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Notes on basic principles and practical methods of procedure by ET Westbury, 1951 Reference: The Model Engineer , Percival Marshall & Co. Ltd. Volume 106, Numbers 2651, 2653, 2655. Introduction EVERY new development in engineering brings with it new problems, or causes old problems to become accentuated, and it is often found that the methods of dealing with them have to be revised to cope with advanced design and more exacting performance. While engineers of today are very fortunate in having available a vast amount of accumulated data, obtained laboriously by the research workers of the past, it is often found that this is inadequate to cover the conditions which arise when producing something entirely new, such as, for instance, a racing engine. In some respects, one may be hampered rather than assisted by faith in ready-made data, and it is often better to tackle the problems from first principles, or even by the much-despised "rule of thumb", which although crude, is often effective. A problem which is brought to my notice with ever-increasing frequency these days is that of balancing engines or other mechanism. Many readers who attempt to construct engines which will go just a little faster than ever before, find themselves in trouble with excessive vibration or overloading of working parts, as a result of unbalanced forces, and ask my advice in finding a practical solution. Some of them are rather

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Notes on basic principles and practical methodsof procedure

by ET Westbury, 1951

Reference:

The Model Engineer , Percival Marshall & Co. Ltd.Volume 106, Numbers 2651, 2653, 2655.

Introduction

EVERY new development in engineering brings with it newproblems, or causes old problems to become accentuated, and

it is often found that the methods of dealing with them have to

be revised to cope with advanced design and more exacting

performance. While engineers of today are very fortunate in

having available a vast amount of accumulated data, obtained

laboriously by the research workers of the past, it is often

found that this is inadequate to cover the conditions whicharise when producing something entirely new, such as, for

instance, a racing engine. In some respects, one may be

hampered rather than assisted by faith in ready-made data,

and it is often better to tackle the problems from first

principles, or even by the much-despised "rule of thumb",

which although crude, is often effective.

A problem which is brought to my notice with ever-increasing

frequency these days is that of balancing engines or other

mechanism. Many readers who attempt to construct engines

which will go just a little faster than ever before, find

themselves in trouble with excessive vibration or overloading of 

working parts, as a result of unbalanced forces, and ask my

advice in finding a practical solution. Some of them are rather

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disappointed to learn that I cannot furnish them with a few

figures and symbols which will clear the whole matter up tidily

and accurately; the childlike faith which some of my querists

have in formulae is most impressive!

It is perhaps necessary for me here to make one of my

frequent disclaimers regarding my attitude to theoretical

solution of problems. I am not, nor have I ever been,

antagonistic to, or contemptuous of, theory, wherever it can

properly be applied; but the factors involved in what may, at

first sight, appear to be quite a simple practical problem, are

often so profound and complex that their solution by theory

alone is almost impossible to a person of normal intelligence.

By all means use theory in its place, and where you can be

quite certain that the premises on which it is based are correct;

but always remember that it must be a supplement to, and not

a substitute for, practical knowledge. In many problems,

practical experiment will find the solution more quickly and no

less accurately than theoretical calculation.

So far as the particular subject of balancing is concerned, I

may mention that many years ago, in the attempt to solve

problems personally encountered, I studied text-books by three

of the best-known authorities on the subject namely, Sharpe,

Dalby, and Schlick; but I must confess that, so far from being

enlightened, I was scared stiff with the immensity of what I

had regarded as a mere elementary problem of design.

First Principles of Balancing

The need for balancing arises by reason of the basic law of 

mechanics which states that "Action and reaction are equal and opposite". Any force which tends to produce motion in a body

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must therefore be balanced by an equal reactive force. For

instance, water or air craft in moving through a fluid, must

necessarily produce a reaction in the opposite direction against

that fluid; motorcars or locomotives produce a backward

reaction on the road or track, through their driving wheels. A

revolving shaft which exerts force to drive a machine is subject

to "torque reaction" which is equal and opposite at all times to

its driving torque. If a piston, in an engine or pump, moves

upwards, under the effect of a given force, an equal downward

reaction is exerted, through the connecting-rod and crankshaft,

to the bearings and foundation of the machine. This brief 

explanation of what reaction really means may not be

necessary to the majority of readers, but it has been

considered worth while in case of any possible

misunderstanding of the term.

