 Myself, Akshay Kumar Sovde, Assistant Professor, Mechanical Engineering Department. Today, we will study VAT Governor. Learning outcome. At the end of this session, student will be able to analyze and determine the height of the VAT Governor. Analysis of VAT Governor. This is a simple form of a VAT Governor. VAT Governor is a type of centrifugal governor, which is a simple conical pendulum governor in which the links are connected to a slew of negligible mass. Now, as shown in the figure, the arms of the Governors are pivoted on the axis of the spindle at point P. So, think in how many ways we can pivot the arms of the spindle, arms of the Governor on the axis of the spindle. So, the first way, the arms of the Governor pivot on the axis of the spindle at point P. The second way, the pivot point P may be offset to the axis of the spindle and when the arms are extended, they will intersect on the axis of the spindle at point O, where height of the Governor will remain same. The third way, the arms of the axis are offset, but they cross the axis of the spindle at point O. This is the third way in which you can arrange the arms of the Governor. Now, some terms which are used in case of VAT Governor, F c is the centrifugal force acting on the fly ball in Newton, W weight of the ball, M mass of the ball in kg, T tension in the arm in Newton, H height of the Governor, radius of rotation of balls in meter, omega angular velocity of arms and balls in variance per second. Now, in the analysis of VAT Governor, it is assumed that weight of the link arm and sleeve is negligible and therefore, the fly ball or Governor ball in equilibrium condition, the fly ball is under a equilibrium condition under the three forces. So, the fly ball will remain in equilibrium condition under three forces that is tension T in the arm. Secondly, the centrifugal force F c acting on the ball in Newton and third the weight of the ball in Newton. Now, taking the moment about point O, we will get F c into perpendicular distance H is equal to weight of the ball into its distance W into R. But, as we know centrifugal force acting on the rotating masses is given by M R omega square, where M is the mass of the ball, R is the radius of rotation of the fly ball and omega is the angular velocity and weight of the ball is nothing but M into G and therefore, putting these values, we will get M R omega square into H is equal to M into G into R and therefore, M will get cancelled R will also get cancelled and therefore, H is equal to G upon omega square, where G is a gravitational constant in meter per second square. Whereas, omega is the angular velocity of the ball which is given by 2 pi N upon 60, where N is the speed of the ball in R p m. So, putting the values of omega and G in above equation, we will get H is equal to 9.81 divided by 2 pi N upon 60 bracket square. So, solving this we will get H is equal to 895 divided by N square. So, this is the relation between height of the governor and the speed of the governor. So, from this equation, we can say the height of the governor is inversely proportional to the square of the speed of the governor and therefore, when at a higher speed, the height of the governor is very small. Hence, for when there is little change in the speed of the governor, there is a insufficient change in the height of the governor, which causes insufficient supply of working fluid to the engine at higher speed. And therefore, the WAD governor is relatively used at low speed. That means, the speed between 60 to 80 R p m, the WAD governor is used. Secondly, the speed of the governor is constant. In this case of governor, you can also calculate the change in the height of the governor due to change in the speed also. So, seen the expression for the WAD governor H is equal to 895 divided by N square. Now, we will see a simple problem. Find out the height of the governor when the WAD governor runs at a speed of 60 R p m. And also find the change in the height of the governor when the speed of WAD governor increases to 61 R p m. So, first of all, we will find out the height of the governor corresponding to 60 R p m. So, as we know the relation between H and speed of the governor for WAD it is given by 895 divided by N square. So, putting the value of speed in this above equation is H is equal to 895 divided by 60 bracket square. So, solving this we will get the height of the governor is equal to 0.248 meter. Now, when the speed increases to 61 R p m, we have to find out the change in the height. So, H is equal to 895 divided by 60 bracket square, which is equal to 895 divided by 61 bracket square. And therefore, in this case the height of the governor will be 0.24 meter. So, change in height of the governor due to increase in speed from 60 to 61 R p m. That is the difference between these two. That is 0.248 minus 0.24, which is equal to 0.08 meter. And hence the change in the height of the WAD governor due to increase in the speed is 0.08 meters. References, this material is referred from theory of machines by R. S. Kurmi, S. Chand publication and S. S. Watton, Tata, McGraw-Hill education, private limited. Thank you. Thank you.