TERM PAPER

OF

MECHANICS-101

TOPIC-STUDY DIFFERENT TYPES OF GOVERNORS AND ALSO STUDY DIFFERENCE

BETWEEN GOVERNOR AND FLYWHEEL.

SUBMITTED TO: SUBMITTED BY:

JASPREET SINGH JASHANDEEP KAUR

ROLL N0- A12

SECTION- B2001

REG NO- 11002566

ACKNOWLEDGEMENT

First and the foremost I would like to thank to my almighty for giving me courage to bring up this term paper.At the outset, I would like to propose a word of thanks to my teacher, friends and other sources that gave an unending support and helped me in numerous ways from the first stage of my term paper conceived.I would also like to thank my family members for their whole hearted support and cooperation.I duly acknowledge the contribution of Mr.Jaspreet Singh for invaluable help. Writing about different types of governors was an uphill task and would have not been possible without proper and timely assistance of Mr.Jaspreet SinghI would also thanks to all my friends for forwarding their suggestions to make necessary modifications.Special thanks to Mr.Jaspreet Singh for his able guidance in my term assignment.

INTRODUCTIONA governor, or speed limiter, is a device used to measure and regulate the speed of a machine, such as an engine. A classic example is the centrifugal governor, also known

as the Watt or fly-ball governor, which uses weights mounted on spring-loaded arms to determine how fast a shaft is spinning, and then uses proportional control to regulate the shaft speed.

History

The Gibbs Governor

Centrifugal governors were used to regulate the distance and pressure between millstones in windmills since the 17th century. Early steam engines employed a purely reciprocating motion, and were used for pumping water – an application that could tolerate variations in the working speed. It was not until the Scottish engineer James Watt introduced the rotative steam engine, for driving factory machinery, that a constant operating speed became necessary. Between the years 1775 and 1800, Watt, in partnership with industrialist Matthew Boulton, produced some 500 rotative beam engines. At the heart of these engines was Watt’s self-designed "conical pendulum" governor: a set of revolving steel balls attached to a vertical spindle by link arms, where the controlling force consists of the weight of the balls.

Building on Watt’s design was American engineer Willard Gibbs who in 1872 theoretically analyzed Watt’s conical pendulum governor from a mathematical energy balance perspective. During his Graduate school years at Yale University, Gibbs observed that the operation of the device in practice was beset with the disadvantages of sluggishness and a tendency to overcorrect for the changes in speed it was supposed to control.

A flywheel is a mechanical device with a significant moment of inertia used as a storage device for rotational energy. Flywheels resist changes in their rotational speed, which helps steady the rotation of the shaft. Flywheels can be used to produce very high power pulses for experiments, where drawing the power from the public network. Recently, flywheels have become the subject of extensive research as power storage devices for uses in vehicles and power plants.

History

The principle of the flywheel is found in the Neolithic spindle and the potter's wheel. The Andalusian agronomist Ibn Bassal (fl. 1038-1075), in his Kitab al-Filaha, describes the flywheel effect employed in a water wheel machine, the saqiya. The flywheel as a general mechanical device for equalizing the speed of rotation is, according to the American medievalist Lynn White, recorded in the De diversibus artibus (On various arts) of the German artisan Theophilus Presbyter (ca. 1070-1125) who records applying the device in several of his machines. In the Industrial Revolution, James Watt contributed to the development of the flywheel in the steam engine, and his contemporary James Pickard used a flywheel combined with a crank to transform reciprocating into rotary motion.

TABLE OF CONTENTS

Governor Types

Principle of operation

Centrifugal governor

1) Gravity loaded controlled governors

a) Watt governor

b) Porter governor

c) Proell governor

2) Spring loaded controlled governors

a) Hartnell governor

b) Hartung governor

Inertia governor

Function of a governor

Requirements of a governor

Examples

Flywheel

Applications

Difference between governor and flywheel

References

GOVERNORA governor, or speed limiter, is a device used to measure and regulate the speed of a machine, such as an engine. It’s a device that automatically maintains the rotary speed of an engine within reasonably close limits regardless of the load. A classic example is the centrifugal governor, also known as the Watt or fly-ball governor, which uses weights mounted on spring-loaded arms to determine how fast a shaft is spinning, and then uses proportional control to regulate the shaft speed. A governor changes its mechanical and/or electrical configuration in response to speed variations. Those changes are used to control the input.