Perfect balance in a machine requires that the reaction of the

forces required to accelerate the working parts, or keep them

moving against load, should neutralise each other in every

phase of the motion, so that no reaction is ever exerted upon

the bedplate of the machine. Such a machine would run

steadily and without vibration at any speed, without the

necessity for bolting down. It may be said that this desirable

condition is rarely, if ever, obtained in practice, and one must

be satisfied with the nearest approximate condition which can

be obtained within the limitations of practical design.

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Balancing Revolving Masses

A truly symmetrical wheel

of homogenous material,

mounted on a true shaft

and running in properly

fitted bearings, produces

no unbalanced forces,

except for torque reaction,

which is generated when

it forms part of a machine

used either to exert or

absorb power; this is a

matter with which we are

not at present concerned.

But it often happens that

the mass of such a wheel

cannot be guaranteedsymmetrical, even when it is machined all over, and any lack of 

mass symmetry introduces an unbalanced force, the reaction of 

which tends to produce vibration of the frame carrying the

bearings of the wheel as shown in Fig. 1A. If the unbalanced

mass U is on the side of the wheel which is travelling upwards

at a given time, the frame is subject to a downward reaction R-

R; and at any phase in the revolution, the effect is always felton the frame, in an opposite direction to the unbalanced force.

The speed of rotation will affect the vibration caused by these

reactions, which may become violent and dangerous at high

speed.

If the foundation of the bearings is held rigidly, it is sometimes

possible to prevent vibration becoming apparent, but the forces

are still there, and are exerted on the bearings of the wheel,

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thereby causing excessive loading. On the other hand, the

frame may be resiliently mounted, so that vibrations are

damped out to a certain extent between the machine and its

actual foundation; but in neither case is this a complete

remedy for lack of balance.

The logical and obvious thing to do in this case is to correct the

bias in the mass of the wheel, either by removing metal at the

heaviest point, or by adding a corresponding amount of mass

at a point exactly opposite to it as in Fig. 1B. In order to locate

the position of the unbalanced mass, and also to check any

correction made, the wheel may be "poised", by rolling the

shaft on levelled knife-edges, rollers, or very free-running

bearings, and noting any tendency for it to stop in one

position; the unbalanced mass will, of course, tend to run by

gravity to the lowest point. This method of static balancing is

often employed in practice, but where high accuracy is

necessary it tends to be tedious and sometimes expensive.

A simple stand for the static balancing of 

flywheels, armature, shafts, etc., is shown in

the photograph. It was made from a piece of 

channel steel, with strips of gauge plate bolted

to the upturned edges, and is provided with

three levelling screws in the base, and a two-way spirit level.

The strips are not finished to a sharp edge on the top surface,

but are honed to a radius to avoid damaging shafts or

mandrels, and must, of course, be dead straight and in parallel

alignment with each other.

Static and Dynamic Balance

So far we have considered the case of a wheel, which

approximates to a simple disc, having all its mass in or near

one plane. If this is statically balanced in the way described, it

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will run at any speed without vibration. But in a rotating body

having a fairly considerable axial length, such as a cylinder, it

is important that any local unbalanced mass should be

balanced out by a mass as nearly in the same cross plane as

possible.

The static method of 

balancing, in this case, is

not reliable because it

gives no indication of the

position of the bias in

relation to axial length.

Thus the cylindrical rotor,

an armature shaft for

instance, shown in Fig. 2,

may be heavy at the point A, as indicated by a static balancing

test. If this unbalanced mass is counteracted by a weight

applied at the point B, the rotor will appear to be in correct

balance; but when running at high speed, the effect of the two

unbalanced masses will cause local reactions R-R which tend to

rock the shaft along its length, or in other words to set up a

"couple." In practice, the effect of this may be worse than that

of a single unbalanced force which tends to vibrate the

structure bodily, and it is often much more difficult to detect

and correct.

The method usually employed for dynamic

balancing is to mount the shaft in bearings on

a frame which is resiliently mounted, usually

by some form of spring suspension, so that it

is capable of being displaced in any plane by the effect of 

unbalanced forces. Means are provided for locking the frame

while the shaft is run up to a fair speed by any convenient

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means, after which it is released and allowed to vibrate or

oscillate under the effect of the unbalanced forces. In modern

dynamic balancing machines, indicating or recording devices

are provided to show the position and extent of the unbalanced

masses. While it would not be impossible to construct a simple

dynamic balancing rig in the home workshop, most of the

problems involved in small machines can be dealt with by

careful consideration of design, and accuracy in construction of 

moving parts. It may be mentioned that even the balancing

machine, unless of very complex design, may leave certain

important considerations out of account.

