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Introduction

Power transmission couplings arewidely used for modification of stiffnessand damping in power transmissionsystems, both in torsion and in otherdirections (misalignment compensa-tion). Technical literature on connect-ing couplings is scarce and is dominatedby trade publications and commercial

coupling catalogs. Many coupling de-signs use elastomers in complex load-

Selection

andPerformance

CRITERIA FOR POWERTRANSMISSIONCOUPLINGS

PART IEugene I. Rivin

compared to the machines it connects, is a critical aspect ofany shaft system, and a good deal of attention must be paidto its choice at the design stage. from the Resolution of theFirst International Conference on Flexible Couplings

ing modes; some couplings have jointswith limited travel distances betweenthe joint components accommodatedby friction; often, couplings have severelimitations on size and rotational inertia,etc. ese factors make a good couplingdesign a very diffi cult task, which canbe helped by a clearer understanding ofthe couplings functions. Stiffness values

of couplings in both torsional and mis-alignment directions, as well as damping

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continued

Figure 1. (Editors note: AGMA 510.02has been superseded by ANSI/AGMA 9009- D02- Nomenclature for Flexible Cou-plings, and the newer standard uses slight-ly diffrent terminology. e older version isused here for illustrative purposes.) If themisaligned shafts are rigidly connected,this leads to their elastic deformations,

and thus to dynamic loads on bear-ings, to vibrations, to increased frictionlosses, and to unwanted friction forcesin servo-controlled systems. Purelymisalignment-compensating couplingshave torsional deformations and mis-alignment-compensating deformationsdecoupled from movements associatedwith misalignments.

3. Torsionally Flexible Couplings.

of couplings in the torsional direction,have a substantial, often determining,effect on the drive system dynamics.Torsionally flexible couplings are oftenused for tuning dynamic characteristics(natural frequencies and/or damping)of the drive/transmission by intentionalchange of their stiffness and damping.

e purpose of this article is to dis-tinctly formulate various couplings rolesin machine transmissions, as well as toformulate criteria for comparative as-sessment, optimization and selectionof coupling designs. To achieve thesegoals, a classification of connecting cou-plings is given and comparative analysesof commercially available couplings areproposed.

General Classification of Couplings

According to their role in transmis-sions, couplings can be divided into four

classes:1. Rigid Couplings. ese couplings

are used for rigid connection of pre-cisely aligned shafts. Besides the torque,they also transmit bending momentsand shear forces if any misalignmentis present, as well as axial force. ebending moments and shear forces maycause substantial extra loading of the

shaft bearings. Principal application ar-eas of rigid couplings are: long shafting;space constraints preventing use of mis-alignment-compensating or torsionallyflexible couplings; and inadequate dura-bility and/or reliability of other types ofcouplings.

2.Misalignment-Compensating Cou-plings. ese are required for connectingtwo members of a power transmissionor motion transmission system that arenot perfectly aligned. Misalignmentmeans that componentscoaxial by de-signare not actually coaxial, due eitherto assembly errors or to deformations ofsubunits and/or foundations. e latterfactor can be of substantial importancefor large turbine installations (thermal/creep deformations leading to drasticload redistribution between the bear-ings) and for power transmission sys-tems on non-rigid foundations (such asship propulsion systems). Various typesof misalignment as they are defined inAGMA standard 510.02 are shown in

Such couplings are used to change dy-namic characteristics (natural frequency,damping and character/degree of non-linearity) of a transmission system. echanges are desirable or necessary whensevere torsional vibrations are likely todevelop in the transmission system,leading to dynamic overloads. Designs

of torsionally flexible couplings usuallyare not conducive to compensating mis-alignments.

