by ET Westbury, 1951
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 is practicable, 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.
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.
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 some small 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 forces have 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 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, 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
(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 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.
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 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.