Tips and tricks
Dynamics of machinery
DYNAMICS OF MACHINERY
BY GAETANO LANZA, S.B., C. & M.E.
NEW YORK, JOHN WILEY & SONS, 1911
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Dynamics of machinery
PREFACE
While Chapter I treats of the principal types of Dynamometers, the remainder of this book has for its chief object to bring together, in one volume, the methods of dealing with the inertia forces that arise in various kinds of machinery especially in cases where high speeds are employed. As examples, may be cited those of high speed steam engines, including high-speed locomotives, and of gas engines.
In these, careful consideration must be given to the action of the reciprocating parts, not only for the purpose of balancing, and hence avoiding undue strains in the machine itself, or in the foundations, and undue distortions in the rails, but also in order that the parts of the engine, including the crank shaft, etc., may be properly designed to resist the stresses to which they are subjected.
Other examples in which the inertia forces must be given careful consideration are: the inertia governor, - inasmuch as these forces affect very considerably the regulation, - pulleys, flywheels, steam turbines, dynamo armatures, centrifugal machines, hydroextractors, etc., which should be in running as well as in standing balance.
Another set of examples includes those in which the gyrosoope is employed in engineering, as
(a) the steering of torpedoes,
(b) the steadying of vessels at sea, (c) the Brennan monorail car,
(d) the gyroscopic compass, etc.
In these, careful consideration must be given to the action of the reciprocating parts, not only for the purpose of balancing, and hence avoiding undue strains in the machine itself, or in the foundations, and undue distortions in the rails, but also in order that the parts of the engine, including the crank shaft, etc., may be properly designed to resist the stresses to which they are subjected.
Other examples in which the inertia forces must be given careful consideration are: the inertia governor, - inasmuch as these forces affect very considerably the regulation, - pulleys, flywheels, steam turbines, dynamo armatures, centrifugal machines, hydroextractors, etc., which should be in running as well as in standing balance.
Another set of examples includes those in which the gyrosoope is employed in engineering, as
(a) the steering of torpedoes,
(b) the steadying of vessels at sea, (c) the Brennan monorail car,
(d) the gyroscopic compass, etc.
TABLE OF CONTENTS
I. Dynamometers
II. Moments and Products of Inertia
III. Action of Reciprocating Parts
IV. Governors
V. Bodies having a High Rotative Speed
Appendix to Chapter II (A)
Appendix to Chapter IV (B)
Appendix to Chaptbb V (C)
DYNAMICS OF MACHINERY
CHAPTER I.
DYNAMOMETERS.
Dynamometers, as their name implies, are instruments for measuring power.
They may be divided into two main classes, viz., traction dynamometers and rotation dynamometers. The first are intended to measure the work done by a direct pull or thrust; as, for instance, the work done by a locomotive in drawing a train, or that required to tow a boat. Rotation dynamometers, on the other hand, are intended to measure the power transmitted to or through a rotating shaft.
Traction dynamometers are all practically some kind of a weighing device, the main part of which consists of a spring, or of a hydraulic cylinder and piston, by means of which the pull exerted is weighed, together with some device for measuring the speed of motion.
When the pull and the speed are both constant, it is only necessary to multiply them together to obtain the work done per unit of time. On the other hand, when one or both vary, it becomes necessary to have recourse to some kind of a recording apparatus, and then to obtain the area of the resulting irregular figure by means of a planimeter or otherwise.
Dynamometer Cars.
Many of the large railroads make use of a dynamometer car, principally for the purpose of obtaining a tonnage rating, for the different parts of the service; determining the amount of energy, the draw-bar pull, and the power, and hence the kind of locomotive required to perform the service.
In all these cases, the force with which the portion of the train behind the dynamometer car pulls upon the drawbar of the latter is weighed, and recorded upon a strip of paper, which is caused by suitable mechanism to travel at a speed proportional to that of the train.
CHAPTER IV GOVERNORS
The function of a governor is to control the speed of a motor by varying the amount of energy supplied to it.
Thus, in the case of some water wheels, the governor operates a clutch, a shield, or some other device, so arranged that it throws into or out of gear the mechanism (driven by the wheel itself) which opens and closes the gate; while, in the case of other water wheels, it controls a valve which sets in motion or stops an auxiliary motor by means of which the gate is opened or closed.
In the case of a windmill, it varies the position of the blades, and thus controls the amount of energy imparted to the wheel by the wind.
In the case of a steam engine, it regulates the amount of steam supplied to the cylinder at each stroke, and its pressure, either by varying the opening of the throttle valve, or else by varying the position of the cut-off gear, and therefore the portion of the stroke during which steam is admitted to the cylinder.
