Determine the maximum stress - spring , Mechanical Engineering

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 = ?

σb = ?

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

Posted Date: 1/21/2013 2:00:02 AM | Location : United States







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