GATE ME 2020 Set 1 — Question 19
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Machine Design → Machine Elements → Shafts, Keys & Couplings
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Question
A helical gear with pressure angle and helix angle mounted at the mid-span of a shaft that is supported between two bearings at the ends. The nature of the stresses induced in the shaft is
- A.normal stress due to bending only
- B.normal stress due to bending in one plane and axial loading; shear stress due to torsion
- C.normal stress due to bending in two planes and axial loading; shear stress due to torsion
- D.normal stress due to bending in two planes; shear stress due to torsion
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Correct answer
(A;C)
Solution
A helical gear transmits power, which involves three force components acting on the shaft:
1.Tangential Force (): This force creates a torque on the shaft () and also causes bending in the plane of rotation (vertical plane).
2.Radial Force (): This force acts towards the center of the gear and causes bending in a plane perpendicular to the tangential force's bending plane (horizontal plane).
3.Axial Force (): Due to the helix angle, an axial force is generated (). This force causes axial stress in the shaft and also an additional bending moment because it acts at the pitch radius of the gear, offset from the shaft axis.
Therefore, the shaft is subjected to:- Normal stress due to bending in two planes (vertical and horizontal).
- Normal stress due to axial loading.
- Shear stress due to torsion.
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