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.
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
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
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
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RE: Flat Spring thickness/Spring Rate
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.
RE: Flat Spring thickness/Spring Rate
RE: Flat Spring thickness/Spring Rate