For instance, suppose

that a rotor having an

unbalanced mass at J

(Fig. 3A) is balanced by

adding two smaller

masses at the points K,

L. The rotor is then in

correct dynamic balance,

and in the case of a fairly

rigid component, such as

an armature, it will be

perfectly satisfactory in

practice. But suppose the same principle is applied to a non-

rigid component, such as a crankshaft; in this case, the

cancelling masses, being in different planes, exert bending

stresses on the shaft, and the latter may be deflected, thereby

altering the moment of the masses and putting the system out

of balance (Fig. 3B).

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This is only one of the

many pitfalls in practical

balancing, which cause

the designer many

headaches, and are

rarely capable of being

dealt with by theoretical

calculation. Another

example occurs in the

case of a rotating body

which for practical

reasons cannot be made

symmetrical in shape, though the moments of mass are

calculated and counterweights added where necessary to

cancel out and give correct balance as in Fig. 4. When running

at high speed, however, the effect of centrifugal forc,e causes

the flywheel to distort, and thereby displace the masses to a

varying extent, thereby unbalancing them. In case readers

think this is an unlikely eventuality, I may say that I once

worked on a certain type of flywheel magneto which gave a

great deal of trouble through this cause, though dynamic

balancing tests gave no indication of the source of error.

Balance weights, whatever their type or purpose, should

always be located as close to the plane of the unbalanced mass

as possible. Thus, in the case of the crankshaft shown in Fig.

3B, it would be better to attach the counterweights to the

crank webs than at the points indicated. The practice of fitting

balance weights to external flywheels, therefore, is one that

cannot be commended; in the case of an overhung crankshaft,

any bias in the flywheel would set up a violent rocking couple.

Flywheels should always be at least in static balance, and if of 

any great width, dynamic balancing is desirable. An exception

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is made in the case of internal flywheels, as in motor-cycle

engines, which are close to the crankpins, and usually form the

crank webs.

Balance of Reciprocating Masses

We have seen that an unbalanced rotating mass may be

cancelled by an equal and opposite rotating mass; in a similar

way, an unbalanced reciprocating mass may be cancelled by an

equal and opposite reciprocating mass. It is essential that this

axiom should be clearly understood; it is no use attempting to

balance completely a reciprocating mass by a rotating

counterweight, or vice versa. A reciprocating mass can only be

balanced by an equivalent mass moving in the same plane, but

in exactly opposite phase. Thus it happens that the most

popular type of small engine, having a single piston working on

a single crank throw, cannot possibly be perfectly balanced;

the best that can be done in practice is to use a rotating

counterweight to produce a partial state of balance, which may

be more or less satisfactory, but can never eliminate, vibration

or abnormal mechanical stresses completely.

This rule applies, whether the engine is single or double-acting,

and whatever method is employed to convert the reciprocating

motion of the piston to rotary motion of the crankshaft. I

emphasise this point because I am often asked to prescribe a

"perfect" balancing formula for a single-cylinder engine, and

some fearfully and wonderfully conceived devices--all of them

either futile, or too complex for practical application--have

been submitted by designers as a solution to this problem.

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Single Cylinder Balance

In the orthodox arrangement of a single-cylinder engine, the

piston is linked to the crankshaft by a rigid connecting-rod,either directly, or through a piston-rod and crosshead. The

piston (with rod and crosshead, where fitted) and its wrist or

gudgeon pin, are, of course, pure reciprocating weight; the

connecting-rod reciprocates at the "small" end and rotates at

the "big" end; while the crankshaft and all its appurtenances

are pure rotltting weight. In any attempt to balance an engine,

the two orders of motion must be isolated, so far as ispracticable, and thus one of the first things to do is to assess

the amount of counterweight which must be applied opposite

the crankpin to balance out all the rotating weight.

A Misleading Term

One point which should be carefully borne in mind here is that

the term "weight" in balancing formulae may be rathermisleading, as what really matters is "moment of mass". A

comparatively large weight on one side of the axis, in a

rotating body, may be cancelled out by a smaller weight acting

at a greater radius on the other side, or vice versa. Similarly, a

large reciprocating weight may be cancelled out by a smaller

weight having a longer stroke, i.e. moving through a greater

distance in the same time, or vice versa. These things look

after themselves when static or dynamic tests are made, but

they can, and often do, complicate matters when one attempts

to work out problems by calculation alone.

