Originally Posted by ppro
I just don't see how the spring rate increases when the spring is cut and I am not getting any math or a practical example to support this.
Surely the book or practical experience you draw this from has more info?
F = spring force.
G = torsional modulus of the material.
d = wire diameter.
n = number of active coils.
D = mean (average) coil diameter.
Therefore the spring rate of a spring does not vary by length but it does vary by number of coils. The equation shows that spring rate has an inverse relationship to the number of coils.
In truth, the above equation is the simplified equation because it is only used to compare the spring rate between identical length springs. To more accurately reflect what is happening, one has to equate a coil spring to a torsion spring.
Apparently, a coil spring is equivalent to a torsion spring which has been wound up into a coil. Therefore, the true spring rate is equivalent to a coil spring flattened out into a torsion spring, which means the equation is actually k=G*d^4/L, which shows the same inverse relationship between spring length and spring rate.
(I only learned this recently while studying the subject, you and I discussing this inspired me to look it up - arguing is good for something
