However, there is another way to calculate the spring rate if you have a set of dial calipers handy. And… you don’t have to be a spring expert to use this method.
The rate formula is as shown.
R = Gd4/ 8NaD3
The components of the formula are basically the spring dimensions.
d = round wire diameter
Na = active coils (on a standard compression spring, the total coils minus 2)
D = mean diameter (outside diameter minus a wire size, or inside diameter plus a wire size)
“8” is a constant, a remnant from the numbers used in the original deflection formula—a nice round number
G = modulus of elasticity in torsion (for carbon steels and chrome alloys use 11,500,000 PSI—For 300 series stainless steel use 10,000,000 PSI)
So now, let us assume that you have a compression spring in front of you. You wield your calipers and yield the following measurements:
d = 0.250″
O.D. = 1.230″
(Therefore, D = 1.230″ n 0.250″ = 0.980″)
Total coils = 9.4
(Therefore, Na = 9.4 – 2 = 7.4)
Material is Chrome Silicon alloy
(Therefore, G = 11,500,000)
From all this data, we can now calculate the rate of the spring in pounds/inch.
Rate = 11,500,000 * 0.2504” / 8 * 7.4 * 0.9803
Rate = 44921 / 55.719
Rate = 806.222 pound for every inch of travel
Now that the spring rate is known, virtually any needed deflection for a given load can be determined, or a load for a given deflection can be found.
And, although any spring company can test the spring for rate in a common load tester, this calculation requires only a few measurements and a little keypad manipulation if you have calipers and a calculator.
What we do not know at this point is what is a safe deflection for this design. Any spring can be manufactured, but the stresses at a load height tells the story if the spring will take a set and require further processing. We discuss this step in the article “The Material Mix – What if I change to….”
By: Randy DeFord, Engineering Manager Mid-West Spring & Stamping