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Flexible Couplings for Internal-C om bustionEnginesBy J. ORMONDROYD,1 ANN ARBOR, MICH.Four typical dynam ical cases of torsionally flexible“linear” couplings are exam ined: (1) In stan tan e o u sapplications of th e m axim um engine to rq u e; (2) in s ta n ­taneous stoppage of th e engine or th e driven m em ber;(3) dangerous torsional resonance; and (4) to o th c h a tte rin geared drives.THE basic purposes of any coupling are to tie together componentparts of a rotating assembly and to transmit theoperating torque safely between the parts. The wide diversityof coupling designs indicates that they are often expectedto be more than mere concatenating links and transmitters oftorque. Even when the component parts of the rotating assemblageare supposed to maintain fixed relative positions, theproblem of alignment has forced the design of couplings withvarious degrees of freedom compatible with carrying out theirbasic functions. A large class of couplings embodying elasticallyflexible elements exists. These couplings are not only expectedto concatenate component parts, transmit torque, and provide acertain amount of leeway in alignment, but they are also expectedto provide a protection to the rotating system which would notexist if the flexibility were omitted.The protection needed by the system is not always clear tothe design engineer. In general, flexible couplings are useful in“dynamic” situations in which angular velocities are changingor in which the driving or delivered torques are variable. Asecond generalization, which cannot be emphasized too strongly,is that a flexible coupling is embodied in a complete rotatingBystem, and its effects depend as much on the system characteristicsas on its own properties. Such data as hub size, installationdimensions, and allowable horsepower per hundred revolutionsper minute based on nominal load torque are necessary,but they are not sufficient to determine a successful application.The effect of a flexible coupling is measured by the differencein operation with the added flexibility and the operation withoutit. The difference to be expected can often be predicted bydynamic analysis of the whole rotating system with and withoutthe coupling.Four typical dynamical situations in which torsionally flexiblecouplings are often considered will be examined. In all casesthe coupling will be considered as “linear,” that is, the angulardeflection or twist between the driving and driven sides of thecoupling will be proportional to the torque transmitted in astatic test. The four cases are:1 Instantaneous application of the maximum engine torque.2 Instantaneous stoppage of the engine or the driven member.3 Dangerous torsional resonance.4 Tooth chatter in geared drives.torque. It is worse than any actual case can be. If a couplingcan be made to meet this situation safely, it will be more thanadequate to meet any rapidly rising torque. To simplify theproblem consider the engine as a single body of moment of inertia hand the driven member as another body of moment of inertiah. The coupling and other connecting shafting has an over-allspring constant K. The suddenly applied engine torque is T.Friction torque and load torque can be ignored since the maximumdistress in the connecting shafting will occur soon after theengine torque is applied and long before any load or friction torquecan be developed. Let $i be the motion of h and be the angleof twist in the coupling members. Under these assumptions,Newton’s second and third laws give the following equations ofThe maximum absolute value of the torque in the couplingmembers occurs when cos pt = —1. It isI n s t a n t a n e o u s l y A p p l i e d T o r q u eThis situation is an idealized limiting case of suddenly applied1 Professor of Engineering Mechanics, University of Michigan.Mem. A.S.M.E.Contributed by the Oil and Gas Power Division and presented a tthe Annual Meeting, New York, N. Y., Dec. 2-6, 1940, of T h eA m e r i c a n S o c i e t y o f M e c h a n i c a l E n g i n e e r s .N o t e : Statem ents and opinions advanced in papers are to beunderstood as individual expressions of their authors, and not thoseof the Society.The torque twisting the connecting members is independentof the spring constant of these members, depends on the ratioI J h , and can never be greater than 2T.Evidently, this is one dynamic problem in which a springcoupling offers no advantages. If the ordinary shafting whichconnects the two rotating members is made strong enough tostand twice the maximum possible torque that the engine canput out, everything has been done that can be done for thisparticular case.577