Thoughts on MDF & Torsion Box Design

[the__extreme]

I made the mistake of buying expensive baltic birch plywood to build my router with. Other than my local hardware stores only stocking 1/2" MDF in 4'x4' sheets, not quite long enough for what I wanted, I was trying to make my machine as light as possible, like many other people on this site are trying to do.

I say this is a mistake because MDF is actually a great material to use for a few reasons.

First, its cheap, dirt cheap. Enough said.

Second, it has good accoustic damping properties. So although your router may not thump like a car stereo, not only will it help to keep the noise down but will also reduce nasty vibrations better than other materials will when you're cutting. This is especially beneficial if you're doing a surface finish operation.

Third, MDF is heavy stuff. "But aren't most people trying to make their machines lighter?" you may ask. Yes, yes they are. "Why?" Well, to be honest, I think it's because as some point someone started making a bunch of cutouts to remove "unnecessary" material to save weight and the trend caught on. I'll agree that reducing the weight of MOVING parts has a benefits: more rapid acceleration and deceleration; and less wear on some components. But I argue that trying to lighten the base and table is waste of time/effort (design and machining), causes unnecessary tool/machine wear and will ultimately reduce the performance of your machine. For anyone who hasn't seen/used a full size metal working mill, lathe, etc., they're all large, heavy, steel structures. The bases and machine surfaces are basically steel blocks. This makes them heavy and stiff. Stiff is good because the cutting loads are large. Heavy is good for two reasons. It lowers the natural frequency of the machine [natural frequency = sqrt (stiffness / mass)], to something which is hopefully below the cutting speeds. A heavy machine also takes more force/energy to excite into vibration [vibration amplitude = (some constants / mass)], so if a machine vibrates up and down 1/32" inches, another identical machine twice as heavy would only vibrate 1/64".

What I'm trying to say is that cutting a bunch of material out of your table is a bad idea. In fact, some of that "unnecessary" material may actually be doing something.

I posted some images from an Finite Element model of a section of a router table. It's 36.5" long, 8.5" wide, with 4" high ribs equally spaced at 6" centres. The skins and ribs are all 1/2" MDF. A point load of 500 N (112lb) was applied at the centre. The modulus of elasticity of MDF used was 3 GPa (it typically varies between 2.5 GPa and 8 GPa, so 3 is conservative) and yield strength of MDF (modulus of rupture) is between 20 MPa and 80 MPa. (sorry, I didn't bother to convert to PSI).

So what the analysis showed is that the maximum stress is about 0.2 MPa, or a safety factor of 100 (20/0.2) and the maximum deflection is 0.07 mm (.0028 in). It also shows that some of that "unnecessary" material may actually be not-so-unnecessary near the ends in the red region.


I would love discuss these and related issues and hear what the rest of the community members think and have learned from their own experiences.

Shawn

[ger21]

I don't know how that Finite Element stuff works, but the pics don't look quite right to me. The strength of a torsion box comes from the skins, and the sdhesive bond of the skins to the framework. Does that analysis take that into consideration? I would think that the stress on the skins would be spread out more evenly.

Having said that, though, I'm mostly in agreement with you. Heavier is generally better, but you have the tradeoff of heavier being more expensive to move faster.
My still unfinished router, is probably the first one using torsion boxes. I started building it in 2003. Another First Router

The torsion box ribs are baltic birch. At the time, I thought it was the best choice. And I drilled lots of holes to make them lighter. But they have a LOT of ribs in them, and they are still far from light. The large table has 1/2" mdf skins, and probably weighs 50-60 lbs. But it spans 60 unsupported inches, so I wanted to keep the weight down to minimize sagging under it's own weight.

Now after spending thousands of hours reading over the last few years, I'm designing a bigger, faster, and better router. (I'll be finishing the first one by the end of the year) Start of a New Design

The torsion boxes in this new router will be MDF. Mainly for two reasons, though. It's cheaper. And the framework material has little to do with the strength. A few years ago I thought that a composite (carbon fiber / wood) machine would be perfect. Light and strong and fast. But I know understand that, as you've said, that light weight is not really the answer here. Although it's still a little important if you want reasonable (or better) acceleration, which is very important as well.

So, my next machine will have a mostly MDF gantry, with reinforced 1/4" MDF skins for light weight, but with some epoxy / granite filler material to dampen vibrations a bit. So since I'll be adding a bunch of weight back in (in hopefully strategically placed locations), I'll still be drilling lightening holes in a lot of the rib materials. I'll have to wait and see how it works out.

As for Baltic Birch, it has it's place. It's stiffer than MDF, and holds screws better. It will usually stay flatter, although it's not really an issue after proper sealing and finishing.

Each material should be chosen based on it's intended application, utilizing it's strengths whenever possible. But your right, for a torsion box, MDF is right at the top of the list as far as materials go. Nothing at all wrong with using it, and no need to waste time and effort lightening it up.

[Gir]

I don't know how that Finite Element stuff works, but the pics don't look quite right to me. The strength of a torsion box comes from the skins, and the sdhesive bond of the skins to the framework. Does that analysis take that into consideration? I would think that the stress on the skins would be spread out more evenly.

