BIZOMAT MAKEOS · Springs
Helical Extension Spring Check
What load and body stress will this extension spring have at its working extension?
Rate, load at extension including initial tension, and Wahl-corrected body stress of a round-wire helical extension spring.
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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. |
| Active coils | coils | Active body coils (hooks or loops are often counted as about one extra coil; follow the maker’s convention). |
| Shear modulus | GPa | Shear modulus of the wire material. |
| Initial tension | N | Initial tension wound into the spring, from the maker’s data or a load test (the load needed before coils separate). |
| Extension from free length | mm | Extension beyond the free length at the working position. |
| Allowable body shear stress | MPa | Allowable body stress for the material and duty; hooks usually limit extension springs. |
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 extension 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 1.6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rate rises with the fourth power of the wire diameter.
- 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 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rate falls with the cube of the mean diameter.
- Get it right
- Do not enter the outside or inside diameter; convert it to the mean first.
What this means: Active coils
- What it is
- The number of active body coils that stretch under load. Hooks or loops are not part of the body.
- Units and format
- Enter a number in coils: a number of coils. The form accepts 0.5 coils to 10000 coils. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 coils as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The rate falls in proportion as active coils increase.
- Get it right
- Makers sometimes count hooks as about one extra coil; follow the convention of your spring’s maker.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the wire material, 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 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 79.3 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter GPa, not MPa. Use the shear modulus, not the elastic (Young’s) modulus.
What this means: Initial tension
- What it is
- The initial tension wound into the spring: the load needed before the tightly wound coils start to separate.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It adds directly to the load at every extension.
- Get it right
- Take it from the maker’s data or a load test; the spring does not extend until this load is exceeded.
What this means: Extension from free length
- What it is
- How far the spring body is stretched beyond its free length at the working position.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 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
- The load above the initial tension rises in proportion to the extension.
- Get it right
- Use the extension from free length, not the total stretched length.
What this means: Allowable body shear stress
- What it is
- The highest shear stress the spring body 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 650 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Hooks and loops usually fail first and are not checked here; confirm them with the maker.
Method and formulas
- Rate k = G d⁴ ÷ 8D³Na.
- Load F = Fi + k x.
- Body stress τ = K × 8FD ÷ πd³ with the Wahl factor K; initial-tension stress τi = 8Fi D ÷ πd³ (uncorrected).
- Example: the default spring has k = 1.8797 N/mm and carries 56.993 N at 25 mm extension.
Limitations
- Hook and loop stresses are not calculated and usually govern failure; check them with the maker.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a return or counterbalance spring
- Specify initial tension and rate
- Compare spring options
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Spring rate
- Load at the working extension
- Body shear stress
- Stress from initial tension
Interpreting the result
- Compare the initial-tension stress with the range your spring maker can achieve for the index.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 325–332. 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
Extension springs: initial tension and the hooks that break
What it covers: How to check an extension spring: rate and initial tension, body stress, bending and torsion at the hooks, natural frequency, and why the hook bend radius decides its life.
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.