4. Combination Purpose Cou-plings. ese combine significant com-pensating ability with significant tor-sional flexibility. e majority of thecommercially available connecting cou-plings belong to this group. Since thetorsional deformations and deforma-

Nomenclature

External diameter

d Internal diameter

Length

Radial force, or bending moment

Ft

Tangential force

efEffective radius

Transmitted torque

Friction coefficient

t ness actor

omom ne st ness o e ast c connectors

Radial misalignment

Dp

Pitch Diameter

Angular misalignment

qound pressure level

Efficiency

kh

hear stiffness

Relative energy displacement

Potential energy

tTangential force

nergy per coup ng revo ut on

Loss factor of rubber

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A L I G N M E N T

Y

P A R A L L E L O F F S E T M I S A L I G N ME N T

A = B

A B

SYMMETRICAL ANGULAR MISALIGNMENT

A > B

A B

NON-SYMMETRICAL ANGULAR MISALIGNMENT

Y

COMBINED ANGULAR-OFFSET MISALIGNMENT

Figure 1 Types of coupling misalignment.

tions due to misalignments are not sep-arated/decoupled by design, changes intorsional stiffness may result in changesin misalignment-compensating stiff-ness, and vice versa. ese couplings willbe discussed in detail in Part II of thisarticle, which will appear next issue.

Rigid Couplings

Typical designs of rigid couplingsare shown in Figure 2.

Sleeve couplings as in Figures 2aand 2b are the simplest and the slim-mest ones. Such a coupling transmits

torque by pins (Fig. 2a) or by keys (Fig.2b). e couplings are diffi cult to as-semble/disassemble, as they require sig-nificant axial shifting of the shafts to beconnected/disconnected. Usually, exter-nal diameter D = (1.51.8) d, and lengthL = (2.54.0) d.

Flange couplings (Fig. 2c) are the

most widely used rigid couplings. Twoflanges have machined (reamed) holesfor precisely machined bolts insertedinto the holes without clearance (nobacklash). e torque is transmitted by

friction between the contact surfaces ofthe flanges and by shear resistance ofthe bolts. Usually, D = (35.5) d, and L= (2.54.0) d.

A split-sleeve coupling (Fig. 2d)transmits torque by friction between thehalf-sleeves and the shafts and, in somecases, also by a key. eir main advan-

tage is ease of assembly/disassembly.Misalignment-Compensating

Couplings

Misalignment-compensating cou-plings are used to radically reduce theeffects of imperfect alignment by allow-ing a non-restricted or a partially re-stricted motion between the connectedshaft ends in the radial and/or angulardirections. Similar coupling designs aresometimes used to change bending nat-

ural frequencies/modes of long shafts.When only misalignment compensa-

tion is required, high torsional rigid-ity and, especially, absence of backlashin the torsional direction, are usuallypositive factors, preventing distortion ofdynamic characteristics of the transmis-sion system. e torsional rigidity andabsence of backlash are especially im-portant in servo-controlled systems.

To achieve high torsional rigidity

together with high compliance in mis-alignment directions (radial or paralleloffset, axial, angular), torsional and mis-alignment-compensating displacementsin the coupling have to be separatedby using an intermediate compensat-ing member. Typical torsionally rigid,misalignment-compensating couplingsare Oldham couplings, which compen-sate for radial misalignments (Fig. 3a);gear couplings, which compensate forsmall angular misalignments (Fig. 3b);and universal or Cardan joints, whichcompensate for large angular misalign-ments (Fig. 3c). Frequently, torsion-ally rigid misalignment-compensat-ing couplings, such as gear couplings,are referred to in the trade literature asflexible couplings.

Usually, transmissions designed forgreater payloads can tolerate highermisalignment-induced loads. Accord-ingly, the ratio between the load gener-ated in the basic misalignment direction(radial or angular) to the payload (rated

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torque or tangential force) is a naturaldesign criterion for purely misalign-ment-compensating (torsionally rigid)couplings.

Selection criteria for misalignment-compensating couplings. Misalignment-compensating (torsionally rigid) cou-plings are characterized by the presence

of an intermediate compensating mem-ber located between the hubs attachedto the shafts being connected and hav-ing mobility relative to both hubs. ecompensating member can be solid orcomprising several links. ere are twobasic design subclasses:

Subclass Acouplings in whichthe displacements between the hubsand compensating member have a fric-tional character (examples include con-

ventional Oldham couplings, gear cou-plings and Cardan joints).

