Short Answer:
Torsional vibrations are the type of vibrations in which the particles of a body move in a circular path about its axis, causing twisting and untwisting motion along the shaft or component. The motion involves angular displacement rather than linear displacement.
In simple words, torsional vibration occurs when a shaft or rotating part twists back and forth about its mean position due to external or internal torque variations. These vibrations are very common in rotating machinery like engine crankshafts, turbine rotors, and transmission shafts. Excessive torsional vibrations can cause fatigue failure or damage to mechanical components.
Detailed Explanation :
Torsional Vibrations
Torsional vibrations are a special kind of mechanical vibration that occur in shafts, rods, and other rotating components when they twist and untwist alternately about their longitudinal axis. In this type of vibration, the motion is rotational rather than translational, meaning that every cross-section of the shaft rotates slightly with respect to the adjacent one.
When a torque is applied to a shaft, it stores energy in the form of strain energy due to twisting. When the torque is removed or reversed, the stored energy is released, causing oscillatory twisting motion. This repeated twisting and untwisting of the shaft is known as torsional vibration.
Such vibrations are important to study because they can lead to resonance in rotating machinery, causing excessive stresses, noise, and even mechanical failure if not properly controlled.
Nature of Torsional Vibrations
In torsional vibration, each particle of the shaft moves in a circular path about the shaft’s axis. The twisting motion produces an angular displacement (θ), and the restoring torque generated by the material’s elasticity tends to bring the system back to its original position. The process continues due to the system’s inertia, leading to oscillatory angular motion.
The torque producing this restoring motion is proportional to the angular twist, and this relationship follows Hooke’s Law for torsional deformation:
where,
- T = restoring torque (N·m)
- C = torsional stiffness or torsional rigidity (N·m/rad)
- θ = angular displacement (radians)
This restoring torque is the main reason for the oscillatory motion of the shaft.
Mathematical Expression of Torsional Vibrations
Consider a uniform shaft of length L, diameter d, and material with modulus of rigidity G, carrying a flywheel of polar moment of inertia I at its free end, while the other end is fixed.
When the shaft twists through an angle θ, the restoring torque (T) is given by:
According to Newton’s second law for rotational motion:
Substituting the value of T,
This is the differential equation of motion for torsional vibration.
The natural angular frequency (ωₙ) of torsional vibration is:
and the natural frequency (fₙ) in cycles per second is:
This shows that the natural frequency depends on the material property (G), shaft dimensions (d and L), and moment of inertia (I) of the rotating body.
Characteristics of Torsional Vibrations
- Type of Motion:
The motion is angular, involving twisting and untwisting about the shaft’s longitudinal axis. - Restoring Force:
The restoring torque is directly proportional to the angular displacement. - Energy Form:
Energy is stored as strain energy during twisting and released as kinetic energy during untwisting. - Resonance Effect:
If the frequency of the external torque matches the shaft’s natural frequency, resonance occurs, leading to dangerously high stresses. - Nodes and Loops:
In long shafts, there exist nodes (points of zero angular displacement) and loops (points of maximum angular displacement).
Examples of Torsional Vibrations
- Engine Crankshaft:
When an engine runs, periodic torque is generated due to the firing of cylinders. This causes torsional vibration in the crankshaft. - Rotating Shafts in Machines:
Shafts carrying pulleys, gears, or flywheels experience torsional vibration due to sudden torque fluctuations. - Turbine and Generator Rotors:
These rotating components experience torsional vibration due to varying load or steam/air pressure changes. - Drive Shafts in Automobiles:
Torsional vibration occurs due to the varying torque transmitted between the engine and wheels. - Helicopter Drive Systems:
Shafts transmitting power to the rotor blades experience torsional vibrations because of varying aerodynamic loads.
Causes of Torsional Vibrations
- Unbalanced Torques:
Periodic torque variations in engines or machines can excite torsional vibration. - Sudden Changes in Load:
Rapid load changes on rotors or shafts cause temporary torsional oscillations. - Elastic Deformation:
The elasticity of the material allows twisting and energy storage, promoting vibration. - Resonance Conditions:
When the forcing frequency equals the shaft’s natural frequency, large amplitude torsional vibrations occur. - Mechanical Misalignment:
Improper alignment of rotating components leads to uneven torque and torsional motion.
Effects of Torsional Vibrations
- Fatigue Failure:
Continuous twisting causes cyclic shear stresses, which may result in fatigue failure. - Noise and Vibration:
Excessive torsional vibration leads to noise and unpleasant mechanical vibrations. - Cracks in Shafts:
High torsional stresses can cause cracks or even breakage in the shaft. - Loss of Efficiency:
Energy loss due to vibration reduces the efficiency of rotating machinery. - Damage to Connected Components:
Couplings, gears, and bearings may wear out quickly due to vibration transmission.
Prevention and Control of Torsional Vibrations
- Dynamic Balancing:
Ensures equal torque distribution and reduces unbalanced forces. - Use of Dampers:
Torsional vibration dampers absorb energy and reduce vibration amplitude (commonly used in automobile engines). - Proper Shaft Design:
Selecting suitable material, length, and diameter to avoid natural frequency matching operating speed. - Flywheels:
Flywheels help stabilize torque fluctuations by storing rotational energy. - Regular Maintenance:
Periodic inspection of rotating machinery ensures misalignment or wear is corrected early.
Conclusion
Torsional vibrations are angular oscillations of a rotating shaft or component about its longitudinal axis, caused by periodic torque variations. The particles move in circular paths around the shaft’s center, leading to twisting and untwisting motion. Such vibrations are very common in engines, turbines, and drive shafts. If uncontrolled, torsional vibrations can cause resonance and serious mechanical damage. Therefore, understanding torsional vibration behavior helps engineers design safer, more efficient, and durable rotating systems.