Part I
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Eugene I. Rivin
Fcom
, or bending moment, acts from one hub to anothe r and is caused by misalignment; only radial misalignments are addressed below.Fcom
is a friction force equal to the product of friction coefficient µ and tangential forceFt
at an effective radiusRef, F, = T/Ref
, whereT
is the transmin ed torque:Fcom
does not depend on the misalignment magnitude. This is a negative feature, since a relatively small real-life misalignment may generate high forces acting on bearings of the connected shafts. Since motions between the hubs and the compensating member are of a "stick-slip" character, with very short displacements alternating with stoppages and reversals, µ might be assumed to be the static friction ("stiction") coefficient.Tr
is tran smined, then the selection criteria isB
, assuming linearity of the elastic connectors,e
= radial misalignment value, andkcom
= combined stiffness of the elastic connectors in the radial direction. In this case,Tr
, Of course, a lower stiffness of the elastic connectors would lead to lower radial forces.e
for an Oldham coupling andDpθ
for a gear coupling (Ref 5), whereDp
is the pitch diameter of the gears and θ is the angular misalignment. If a radial misalignment e has to be compensated by gear couplings, then two gear couplings spaced by distance L are required, and θ = e/L. Such a motion pattern is not conducive to good lubrication, since at the ends of the relative travel, where the sliding velocity is zero, a metal-to-m etal contact is very probable. The stoppages are associated with increasing friction coefficients, close to the static friction values. This is the case for low-speed gear couplings and for Oldham couplings; for high-speed gear couplings, the high lubricant pressure due to centrifugal forces alleviates the problem (Ref 5).Tr
= 150 N-m, external diameterDex
= 0.12 m,e
= 1 mm andn
= 1,450 rpm) exerted radial force on the connected shaftsFcom
= 720 N.Leq
= 96 dBA was measured at the experimental Oldham coupling described above.e
) ≈ 0.5D
. However, the clearance is necessary during assembly, and it increases due to inevitable wear of the contact surfaces. Presence of the clearance changes the contact area as shown in Figure 4b, so that the contact length is 1 ≈ 0.3(D -e
) ≈ 0.3D
(or the contact length is 0.5c
(D -e
),c
≈ 0.68), thus significantly increasing the peak co ntact pressures and further increasing the wear rate. This leads to a rapid increase of the backlash, unless the initial (design) contact pressures are greatly reduced. Such non-uniform contact loading also results in very poor lubrication conditions in the stick-slip motion. As a result, friction coefficients in gear and Oldham couplings are quite high, especially in the latter.e
≈ 10-3Dex
. This effect seems to be one of the reasons for the trend toward replacing misalignment-compensating couplings by rigid couplings, such as the rigid flange coupling in Figure 1c, often used in power generating systems.Dex
≤ 0.04 ise
= 0.01Dex
, η = 0.987 and for µ = 0.3 , η = 0.99. Similar (slightly better due to better lubrication) efficiency is characteristic for singlegear couplings.D
= 55 mm), as well as angular misalignment s of , ±10 degrees. The torque ratings of such couplings are obviously quite low; e.g., a coupling with outside diameterD
= 55 mm has a rated torqueTr
= 4.5 N-m.e
) is equal toT/Dex
is tangential force reduced to the external diameterDex
andT
is the transmitted torque. Efficiency of a coupling is therefore equal toDex
= 0.12 m), the parameters are: a laminate with rubber layers 2 mm in thickness; ψ = 0.2;ksh
= 1.8 x 105 N/m;T
= 150 N-m;e
= 0.001 m; thus η = 1 - (0.2 x 1.8 x 105 x 10-6)/150π = 1 - 0.75 x 10-4 = 0.999925, or the losses at full torque are reduced 200 times as compared to the conventional coupling.Dex
= 0.12 m have shown th at the maximum transmited torque was the same, but there was a 3.5 times reduction in the radial force transmitted to the shaft bearings with a modified coupling. Actually, the coupling showed the lowest radial force for a given misalignment compared with any commercially available compensating coupling, including couplings with rubber elements. In addition to this, the noise level at the coupling was reduced by 13 dBA toLeq
= 83 dBA. Using ultra thin-layered laminates for the same coupling would further increase its rating by at least one order of magnirude, and may even require a redesign of the shafts to accommodate such a high transmitted load in a very small coupling.ktor
is the torsional stiffness of the connection between the intermediate member and one yoke. It can be compared with efficiency of a conventional u-joint whered