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In the simple engine shown diagrammatically in

Fig. 5, the balance weight may either be made

integral with the crank web or attached to it in any

convenient and secure way. It must, primarily,

have sufficient moment of mass to balance out all

the rotating weight in the system; but if no more

than this is accounted for, it leaves the whole of 

the reciprocating weight of the piston, gudgeon-

pin and small end of the connecting-rod

unbalanced. The result is that a powerful reaction

force, tending to cause vibration in the plane of 

the piston motion, but opposite in phase, will be

set up when the engine is running.

If now sufficient mass is added to the counterweight to cancel

out entirely the reciprocating weight, it will be clear that when

the piston is moving downwards at maximum velocity (i.e. at

mid-stroke), the counterweight is moving upwards at such a

rate as to cancel out the unbalanced reaction; and at the same

point in the up-stroke, the downward movement of the balance

weight is also in direct and equal opposition. But whereas the

rate of motion of the piston varies from zero to maximum on

each stroke, that of the counterweight is constant, so that the

latter itself becomes unbalanced when the piston is at the top

or bottom of its stroke. The result is that the vibration in the

plane of the piston movement may be more or less completely

cancelled out, but in its place is substituted a vibration,

practically of equal magnitude, at a right angle to the plane of 

piston movement. The last state is, therefore, no better than

the first.

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Partly Cancelled Out

In practice, the best results are obtained by using a

counterweight capable of cancelling out only a portion of the

reciprocating weight. The exact amount is often a subject of 

fierce dispute, but in actual fact it depends on a number of 

(sometimes incalculable) factors, such as the way the engine is

mounted, the moments of inertia in the fixed and moving

masses (which influence "critical speeds"), and so on. What

really happens is that some of the forces which tend to cause

vibration are diverted into other planes, where they may be

more tolerable, or more readily absorbed in the structure; in no

case is the vibration in a single plane so violent as it would be

in an entirely unbalanced engine.

As a general rule, it may be said that engines which are

required to run at widely varying speeds require a greater

portion of reciprocating weight to be balanced out than those

which can be kept running at well above critical speed. In somesmall high-speed engines it is possible to "get away with

murder", by using very sketchy balance weights, or even none

at all. This is because the reciprocating parts of these engines

can be made extremely light, and their structure resilient

enough to absorb vibration; but it should be remembered that

the unbalanced forces are still there, and are registered in the

mechanical stresses and bearing loads, also that these forceshave to be generated by the engine itself, thereby detracting

from the power available for useful work.

In most of the engines which I have described in THE MODEL

ENGINEER, I have found it satisfactory to balance out about

half the reciprocating weight, except in one or two cases where

the engines were designed for special purposes. The methods

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employed in finding the correct counterweight to apply to the

crankshaft are illustrated here, in the following order:

First , weigh the piston, complete with its rings,

gudgeon-pin, and pads, or other retaining devices

(this is pure reciprocating weight). It may be

mentioned that sufficient accuracy for this purpose

may be obtained by using a simple spring balance

(since it is only necessary to find comparative figures),

and a suitable type of balance has been obtained from the

surplus market, as advertised in THE MODEL ENGINEER.

Second , weigh the two ends of the connecting-rod,

either separately or simultaneously (preferably the

latter) keeping the rod quite horizontal during the

process. The small-end is taken as reciprocating

weight, and the big-end as rotating weight.

Third , assess the amount of weight to be cancelled out

in the counterweight. This is done by adding together

reciprocating weights of the complete piston assembly, and the

small-end of the rod, which (if we accept the proportion

recommended above), is then halved, and added to the

rotating weight of the big-end.

Fourth, the crankshaft is poised on knife

edges or rollers, to act as a balance, and the

assessed weight is hung on the crankpin; the

counterweight is then adjusted until it "stays

put" in any position of rotation. This may

entail either adding or subtracting metal at the

counterweight, such as by fitting lead "slugs" in suitable

recesses where they cannot be thrown out centrifugally, or by

filing or machining away the surplus. In some cases, lightness

of the balance weight may be remedied by reducing the web on

the crankpin side, or enlarging the centre hole in the later,

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always having due regard for retaining a margin of mechanical

safety.

