Truss style Gantry

[D.C.]

thats why there isn`t loads of commercial machines with lightweight truss gantrys

Oh look a truss.
DSG 1609 - YouTube

I guess Dean Smith and Grace know sweet FA about designing machines, bunch of cowboys...


The main reason why I started exploring down this route was by looking at the design decision taken by other builders, my budget and my desires for the machines performance.

I need at least 6 inches of travel as I want to 4 axis work, the wood lathe I'm planning to canibalise will turn 12" wood and I have a few design ideas that need hefty chunks of wood.

I'll stick another picture in with axis labels: (This is missing a piece of box section either end)




Lets compare this design of gantry against some of the others bearing in mind this going on 'my gut' and I have no actual engineering experience and I have never built a cnc machine in my life and I have not yet been able to find an open source FEA package that I can get to grips with. (I've been trying to learn Z88 but it keeps speaking German to me :( )

Leaving aside gravity, the gantry momentum and motor problems etc I assume all the forces that this gantry will encounter will be coming from the tip of the cutting and will be transmitted to the gantry via the four bearing blocks on the rail. (Is this right?)

If the machine is moving forward in a straight line on along the x-axis, the forces it will generate will want to push back against the front bottom beam and pull the front top beam forward.

Another assumption of mine, the distortion of steel is does not have a linear relationship to the force it is put under so if there is a small amount of force the deflection is negligible, increasing slowly until it approaches breaking point and then the deflection increases extremely quickly. (The graphs I was looking at for this seemed to be exponential or worse, is this about right?)

In this design the point forces that are acting on the gantry through the bearing blocks get spread out and transmitted through the rear struts to the back beam. What musht was saying about a plate being stronger is true, but this design can come out of £17 worth of steel angle, to plate three sides of this gantry in 10mm alu would mean buying a 8x4 sheet of the stuff and a quick check online puts that at about £500 + VAT. Which is just taking the piss cost wise, a single offcut piece of alu plate this length will cost more than the entire gantry...

For twisting forces or forces parallel to the y-axis the same should apply, because the truss system isn't in one plane but is in three planes this style of truss creates a very stable form in all directions.

If I had the ability and software to model dozens of different designs and do FEA on them I would be doing it right now, but I don't so I'm fudging it. I do have a hard time believing this design (which is cheap) is going to distort more under load than a couple of bits of alu extrusion bolted to an alu plate or the L style gantries that I've seen.

That said, I'm absolutely clueless about vibration and resonance. :(

Just one extra question about the gantry, for mounting SBR rails they don't have to be 'that' flat do they? Would mounting onto some cold rolled bright steel bar be accurate enough? I'm working without access to a good straight edge or surface plate, the closest I can get is sheet glass or MDF, neither of which seem really flat enough for a good cheap epoxy transfer, the price for the high viscosity self leveling specialist epoxy is also very high. :(

[Jonathan]

Oh look another truss.

I think you should make ends of the diagonal pieces meet, or at least close.

Lets compare this design of gantry against some of the others

Most of the gantry designs posted on this site are essentially two beams with something in between. You've added a third beam to the back and braced it, so it's bound to have better stifness, both linear and torsional, to a design with only two beams, for the same amount of material. Where you gain is you can use less material to get the required stiffness since this is an inherently more rigid structure, so you save money. Often people discount this idea due to the apparent complexity and time required to build it, but evidently that's not a problem here.

Leaving aside gravity, the gantry momentum and motor problems etc I assume all the forces that this gantry will encounter will be coming from the tip of the cutting and will be transmitted to the gantry via the four bearing blocks on the rail. (Is this right?)

Yes, let:
F_x=forces due to gantry parallel to X=force on X ballnut.
F_y=forces due to gantry parallel to Y=force on Y ballnut, total radial force on X bearings.
F_z=forces due to gantry parallel to Z=vertical component of force on X bearings.
m_g=mass of gantry
m_y=mass of Y-axis carriage
m_z=mass of Z-axis
f_cn=cutting force parallel to axis n, where n=x,y,z
an= acceleration of axis n, where n=x,y,z

Hence the forces on the gantry are:
F_x=(m_g+m_y+m_z)a_x+f_cx
F_y=(m_y+m_z)a_y+f_cy
Fz=m_za_z+f_cz+(m_g+m_y+m_z)g
There are also forces on the gantry due to the moments in each plane, but it doesn't really achieve much to list them. There's an old thread where I mentioned it here. There are some other forces involved, but they're generally negligible.

