Design of Springs free study notes for Diploma / BTech.

1. What is Spring ?

A spring is an elastic machine element used to store mechanical energy and release it when required. Springs are widely used in machines to absorb shocks, maintain force between parts, and control motion.

The design of springs ensures:

• Required load carrying capacity
• Desired deflection
• Adequate fatigue life
• Safety against failure

Explore more on Design of Spring

2. Types of Springs

3. Material Selection for Springs

Spring materials must have:

• High yield strength
• High fatigue strength
• Good elastic properties

Common Materials:

• High carbon steel
• Alloy steels (Cr-V, Cr-Si steels)
• Stainless steel
• Phosphor bronze (for corrosion resistance)

4. Terminology of Helical Springs

• Wire diameter (d)
• Mean coil diameter (D)
• Spring index (C = D/d)
• Number of active coils (n)
• Pitch (p)
• Free length (L₀)
• Solid length (Lₛ)

Recommended spring index: 4 to 12

Stress in Helical Springs

Maximum Shear Stress:

$$\tau = \frac{8WD}{\pi d^3} \times K$$

Where:

• $W$W = Load
• $D$D = Mean diameter
• $d$d = Wire diameter
• $K$K = Wahl’s stress factor

Wahl Factor:

$$K = \frac{4C – 1}{4C – 4} + \frac{0.615}{C}$$​

Deflection of Spring

$$\delta = \frac{8WD^3 n}{G d^4}$$

Where:

• $G$G = Modulus of rigidity
• $n$n = Number of active coils

Spring Stiffness (Spring Rate)

$$k = \frac{W}{\delta} = \frac{G d^4}{8D^3 n}$$

Design Procedure for Helical Compression Spring

1. Determine load (W) and deflection (δ)
2. Select spring material and allowable stress
3. Assume spring index (C)
4. Calculate wire diameter (d) using stress equation
5. Find mean coil diameter (D = C × d)
6. Calculate number of coils (n) from deflection
7. Determine free length: $$L_0 = n \times p + \text{clearance}$$L0​=n×p+clearance
8. Check for buckling and stability

Design of Leaf Springs

Types:

• Semi-elliptic
• Quarter elliptic

Bending Stress:

$$\sigma = \frac{6WL}{nbt^2}$$σ=nbt26WL​

Where:

• $W$W = Load
• $L$L = Length
• $n$n = Number of plates
• $b$b = Width
• $t$t = Thickness

Deflection:

$$\delta = \frac{12WL^3}{E n b t^3}$$

Design of Torsion Springs

• Works under twisting
• Stores energy by angular deflection

Torque Relation:

$$T = \frac{\pi d^3 \tau}{16}$$

Failure of Springs

1. Fatigue failure (most common)
2. Overloading
3. Corrosion
4. Buckling (in compression springs)

Design Considerations

• Provide factor of safety (1.5–3)
• Avoid stress concentration
• Use shot peening to improve fatigue life
• Proper heat treatment
• Ensure adequate clearance between coils

Applications

• Automobile suspension systems
• Railway buffers
• Shock absorbers
• Clutches and brakes
• Industrial machinery

---