KEVOS® MAKEOS · Springs
Helical Torsion Spring Check
How far will this torsion spring wind, how highly stressed is it and will it still fit its arbor?
Angular deflection, rate, bending stress (with the inner-fibre correction factor) and reduced coil diameter of a round-wire helical torsion spring under a moment.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire diameter | mm | Wire diameter. |
| Mean coil diameter | mm | Mean coil diameter = outside diameter − wire diameter. |
| Body turns | turns | Number of body coils (turns), excluding the legs. |
| Elastic modulus | GPa | Elastic (tensile) modulus of the wire (about 207 GPa for spring steel). |
| Load at arm | N | Force applied at the end of the arm. |
| Moment arm (load to coil axis) | mm | Perpendicular distance from the load to the coil axis. |
| Arbor diameter (0 = none) | mm | Diameter of the pin the spring winds onto; 0 if none. |
| Allowable bending stress | MPa | Allowable bending stress for the wire and duty, from the spring maker or design data. |
Method and formulas
- Moment M = F × arm. Deflection θ = 64 M D Nb ÷ (E d⁴) radians (legs not included).
- Rate = E d⁴ ÷ 64 D Nb per radian; × 2π per turn.
- Stress σ = Ki × 32M ÷ πd³ with Ki = (4C² − C − 1) ÷ 4C(C − 1).
- Wound mean diameter D′ = D Nb ÷ (Nb + θ/2π); inside diameter = D′ − d.
- Example: 20 N on a 25 mm arm winds the default spring 66.43° with σ = 687.9 MPa.
Limitations
- Leg deflection and coil friction are ignored; some references increase the deflection by about 6% for friction (constant 10.8 instead of 10.19 per turn).
- Load must wind the spring (close the coils); unwinding loads raise stress.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check hinge, lid and return torsion springs
- Choose an arbor that will not bind
- Specify rate per turn
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Moment and angular deflection
- Rate per radian and per turn
- Corrected bending stress
- Inside diameter after winding and arbor clearance
Interpreting the result
- Keep about 10% diametral clearance between the wound inside diameter and the arbor.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 333–343. Topic reference; no source tables or recommended settings are reproduced.
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