Helical Spring Design
How stiff is a coil spring, how far does it compress under a load, and how hard is the wire working? Combine several springs in series or in parallel.
Inside a Coil Spring
A coil spring is really a twisted wire: pushing on it turns the wire and puts it in shear. Its stiffness grows with the fourth power of the wire diameter but falls with the cube of the coil diameter — a slightly thicker wire makes a much stiffer spring.
Springs side by side (parallel) share the load and add up their stiffness; springs end to end (series) each carry the full load, so the set becomes softer. Never compress a spring to coil bind, where the coils touch and the stress jumps.
Force vs. Compression
N/mmKey Relations
From the twisting of the wire. With G = 79.3 GPa, d = 2 mm, D = 16 mm and 8 coils: k = 4.84 N/mm.
The Wahl factor KW adds the direct shear and the extra stress on the inside of the curved wire.
Parallel springs share the force; springs in series share the deflection.
The work done compressing the spring.
Sources & Verification
- R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — Ch. 10 (Mechanical Springs).