How to calculate V-Slot® deflection V2

I took this down from the site as there is a thin line between a good assumption and a poor one. The original formulas and values I posted were experimentally verified on an OX build (yes there is a moment on the plate and does contribute) on the 20x60 and 20x20. Deflection measured center beam no integration done to check other areas, simplest case possible. Various (non calibrated) weights were used to confirm results. The original discussion came from guys mounting 2.2kW spindles on a 1000mm length double 20x60 (OX "X" gantry). I did not run FEA. The discussion seen above would come to me in an email about once a week.

Glad you guys took this one over Mark!

 

I want to use the C Beam vertically. Is there a resource to calculate deflection fo fit in the vertical orientation? I am building a 96" long router table 48" wide - Can put as many "legs" on it as needed to prevent deflection but prefer as few as possible. The router motor is a 14 lb Porter Cable router

 

I'm late to this discussion but my guess is that the play in the bearings and the compression of the plastic rim of the wheels contribute more to the deflection than purely the deflection of a C-beam at lengths of under 1 meter. Twisting of the beam shouldn't be neglected either since the lever of a fully extended Z-axis can be pretty large depending on the specifics of the machine design.

 

In the 'simply supported beam with uniform distributed load' case the value shown in teh pdf as '348' should be 384.

I appreciate that claiming an error exists in something unchallenged for a decade might want some evidence, a google 'deflection UDL simple supports' will find loads, e.g. Simply Supported Beam - With UDL

 

Better to use a point loading moment calclulation than a uniform-loading one, which is more suited to building construction than CNC gantries. I don't know how this affects whatever calculation is in question, just a point of clarification.

 

Hey there fellow lurker

Interesting that this thread should pop up right when I was getting ready to ask the experts what they would think of a sandwiched composite that had two 500mm pieces of 2060 for the outer layers back-filled with an epoxy granite mix for the purpose of adding stiffness and improving dampening?

 

Hey! Long time no see.

When you say sandwiched and backfilled, do you mean connected together back-to-back and then internally filled, or do you mean parallel but separated and the gap filled with EG? Either way, I'd suspect the performance increase to be quite substantial due to shear-limitation of twist alone.

 

Two parallel pieces end mounted to 1/4" plate separated by a 20mm gap that would be filled with the epoxy granite.

 

I love everything about this idea, to be honest. It might be the "perfect gantry" (within its size class, at least). I'd throw some 15mm T-nutted bolts into each piece inside the gap along the length for better vibrational coupling- maybe some tapped through the backstrap too- but it should be quite damping and very stiff in both axes of bend, and twist. It'll be on the heavy side, of course, but not too bad given that it's only 60x20mm. And since it's a moving bed, that's irrelevant anyway. Just focus on getting a good aggregate mix, try and maximize solids.

Looks like a fun machine, you should do a build! I like moving tables, I think they're underrated as gantry machines.

 

Thanks. Right now I have 3 sizes of aggregate on hand, fine sand, 2mm, and the largest is pushing 5mm+ which I think is a little large for this app so I will swap that out for something smaller (Maybe even a 1mm) so it gets up into the slots easier and that should give me a good pack. I still have some work to complete the x axis and I am working on the drawings as we speak, but will get it posted up to the board soon.