Subclass Bcouplings in which thedisplacements are due to elastic deforma-tions in special elastic connectors.

For Subclass A, the radial force Fcom

,or bending moment, acts from one hubto another and is caused by misalign-ment; only radial misalignments areaddressed below. F

comis a friction force

equal to the product of friction coeffi -

cient and tangential force Ft at an ef-fective radius Ref, F

t= T/R

ef, where Tis

the transmitted torque:

(1)

e force Fcom

does not depend onthe misalignment magnitude. is is anegative feature, since a relatively smallreal-life misalignment may generatehigh forces acting on bearings of theconnected shafts. Since motions be-tween the hubs and the compensatingmember are of a stick-slip character,with very short displacements alter-nating with stoppages and reversals, might be assumed to be the static fric-tion (stiction) coeffi cient.

When the rated torque Tr

is trans-mitted, then the selection criteria is

(2)

A lower friction and/or larger effec-tive radius would lead to lower forces on

1

Figure 2Typical designs of rigid couplings: simple designs, which transmit torqueby pins (a) or keys (b); flange couplings (c) and split-flange designs (d).

a

b)

c)

d)

com

r ef

F

T R

=

com

ef

TF

R=

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the bearings.For Subclass B, assuming linearity

of the elastic connectors,

(3)

Where e= radial misalignment val-ue, and k

com= combined stiffness of the

elastic connectors in the radial direction.In this case,

(4)

Unlike the Subclass A couplings,Subclass B couplings develop the sameradial force for a given misalignment,regardless of the transmitted torque;thus they are more effective for large T

r.

Of course, a lower stiffness of the elastic

connectors would lead to lower radialforces.

Conventional Oldham couplings, gearcouplings and u-joints (Subclass A). Mis-alignment-compensating couplings areused in cases where a significant torsionalcompliance can be an undesirable factorand/or a precise alignment of the con-nected shafts cannot be achieved. Univer-sal joints (u-joints or Cardan joints) areused in cases where the dominant type of

shaft misalignment is angular misalign-ment. Use of a single joint results in anon-uniform rotation of the driven shaft,which can be avoided by using doublejoints or specially designed constant ve-locity joints. Compensation of a radialmisalignment requires using two Cardanjoints and relatively long intermediateshafts. If bearings of the u-joint are notpreloaded, the joint has an undesirablebacklash, but preloading of the bearingsincreases frictional losses and reduces ef-ficiency. More sophisticated linkage cou-plings are not frequently used, due to thespecific characteristics of general-purposemachinery, such as limited space, limitedamount of misalignment to compensatefor, and cost considerations.

While u-joints use sliding or roll-ing (needle) bearings, both Oldhamand gear couplings compensate for mis-alignment of connected shafts by meansof limited sliding between the hub sur-faces and their counterpart surfaces onthe intermediate member. e sliding

SPIDER TRUNNION YOKEYOKE

YOKE

a

a

c)

Figure 3Torsionally rigid, misalignment-compensating couplings: Oldhamcouplings (a), gear couplings (b) and universal joints or Cardan joints (c).

1

ef

TF

R=

1

ef

TF

R=

1

ef

TF

R=

Y X

1

a

b

3

2

d

om=

com

com com

r r

F ke

T T=

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continued

c(D-e)

P

(D-e)

e

P

D

a)

(D-e)

e

P

D

b)

P

101

106

103a108a

105

111 112

108b

103b

107

102

125

118

Figure 4Stress distribution between the contacting surfaces a and b of hub andintermediate member of the Oldham coupling shown in Figure 3a, assembled

without clearance (a) and with clearance (b).

Figure 6A torsionally rigid, misalignment-compensating coupling.

