Ask help for Cantilever spring design

[zhutao73]

Hello

I am an electrical engineer however have to design a cantilever suspension system even though I do not know much about the spring design.

Please look at the attached sketch. I use a flat spring (beam) to suspend an inertial mass to sensoring the ground motion. The beam is intially made of berrylim copper (c17200) solution annealed (TB00). Then the beam is pre-bent to a deflection of D at the end of beam (or a radius of R). Then it is heat treated hardened and acquire the elasticity.

The beam is fixed on the ground at one end. The other end is loaded with an inertial mass. When the beam is loaded, it is desirably the beam is flat.

Evidentally, the larger the pre-bend deflection D (i.e. the smaller the pre-band radius of curveture) of the beam, the more inertial mass M the beam can support when it is loaded to flat position.

My QUESTION is: what is the maximum deflection D (the minimum radius R) that I can pre-bend the beam (giving the beam dimensions)before the heat treatment, such that after hardening, the spring will work properly around flat position and would not fail due to the excessive stress?

Thank you a lot in advance

Tao

 

[PaulPepka]

First I want to say I don’t have much experience with cantilever springs, so if someone else replies with more history defer to them, but that said here is what I found.
If you want fixed predetermined Mass then I think you should expect several trials to get the final result.
Your need appears to fall under the category of a “Cantilever beam with large deflection”, because you will start with a beam largely bent (deflected) then deflect it approximately straight. Straight beams, slightly deflected are better predicted as a normal application, so things will not easily adapt to you needs.
The Radii you asks for is unfortunately a complex relation, calculated (thickness to the 3rd exponent, length to the 2nd exponent, then the width of the bar and the force), then a factor derived from the chart to give you the deflection.
If you could give me your mass and an idea of the length you need, I will look at the formula and charts and show you what I find.
If you want to have control and be able to do a lot of calculations and math work to reduce the number of trials then:
The only source I had on the shelf with relevant formulas was “Mechanical Springs” (a.m. Wahl 1963, 1983,or 1991), It’s listed available at SMIhq.org website for less than $100 USD. If you want the ability to crunch out your own design. I would offer the design formula but it’s actually reliant on a charted set of Curves from a source called “Quart. Appl. Math” (vol3 no3 p272-275 1945). I also should mention all the information is for a straight bar that is deflected into the bent form. You would have to manipulate the math because you would be using it “backwards” to the expectations. I also would expect using it backwards to actually give you more force and higher stresses than the calculations. I’m sorry to say that I can only guess, my gross guess would be 20-30% more force & stress.
The material is sold by thickness, then width, in long lengths so you 1st step is to pick (for calculation) a material thickness that relates to the length and mass you need. The smaller you keep your thickness the more sensitivity to motion you get, but the length of your material can also be adjusted longer to give you more sensitivity.
If you can mathematically choose the thickness and width then you could make a modest-aggressive bend to a very long piece. Then mount it for a test, adjusting your hanging mass and the length you hang the mass until you get it level.
Paul Pepka

 

[zhutao73]

Thank you Paul

Your information is helpful. I think I really need to get the book you mentioned. It should help a lot.

Tao

 

[PaulPepka]

Sure I understand.
It’s a good book, but it just occurred to me though that I would feel bad if you got the book just to find out you don’t have enough space. So if you have size constraints, I would be happy to calculate a sample to check for rough fit.
Other info you might need from another SMI source is:
Emod. Of beryllium copper is listed as 16-18.5 x10^6 psi or (111-128 MPa x 1000)
Tensile Strength of C17200 is 110 ksi Nominal
Don’t forget about the extra safty factor for ‘backword’ use.
I set this to email me to keep me informed, so let me know if I can help with anything.

If you’re not in a real urgent need you might wait a bit and see if someone else has better info then I, had.

Paul

 

[desertfox]

Hi zhutao73

I very much doubt you will get a spring bent as you have shown, which will then unfold to a straight position afterwards.
What you might be able to do is bend a flat spring up and then when the load is applied the spring will deflect to make the load perfectly vertical.

desertfox