GRAVITY CONTROLLED CENTRIFUGAL GOVERNORS

14.6.1  Watt Governor

This governor was initially used by James Watt in steam engine. The spindle is driven by the output shaft of the prime mover. The balls are mounted at the junction of the two arms. The upper arms are connected to the spindle and lower arms are connected to the sleeve as shown in Figure 14.4.

Figure 14.4 Watt Governor

Masses of the sleeves and upper and lower arms are considered as negligible for simplicity of analysis. We can ignore the frictional forces also. The ball is subjected to the three forces: centrifugal force (F_c), weight (mg), and tension in upper arm (T). Taking moment about point O

(Intersection of arm and spindle axis), we get

Example 14.2: Calculate the vertical height of a Watt governor rotating at the speed of 80 rpm. Also calculate the change in the height when the speed increases to 100 rpm.

Solution:

14.6.2  Porter Governor

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

    F_c 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