BIZOMAT 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.
Open the calculatorRuns in your browser. No account needed.
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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Wire diameter
- What it is
- The diameter of the round wire the torsion spring is wound from, measured with a micrometer across the wire.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress falls roughly with the cube of wire diameter and the wind-up angle with its fourth power.
- Get it right
- Measure the wire, not the coil; the wire size enters the wind-up angle to the fourth power.
What this means: Mean coil diameter
- What it is
- The diameter of the coils measured to the centre of the wire: outside diameter minus one wire diameter. The coils close down from it as the spring winds up.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not enter the outside or inside diameter; mean diameter = outside diameter − wire diameter.
What this means: Body coils
- What it is
- The number of complete turns in the coiled body of the spring, not counting the legs. Count the turns from one leg to the other, including any part turn.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 200. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More body coils give a larger wind-up angle for the same load; the stress does not change.
What this means: Length of leg 1 (load leg)
- What it is
- The length of the straight leg the load acts on, from the coil body to its end. Long legs bend too, so the tool adds them as extra active coils.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer legs add to the wind-up angle; the bending stress in the body does not change.
- Get it right
- Enter 0 if the leg is very short or the load acts right at the body.
What this means: Length of leg 2 (fixed leg)
- What it is
- The length of the straight leg that is held fixed, from the coil body to where it is supported. It also flexes and adds to the active coils.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer fixed leg adds to the wind-up angle; the body stress does not change.
What this means: Elastic modulus
- What it is
- The tensile (Young’s) modulus of the spring wire, from the wire supplier or a spring materials standard. A torsion spring bends its wire, so this modulus applies.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 300 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 207 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The wind-up angle is inversely proportional to the modulus; the stress does not change.
- Get it right
- Use the elastic modulus, not the shear modulus used for compression and extension springs; GPa, not MPa.
What this means: Load at the arm
- What it is
- The force applied at the end of the moment arm that winds the spring up. With the arm it sets the moment on the spring.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moment, bending stress and wind-up angle rise in proportion.
- Get it right
- Use the force component square to the arm; a force at an angle to the arm gives less moment.
What this means: Moment arm
- What it is
- The distance from the spring’s coil axis to the line along which the load acts, so that moment = load × arm.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moment, bending stress and wind-up angle rise in proportion.
- Get it right
- Measure from the coil axis, not from the edge of the coils.
What this means: Arbor diameter (0 = none)
- What it is
- The diameter of the rod or pin the spring fits over. The coils close down as the spring winds up, so the wound inside diameter must stay clear of it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 when there is no arbor; the clearance check is then skipped.
What this means: Allowable bending stress
- What it is
- The bending stress you allow in the wire at this load, from the spring maker or a spring design standard, for the wire grade and duty.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 4000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The tool assumes the load winds the coils tighter; a load that unwinds them needs a lower allowable.
What this means: Least arbor clearance (share of arbor diameter)
- What it is
- The least gap you want between the wound inside diameter and the arbor, expressed as a share of the arbor diameter.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 50%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A share of the arbor diameter, not of the wire or coil diameter; type 10 for 10 %.
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.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Torsion springs and counterbalanced lids
What it covers: How helical torsion springs work and how to check one: bending stress, wind-up angle, legs and arbor clearance, and balancing a hinged hatch over its whole opening.
BIZOMAT 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