BIZOMAT MAKEOS · Springs
Nested Compression Spring Check (Load Share, Stresses, Solid Length, Clearance)
If I nest an inner spring inside an outer one, what load does the pair give at the working length, how is it shared, are both springs within stress, and do they fit together?
Check of two helical compression springs nested one inside the other and compressed together: each spring’s rate, load and corrected shear stress at the working length, solid length and stress at solid (as the compression spring tool), the combined rate and load share in parallel (as the springs in series or parallel tool), the radial clearance between the inner spring’s outside and the outer spring’s inside, and the total load against what you need.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Outer spring | ||
| Wire diameter | mm | Wire diameter of the outer spring. |
| Mean coil diameter | mm | Mean coil diameter of the outer spring. |
| Active coils | coils | Active coils of the outer spring. |
| Inner spring | ||
| Wire diameter | mm | Wire diameter of the inner spring. |
| Mean coil diameter | mm | Mean coil diameter of the inner spring. |
| Active coils | coils | Active coils of the inner spring. |
| Common | ||
| End type (both) | choice | End type of both springs. |
| Shear modulus | GPa | Shear modulus of the spring wire. |
| Unloaded length (both) | mm | Unloaded length of both springs (equal unloaded lengths share the deflection). |
| Working length | mm | Length both springs are compressed to. |
| Allowable shear stress | MPa | Allowable corrected shear stress of the wire. |
| Load needed at the working length | N | Total load the pair must give at the working length. |
| Least radial clearance between springs | mm | Least radial gap between the inner spring’s outside and the outer spring’s inside. |
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.
Outer spring
What this means: Wire diameter
- What it is
- The diameter of the wire the outer (larger) spring is wound from, measured with a micrometer on a straight part of a 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 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rate rises with the fourth power and stress falls with the cube of wire diameter, so small changes matter.
- Get it right
- Wire diameter, not coil diameter.
What this means: Mean coil diameter
- What it is
- The mean coil diameter of the outer spring: the diameter of the circle through the centre of the wire, equal to 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 32 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rate falls with the cube of the mean diameter; it also sets the room for the inner spring.
- Get it right
- Use the mean diameter, not the outside or inside diameter.
What this means: Active coils
- What it is
- The number of coils of the outer spring that are free to deflect, excluding the closed end coils that do not flex.
- Units and format
- Enter a number in coils: a number of coils. The form accepts 0.5 coils to 1000 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
- Rate is inversely proportional to active coils.
- Get it right
- Do not count the dead end coils; total coils are worked out from the end type.
Inner spring
What this means: Wire diameter
- What it is
- The diameter of the wire the inner (smaller) spring is wound from.
- 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 2.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rate rises with the fourth power and stress falls with the cube of wire diameter.
- Get it right
- Wire diameter of the inner spring, not its coil diameter.
What this means: Mean coil diameter
- What it is
- The mean coil diameter of the inner spring: outside diameter minus one wire diameter. Its outside must clear the inside of the outer spring.
- 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
- Rate falls with the cube of the mean diameter, and a larger value reduces the radial clearance.
- Get it right
- Use the mean diameter, not the outside diameter.
What this means: Active coils
- What it is
- The number of active coils of the inner spring, the coils free to deflect, excluding closed end coils.
- Units and format
- Enter a number in coils: a number of coils. The form accepts 0.5 coils to 1000 coils. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 coils as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rate is inversely proportional to active coils.
Common
What this means: End type (both)
- What it is
- How the ends of both springs are finished. It sets how many inactive coils are added to the active coils and therefore the solid length.
- Units and format
- Choose one of 4 options from the list: Closed and ground (squared and ground); Closed, not ground; Plain and ground; Plain (open).
- Example
- The form opens with “Closed and ground (squared and ground)” selected as a worked example. Choose the option that matches your case.
What this means: Shear modulus
- What it is
- The shear (torsional) modulus of the spring wire material, from the wire supplier’s data sheet or a spring 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
- Both spring rates, and so the loads, rise in proportion to it.
- Get it right
- This is in gigapascals; do not type a value in megapascals.
What this means: Unloaded length (both)
- What it is
- The free length of the springs with no load. The tool assumes both springs have the same free length, so they deflect together.
- 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 80 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer free length means more deflection to the working length, so more load and stress.
- Get it right
- If the free lengths differ, one spring starts working before the other and this check does not apply.
What this means: Working length
- What it is
- The length both springs are compressed to in service, such as the installed length with the valve or die closed.
- 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.
- Effect on the result
- A shorter working length raises the deflection, load and stress.
- Get it right
- It must be longer than the solid length of both springs.
What this means: Allowable shear stress
- What it is
- The largest Wahl-corrected shear stress you accept in the wire, from the wire supplier, a spring standard or your design rules for the material and duty.
- 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 700 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The comparison uses the corrected stress (with the Wahl factor), so use an allowable stated on that basis.
What this means: Load needed at the working length
- What it is
- The total force the nested pair must give at the working length, from the design of the valve, die or mechanism.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the springs; it sets the pass or fail of the load check.
What this means: Least radial clearance between springs
- What it is
- The smallest radial gap you accept between the outside of the inner spring and the inside of the outer spring, so the coils do not rub or tangle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is a radial gap (one side), not a diametral difference.
Method and formulas
- k = G d⁴ ÷ 8 D³ N_a; F = k (L₀ − L_w); τ = K 8 F D ÷ π d³ with the Wahl factor K (as the compression spring tool).
- Parallel rate = k_outer + k_inner; each spring carries its own k × deflection (as the springs in series or parallel tool).
- Radial clearance = [(D_o − d_o) − (D_i + d_i)] ÷ 2; solid length from total coils × wire diameter.
- Example: the pair gives 274.27 N (outer 193.6 N, inner 80.668 N); stresses 291.86 and 311.32 MPa; radial clearance 2.75 mm.
Limitations
- Equal unloaded lengths; unequal lengths make one spring act first.
- Static load; fatigue and buckling of the inner spring need separate checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Increase spring force in a fixed space
- Check a nested valve or die spring pair
- Balance stresses between inner and outer springs
Who it is for
- Design engineers
- Toolmakers
- Spring designers
What you get
- Rate, load and stress of each spring
- Combined rate, total load and share
- Solid length and radial clearance
Interpreting the result
- Wind the inner and outer springs in opposite hands so the coils cannot tangle.
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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Open the Nested Compression Spring Check (Load Share, Stresses, Solid Length, Clearance) calculator