[Ron: Notice the "knife-edges" in the photo? Looks to me like

two pieces of drill rod held in position on the leveled surface-

 plate by four small lumps of modelling clay. That is an idea well 

worth remembering!]

The weight necessary to carry out this operation may be made

up from sand, lead shot, or any suitable material to hand; as

may be seen, metal washers were used in the case illustrated.

In the absence of a scale pan, a small bag may be used. It is

important that the means of suspension on the crankpin should

be arranged to produce the minimum friction. In the example

shown, a small plug was made to fit inside the hollow crankpin

(its weight being duly allowed for), having an extended pin of 

small diameter, on which the hook of the scale pan was hung.

The figures in the example illustrated are as follows:

Piston, with rings and gudgeon-pin..83 grms.

Small-end of connecting-rod ..21 "

Big-end of connecting-rod ..25 "

(83 + 21)

----------- + 25 = 77 grms

2

(the amount to be cancelled out by counterweight)

Should the designer adopt a different figure for the proportion

of reciprocating weight to be balanced, this part of the

calculation must be suitably modified. This formula, however,

has been used with success, not only in models, but also for

larger engines which have had to work under exacting

conditions.

I have described this procedure in detail, as it is of interest to a

large number of readers, to judge by the number of individual

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queries I have had to deal with, and I trust that this will clear

away the last remnants of mystery regarding this subject.

I have stated that these conditions apply to any orthodox

single-cylinder engine; it is also correct for machines having a

similar order of motion, such as high-speed pumps or air

compressors. Balancing problems should not be confused with

effects caused by working pressures, though these produce

their own reactions, and may affect smoothness of working. In

many small machines which are not required to run at very

high speeds, little attention is given to the finer points of 

balancing, and within certain limits, the results are fairly

satisfactory.

Locomotive Balancing

Constructors of small locomotives do not usually take a great

deal of pains, either by calculating unbalanced forces or by

experimental tests, though the balance weights of full-sized

locomotives are usually copied more or less correctly to scale.

It may be mentioned that the principle generally adopted in

locomotive balancing is to treat each set of cylinders and

motion work as a separate single-cylinder engine, as shown in

Fig. 5; it can thus be dealt with in the manner already

described. Balance weights may sometimes be distributed over

all the coupled wheels; the coupling-rods, it should be noted,

are taken as rotating weight, as any single point on them

describes a true circle. Linkages, such as those used in certain

types of valve-gear, however, have more complex orders of 

motion, and are difficult to balance; fortUnately their mass and

velocity can be kept fairly low, at least on any locomotives

likely to be built by readers of THE MODEL ENGINEER.

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It may be observed that the balance weights on the different

coupled wheels of some locomotives are placed out of phase,

so that they do not all oppose the crankpin; there are various

reasons for this, one being that it is possible for the combined

reactions of three or more balance weights, moving

simultaneously, to produce the effect of a hammer blow on the

rails; the locations of the weights are, however, arranged to

produce, in combination, the correct moment of mass and

phasing to balance the motion work as well as possible (See

Fig. 6).

If one wishes to study the subject of locomotive balancing in

greater detail, it may be noted that an authoritative book on

the subject was written several years ago by Professor Dalby,

and may still be available for reference in technical libraries.

Steam engines having several cylinders, especially those of 

multiple-expansion type, where the pistons vary in size and

mass, present special balancing problems, and these are

accentuated by the fact that the disposition of the cranks must

be arranged to avoid dead centres, so that the engine can be

started from any position without outside assistance. In large

marine engines, the Yarrow-Schlick-Tweedy system of 

balancing, which involves a special method of unsymmetrical

crank angle spacing, is usually employed. In such engines, it is

not usually convenient to fit balance weight to the crank

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throws, but the shaft and bearings are sufficiently rigid and

firmly mounted to allow of using the unbalanced masses of one

or more pistons to cancel out those of adjacent pistons.

Balancing Multi-cylinder Engines

Before dealing specifically with engines having more than one

cylinder, it may be mentioned that there is one type of single-

cylinder engine in which perfect dynamic balance is possible;

namely, the opposed-piston type, in which two pistons moving

in opposite directions are used in one cylinder. The advantages

of this type, however, are somewhat marred by the fact that its

mechanical arrangement is more complex, and often

convenient or inefficient; it is much better suited for dealing

with the heavy masses in very large slow-running engines than

for those of small high-speed engines, where the improved

dynamic balance may hardly be perceptible under practical

conditions.

