34 Questions
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?
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?
A shaft is subject to primary bending and torque.
How does the design complexity of a shaft compare to that of an axle?
The design of a shaft is more complex than that of an axle.
What is the formula for calculating the first critical speed of a shaft with more than one concentrated masses?
The Dunkerley-approximation method
How can the natural frequency of torsional oscillations be calculated in case of a single-mass oscillating system?
st ωtk = Θ
What is the reduced moment of inertia formula to be used in the case of two rotating masses?
1/Θ = 1/Θ1 + 1/Θ2
What is the recommended residual imbalance for gas and steam turbines, turbo generators, and machine tools?
2,5
What is the formula for calculating the stiffness of the shaft?
s = c/Tengelyek
How is the first critical speed of a shaft with more than one concentrated masses calculated?
Using the Dunkerley-approximation method
What is the formula for the reduced moment of inertia to be used in the case of two rotating masses?
1/Θ = 1/Θ1 + 1/Θ2
What is the natural frequency formula for torsional oscillations in case of a single-mass oscillating system?
st ωtk = Θ
What are the crucial components in various machines, including electric motors, I.C. engines, gearboxes, and vehicles?
Shafts and axles
What is the usual cross-section of a shaft?
Circular
How are shafts categorized based on their function?
Rotating shafts, connecting shafts, and special connecting shafts
What are the different classifications of axles?
Transmission axles, rotating shafts, and special axles
What is the primary material used for making shafts and axles?
Steel
What is the most advantageous design for bending stress in shafts?
Varying cross-sectional beam
What type of stress are axles used in vehicles subjected to?
Pulsating fatiguing stress
What types of stress do shafts and axles undergo?
Rotary bending and twisting stress
What is involved in pre-planning for shafts?
Determining characteristic size based on allowable stress and bending stress
How can complex static stress in shafts be checked?
By determining reaction forces and bending stress through the principle of superposition
What is the formula for the reduced stress for tough shafts using Huber-Mises-Hencky theory?
σred = σh^2 + 3τcs^2
What is the limitation for elastic deformation's angular rotation (beta)?
beta <= 0.05 degrees
What is the condition for checking critical speed in relation to natural frequency?
Operating speed should not be near natural frequency (critical speed)
What is the formula for stiffness calculation for stepped shafts using a one-mass oscillating system?
F = Is1 + Is2, Mi = m, and Mn = M i+1
What is the relationship between twisted angle (psi) and the length of the shaft (l)?
psi <= 0.005l
What is the condition for comparison of reduced stress and allowable stress?
σred <= σred * z with z = 1.5 or 2 and a safety factor of 2
What is the permissible value for elastic deflection (sagging) based on the distance between bearings?
f <= 0.00035l (where l is the distance between bearings)
What is the formula for the reduced stress for cast iron shafts using the relationship for brittle materials?
σred = 3/8 (σh + 5σh^2 + 4τcs^2)
What are the factors affecting the elastic deformation of the shaft that should be checked?
Flexible bending and twisting, permissible deflection, and angular rotation
What is the formula for the resultant bending moment for a shaft?
Mh = Mhr + Mah + M2hkT
What is the formula for the calculation of normal stress (σh) at the dangerous cross-section?
σh = Mh / Sh
What is the formula for the determination of torque and shear stress (τcs) from circumferential force Fk?
τcs = Fk / A
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 (τcs) 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.
Test your knowledge on engineering and design principles of shafts, including determination of resultant bending moment, normal stress calculation, and consideration of axial loads. This quiz covers important concepts for mechanical and structural engineers.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
