Torsion Spring Calculator

Inputs

View results
Diameter of the spring wire.
mm
Center-to-center across the coil (outside diameter − wire diameter).
mm
Number of active body coils that wind up under load.
coils
Torque applied about the coil axis to wind the spring.
N·m
Music wire ≈ 207 GPa, stainless ≈ 193 GPa.
GPa

Results

Default result
Edit inputs
Deflection angle (θ)
140.9 °

Wind-up under the applied moment.

Also computed

Max bending stress (σ) 1,376 MPa

At the inner fibre of the wire.

Spring index (C) 10

Rate per turn (R) 2.556 N·m

Moment per 360° turn.

Method notes 4 notes
  • A torsion spring is loaded in bending, so the rate uses Young’s modulus E (not the shear modulus G) and the bending Wahl factor Kb (not the shear Kᵥᵥ of a compression spring).
  • Rate per turn R = E·d⁴ / (10.8·D·Nₐ); the deflection is the applied moment divided by the rate, in turns.
  • The peak bending stress σ = Kb · 32·M / (π·d³) occurs at the inner fibre of the wire; as the spring winds up the body coils tighten and the inside diameter shrinks.
  • Static load; ignores fatigue, set and stress relaxation. The arm leverage and end effects are not modelled.

Powered by MachineCalcs ↗