TYPES:

The type of governor used on diesel engines is dependent upon the application required. The six basic types of governors are as follows: 1. Mechanical centrifugal flyweight style that relies on a set of rotating flyweights and a control spring; used since the inception of the diesel engine to control its speed.

2. Power-assisted servo mechanical style that operates similar to the mechanical centrifugal flyweight but uses engine oil under pressure to move the operating linkage.

3. Hydraulic governor that relies on the movement of a pilot valve plunger to control pressurized oil flow to a power piston, which, in turn, moves the fuel control mechanism.

4. Pneumatic governor that is responsive to the air flow (vacuum) in the intake manifold of an engine. A diaphragm within the governor housing is connected to the fuel control linkage that changes its setting with increases or decreases in the vacuum.

5. Electromechanical governor uses a magnetic speed pickup sensor on an engine-driven component to monitor the rpm of the engine. The sensor sends a voltage signal to an electronic control unit that controls the current flow to a mechanical actuator connected to the fuel linkage.

6. Electronic governor uses magnetic speed sensor to monitor the rpm of the engine. The sensor continuously feeds information back to the ECM (electronic control module). The ECM then computes all the information sent from all other engine sensors, such as the throttle position sensor, turbocharger-boost sensor, engine oil pressure and temperature sensor, engine coolant sensor, and fuel temperature to limit engine speed

The governors, used on heavy-duty truck applications and construction equipment, fall into one of two basic categories:

1. Limiting-speed governors sometimes referred to as minimum/maximum models since they are intended to control the idle and maximum speed settings of the engine. Normally there is no governor control in the intermediate range, being regulated by the position of the throttle linkage.

2. Variable-speed or all range governors that are designed to control the speed of the engine regardless of the throttle setting.

Other types of governors used on diesel engines are as follows:

1. Constant-speed, intended to maintain the engine at a single speed from no load to full load.

2. Load limiting, to limit the load applied to the engine at any given speed. Prevents overloading the engine at whatever speed it may be running.

3. Load-control, used for adjusting to the amount of load applied at the engine to suit the speed at which it is set to run.

4. Pressure regulating, used on an engine driving a pump to maintain a constant inlet or outlet pressure on the pump.

Mechanical Governors In most governors installed on diesel engines used by the Navy, the centrifugal force of rotating weights (fly balls) and the tensions of a helical coil spring (or springs) are used in governor operation. On this basis, most of the governors used on diesel engines are generally called mechanical centrifugal flyweight governors.

PRINCIPLE OF OPERATION When the load on an engine increases or decreases, obviously its speed will respectively decrease or increase to the extent of variation of load. This variation of speed has to be controlled by the governor, within small limits of the mean speed. This necessities that when the load increases and consequently the speed decreases, the supply of fuel to one engine has to be increased accordingly, to compensate for the loss of the speed, so as to bring back the speed close to the mean speed. Conversely when the load decreases, and the speed increase, the supply of fuel has to be reduced. This implies that the governor should have its mechanism working such a way, that

the supply of fuel is automatically regulated according to the load requirement for maintaining approximately a constant speed.

Governors are classified based upon two different principles:

1. Centrifugal 2. Inertia

In the first type two or more masses termed the governor balls are caused to revolve about the axis of the shaft, which is driven through suitable gearing from the engine crankshaft. Each ball is acted upon by a force, which acts in the radially inward direction and is provided by a dead weight, a spring or a combination of the two. This force is termed as the controlling force and it must increase in magnitude as the distance of the ball from the axis of rotation increases. When the governor balls are revolving at a uniform speed, the radius of rotation clearly will be such that the outward inertia or centrifugal force is just balanced by inward controlling force. If the speed of rotation now increases owing to decrease of a load on the engine, the governor balls will move outward until the centrifugal force is again balanced by the controlling force. Conversely, if the speed of rotation decreases owing to the increase of the load on the engine, the governor balls will move inward until the centrifugal force is again balanced by the controlling force. This movement of balls is transmitted by the governor mechanism to the valve, which controls the amount of energy supplied to the engine, so that movement in the outward direction reduces the valve opening and movement in the inward direction increases the valve opening.

