The Balancing of Engines (Google eBook)

Front Cover
E. Arnold, 1920 - Balancing of machinery - 303 pages
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Contents

the Reaction on the Axis
11
Dynamical Load on a Shaft
12
Balancing a Single Mass by means of a Mass in the Same Plane of Revolution Example
13
Balancing Two rigidly connected Masses by means of a Third Mass all 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
Experimentally Testing 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
and Couple Vectors
33
Reduction of the Unbalanced Force and Couple to a Central Axis Example
39
Relation between the Polygons Example
46
Experimental Apparatus
52
ABT PAGE 53 To find the Resultant Unbalanced Force and Couple due to the Revolving
53
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 Includes 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
Analytical Expression for the Acceleration of the Reciprocating Masses to include the Secondary Effect
125
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
Effect of More than One Crank on the Same Shaft 130
130
Analytical Representation of a Vector Quantity
131
Relation between the Quantities defining the Directions a and la
132
ART PAO 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
Fivecrank Engine
158
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
Proof
173
Data of a Typical Engine Schedules 19 and 20
175
Calibration of a Klein Curve to give the Accelerating Force
176
Derivation of Curves to represent the Forces due to the Other Recipro cating Masses in the Engine the Ratio of Crank to Rod being Constant
177
Combination of the Curves for their Phase Differences to obtain the Total Unbalanced Force in Terms of one crank Angle
178
Calibration and Combination of Klein Curves to obtain the Total Un balanced Couple belonging to the Reciprocating Masses
180
Addition of Forces and Couples due to the Revolving Parts
181
Acceleration Curve corresponding to the Approximate Formula 2
182
Process for finding the Primary and Secondary 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 Ordinates of the Components of the Resultant Force and Couples Curves Extension to any Number of Terms in the Gen...
188
Application to the Example
189
General Formulas for Typical Cases
191
Comparative Examples Schedule 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 Bod 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 Bod
234
Equivalent Dynamical System
235
Constructions for fixing a Point in the Line of Action of B
237
Combined Construction
239
Effect on the Frame and on the Turning Moment exerted by the Crank
240
Examples 212
242
Balancing the Bod
246
Particular Form of Balanced Engine
248
Analytical Method of finding B and L
250
Values of j 4 and x y at the Dead Centres
253
The Acceleration of the Crosshead in the Line of Stroke
254
The Acceleration of the Piston Bennetts Construction
257
I On the Maximum Amplitude of the Forced Vibration
260
Weight of the Parts and the Turning Moment on the Crank
261
trr rioi
262
Exercises
277
Index
299

Common terms and phrases

Popular passages

Page iii - Railways, and many cases of undue wear and tear and hot bearings in Mills and Factories undoubtedly arise from unbalanced machinery, though the actual vibration produced may not be great. In general, the running of an unbalanced engine or machine provokes its supports to elastic oscillations, and adds a grinding pressure on the bearings, and the obvious way to prevent these undesirable effects from happening is to remove the cause of them, that is to say, balance the moving parts from which the unbalanced...
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 - 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 177 - FIG. 126. scale of the drawing at the points where these parallels cut the line XR. The curve is properly calibrated by drawing horizontals through these points, repeating them and subdividing the intervals as much as may be required. The curve shows that the force at the top, dead centre, is about 51 tons, and on the bottom centre 31 tons, that when the crank is at right angles to the line of stroke it is 10 tons ; in fact, the disturbing force for this particular cylinder is known for any assigned...
Page 211 - K the radius of gyration of the section about an axis perpendicular to the plane of bending and inversely as the square of the length.
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 system.
Page 214 - For example, if the force be periodic in time r, so will be the resulting vibration. Each harmonic element of the force will call forth a corresponding harmonic vibration in the system. But since the retardation of phase e, and the ratio of amplitudes a : E, is not the same for the different components, the resulting vibration, though periodic in the same time, is different in character from the force. It may happen, for instance, that one of the components is isochronous, or nearly so, with the...

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