BIZOMAT MAKEOS · Springs
Square-Wire Compression Spring
What rate, load and stress does this square-wire compression spring have?
Rate, load at working length and torsional stress of a helical compression spring wound from square wire, using the handbook’s square-wire constants.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire side | mm | Side of the square wire (radial and axial thickness). |
| Mean coil diameter | mm | Mean coil diameter. |
| Active coils | coils | Active coils. |
| Shear modulus | GPa | Shear modulus of the wire. |
| Unloaded (free) length | mm | Length with no load. |
| Working length | mm | Installed or working length. |
| Allowable shear stress | MPa | Allowable shear stress for the material and duty. |
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 side
- What it is
- The side length of the square wire the spring is coiled from, equal to both its radial and its axial thickness in the coil.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 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 side, so small size changes matter.
- Get it right
- Measure the finished coil if possible: square wire bulges on the inside of the coil (keystoning).
What this means: Mean coil diameter
- What it is
- The mean coil diameter, measured to the centre of the wire: outside diameter minus one wire side, or inside diameter plus one wire side.
- 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 rate falls with the cube of D, so the load at the working length falls too.
- Get it right
- Do not enter the outside diameter; it overstates D and understates the rate.
What this means: Active coils
- What it is
- The number of coils that are free to deflect, not counting closed or ground end coils that sit against their neighbours.
- 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 8 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 is inversely proportional to the number of active coils.
- Get it right
- Count total coils minus the inactive end coils; the spring drawing or supplier states how many end coils are inactive.
What this means: Shear modulus
- What it is
- The shear modulus (modulus of rigidity) of the spring wire material, from the wire supplier or a spring materials standard.
- 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.
- Effect on the result
- The rate is directly proportional to G.
- Get it right
- Enter GPa; the shear modulus G is much lower than Young’s modulus E, so do not swap them.
What this means: Unloaded (free) length
- What it is
- The overall length of the spring standing free with no load on it.
- 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 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure on a flat surface without compressing the spring.
What this means: Working length
- What it is
- The length the spring is compressed to when installed or working; the deflection is the free length minus this length.
- 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 45 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter working length means more deflection, so more load and stress.
- Get it right
- It must not exceed the free length, and must stay above the solid length.
What this means: Allowable shear stress
- What it is
- The highest corrected shear stress allowed for this wire material, size and duty, from the spring wire supplier or a spring design standard.
- 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 600 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 limit than static duty; use the value for your duty.
Method and formulas
- Deflection F = 5.58 P N D³ ÷ (G a⁴), so rate = G a⁴ ÷ (5.58 N D³) (round wire uses 8 and d⁴).
- Uncorrected stress S = P D ÷ (0.416 a³).
- Corrected stress uses the Wahl factor reduced by about 4% for square wire.
- Example: 3 mm square wire at 20 mm mean diameter gives k = 17.986 N/mm and 269.8 N at 45 mm.
Limitations
- Square wire keystones (deforms) during coiling; the formulas assume a square section in the coil.
- Solid length and buckling as for round-wire springs.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check square-wire and die springs
- Compare square and round wire for the same space
- Specify a replacement spring
Who it is for
- Design engineers
- Spring buyers
- Toolmakers
What you get
- Spring rate
- Load at working length
- Corrected shear stress
- Spring index
Interpreting the result
- Square wire stores more energy than round wire in the same space but costs more.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 304–324. 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
More force in less space: square-wire and nested springs
What it covers: What to do when a round-wire spring will not fit: square and rectangular wire, nested pairs, load sharing, coil clearance and hand of winding, compared on one fixture.
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