Structure adding rotational stiffness to a plate

[petterg]

TL;DR

What is the most lightweight structure you can add to a rectangular board to improve the rotational stiffness?

I'm 3d-printing a part that is 110mm x 40mm (XY-plane). I have to keep it light weight, so I made it thin - 0.6mm (Z direction) and filled the surface with holes to remove as much weight as possible. Then I added a grid of 2,5 mm high "walls" in the XY directions to make it stiffer and a couple of diagonal "walls". That made it stiff enough in all directions except for one: rotation. What is the most lightweight structure I can print on the board to improve the rotational stiffness?

(By "rotational stiffness" I'm thinking of the twist that happens to the board when left side of the board is rotated away from you, while the right side is turned towards you (or the other way around), assumed you're holding the board with a long edge towards you.)

This problem is somewhat similar to having a horizontal rectangular picture frame resting on two diagonal corners and some weight on the two corners that are hanging in free air. How do you make the two corners with weights bed down less?
I'm not limited in height for this print, but I cannot print in free air. So if I should make an arc up between each diagonal corner, the arc itself would need support, which in total will make the build too heavy.

 

[berkeman]

Can you post a diagram/picture of your current part, and how forces are going to be applied to it? I'm having trouble visualizing it. Thanks.

 

[Lnewqban]

Yes, a picture would be very helpful.

For torsional stiffness of a plank, the best solution is a hollow box with all its sides closed (think of an interior plywood door or an airplane metal wing).
Improving that to a maximum, requires internal diagonal bracing.

Please, see these examples for metal, which are applicable to any material:
https://metalartspress.com/books/chapters/chapter-13-design-tips

Any external bracing to a thin sheet will not achieve much but increasing weight.

 

[petterg]

Attached is picture of the board without the diagonals. (I don't consider the X in the middle as structural.) The function of this part is to hold on to the top of some cylinders (that fits into the holes) to keep them in position. The diagonals I used for testing went through the holes, which made the holes loose their function.

 

[berkeman]

Attached is picture of the board without the diagonals. (I don't consider the X in the middle as structural.) The function of this part is to hold on to the top of some cylinders (that fits into the holes) to keep them in position. The diagonals I used for testing went through the holes, which made the holes loose their function.

Do you have a picture of the setup holding the cylinders, and a picture of the damage to the piece afterwards? Are you doing some shock/vibration testing that is resulting in these failures, or is it just in normal use? How large/heavy are these cylinders?

 

[Baluncore]

I'm not limited in height for this print, but I cannot print in free air.

Where an object must hang from a support, and be free to align, it is hung from a ribbon, not from a round wire or tube. You have designed a structure with minimum torque rigidity.

You need to integrate a “torque tube” into the structure. That could be done by placing a drinking straw structure along one or both long edges. The tube might be prefabricated, or printed with the object. Two parallel printed walls rise and approach, then are bridged to form the closed section tube. The cross section shape of the tube formed is not important, but use the greatest radius available. If it was a larger object, a tubular lattice could be fabricated.

 

[hutchphd]

How stiff is enough?

1. Can you make the ribs and circles deeper?
2. Put the ribs at the ends of the box
3. Tie all the circles and ribs together wherever they can touch

 

[petterg]

The hole project, including other parts and 4 pieces of this part, is limited to 64g. I'm currently at 63g (including the diagonals not shown in the picture) after stripping all parts as much as I can. I hope to be able to find a couple of grams more somewhere that can be removed. So if the extra structure on this board adds 1g, I'll need to remove 3g from somewhere.
(I've done a pretty good job removing weight though. Before I realized weight was an issue the model was 383g!)

The idea of using a drinking straw is good. If I get the straws properly attached to the board
I can probably remove the "walls" I currently have. I guess the walls weights more than the straws. But how do I fix the straw to the board without adding much weight? Could a U-shape and some superglue be enough the hold the straws?
And I guess the straws has to be held to the board at least in 4 places each in the longest direction in order to provide the stiffness. From the link in post #3 I guess the best way would be to make an surounding box of straws (without a top surface) and two half-length diagonals.