Governors of the second type operate on a different principle. The governor balls are so arranged that the inertia force caused by an angular acceleration or retardation of the governor shaft tend to alter their positions. The amount of the displacement of the governor balls caused by inertia forces is controlled by suitable springs and, through governor mechanism, alters the amount of energy supplied to the engine. The obvious advantage of this type of governor lies in its more rapid response to the effect of the change of load, since the displacement of the balls is determined by the rate of change of speed of rotation, as distinct from the actual change of speed of rotation, such as is required in governors of the first type. This advantage is offset, however, by the practical difficulty of arranging for the complete balance of the revolving parts of the governor. For this reason centrifugal governors are much more frequently used than the inertia governors.

CENTRIFUGAL GOVERNOR

Drawing of a centrifugal "flyball" governor

Centrifugal governors may be divided into:a) Gravity loaded- controlled governors as in fig. 3.1b) Spring loaded- controlled governors as in fig. 3.2

In the gravity loaded- controlled governors, an equation of equilibrium is obtained by taking moments of forces about instantaneous center, I, of the lower link, thus eliminating the tension in the upper link and the side thrust at the sleeve.

In the spring loaded- controlled governors, moment of forces are taken about the fulcrum of the bell-crank levers, eliminating the reaction at the point, and in the type shown in fig. 3.2© moments are taken about the instantaneous center, I, for the upper bell-crank arm to eliminate the reaction between the roller and the top of the spindle. GRAVITY LOADED CONTROLLED GOVERNORS

a) WATT GOVERNORb) PORTER GOVERNORc) PROELL GOVERNOR

a) WATT GOVERNOR

Probably the most widely used governor in the early days, it is named the Watt governor because James Watt applied it to his early beam engines. He did not however invent it as it had been in use on wind and water mills many years before this.

A belt or gearing from the engine crankshaft drives the input shaft 'm' causing the bevel gears 'l' to revolve and in turn rotate the vertical shaft 'a'. The bracket 'b' at the top of 'a' supports two arms 'c' which are pivoted at the top, at the end of the arms are two very heavy metal weights 'B' partway along the arms 'c' are fixed two pivoted link arms’d’ which link to a collar 'c' which rotates with them but is able to slide up and down shaft ‘a’.

The up and down motion of this collar is followed by a pair of pins 'f' which move a bell crank 'g' which is in turn linked to a throttle actuating rod 'i' linked to a throttle or butterfly valve in the supply of steam to the engines cylinder which can allow more or less steam through.

At rest the governor weights are held in the lowest position by gravity, the throttle will be in its most open position. As the engine speed increases these weights rotate faster until centrifugal force exceeds that of gravity and they fly further outwards and as a result of the linkages, upwards, this movement is transmitted to the throttle valve which begins to close. The faster the governor is driven the further out the weights move and the more the throttle is closed, until the amount of steam it lets through balances the demand and the engine speed stabilises.

If the load the engine drives is reduced it will increase speed, the governor restricts steam flow more until the speed stabilises, if load is added to the engine the speed drops, the throttle is opened more and more steam allowed in to compensate for the demand.

The Watt governor is a simple governor but is not terribly accurate where very fine control of speeds in needed and so was superseded in many applications by more specialised and accurate governors, however for many agricultural end pumping engines where absolute speed was not essential it survived and can still be seen on numerous preserved engines.

The height of a watt governor is inversely proportional to the square of speed. At high speeds, the movement of the sleeve becomes very small and thus this type of governor is unsuitable for high speeds.

b) PORTER GOVERNOR

The Porter Governor was the first effective High Speed engine governor, Designed by the American engineer George Porter. The governor is driven via a pulley (k) through a set of bevel gears (not shown) a vertical shaft (d) is rotated, this in turn drives from above the governor balls (a), through linkages (c) the large and heavy governor deadweight (b) is also rotated, this is free to slide up and down the shaft (d) but rotates at the same speed as the balls.

As rotational speed increases centrifugal force acts on the balls and they try to fly outwards, they are restricted by the linkages (c) held by the weight of the dead-weight (b), however, when a speed is reached at which this force exceeds the resistance imposed by the dead-weight they will lift the weight up and be allowed move outwards.

This action lifts the collar at the base of the dead-weight at point (f) this lifts the lever (g) which is pivoted at point (e) the lever has a counterbalance weight (a) and a dashpot or oil damper (i) which prevents rapid movements of the governor mechanism which can lead to the engine 'hunting' which is unwanted speed fluctuations due to the sensitivity of the governor.

