Compression springs deflect in a straight line, whether it might be vertical or horizontal. The amount of force they exert is based on physical dimensions like the wire diameter, outer diameter, free length, active coils (space in between active coils), and the material type used. Some springs may be very similar in shape or size but the force they exert and their elasticity depends on the proportion of all of the dimensions that make up the linear spring. This is due to stress factors like spring index or the proportion within the amount of coils (or space in between these coils) and the free length. If your spring has a tight index (a large wire diameter in proportion to the outer diameter), it is going to be under stress so it will be able to carry a significant load but might not be able to travel (or deflect) much. The same goes for when your spring has a long free length with very few coils. The opposite of these given examples (large index or many coils in proportion to the free length) gives you the opposite reaction because it’ll be under less stress: the spring will be able to deflect much more but it will not be very strong. The following formulas and examples will demonstrate how this works.
(This formula works for both compression and extension)
Spring index is the proportional ratio between your spring’s diameter and its wire diameter. To calculate spring index, you must subtract one wire diameter from the outer diameter. The result is what we call the mean diameter as shown in the diagrams. Then, you must divide the mean diameter by the wire diameter. The outcome of this calculation is your spring’s index. A 4:1 index is too tight while a 15:1 index is too loose so you want to make sure that you’re somewhere in between.
Formula for Spring Index:
Index = (Outer Diameter – Wire Diameter) ÷ Wire Diameter
I = (OD – WD) ÷ WD
Example: You have an outer diameter of 0.5” and a wire diameter of 0.05”.
I = (0.5 – 0.05) ÷ 0.05
I = 0.45 ÷ 0.05
I = 9
Spring rate derives from your spring’s working loads. Knowing the two values that make up your spring’s working loads will help you calculate how strong your spring needs to be in order to meet those working loads.
Formula for Spring Rate:
Rate = Load ÷ Travel
k = L ÷ T
Example: Your spring should travel 2” under a 15 lb. load.
k = 15 ÷ 2
k = 7.5