Moment to bend tube

[joao100]

I am projecting a small machine to bend tubes untill 31,75mm OD x 0,9mm wall thickness , steel SAE 1020. This machine works with a bend die, a clamp die, a pressure die and a mandrel. The radius of the bend die is about 200mm. Hom can I calculate the moment with this parameters, with 90 degrees bend?

 

[brad]

I don't believe that you can within a reasonable error value, as this is a highly nonlinear problem. You could calculate initial yield, but not much beyond that with significant accuracy.

I would not expect to find a "textbook" answer to a problem like this, as this is nonlinear and highly dependent on post-yield material behavior. My best recommendation would be to do an nonlinear FEA analysis on this.

Although I am an FEA "geek" I first try to apply basic principles to problems such as this; I don't believe that this one can be solved with basic principles.

Brad

 

[JamesBarlow]

Bradh is correct. This is a nonlinear problem. The bend will start as a elastic deformation, followed by a plastic deformation.

The pipe will also have both plastic and elstic components to the bend until the entire pipe is bent to a point were the entire area of the bend is yielding. The wall also becomes thinner as the bend progresses reducing the force required to bend the pipe.

If this were my job I would make an approximate solution by solving multiple problems bending the pipe a little at a time. Bend 10deg, and then recalculation based on new geometry to bend another 10 deg.

The easiest way to do this would be to just find the force necessary to initiate yeilding of the pipe. This initial yield will take the most the power and from there on in your power requirements will reduce.

 

[butelja]

The two previous poster's are correct about this being a complex nonlinear problem.

However, to get an estimate of the force, calculate what the plastic moment for the tube is. This is the moment that results when all of the material above the nuetral axis is at the yield stress in tension, and all of the material below the nuetral axis is at the yield stress in compression. If you take this number and apply a suitable "fudge factor" you should come reasonably close to the answer.

I did a quick check using your information. Assuming a yield stress of 200 MPa, I calculate a plastic moment of ~170 N*m. I would use a value of at least 200 N*m, and maybe as much as 250 N*m in designing your bending machine.

 

[Tatonka]

Since not all of the cross section of the pipe will be at the yield point, though, there will be some degree of "rebound" that will need to be accounted for...some additional "fudge factor" will be required to account for this remaining elastic stress.

 

[Viktor]

This ‘rebound’ is knows as elastic spring back. However, it does not affect the bending moment. It is a standard problem having an easy solution with FEA providing that the constitutive equation for the tube material is known. Automakers solve such problems every day in their analysis of crash problems.
Regards
Viktor

http://viktorastakhov.tripod.com