 Today, we will study Governors' learning outcomes. At the end of this session, students will be able to examine the stability and sensitiveness of the Governor, analyze and identify the various terms in Governor. The content of this session is stability of Governor, isochronous Governor, hunting Governor, sensitiveness of Governor, controlling force diagram and references. So, stability of Governor, when for every speed within the working range, there is definite configuration that is, there is a only one radius of rotation of the balls at which Governor is in equilibrium that is known as stability of Governor. For a stable Governor, if the equilibrium speed increases, the radius of rotation of the ball must also increases. For unstable Governor, if the radius of rotation decreases as the speed increases that is nothing but unstable Governor. Isochronous Governor, a Governor is said to be isochronous when the equilibrium speed is constant for all radius of rotation of the balls within the working range neglecting the friction that is known as isochronous Governor. Now, let us consider a Porter Governor in which minimum and maximum equilibrium speed is given as shown in the presentation. So, n 1 square is equal to m plus m by 2 into 1 plus q divided by m into 895 divided by h 1 and similarly, n 2 square will be equal to m plus capital M divided by 2 into 1 plus q divided by m into 895 divided by h 2. Now, think for a while, if the equilibrium speed is constant for all radius of rotation of the balls, what will be the effect on the height of the Governor. So, if the equilibrium speed is constant for all radius of rotation, then the range of the speed that is n 2 minus n 1 will be equal to 0 or in other words n 2 is equal to n 1. And from above these two equation, we will get h 1 is equal to h 2 which is impossible in case of Porter Governor and hence the Porter Governor cannot be a isochronous Governor. In case of Hartnell Governor, running at a speed of n 1 and n 2 rpm, we have mg plus s 1 is equal to 2 times f c 1 into x 1 x divided by y is equal to 2 times m in bracket to power n upon 60 bracket square into r 1 multiplied by x by y. And similarly, for highest equilibrium speed, mg plus s 2 is equal to 2 times f c 2 into x by y is equal to 2 times m multiplied by 2 power n upon 60 bracket square into r 2 multiplied by x upon y. So, from these two equation for isochronous Governor, n 2 will be n 1, n 2 is equal to n 1 and therefore, from above two equation, we get mg plus s 1 divided by mg plus s 2 is equal to r 1 divided by r 2. And from above equation, isochronous Governor is not a practical case because the slew moves to one of its extreme position immediately if the speed deviates from isochronous speed. Hunting of the Governor, a Governor is said to be hunt if the speed of the engine fluctuates continuously above or below the mean speed of the engine. It is caused by two sensitive Governor, which changes the fuel supply by a large amount when a small change in speed of rotation take place. Let us consider the example, load on the engine increases, the speed of the engine decreases. If your Governor is too sensitive, then the slew falls to its lowest position. As a result of this, the throttle valve gets open widely and large amount of fuel is supplied to the engine as compared to its requirement. This results in increase in the speed rapidly. Due to increase in the speed, the slew rises to its highest position and therefore, which will results in cutting down the supply of working fluid to the engine. Of hunting of Governor, either Governor admits large amount of working fuel to the engine or it will cut down the supply of working fluid to the engine. That is called as hunting of a Governor. Sensitiveness of Governor, if we consider two Governors A and B running at same speed, when this speed increases or decreases by certain amount, the lift of A is greater than B, then Governor A is more sensitive than B. Generally, greater the lift of the slew corresponding to fractional change in the speed, the greater the sensitiveness of the Governor or in other word, sensitiveness of the Governor is defined as ratio of difference between maximum and minimum equilibrium speed to the mean equilibrium speed of the Governor, where n 1 and n 2 are the minimum and maximum equilibrium speed and is the mean equilibrium speed, which is equal to n 1 plus n 2 divided by 2 and therefore, sensitiveness of the Governor is equal to n 2 minus n 1 divided by n again, which is equal to n 2 minus n 1 multiplied by 2 divided by n 2 plus n 1. Controlling force diagram, when a body revolves in a circular path, there is an inward radial force or centripetal force acting on it. When a Governor is running at a steady speed, the inward force acting on the rotating ball is known as controlling force. It is equal and opposite to the centrifugal force, which is given by f c is equal to m r omega square. Controlling force is provided by weight of the slew and ball in case of Porter Governor, when the graph between controlling force and radius of rotation of the ball is drawn is called as controlling force diagram. This diagram enables the stability and the sensitiveness of the Governor to be examined. So, the figure shows the controlling force diagram for a Porter Governor. So, in case of Porter Governor, the centrifugal force acting on the ball f c is equal to m r omega square, put the value of omega 2 pi n by 60 and therefore, we will get n square is equal to 1 upon m multiplied by 60 upon 2 pi bracket square multiplied by f c upon r, where from the diagram f c upon r is nothing, but tan phi and therefore, putting the value of f c upon r is equal to tan phi and is equal to tan phi divided by m bracket raised to half multiplied by 60 upon 2 pi, where phi is the angle between the radius of rotation and the line joining the given point on the curve on the origin o. A Governor satisfying the condition of stability, the angle must increase with radius of rotation of ball. That means, phi must increase with increase in radius of rotation of the ball as shown in the figure. In other words, the equilibrium speed increases with radius of rotation of ball. For Governor to be more sensitive, the change in the value of phi over the change in the radius of rotation should be as small as possible. For isochronous Governor, the controlling force curve is straight line passing through origin. The angle phi is constant for all radius of rotation of Governor. So, tan phi is equal to f c upon r, putting the value of f c m r omega square divided by r, we will get 2 pi n upon 60 bracket square, which is equal to c into n square, where c is equal to m multiplied by in bracket 2 pi n upon 60 bracket square, where c is a constant. Using above relation, the angle phi may be determined for different values of n. And the lines are drawn from the origin. These lines enables the equilibrium speed corresponding to given radius of rotation to be determined. Reference says, this material is referred from a book of theory of machine by R S Kurmi.