How much deflection is too much?

[Dman65]

I am looking at building a router along the lines of what FandZ built in this thread: Little Brute

I am planning to make my unit a little bit larger, but I am trying to figure out if the unsupported rails are going to experience too much deflection. But first, I have to determine how much is too much. Can anyone give me some guidelines for this?

I have used Beam Boy to calculate the deflection of various thicknesses of 1" square steel tube assuming a gantry that weighs 80lbs and puts 40lbs on each of the two four feet rails.
.049 thickness = .0273 deflection at center
.065 thickness = .0216 deflection at center
.083 thickness = .0179 deflection at center
.120 thickness = .0138 deflection at center

Are any of these numbers sufficient? .0138 would work out to be less than 1/64th of an inch and I don't think my tape measures go that small.

Any input would be appreciated.

[Geof]

It is not just static deflection you need to worry about. The tool puts an additional load on and so does acceleration and decceleration. Also you can get resonance effects that build up to much larger deflections than you measure with a simple static load. Your theoretical deflection of about 0.014 could easily turn into 0.05, or more, which is in tape measure territory. In addition if you are making parts that fit together even 0.014 turns into a gap of 0.024 which is noticeable. This may be tolerable in wood working but as soon as you try doing plastic you will start finding it a nuisance and if you try any fine engraving it will be intolerable.

Figure out some way to support the rails; one central support will reduce the deflection by a factor of 8, I think deflection goes with the third power of the length.

Alternatively go to a slightly larger tube because the deflection depends on the thrid or fourth power of the beam depth.

Incidentally were you using simple end supports or rigid? That also influences the deflection.

[Dman65]

Thanks for the reply Geof.

It looks like going to 1.25" square at .120" thickness gives a static deflection of .00658. And 1.5" gives a deflection of .00363.

Is there any kind of formula for going from static deflection to include the acceleration and deceleration? Or is there any static number I should shoot for that will put me in the ball park once acceleration and deceleration are factored in? Your example above seems to indicate about an x4 from the static to the "dynamic". Does that mean if I want to be within 1/64 I should shoot for about .0039?

[Geof]

My totally off the top of my head gut feeling is yes go for a 4 to 1 ratio. I don't have any scientific reason for it just a feeling from many years experience.

[Ed from NY]

In my limited experience, given a load, I have seen 3 ways to reduce deflection:

a) Put a support in the middle like Geof said. This has the biggest payoff.

b) Scale up the material, but you get very large very quickly.

c) Change the geometry of your support members.

On (c), it seems that you have two rails spaced a few inches apart. If you can hang whatever you need sideways and weld/screw a sheet of material between the two rails that will make the whole thing into an i-beam. The deflection will be a function of the mass distribution (google "moment of inertia"). The more of the profile you have away from the center of your newly formed beam the better it will handle whatever loads. The catch is that you have to really make it one. Meaning if you are not welding, make sure you have lots of screws/rivets. And if your profile is not symmetric you will be introducing torsion.