If the machine is moving forward in a straight line on along the x-axis, the forces it will generate will want to push back against the front bottom beam and pull the front top beam forward.

Yes...although it's not clear in what direction the force on the front top beam is since in addition to the force you describe from cutting, there is a force in the opposite direction due to the beam's mass, which will partially cancel. Either way there is a force on the top beam in the X direction, so having the material there to resist it is necessary.

Another assumption of mine, the distortion of steel is does not have a linear relationship to the force it is put under so if there is a small amount of force the deflection is negligible, increasing slowly until it approaches breaking point and then the deflection increases extremely quickly. (The graphs I was looking at for this seemed to be exponential or worse, is this about right?)

It depends on how the 'steel' you're analysing is supported. If you're just squashing or stretching a lump of steel, then the relationship between force and deflection is linear, like a spring (F=kx). That is until you reach the elastic limit (which clearly isn't going to happen here) and the material fails which is probably the graph you were thinking of?

If the beam is supported at both ends, then the deflection formula has a different exponent depending on the position of the force:
Euler

For twisting forces or forces parallel to the y-axis the same should apply, because the truss system isn't in one plane but is in three planes this style of truss creates a very stable form in all directions.

Agreed...

That said, I'm absolutely clueless about vibration and resonance. :(

You've said you're putting expoxy between the joints in the steel box section, presumably this is to damp vibrations in which case resonance should be less of a problem? Also note how in the .pdf I linked to earlier their analysis was based on finding the minimum number of beams to achieve the required stiffness, since by reducing the mass you increase the resonant frequency, ideally making that resonant frequency above the frequency of any forces imposed on the gantry.

Just one extra question about the gantry, for mounting SBR rails they don't have to be 'that' flat do they?

Not compared to linear guides, but what if you decide to change to linear guides at a later date? You should still aim to get it close.

Would mounting onto some cold rolled bright steel bar be accurate enough?

It depends how you mount the bar. If the bar is just bolted to the box section it will simply bend and conform to the box section, so you haven't gained anything except for maybe a smooth surface. You'd need to fix it with adjustment - for instance use lots of bolts with nuts to sandwich the steel flat bar between nuts, so you can then adjust them to make it flat. Ideally you then need an accurate reference...but for mounting SBR rails a 1m steel ruler is probably good enough.

the price for the high viscosity self leveling specialist epoxy is also very high. :(

The epoxy is cheap, i.e. west system 105, but the hardener (west system 209) isn't. If you did use it the surface would be accurate enough for either type of rail, and you wont increase the overhang as much as with other methods. The interesting bit will be making sure the surface doesn't get twisted when you fix the gantry to the X-bearings/rails, so you would ideally cast a resin surface on both.

[D.C.]

The model at the moment is just a rough, I will join up the supports it was just pain in the butt trying to rotate things in to odd angles in sketchup. :)
I was going to epoxy to avoid any welding distortions, the rear struts I will weld onto plates and then epoxy all the rear strut plates on to the beams in one go.
My maths still isn't good enough to confidently sit down and work it out, so thanks for that!
I'm almost positive I won't upgrade to guides, if I upgrade this machine it will be to extend the x-axis to cater for 8x4 wood sheets and I can't really see anything I'll be doing at size needing the accuracy of guides.
If resonance does become an issue I always have the option of filling the beams with vermicrete or something similar, a poster over on practicalmachinist reckons truck driveshafts just use thick cardboard tubes inside to dampen vibrations.
The epoxy path is starting to get expensive, £120 quid just for a flatish surface which would mean I would have to ditch the shiny leadshine drives. I think I'm going to have to see if I can find some where local with a decent sized surface table and use the cheap stuff & clingfilm method...

[mocha]

DC, you'll love this one then! :-)

MOAT

[D.C.]

DC, you'll love this one then! :-)

MOAT

Pass me the tissue paper, I may be some time...

[Ricardoco]

Hi DC, ive been reading this thread with interest and i was wondering, what is the maximum tool size you will be using and what forces would be required to break it, Im not sure but isnt there a relationship with that information and the gantry stiffness required? I would be interested to know..

