Determine the greatest load carried by the composite springs, Mechanical Engineering

Determine the greatest load carried by the composite springs:

A composite spring contain two close-coiled helical spring associated in series, each spring has 10 coils at a mean radius of 15 mm. Determine the diameter of one if the other is 2.5 mm and the stiffness of the composite spring is 750 N/mm. Determine the greatest load that may be carried by the composite springs, and the corresponding extension, for a maximum shearing stress of 200 N/mm2.

G = 80 GPa.

Solution

For spring in series, W is similar.

 Δ = Δ1 + Δ2       --------- (1)

1/ K  =  1/ K1  +   1/ K2                                 --------- (2)

Δ= 64 W R3 n / Gd 4

Δ1 =64 W × 153 × 10 / (80 × 103 × 2.54)

W/ Δ1 = K1 = 1.45 N/mm       ---------- (3)

 K = 750 N/m = 0.75 N/mm ------- (4)

Δ2 =64 W × 153 × 10/80 × 103 × d 4

W/ Δ2 = K2  = d4 (0.037)                             ----------- (5)

By using (2), (3), (4) and (5), we obtain

1/0.75  = (1/1.45 )+1/ (0.037 × d 4)

∴          d = 2.55 mm

τmax      = 16 W R /π d3

⇒         200 = 16 W × 15 /π (2.5)3

∴          W = 40.9 N

 Total extension, Δ=    W /K = 40.9/0.75 = 54.5 mm

Posted Date: 1/21/2013 1:35:43 AM | Location : United States







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