Figure 5Kudriavetz coupling.

has a cyclical character, with double am-plitude of displacement equal to radialmisalignment efor an Oldham couplingand D

pfor a gear coupling (Ref. 5),

where Dp

is the pitch diameter of thegears and is the angular misalign-ment. If a radial misalignment ehas tobe compensated by gear couplings, then

two gear couplings spaced by distance Lare required, and = e/L. Such a motionpattern is not conducive to good lubri-cation, since at the ends of the relativetravel, where the sliding velocity is zero,a metal-to-metal contact is very prob-able. e stoppages are associated withincreasing friction coeffi cients, close tothe static friction values. is is the casefor low-speed gear couplings and forOldham couplings; for high-speed gear

couplings, the high lubricant pressuredue to centrifugal forces alleviates the

problem (Ref. 5).Figure 3a shows a compensating

(Oldham) coupling, whichat leasttheoreticallyallows the connectionof shafts with a parallel misalignmentbetween their axes without induc-ing nonuniformity of rotation of thedriven shaft and without exerting highloads on the shaft bearings. e cou-

pling comprises two hubs, (1) and (2),connected to the respective shafts andan intermediate disc (3). e torque istransmitted between driving member(1) and intermediate member (3), andbetween intermediate member (3) anddriven member (2), by means of twoorthogonal sliding connections, a-band c-d. By decomposition of the mis-alignment vector into two orthogonalcomponents, this coupling theoreticallyassures ideal radial compensation whilebeing torsionally rigid. e latter featuremay also lead to high torque-to-weightratios. However, this ingenious designfinds only an infrequent use, usuallyfor noncritical, low-speed applications.Some reasons for this are as follows.

For the Oldham coupling, radialforce from one side of the coupling (onehub-to-intermediate member connec-tion) is a rotating vector aimed in thedirection of the misalignment and withthe magnitude

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(5)

whose direction reverses abruptly twiceduring a revolution. e other side ofthe coupling generates another radialforce of the same amplitude, but shifted90 degrees. Accordingly, the amplitudeof the resultant force is

(6)

Its direction changes abruptly fourtimes per revolution. Similar effects oc-cur in gear couplings. An experimentalOldham coupling (T

r= 150 N-m, exter-

nal diameter Dex

= 0.12 m, e= 1 mm andn = 1,450 rpm) exerted radial force onthe connected shafts F

com= 720 N.

e frequent stoppages and direc-

tion reversals of the forces lead to thehigh noise levels generated by Oldham

and gear couplings. A gear coupling canbe the noisiest component of a largepower-generation system (Ref. 6). Asound pressure level L

eq= 96 dBA was

measured at the experimental Oldhamcoupling described above.

Since a clearance is needed fornormal functioning of the sliding con-nections, the contact stresses are non-

uniform with high peak values (Fig.

rial (usually heat-treated steel) since thesame material is used both for the huband the intermediate disc structures andfor the sliding connections. Friction canbe reduced by making the intermedi-ate member from a low-friction plastic,such as ultra-high molecular weight(UHMW) polyethylene, but this may

result in a reduced rating due to loweredstructural strength.

Because of high misalignment-compensating forces, deformations ofthe coupling assembly itself can be verysubstantial. If the deformations becomeequal to the shafts misalignment, thenno sliding will occur and the couplingbehaves as a solid structure, being ce-mented by static friction forces. It canhappen at misalignments belowe 10-

3Dex. is effect seems to be one of thereasons for the trend toward replacing

misalignment-compensating couplingsby rigid couplings, such as the rigidflange coupling in Figure 1c, often usedin power generating systems.

Due to internal sliding with highfriction, Oldham and gear couplingsdemonstrate noticeable energy losses.e effi ciency of an Oldham couplingfor e/D

ex 0.04 is

(7)

For = 0.4 and e = 0.01Dex, =

0.987 and for = 0.3, = 0.99. Similar(slightly better due to better lubrication)effi ciency is characteristic for single-gear couplings.

is inevitable backlash in the gearand Oldham connections is highly un-desirable for servo-controlled transmis-sions.

