## 14 February 2018

### Watt governor | Working | Limitations | Height calculation

Watt governor is the simplest form of a centrifugal governor. It is also called a simple conical pendulum governor. It is basically a conical pendulum with a link attached to a sleeve of negligible mass. This governor is used by James Watt in his steam engine and it also has many applications.

Working of Watt governor :

The upper sides of arms are pivoted with the governor balls so the governor balls can move upward and downward as they revolve with a vertical spindle. Bevel gears drive the engine. A bevel gear is driven by the spindle. The lower arms are connected to the sleeves and are keyed to the spindle in such a way that revolves around the spindle. At that time, it can slide up and down according to the spindle speed. Two stoppers are provided at the bottom and top of the spindle to limit the movement of the sleeve.

If the load on the engine decreases, the speed of the engine and then the angular velocity of the governor spindle increase. The centrifugal force on the ball increases that tends balls to move outward and the sleeve to move upward thus sleeve actuates a mechanism that operates the throttle valve at the end of the bell crank lever to decrease the fuel supply. Thus the power output is reduced.

If the speed of the engine decreases as the load on the engine increase, the centrifugal force decreases. So that the inward movement fly balls and downward movement of the sleeve cause a wide opening of the throttle valve. Engine speed increase with increasing the fuel supply.

Types of Watt governor :

The Watt governor was classified based on the position of upper arms. The arms can be connected by the way we describe below :

1. Pivot is on the axis of the spindle
2. Pivot is offset from spindle
3. The pivot is offset, and arms cross the axis.
Based on this Watt governors are classified into three types :
1. Simply pinned type governor
2. Open arm type governor
3. Crossed arm type governor
Simply pinned type governor: The upper arms are joined to a point O on the axis of the spindle, where both arms intersect the spindle axis.

Open arm type governor:
The upper arm of Watt governor is hinged on a collar attached to the spindle or joined by a horizontal link as shown in fig below i
nstead of connecting directly to the spindle. The arms, when produced, meet the axis of the spindle at O.

Crossed arm type governor:
The upper arms o governor in hinged on a collar on the axis of the spindle or arms are joined through a fixed horizontal link as shown in fig below. The arms intersect the axis at a point O.

Limitations of Watt governor :
• Its use is limited up to vertical position applications.
• It is used in a very slow speed engines because, at a higher speeds, the sensitivity of the governor will decrease.
Height Calculations :

The vertical distance from the plane of rotation of the balls to the point of intersection of the upper arms along the axis of the spindle is called the height of the governor.

The height of the governor decreases with an increase in speed and increases with a decrease in speed.

Let,
m = mass of each ball
h = height of governor
w = weight of each ball ( w = mg )
ω = angular velocity of the balls, arms and the sleeve
T = Tension in the arm
r = radial distance of ball-centre from spindle-axis

For the finding h, the height of governor the equilibrium of the mass provides

Tcosθ = mg and Tsinθ = mrω2
Tanθ = mrω2 / mg = rω2 / g
r / h = rω2 / g
h = g / ω2 = g / ( 2πN / 60 ) = ( 60 / 2π )2 * 9.81 / N2
h = 859 / N2 m
h = 859000 / N2 mm

Thus, the height of a Watt governor is inversely proportional to the square of the speed.