Rigidity of aluminium profiles and rectangular tube sections....

[Voicecoil]

So, I'd worked out roughly what sort of machine I need to build and had done some basic sums using both the excellent spreadsheet @routercnc provided and some other calculations and was just about to order in some great big lumps of profile. It seemed clear that for the gantry, torsion (twisting moment) was going to be the dominant source of cutting tool movement, kind of obvious when the tool tip is down near the bed as the length of the Z axis acts a a lever. I'd assumed that the performance of a piece of rectangular box section and a profile of roughly the same dimensions would be fairly similar as the moments of area (Ix, Iy) for normal flexing do seem to roughly match up weight for weight, so had happily gone ahead assuming I could plug values into the spreadsheet and get meaningful tool deflection figures for profiles.

THEN, I happened to come across the Item24 website, those guys are possibly the Nirvana of aluminium profiles, they have something to solve pretty well every problem ina very efficient german way. And, uniquely they state the torsion constant (J) for most of their profiles (basically how hard it is to twist it). AND the figures are very different (i.e. a LOT smaller) than the equivalent sized rectangular tube. Thinking about it now, it kind of makes sense, as playing around with anti-roll bars taught me that to get a stiff tube, you need to get as much thick, continuous metal as far away from the centre of rotation as possible. Whilst all the slots might add or certainly won't detract much from flexural stiffness, profiles only have a continuous "tube" at the bottom of the slots, a fair way in from the outer periphery, and the bits at each corner (where the stress is concentrated in a rectangular tube) do practically nothing to add torsional strength.
Anyway, here's a little comparative table of profiles and rectangular tubes: the profiles are all Item/KJN/Motedis patterns (they all are the same sort of shape and have similar Ix,Iy within a few %), stated prices are from whoever was cheapest when I looked. Prices for box are from my local stockholder, there's obviously money to be saved as well as gaining torsional stiffness

Profile	Moment of Area x	Moment of area y	Torsion constant	weight	cost per metre
Item 80 x 120 lite	201	422	165	8Kg	£55
Item 80 x 120	273	575	261	11Kg	£81
Item 80 x 160 Lite	270	919	250	11Kg	£77
Item 80 x 160	362	1232	397	13.5Kg	£101
Item 120 x 120	799	799	578	12.4Kg	£158
80x120x6.75 tube	251	482	498	6.9Kg	£48
2"x6"x1/4" tube	104	642	287	6.7Kg	£43
3"x6"x3/8" tube	352	1152	853	10.9Kg	£58
70x80x4.4 tube	191	860	493	5.9Kg	£39
80x200x6mm tube	360	1570	922	8.8Kg	£56
100x200x5mm tube	515	1522	1183	7.8Kg	£56

You can probably guess what I'm going to be using for my gantry

[driftspin]

So, I'd worked out roughly what sort of machine I need to build and had done some basic sums using both the excellent spreadsheet @routercnc provided and some other calculations and was just about to order in some great big lumps of profile. It seemed clear that for the gantry, torsion (twisting moment) was going to be the dominant source of cutting tool movement, kind of obvious when the tool tip is down near the bed as the length of the Z axis acts a a lever. I'd assumed that the performance of a piece of rectangular box section and a profile of roughly the same dimensions would be fairly similar as the moments of area (Ix, Iy) for normal flexing do seem to roughly match up weight for weight, so had happily gone ahead assuming I could plug values into the spreadsheet and get meaningful tool deflection figures for profiles.

