Short Answer:

Frictional torque is the torque that resists the motion of a rotating body due to friction between its contacting surfaces. It acts opposite to the direction of rotation and must be overcome by the driving torque for the system to move. This torque arises in machine parts like bearings, gears, shafts, and brakes, where surfaces rub against each other.

In simple terms, frictional torque reduces the efficiency of rotating systems by converting a portion of the input energy into heat. Understanding and calculating frictional torque is essential for designing mechanical systems that operate smoothly and with minimum energy loss.

Detailed Explanation :

Frictional Torque

Frictional torque is one of the most important concepts in mechanical engineering because it affects almost every rotating system. It is the resisting torque generated by frictional forces acting at the surfaces in contact when a body rotates or tries to rotate about an axis. This torque opposes the motion of the system and is responsible for power loss and wear in machine elements.

When two surfaces come into contact, microscopic irregularities interlock, leading to friction. As one surface moves over another, this friction produces a tangential force at the point of contact. When the force acts at a distance from the axis of rotation, it creates a torque. The torque caused by this resistance is known as frictional torque.

1. Definition and Expression

Frictional torque can be defined as the product of the frictional force and the effective radius at which the force acts.

Where,
= Frictional torque (N·m)
= Frictional force (N)
= Radius or distance of force from the axis of rotation (m)

If the frictional force is distributed over an area, such as in a bearing or clutch, the total frictional torque is obtained by integrating the frictional force over the entire contact surface.

2. Origin of Frictional Torque

Frictional torque arises due to:

• Contact between rotating and stationary parts.
• Pressure acting on the contact area.
• The coefficient of friction between surfaces.
• The radius of contact surface.

In systems such as bearings, shafts, gears, brakes, and clutches, frictional torque develops naturally as a result of motion. Although friction helps in transmitting torque in clutches or brakes, it becomes undesirable in bearings and shafts where it leads to energy loss.

3. Factors Affecting Frictional Torque

Several factors influence the magnitude of frictional torque:

1. Coefficient of Friction (μ):
   Higher coefficient means greater resistance and higher frictional torque. Using lubrication helps to reduce μ.
2. Normal Force (W):
   The torque increases as the load or normal reaction between surfaces increases.
3. Contact Radius (r):
   Frictional torque is directly proportional to the radius of contact. Larger radius leads to higher torque for the same frictional force.
4. Surface Roughness:
   Rougher surfaces increase interlocking of asperities, increasing frictional resistance and torque.
5. Speed of Rotation:
   At higher speeds, heat generation can change the frictional behavior and sometimes reduce effective torque due to lubrication effects.

4. Applications in Mechanical Systems

Frictional torque appears in many mechanical components, including:

• Bearings: Frictional torque opposes shaft rotation, leading to power loss. Engineers try to minimize it using lubricants or rolling elements.
• Brakes: Here, frictional torque is intentionally created to slow down or stop motion by applying friction pads on a rotating drum or disc.
• Clutches: Frictional torque helps in transmitting power between shafts by allowing controlled engagement and disengagement.
• Gears: Friction at gear teeth contact generates torque loss that slightly reduces transmission efficiency.
• Flywheels: Small frictional torque acts in bearings, slowly reducing the rotational speed when no external torque is applied.

5. Measurement of Frictional Torque

Frictional torque can be measured experimentally by applying a known force at a known radius and observing the equilibrium condition. Alternatively, it can be calculated using torque meters or dynamometers that measure the resisting torque during operation.

In bearings, for example, the frictional torque is calculated as:

where  is the normal load and  is the mean radius of the bearing surface.

6. Effect of Lubrication

Lubrication plays a key role in reducing frictional torque. A thin film of lubricant separates the surfaces, minimizing direct metal-to-metal contact. Depending on the regime (hydrodynamic, boundary, or mixed lubrication), the frictional torque can be significantly reduced, improving mechanical efficiency and life of components.

7. Power Loss Due to Frictional Torque

When a shaft rotates under the effect of frictional torque, part of the input power is consumed to overcome this resistance. The power loss due to friction is given by:

where  is the angular velocity in radians per second. This loss appears as heat, which can cause thermal expansion or degradation of materials if not properly managed.

8. Importance in Design

While frictional torque cannot be completely avoided, it must be minimized in systems where smooth motion and efficiency are required. Proper selection of materials, lubrication type, surface finish, and load distribution are essential to control frictional torque.

In contrast, in components like brakes and clutches, frictional torque must be sufficient to perform its function. Therefore, understanding its behavior helps in achieving the desired balance between performance and efficiency.

Conclusion

Frictional torque is the torque that resists rotation due to friction between contact surfaces. It plays both beneficial and adverse roles depending on the application. In brakes and clutches, it helps in controlling or transmitting power, while in bearings or shafts, it causes power loss and wear. By using suitable materials, lubrication, and surface treatments, frictional torque can be optimized for better machine performance and efficiency. Understanding and managing frictional torque is therefore a key part of mechanical system design and maintenance.