Short Answer:

Equilibrium speed is the speed at which the centrifugal force acting on the governor balls becomes exactly equal to the controlling force (spring force or gravity). At this speed, the governor is in a balanced condition, and there is no movement of the sleeve either upward or downward. This means the fuel supply to the engine remains constant, and the engine runs steadily without acceleration or deceleration.

It is the mean speed of the engine for which the governor maintains equilibrium. If the engine runs at equilibrium speed, it is said to be in stable operation since both the driving and resisting forces are equal.

Detailed Explanation:

Equilibrium Speed

The equilibrium speed of a governor is a very important concept in the study of speed control mechanisms of engines. It represents the condition when the forces acting on the rotating balls of the governor are perfectly balanced. At this speed, the governor neither moves the sleeve up nor down, ensuring that the engine maintains a steady speed.

In a centrifugal governor, two main forces act on the rotating balls — the centrifugal force due to the rotation of the balls and the controlling force produced by the weight of the balls or a spring. The equilibrium condition occurs when these two forces become equal. Thus, equilibrium speed is the specific speed at which the centrifugal and controlling forces balance each other exactly.

Concept of Equilibrium Speed

To understand equilibrium speed clearly, let’s consider a centrifugal governor, such as a Watt or Porter governor. When the engine runs, the governor balls rotate around the spindle due to the centrifugal force. This force acts radially outward and tends to lift the balls and the sleeve upward. The upward motion of the sleeve reduces the fuel supply to the engine, thereby decreasing the speed.

However, a downward force acts on the balls due to gravity or spring tension, which tends to bring the balls back to their original position. When these two forces — centrifugal and controlling — are equal, the sleeve remains stationary. This condition of balance defines the equilibrium position, and the corresponding speed of the engine at that position is called the equilibrium speed.

If the engine speed increases beyond equilibrium speed, the centrifugal force becomes greater than the controlling force, causing the sleeve to rise. This movement reduces fuel supply, bringing the speed back to equilibrium. On the other hand, if the speed decreases below equilibrium speed, the centrifugal force becomes smaller, the sleeve moves downward, increasing fuel supply until the equilibrium speed is restored. Thus, the equilibrium speed acts as a reference speed around which the governor regulates engine operation.

Mathematical Expression

The centrifugal force acting on each ball is given by:

where,
= centrifugal force,
= mass of the ball,
= angular speed in rad/sec,
= radius of rotation,
= acceleration due to gravity.

At equilibrium speed,

The controlling force depends on the type of governor. In a Watt governor, it is due to the weight of the balls; in a spring-controlled governor, it comes from the tension in the spring. The corresponding speed at which these two forces balance gives the equilibrium speed.

Importance of Equilibrium Speed

1. Stable Engine Operation:
   The engine runs smoothly when it operates at equilibrium speed, as there are no sudden changes in fuel supply.
2. Basis of Governor Design:
   While designing a governor, engineers ensure that the equilibrium speed falls within the desired operating range of the engine.
3. Prevention of Speed Fluctuation:
   If the engine speed fluctuates above or below equilibrium speed, the governor automatically adjusts fuel supply to restore the balance.
4. Energy Efficiency:
   Maintaining the equilibrium speed ensures efficient fuel consumption since the engine does not over-speed or under-speed.
5. Safety of Engine Components:
   Continuous operation at equilibrium speed reduces mechanical stress on the parts of the engine and the governor.

Example

Suppose a governor is adjusted such that when the sleeve is at the mid-position, the engine speed is 300 rpm. If the speed increases above this, the sleeve moves upward; if it falls below, the sleeve moves downward. Thus, 300 rpm represents the equilibrium speed — the speed at which the governor is perfectly balanced.

Conclusion

In summary, equilibrium speed is the steady-state speed of an engine where the centrifugal force of the governor balls equals the controlling force. It represents the balanced condition of the governor mechanism, during which no corrective movement occurs. This speed is crucial for maintaining smooth and efficient engine operation, as it defines the point of stability around which the governor controls the speed variations.