Short Answer:

Centrifugal tension is the tension that develops in a belt when it moves over pulleys at high speed. As the belt rotates, the mass of the belt tries to move outward due to centrifugal force, creating an additional pull on the belt. This extra tension increases the total tension on both the tight and slack sides of the belt, which affects the power transmission efficiency of the belt drive system.

When the speed of the belt increases, the centrifugal tension also increases, which can reduce the effective tension available for transmitting power. Therefore, it is important to consider centrifugal tension while designing belt drives for high-speed applications.

Detailed Explanation:

Centrifugal Tension

Centrifugal tension is a very important concept in the study of belt drives used for power transmission between two rotating shafts. When a belt moves at a high velocity around pulleys, each small portion of the belt experiences a force acting outward from the center of rotation. This outward acting force is known as the centrifugal force. Because of this centrifugal force, the belt tends to stretch, which increases its tension. The tension that arises due to this effect is called centrifugal tension.

When the belt is stationary, there is no centrifugal tension. However, as the speed of the belt increases, the centrifugal force acting on each unit length of the belt also increases. This force causes an additional tensile stress in the belt, which adds to the existing tension on both the tight and slack sides of the belt.

Expression for Centrifugal Tension

Let the following symbols be used:

•  = mass of belt per unit length (kg/m)
•  = velocity of the belt (m/s)
•  = centrifugal tension (N)

The centrifugal force acting on a small element of the belt is given by:

Hence, the centrifugal tension in the belt is:

This formula shows that centrifugal tension depends on the mass of the belt and the square of its velocity. Therefore, if the belt speed doubles, the centrifugal tension increases by four times.

Effect of Centrifugal Tension on Belt Drive

The centrifugal tension affects the performance and design of the belt drive system in several ways:

1. Increase in Total Tension:
   The total tension in the tight and slack sides increases due to centrifugal tension.
   • Tension in tight side =
   • Tension in slack side =
     Here,  and  represent the tensions without considering centrifugal force.
2. Reduction in Effective Tension:
   The effective tension available for power transmission is the difference between the tight side and slack side tensions. Although both sides gain equal centrifugal tension, it does not directly affect the effective tension, but it increases the total load on the belt and pulley, which may affect life and performance.
3. Limitation on Speed:
   If the speed is too high, centrifugal tension becomes large enough to reduce the frictional grip between the belt and pulley, leading to slippage. Hence, there is always a limiting speed above which a belt cannot operate efficiently.
4. Design Considerations:
   While designing belt drives, engineers must consider centrifugal tension, especially in high-speed drives such as those used in turbines, compressors, and engines. If neglected, it can lead to belt failure due to excessive tension or pulley wear.

Power Transmission with Centrifugal Tension

The power transmitted by the belt is given by:

Here  and  include the centrifugal tension component. When the belt speed increases, initially the power transmitted increases, but after a certain point, centrifugal tension increases rapidly, reducing the effective tension difference . Hence, there is an optimum belt speed at which maximum power can be transmitted.

The condition for maximum power is:

This means that when centrifugal tension equals one-third of the maximum tension in the belt, the power transmitted is maximum.

Practical Importance

Centrifugal tension becomes significant only in high-speed belt drives. In slow-speed systems, it is often negligible. For example, in agricultural machinery or small engines, belt speed is low, so centrifugal tension is not considered. But in machines like turbines, fans, or high-speed conveyors, ignoring it can result in belt stretching, slippage, or even failure.

Engineers therefore select materials with good flexibility, low mass per unit length, and high tensile strength to minimize centrifugal effects and maintain efficiency.

Conclusion:

Centrifugal tension is the additional tension developed in a moving belt due to the centrifugal force acting outward when the belt moves at high speed. It plays a vital role in the design and analysis of high-speed belt drives. Understanding and controlling this tension helps in improving belt life, maintaining grip, and ensuring safe and efficient power transmission. Proper calculation of centrifugal tension ensures that the belt drive system works smoothly without unnecessary wear or energy loss.