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Questions and Answers
What is the primary function of a shaft?
What is the primary function of a shaft?
To carry the rotating structural elements as well as to transmit torque.
How does an axle differ from a shaft in terms of primary function?
How does an axle differ from a shaft in terms of primary function?
An axle's primary function is to provide support to parts like a wheel, pulley, drum, etc, and it does not transmit power.
What are the main types of stress that a shaft is subject to?
What are the main types of stress that a shaft is subject to?
A shaft is subject to primary bending and torque.
How does the design complexity of a shaft compare to that of an axle?
How does the design complexity of a shaft compare to that of an axle?
What is the formula for calculating the first critical speed of a shaft with more than one concentrated masses?
What is the formula for calculating the first critical speed of a shaft with more than one concentrated masses?
How can the natural frequency of torsional oscillations be calculated in case of a single-mass oscillating system?
How can the natural frequency of torsional oscillations be calculated in case of a single-mass oscillating system?
What is the reduced moment of inertia formula to be used in the case of two rotating masses?
What is the reduced moment of inertia formula to be used in the case of two rotating masses?
What is the recommended residual imbalance for gas and steam turbines, turbo generators, and machine tools?
What is the recommended residual imbalance for gas and steam turbines, turbo generators, and machine tools?
What is the formula for calculating the stiffness of the shaft?
What is the formula for calculating the stiffness of the shaft?
How is the first critical speed of a shaft with more than one concentrated masses calculated?
How is the first critical speed of a shaft with more than one concentrated masses calculated?
What is the formula for the reduced moment of inertia to be used in the case of two rotating masses?
What is the formula for the reduced moment of inertia to be used in the case of two rotating masses?
What is the natural frequency formula for torsional oscillations in case of a single-mass oscillating system?
What is the natural frequency formula for torsional oscillations in case of a single-mass oscillating system?
What are the crucial components in various machines, including electric motors, I.C. engines, gearboxes, and vehicles?
What are the crucial components in various machines, including electric motors, I.C. engines, gearboxes, and vehicles?
What is the usual cross-section of a shaft?
What is the usual cross-section of a shaft?
How are shafts categorized based on their function?
How are shafts categorized based on their function?
What are the different classifications of axles?
What are the different classifications of axles?
What is the primary material used for making shafts and axles?
What is the primary material used for making shafts and axles?
What is the most advantageous design for bending stress in shafts?
What is the most advantageous design for bending stress in shafts?
What type of stress are axles used in vehicles subjected to?
What type of stress are axles used in vehicles subjected to?
What types of stress do shafts and axles undergo?
What types of stress do shafts and axles undergo?
What is involved in pre-planning for shafts?
What is involved in pre-planning for shafts?
How can complex static stress in shafts be checked?
How can complex static stress in shafts be checked?
What is the formula for the reduced stress for tough shafts using Huber-Mises-Hencky theory?
What is the formula for the reduced stress for tough shafts using Huber-Mises-Hencky theory?
What is the limitation for elastic deformation's angular rotation (beta)?
What is the limitation for elastic deformation's angular rotation (beta)?
What is the condition for checking critical speed in relation to natural frequency?
What is the condition for checking critical speed in relation to natural frequency?
What is the formula for stiffness calculation for stepped shafts using a one-mass oscillating system?
What is the formula for stiffness calculation for stepped shafts using a one-mass oscillating system?
What is the relationship between twisted angle (psi) and the length of the shaft (l)?
What is the relationship between twisted angle (psi) and the length of the shaft (l)?
What is the condition for comparison of reduced stress and allowable stress?
What is the condition for comparison of reduced stress and allowable stress?
What is the permissible value for elastic deflection (sagging) based on the distance between bearings?
What is the permissible value for elastic deflection (sagging) based on the distance between bearings?
What is the formula for the reduced stress for cast iron shafts using the relationship for brittle materials?
What is the formula for the reduced stress for cast iron shafts using the relationship for brittle materials?
What are the factors affecting the elastic deformation of the shaft that should be checked?
What are the factors affecting the elastic deformation of the shaft that should be checked?
What is the formula for the resultant bending moment for a shaft?
What is the formula for the resultant bending moment for a shaft?
What is the formula for the calculation of normal stress (σh) at the dangerous cross-section?
What is the formula for the calculation of normal stress (σh) at the dangerous cross-section?
What is the formula for the determination of torque and shear stress (Ï„cs) from circumferential force Fk?
What is the formula for the determination of torque and shear stress (Ï„cs) from circumferential force Fk?
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Study Notes
- Determination of the resultant bending moment Mh for a shaft: Mh = Mhr + Mah + M2hkT (Location of dangerous cross-section may not be where largest moment occurs)
- Calculation of normal stress (σh) at dangerous cross-section
- Determination of torque and shear stress (Ï„cs) from circumferential force Fk
- Reduced stress calculation for tough shafts using Huber-Mises-Hencky theory: σred = σh2 + 3τcs2
- Reduced stress calculation for cast iron shafts using relationship for brittle materials: σred = 3/8 (σh + 5σh2 + 4τcs2)
- Comparison of reduced stress and allowable stress: σred <= σred * z with z = 1.5 or 2 and a safety factor of 2
- Checking for elastic deformation, including:
- Flexible bending and twisting affecting operation of gear connections, electric motors, pumps or turbine impellers, shaft seals, and bearings
- Permissible value for elastic deflection (sagging): f <= 0.00035l (where la is distance between bearings)
- Limitation of elastic deformation's angular rotation (beta): beta <= 0.05 degrees
- Twisted angle (psi) and length of shaft (l) relationship: psi <= 0.005l
- Checking for critical speed:
- Rotors oscillate under centrifugal forces and external forces/torque fluctuations
- Operating speed should not be near natural frequency (critical speed)
- Excitations and corresponding critical speeds: bending swing and torsion swing
- Determination of bending stiffness s using weight force and elastic deflection
- Stiffness calculation for stepped shafts using one-mass oscillating system:
- Unit force applied at disk location
- Bending moment diagram drawn
- Calculate stiffness F = Is1 + Is2, Mi = m, and Mn = M i+1
- Calculate stiffness using moment of inertia and applied force.
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