Oldham couplings and u-joints withelastic connections (Subclass B). e basicdisadvantages of conventional Oldhamand gear couplings high radial forces,jumps in the radial force direction, en-ergy losses, backlash, nonperformanceat small misalignments, noise) are allassociated with reciprocal, short travel,poorly lubricated sliding motion be-tween the connected components. ereare several known techniques of chang-ing friction conditions. Rolling frictionbearings in u-joints greatly reduce fric-

6Figure 7A large u-joint with thin-layered, rubber-metal bearings.

39

33

4437

38

31

32

41

40

35

4334

35

1 3.2

ex

eD

=

2ref

TF

R=

1

ef

TF

R=

4). Figure 4a shows stress distributionbetween the contacting surfaces a and bof hub (1) and intermediate member (3)of the Oldham coupling shown in Fig-ure 3a assembled without clearance. econtact pressure in each contact area isdistributed in a triangular mode alongthe length 0.5(D e) 0.5D. However,

the clearance is necessary during assem-bly, and it increases due to inevitablewear of the contact surfaces. Presenceof the clearance changes the contactarea as shown in Figure 4b, so that thecontact length is l 0.3(D e) 0.3D(or the contact length is 0.5c(D e), c 0.68), thus significantly increasingthe peak contact pressures and furtherincreasing the wear rate. is leads toa rapid increase of the backlash, unless

the initial (design) contact pressuresare greatly reduced. Such non-uniform

contact loading also results in very poorlubrication conditions in the stick-slipmotion. As a result, friction coeffi cientsin gear and Oldham couplings are quitehigh, especially in the latter.

Experimental data for gear cou-plings show = 0.30.4. Similar frictioncoeffi cients are typical for Oldham cou-plings. e coupling components must

be made from a wear-resistant mate-

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and energy dissipated per cycle of de-formation is

(9)

Each of the two connections experi-ences two deformation cycles per revo-lution; thus the total energy dissipated

per revolution of the coupling is

10

Total energy transmitted throughthe coupling per revolution is equal to

11

where Pt= T/D

exis tangential force re-

duced to the external diameter Dx

and

is the transmitted torque. Effi ciencyof a coupling is therefore equal to

(12)

where is the loss factor of the rubber.For the experimentally tested cou-

pling = 0.12 m , the parameters are:

a laminate with rubber layers 2 mm inthickness; = 0.2;sh

= 1.8 x 105 N/m; T 150 N-m; e = 0.001 m; thus

= 1 (0.2 x 1.8 x 105 x 10-6)/150 = 1 0.75 x 10-4 = 0.999925, or the lossesat full torque are reduced 200 times ascompared to the conventional coupling.

Test results for the conventional andmodified Oldham couplings having D

ex

= 0.12 m have shown that the maxi-mum transmitted torque was the same,but there was a 3.5 times reduction inthe radial force transmitted to the shaftbearings with a modified coupling. Ac-tually, the coupling showed the lowestradial force for a given misalignmentcompared with any commercially avail-able compensating coupling, includingcouplings with rubber elements. In ad-dition to this, the noise level at the cou-pling was reduced by 13 dB to

q=

dBA. Using ultra thin-layered laminatesfor the same coupling would furtherincrease its rating by at least one order

121

continued

tan1 sh

ke

T

21 1 sh

kVe

W T

= = =

2

1

2sh

eV k=

V= 2V1 = 2 kshe

2

W =PDex

= 2T

2

1

2sh

eV k =

tion forces. However, they do not per-form well for small-amplitude recipro-cal motions. In many applications, shaftsconnected by u-joints are installed withan artificial 23 initial misalignment toprevent jamming of the rolling bodies.

Another possible option is using hy-drostatic lubrication. is technique is

widely used for rectilinear guide ways,journal and thrust bearings, screw andworm mechanisms, etc. However, thistechnique seems impractical for rotat-ing systems with high loading intensity(and thus high required oil pressures).

