Determine the maximum stress:

A laminated spring of the quarter elliptic type, 0.6 m long, is to give a static deflection of 80 mm under an end load of 2000 N. If the leaf material is 60 mm wide and 5 mm thick, determine the number of leaves needed and the maximum stress.

From what height may the load be dropped on to the undeflected spring to cause of maximum stress of 8000 N/mm²?  E = 200 GPa.

Solution

 Quarter Elliptic Leaf Spring l = 0.6 m

Δ = 80 mm

W = 2000 N

b = 60 mm

t = 5 mm

n = ?

σ_b = ?

Δ= 6W l ³/ nbt ³ E

⇒         80 = 3 × 2000 × 600³ / n × 60 × 5³ × 200 × 10³

∴          n = 21.6 (say 22 leaves)

σ  = 6Wl / nbt

= 6 × 2000 × 600 /22 Δ× 60 × 5²

= 369 N/mm²

For maximum stress of 800 N/mm²

800 = 6 × W × 600 / 22 × 60 × 52

⇒         W = 7333.3 N

Corresponding deflection = 6 × 7333.3 × 600³/22 × 60 × 5³ × 200 × 10³

                                         = 288 mm

Loss of PE = Gain of KE

2000 (h + 288) = (½) × 7333.3 × 288

∴ h = 240 mm