Design the keys - shear keys, Mechanical Engineering

Design the keys - Shear Keys:

A solid circular shaft is to transmit 200 kN at 200 rpm. If the maximum shear stress is not to exceed 80 n/mm2 design the shaft. Design the keys and discover number of 16 mm diameter bolt needed to connect coupling along with a bolt circle of 240 mm diameter.

Permissible stress in keys = 100 N/mm2

Permissible stress in bolts = 100 N/mm2       

Solution

Length of the key = 200 mm

P = 200 kN N = 200 rpm Shaft

d = ?

P = 2π NT / 60

⇒200 × 103  = (2π × 200 × T) /60

∴ T = 9.5 × 103 N-m

T /J = τmax /R  ∴ τ max    = 16T/ π d 3

⇒         80 × 106  = 16 × (9.5 × 10 ) / π d 3

∴          d = 0.085 m ≈ 85 mm

Shear Keys

T = 9.5 × 103 N-m

τ1 = 100 N/mm2

L = 200 mm = 0.2 m

T = τ1 L b R

⇒  9.5 × 103  = (100 × 106 ) (0.2) b ( 0.085/2)

∴  b = 0.011 m ≈ 11 mm

Bolts

τ2 = 100 N/mm2

d = 16 mm

F  = τ2  (π/4) d 2

= 100 × (π /4 )× 162  = 20106.2 N

R1  = 240 /2 = 120 mm = 0.12 m

T = η . F2  . R1

⇒  9.5 × 103  = η × 20106.2 × 0.12

∴  η = 3.9 ≈ 4

Posted Date: 1/21/2013 5:16:27 AM | Location : United States







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