KEVOS® MAKEOS · Springs
Flat and Leaf Spring
How much does this flat or leaf spring deflect, and how highly is it stressed?
Deflection, rate and bending stress of a single flat cantilever spring, a graduated multi-leaf cantilever, or a semi-elliptic leaf spring loaded at the centre.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Spring type | choice | Spring arrangement. |
| Load (total load for semi-elliptic) | N | Load at the free end (cantilever) or total centre load (semi-elliptic). |
| Length (span for semi-elliptic) | mm | Length from the clamp to the load, or span between eyes (semi-elliptic). |
| Width | mm | Width of the strip or leaves. |
| Thickness (each leaf) | mm | Thickness of each leaf. |
| Number of leaves | leaves | Number of leaves (1 for a single strip). |
| Elastic modulus | GPa | Elastic modulus of the spring material. |
| Allowable bending stress | MPa | Allowable bending stress for the spring material and duty. |
Method and formulas
- Single: σ = 6FL ÷ (b t²); δ = 4FL³ ÷ (E b t³).
- Multi-leaf (graduated): σ = 6FL ÷ (n b t²); δ = 6FL³ ÷ (n E b t³).
- Semi-elliptic (total load W, span L): σ = 3WL ÷ (2 n b t²); δ = 3WL³ ÷ (8 n E b t³).
- Example: 15 N on a 60 × 10 × 1 mm flat spring deflects 6.2609 mm with σ = 540 MPa.
Limitations
- Small deflections; large deflections of slender strips need large-deflection theory.
- Friction between leaves and the effect of clamp bolts are ignored.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design flat spring clips, contacts and detents
- Check vehicle or trailer leaf springs
- Choose strip thickness for a rate
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Deflection
- Spring rate
- Maximum bending stress
Interpreting the result
- For flat springs, stress at the clamp governs; avoid sharp clamp edges.
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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