design the keys - shear keysa solid circular

Question

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 = τ_max /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