Need Help!- Deflection Calculation

[Freff]

Could someone help me out with a calculation please. I have a build with 20mm x 600mm hardened unsupported rods as X rails. The weight of the Z assembly is about 12-14lbs inclusive. Routing will mainly be small wood projects ie. model planes and occasionally some very light aluminium. I need to know the approximate deflection on the rails please. I have tried various calculating progs, but get myself a bit tied up with the different technologies. Many thanks.

Tony

[rlwoodjr]

With 7 lbs on each rail the deflection would be 0.09 mm if the gantry was in the middle of the 600 mm.

[TOTALLYRC]

Hey Freff


Don't forget the inertial effect of the z axis starting and stopping and changing directions. Certain milling and drilling operations will make it bounce. The rod diameter sounds small for its length, especially for unsupported rod. Plus the force required to push a drill bit into the material will be significant. Take a drill bit of the biggest that you think you will drill in al and do it by hand on a scale and see how much force is applied. I think you will be surprised.

Is the X axis supporting the Y and the Z and cutter head? 12 lbs sounds lite to me if that is the case, but it you have weighed it, my bad.

If it is a gantry style machine, remeber that as the cutter head gets all the way to one side that x axis rail will see a large increase in load will the other side will get lighter.

Static load calculations don't always tell the whole picture.

Just my .002 worth.
Mike

[rlwoodjr]

Mike is correct. The deflection I gave was static. Tool forces also play a part of deflection. These effects can be minimized by slow feed rates and high spindle feeds. 12 lbs does sound light.

The static deflection formula for each rail is : ymax=PL^3/(48EI). for your setup the deflection = pounds on the rail * 0.01253 (example 7*0.01253 = 0.09 mm,
40 lbs would be 0.5 mm, 80 lbs would be 1 mm).

I have a cnc dremel and mill. The mill has a lot better tolerances and negligible deflection. However, the amount of deflection you can allow depends on what you are making. The dremel I have makes great looking parts with decent tolerances.

[Freff]

Many thanks for the replies. I will weigh the Z/X assembly again, but I'm sure that it is in the range above. I have most of the main structure completed with just the rails and the gantry assembly to finish. I will post some pictures at that stage and perhaps you can give me some feed back. At present the whole thing is very solid with no flex. The Y axis is on supported rails but unfortunately on this build the budget would not allow for supported X axis.
Again, many thanks.
Tony

[slickrick]

Remember that the rail does not need to be supported 100% along the length.

I plan to place small 1" long supporting blocks spaced out along the length. This will increase the work for me to build it, but will also reduce the cost.

Say you have a 36" rail and you support it every three inches, you save a third of what you would spend to support the whole length.

I don't see a downside.

Rick

[TOTALLYRC]

Originally Posted by slickrick Remember that the rail does not need to be supported 100% along the length. I plan to place small 1" long supporting blocks spaced out along the length. This will increase the work for me to build it, but will also reduce the cost. Say you have a 36" rail and you support it every three inches, you save a third of what you would spend to support the whole length. I don't see a downside. Rick

I believe freff has slides that are not open on one side and can't be supported except for their ends.

[slickrick]

Originally Posted by TOTALLYRC I believe freff has slides that are not open on one side and can't be supported except for their ends.

Ahhhh.........That would create a problem...

[Freff]

Here is where I am so far with the build. All the parts for the Z assembly including the router (rotozip type) is 15lbs. I will try and measure any deflection on the rails tomorrow, but as it is it's very rigid.

Thanks for the replies.

[TOTALLYRC]

Originally Posted by Freff Here is where I am so far with the build. All the parts for the Z assembly including the router (rotozip type) is 15lbs. I will try and measure any deflection on the rails tomorrow, but as it is it's very rigid. Thanks for the replies.

I like the looks of it so far. You seem to have the Y axis rails a good distance apart which should minimise the tortional deflection caused by the forces of the z axis.

I am not sure about how you have the y rails on one side and the z axis on the other side, as the distance from the center line of the cutter will be greater than if you went with it all on one side. But at this stage, check the flex/torsional flex and see what you come up with.

Seeing how short the Y axis is and how well made the rest of it is, I think you will make out well.

Keep up the good work.

Mike

[irving2008]

I dont know how thick the z-plate on freff's design is, and I agree the design increases the turning moment on the rails, but when I did the calculations for mine I found there was more deflection due to bending in the planned 6mm thick alu z-plate due to sideways cutting forces when the tool was at its lowest Z extension than in the 20mm end-supported Y-rails themselves...

[TOTALLYRC]

Originally Posted by irving2008 I dont know how thick the z-plate on freff's design is, and I agree the design increases the turning moment on the rails, but when I did the calculations for mine I found there was more deflection due to bending in the planned 6mm thick alu z-plate due to sideways cutting forces when the tool was at its lowest Z extension than in the 20mm end-supported Y-rails themselves...

That's good to know.
If his plate has flex, an easy fix is to put a couple of ribs on the plate, say the same thickness and 1/2-3/4 " wide.
I think I would run it as it is and see how it goes since it is already built.

All in all it looks quite sturdy and should serve him well.

Mike.