inadequate 8mm rods, single lead screw, cantilevered bed with insufficient support

The Fusebox is a low-cost design that highlights a huge number of flaws with the average classic cantilevered printbed.

Highlighting the flaws of a cantilevered design

The flaws in this design are numerous:

  • Firstly, the rods are only 8mm. With almost 250mm to the end of the printbed, a "lever" effect can create significant amounts of bend to adversely affect the quality of the print as weight accumulates on the printbed.
  • Secondly, there is only a single lead screw with a distance between the rods of 140mm, spanned by a single piece of plastic only 20mm in height (and 130mm in length). This creates the possibility of a rotational moment about the Y-axis, where one linear bearing can go up whilst the other can go down. If a print is ever made off-centre on this design it will gradually push the printbed further down on that side and will no longer be straight!
  • Thirdly, the 130x20mm horizontal piece between the rods and spanning that 140mm gap is simply not strong enough: it will bend under load.
  • Fourthly: LM8LUU bearings, even at 45mm in length, are of insufficiently high quality machine tolerances to prevent rotation about the X-axis (drooping of the front of the printbed)
  • Fiftly: the LM8LUU bearing holders are not sufficiently long - or strong - to be able to hold up the weight of the printbed itself.

This example therefore highlights a huge number of classic design mistakes with cantilevered printbeds that are sadly extremely common. To fix these issues, the following needs to be considered:

  • Replacing the 8mm rods with at least 10mm (preferably 12mm) rods, or, better, going to linear rails attached firmly and properly to the aluminium frame, at least 20x20 in size. This ensures that there is no "bend" (flex).
  • Use of an L-shaped piece of aluminium between the rods, and, if sticking to rods, using four blocks of high precision of the type which have four mounting points. The height of the L-shape should be at least 75mm so as to prevent rotation.
  • Rigid (metal) triangular bracing struts on both sides, from the bottom of the L-shaped aluminium to the centre of the printbed.
  • The L-shape of the aluminium plate has two effects: first it stops bending of the plate (without needing huge amounts of material) and second a hole may be drilled in the horizontal part so that the lead screw can be attached through it.