# 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 is achieved if and only if all parts are either under tension or compression. THIS IS ABSOLUTELY CRITICAL.
• 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. If absolutely every single open hole is not a triangle, then there's probably a problem.
• 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.

# Frames

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 (3030 or preferably 4040 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.

## Frame Examples

For further illustration, examples have been split into their own sub-page, with a quick summary on each:

## Frame Video demonstrations

Using easy-access low-cost materials (paper, straws, tape) this is a series of videos showing the principles of mechanical rigidity for frames. Each only took minutes to prepare, did not require hours of 3D CAD design, did not require expensive proprietary CAD software with "mechanical analysis" capabilities, did not require days to weeks of prototyping parts that might turn out to be incorrectly designed. The use of such low-cost materials has significant advantages in that the flaws inherent in the materials is significantly amplified, visually, clearly and quickly.

• Mechanical_Rigidity/Video_demo_cube_design - showing how an otherwise wobbly cube with inadequate corner-bracing and way too bendy struts can be turned into a rigid frame with panels and diagonal bracing. It also graphically illustrates quite how extraordinarily comprehensive the number of attachment points needed to create a properly rigid cube frame.
• Mechanical_Rigidity/Video_demo_toblerone_design - showing how a toblerone frame (Mendel, Kossel) is basically completely inadequate as far as rigidity is concerned. Illustrates how the Fisher is a huge improvement thanks to its panels.
• Mechanical_Rigidity/Video_demo_Fisher_improvement - showing a potential dramatic improvement in the Fisher design could be made with an additional outer triangular brace half way down.

# Printbeds

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 with separation of at least 75mm vertical separation between centres, 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).

## Printbed Examples

Examples are illustrated here, with general relevant guidelines below:

## 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. For a 200x200mm Printbed, 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.

# Rods and Bearings

Selection of good bearings and rods is absolutely critical, as is ensuring that the length of the rods used are adequate to support the intended load. One experienced engineer (nophead) gives some extremely valuable advice http://forums.reprap.org/read.php?292,767715,769876#msg-769876 - the machine tolerance specification that should be selected on the rods is "H6". nophead also describes http://forums.reprap.org/read.php?292,767715,768709#msg-768709 how the bearings are deliberately designed to be slightly oversized, so that they will compress during travel. This causes a slight resistance to movement but this is deliberate. The following video shows how bad bearings (LM8LUU in this case) can have so much "play" that it causes audible rattling sounds, as well as showing how the replacement of a single LM8LUU with a pair of LM8UU bearings can eliminate "play": https://youtu.be/a60TAQTHtJ0

Hardened rods are still made of metal that will bend under load. As a general rule (see printbed section) the use of 8mm rods for cantilevered printbeds is an absolute no: 10mm or preferably 12mm rods are better. A span of 300mm with two 8mm rods to support a carriage and a direct-drive extruder is acceptable for a 200x200mm printbed, but it is completely unacceptable to use two 400mm x 8mm rods to span a 300x300mm printbed: the weight of the carriage is simply too much and the rods over that length will noticeably bend, resulting in uneven printing.

Also, as outlined in more detail in the carriage mounting section, any kind of bend in the rods or any amount of "play" is amplified by the ratio of distance that the "key part" (such as the hotend on the extruder) is away from the centre line between pivot points. So, if two bearings are 100mm apart and the hotend is 50mm away from the centre of the two rods, the rotational "multiplier" effect of any "play" will be 50 / 100 (or 0.5). If however the distance between bearings is 40mm and the distance that the hotend is from the centre line is, for example, 80mm (as could genuinely be the case for a vertical carriage arrangement) then the multiplier effect is 80 / 40 = 2.0, meaning that a 0.5mm combined amount of "play" from the combination of (a) bend in the rods (b) flex in any plastic parts and (c) loose bearing travel could result in a whopping 1mm of unintended movement.

The basic conclusion is that it is not just about selecting parts that are machined to accurate tolerances (as often does not occur with many rods sourced from China), but it is also about knowing the stiffness of the materials themselves, whether it be plastic or whether it be metal.

# Vertical vs Horizontal Carriage Mounting

In the Vertical_X_Axis_Standard page the advantages of vertical carriage mounting were discussed. Of particular note was the fact that collaboration to develop a standard at all took place, which is of clear benefit to anyone developing a 3D printer, but, it has to be pointed out, does not have anything to do with the mechanical advantages or disadvantages per se.

One of the specific disadvantages listed in a Horizontal Carriage Mounting arrangement is that there is typically quite a lot of plastic needed to be printed. Another is that the distance between rods is believed to have to be needed to be quite significant. Design examples below show neither of these to be an absolute necessity.

One of the specific advantages listed of a Vertical Carriage Mounting arrangement is that it is easier to access (and change) printheads. The Mendel90 and other designs however demonstrate that this is not absolutely the case (the Mendel90's carriage having a D-Sub connector and using butterfly nuts to make changes faster).

The main disadvantage of a Vertical Carriage Mounting arrangement is clearer when rods and LM8UU bearings are used. The typical amount of "play" in lower-quality (or worn) LM8UU bearings can be as high as 0.25mm. That means that the amount by which a carriage can be rotated is as high as 0.5mm: +0.25mm on one rod and -0.25mm on the other. The factors that are then important to take into account are:

• The distance between the two vertical rods
• The distance that the print nozzle is from the centre line between the two vertical rods.

Dividing these two numbers gives the "multiplier effect" that the 0.5mm "play" of the LM8UU bearings will truly have. In many carriage designs this can be over 2.0 leading to a whopping 1mm of "wobble" in the actual position of the nozzle. This is easily demonstrated by grabbing the printhead and lifting it up and down. Even the most gentle pressure can often result, shockingly, in over 2mm of movement.

The "Horizontal" Carriage arrangement has, by complete contrast, a multiplier that is often significantly less than 1.0 because the actual print nozzle is positioned directly between the rods. In addition to that, the effects of gravity ensure that the "play" of the LM8UU bearings is minimised, resulting in, apart from anything, less wear-and-tear on the bearings and the rods.

But that's not all: there can also be flex in the materials used, which can adversely affect both a Horizontal and a Vertical carriage design:

• Rods are not completely rigid: an 8mm rod can actually flex under load.
• Any plastic (if used) either in the X-ends or the carriage can also flex if not sufficiently strong or properly designed.

As a general rule, if rigidity and accuracy is desired, a Vertical Carriage arrangement when using rods and particularly when using plastic 3D-printed parts, is something that really should be avoided. However if using Linear rails or V-rollers this is a completely different proposition, as the amount of "play" with these higher-cost components and assemblies is far, far less than with the average LM8UU bearings.