28 November 2019

Porter Governor | Construction | Working | Equation of height

Porter governor is same as Watt governor. If the watt governor sleeve is loaded with a heavyweight, it becomes a Porter governor. 

Let M = Mass of the sleeve
m = Mass of each ball
f = Force of friction at the sleeve
Porter Governor
Porter Governor

The frictional force always acts in the opposite direction to the motion, so when the sleeve moves up, the frictional force acts in the downward direction, and the downward force acting on the sleeve is Mg+f. Likewise, the force on the sleeve will be Mg-f when the sleeve moves down. Depending on whether the sleeve is going up or down, the net force acting on the sleeve is mg+f or Mg-f.

Forces acting on the sleeve and on each ball have been shown in the figure. 

Let h = height of the governor
r = distance of the centre of each ball from the axis of rotation

The instantaneous rotation centre of AB link is at I. It is because of the motion of its two points A and B relative to the link. The point A oscillates about the point O and B moves in the verticle direction parallel to the axis. 

Now, the equilibrium of the left-hand half of the governor and taking moments about I. We equate the equation form given below to find the height of governor. 

N2 = 895/h × [ 2mg + ( mg + or -  f ) ( 1 + k ) / 2mg ] 

This equation would provide two values of N for the governor for the same height depending upon the sleeve movement.