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A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal?
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A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in...
Solution:
Given data:
- Power transmitted (P) = 97.5 kW
- Rotational speed (N) = 180 rpm
- Allowable shear stress (τ) = 60 MPa
- Length of the shaft (L) = 3 m
- Maximum allowable twist angle (θ) = 1 degree = 0.0175 radians
- Modulus of rigidity (G) = 80 GPa = 80 × 10^3 MPa
Finding the torque:
- Torque (T) = (P × 60) / (2πN) = 33.17 kNm
Finding the suitable diameter of the shaft:
- Maximum shear stress (τmax) = (T × r) / J
- r is the radius of the shaft, J is the polar moment of inertia
- J = πd^4 / 32
- τmax = (16T / πd^3)
- For τmax = 60 MPa,
d = (16T / πτmax)^{1/3}
- Substituting the values, we get d = 76.98 mm
Checking for the maximum twist angle:
- Maximum twist angle (θmax) = TL / (JG)
- For θmax = 0.0175 radians,
d^4 = 16TL / (πGθmax)
- Substituting the values, we get d = 63.06 mm
Hence, the suitable diameter of the shaft is 76.98 mm (considering maximum shear stress) or 63.06 mm (considering maximum twist angle).
Conclusion:
The suitable diameter of the shaft is calculated considering both the maximum shear stress and the maximum twist angle. The diameter of the shaft should not exceed 76.98 mm (considering maximum shear stress) or 63.06 mm (considering maximum twist angle) to ensure safe and reliable operation.
Given data:
- Power transmitted (P) = 97.5 kW
- Rotational speed (N) = 180 rpm
- Allowable shear stress (τ) = 60 MPa
- Length of the shaft (L) = 3 m
- Maximum allowable twist angle (θ) = 1 degree = 0.0175 radians
- Modulus of rigidity (G) = 80 GPa = 80 × 10^3 MPa
Finding the torque:
- Torque (T) = (P × 60) / (2πN) = 33.17 kNm
Finding the suitable diameter of the shaft:
- Maximum shear stress (τmax) = (T × r) / J
- r is the radius of the shaft, J is the polar moment of inertia
- J = πd^4 / 32
- τmax = (16T / πd^3)
- For τmax = 60 MPa,
d = (16T / πτmax)^{1/3}
- Substituting the values, we get d = 76.98 mm
Checking for the maximum twist angle:
- Maximum twist angle (θmax) = TL / (JG)
- For θmax = 0.0175 radians,
d^4 = 16TL / (πGθmax)
- Substituting the values, we get d = 63.06 mm
Hence, the suitable diameter of the shaft is 76.98 mm (considering maximum shear stress) or 63.06 mm (considering maximum twist angle).
Conclusion:
The suitable diameter of the shaft is calculated considering both the maximum shear stress and the maximum twist angle. The diameter of the shaft should not exceed 76.98 mm (considering maximum shear stress) or 63.06 mm (considering maximum twist angle) to ensure safe and reliable operation.
Community Answer
A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in...
104mm
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A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal?
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A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal?.
A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shaft transmitting 97.5Kw at 180rpm if the allowable shear stress in the material is 60mp find the suitable diameter of the shaft the shaft is not to twistore than 1degree in the length of 3meter take c=80giga pascal?.
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