I believe these types of models will model the joints as though they're fully connected and won't give (other than the materials elasticity and such). This is probably a very accurate model, provided values of elasticity and such are correct.

I too will be using torsion boxes, but I'm not going to go crazy on the sealing and hole cutting. I plan on using the CNC to re-cut my shotty wood working : \ Then I'll finish it up properly : )

[Khalid]

I belive these software gives best results if modeling and input parameters are realistic and accurate... this figure of deflection 0.07 mm seams realistic...

[the__extreme]

Hey Ger,

I've definitely looked at your work, on several occasions, and am always impressed. I liked the "Alternative to round pipe" thread too. Glad to hear your router is going to be completed soon. I started university in 2003 and finished a little over a month ago, so if you look at it that way, someone can either build a router or go to school. The router is definitely cheaper.

I added a few other pictures in response to your question about the images not looking quite right. You are right, the stress results aren't intuitive, so I added the maximum and minimum principal stress results. FEA works by breaking the body into a bunch of tiny pieces and analysing the interactions between the pieces. If the pieces are assumed to be little cubes, because cubes are easy, and I like easy, you can imagine rotating them around in different orientations and having the reactions at each face change as the cube is rotated. The maximum and minimum principal stresses are 90 deg apart and correspond to the orientation of the cube when the forces on its faces are at a maximum/minimum. Maximum doesn't necessarily mean largest, rather "biggest positive value or negative value closest to zero," whereas minimum means "biggest negative number or positive value closest to zero." This is important because a negative stress implies compression and positive implies tension.

As for the model itself, I did it as if the skins and ribs are all one continuous body. So it actually considers the skin-rib and rib-rib joints to be perfect. I also extended the legs to minimize the effects the constraints have on the torsion box itself.



Before I make some comments about the pictures, note that RED DOES NOT NECESSARILY MEAN BAD. It just represents the upper range on the scale.

This first one shows how the torsion box section would deform. Ignoring the legs, the ends deflect very little while the most sag is in the middle, the blue section.



Here we have the maximum principal stress. The orange on the bottom, according to the legend, means that the bottom has a positive stress, ie tension, and that this is where the highest tension occurs. The blue on the top shows that if the "cubes" are rotated in a particular orientation, they experience a very small amount of tension (but it could actually be zero because zero lies in that colour band). Conclusion: The bottom is stretched in tension, and physically this makes sense.



Next up is the minimum principal stress. The red on the bottom, according to the legend, has a stress somewhere between -0.09 MPa and + 0.12 MPa. (Note that zero stress is also in this range.) And the orange, green and blue sections on the top all show a negative stress, meaning the top is being compressed. Conclusion: The top is under compression from the bending, and this also makes physical sense.



Putting the previous conclusions together, the model behaves as expected if a force was applied to the top of this section of a torsion box. Also notice that the ribs don't experience a lot of stress, but do keep in mind that they still must transmit force from the top to the bottom. In order to come up with a meaningful failure model, the maximum and minimum principal stresses need to be combined. This is done using the Von Mises criterion, which is based on material failure theory. The equation used to do this is:

equivalent stress = sqrt ( max_princip_stress^2 - max_princip_stress * min_princip_stress + min_princip_stress^2 )

So for the most part, the highest stress is in the skins towards the middle, where it would be expected. The cross ribs don't appear support a whole lot, which makes sense because they're perpendicular to the bending direction. The longitudinal rib has interesting stress patterns, with some high shear areas near the ends but supporting very little towards the middle. It appears as though most of the loads are transmitted from the top to the bottom through the yellow bands in the longitudinal rib.




A simple beam in bending would have purely axial compression on the top and axial tension on the bottom, with the highest stresses and deflection in the middle and no stress or deflection on the ends. I think that for the most part this model's behaviour agrees with a simple beam.

Shawn

[Khalid]

Nice to see your work SHAWN...Can you do stress analyses on Joes 2006 design???...
I didn't work on ANSYS...As I mechanical engineer and working in process plant,I have a little experience working on CAEPIPE/CEASERII,COMPRESS, COADE CODECALC etc..

These softwares are great to get optimum designs and tell us the problamatic areas...

[ger21]

Originally Posted by the__extreme This first one shows how the torsion box section would deform. Ignoring the legs, the ends deflect very little while the most sag is in the middle, the blue section............................................ A simple beam in bending would have purely axial compression on the top and axial tension on the bottom, with the highest stresses and deflection in the middle and no stress or deflection on the ends. I think that for the most part this model's behaviour agrees with a simple beam.

Wouldn't a torsion box deform more evenly, as the skins should spread the load out?

And a torsion box should not behave like a simple beam, should it?

[High Seas]

Just another thought on comparing MDF and plywood (Baltic Birch -- very nice, but any marine ply would suffice -- no voids, good glues) for the torsion box:
Sheer failure in the webs.
MDF will sheer when loaded due to its lack of "grain" -- which is not unlike the filaments of glass in fiberglass. The loads are taken along the "grain/filaments, and reduce sheer stress in the webs.