Balancing problems may

sometimes (but not

always) be simplified by

the use of more than one

cylinder. A very common

arrangement consists of placing two cylinders

alongside, and parallel

with each other,

connecting the pistons of 

these cylinders to cranks

disposed at 180 deg. as

in Fig. 7. In practice, thisis by no means a complete solution of the problem, because of 

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the distance apart of the two cranks, with a corresponding

offset in the plane of the pistons, which sets up a pronounced

rocking couple. For an engine of given capacity, however, the

pistons are smaller, so that the unbalanced forces are reduced

in proportion, and another advantage (unconnected with

balancing) is that the frequency of power impulses, at a given

speed, is doubled, producing a more even torque at the shaft.

The effect of the couple can be reduced to some extent by

counterweighting the end crank throws.

In the attempt to ,reduce

the offset in the plane of 

the pistons, the cylinders

can be located on

opposite sides of the

crankshaft, as in the

popular "flat twin", and

use a two-throw crank so

that the pistons move in opposite phase. It is not usually

desirable in practice to place the two cylinders in exactly the

same plane, so that there is usually a slight couple as shown,

in Fig. 8, but it is much less than in the side-by-side

arrangement, and balance, on the whole, is fairly satisfactory.

The same principle can be applied to any even number of 

cylinders, and "flat fours" and "flat sixes" have become

increasingly popular in recent years,

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Yet another arrangement

for a twin-cylinder engine

is to place the cylinders

at right angles to each

other, and connect the

two pistons to a single

crank throw, as shown in

Fig. 9. The crankpin is

counterweighted as for a

single-cylinder engine,

counterweight is always

acting in direct opposition to one or other of the pistons, and

therefore it is practicable to balance completely the

reciprocating weight one one piston (the other being of exactly

equal weight). Such an engine is very well balanced, but the

arrangement has its disadvantages, particularly in petrol

engines, as it introduces unequal firing intervals, unless the

pairs of cylinders are multiplied, as in the "vee eight" now

popular in motor cars. Note that the complete state of balance

is only obtained when the cylinders are set exactly at 90 deg.;

the narrow-angle vee twin commonly employed in motor-cycles

is not so good in this respect, being more of a compromise

between the single and the two-crank twin. Radial engines

having a symmetrical arrangement of cylinders may be

balanced on the same principle as the 90 deg. vee twin, but it

should be noted that when the rods do not all articulate on the

crankpin centre, their order of motion is modified, and this may

complicate balancing problems.

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Side-by-side twins are

often arranged with the

pistons in the same

phase, as shown in Fig.

10, the object being

usually to obtain equal

firing intervals, with

smooth torque. From the

balancing aspect, this

may be considered a

retrogression, as the

problem is the same as

that in a single-cylinder engine; but there is no doubt that the

arrangement works well in practice, at least in engines of 

moderate cylinder capacity. The complete absence of a rocking

couple, when the balance weights are symmetrically arranged

relative to the reciprocating masses (which taken individually,

are lower than those in a single of equal total capacity), is also

a probable factor in the success of this type of engine.

Sometimes a centre bearing is provided between the crank

throws, but in other cases the space is occupied by an internal

flywheel, which may be balanced in itself, or counterweighted

to contribute to the partial cancellation of reciprocating forces.

In the attempt to improve the balance of this type of engine, a

centre crank throw is sometimes introduced, opposite in phase

to the other two, and this is used to drive a charging pump or

compressor, or even simply reciprocate a counterweight equal

in moment of mass to that of the two main pistons. Split-single

two-strokes, having two cylinder barrels with a common

combustion head, sometimes have two separate crank throws

slightly different in phase, and may have an opposed centre

throw which drives a "displacer" to increase the volume of air

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displaced in the crankcase, thereby acting as a supercharger.

An example of an engine of this type was the 15 c.c. engine. of 

Mr. A. D. Rankine's Oigh Alba Junior , which unfortunately came

to an untimely end in a fire at Kilmarnock some years ago.

