by ET Westbury, 1951
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.
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, 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.
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 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).
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 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.
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.