The balancing of engines

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Longmans, Green, and Co., 1902 - History - 287 pages
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Contents

the Reaction on the Axis
11
Dynamical Load on a Shaft
12
Revolution Example
13
being in the Same Plane of Revolution
15
Balancing any Number of Masses rigidly connected to an Axis by means of a Single Mass all being in the Same Plane of Revolution Example
16
Magnitude of the Unbalanced Force due to a Given System of Masses in the Same Plane of Revolution
18
ExperimentallyTesting the Balance Example of L N W R Carriage Wheels
19
Centrifugal Couples Digression on the Properties of Couples
22
Equivalent Couples
24
Axis of a Couple
25
Addition of Couples
26
Condition for no Turning Moment
27
Typical Example illustrating the General Method
38
Relation between the Polygons Example
46
Experimental Apparatus
52
Method of investigating the Balancing Conditions of a System of Recipro
58
General Method of Procedure for Balancing an Engine
64
Example Typical of Torpedo Boats Iucludes the Valvegear
71
Conditions that an Engine may be balanced without the Addition
78
Experimental Apparatus
79
Balancing Reciprocating Masses by the Addition of Revolving Masses
80
CHAPTER IV
82
Example
85
Method of Balancing the Reciprocating Parts of a Locomotive
87
A Standard Set of Reciprocating Parts
88
Corresponding Set of Revolving Parts
89
Balancing an Outside Single Engine
92
Balancing an Inside Sixcoupled Engine
96
Hammer Blow
102
Example
105
Speed at which a Wheel lifts
106
Slipping
107
Example
108
Distribution of the Balance Weights for the Reciprocating Parts amongst the Coupled Wheels
112
American Practice
115
Fourcylinder Locomotives
116
Crank Angles for the Elimination of the Horizontal Swaying Couple
118
Comparative Schedules
119
Experimental Apparatus
123
CHAPTER V
124
On the Error involved by the Approximation
126
Graphical Interpretation of Expression 2 Art 78
127
The Effect of the Primary and Secondary Unbalanced Forces with respect to a Plane a Feet from the Plane of Revolution of the Crank
128
Effeot of More than One Crank on the Same Shaft 83 The Conditions of Balance
130
Analytical Representation of a Vector Quantity
131
ART FAOK 86 Application to the Balancing Problem
133
On the Relation between the Number of Conditional Equations and the Number of Variables
134
On the Number of Variables
135
Application of the Method to One and Twoorank Engines
137
Sixcrank Engine
161
Extension of the General Principles to the balancing of Engines when the Expression for the Acceleration is expanded to contain Terms of Higher Or...
163
General Summary
168
CHAPTER VI
172
Relation between the Quantities defining ihe Directions a and 2a 125
173
Data of a Typical Engine Schedules 19 and 20
175
127
176
Derivation of Curves to represent the Forces due to the Other Recipro cating Masses in the Engine the Batio of Crank to Bod being Constant
177
128
178
130
180
Addition of Forces and Couples due to the Revolving Parts
181
131
182
132
183
Process for finding the Primary and econdary Components of the Resultant Unbalanced Force and Couple Curves
184
Application to the Couple Curve of the Example
185
Valvegear and Summary
186
Calculation of the Maximum Ordinatesof the Components of the Resultant Force and Couples Curves Extension to any Number of Terms in the Gene...
188
Application to the Example
189
General Formulas for Typical Cases
191
Comparative Examples Sohedule 21
195
CHAPTER VII
199
Natural Period of Vibration of a Simple Elastic System
200
Damping
204
Vibration of the System under the Action of a Periodic Force
207
Natural Vibrations of an Elastic Rod of Uniform Section
209
On the Point of Application of a Force and the Vibrations produced
211
Longitudinal and Torsional Vibrations
212
Simultaneous Action of Several Forces and Couples of Different Periods
213
Possible Modes of Vibration of a Ships Hull and the Forces present to produce them
214
Experimental Results
216
Turning Moment on the Crankshaft
219
Uniformity of Turning Moment
225
Example
229
Shortframed Engines
230
CHAPTER VIII
232
Graphical Method for finding the Acceleration of the Mass Centre of the Rod
234
Equivalent Dynamical System
235
Constructions for fixing a Point in the Line of Action of R
237
Combined Construction
239
Effeot on the Frame and on the Turning Moment exerted by the Crank
240
Examples
242
Balancing the Rod
246
Particular Form of Balanced Engine
248
Analytical Method of finding R and L
250
Values of j j and as y at the Dead Centres
253
The Acceleration of the Crosshead in the Line of Stroke
254
Exercises
257
Index
279

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Page 2 - Wvl 9 is the angular momentum relatively to the given point. Angular momenta are compounded and resolved like forces, each angular momentum being represented by a line whose length is proportional to the magnitude of the angular momentum, and whose direction is perpendicular to the plane of the motion of the body and of the fixed point, and such, that when the motion of the body is viewed from the extremity of the line, the radius vector of the body seems to have right-handed rotation. The direction...
Page 22 - Proposition 1. — The turning effort of a couple with respect to any axis at right angles to its plane is the same, and is measured by the product of one of the forces and the arm of the couple. Let AB, CD (Fig. 21) be the directions of action of two equal, opposite, and parallel forces, acting upon a rigid body free to turn about the axis, O, at right angles to the plane of the couple.
Page 285 - Demy 8vo, 2S. 6d. net. THE CALCULUS FOR ENGINEERS. By JOHN PERRY. ME, D.Sc., FRS, late Emeritus Professor of Mechanics and Mathematics in the Royal College of Science, London.
Page 22 - DIGRESSION ON THE PROPERTIES OF COUPLES. 19. A Couple. — A couple is the name given to a pair of equal and opposite forces acting in parallel lines. The perpendicular distance between the lines of action of the forces is called the arm of the couple. In Fig. 20 the pair of equal and opposite forces F, acting in parallel lines a feet apart, form a couple whose arm is a feet long.
Page iii - Without undervaluing other modern writers, it is not too much to say that his investigations at present take completely the lead in this very important question — most important to a maritime nation. " Mr. Froude's papers are mainly to be found in the Transactions of the Institution of Naval Architects and of the British Association, as also in separate official reports published in 'Blue Books.
Page 3 - ... lines. In order to produce a long line by this movement it is only necessary to make a succession of short lines with the ends touching each other but not overlapping, or by leaving the smallest possible space between the end of one line and the beginning of the next. The wrist movement produces a longer line and is used naturally to make horizontal lines.
Page 213 - From the linearity of the equations it follows that the motion resulting from the simultaneous action of any number of forces is the simple sum of the motions due to the forces taken separately. Each force causes the vibration proper to itself, without regard to the presence or absence of any others. The peculiarities of a force are thus in a manner transmitted into the motion of the system.
Page 103 - The sign of w is determined by the sign of sine a ; a positive value indicates a diminution of rail-load, a negative sign an increase. If V is the speed of the train in miles per hour, and D the diameter in feet of the driving-wheel, containing the balance weight — _ 2 X 5280V '" 3600D Substituting this in 4, and dividing by 2240 to obtain w in tons weight (m is in pounds...
Page 286 - Association, experience, perception, analysis, generalization, description and explanation, mental development, language and thought, literature, character and conduct follow in this order.
Page 134 - If the number of equations be less than the number of variables, the solution is in general indeterminate " (that is, several solutions are possible). (3) " If the number of independent equations be greater than the number of variables, there is in general no solution, and the system of equations is said to be inconsistent.

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