Variable diameter springs do not have a constant diameter when measured across the length of the spring.
The variable diameter means that the spring does not follow Hooke’s law F=- kX
Where F = Force, k is the proportional constant and x is the change in length from the equilibrium.
The minus is there as the force we are talking about is the counter to the force of exertion. In other words it is a responsive force. “-k” the force within the spring, is countering “k” the force exerted on the spring.
The constant force spring is a resilient, rolled up spring that provides a constant and lasting force to the connection. A variable diameter spring, depending on how it is set up can provide either decreasing or increasing resistance to force as the spring is extended or compressed.
The helical nature of the spring means that each full diameter of a variable diameter spring fits inside the preceding diameter.
Within a battery compartment. There may be a pressure leaf or, more commonly to provide stronger force, a variable diameter spring. When placing a AA battery the positive end will often be pressed against a leaf, and the negative (flat) end will then be pushed into place against pressure from
High end mattresses may be sprung. Often having pocketed springs that compress to provide support for the sleeper. They also provide lateral flex so as not to resist movement of the sleeper and give even support regardless of the angle of compression.
Vehicle suspension systems. The ability for the spring to compress to a low height is an important consideration for some applications where space is at a premium.
The spring’s characteristic is determined by two factors. On one hand, by the minimum distance between two adjacent coils, for the unloaded spring, distance which decreases with increasing wire diameter.
On the other hand, by the coils’ deflection, which decreases with increasing wire diameter. Consequently, the actual distance between the adjacent coils represents the difference between the two sizes. As a result, the adjacent coils will successively touch each other, depending on the actual distance between them, and the spring stiffness will usually be increasing.