BIZOMAT 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. |
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 coiled from, measured with a micrometer or taken from the specification.
- 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 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 with the cube of the wire diameter and deflection with its fourth power.
- Get it right
- Measure the wire itself, not the coil.
What this means: Mean coil diameter
- What it is
- The mean coil diameter: the diameter of the circle through the centre of the wire, equal to the outside diameter minus one wire diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 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.
- Effect on the result
- The angular deflection rises in proportion to the mean diameter.
- Get it right
- Do not enter the outside or inside diameter; convert it to the mean first.
What this means: Body turns
- What it is
- The number of body turns in the coil, not counting the straight legs.
- Units and format
- Enter a number in turns: a number of turns. The form accepts 0.5 turns to 10000 turns. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 turns as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The angular deflection rises in proportion to the body turns.
- Get it right
- Count turns of the body only; leg deflection is not included in the result.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the wire material, because a torsion spring’s wire works in bending. From the spring maker or material data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 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.
- Get it right
- Enter GPa. Use the elastic modulus, not the shear modulus used for compression springs.
What this means: Load at arm
- What it is
- The force applied at the end of the spring arm, at right angles to the arm, that winds the spring.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 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, deflection and stress all rise in proportion to the force.
- Get it right
- The load should wind the coils tighter; an unwinding load raises the stress beyond this model.
What this means: Moment arm (load to coil axis)
- What it is
- The moment arm: the perpendicular distance from the line of the applied force to the coil axis.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 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, deflection and stress all rise in proportion to the arm.
- Get it right
- Measure to the coil axis, not to the edge of the coil.
What this means: Arbor diameter (0 = none)
- What it is
- The diameter of the pin or arbor the spring fits over. As the spring winds up its inside diameter shrinks, and the tool checks it still clears the arbor. Zero skips the check.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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
- Measure the actual pin; the tool wants a 10 % clearance between the wound inside diameter and the arbor.
What this means: Allowable bending stress
- What it is
- The highest bending stress the wire may reach for its material and duty, from the spring maker or design data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 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
- Fatigue duty needs a lower allowable than static duty; use the maker’s value for your case.
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.
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.
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