In the case of a steam turbine, the governor controls either the position of the steam-admission valve, or the number of nozzles, and hence the cross section of the steam passages, or the time of admission, or else, in cases of overload, it operates valves which admit steam at boiler pressure, at various points of the path of the steam in the turbine.
In the case of a gas engine, the methods by which the governor controls the supply of energy may be classified as follows, viz.:
(a) Hit-or-miss regulation. In this case the inlet valve is kept closed, and the charge is omitted for one or more firing strokes when the speed increases above the normal.
(b) Regulation by varying the quality, the quantity, or both, of the explosive mixtures. In this case, the amount of gas, the amount of air, or both, or the amount of the mixture, is varied by means of suitable valves controlled by the governor.
(c) In very small engines, where economy is not an object, governing for temporary changes of load may be effected by varying the time of ignition. This is a wasteful method.
In certain cases where both the loads and speeds vary very considerably, as in the case of the locomotive, the regulation is performed by hand, but in most cases it is accomplished automatically by an apparatus driven by the motor itself.
In almost all cases, the direct cause of the action of the governor is the variation of speed, while the first result of the variation of load is a variation of speed, which in its turn causes the governor to act. An exception to this rule may be found, however, in a governor at one time employed on the Ball engine, in which the variation of load was also a direct cause of the action of the governor.
In almost all governors, use is made of the centrifugal force of some rapidly revolving body, counteracted by some other force or forces, as gravity, the tension or compression of a spring, the resistance of some fluid, friction, the resistance of the mechanism operated, etc.
An exception to the above is to be found in the so-called pressure governors, sometimes used on small direct-acting pumps, the air pump of the air-brake system, etc., where the pressure in the pump itself causes the governor, which is in reality a small auxiliary motor, to move the valve of the pump so as to cut off the steam supply, and vice versa.
One of the oldest and most common forms of governor has for its fundamental principle the revolving pendulum; hence this will be treated first, and its application to governors suitable for service will be shown later.
Thus, in the case of some water wheels, the governor operates a clutch, a shield, or some other device, so arranged that it throws into or out of gear the mechanism (driven by the wheel itself) which opens and closes the gate; while, in the case of other water wheels, it controls a valve which sets in motion or stops an auxiliary motor by means of which the gate is opened or closed.
In the case of a windmill, it varies the position of the blades, and thus controls the amount of energy imparted to the wheel by the wind.
In the case of a steam engine, it regulates the amount of steam supplied to the cylinder at each stroke, and its pressure, either by varying the opening of the throttle valve, or else by varying the position of the cut-off gear, and therefore the portion of the stroke during which steam is admitted to the cylinder.
In the case of a steam turbine, the governor controls either the position of the steam-admission valve, or the number of nozzles, and hence the cross section of the steam passages, or the time of admission, or else, in cases of overload, it operates valves which admit steam at boiler pressure, at various points of the path of the steam in the turbine.
In the case of a gas engine, the methods by which the governor controls the supply of energy may be classified as follows, viz.:
(a) Hit-or-miss regulation. In this case the inlet valve is kept closed, and the charge is omitted for one or more firing strokes when the speed increases above the normal.
(b) Regulation by varying the quality, the quantity, or both, of the explosive mixtures. In this case, the amount of gas, the amount of air, or both, or the amount of the mixture, is varied by means of suitable valves controlled by the governor.
(c) In very small engines, where economy is not an object, governing for temporary changes of load may be effected by varying the time of ignition. This is a wasteful method.
In certain cases where both the loads and speeds vary very considerably, as in the case of the locomotive, the regulation is performed by hand, but in most cases it is accomplished automatically by an apparatus driven by the motor itself.
In almost all cases, the direct cause of the action of the governor is the variation of speed, while the first result of the variation of load is a variation of speed, which in its turn causes the governor to act. An exception to this rule may be found, however, in a governor at one time employed on the Ball engine, in which the variation of load was also a direct cause of the action of the governor.
In almost all governors, use is made of the centrifugal force of some rapidly revolving body, counteracted by some other force or forces, as gravity, the tension or compression of a spring, the resistance of some fluid, friction, the resistance of the mechanism operated, etc.
An exception to the above is to be found in the so-called pressure governors, sometimes used on small direct-acting pumps, the air pump of the air-brake system, etc., where the pressure in the pump itself causes the governor, which is in reality a small auxiliary motor, to move the valve of the pump so as to cut off the steam supply, and vice versa.
One of the oldest and most common forms of governor has for its fundamental principle the revolving pendulum; hence this will be treated first, and its application to governors suitable for service will be shown later.
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