KEVOS® MAKEOS · Springs
Semi-Elliptic Leaf Spring Design (Leaves for Stress and Deflection)
How many leaves does this semi-elliptic spring need for the load within the allowable stress and deflection, and what rate will it have?
Design of a semi-elliptic (centre-loaded, end-supported) leaf spring of equal-strength graduated leaves: the number of leaves needed to keep the bending stress within the allowable, the number needed to keep the deflection within your limit, the governing count, and the stress, deflection and rate with the leaves you choose (as the leaf spring tool, semi-elliptic case).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load at the centre | N | Load applied at the centre clamp (both ends supported). |
| Span between the ends | mm | Distance between the end supports (eyes or slippers). |
| Leaf width | mm | Width of each leaf. |
| Leaf thickness | mm | Thickness of each leaf. |
| Elastic modulus | GPa | Elastic modulus of the spring steel. |
| Allowable bending stress | MPa | Allowable bending stress for the duty (your value). |
| Largest deflection allowed | mm | Largest centre deflection you allow (for clearance or ride). |
| Leaves chosen | Number of leaves you intend to use. |
Method and formulas
- Semi-elliptic, graduated leaves: σ = 3FL ÷ (2 n b t²); δ = 3FL³ ÷ (8 n E b t³) (as the leaf spring tool).
- Leaves for stress n = 3FL ÷ (2 b t² σ_allow); for deflection n = 3FL³ ÷ (8 E b t³ δ_max); round the larger up.
- Rate = F ÷ δ.
- Example: 5000 N on a 1000 mm span needs 4 leaves; 6 leaves run at 325.52 MPa and deflect 49.143 mm.
Limitations
- Equal-strength (graduated) leaves without inter-leaf friction; real springs are stiffer and show hysteresis.
- Static stress; fatigue and the centre bolt hole need their own checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a leaf spring for a trailer, cart or machine mount
- Check a spring for a higher load
- Trade leaf thickness against leaf count
Who it is for
- Design engineers
- Vehicle engineers
- Maintenance engineers
What you get
- Leaves needed for stress and for deflection
- Stress, deflection and rate with the leaves chosen
Interpreting the result
- Thicker leaves cut the stress-limited count fast, but the spring gets much stiffer (thickness cubed).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 344–345. Topic reference; no source tables or recommended settings are reproduced.
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Open the Semi-Elliptic Leaf Spring Design (Leaves for Stress and Deflection) calculator
