STATIONARY ENGINES.] STEAM-ENGINE 511 cli txTinined from actual indicator diagrams) combined with the moments due to the inertia of the reciprocating parts. The line marked is the steam line without inertia or, in other words, FIG. 117. Circular Diagram of Crunk-Effort fur a Three-Cylinder Engine. the curve corresponding to an indefinitely slow speed. The other curves refer to the number of revolutions per minute marked on them. ?luctua- 189. To determine the fluctuations of speed during a revolution,
- ions of the resultant diagram of work done on the crank-shaft is to be
speed. compared with a similar diagram drawn to show the work done ly the shaft in overcoming its own friction, and in overcoming the resistance of the mechanism which it drives. In general the re- sistance may be taken as constant, and the diagram of effort exerted by the crank-shaft is then a straight line, as EFGHIJKL in fig. 118. At F, G, H, I, ,T, and K the rate at which work is being done on and by the shaft is the Function same ; hence at of fly- these points the wheel. fly - wheel is neither gaining norlosingspeed. The shaded area above FG is an excess of work done on the crank, and raises the speed of the fly-wheel from a mini- mum at F to a maximum at G. From G to H the fly-wheel supplies the defect of energy shown by the shaded area below GH, by which the demand for work exceeds the supply ; its speed again reaches a minimum at H, and again a maximum at I. The excesses and de- fects balance in each revolution if the engine is making a constant number of turns per second. In what follows it is assumed that they are only a small fraction of the whole energy held by the fly-wheel. Let AE be the greatest single amount of energy which the fly- wheel has to give out or absorb, as determined by measuring the shaded areas of the diagram ; and let w l and &>., be the maximum and minimum values of the wheel's angular velocity, which occur at the extremes of the period during which it is storing or sup- plying the energy AE. The mean angular velocity of the wheel ci> will be sensibly equal to ^(o^ + cu,,) if the range through which the speed varies is moderate. Let E be the energy of the fly-wheel at this mean speed. Then where I is the moment of inertia of the fly-wheel. AE = 1 u - = 10)0(0)! - a*;) - 2E . -^ ^- . The quantity which we may write q, is the ratio of the extreme range of speed to the mean speed, and measures the degree of unsteadiness which the fly-wheel leaves uncorrected. If the problem be to design a fly-wheel which will keep q down to an assigned limit, the energy of the wheel must be such that AE E =2^ The Moscrop recorder, alluded to in 182, exhibits the degree of unsteadiness during a single revolution by the width of the line which it draws. On the other hand, any bending of the line implies the quite independent characteristic of unsteadiness from one revolution to another. The former is due to insufficient fly-wheel energy, the latter to imperfect governing. 190. An interesting consequence of the periodic alternations in crank-effort which occur in each revolution lias been pointed out l>y ilr M. Longridge. 1 The fly-wheel receives its alternate ac- celeration and retardation through changes of the torsional stress in the shaft. If these occur at intervals nearly equal to the period of free torsional vibration which the fly-wheel possesses in virtue of the torsional elasticity of the shaft between it and the crank, strains of great amplitude will arise ; and Mr Longridge has suggested that this may account for the observed fact that engine- shafts have been ruptured when running so that the fluctuations of crank-effort occurred with one particular frequency, although the greatest effort was itself much less than the shaft would safely bear. XI. EXAMPLES OF STEAM-ENGINES. STATIONARY ENGINES. 191. In classifying engines with regard to their general Descrip- arrangement of parts and mode of working, account has tive to be taken of a considerable number of independent terms - characteristics. We have, first, a general division into condensing and non-condensing engines, with a subdivision of the condensing class into those which act by surface condensation and those which use injection. Next there is the division into compound and non-compound, with a further classification of the former as double-, triple-, or quadruple-expansion engines. Again, engines may be classed as single or double-acting, according as the steam acts on one or alternately on both sides of the piston. Again, a few engines such as steam-hammers and certain kinds of steam-pumps are non-rotative, that is to say, the reciprocating motion of the piston does work simply on a reciprocating piece ; but generally an engine does work on a continuously revolving shaft, and is termed rotative. In most cases the crank-pin of the revolving shaft is connected directly with the piston-rod by a con- necting-rod, and the engine is then said to be direct-acting ; in other cases, of which the ordinary beam-engine is the most important example, a lever is interposed between the piston and the connecting-rod. The same distinction applies to non-rotative pumping engines, in some of which the piston acts directly on the pump-rod, while in others it acts through a beam. The position of the cylinder is another element of classification, giving horizontal, vertical, and inclined cylinder engines. Many vertical engines are further distinguished as belonging to the inverted cylinder class ; that is to say, the cylinder is above the connecting- rod and crank. In oscillating cylinder engines the connect- ing-rod is dispensed with ; the piston-rod works on the crank-pin, and the cylinder oscillates on trunnions to allow the piston-rod to follow the crank-pin round its circular path. In trunk engines the piston-rod is dispensed with ; the connecting-rod extends as far as the piston, to which it is jointed, and a trunk or tubular extension of the piston, through the cylinder cover, gives room for the rod to oscillate. In rotary engines there is no piston in the ordinary sense ; the steam does work on a revolving piece, and the necessity is thus avoided of afterwards converting reciprocating into rotary motion. 192. In the single-acting atmospheric engine of New- comen the beam was a necessary feature; the use of water- packing for the piston required that the piston should move down in the working stroke, and a beam was needed to let the counterpoise pull the piston up. Watt's improve- ments made the beam no longer necessary ; and in one of the forms he designed it was discarded namely, in the form of pumping-engine known as the Bull engine, in which a vertical inverted cylinder stands over and acts directly on the pump-rod. But the beam type was generally 1 Proc. Inst. Mech. Eng., May 1884, p. 163.
