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Flat Spring thickness/Spring Rate

Flat Spring thickness/Spring Rate

Flat Spring thickness/Spring Rate

(OP)
I am looking to come up with a relationship between the thickness of a flat spring and the resultant spring rate.  For this example, we will assume that width, length, and spring deflection are constant.  The material properties of the flat spring is:

UNS G10950 (Pretempered Spring Steel) being stress relieved after forming.  Finish to be black oxide.

Obviously, increasing flat steel thikcness increases the spring rate (lb/in), but looking for a formula that relates the two.  I've looked into leaf spring calculators but am not confident that leaf springs and flat springs would produce the same results.

RE: Flat Spring thickness/Spring Rate

Can't you just use simple beam theory from a mechanics of materials book? It seems straightforward enough, P=kx, where k is the spring rate and x is the lateral displacement.

The type/temper of the steel should not matter much if it is in the elastic range. That is, the elastic modulus of steel is about 30Msi.

Brian
www.espcomposites.com

RE: Flat Spring thickness/Spring Rate

Depends on the configuration.

e.g. if you have a cantilevered (///) rectangular plate, then the spring constant is
                                 F
K=Ebt^3/4L^3       ///____________

E modulus of elasticity         
b width of plate    
L  length of plate
t thickness

If the plate is pin connected on both ends and the deflection is
                        F
in the center   ______________
K=4Ebt^3/L^3     ^             ^
              
Thus for almost any configuration, the spring constant varies directly as the cube of the thickness.

As pointed out, heat treatment and stain relief does not affect E and thus does not affect K.



 

RE: Flat Spring thickness/Spring Rate

zekeman,

   Be careful.  Double Integration method is only accurate for small deflections.  One of my textbooks defines this as less than 10% of the length.  

   A quick glance at my SAE Spring Design Manual shows signs of double integration, but I did not read carefully.  It is time for a careful reading of your mechanics of materials text on beam theory.

               JHG

RE: Flat Spring thickness/Spring Rate

If a beam is wide and flat, there is an adjustment required to the regular beam deflection equations.  These assume that the tension and compression faces are unrestrained laterally.  In a wide thin plate, they are tied together.  If I remember correctly, it is a (1-nu^2) factor that gets involved as the correction.

 

RE: Flat Spring thickness/Spring Rate

If your application is similar to a reed valve, I recommend measuring the force vs deflect.  FEA is not likely to help much, unless you have small deflections.  Also, in measuring and in FEA - make sure your force measurement is perpendicular to the surface (which is rotating in the case of a reed valve opening and closing).

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