Replacement of sliding and rollingfriction by elastically deformable con-nections can resolve the above problems.Figure 5 shows a K or Kudriavetzcoupling made from a strong, flexible

material polyurethane connected withthe hubs by two tongues each. If the

connected shafts have a radial offset, it iscompensated by bending of the tongues,thus behaving like an Oldham couplingwith elastic connections between theintermediate member and the hubs. Ifthe connected shafts each have an an-gular misalignment, the middle mem-brane behaves as a cross, while twist-ing deformations of the tongues create

kinematics of a u-joint. s a result, thiscoupling can compensate large radialmisalignments ( 2.4 mm for a couplingwith external diameter ofD = 55 mm),as well as angular misalignments of 10degrees. e torque ratings of such cou-plings are obviously quite low; e.g., acoupling with outside diameter D = 55mm has a rated torque T

r= 4.5 N-m.

Since displacements in the slidingconnections a-b and c-d in Figure 3aare small (equal to the magnitude of theshaft misalignment), the Oldham cou-pling is a good candidate for applicationof the thin-layered rubber metal lami-nates Ref. 1 . Some of the advantagesof using laminates are their very highcompressive strength, up to 100,000 psi(700 MPa), and insensitivity of theirshear stiffness to the compressive force.is property allows the preloading ofthe flexible element without increasingdeformation losses.

igure 6 (from Ref. 2) shows suchan application. Hubs 101 and 102 have

slots 106 and 107, respectively, whoseaxes are orthogonal. e intermediatedisc can be assembled from two iden-tical halves 103a and 103b. Slots 108aand 108b in the respective halves arealso orthogonally oriented. Holders 105are fastened to slots 108 in the interme-diate disc and are connected to slots 106

and 107 via thin-layered rubber-metallaminated elements 111 and 112 as de-tailed in Figure 6b. ese elements arepreloaded by sides 125 of holders 105,which spread out by moving preloadingroller 118 radially toward the center.

is design provides for all kine-matic advantages of the Oldham cou-pling without creating the above-listedproblems associated with conventionalOldham couplings. e backlash is to-

tally eliminated since the coupling ispreloaded. For the same rated torque,

the coupling is much smaller than theconventional one due to the high load-carrying capacity of the laminates andthe absence of stress concentrations likeones shown in Figure 4b. e interme-diate disc (the heaviest part of the cou-pling) can be made from a light, strongmaterial, such as aluminum, since it isnot exposed to contact loading. is

makes the coupling suitable for high-speed applications.e misalignment compensation

stiffness and the rated torque can bevaried by proportioning the laminatedelements their overall dimensions,thickness and number of rubber layers,etc.). e loads on the connected shaftsare greatly reduced and are not depen-dent on the transmitted torque since theshear stiffness of the laminate does notdepend on the compression load.

To derive an expression for effi cien-cy of the Oldham coupling with lami-nated connections, let the shear stiffnessof the connection between one hub andthe intermediate member be denoted byksh and the relative energy dissipation inthe rubber for one cycle of shear defor-mation by. en, maximum potentialenergy in the connection at maximumshear e is equal to

(8)

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the elastomeric bearing sleeve. To per-form assembly operation, the taperedbearing sleeve is inserted into the wideropening of the tapered annular spacebetween the internal surface of the boreand the external surface of the trunnionand pressed into this space by a punchshaped to contact simultaneously both

end surfaces. Wedge action of the ta-pered connection between the conform-ing inner surface of metal layer 40 andouter surface of trunnion33 results inexpansion of metal layer 40, in compres-sion (preloading) of rubber layers andin gradual full insertion of the bearingsleeve into the annular space betweenthe yoke and trunnion. e simultane-ous contact between the pressing punchand both end surfaces of inner metal

layer 40 and outer metal layer 41 assuresinsertion of the bearing sleeve without

inducing axial shear deformation insidethe bearing sleeve, which can cause dis-tortion or even damage of the bearingsleeve.