Three-cylinder Engines

These have never been very popular in small or medium sizes,

despite the fact that they can be arranged to give equal firing

intervals in either two-stroke or four-stroke types. In a three-

inline engine with the cranks arranged as in Fig. 11, there is

obviously a pronounced rocking couple which cannot easily be

eliminated. Generally speaking, this arrangement is not well

suited to high speed, but if it must be used, the best way is to

treat each crank throw as a separate singlecylinder engine and

counterweight the crank webs accordingly. Where it can

conveniently be used, the radial arrangement of cylinders,

acting on a single crank, is much to be preferred for high

speed.

Four or More Cylinders

The orthodox four-in-line engine can be quite well balanced if 

the cranks are arranged in pairs at 180 deg., each pair being

opposed to the other to cancel out the individual couples, as

shown in Fig, 12. This arrangement is sometimes termed "

mirror" balance, as each half of the engine resembles a

reflection of the other as seen in a mirror. If the pistons and

other working parts of such an engine are of uniform mass, the

engine is capable of working smoothly, and with very little

vibration. A similar arrangement can be used in a six-cylinder

engine, with two opposed sets of three cranks at 120 deg., or

eight cylinders, with two opposed sets of four cranks at 90 deg.It should, however, be noted that the stiffness of the

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crankshaft, and of the engine structure generally, has an

important bearing on the success of such engines, 'as the

cancelling of the two opposed couples has a tendency to bend

the crankshaft in the middle.

The shorter and stiffer the complete engine structure can be

made, the more likely it is to be successful in practice. This

accounts for the decline in the popularity of the once-favoured

"straight sixes" and "straight eights", some of which were of 

prodigious length. It may here be appropriate to make some

observations on the advisability of providing bearings between

crank throws, as this matter has a pronounced influence on

design from this aspect, and is often in dispute. Beyond doubt,

it is a good thing to support the crankshaft between crank

throws, provided that the bearings are held rigidly in true

alignment, and the shaft also remains true under working

stresses. But these conditions cannot be guaranteed in practice

in an engine which must be kept as light as possible for a given

size; moreover the provision of inter-throw bearings, if they

are to be of any use at all, adds very considerably to the length

of the engine, and therefore increases the effects of rocking

couples. A further effect, not directly connected with balance,

but capable of causing very troublesome vibration, is that of 

torsional deflection in a long and intermittently loaded shaft. As

with many other things in engine design, a compromise is often

necessary to get the best practical results from the most

desirable features and avoid the worst of their disadvantages.

Primary and Secondary Balance

So far, I have dealt only with the means of dealing with the

most important unbalanced forces in orthodox types of engines

or machines; and quite frankly, I believe that if these principles

are fully grasped, they will cover most practical problems

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encountered by "M.E." readers. There are, however, other

forces of the second, third and further orders, ad infinitum, but

it would be impossible to do so without taking up a

considerable amount of space, and going very deeply in theory

and mathematics, which I feel sure would be out of place in a

practical journal.

It may, however, be

observed that secondary

unbalanced forces occur

in mechanisms where the

motion is not truly

harmonic, and this

applies where a connecting-rod of limited length is used to link

reciprocating and revolving parts. As short rods, involving

considerable maximum angularity, are common in high-speed

engines, no simple system of balancing can eliminate these

secondary forces completely, even in engines where the

reciprocating masses can be directly opposed in identical

planes. But as we have already seen, theoretical balancing

systems do not always give the best results in practice, and

again the importance of compromise must be stressed.

I have tried to assist

readers to solve their

own balancing problems

in a strictly practical way,

well knowing that nearly

all model engineers are

men of action, who

would much rather spend

their time at the lathe or

bench than in working

out theoretical problems on paper. I know from experience that

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these problems can be capable of purely practical solution, and

I am not prepared to admit that this takes longer, or involves

more labour, than the theoretical approach, always provided,

of course, that basic principles are correctly grasped, and that

one does not attempt to fly in the face of all physical laws.

There is much more that could be said about practical

balancing problems, but I trust that readers will be able to

apply this elementary, and admittedly limited, information to

advantage, and be encouraged to work things out for

themselves by practical experiment. The mechanisms dealt

with here are those most likely to be encountered in model

engineering, but unusual types of machines generally embody

combinations of simple motions which can be isolated and

analysed. Perfection in the balancing of any machine is rarely

attained, but the higher the speed and the more exacting the

duty, the closer must be the approach to perfection if the

machine is to be a practical success.