This is how I made my own springs!
I needed stronger return springs for my press, so I made them!
To start out, I created a spreadsheet to calculate the spring diameter and coils required to at least double the spring rate of the old spring, using .105" spring wire that I had laying around. I also checked the spring stress at max extension to make sure my spring wouldn't get "over-stretched" in use.
Once I had some ballpark dimensions, I grabbed a piece of bar stock that was close to the desired spring I.D. and drilled a cross hole through it to use as a mandrel. I also made a tool post guide from bar stock to help feed the wire. I chucked the mandrel in the lathe spindle, ran the wire through the guide and cross hole, and started turning by hand.
After each coil, I advanced the carriage by about .100", although I did it more by look and feel than anything. On a geared manual lathe, you can set your pitch and run it like you would for thread cutting, which would have been a lot easier. This was a pretty big spring, so there was a lot of torsional resistance and it took a while.
Some things to keep in mind that the calculations don't tell you: the spring will want to "uncoil" a bit, so your finished diameter will be a little bit larger than expected. With a 0.750" mandrel and 0.105" wire diameter, I ended up with a final O.D. of 1.085", not 0.960". The total length with also shrink slightly as you lose a few coils. Mine went from about 5.00" to 4.65". This can all be compensated for with a smaller mandrel and some extra coils, but I wasn't really too worried about it for my application.
Here are the formulas used:
P = (GFd^4)/(8ND) and S = PD/(0.393d^3)
where P is force, G is shear modulus (109,000,000 psi for steel) F is deflection in inches, d is wire diameter, N is number of coils (or desired length divided by wire diameter), D is mean diameter (I.D. + d), and S is the torsional stress in the wire in psi.