Rick

[routercnc]

Hi D.C.

If it helps answer your first questions about the suitability of this design for a cnc router gantry, then my answer would also be yes. Trying to avoid getting to technical:

Although your individual box sections are slightly smaller than a typical size used for a 'single piece gantry', they are located along way from the 'neutral axis' (region of ZERO stress which for your shape is the exact centre of the triangular shape). This makes it much stiffer than the 'single gantry' designs under all loading conditions because the 'distance of material away' factor in stiffness is to the power 4 for torsion and to the power 3 for bending. Doubling the distance away from the neutral axis makes the structure 2^3 or 2x2x2 or 8 times stiffer in bending.

There are 3 loading conditions you need to consider:

X axis cutting loads put bending into the frame are resisted by both front beams in compression and the rear lower beam in tension. Because the beams are spread well apart (and linked by the connection pieces) this is what mainly makes it very stiff. Cutting loads in the other X direction reverse the compression and tension.

X axis cutting loads also put torsion loads into the frame because the tool cutting forces are offset from the centre of the beam. This tries to bend the beams which in themselves are not that stiff, but are prevented from bending by the bracing connection pieces. A structure under torsion has maximum stress at a 45 degree angle to the central axis, therefore angling your bracing pieces at about 45 degrees will be optimal.

Z axis cutting/plunging loads are resisted by both bottom beams in compression and the top beam in tension. Weight of the spindle is resisted with these forces reversed. Again wide beam spacing is the dominant factor to give good stiffness.

So the only thing 'wrong' with this idea is the work involved.

All simply supported beams (of any shape) will suddenly fail when they get to the yield stress, but the loads are massive. You are at the other end of the graph so don't worry about that.

[D.C.]

Hi DC, ive been reading this thread with interest and i was wondering, what is the maximum tool size you will be using and what forces would be required to break it, Im not sure but isnt there a relationship with that information and the gantry stiffness required? I would be interested to know..

Rick

To be honest I can not answer your questions, I'm approaching things from the exact opposite direction.

I don't have any calculations for minimum acceptable tolerances, I'm just trying to make the best that I can knowing the skills and budget that I have. This is a hobby cnc, more one off multirole artsy kind off stuff and not industrial high tolerance required scenario.

Despite all the fussing about the arrangement of bits of steel, I will initially be using MDF plates for many parts of the machine, horrible I know but I can cut the alu parts I require and destroy the MDF in the process of doing so.

For what I want to do I need to 4 axis woodwork, I need to cut acrylic, I need to do PCB work and any alu past upgrading the machine is strictly artistic so the tolerances are not very high, as long as a curve is smooth enough for the human eye, I'm a happy bunny, most of that smoothness can be achieved by a good walnut finish, exterme accuracy not required.

Despite that it just is not in my nature not to study, investigate and attempt to the best job possible, if I can make a better machine than I need I would be disappointed in myself to settle for anything less.

[Ricardoco]

To be honest I can not answer your questions, I'm approaching things from the exact opposite direction.

I don't have any calculations for minimum acceptable tolerances, I'm just trying to make the best that I can knowing the skills and budget that I have. This is a hobby cnc, more one off multirole artsy kind off stuff and not industrial high tolerance required scenario.

Despite all the fussing about the arrangement of bits of steel, I will initially be using MDF plates for many parts of the machine, horrible I know but I can cut the alu parts I require and destroy the MDF in the process of doing so.

For what I want to do I need to 4 axis woodwork, I need to cut acrylic, I need to do PCB work and any alu past upgrading the machine is strictly artistic so the tolerances are not very high, as long as a curve is smooth enough for the human eye, I'm a happy bunny, most of that smoothness can be achieved by a good walnut finish, exterme accuracy not required.

Despite that it just is not in my nature not to study, investigate and attempt to the best job possible, if I can make a better machine than I need I would be disappointed in myself to settle for anything less.

Hey DC thanks for Answering anyhow, i guess i will have to wait till someone else knows the answer, i do look forward to seeing your machine come together as ive not seen one like this before, and to be fair MDF machines are a lot more usefull than may be first imagined, when i had Mine it surprised me.

Rick