is the effective diameter of the trunnion bearing, 2R is the distance between centers of the opposite trunnion bearings, and µ is the friction coefficient in the bearings.Power transmission couplings are widely used for modification of stiffness and damping in power transmission systems, both in torsion and in other directions (misalignment compensation). Technical literature on connecting couplings is scarce and is dominated by trade publications and commercial coupling catalogs. Many coupling designs use elastomers in complex loading modes; some couplings have joints with limited travel distances between the joint components accommodated by friction; often, couplings have severe limitations on size and rotational inertia, etc. These factors make a good coupling design a very difficult task, which can be helped by a clearer understanding of the coupling's functions. Stiffness values of couplings in both torsional and misalignment directions, as well as damping of couplings in the torsional direction, have a substantial, often determining, effect on the drive system dynamics. Torsionally flexible couplings are often used for tuning dynamic characteristics (natural frequencies and/or damping) of the drive/transmission by intentional change of their stiffness and damping.The purpose of this article is to distinctly formulate various couplings' roles in machine transmissions, as well as to formulate criteria for comparative assessment, optimization and selection of coupling designs. To achieve these goals, a classification of connecting couplings is given and comparative analyses of commercially available couplings are proposed.General Classification of Couplings According to their role in transmissions, couplings can be divided into four classes:1.These couplings are used for rigid connection of precisely aligned shafts. Besides the torque, they also transmit bending moments and shear forces if any misalignment is present, as well as axial force. The bending moments and shear forces may cause substantial extra loading of the shaft bearings. Principal application areas of rigid couplings are: long shafting; space constraints preventing use of misalignment-compensating or torsionally flexible couplings; and inadequate durability and/or reliability of other types of couplings.2.These are required for connecting two members of a power transmission or motion transmission system that are not perfectly aligned. "Misalignment" means that components-coaxial by design-are not actually coaxial, due either to assembly errors or to deformations of subunits and/or foundations. The latter factor can be of substantial importance for large turbine installations (therma/creep deformations leading to drastic load redistribution between the bearings) and for power transmission systems on non-rigid foundations (such as ship propulsion systems). Various types of misalignment as they are defined in AGMA standard 510.02 are shown in Figure 1. (Editors note: AGMA 510.02 hasbeen superseded hyANSIIAGMA 9009 - D02 - Nomenclature for Flexible Couplings, and the newer standard uses slightly different terminology. The older version is used here for illustrative purposes.) If the misaligned shafts are rigidly connected, this leads to their elastic deformations, and thus to dynamic loads on bearings, to vibrations, to increased friction losses, and to unwanted friction forces in servo-controlled systems. Purely misalignment-compensating couplings have torsional deformations and misalignment-compensating deformations decoupled from movements associated with misalignments.3.Such couplings are used to change dynamic characteristics (natural frequency, damping and character/degree of nonlinearity) of a transmission system. The changes are desirable or necessary when severe torsional vibrations are likely to develop in the transmission system, leading to dynamic overloads. Designs of torsionally flexible couplings usually arenot conducive to compensating misalignments.4.These combine significant compensating ability with significant torsional flexibility. The majority of the commercially available connecting couplings belong to this group. Since the torsional deformations and deformations due to misalignments are not separated/ decoupled by design , changes in torsional stiffness may result in changes in misalignment-compensating stiffness, and vice versa. These couplings will be discussed in detail in Part II of this article, which will appear next issue.Typical designs of rigid couplings are shown in Figure 2. Sleeve coup lings as in Figures 2a and 2b are the simplest and the slimmest ones. Such a coupling transmits torque by pins (Fig. 2a) or by keys (Fig. 2b). The couplings are difficult to assemble/disassemble, as they require significant axial shifting of the shafts to be connected/disconnected. Usually, external diameter= (1.5-1.8), and length= (2.5-4.0)Flange couplings (Fig. 2c) are the most widely used rigid couplings. Two flanges have machin ed (reamed) holes for precisely machined bolts inserted into the holes without clearance (no backlash). The torque is transmitted by friction between the contact surfaces of the flanges and by shear resistance of the bolts. Usually,= (3- 5.5), and= (2.5-4.0)A split-sleeve coupling (Fig. 2d) transmits torque by friction between the half-sleeves and the shafts and, in some cases, also by a key. Their main advantage is ease of assembly/disassembly.Misalignment -compensating couplings are used to radically reduce the effects of imperfect alignment by allowing a non-restricted or a partially restricted motion between the connected shaft ends in the radial and/or angular directions. Similar coupling designs are sometimes used to change bending natural frequencies/modes