THEN, I happened to come across the Item24 website, those guys are possibly the Nirvana of aluminium profiles, they have something to solve pretty well every problem ina very efficient german way. And, uniquely they state the torsion constant (J) for most of their profiles (basically how hard it is to twist it). AND the figures are very different (i.e. a LOT smaller) than the equivalent sized rectangular tube. Thinking about it now, it kind of makes sense, as playing around with anti-roll bars taught me that to get a stiff tube, you need to get as much thick, continuous metal as far away from the centre of rotation as possible. Whilst all the slots might add or certainly won't detract much from flexural stiffness, profiles only have a continuous "tube" at the bottom of the slots, a fair way in from the outer periphery, and the bits at each corner (where the stress is concentrated in a rectangular tube) do practically nothing to add torsional strength.
Anyway, here's a little comparative table of profiles and rectangular tubes: the profiles are all Item/KJN/Motedis patterns (they all are the same sort of shape and have similar Ix,Iy within a few %), stated prices are from whoever was cheapest when I looked. Prices for box are from my local stockholder, there's obviously money to be saved as well as gaining torsional stiffness

Profile	Moment of Area x	Moment of area y	Torsion constant	weight	cost per metre
Item 80 x 120 lite	201	422	165	8Kg	£55
Item 80 x 120	273	575	261	11Kg	£81
Item 80 x 160 Lite	270	919	250	11Kg	£77
Item 80 x 160	362	1232	397	13.5Kg	£101
Item 120 x 120	799	799	578	12.4Kg	£158
80x120x6.75 tube	251	482	498	6.9Kg	£48
2"x6"x1/4" tube	104	642	287	6.7Kg	£43
3"x6"x3/8" tube	352	1152	853	10.9Kg	£58
70x80x4.4 tube	191	860	493	5.9Kg	£39
80x200x6mm tube	360	1570	922	8.8Kg	£56
100x200x5mm tube	515	1522	1183	7.8Kg	£56

You can probably guess what I'm going to be using for my gantry

Hi voicecoil.

Did you consider steel box section?
And some epoxy leveling?

Grtz Bert.


Verstuurd vanaf mijn SM-A320FL met Tapatalk

[Voicecoil]

Hi voicecoil.

Did you consider steel box section?
And some epoxy leveling?

Grtz Bert.


Verstuurd vanaf mijn SM-A320FL met Tapatalk

Well, yes I have thanks Bert : however at the moment I'm much better set up for machining aluminium than steel. And part of the reason for the post was to highlight the low torsional performance of normal slotted profiles.

[magicniner]

Hmm, you assumed a profile with a trench to near centre had any torsional strength?
LOL!

[Voicecoil]

Hmm, you assumed a profile with a trench to near centre had any torsional strength?
LOL!

.....not forgetting the "trenches" near each corner.

[driftspin]

Well, yes I have thanks Bert : however at the moment I'm much better set up for machining aluminium than steel. And part of the reason for the post was to highlight the low torsional performance of normal slotted profiles.

Hi Voicecoil,


I think you did a very good job explaining how the most 8040 t sloted and alike style alu profiles have the less disireable shape for torsion resistance.

And yes round tube is best shape to resist torsion.

I agree the steel/epoxy route is harder to do.

Wish i had someone that could have milled / grind flat my bed / gantry...
Epoxy was a gamble that luckily worked out great for me.

Just buy the biggest heaviest best shaped profile that fits your design / needs / budget.

Rigidity rules.

Grtz Bert.





Verstuurd vanaf mijn SM-A320FL met Tapatalk

[routercnc]

Glad someone is still finding the spreadsheet helpful !

Yes Ixx and Iyy values relate to relative bending performance in the up/down or fore/aft direction (independent of material, just relating to the geometry).

Whilst this is important for a gantry what will dominate the requirement is the torsional stiffness as you point out. My spreadsheet allows you to calculate this for simple shapes but for complex shapes like profiles you need to use FEA which is probably what that company used.

As you and others noted continuous shapes with material away from the centre are best, and many quote a circle as the stiffest shape for torsion but actually there is a stiffer shape. A 50mm diameter square box section will twist less than a 50mm round tube. The extra bits in the corners of the box which are further away from the centre resist the torsion even more so it wins out. This is good news for gantries which can be square or rectangular which are more practical and be better for torsion plus way better for bending than the tube.

Also popular is adding 2 rectangles into an L shape and getting more stiffness with a very practical shape.