Transactions

570 TRANSACTIONS OF THE A.S.M.E. OCTOBER, 1941excitation current is normally reduced with correspondingly lessheat to be dissipated.M e t h o d o p C o u p l in g C o n t r o lCoupling control under operating conditions is quite simple.The coupling is made or broken instantaneously by operation ofa switch located at the engine control board. Thus, both engineand coupling are operated by the engine attendant. Normally,the excitation circuit is kept closed and the engines handledexactly as in a direct-connected installation. During dockingor channel maneuvering, the engines may be left running and thepropeller shaft controlled by means of the excitation switch.Where several units drive a common shaft, the load must bedivided equally among the engines, i.e., the slip at each couplingmust be the same. This latter quantity is measured by a simplestroboscopic arrangement and the necessary adjustment thenmade by variation of the fuel supply. The stroboscope consistsof two concentric bands with a number of equally spacedholes drilled in their peripheries. One band is carried on eachof the two coupling rotors. The relative rotational movementcan be clearly seen when a light source is placed within the innerband; measurement is then accurately made by a stop watch.Two years ago, the author had the opportunity to observe theoperation of two A.S.E.A. couplings during a trip of several days’duration aboard the Swedish motor vessel Astri. No occasionarose for an emergency-speed reversal, but all other normalmaneuvers at docking and in free route were carried out. Changesor reversals in speed were rapidly made without signs of shock orlag between engine and propeller speeds. Some of these operationswere timed and may be of interest; the interval measuredwas that from the initial telegraph bell to the moment thepropeller shaft reached speed, and includes the time taken bythe attendant to reset the telegraph prior to adjusting theengine throttle. Incidentally, the excitation circuit was keptclosed at all times. The values follow:FromStop‘/s Speed aheadStopToVj Speed aheadStopl/i Speed asternTime, sec101014These times represent average performance.When a wide operating speed range, of the order of 3 to 1, isused, the excitation current is usually reduced for low-speedoperation. This is done by means of an additional resistanceplaced in series with the excitation circuit. By such control,the efficiency of the coupling can be held approximately to aconstant value over the entire operating range.V ib r a t o r y C h a r a c t e r is t ic s o f C o u p l in gThe slip-torque characteristics previously discussed are thosewhich obtain under conditions of uniform driving torque. Actually,the torque delivered by the Diesel engine is periodic innature and may contain large variations from the mean value.The net motion at the driving rotor is a combination of harmonicmotions of differing frequencies superposed upon a uniformrotation. Tests, conducted on early installations, showed amarked suppression of oscillating motion across the coupling andthe action was interpreted as equivalent to that of a viscous-fluiddevice. Recent experimental and analytical data, however,show that the electrical effects which obtain under vibratoryconditions give rise to both elastic and damping components oftorque within the coupling. This effect was first brought to theauthor’s attention by G. J. Dashefsky of the New York NavyYard, who noticed the characteristic during tests conducted ona coupling furnished by the Westinghouse Company. Modeltests recently made available by the A.S.E.A. to the ElectricBoat Company and tests on a full-size coupling made at thelatter plant confirm Dashefsky’s observations. A mathematicalanalysis has also been developed by two members of the A.S.E.A.staff, Dr. Dreyfus and H. Arnemo, and is given in the Appendix.Values computed on this basis agreed closely with those obtainedexperimentally on the model coupling; these tests incidentallycovered a vibratory range from zero to 20 cycles per sec frequencyat the driving rotor. Since the preparation of this paper, asimilar mathematical analysis was presented to the AmericanInstitute of Electrical Engineers (A.I.E.E.) by Lory, Kilgore,and Baudry.4 This approach differs from that of A.S.E.A.,and, since a check of results is afforded, no duplication is involvedin presentation of the latter.F r e q u e n c y R a n g eThe frequency range of practical interest is considerably higherthan that covered in the model-coupling tests. Calculations foran 850-hp 460-rpm coupling have been made by the author upto a value of 100 cycles per sec. This corresponds to a naturalfrequency of 6000 vibrations per min and covers in general allcritical speeds of practical interest in marine drives. Thecomputed values are given in Fig. 5. At low frequencies, thedamping component is larger and the two become equal, in thisparticular design, at about 5 cycles per sec. Beyond this point,the decrease in elasticity is large compared to that of the damping.Both components may be considered as constant in valueabove 30 cycles per sec. In a previous reference,4 the elasticcharacteristic is compared to a weak mechanical spring, and thetendency is to treat the driving and driven systems as separateentities. While in many cases the treatment is perfectly applicable,it must nevertheless be noted that the term “weak” isa comparative one and therefore somewhat misleading. Inmarine installations, where a long length of shafting from theengine to the propeller is involved, it is possible for the line-shaftflexibility to exceed that of the coupling. While the conditionis not a usual one, its possibility shows that the device shouldonly be applied on the basis of a careful analysis of the entirevibratory system.Generally, the elasticity of both the driving and driven portionswill be quite low compared to that of the coupling. Theeffect of the coupling elasticity under these conditions is to introducean additional mode of vibration of very low frequency,compared to those of either portion treated separately. Thehigher modes of vibration correspond closely to those obtainedfor the separate portions of the system. In the fundamentalmode, all masses to one side of the coupling move practically inphase. The accompanying stress in the shafting is consequentlyvery low. Actually, the system is equivalent to one of twomasses, i.e., the driving and driven portions connected by thecoupling elasticity. The dynamic effect may be evaluatedsimply, if the damping between rotors is neglected. Let m =circular frequency of forced vibration; J\, Ji = driving anddriven inertias, respectively; K = coupling elasticity; p =circular frequency of natural vibration, i.e., p —\/[K (Ji + J^/JiJi]; M sin mt = vibratory torque deliveredto the driven member. Then it can be shown thatIn a twin-engined single-screw geared drive the phase relationbetween torque components delivered by each engine will modifyEquation [1] as follows: Introducing the additional notationr = vibratory order under consideration, = phase anglebetween similar cranks of the two engines, and Ji — moment of4 “ Electric Couplings,” by M. R. Lory, L. A. Kilgore, and R. A.Baudry, Trans. A.I.E.E., vol. 59, 1940, pp. 423-428.