Originally Posted by
Jonny5
Ok, so I had it right earlier, but was second guessing myself. The formula to calculate a dual spring rate is (a x b)/(a + b). So, for example we have a 10 and a 20 lb spring. (10x20)/(10+20) is 200/30= 6.67lb/in. Seems odd that the combined rate is less than the effective rate of each spring individually, but that's how it works.
For simplicity sake, assume you have two 10 lb/in springs. Assuming you apply a 10 force to one of the springs, it will compress 1 inch. Now stack them, and apply that same 10 lb force. The bottom spring now has 10 additional pounds on it so it compresses 1 inch. The top spring also has 10 additional pounds of force on it so it compresses 1 inch. This means your stack compressed 2 inches from 10 pounds of force which is a 5 lb/in equivalent.
This is why a longer spring that is wound exactly the same as a shorter one will be softer. Each coil deflects the same amount for a given load, but you have more coils on the longer spring so your total deflection is greater.
Using your example above and applying 10 pounds of force, you get the 1 inch from the 10 lbs/in spring and 0.5 inches for the 20 lbs/in spring for a total of 1.5 inches which you correctly calculated as 6.67 lbs/in.
Where dual rate springs react differently that simply using a single spring is when the softer spring exceeds its ability to compress linearly (overly simplified: it gets flattened and can't compress anymore), then any additional force is only compressing the stiffer spring. In the 10/20 lbs/in example you get 6.67 lbs/in until the 10 lb spring fully compresses, then you get 20 lbs/in. It is not quite that linear in the real world, but this should give you an understanding of what is going on.
-Chocula