THE BALANCING OF ENGINES BY W. E. DALEY, PREFACE. DURING the last ten years the subject of Engine Balancing has gradually forced itself upon the attention of Marine Engineers, chiefly because the unbalanced periodic forces of the engine and the natural periods of vibration of the hull have mutually approached the sensitive region of synchronism. Electrical Engineers have had vibration troubles at Central Stations and on Electric Eailways, and many cases of undue wear and teai 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 forces arise. The balancing of the marine engine and the peculiar problems connected therewith have been investigated by many engineers, and most of the original papers on the subject are to be found in the Transactions of the Institution of Naval Architects. The gradual introduction of the Yarrow-Schlick-Tweedy system of balancing the reciprocating parts of an engine amongst them- selves, is familiar to all who are in touch with modern marine engine design. The Balancing of Locomotives is carried out in a traditional way, and the compromise which makes a hammer blow on the rails a necessary accompaniment to approximate uni- formity of tractive force is accepted by Eailway Engineers as the best practical .solution of the problem. The advent of the four-cylinder locomotive, however, brings with it practical possi- bilities of balancing the inertia forces as great as in a four-cylinder marine engine. The main object of this book is to develop a semi-graphical method which may be consistently used to attack problems connected with the balancing of the inertia forces arising from the relative motion of the parts of an engine or machine. In the case of a system of revolving masses, or a system of reciprocating masses where the motion may be assumed simple harmonic without serious error, the application of the method is simple in the extreme, as it requires nothing but a knowledge of the four rules of arith- metic and good draughtsmanship. Moreover, the work can be easily checked, and in the case of symmetrically arranged engines, like locomotives, for example, the method is self-check- ing. The application of the method to the case of a recipro- cating system, in which the motion of the several masses is con- strained by connecting-rods which are short relatively to the cranks they turn, is considered in Chapter V. The use of the method to compute the unbalanced forces arising from the running of an engine or machine of given dimensions in which the mass of each moving part is known, is illustrated in Chapter VI. The precise effect of an engine on its supports cannot be predicted from a knowledge of the magnitudes of the unbalanced forces alone. The effect depends upon the elastic peculiarities of the support in relation to the periodic times and places of action of the unbalanced external forces acting upon it. A brief V discussion of the principles governing the behaviour of elastic supports under the action of external forces is given in Chapter VII. I am indebted to Lord Kayleighs Sound, Vol. I, for the fundamental ideas of the first seven articles of the chapter. The motion of the connecting-rod and its action upon considered in Chapter VIII...