of long shafts. When only misalignment compensation is required, high torsional rigidity and, especially, absence of backlash in the tor sional direction, are usually positive factors, preventing distortion of dynamic characteristics of th e transmission system. The torsional rigidity and absence of backlash are especially important in servo-controlled systems.To achieve high torsional rigidity together with high compliance in misalignment directions (radial or parallel offset, axial, angular), torsional and misalignment-compensating displacements in the coupling have to be separated by using an intermediate compensating member. Typical torsionally rigid, misalignment-compensating couplings are Oldham couplings, which compensate for radial misalignments (Fig. 3a); gear couplings, which compensate for small angular misalignments (Fig. 3b); and universal or Cardan joints, which compensate for large angular misalignments (Fig. 3c). Frequen tly, torsionally rigid "misalignment-compensating" couplings, such as gear couplings, are referred to in the trad e literature as "flexible" couplings.Usually, transmissions designed for greater payloads can tolerate higher misalignment-induced loads. Accordingly, the ratio between the load generated in th e basic misalignment direction (radial or angular) to the payload (rated torque or tangential force) is a natural design criterion for purely misalignment-compensating (torsionally tigid) couplings.Misalignmentcompensating (torsionally rigid) couplings are characterized by the presence of an intermediate compensating member located between the hubs attached to the shafts being connected and having mobility relative to both hubs. The compensating member can be solid or comprising several links. There are two basic design subclasses:• Subclass A—couplings in which the displacements between the hubs and compensating member have a frictional character (examples include conventional Oldham couplings, gear couplings and Cardan joints).• Subclass Be—couplings in which the displacements are due to elastic deformations in special elastic connectors.For Subclass A, the radial force, or bending moment, acts from one hub to anothe r and is caused by misalignment; only radial misalignments are addressed below.is a friction force equal to the product of friction coefficient µ and tangential forceat an effective radius, whereis the transmin ed torque:The forcedoes not depend on the misalignment magnitude. This is a negative feature, since a relatively small real-life misalignment may generate high forces acting on bearings of the connected shafts. Since motions between the hubs and the compensating member are of a "stick-slip" character, with very short displacements alternating with stoppages and reversals, µ might be assumed to be the static friction ("stiction") coefficient.When the rated torqueis tran smined, then the selection criteria isA lower friction and/or larger effective radius would lead to lower forces on the bearings.For Subclass, assuming linearity of the elastic connectors,Where= radial misalignment value, and= combined stiffness of the elastic connectors in the radial direction. In this case,Unlike the Subclass A couplings, Subclass B couplings develop the same radial force for a given misalignment, regardless of the transmitted torque; thus they are more effective for large, Of course, a lower stiffness of the elastic connectors would lead to lower radial forces.Misalignment-compensating couplings are used in cases where a significant torsional compliance can be an undesirable factorand/or a precise alignment of the connected shafts cannot be achieved. Universal joints (u-joinrs or Cardan joints) are used in cases where the' dominant type of shaft misalignment is angular misalignment. Use of a single joint results in a non-uniform rotation of the driven shaft, which can be avoided by using double joints or specially designed "constant velocity" joints. Compensation of a radial misalignm ent requires using two Cardan joints and relatively long intermediate shafts. If bearings of the u-joint are not preloaded, the joint has an undesirable backlash, but preloading of the bearings increases frictional losses and reduces efficiency. More sophisticated linkage couplings are not frequendy used, due to the specific characteristicsof general-purpose machinery, such as limited space, limited amount of misalignment to compensate for, and cost considerations.While u-joints use sliding or rolling (needle) bearings, both Oldham and gear couplings compensate for misalignment of connected shafts by means of limited sliding between the hub surfaces and their counterpart surfaces on the intermediate member. The sliding has a cyclical character, with double amplirude of displacement equal to radial misalignmentfor an Oldham coupling andfor a gear coupling (Ref 5), whereis the pitch diameter of the gears and θ is the angular misalignment. If a radial misalignment e has to be compensated by gear couplings, then two gear couplings spaced by distance L are required, and θ = e/L. Such a motion pattern is not conducive to good lubrication, since at the ends of the relative travel, where the sliding velocity is zero, a metal-to-m etal contact is very