Linkage (l) moves up or down and is connected to the engine this controls the steam allowed into the cylinder either by the amount allowed through a valve or the amount of time a valve is open for, if the engine runs too fast either the quantity of steam allowed in will be reduced or it will be let in for a shorter time, if the engine runs slower then either more steam is let in or it is let in for a longer time.

In porter governor, the sleeve is loaded with a heavy mass which improves the action of the governor.

c) PROELL GOVERNOR

It is similar to the porter governor having a heavy central load at the sleeve. But it differs from the porter governor at the arrangement of balls. The balls are carried on the extension of the lower arms instead at the junction of upper and lower arms. The action of this governor is similar to the watt’s governor. An increase in the speed of rotation increases the radius of rotation and raises the sleeve, thus reducing the amount of energy supplied to the engine. Conversely, a decrease in speed results in decrease in radius of rotation, thus lowering the sleeve and increasing the amount of energy supplied to the engine.

Proell governor runs at a lower speed then the porter governor. In order to give the same equilibrium speed a ball of smaller mass maybe used.

SPRING LOADED CONTROLLED GOVERNORS

a) HARTNELL GOVERNOR A Hartnell governor is a spring loaded governor in which the balls are controlled by a spring. It consists of a casing in which a pre-compressed spring is housed so as to apply the force to the sleeve. Two bell crank levers, each carrying a ball at one end and the roller at another end, are fitted on the frame of casing. The casing along with the frame and spring rotates about the axis of governor. When the speed of governor is increased, the balls flyout away from the governor axis, the bell crank lever moves on pivot and its roller end lifts the sleeve against the spring force. This movement of sleeve is transferred to the throttle of an engine through suitable intermediate links. The spring force can be adjusted with the help of a nut.

b) HARTUNG GOVERNORIt is a spring controlled governor which is a modification of the Wilson-hartnell governor.the balls here are directly controlled by separate springs. The vertical arms of the bell crank levers are fitted with spring balls which compress against the sleeve of the governor when the roller at the horizontal arm presses against the sleeve.

CHARACTERISTICS OF CENTRIFUGAL GOVERNOR

Force at the sleeve to operate the control & mechanism For satisfactory performance and working a centrifugal governor should possess the following qualities.

a. On the sudden removal of load its sleeve should reach at the top most position at once.

b. Its response to the change of speed should be fast.

c. Its sleeve should float at some intermediate position under normal operating

conditions.

d. At the lowest position of sleeve the engine should develop maximum power.

e. It should have sufficient power, so that it may be able to exert the required

2. INERTIA GOVERNORS

The inertia type governors are fitted to the crankshaft or flywheel of an engine and so radically in appearance from the centrifugal governors. The balls are so arranged that the inertia forces caused by an angular acceleration or retardation of the shaft tend to alter their positions. The amount of displacement of governor balls is controlled by the suitable springs and through the governor mechanism, alters the fuel supply to the engine. This governor is more sensitive than the centrifugal, but it becomes difficult to completely balance the revolving parts. For this reason centrifugal governors are more frequently used.

The advantage of this type of Governor is that the positions of the balls are affected by the rate of change of speed of the governor shaft. Consequently a more rapid response to a change of load is obtained, since the action of the governor is due to acceleration and not to a finite change of speed. The advantage is offset, however by the practical difficulty of arranging for a complete balance of the revolving parts of the governor. For this reason centrifugal governors are much more frequently used.

FUNCTION OF GOVERNORThe function of the governor, as applied to the engines, is to adjust the supply of fuel according to the load requirements so as to keep the speeds at various, loads, as close to the mean speed as possible, over long range of working of the engines.

Its function is distinct from that of a flywheel, which acts as a reservoir and keeps the speed within certain limits of the mean speed during the thermodynamic cycles. The

function of a flywheel is continuous from cycle to cycle, nut that of governor it is more or less intermittent i.e. it reacts only whenever there is variation of load.

In brief governor takes care of the change of speed due to load variation over periods of the engine’s running and tends to keep it as close to the mean speed as possible, where as the flywheel is responsible only in keeping the speed fluctuations, during each cycle within certain permissible limits of the mean speed. As such, one cannot be replaced by the other.

