Seven Questions on Governor

 Seven Questions on Governor

Question.1. Draw a neat sketch of centrifugal governor.

Answer.

Fig. Centrifugal Governor

Question.2. Classify centrifugal governors.

Answer.

Question.3. Differentiate between flywheel and governor.

Answer.

 

Question.4. Derive an expression for the height of a porter governor.

Answer. 

Porter governor is modification of a simple Watt governor. A central load is attached to the sleeve as shown in fig. The central load moves along the central spindle. This additional downward force increases the speed of rotation required to enable the balls to rise to any predetermined level.

Fig. Porter Governor

Neglecting the friction between the spindle and sleeve and considering the equilibrium of right half configuration, let us take moments about I.

if the arms of the governor are equal and pivoted on the axis of spindle or are at equidistant from the axis of spindle, then

Now let us consider the force of friction between the sleeve and the spindle.

The force of friction always acts in a direction opposite to that of motion. Thus, when the sleeve move upward, the force of friction on sleeve acts downward. Similarly, when sleeve moves downward, the force of friction on sleeve acts upward. In general, the net force acting on the sleeve is  depending upon the movement of sleeve.

After considering friction, the equation (i) becomes

Question.5. Explain the construction and working of hartnell governor with the help of neat sketch.

Answer. Hartnell governor is a spring loaded governor. Initially, the spring is fitted in compression so that a force is applied to the sleeve. It consists of two bell crank levers hinged in the frame. The frame is attached to the governor spindle and therefore, rotates with it. Each bell crank lever carries a mass at one and a roller at the other. The rollers fit into a groove in the sleeve as shown in fig.

As the speed increases, the balls move away from the spindle axis, the bell crank levers move on the pivot and lift the sleeve against the spring force. As the speed decreases, the sleeve moves downwards. The movement of the sleeve is further taken to the throttle of the engine. The spring force can be adjusted with the help of a screw cap nut.

Fig. Hartnell Governor

Q.6. Derive an expression for the effort of a governor.

Answer.

When a governor is running at constant speed, it is in equilibrium and the net force acting on the sleeve is zero. If the load on the engine changes, the speed also changes and hence, the sleeve of the governor changes its position. This can take place only if, a certain force acts on the sleeve and the sleeve will occupy a new equilibrium position when the resultant force acting on it becomes zero again. The average force which acts on the sleeve for a given percentage change of speed is called effort of the governor.

The governor effort may be calculated in the following way:

Let us consider a Porter governor. Let  be the equilibrium speed of the governor and let it change to .

If the arms of the governor are equal and pivoted on the axis of rotation, then

Let R is the force applied on the sleeve which prevents its motion at new speed .

Dividing equation (i) by (ii), we get

Let  is the frictional force between the sleeve and the spindle of the governor, then

Let  are the angles of inclination of the upper and lower arms with the axis of governor spindle respectively, then neglecting friction,

For a simple watt governor,

It can be seen from the equation (iii) and (iv) that the effort of Porter governor is more than Simple Watt governor.

Question.7. Derive an expression for the power of governor.

Answer.

Power of a Governor : The power of governor is defined as the workdone on the sleeve of governor for a given percentage of change in speed of the governor. It is calculated by the product of effort and the displacement of the sleeve.

Let us consider a Porter governor. Let  be the equilibrium speed of the governor and let it changes to .

If the arms of the governor are equal and pivoted on the axis of rotation, then

At new speed ,

Change in the level of balls,

For a simple Watt governor,