How to calculate V-Slot® deflection V2

Thanks very much for this - very useful.

One quick typo spot: Iy for 20x20 should be 6.988 x 10^-9

 

Hi, the moments of inertia listed on SketchUp V-Slot Model | OpenBuilds seem to be quite different than those used in the pdf. Or am I not getting something?

 

Ok, thanks

 

could this theory be expanded to include the impact of the dynamic forces, ie the bounce caused by the z access going up and/or down.

also could it also be expanded to torsion forces, ie how much the y gantry may flex as the cutter cuts through the material

I offer the above only on the basis that this has wetted my appetite for more design calcs as they will assist in the honing of my design.

 

Great post! Might want to look at the pinning methods typically used and associated formulas provided here. End type is critical, pinned, single reaction, or free.

John Harvey - you absolutely can! The math becomes considerably more complicated in dynamic situations. If you are familiar with ordinary differential equations it's not too bad.

 

Hi,

Thanks a lot for this resource. This is the kind that really helps new comers like me

A few questions for experienced makers and engineers around:
* As far as I understand, drawings represent "fixed" beams better than simply supported ones ?
* Aren't values labels inverted in the table for "standard" profiles, and shouldn't the axis be inverted or the cross-section rotated 90° for the C-Beam (also in the table) ?
* How should the calculated values be used in cases where several profiles are combined to form a single beam ? Is it just a matter of adding the moments of inertia of the individual profiles ? Surely, it must be much more complex ! But is it a tolerable approximation ?

It's been a few days that I'm thinking of assembling profiles in "II", "H", or "U" to build a super rigid 1500mm Y gantry for a 2,2KW/5Kg spindle so any further info will be very welcome !

Bests

PS: I've built a simple spreadsheet based on the data in the PDF that I'm attaching here for everyone to use, abuse and comment

EDIT: Update 1: Add Fixed ends calculations

 

Re-uploaded (from mobile) hope the file is OK now. Btw, it'd be nice to allow upload of ODF formats w/o compression

 

You very welcome Mark ! This is still a tiny contribution, hope a valuable design will follow sooner or later...

I'd love to add hability to calculate deflection when several profiles are combined, but have to figure how to properly do it...

 

@Mark Carew, this is unfair teasing ! ;-)

 

Well, men, seems like I'll have to make my own assumption on this point so I've added fixed end uniform and centered load calculations to the spreadsheet (updated).

Still have to figure what could be a simple and informative/useful way to add "load at any location"... Is there any more significant distance(s) than the usual suspects (center, end, half way) ?

Also, can I add, respectively, X and Y components of area moment of inertia to calculate deflection of an assembled dual, triple, "L", "I", "H", "C" or "U" beam ?

EDIT: This would mean that two beams made of, say, 2 vertical 20x60 profiles and one 20x20, the first assembled in "|-|" configuration, and the other in "|_|, would have the same stiffness and experience the same deflection under load ?!

Hope someone will light my candle...

Bests

PS: @Mark Carew, the actual files extensions for ODF documents are '.odt' for texts and '.ods' for sheets. I should have been more explicit, sorry for that :/

 

Good catch! I'll fix that.

 

These formulas are for simple static cases. Things get considerably more complicated when you introduce dynamic loads. Not something I would want to attempt

 

I double checked the moment of inertia in Solidworks and they seem to be right. I did it by highlighting the end face and clicking on section properties. I converted the values in the table to metres^4 so you don't need to worry about unit conversions in the calculations.

 

Regarding the discussion of fixed versus simple supports, I would imagine a bolted joint is somewhere in between, since it is not completely rigid, nor is it free to pivot. But I think the main point here is that these calculations are over simplified anyway. They are useful for making relative comparisons between two different beams, but they are not going to give incredibly accurate predictions of actual deflection values on your build. But that's okay, they can still help to inform your design choices.

 

Arguing engineers are hilarious yet incredibly educational. Long may it continue!

FWIW, I'd like to see an FEA breakdown of the deflections on various structure types arranged into a C shape (ie. a gantry platform and its support pillars with variable corner connections)- from aluminum extrusions through solid 50mm square 1045 bar to triangular-cross-braced quad tubes (like a construction crane) and various half-way permutations (aluminum sandwiched inside high tensile steel? Solid steel bar with cross-drilled circular holes?). It wouldn't necessarily translate to everyone's exact intended use, but it might be a good starting point for comparisons.

Plus, obviously the "best" materials and geometries as they apply to mass and torsional and flexural rigidities may have to be tempered by the needs of vibration damping or other practical concerns. I wonder when we'll start filling 4040 V-Slot with concrete? But yeah, while V-Slot's modularity embraces the precepts of rapid machine design- at least as it applies to hobby-level tooling- it would be equally interesting to see how it stacks up against other, perhaps slower, possibilities.

(PS. I never left, I've been lurking whilst working on actually creating real things other than tooling! Got a LinuxCNC V-Slot machine build planned to start this coming spring, but I just bought a bench lathe, so that's gonna be fun in the meantime!)