How to Design a Mechanical Spring – Step-by-Step Guide with Example
Introduction
Mechanical springs are essential components in engineering and manufacturing. They store energy, absorb shocks, and maintain force between surfaces. Common types include:
- Compression springs – resist compression.
- Extension springs – resist pulling forces.
- Torsion springs – resist twisting forces.
In this guide, we’ll focus on compression spring design using practical formulas and a worked example.
Step 1 – Define Requirements
- Load (F): 100 N
- Deflection (Δx): 20 mm
- Type: Compression spring
- Operating conditions: Room temperature, no corrosion issues
Step 2 – Select Spring Material
We choose music wire (ASTM A228) because it has:
- High tensile strength (~2068 MPa)
- Modulus of rigidity \( G = 79,300 \, \text{MPa} \)
- Good fatigue resistance
Step 3 – Calculate Spring Constant (k)
Hooke’s Law: \( F = k \cdot x \)
Spring constant: \( k = \frac{F}{x} = \frac{100}{20} = 5 \, \text{N/mm} \)
The spring should resist 5 N/mm of compression.
Step 4 – Estimate Dimensions Using Formula
Compression spring formula: \( k = \frac{G d^4}{8 D^3 N} \)
Where: \( G = 79,300 \, \text{MPa}, \, d = \text{wire diameter}, \, D = \text{mean coil diameter}, \, N = \text{active coils} \)
Assume Initial Values
- Wire diameter \( d = 2.5 \, \text{mm} \)
- Mean coil diameter \( D = 20 \, \text{mm} \)
Solving: \( N \approx 9.68 \) → use 10 active coils.
Step 5 – Check Shear Stress
Max shear stress: \( \tau_{\text{max}} = \frac{8 F D K_w}{\pi d^3} \)
Wahl factor: \( K_w = \frac{4C - 1}{4C - 4} + \frac{0.615}{C}, \, C = \frac{D}{d} = 8 \)
Result: \( \tau_{\text{max}} \approx 384.6 \, \text{MPa} \) → safe.
Step 6 – Final Dimensions
- Wire diameter: 2.5 mm
- Mean coil diameter: 20 mm
- Active coils: 10
- Free length: 50 mm
- Spring constant: 5 N/mm
Example Summary Table
| Parameter | Value |
|---|---|
| Load (F) | 100 N |
| Deflection (Δx) | 20 mm |
| Spring Constant (k) | 5 N/mm |
| Wire Diameter (d) | 2.5 mm |
| Mean Coil Diameter (D) | 20 mm |
| Active Coils (N) | 10 |
| Max Shear Stress | 384.6 MPa |
| Material | Music Wire |
Conclusion
Designing a mechanical spring involves defining load and deflection, choosing a suitable material, applying formulas, and checking stress limits. With proper calculations, you can create safe, efficient, and cost-effective springs.
Tip: Check standard spring catalogs — you might find a ready-made spring close to your design, saving time and cost.
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