BIZOMAT MAKEOS · Springs
Compression Spring Fatigue Check (Working Stroke, Goodman Factor)
Will this compression spring survive millions of cycles between its preload and working lengths, by the Goodman criterion and against first-cycle yield?
Fatigue check of a helical compression spring cycling between two lengths: rate, loads and corrected shear stresses at the preload and working lengths and the solid length (as the compression spring tool), the alternating and mean shear stresses, and the Goodman, Soderberg and Gerber factors with first-cycle yield (as the Goodman fatigue tool, using the torsional endurance limit, ultimate and yield of the wire), against your required factor.
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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. |
| Active coils | coils | Active coils. |
| End type | choice | End type of the spring. |
| Shear modulus | GPa | Shear modulus of the wire. |
| Unloaded length | mm | Length with no load. |
| Preload (longest working) length | mm | Length at the smallest working load (preload). |
| Working (shortest) length | mm | Length at the largest working load. |
| Wire strength (torsional) | ||
| Torsional endurance limit (corrected) | MPa | Torsional endurance limit of the wire, corrected for surface finish and shot peening (from your spring data). |
| Torsional ultimate strength | MPa | Torsional ultimate strength of the wire (often about 0.67 × tensile). |
| Torsional yield strength | MPa | Torsional yield strength of the wire. |
| Required fatigue safety factor | Safety factor you need against fatigue. | |
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 spring wire, measured with a micrometer across the wire, not across 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 2 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 of wire diameter, so small changes matter.
What this means: Mean coil diameter
- What it is
- The mean coil diameter: the outside coil diameter minus one wire diameter, measured to the centre line of the wire.
- 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 16 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 coil diameter.
- Get it right
- Use the mean diameter, not the outside diameter; subtract one wire diameter from the outside diameter.
What this means: Active coils
- What it is
- The number of coils that deflect under load, excluding the inactive end coils that rest on the spring seats.
- 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 the number of active coils.
- Get it right
- Do not enter total coils; the tool adds the end coils from the end type to get the solid length.
What this means: End type
- What it is
- How the spring ends are formed; the tool uses it to work out the total coils and the solid length, which the working length is checked against.
- 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 or a spring design 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
- Rate is proportional to the shear modulus.
- Get it right
- Enter GPa, not MPa: the tool multiplies by 1000 internally.
What this means: Unloaded length
- What it is
- The overall length of the spring standing free with no load on it, the reference for both working deflections.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Preload (longest working) length
- What it is
- The length of the spring in its installed position at the lowest working load, the longest length it reaches in each cycle.
- 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 42 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be no more than the unloaded length and more than the working length, or the tool rejects it.
What this means: Working (shortest) length
- What it is
- The length of the spring at full working deflection, the shortest length it reaches in each cycle.
- 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 35 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must stay above the solid length the tool calculates from the coils, end type and wire diameter.
Wire strength (torsional)
What this means: Torsional endurance limit (corrected)
- What it is
- The torsional endurance limit of the wire for infinite life, already corrected for surface finish and shot peening, from spring wire data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 310 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the torsional (shear) value, not the tensile endurance limit of the material.
What this means: Torsional ultimate strength
- What it is
- The ultimate shear strength of the spring wire, which fixes the mean-stress end of the Goodman line.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1100 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a torsional value; if your data gives tensile strength, convert it with the relation in your spring standard.
What this means: Torsional yield strength
- What it is
- The torsional yield strength of the spring wire, used for the first-cycle yield check and the Soderberg factor.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 800 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Required fatigue safety factor
- What it is
- The least fatigue safety factor you accept for the spring; the governing value is the lower of the Goodman and first-cycle yield factors.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- k = G d⁴ ÷ 8 D³ N_a; F = k (L₀ − L); τ = K 8 F D ÷ π d³ with the Wahl factor (as the compression spring tool).
- τ_a = (τ₂ − τ₁) ÷ 2; τ_m = (τ₂ + τ₁) ÷ 2.
- Goodman n = 1 ÷ (τ_a ÷ S_es + τ_m ÷ S_us); yield n = S_sy ÷ (τ_a + τ_m) (as the Goodman fatigue tool).
- Example: the spring cycles between 233.49 and 437.8 MPa; Goodman factor 1.5757.
Limitations
- Wahl factor applied to both mean and alternating stress (conservative).
- Infinite-life criteria; surge and resonance at high speed need a separate check.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a valve, clutch or die spring for fatigue life
- Choose a working stroke that gives infinite life
- Compare spring wire grades
Who it is for
- Design engineers
- Spring designers
- Machine designers
What you get
- Loads and stresses at both lengths
- Alternating and mean stresses
- Goodman, Soderberg, Gerber and yield factors
Interpreting the result
- Shot peening raises the endurance limit far more than a stronger wire does.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 304–324, 200–211. 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
Springs: high stress, every cycle
In Metal Fatigue by the Numbers
What it covers: How a compression spring's working stroke sets its stress cycle, how to check it for fatigue with wire strengths and Zimmerli's data, and what a longer stroke did to the PK-20's return spring.
Method explained here · BIZOMAT original book
Compression springs that cycle: stroke, stress range and fatigue
What it covers: How to check a compression spring that cycles: the stress range from preload and stroke, wire endurance from Zimmerli's data, Goodman factors, and finding the real stroke.
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 Compression Spring Fatigue Check (Working Stroke, Goodman Factor) calculator