A schematic diagram of the porter governor is shown in Figure 14.5. There are two sets of arms. The top arms OA and OB connect balls to the hinge O. The hinge may be on the spindle or slightly away. The lower arms support dead weight and connect balls also. All of them rotate with the spindle. We can consider one-half of governor for equilibrium.
Figure 14.5 Force Analysis in Porter Governor
Let w be the weight of the ball
W be the central load
T1 and T2 be tension in upper and lower arms, respectively
Fc be the centrifugal force
r be the radius of rotation of the ball from axis
I is the instantaneous centre of the lower arm
Taking moment of all forces acting on the ball A or ball B about I and neglecting friction on the sleeve, we get
If friction acting on the sleeve be f, the force at the sleeve can be replaced by W + f for rising and (W − f) for falling speed as friction opposes the motion of sleeve. Therefore, if the friction at the sleeve is to be considered, W should be replaced by (W ± f). The expression for ω2 can be written as
Example 14.3: A porter governor has equal arms length of 240 mm long and pivoted at the axis of rotation. Each ball has a mass of 5 kg and the mass of central load on the sleeve is 20 kg. When the governor begins to lift, the radius of rotation of the ball is 120 and 150 mm when the governor is at maximum speed. Find the minimum and maximum speeds and range of speed of the governor.
Solution:
Let N1 = Minimum speed
Here, arms length is equal, therefore, tan α = tan β and k = 1
At maximum speed
Leave a Reply