Semi-Cylinder Gantry for Fiberglass CNC Build

Hello,

I am in the process of designing a CNC router with a 4’x4’ cutting area. It will be built mostly with fiberglass cloth, epoxy, and foam.

The design question I have is in regards to the gantry. The geometry that I have chosen for the gantry is a hollow semi-cylinder (which will be fabricated with biaxial fiberglass at +\- 45 degree angles over a foam core).

This is my reasoning:

1. The weakest link in a router is often the gantry.

2. The weakest link in the gantry is often torsional strain.

3. A circle has a much better polar moment of inertia than a rectangle. However, using a whole cylinder makes it difficult to mount the linear rails to, and offsets the spindle from the gantry’s axis of rotation, giving the spindle extra leverage.

4. A square tube has a worse polar moment of inertia given the same perimeter as a semi-circular tube and stresses the skin unequally, putting a higher proportion of stress on the corners of the tube.

5. A semi cylinder gives me a flat surface on the front to mount the rails/ball screws to, and gives me better resistance to torque than using a rectangle tube.


For now I am only soliciting advice for this one problem, I.e., the merits of a semi-cylinder versus a rectangular tube. Discussing other aspects of the build would require many cans of worms to be opened. I will post a full build thread once I am ready to commence the build in order to get feedback on the overall design.

Am I missing something?


Thanks!

Update: I've decided to go with steel instead of fiberglass, but I'm still really intrigued by using a semi cylinder profile as apposed to hollow rectangle. Is there a drawback here besides difficulty of fabrication? Thanks.

Hi Paul - There are some commercial machines that use semicircular gantries. The most troublesome issue to achieve good machine stiffness is a good Z axis. These are usually underdone by DIY builders. In terms of gantry torsional stiffness its more the issue that the loading point is far away from the shear centre of the gantry vs its shape. If you use a square gantry for instance and have one rail at the bottom front and one rail at the top back this puts the action line of the bearing reactions closer to the shear centre of the beam and it behaves stiffer as it is more efficient. If you place a force at the shear centre of a beam it does not twist it only bends... This will be the same issue with a semicircular beam, getting the forces to pass thru the shear centre which they can't do with any flat front gantry with bearings on it.... Many gantries are also triangular and I think this is the way to go. Look up the Milli thread it covers a lot of territory with the gantry...Peter

Hi Paul - You have to consider maximising every parts geometry (dimensions) to maximise its stiffness. The semicircular shape has 40% less torsional inertia then the RHS in its envelope. Then there is the issue of getting the applied torsion to act at the shear centre. This can be done by using a "flat" rectangle rather then a tall RHS see attached. The shear centre issue is a secondary issue but worth dealing with if you can. A gantry is under shear, bending and torsion. Each of these have primary deflection and secondary deflection effects that can be minimised if you understand the engineering mechanics... Peter

Hi Peter,

I totally did not see these posts until now. Thanks for taking the time to respond. I guess I wasn't subscribed to notifications, but I am now.

Ideally the gantry would be a circle or circle-like-geometry, and the rails would be on opposite sides. But chasing that ideal has a few real-world drawbacks that I can see:

1) I would have more planes to square and more room for error in fabrication and alignment
2) The Z-assembly would have to be bigger and would be more prone to deflect itself

I'm really looking forward to your response. Thanks.

Hi Paul - Circular is not ideal for a gantry, a square section is stiffer in the same space. Model it and you will find out. If you make decisions based on convenience then performance suffers. You have to do the best you can with what you have. All elements of machine design are compromises and every compromise has a consequence.

The Z axis has to be different but not necessarily less stiff. The forum is full of opinions and thought experiments. Since you have FE you need to use it and develop solid evidence for results vs thought experiments eg 2) :) Regards Peter

Hi Peter,

In the Bamberg thesis, he states that give the same weight and wall thickness, a square tube is -18% less rigid in bending and -38% less rigid in torsion than a round tube. However, it would be difficult to mount rails to a round tube. If faced with the limitation that the rails must be mounted on the front face, a semi-circle gives the highest torsional inertia for a given mass. If you were able to mount rails on opposite sides of the gantry, it would be better to go with a circular polygon or even a square. I wouldn't exactly say my design is about convenience, but it does take into account the feasibility of precisely executing the fabrication and assembly.

Best Regards,
Paul

Hi Paul - The numbers work for the same weight tube but this is an erroneous consideration in machine design. You are interested in the envelope of the member. eg compare a 100mm dia circular tube to a 100mm square tube and the SQ tube is stiffer, machine design is about using maximum geometric space (maximise second moment of inertia) not about making equal weight members... again do the math vs thinking the logic. Peter