To disassemble the connection, boltsattaching the cover to the yoke are re-moved, and then a bolt is threaded intoa hold until contacting the end surfaceof the trunnion. e further threading

of the bolt pushes the outside cover to-gether with the outer metal layer of thebearing sleeve, to which the cover is at-tached by bolts. e initial movementcauses shear deformation in the rub-ber layers until disassembly protrusionsengage with the inner metal layer, thusresulting in a uniform extraction of thebearing sleeve.

It is highly beneficial that u-jointswith the rubber-metal laminated bear-ings do not need sealing devices and arenot sensitive to environmental contami-nation (dirt, etc.).

e effi ciency analysis for such u-joints is very similar to the analysis forthe modified Oldham coupling. e ef-ficiency of the joint is

(13)

where ktor

is the torsional stiffness of theconnection between the intermediatemember and one yoke. It can be com-

6

6

7

9

11

7 10

6

10

Figure 8A modified spider coupling.

2tan1 tor

k

T

21 1

torkV

W T

= = =

of magnitude, and may even require aredesign of the shafts to accommodatesuch a high transmitted load in a verysmall coupling.

-joints transmit rotation betweentwo shafts whose axes are intersectingbut not coaxial (Fig. 3c). A u-joint alsohas an intermediate member (spider

or cross) with four protruding pinstrunnions whose intersecting axes

are located in one plane at 90 to eachother. As in the Oldham coupling, twotrunnions having the same axis are mov-ably engaged with journals machined inthe hub (yoke) mounted on one shaft,and the other two trunnions, with theyoke attached to the other connectedshaft. However, while the motions be-tween the intermediate member and the

hubs in the Oldham coupling are trans-lational, in the u-joint these motions

are revolute. is design is conducive tousing rolling friction bearings, but thesmall reciprocating travel regime un-der heavy loads requires derating of thebearings.

A typical embodiment of the u-jointwith thin-layered rubber-metal bear-ings (Ref. 3) is illustrated in Figure 7for a large-size joint. Figure 7 shows

two basic units (out of four constitut-ing the universal joint): yoke-trunnion-elastomeric bearing sleeve (parts 31, 33and 35 respectively) and yoke-trun-nion-elastomeric bearing sleeve (parts32, 34 and 35, respectively). Sleeves(35) comprise rubber-metal laminates

(37) having sleeve-like rubber layers(38). Separating them and bonded tothem are sleeve-like thin, reinforcing,intermediate metal layers (39) and inner(40) and outer (41) sleeve-like materiallayers bonded to the extreme inner andouter sleeve-like rubber layers. e innerand outer metal layers of the laminated

bearing sleeve are made thicker than theintermediate metal layers, since they de-termine the overall shape of elastomericbearing sleeves.

e inner surface of the inner layer(40) is made tapered and conformingwith the tapered outer surfaces of trun-nions 33 and 34. e outer surface of theouter layer (41) is made cylindrical andconforming with the internal cylindri-cal surface of the bore in yoke 31. Each

bearing sleeve (35) is kept in place by acover (44) abutting the end surface (43)

of the outer metal layer (41). e coveris fastened to the outer metal layer andto the yoke by bolts. A threaded hole isprovided in the center of the cover.

Before assembly, the wall thicknessof the elastomeric bearing sleeve (a sumof total thickness of rubber layers, inter-mediate metal layers and inner and outermetal layers) is larger than the annular

space between the inside surface of thebore in the yoke (31) and the respectiveoutside surface of the trunnion (33). edifference between the wall thicknessof the bearing sleeve and the availableannular space is equal to the specifiedpreloading compression deformation of

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10/10wwwpowertransmission com october 2008 powertransmissionengineering 21

pared with effi ciency of a conventionalu-joint where dis the effective diameterof the trunnion bearing, 2R is the dis-tance between centers of the oppositetrunnion bearings, and is the frictioncoeffi cient in the bearings.