An other option I've had in mind is to build some "towers" about 20mm apart and lift the walls up to the top of those towers. (Printer is able to make small bridges) This approach would require the walls to be thicker though. (If they're not connected to the board in full length they'll be vulnerable to horizontal forces. Not that there is supposed to be any, but suddenly it's hit by something.)

 

[Tom.G]

The deformation you describe causes the distance between diagonal corners to change. A way is needed to more assuredly fix those distances. Of course the obvious approach is diagonal struts, which interferes with the parts function.

I believe @hutchphd had the right idea:

Tie all the circles and ribs together wherever they can touch
Can you make the ribs and circles deeper?

To evaluate the critical weak spots, twist the structure and take some photos so you/we can evaluate where the maximum twist occurs.Another way to evaluate strain concentration is to use a transparent or translucent plastic to make test versions of your holder. Illuminate it with, or shine polarized light thru it and view it thru another polarizer acting as the analyzer.

You will see color bands that show where the strain concentrations are. The closer the bands, the higher the strain at that area. You can take photos thru the second polarizer for documentation or easier comparison later.

An easy source of polarizers is Polarized sunglasses. Cut/break them apart and use one lens for the source polarizer and the other for viewing. You will have to rotate one or both of them to get the best effect.

Note: Not all Polarized sunglasses really are. There are some knockoffs on the market. Test by shining a light thru, or looking at a light thru, two of them and rotate one of them. Transmission should vary between
maximum and minimum thru 90° of rotation.

Cheers,
Tom

 

[Baluncore]

Of course the obvious approach is diagonal struts, which interferes with the parts function.

Unfortunately, diagonal struts will not increase the torsional rigidity.
Where the distortion is a twist along the length of the plate, more flat surfaces will not significantly increase the torsional rigidity. It requires a tube running the length of the plate. A solid rod or bar would be heavier than a tube of the same size. The ends of the tubes can remain open.

 

[Tom.G]

Unfortunately, diagonal struts will not increase the torsional rigidity.

Perhaps it is an illusion then with the paper mockup I just built. It sure SEEMS to increase the torsional rigidity if the side rails are present. There is not much, if any, improvement without the side rails.

It seems some rigorous testing with the actual item is called for.

 

[petterg]

Thinking of how to make holders for the drinking straws... Does the drinking straws need to be held so that it cannot rotate in the holders? For the one type of straws I tested, superglue just pealed off when dried.

 

[Baluncore]

Does the drinking straws need to be held so that it cannot rotate in the holders?

The ends of the straw must be bonded to the ends of the plate, so rotation of the straw is not possible.

 

[petterg]

I got it! Fairly stiff and clocked in on 63,83g. The solution I came up with is creating Y-shaped walls on top of the flat bottom face. The vertical part of the Y is 3mm high, the V-part is 0.9mm high and there is a 30 degree angle in the V-split. (15 degree off vertical to each side). The material thickness in the Y and the face they lay on is 0.6mm and I've left face material at least 1mm to each side of the walls.

These walls are laid out in a pattern of 0, 30, 60 and 90 degrees from each corner of the board. At least that's the theory I was aiming for. Because of the holes I could not make the walls meet exactly in the corners, and they didn't get exactly those angles, but they are close. And the board is surpricingly stiff.

To remove as much weight as possible I filled the walls with holes, 2,8mm diameter and only 0.6mm apart. As the printer might have an error of up to 0.2mm there are some spots where the space between holes is less than 0.4mm. These places the walls broke when I was pushing the cylinders into them (my fingers broke the walls while holding the board), so I'll do a modification making 0.8mm between the holes. Hopefully this does not add more than the 0.17g margin I have available.

 

[Tom.G]

A picture, a photo, a drawing! Please. Please.

 

[petterg]

Attached is a picture of the stiffest design I printed. It's hard to see that the walls widens above the holes. Based on how the printer works, it would have been even better to use half circle arcs with the (curved side up) for the holes rather than full circle. But I didn't have time to test that - the printer was just borrowed for a few days.