Another example - consider the number of homebuilt aircraft built with MDF -- 0. And the wing structure is an oversize torsion box! MDF has its place, but a plywood - torsion box will have much better mechanical properties.

Like the idea of using FEA though!

Jim

[the__extreme]

A torsion box works much the same as an I-beam. They both have a high moment of area about their neutral (central) axis for their weight and for this reason resist bending very well. If you have a beam, say a 4' long 2"x4", and support it at its ends and push on the middle of it, it bends a lot more easily if it's flat then if it's on edge. That's because the moment area is the width * height^3 x (1/12), so its 4 times as stiff in that direction.

_______
|______| (1/12) * 4 * 2^3 = 32/12
vs
___
| | (1/12) * 2 * 4^3 = 128/12
| |____________central/neutral axis
| |
|__|

Since I-beams and torsion boxes put more of the material farther away from the central axis, they make good use of a small amount of material.

The stress in a bending beam varies with the distance from the central axis also, but linearly, not cubed: Stress = bending moment * distance / moment area. Since nothing we're making is breaking...I hope...everything should behave elastically, so the strain, or deformation, is related directly to the stress. By placing material as farther away from the central axis, the member is stiffened, which reduces stress, reducing deformation and deflection.

This will be true of any structure, simple beam or torsion box. The difference between a torsion box and an I-beam is that the torsion box essentially has I-beams running in both directions, so it resists bending in 2 directions. As for the 'torsion' aspect, again, having the material farther from the neutral axis has the same effect. The ideal shape to minimize torsion/twisting is a large diameter, hollow pipe, because the material all as far away from the pipe's axis as possible.

It's actually kind of interesting to note that most people, myself included, only support their torsion boxes at the two ends. In this configuration, it really acts more like a couple I-beams than a torsion box, and would actually be much stiffer if it was supported around all its edges.


As for the simple beam, I decided to analyse it too to see what the differences were. Turns out, not too many. But really, bending is bending and I shouldn't have expected there to be any huge differences. The top surface is compressed, the bottom is stretched and the highest stress is in the middle, pretty much the same as the torsion box.



High Seas,

I agree with the shear failure. In fact most materials fail in shear, except brittles like ceramic. That is essentially what the "equivalent stress" images show. Its approximately the difference between the maximum and minimum principal stresses at any point, which is the shear. A plywood will resist shear much better because of the different lamination/grain directions. I'm actually in the process of designing some fibreglass wind turbine blades, but our problem is fatigue not shear. Don't want to throw a blade...another blade...


Khalid,

I'm hoping to fun my own machine through some of the advanced analysis tools, like interactions of all the components (gantry, router carriage, table, etc.) and maybe a modal analysis to see if it will resonate at any cutting speeds. Still some learning to do first though. I think it would be really interesting to run Joe's routers through the program, I'm a big fan of his work. Keep in mind that software is great stuff, but it can still give poor or inaccurate answers if the inputs are incorrect. The results should always be compared with the expected behaviour.


Cheers,
Shawn

[ger21]

Originally Posted by High Seas Just another thought on comparing MDF and plywood (Baltic Birch -- very nice, but any marine ply would suffice -- no voids, good glues) for the torsion box: Sheer failure in the webs. MDF will sheer when loaded due to its lack of "grain"

If your talking about the edge of the MDF, I'll disagree. Bond the skins with epoxy, which will soak deep into the edge of the grain, and it'll be very difficult for the edges to shear off. If you're talking about the skins, then I'll agree a little. But the quantity of interior members greatly affects the load required for this shear to occur. If you want a stronger box, increase the density of the core.

Also, at what force do you think this shear will occur? A cheap hollow core door, with 1/8" masonite skins and a CARDBOARD core, will support a few hundred pounds pretty easily.

[the__extreme]

I think Jim was talking about general shear in the MDF/plywood, not necessarily the edges. It's easy to peel apart the grains in a sheet of plywood, but takes much more force to break a grain if you're pulling on it from the two ends, in other words the directional nature of wood. Since MDF is a very nondirectional, uniform material, you don't get the advantage of longitudinal tensile grain strength as in a laminated plywood or fibreglass.

I agree, I wouldn't expect that your joints would ever come apart at the edges they way you've bonded them. I read that MDF has a tensile strength / modulus of rupture between 20 - 80 MPa (2900 - 11600 PSI). The actual force would depend on the size/orientation of the piece.

[Gir]

Another example - consider the number of homebuilt aircraft built with MDF -- 0. And the wing structure is an oversize torsion box! MDF has its place, but a plywood - torsion box will have much better mechanical properties.

They also build model planes out of balsa wood, but I wouldn't be building a router out of one.

Comparing planes to a router is nonsensical. The wings in a plane are designed to act as shock absorbers. They can bend and flex in strong wind, and especially in high turbulence. Taking a look at this video will clearly show their design goals of a wing. To top it off, planes need to be kept light and vibrations are less of a concern. In that sense, MDF makes no sense at all.

On the contrary the weight of a router is the opposite of a plane. The more the merrier. Making it heavier you will be dampening the vibrations caused by the router, allowing for smoother finishes. Also, denser materials tend to bend less, making for a structure that flexes less.