X3 column rigidity?

[lagfish]

I've heard a few people say that when they push on the side of the column of the X3 with very minimal force, they measure a deflection of a few thou. Any idea where this is from?

[Rodm1954]

The column is open "U" channel and this results in the some flex. A closed box would be a lot stronger.

[lagfish]

Hi Rod,
While I agree that the closed box design would improve rigidity, there is definitely another source of the flex. If we assume that most of the flex is coming from the column and model the column as a cantilever U-beam, the deflection located at a load applied at 20 in (about 2/3 of the way up) from the fixed end would be:

y= Fx^2/6EI *(x-3a)

For the X3, the column is approx 5.5in wide and 3.75in deep. Wall thickness is about 0.5in. This is a conservative estimate, since there are ribs inside the column to keep it more rigid. This gives a moment of inertia of

I=1/12 * (0.5)(4.5)^3 + 2*[ 1/12 (3.75)(0.5)^3 + (0.5)(3.75)(2.5^2)]
= 27.32in^4

(it turns out, adding a closed box design would only give 14% increase in sideway rigidity, since most of the strength comes from the sides)

a=20in
x=a
E for cast iron = 13E6psi

Say we apply a load of 100lbs

Deflection would be given as:
y = 100*20^2 / 6*13E6 * 27.32 *2*20
= 0.00075"

Less than 1 thou for 100 lbs of sideward load. I've heard people say they get a few thou with just finger pressure, which is max around 20lbs.
So the deflection is not coming from the column, but probably the base. Maybe from the connection between the column and the base? I'm going to do some tests on my mill to see where the deflection is coming from, and build some sort of truss structure to improve the rigidity.

[Rodm1954]

Hi Lagfish,
I got lost on your first formula so I am not even going to try to understand what you have said.
Just a thought though - have you allowed for the lever effect of the head as I think this would magnify the deflection more than the 1 thou you have calculated and could well bring it to the figures quoted.
I am all for finding and fixing the problem and will be very keen to see what you discover.

For your information I have seen a 200mm square RHS column fitted to the rear of an X3 column and it measured zero deflection with 10kg sideways pressure on the spindle. It did have a connection to the base so you could well be on the right track about the column to base connection.

Look forward to your findings.

[cjdavis618]

I would like to see this also.

My first thoughts are whether the mill column was torqued down well on the base. The next is whether the base was bolted to a solid structure to keep it from twisting.

Most people posted that the deflection was one the front pushing the mill head up or column back (or at least I thought that). I would attribute that to the gibs and boxway. Mine is the same and very noticeable with the counterweight attached when the balance is changed.

I would like to see an alternative way of moving the z axis than the side bar system. Then the entire column could be one piece and since there is an empty base now with the CNC kits added. That would be a great place to fill in as well.

I would do this, but I lack the tools to do this with metal and concrete doesn't have enough mass to help there I don't think.

[pzzamakr1980]

There is definitely more flex than just .00075. Where it comes from is the question. When the head is at the top of the column I can push the column back with just a moderate push and I can see it move. So if I can see it, I know its more than computed.

[tauntdesigns]

I tried to plunge a hole with a new 1/2" cobalt end mill in 6061 al the other nite. You can diffidently see all kinds of stuff moving around. I decided to drill a hole first, then end mill to size.

[lagfish]

Rod:
I should have clarified my formula more. I used the moment of inertia formula for calculating the deflection of the column with a sideways applied load.
I = 1/12 *bh^3 + Ad^2

I'm not sure what you mean by lever effect of the head. If you mean that the distance between the endmill and the column creates a torque around the column, then this torque will only tend to twist the column into an S shape rather than causing a great amount of deflection. I also didn't put this into my calculation because people have noted deflection when pushing against the column rather than the endmill.

I previously thought you only saw considerable deflection when pushing the head sideways, but cjdavis noted that this is also the case when pushing it back.

One way I thought of determining the source of flex is to give the column a fixed load, and measuring the deflection at many points along its height. Plot this on a graph to get the shape of the deflection of the beam. If the shape is curved, then it means the column itself is flexing. If the shape is slanted but straight, it means the base is flexing. If the shape remains vertical but is translated, it means there is sliding between the base and the column. However, this would be hard to do because the total displacement is only a few thou, and my indicator can only measure 0.0005.

