Chapter-9 •
Torsion
2π NT = 4500
P (in hp)
S K Mondal’s
(1 hp = 75 Kgm/sec). [Where N = rpm; T = Torque in N-m.]
5. Safe diameter of Shaft (d) •
Stiffness consideration
T Gθ = J L •
Shear Stress consideration
T τ = J R We take higher value of diameter of both cases above for overall safety if other parameters are given.
6. In twisting 16T π d3
•
Solid shaft, τ max =
•
Hollow shaft, τ max =
•
Diameter of a shaft to have a maximum deflection " α "
16Td o π (d o 4 − di 4 ) d = 4.9 × 4
TL Gα
[Where T in N-mm, L in mm, G in N/mm2]
7. Comparison of solid and hollow shaft •
A Hollow shaft will transmit a greater torque than a solid shaft of the same weight & same material because the average shear stress in the hollow shaft is smaller than the average shear stress in the solid shaft
(τ max )holloow shaft 16 • = (τ max ) solid shaft 15 •
Strength comparison (same weight, material, length and τ max )
Th n2 + 1 = Ts n n 2 − 1 •
Where, n=
External diameter of hollow shaft Internal diameter of hollow shaft
[ONGC-2005]
Weight comparison (same Torque, material, length and τ max )
(
)
n 2 − 1 n 2/3 Wh = 2/3 Ws n4 − 1 •
⎡ If solid shaft dia = D ⎤ ⎢ ⎥ ⎢ Hollow shaft, d o = D, di = D ⎥ 2⎦ ⎣
(
)
Where, n=
External diameter of hollow shaft Internal diameter of hollow shaft
Strain energy comparison (same weight, material, length and τ max )
Uh n 2 + 1 1 = 1+ 2 = 2 Us n n
Page 278 of 429
[WBPSC-2003]