Small background: for a project of mine I need to develop a (very light) conical spring.

While there are plenty resources out there for regular springs I really struggled to find anything on conical springs (non-linear and telescoping conical springs, to be precise).

Since the main constraint for my spring are its dimensions, I tried to calculate the wire diameter needed that can accomodate for compression force of around 5 cN.

After some digging I managed to find this paper and made some calculations according to it.

D_1 = 0.003 m    # upper mean diameter
D_2 = 0.011 m    # lower mean diameter
n = 10           # number of coils
H = 0.0055 m     # height of spring at rest
G = 79.3 GPa     # steel shear modulus
F_C = 0.05 N     # full compression force

$ F_C $ is the load for which the smallest active coil (with local spring diameter $ D_1 $) reaches its maximum deflection $ H $

$ F_C = \frac{Gd^4H}{8D_1^3n} $

Hence, $ d = \sqrt[4]{\frac{8F_CD_1n}{GH}} $

Given the inputs above, I calculated that wire diameter should equal approximately d = 0.12544 mm. (By the way if you can see it's wrong, I'd greatly appreciate some directions)

However, when I approached some manufacturers with these numbers, several of them said it could not be done.

Could you please tell me what kind of constraints are typically taken into consideration when manufacturing such springs?

Is it that it's impossible to create a spring of this shape that will hold its properties or are they simply lacking proper machinery?

  • $\begingroup$ For the record, Brown & Sharpe Gauge 36 wire would be 0.13mm in diameter, so it should be sufficient. Don't know if there are any technical complications in working with wire that thin, though. $\endgroup$
    – Wasabi
    Sep 4, 2018 at 3:24


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