What Factors Affect the Value of Spring Constant?

[A Dhingra]

hello everyone!

can you please explain on factors the value of spring constant depends?
And please provide me with the required maths to get to that idea..

Thanks..

 

[Philip Wood]

I assume you have in mind a helical spring. The main process involved in stretching such a spring is twisting the wire of which it is made. The torque needed to twist the wire through a given angle is proportional to r⁴ in which r is the radius of the wire, and is also proportional to the rigidity modulus, n, of the wire. Provided the turns of the spring remain almost at right angles to the longitudinal axis of the spring, then the spring constant is given approximately by
$$k = \frac{\pi r^4 n}{2 a^2 L}$$
in which $a$ is the radius of a turn of the spring and $L$ is the length of the wire from which the spring is made.

 

[A Dhingra]

Hence the springiness of a helical spring is only due to the energy stored as potential due to the application of torque to twist the wire. Is it correct? or there is something more to it?

Thanks a lot..

 

[Philip Wood]

There is also extension due to the bending of the wire (as the wire is effectively a compacted cantilever). This bending is inversely proportional to the Young's modulus. The geometry of the spring is usually such that this component of extension is smaller than that due to the wire twisting.

Champion & Davy treat springs in their 'Properties of Matter' (no doubt long out of print - it was beginning to look old fashioned in the late 1960s!) No doubt mechanical engineering textbooks would be a good bet.

 

[A Dhingra]

Thanks a lot.
one more request, i tried looking up for a derivation of this formula on Google but could not find it. Can u suggest me a required link for the same or some book to refer this from.

 

[Philip Wood]

I know of two 'Properties of matter' books that deal with springs.
'Properties of Matter' by Champion & Davy published by Blackie in the UK.
'The General Properties of Matter' by Newman & Searle published by Arnold in the UK.

These books are (long?) out of print, but they still seem to be available quite cheaply secondhand on the internet.

And, as I said before, I'd guess that springs are still treated in some engineering textbooks.

 

[A Dhingra]

Ok Thanks a lot...