(14)

A comparison of Equations 7 and 14with Equations 12 and 13, respectively,shows that while effi ciencies of conven-tional Oldham couplings and u-jointsfor a given e, are constant, effi ciencyof the modified designs using rubber-metal laminated connections increaseswith increasing load (when the energy

losses are of the greatest importance).e losses in an elastic Oldham coupling

and u-joint at the rated torque can be12 decimal orders of magnitude lowerthan the losses for conventional units.Due to high allowable compression loadson the laminate (in this case, high radialloads), the elastic Oldham couplings andu-joints can be made smaller than theconventional units with sliding or rollingfriction bearings for a given rated torque.

e laminates are preloaded to eliminatebacklash, to enhance uniformity of stressdistribution along the load-transmittingareas of the connections, and to increasetorsional stiffness. Since there is no actualsliding between the contacting surfaces,the expensive surface preparation neces-sary in conventional Oldham couplingsand u-joints (heat treatment, high-fin-ish machining, etc.) is not required. emodified Oldham coupling in Figure 6and the u-joint in Figure 7 can trans-mit very high torques while effectivelycompensating large radial and angularmisalignments, respectively, and havingno backlash since their laminated flex-ible elements are preloaded. However, forsmall-rated torques, there are very effec-tive and inexpensive alternatives to thesedesigns whose kinematics are similar.ese alternatives are also backlash-free.

One is a Kudriavetz coupling, shownin Figure 5. Another alternative is amodified spider or jaw coupling whosecross section by the mid-plane of the

six-legged spider is shown in Figure 8(Ref. 4). In this design the elastomericspider of the conventional jaw couplingshown in Figure 10a is replaced witha rigid spider (9, 11) carrying tubularsleeves or coil springs (10) supported byspider pins (11) and serving as flexibleelements radially compressed between

cams (6 and 7) protruding from the re-spective hubs. If the number of spiderlegs is four, at 90 to each other, thenthe hubs have relative angular mobility,and the coupling becomes a u-joint withangular mobility greater than 10, butwith much higher rated torque than anequivalent size Kudriavetz coupling.

Purely misalignment compensatingcouplings described in this section havetheir torsional and compensating prop-

erties decoupled by introduction of theintermediate member. Popular bellows

couplings have high torsional stiffnessand much lower compensating stiffness,but their torsional and compensatingproperties are not decoupled, so theyare representatives of the combinationpurpose couplings group, which willbe discussed in detail in Part II of thisarticle, which will appear next issue.

References1. Rivin, E.I. Stiffness and Dampingin Mechanical Design, 1999, MarcelDekker, Inc., NY.2. Torsionally Rigid MisalignmentCompensating Coupling, U.S. Patent5,595,540.3. Universal Cardan Joint with Elasto-meric Bearings, U.S. Patent 6,926,611.4. Spider Coupling, U.S. Patent6,733,393.5. Torsional Connection with RadiallySpaced Multiple Flexible Elements,U.S. Patent 5,630,758.6. Rivin, E.I. Shaped ElastomericComponents for Vibration ControlDevices, Sound and Vibration, 1999,Vol. 33 No. 7, pp. 1823.

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Eugene I. Rivin was a Prin-c pa ta ng neer at orMotor Co., from 1976-1981. Since1981 he has been professor at WayneState Univ. Major professional achieve-ments of Dr. Rivin are in transmissionynam cs, v rat on no se contro , mac netools/tooling, robotics, advanced machineelements, creative problem solving. He pub-lished many monographs, book chapters andarticles. Most recent books: Mechanical

es gn o o ots, ; t ness anDamping in Mechanical Design, 1999;Passive Vibration Isolation, 2003; In-novation on Demand, 2005 (with V. Fey).

e aut ore co-aut ore + patents, w tsome nvent ons w e y mp emente wor -wide. Out of this number, 18 patents relateto power transmission components gears,flexible and rigid couplings, keys and otherr g nter aces connect ons or mac ne too sand other mechanical systems . He is anelected Fellow of the International Academyof Production Engineering Research CIRP ,

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