KEVOS® MAKEOS · Springs
Torsion Spring Designer (Angle, Stress, Legs and Arbor)
How far will this torsion spring wind under the load, is the bending stress within the allowable, and will it still clear the arbor when wound up?
Design check of a helical torsion spring: the moment from the load and arm, angular deflection including the bending of straight legs (as extra active coils), rate per radian and per turn, bending stress with the inner-fibre curvature factor (as the torsion spring tool), the largest angle before the allowable stress is reached, the coil diameter and body length after windup, and the clearance over the arbor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire diameter | mm | Diameter of the spring wire. |
| Mean coil diameter | mm | Mean diameter of the coils. |
| Body coils | Number of coils in the body. | |
| Length of leg 1 (load leg) | mm | Length of the leg the load acts on. |
| Length of leg 2 (fixed leg) | mm | Length of the leg that is held. |
| Elastic modulus | GPa | Elastic modulus of the wire. |
| Load at the arm | N | Load applied at the arm. |
| Moment arm | mm | Distance from the spring axis to the load. |
| Arbor diameter (0 = none) | mm | Diameter of the rod the spring winds onto (0 if none). |
| Allowable bending stress | MPa | Allowable bending stress for the wire and duty (your value from the spring maker). |
| Least arbor clearance (share of arbor diameter) | % | Least clearance you want between the wound inside diameter and the arbor, as a share of the arbor diameter. |
Method and formulas
- Moment M = F × arm; equivalent active coils N_a = N_b + (L₁ + L₂) ÷ (3πD) for straight legs.
- Angle θ = 64 M D N_a ÷ (E d⁴) radians; rate = M ÷ θ.
- Bending stress σ = K_i 32 M ÷ (π d³), K_i = (4C² − C − 1) ÷ [4C(C − 1)], C = D ÷ d (as the torsion spring tool).
- Wound mean diameter D′ = D N_b ÷ (N_b + θ_body ÷ 2π); inside diameter = D′ − d; body length ≈ d (N_b + 1 + θ_body ÷ 2π).
- Example: 20 N on a 25 mm arm winds the spring 69.367° at 687.9 MPa; the wound inside diameter is 17.403 mm.
Limitations
- Static design stress; fatigue needs the stress range and the maker’s fatigue data.
- Load in the direction that winds the coils tighter; unwinding loads need a lower allowable.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a return spring for a hinge, lever or lid
- Check that a wound-up spring still clears its arbor
- Find the safe working angle of a spring
Who it is for
- Design engineers
- Spring buyers
- Product designers
What you get
- Moment, angle and rate
- Bending stress and largest safe angle
- Wound diameter, body length and arbor clearance
Interpreting the result
- Long legs add deflection: shorten them for a stiffer spring rather than adding wire size.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 333–343. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Torsion Spring Designer (Angle, Stress, Legs and Arbor) calculator
