. A text-book of electrical engineering;. ut four times persecond, twice going forward and twice moving backward. We turn now from these natural oscillations of the alternator to theforced oscillations caused by the inequality of turning-moment of anyreciprocating engine. To simplify the matterwe may imagine the alternator to be replacedby a dynamo. We shall let t-^ representthe time which elapses between two succes-sive maxima of the turning-moment. Theturning-moment diagram wUl be irregular,but may be represented approximately bya sine curve, as shown in Fig. 349 a, in whichthe ordinate
. A text-book of electrical engineering;. ut four times persecond, twice going forward and twice moving backward. We turn now from these natural oscillations of the alternator to theforced oscillations caused by the inequality of turning-moment of anyreciprocating engine. To simplify the matterwe may imagine the alternator to be replacedby a dynamo. We shall let t-^ representthe time which elapses between two succes-sive maxima of the turning-moment. Theturning-moment diagram wUl be irregular,but may be represented approximately bya sine curve, as shown in Fig. 349 a, in whichthe ordinates measured from EH representthe total torque of the engine, while, byPleasuring from OD, we get the amount bywhich the torque differs froni its mean Mil — AG, the maximum excess turning-moment, then we have for the maximumangular acceleration «,= 9-8i^. This is the rate at which the angular velocityof the dynamo or flywheel is changing at anymoment. It is a maximum when the turning-moment is a maximum, as shown in Fig. 349 Fig- 349 So long as the accelerationis positive the angular velocity wiU increase, and will therefore attain itsmaximum value at the moment B (Fig. 349 c). At this moment it will exceedthe normal angular velocity by an amount cd-^. To find w^ we must multiply the average value of the acceleration by the time j, since the velocity was normal at A. The mean value of a sine function is equal to its maximumvalue multiplied by 2/77, so that oJi = Cl-i 2 i^ ,^ TT 4 477 M, .(c). So long as the velocity is above the normal, whUe w is positive, theforward displacement of the flywheel increases. It will reach its maximumvalue of e^ radians at the moment C. To find the value of e^ we mustmultiply the average value of o by the time ^1/4, thus ei = = - .Oi, .- = 9-8i k^.M,^ in- M, ■id). This is due entirely to the steam engine, and is true for any load, elec-trical or otherwise. We must now consider the effect of the alternator onthe angul
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