Short Answer:

Torsional vibrations are the oscillatory motions that occur when a shaft or rotating body twists back and forth about its axis of rotation. These vibrations are caused by the periodic variation of torque in machines such as engines, turbines, or motors. If not controlled, torsional vibrations can cause fatigue failure, noise, and excessive wear of mechanical components. Engineers use dampers, flexible couplings, and proper shaft design to minimize such vibrations and ensure smooth operation of the system.

Torsional vibration mainly occurs in systems that involve rotating masses connected by elastic shafts. When torque is suddenly applied or varies periodically, it produces twisting and untwisting motion. This vibration is common in crankshafts of internal combustion engines, gear drives, and power transmission shafts. The frequency and amplitude of torsional vibration depend on system stiffness, mass moment of inertia, and damping.

Detailed Explanation:

Torsional Vibrations

Torsional vibration refers to the angular oscillation of a shaft or rotating body about its longitudinal axis due to the action of alternating or fluctuating torque. Unlike linear or transverse vibrations, torsional vibration does not cause any lateral movement of the shaft; instead, it involves twisting and untwisting motion. These vibrations occur whenever the torque transmitted through the shaft changes with time, causing one end of the shaft to lag or lead the other.

In mechanical systems like engines, compressors, and turbines, torque is rarely constant. The intermittent firing of cylinders or fluctuating loads leads to variation in the angular velocity of the shaft. This fluctuation causes torsional stress and periodic angular displacements, resulting in torsional vibrations. The study of these vibrations is crucial to avoid resonance and prevent structural or mechanical failure.

Causes of Torsional Vibrations

1. Fluctuating Torque: The primary cause of torsional vibration is the irregular torque output from power sources like engines or electric motors.
2. Sudden Load Changes: Rapid variation in load or speed can induce torsional oscillations in rotating components.
3. Elastic Shaft Behavior: The elastic nature of the shaft allows twisting, which leads to oscillation when torque varies.
4. Imbalance in Rotating Components: Uneven mass distribution in rotating parts causes periodic twisting moments.
5. Gear Mesh Stiffness Variation: In gear trains, the variation in stiffness during tooth engagement also contributes to torsional vibration.

Types of Torsional Vibrations

1. Free Torsional Vibration:
   This type occurs when the system vibrates about its equilibrium position without any external torque acting on it. The frequency of such vibration depends on the shaft stiffness and mass moment of inertia.
2. Forced Torsional Vibration:
   In this type, the system is subjected to an external periodic torque. If the frequency of the applied torque matches the natural frequency of the system, resonance occurs, leading to large amplitude oscillations and possible damage.

Mathematical Representation

For a shaft of stiffness   (torsional stiffness) and a rotor of moment of inertia  , the equation of motion for free torsional vibration is:

Where   is the angular displacement.

The natural frequency   of torsional vibration is given by:

Here,   represents the angular natural frequency, and it determines how fast the system oscillates when disturbed.

Effects of Torsional Vibrations

1. Fatigue Failure: Repeated twisting and untwisting cause alternating stresses that may lead to fatigue cracks in the shaft.
2. Noise and Vibration: Excessive torsional vibration results in undesirable noise and mechanical vibrations in the system.
3. Damage to Couplings and Gears: Components like couplings, gear teeth, and bearings may wear out quickly due to cyclic torque.
4. Power Loss: The oscillating motion causes energy loss in the form of heat and friction.

Control and Reduction of Torsional Vibrations

1. Torsional Dampers: Devices such as viscous dampers absorb energy from vibration and reduce its amplitude.
2. Flexible Couplings: These are used to isolate vibrations between connected shafts.
3. Proper Shaft Design: Increasing shaft stiffness and reducing uneven mass distribution help minimize vibration.
4. Avoiding Resonance: Designing the system such that the operating speed avoids the natural frequency of torsional vibration.
5. Flywheels: Flywheels store rotational energy and maintain uniform torque transmission.

Importance in Engineering Design

Understanding torsional vibration is very important in designing rotating machinery. In crankshafts of internal combustion engines, torsional oscillations occur due to uneven firing intervals of cylinders. Engineers analyze the system using torsional vibration models to find critical speeds and resonance conditions. Based on these analyses, suitable materials, shaft dimensions, and damping systems are selected to prevent failure.

Torsional vibration analysis also plays a key role in marine engines, gas turbines, and generator shafts. Any neglect in considering torsional effects can lead to severe mechanical damage, system failure, or even accidents.

Conclusion:

Torsional vibrations are the twisting oscillations of rotating components caused by fluctuating torque or load. These vibrations can be dangerous as they produce alternating stresses and fatigue failure in mechanical systems. Proper design, damping, and vibration isolation techniques are used to control them. Understanding torsional vibrations helps engineers improve the safety, reliability, and performance of rotating machinery in various mechanical applications.