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MECHANICS OF MACHINES(BMFG 1833)

GOVERNOR

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Today’s Objectives:Students will be able to:•Apply free body diagram to solve problems in flywheel and governor

Contents: Function of Governor Centrifugal Governor Watt Governor Porter Governor Proell Governor Hartnell Governor Sensitivity and Friction Controlling Force

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The function of governor is to control the mean speed of engine, as distinct from that of flywheel, which controls only cyclic fluctuations in speed.

If the mean speed varies due to a variation in the load, the governor adjusts the fuel supply to the engine and restores the speed to its former value.

Governor can be divided into two types: Centrifugal governor and Inertial governor. Our focus is only on the centrifugal types of governor.

In the centrifugal types of governor, the effect of centrifugal force on the rotating balls causes a sleeve to rise until equilibrium is obtained. Any change in engine speed produces a change in the sleeve position, which adjusts the fuel supply accordingly.

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DEAD WEIGHT GOVERNOR

SPRING LOADED GOVERNOR

CENTRIFUGAL GOVERNOR

Watt Governor

Porter Governor

Proell Governor`

Hartnell Governor

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INERTIA GOVERNOR

In this type of governor the balls are adjusted in such a way that the inertia forces caused by the angular acceleration or retardation (rate of change of speed) of the governor shaft tend to change their positions.

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CENTRIFUGAL GOVERNOR

It consists of two balls connected to spindle through arms. The upper arms are keyed to the spindle and the lower arms which are known as links are connected to the sleeve. The sleeve is free to move or slide on the spindle.

The balls rotate with spindle (shaft), giving rise to the centrifugal force which radially acts outwards. The balls are in action because of change in speed. When the speed increases, the balls rotate at larger radius and the sleeve slides upwards on the spindle and with the help of lever the throttle is closed to the required extent.

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With the decrease in speed, the governor balls rotates at smaller radius of rotation, competing the sleeve to move down on the spindle. The downward movement of the sleeve opens the throttle to the required extent to admit the required fuel into the engine.

Any change in engine speed will produces a change in the sleeve position, which adjusts the fuel supply accordingly. As a result the speed of the engine will restore.

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WATT GOVERNOR

The Watt governor is basically a conical pendulum with the lower links attached to a sleeve of negligible mass. If the mass of the ball is m and the centrifugal force upon it is F, then taking moments about the instantaneous centre for the lower link, I:

IZmgXZF

IZmgXZFM I

0:

ball

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PORTER GOVERNOR

IZgMmIZMg

IZmgXZF

IZIYIYMg

IZmgXZFM I

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2 where;02

:

The Watt governor is only suitable for a speed range of about 60-80 rpm, and for higher speeds it is necessary to add a mass, M to the sleeve to increase the speed as in Porter governor. Taking moments about I:

M

Central weight

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PROELL GOVERNOR

IZgMmIZMg

IZmgXZF

IZIYIYMg

IZmgXZFM I

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2 where;02

:

The Proell governor is similar to the Porter governor, except that the balls are attached to extensions to the lower arms. This has the effect of reducing the change of speed necessary for a given sleeve. Taking moments about I:

M

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HARTNELL GOVERNOR

bMgP

aF

bMgP

aFM I

2

02

:

The Hartnell governor is assembled with the central spring initially compressed and this compression can be adjusted to give any required equilibrium speed for a given ball radius. If F is centrifugal force acting on the ball, P is the force exerted on the sleeve by the spring and M is the mass of the sleeve. Taking moments about the fulcrum, O of the bell-crank lever.

When the ball arm is not vertical, the moment of the ball weight about the fulcrum and the changes in length of the moment-arms are usually neglected.

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SENSITIVITY AND FRICTION

If the maximum and minimum speeds of a governor are ω1 and ω2 respectively and its mean speed is ω, the sensitivity of the governor is defined as:

The governor is sensitive if the difference in speeds is small for any position of sleeve.

If there is a friction force, f between the sleeve and the spindle, the effective sleeve load becomes:

falling is sleevewhen

rising is sleevewhen

fMg

fMg

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CONTROLLING FORCE

The radially inward, or centripetal force acting on each rotating ball due to the sleeve weight, spring force, etc., is termed the controlling force.

At any equilibrium speed, ω, the controlling force is equal and opposite to the centrifugal force.

mr

F

rmF

2

2

force, Controlling

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CONTROLLING FORCE

The variation of this force against radius is called controlling force curve.

For Porter governor For Hartnell governor

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CONTROLLING FORCE

A governor is stable if for each speed within the working range there is only one radius of rotation for equilibrium. Thus r must increase as ω increases. The ratio F/r increase as ω increases. This condition is satisfied in the case of the Porter governor curve.

But, for the Hartnell governor, it is only satisfied if the straight line intercepts the vertical axis below the origin, such as the line ab.

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CONTROLLING FORCE

A governor is isochronous (equal time interval) if the equilibrium speed is the same for all radii of rotation. The ratio F/r is then constant and corresponds to the controlling force line cd, passing through the origin.

A governor is unstable if the radius of rotation decreases as the speed increases. The ratio F/r decrease as r increases. This corresponds to a controlling force line which intercepts the vertical axis above the origin, such as the line ef.