Anyway, attached are what I thought of to reinforce it. Basically a box frame with X braces on the back and sides, and it doubles as an enclosure. The green is the connection between the mill and the frame. If I used 3x3x0.125 steel tubing, it would run less than $150 for the steel. I calculated a deflection of less than 0.00001 with a 200 lbs load, which is most likely more than what the X3 can generate with cutting forces. I would weld the frame and drill holes into the column to attach to the frame via bolts.

If anyone with any experience with this could chime on this, it would be great. I have zero experience with this stuff, and just basing it off what I learned in school.

[philbur]

That would certainly stiffen things up a bit. Although 0.00001 with a 200 lbs. load for what is effectively a lightweight box section frame seems somewhat optimistic. My other comment would be to take a more holistic approach to the issue of cutter deflection under load, rather than concentrating all effort on one particular aspect.

Lots of good thinking though, keep going.

When you measure excessive deflection the best way to track it down is to put your DTI across every "joint" individually in order to find the culprit or culprits.

Just some thoughts and opinions.

Phil

Originally Posted by lagfish Rod: I should have clarified my formula more. I used the moment of inertia formula for calculating the deflection of the column with a sideways applied load. I = 1/12 *bh^3 + Ad^2 I'm not sure what you mean by lever effect of the head. If you mean that the distance between the endmill and the column creates a torque around the column, then this torque will only tend to twist the column into an S shape rather than causing a great amount of deflection. I also didn't put this into my calculation because people have noted deflection when pushing against the column rather than the endmill. I previously thought you only saw considerable deflection when pushing the head sideways, but cjdavis noted that this is also the case when pushing it back. One way I thought of determining the source of flex is to give the column a fixed load, and measuring the deflection at many points along its height. Plot this on a graph to get the shape of the deflection of the beam. If the shape is curved, then it means the column itself is flexing. If the shape is slanted but straight, it means the base is flexing. If the shape remains vertical but is translated, it means there is sliding between the base and the column. However, this would be hard to do because the total displacement is only a few thou, and my indicator can only measure 0.0005. Anyway, attached are what I thought of to reinforce it. Basically a box frame with X braces on the back and sides, and it doubles as an enclosure. The green is the connection between the mill and the frame. If I used 3x3x0.125 steel tubing, it would run less than $150 for the steel. I calculated a deflection of less than 0.00001 with a 200 lbs load, which is most likely more than what the X3 can generate with cutting forces. I would weld the frame and drill holes into the column to attach to the frame via bolts. If anyone with any experience with this could chime on this, it would be great. I have zero experience with this stuff, and just basing it off what I learned in school.

[BrendaEM]

I guess that if longer sideplates could be made, you could then add an additional plate on the back of the column, which would help keep the column from twisting on the Z-axis. The plate could be pinned in countersunk bolted to the back of the column. Even then, everything would have to be just so.

It appears that there is also little clearance between the acme/ball nut attachment on the rear strap.

[pzzamakr1980]

What I was thinking of doing was making a brace that went across the front of the column and bolted to the sides with a tee shaped brace. Make it high enough to go over the table lip so it wont affect y travel. I was thinking aluminum, 1/2 inch or maybe 3/4 inch and that should be enough to prevent the column from tilting forward and backward, which seems to be the only flex that affects my cutting. Put some slots in the braces and it could be used to tram the column too.

[lagfish]

Hi phil,
Thanks for the input. My theory on the frame is this: The flex can only come from 4 different places. 1. The head, which cannot be easily stiffened, since it moves. Although attacking ribs to it would probably make it stiffer. But my intuition tells me the head is not flexing very much. 2. The colum itself, which can be stiffened. 3. The connection between the column and the base, which can be stiffened 4. The casting that forms the base, which might be able to be stiffened by filling it with concrete or something.
The frame I have designed improves stiffness in 2 and 3, because it connects directly to the column and base.

Also, I added one too many zero to the deflection, I meant 0.0001", which is reasonable when you think about it, because you're adding essentially 2-3x the volume of the column in steel, which has a higher modulus than cast iron, and is oriented in such a way to provide high rigidity. I was also thinking of sandwiching the the beams with heavy gauge plate, like how on some furniture, as soon as you nail on what seems to be very flimsy cardboard backing onto an otherwise wobbly structure, the whole structure becomes stable.

Hi Pizzamaker,
I don't see why you would make it out of aluminum, since steel is cheaper, stronger, and easier to weld. I think your idea would work well too. But since i'm building an enclosure for my mill as well, I thought why not make the frame out of heavy tubing, which would only increase fabrication time slightly, and attach the mill to it to improve rigidity. Kill two birds with one stone.