To sum up, the function of governor is:

a) To control the engine speed

b) To maintain the speed of an engine within prescribed limits for varying load conditions.

c) To maintain constant speed of the piston

d) To maintain constant engine speed

GOVERNOR EFFORTA governor running at a constant speed is in equilibrium and the resultant force acting on the sleeve is zero. If the speed of the governor increases there is a force on the sleeve which tends to lift it. This force will gradually go on decreasing till the governor starts rotating in equilibrium at the new position of rotation. The mean force acting on the sleeve for a given change of speed or lift of the sleeve is known as the governor effort.

EQULIBRIUM SPEED

The speeds at which the governor balls, the arms etc. are in complete equilibrium and the sleeve does not tend to move upward or downward are called the equilibrium speeds. The speed at the mean position of the balls or the sleeve is the mean equilibrium speed and at the maximum and minimum radius of rotation of the balls without tending to move either way are termed as maximum and minimum equilibrium speeds respectively. There can be many equilibrium speeds between the mean and maximum and the mean and the minimum equilibrium speeds.

CONTROLLING FORCE

The force acting radially upon the rotating balls to counteract its centrifugal force is called the controlling force. It is provided by weight of the sleeve, central load on the sleeve, compressed spring and the weight of the balls.

REQUIREMENTS OF A GOVERNOR

Isochronism: This is an extreme case of sensitiveness. When the equilibrium speed is constant for all radii of rotation of the balls within the working range, the governor is said to be in isochronism. This means that the difference between the maximum and minimum equilibrium speeds is zero and the sensitiveness shall be infinite.

Stability: Stability is the ability to maintain a desired engine speed without fluctuating. Instability results in hunting or oscillating due to over correction. Excessive stability results in a dead-beat governor or one that does not correct sufficiently for load changes. Thus, the stability and the sensitivity of a governor are opposite in character.

Hunting: The phenomenon of continuous fluctuation of the engine speed above and below the mean speed is termed as hunting. This occurs in over- sensitive orisochronous governors.

Rapidity of action: The governor should respond quickly to change in load.

Suppose an isochronous governor is fitted to an engine running at a steady load.With a slight increase of load, the speed will fall and the sleeve will immediatelyfall to its lowest position. This shall open the control valve wide and excess supplyof energy will be given, with the result that the speed will rapidly increase and thesleeve will rise to its higher position. As a result of this movement of the sleeve,the control valve will be cut off; the supply to the engine and the speed will againfall, the cycle being repeated indefinitely. Such a governor would admit eithermore or less amount of fuel and so effect would be that the engine would hunt.

Sensitiveness: A governor is said to be sensitive, if its change of speed s from no load to full load may be as small a fraction of the mean equilibrium speed aspossible and the corresponding sleeve lift may be as large as possible.

Supposeω1 = max. equilibrium speedω2 = min. equilibrium speedω = mean equilibrium speed = (ω1+ ω2)/2Therefore sensitiveness = (ω1- ω2)/2

The sensitivity also determines the change in the position of the governor affected by small change in the speed of the turbine.

Height of governor:It is the vertical distance between the center of the governor halls and the point of intersection between the upper arms on the axis of spindle is known as governor height. It is generally denoted by h.

Sleeve lift:

The vertical distance the sleeve travels due to change in the equilibrium speed is called the sleeve lift. The vertical downward travel may be termed as negative lift.

EXAMPLES:

On aircraft propellers the governor senses shaft rpm, and adjusts or controls the angle of the blades to vary the torque load on the engine. Thus as the aircraft speeds up (as in a dive) or slows (in climb) the RPM is held constant.

A Pneumatic governor mechanism sense air flow from the flywheel blower used to cool an air-cooled engine. The typical design includes a air vane mounted inside the engine's blower housing and linked to the carburetor's throttle shaft. A spring pulls the throttle open and as the engine gains speed, increased air flow from the blower forces the vane back against the spring, partially closing the throttle. Eventually a point of equilibrium will be reached and the engine will run at a relatively constant speed. Pneumatic governors are simple in design and inexpensive to produce. However, they do not regulate engine speed very accurately and are affected by air density, as well as external conditions that may influence airflow.

Centrifugal flyweight mechanism driven by the engine is linked to the throttle and works against a spring in a fashion similar to that of the pneumatic governor, resulting in essentially identical operation. A centrifugal governor is more complex to design and produce than a pneumatic governor. However, the centrifugal design is more sensitive to speed changes and hence is better suited to engines that experience large fluctuations in loading.

