Question

The following particulars refer to a pro-ell governor with open arms: Length of all arms = 200 mm, distance of pivot of arms from the axis of rotation = 40 mm, length of extension of lower arms to which each ball is attached =100 mm, mass of each ball = 6 kg and mass of the central load = 150 kg. If the radius of rotation of the balls is 180 mm when the arms are inclined at an angle of 40° to the axis of rotation, find the equilibrium speed for the above configuration.  

Answer 1

Given  PF = FD = 200 mm = 0.2 m; DK = 40 mm = 0.04 m; BF = 100 mm = 0.1 m;  m = 6 kg; M = 150 kg; r = JG = 180 MM = 0.18 M; f = 20 N

(i) Equilibrium speed

Let N = Equilibrium speed.

From the equilibrium position as shown in Fig, We find that tat height governor,

IM = IN - MN = FH - JF = 0.1286 -  0.0114  = 0.1172 m

ID = 2 x IN = 2 x FH = 2 x 0.1286 = ) = 2572 m

We know that centrifugal force,

Now taking moments about I,