Determine the number of leaves and initial curvature, Mechanical Engineering

Determine the number of leaves and initial curvature:

A leaf spring with a span of 1.40 m consist width and thickness of leaves to be 100 mm and 12 mm respectively. The maximum bending stress is equal to 150 N/mm2 and the spring should absorb 125000 N-mm when straightened. Determine the number of leaves and initial curvature. Take E = 200 GPa.

Solution

d = 1400 mm

b = 100 mm

t = 12 mm

σb = 150 N/mm2

U = 125000 N-mm

n =?

R0 =?

E = 200 × 103 N/mm2

σ  =  3Wl  /2 nbt2

⇒         150 = 3W × 1400 / 2 n (100) (12)2

∴          W = 1029 n      --------------- (1)

Δ= 3W l 3 / 8 nE b t 3  = 3 (1029 n) (1400)3 / 8 n (200 × 103 ) (100) (12)3  = 30.6 mm

U = (½) W Δ

⇒         125000 = 1029 n × (30.6/2)

∴          n = 79; 8

R0 = l 2 / 8 Δ = (1400)2 /8 × 30.6 = 8007 mm

Posted Date: 1/21/2013 2:01:34 AM | Location : United States







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