Electronic servo motor is linked to the throttle and controlled by an electronic module that senses engine speed by counting electrical pulses emitted by the ignition system or a magnetic pickup. The frequency of these pulses varies directly with engine speed, allowing the control module to apply a proportional voltage to the servo to regulate engine speed. Due to their sensitivity and rapid response to speed changes, electronic governors are often

fitted to engine-driven generators designed to power computer hardware, as the generator's output frequency must be held within narrow limits to avoid malfunction.

FLYWHEEL

A flywheel is a mechanical device with a significant moment of inertia used as a storage device for rotational energy. Flywheels resist changes in their rotational speed, which helps steady the rotation of the shaft when a fluctuating torque is exerted on it by its power source such as a piston-based (reciprocating) engine, or when an intermittent load, such as a piston pump, is placed on it. Flywheels can be used to produce very high power pulses for experiments, where drawing the power from the public network would produce unacceptable spikes. A small motor can accelerate the flywheel between the pulses. Recently, flywheels have become the subject of extensive research as power storage devices for uses in vehicles and power plants; see flywheel energy storage.

A flywheel is a spinning wheel or disc with a fixed axle so that rotation is only about one axis. Energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:

where

ω is the angular velocity, and I is the moment of inertia of the mass about the center of rotation. The moment of inertia is the measure of resistance to torque applied on a spinning object (i.e. the higher the moment of inertia, the slower it will spin after being applied a given force).

a) The moment of inertia for a solid-cylinder is ,

b) for a thin-walled empty cylinder is ,

c) and for a thick-walled empty cylinder is

where m denotes mass and r denotes a radius.

When calculating with SI units, the standards would be for mass, kilograms; for radius, meters; and for angular velocity, radians per second. The resulting answer would be in joules.

The amount of energy that can safely be stored in the rotor depends on the point at which the rotor will warp or shatter. The hoop stress on the rotor is a major consideration in the design of a flywheel energy storage system.

where

σt is the tensile stress on the rim of the cylinderρ is the density of the cylinderr is the radius of the cylinder, andω is the angular velocity of the cylinder.

High energy materials For a given flywheel design, it can be derived from the above equations that the kinetic energy is proportional to the ratio of the hoop stress to the material density and to the mass.

could be called the specific tensile strength. The flywheel material with the highest specific tensile strength will yield the highest energy storage per unit mass. This is one reason why carbon fiber is a material of interest.

APPLICATIONSIn application of flywheels in vehicles, the phenomenon of precession has to be considered. A rotating flywheel responds to any momentum that tends to change the direction of its axis of rotation by a resulting precession rotation. A vehicle with a vertical-axis flywheel would experience a lateral momentum when passing the top of a hill or the bottom of a valley (roll momentum in response to a pitch change). Two counter-rotating flywheels may be needed to eliminate this effect.

In a modern application, a momentum wheel is a type of flywheel useful in satellite pointing operations, in which the flywheels are used to point the satellite's instruments in the correct directions without the use of thruster rockets.

Flywheels are used in punching machines and riveting machines, where they store energy from the motor and release it during the operation cycle (punching and riveting).

A tractor with a massive flywheelDIFFERENCE BETWEEN FLYWHEEL AND GOVERNOR

The function of the governor must be carefully distinguished from that of the flywheel. The former is required to maintain, as closely as possible, a constant mean speed of rotation of the crankshaft overlong periods during which the load on the engine may vary. The latter serves to limit the inevitable fluctuations of speed during each cycle, which arise from the fluctuations of turning moment of the crankshaft. On the other hand the governor exercises not control over the cyclical fluctuations of the speed, while on the otherhand, flywheel has no effect on the mean speed of rotation.

If the load on the engine is constant, the mean speed of rotation will be constant from cycle to cycle. However, if the load changes, the mean speed will also change while the output of the engine is not adjusted to the new demand. It is the purpose of the governor to make this adjustment automatically.

REFERENCES:

1) www.wikipedia.org 2) www.google.com 3) www.scribd.com 4) Automotive engines-S.Srinivasan5) A text book of theory of machines- R.K.Kansal, J.S.Brar6) Wheeler, Lynder Phelps (1947), "The Gibbs Governor for Steam Engines", in

Wheeler, Lynder Phelps; Waters, Everett Oyler; Dudley, Samuel William, The Early Work of Willard Gibbs in Applied Mechanics, New York: Henry Schuman, pp. 63–78