Deflection of beam with right angle base

[Darren2K4]

I'm considering the elimination of a coil spring by using the elasticity of a beam folded out of a sheet metal part.

A standard force calculation for an end-loaded cantilever beam can be done using P = -3EI/(δL^3), which for a rectangular beam is P = -Ebh^3/(4δL^3). This should be a pretty good approximation for a beam folded off of a sheet metal part like this:

However, my space constraints don't allow enough room for L to get a low enough force for P, so I'm considering folding the beam out sideways like this, where the screw hole is where the force would be applied to the beam. Then I can easily make a beam long enough to get the low force I require.

Is there a way to somewhat reliably approximate this beam end type so I can still calculate the force for a specific deflection on this beam?

 

[Tmoose]

How much operating deflection do you need. Or do you just need a certain force?

 

[drawoh]

Darren2K4,

Have you looked into strain energy methods? I see two cantilever beams in your diagram. It took me a couple of minutes to see that your spring is punched out of the middle of a sheet metal panel.

Don't forget to check for stresses.

--
JHG

 

[Darren2K4]

This is 1mm thick steel, and I need a force of >=22N, which I want to minimize. I estimate I won't be able to do much more than 2mm of deflection before it yields, but the smaller the deflection, the bigger the I'll need to make the nominal force to maintain the 22N minimum. Some yielding is acceptable, as long as 22N minimum is maintained after yielding, but that would also require a bigger nominal force and complicate the calculations.

 

[BiPolarMoment]

Could you use a varying cross-section instead? e.g. make it like example #1 but with a reduced width (not thickness) closer to the base to reduce the overall stiffness; has strength limitations but you haven't indicated if that is a concern.

 

[Darren2K4]

Strain energy methods might work, but would I need a very accurate stress-strain table to calculate the strain energy density? And I'm still not sure how to model the right angle bend in the beam.

I was wondering if an approximation like this would be valid, breaking up the beam into two end-loaded beams, and then treating the total length as the length of a single straight cantilever:

 

[Darren2K4]

@BipolarMoment No, the space constraint (about 10mm available for length of beam) is way too tight to even get close. Anyway, I don't want to pick a sub-optimal design simply because calculations are complicated.

 

[drawoh]

Darren2K4,

How accurate are you trying to be? Sheet metal bending tolerances are something like ±0.4mm. If you want an accurate force, you can going to have to build in some adjustment.

--
JHG

 

[Darren2K4]

Accuracy is not critical, but I need to design in enough extra force so the total tolerance range meets the minimum of 22N. But since I want to minimize the force, higher accuracy is preferable.

 

[MintJulep]

Just cut an L out of the sheet, clamp it in a vise and start pushing on it with a a force gauge.

Change where it's clamped and where you push until the gauge reads 22, then go have a beer.

Any attempt at a simplified manual calculation will be an approximation, and I'm guessing you don't have access to FEA software since you're asking the question in the first place.

 

[Darren2K4]

@MintJulep
Yeah, I think my question is answered by the lack of answers--there's no clear formula that could be used to design this thing.

I'll follow your suggestion, although it's not quite that simple. Will require a little DOE to find the resultant force's relation to tolerances in each of the design parameters (dimensions and amount of deflection).

My company has a CAE department that handles all FEA. They have told me in the past that FEA is really only reliable for A-to-B comparisons of similar designs, not for designing to a specific stress or force. Not sure if they were only talking about plastic, though.

 

[dvd]

A couple of questions/comments that occurred to me:

1. is the spring designed to properties associated with low-end of sheet thickness tolerance, or high-end, or nominal?
2. what degree of cold-work is in the sheet; i.e. is this cold-rolled sheet or hot-rolled?
3. what is the range of cold-working in sheet bought to a specific condition?
4. there is varying degree of cold-work at the bend.
5. as usual, FEA is based on explicit geometry and material properties. Multiple studies required to cover range of tolerances and property variations.

 

[dvd]

... also, might consider perforating the beam to get better properties.

http://iperf.org/elastic.html

 

[chicopee]

Bipolarmoment's suggestion seems to be the way to go. It is simple and the math is well established in ME handbooks and technical literatures.

 

[Engdoitbetter]

Hello Darren2K4,

I'd suggest to treat the two beams as separate, considering their free body diagrams.

The vertical beam undergoes axial stress, the horizontal one bending and shear, while the beam-sheet joint undergoes shear and torque, which I believe to be the most likely cause of failure (at first sight) beacuse of the thin cross section.

Anyway, this is only an approximation since beam length has the same order of magnitude as the transverse dimension.

Even if you try to model the system as beams whose shear strain is not neglected (Timoshenko), you still have singularities at the joints, so in that case I would switch to FEA or experiment.

Regards,

Stefano

 

[JStephen]

The way it's drawn, it looks to me like deflection in the big flat plate with hole would be a lot more than deflection in the beam part. Unless there's some solid support right there at that point, which it doesn't look like there is.