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ORMONDROYD—FLEXIBLE COUPLINGS FOR INTERNAL-COMBUSTION ENGINES 581Other values of —and their respective shaft torques are shown12in the following tabhh .......................Mmax for flexible!coupling /M max for solid!coupling / ' 'Referring to the author’s case 4, tooth chatter in gear drives,it is pointed out in the concrete example given that, in the case ofa solid coupling, the major critical fourth-order speed occurs at725 rpm and, in the case of the flexible coupling, the minor secondordercritical is at 400 rpm. Inasmuch as the operating range ofthis drive is from 700 to 900 rpm and the lowest possible runningrange would be 500 rpm, it is evident that the use of a flexiblecoupling here is advantageous. Fig. 1 of the paper could beslightly revised by drawing two horizontal lines at 700 and 900rpm to show the operating-speed range for gear-chatter comparison.In regard to the equations on the third page of the paper, it isfound that 7r2 has been omitted. These equations should read asfollowsandW. P. S c h m i t t e r . 4 Reduction of Dynamic Loads. The authorhas reduced four typical dynamical situations to relatively simpleexpressions. Many practical cases cannot be so readily analyzed.Take, for instance, the rather complex example of an enginedrivensystem containing a gear train with known tooth-spacingerrors. The magnitude of the dynamic loading of the gears willdepend, among other things, upon the rigidity of the system.Resilient couplings on both sides of the gears will permit a greaterdegree of acceleration and deceleration of the gear masses in responseto the errors, thus, not only localizing their effects, butmaking for materially lower tooth stresses than with nonresilientcouplings. The solution for any given case may be obtained byfollowing the methods developed in a, bulletin6 published by theSociety.Impact Loading From Driven Machine. Practical examples ofcase 2 are seen in systems in which sudden load decelerations ofthe driven machine take place, thus requiring considerable energyto be absorbed. There are numerous cases of the use of resilientcouplings to alleviate bad situations in severe rolling-mill andsimilar drives. Where all the factors are known, the relativestresses can be computed.Torsional Resonance. Severe resonance may frequently beavoided by application of nonlinear resilient couplings, becausethe tuning changes with the increased amplitude. We agreethat complete analysis of the rotating system is necessary in orderto avoid unfavorable situations. No flexible coupling can be expectedto operate satisfactorily in a bad critical.We consider damping a most important property of the “Steelflex”(Bibby) coupling of the writer’s company. The hysteresisloop obtained in static testing is due to its characteristic design.This is further increased dynamically by the action upon the greasewithin the sealed enclosure.4 Chief Engineer, The Falk Corporation, Milwaukee, Wis.s “Dynamic Loads on Gear T eeth,” A.S.M.E. Report of SpecialResearch Committee on Strength of Gear Teeth, 1931.Gear-Tooth Chatter. Resilient couplings of this type may berelied upon to avoid certain types of tooth chatter. In the rotarydrumcrushing field, herringbone pinions had formerly to beshrouded to avoid their axial displacement during the break intooth contact from effects of the cascading material. Theshrouds are eliminated whenever the couplings mentioned areapplied because the potential energy stored is sufficient tomake the pinion follow the gear when rapid speed fluctuationsoccur.Coupling Strength and Safety. It is exceedingly difficult todraw any arbitrary conclusions with respect to the most efficacioususe of materials in flexible couplings since so much dependson design, as the following analysis will demonstrate. Maximumstrength in an articulated double-acting coupling is obtainedwhen the shear strength of the individual interlocking elements isequal. If a nonlinear resilient coupling of the type previouslymentioned is designed so that the grid is in shear at the limit-loadpeak, its strength at that point is equal to that of the nonresilientcoupling. At lower torques, the grid transmits the load through acontinuous variable-span beam. The entire grid material includingloops is constantly under stress, thus the resilience of thecoupling is unusually high, despite comparable size and safetyfactors.A. M. W a h l . 6 For some time past, the writer has been interestedin the design of couplings for induction-motor drives,7 particularlythose subject to frequent starts and stops as is the case,for example, in the roll-table drive used in continuous strip mills.Because of the electrical characteristics of the induction motor,such systems on starting are subject to a suddenly applied pulsatingtorque at the line frequency which dies out after a time. Thistype of transient-torque application gives rise to two effects, i.e.(1) if the natural frequency of the drive approaches the line frequency,a resonant condition will be present, and (2) because ofthe sudden application of torque an impact effect occurs, whichis augmented by the nonlinear characteristic of the usual coupling.In certain practical applications, considerable trouble hasarisen from these causes. In cases where motors are startedand stopped frequently, this problem is of particular importance,since a sufficient number of cycles of stress may takeplace eventually to cause failure of the mechanical parts of thesystem.The writer wonders whether or not a similar condition may notbe present during the starting of an internal-combustion engine,coupled to its load by means of a flexible coupling. In such acase, a suddenly applied pulsating torque, set up as a consequenceof the explosions of individual cylinders, would be present.For the nonlinear coupling usually applied in such cases, such atorque might give rise to stresses of considerable magnitude as aconsequence of impact effects. In addition, because of the pulsatingtorque, due to the explosions of individual cylinders, itwould appear that there is a possibility of increased torque due toresonance for certain values of the natural frequency of the system.It is realized that such conditions probably occur butrarely in practice, however, in cases where such systems arestarted and stopped frequently an analysis of such torques mightbe worth-while.The writer agrees with the author that conditions resemblingresonance may occur even with nonlinear couplings. Such conditionshave, in fact, been observed in tests on induction-motordrives, the torque being measured by means of a magnetic torsisMechanics D epartm ent, W estinghouse Research Laboratories,E ast Pittsburgh, Pa. Mem. A.S.M.E.’ “Transient Torques in Induction-M otor Drives,” by A. M . Wahl,Journal of Applied Mechanics, Trans. A.S.M.E., vol. 63, 1941, pp.A-17-A-22.