Flat Spring thickness/Spring Rate

[kevc70]

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.

 

[ESPcomposites]

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

http://www.espcomposites.com

 

[zekeman]

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.

 

[desertfox]

Hi this might help:-

http://www.roymech.co.uk/Useful_Tables/Springs/Springs_Leaf.html

 

[drawoh]

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

 

[JStephen]

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.

 

[JustinMEEE]

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).