probable. The stoppages are associated with increasing friction coefficients, close to the static friction values. This is the case for low-speed gear couplings and for Oldham couplings; for high-speed gear couplings, the high lubricant pressure due to centrifugal forces alleviates the problem (Ref 5).Figure 3a shows a compensating (Oldham) coupling, which-at least theoretically-allows the connection of shafts with a parallel misalignment between their axes without inducing nonuniformity of rotation of the driven shaft and withou t exerting high loads on the shaft bearings. The coupling comprises two hubs, (1) and (2), connected to the respective shafts and an intermediate disc (3). The torque is transmitted between driving member (1) and intermediate member (3), and between intermediate member (3) and driven member (2), by means of two orthogonal sliding connections, a-b and c-d. By decomposition of the misalignment vector into two orthogonal components, this coupling theoretically assures ideal radial compensation while being torsionally rigid. The latter feature may also lead to high torque-to-weight ratios. However, this ingenious design finds only an infrequent use, usually for noncritical, low-speed applications. Some reasons for this are as follows.For the Oldham coupling, radial force from one side of the coupling (one hub-to-intermediate member connection) is a rotating vector aimed in the direction of the misalignment and with the magnitudewhose direction reverses abruptly twice during a revolution. The other side of the coupling generates another radial force of the same amplitude, but shifted 90 degrees. Accordingly, the amplitude of the resultant force isIts direction changes abru ptly four times per revolution. Similar effects occur in gear couplings. An experimental Oldham coupling (= 150 N-m, external diameter= 0.12 m,= 1 mm and= 1,450 rpm) exerted radial force on the connected shafts= 720 N.The frequent stoppages and direction reversals of the forces lead to the high noise levels generated by Oldham and gear couplings. A gear coupling can be the noisiest component of a large power-generation system (Ref 6). A sound pressure level= 96 dBA was measured at the experimental Oldham coupling described above.Since a clearance is needed for normal functioning of the slid ing connections) the contact stresses are nonuniform with high peak values (Fig. 4). Figure 4a shows stress distribution between the contacting surfaces a and b of hub (1) and intermediate member (3) of the Oldham coupling shown in Figure 3a assembled without clearance. The contact pressure in each contact area is distributed in a triangular mode along the lengrh 0.5(D -) ≈ 0.5. However, the clearance is necessary during assembly, and it increases due to inevitable wear of the contact surfaces. Presence of the clearance changes the contact area as shown in Figure 4b, so that the contact length is 1 ≈ 0.3(D -) ≈ 0.3(or the contact length is 0.5(D -),≈ 0.68), thus significantly increasing the peak co ntact pressures and further increasing the wear rate. This leads to a rapid increase of the backlash, unless the initial (design) contact pressures are greatly reduced. Such non-uniform contact loading also results in very poor lubrication conditions in the stick-slip motion. As a result, friction coefficients in gear and Oldham couplings are quite high, especially in the latter.Experimental data for gear couplings show µ = 0.3-0.4. Similar friction coefficients are typical for Oldham couplings. The coupling components must be made from a wear-resistant material (usually heat-treated steel) since the same material is used both for the hub and the intermediate disc structures and for the sliding connecrions. Friction can be reduced by making the intermediate member from a low-friction plastic, such as ultra-high molecular weight (UHMW) polyethylene, but this may result in a reduced rating due to lowered structural strength.Because of high misalignment compensating forces, deformations of the coupling assembly itself can be very substantial. If the deformations become equal to the shafts' misalignment, the no sliding will occur and the coupling behaves as a solid structure, being cemented by static friction forces. It can happen at misalignments below≈ 10-3. This effect seems to be one of the reasons for the trend toward replacing misalignment-compensating couplings by rigid couplings, such as the rigid flange coupling in Figure 1c, often used in power generating systems.Due to internal sliding with high friction, Oldham and gear couplings demonstrate noticeable energy losses. The efficiency of an Oldham coupling for e/≤ 0.04 isFor µ = 04 and= 0.01, η = 0.987 and for µ = 0.3 , η = 0.99. Similar (slightly better due to better lubrication) efficiency is characteristic for singlegear couplings.This inevitable backlash in the gear and Oldham connecrions is highly undesirable for servo-controlled transmissions.The basic disadvantages of conventional Oldham and gear couplings (high radial forces, jumps in the radial force direction) energy losses) backlash, nonperformance at small misalignments, noise) are all associated with reciprocal, short travel, poorly lubricated sliding motion between the connected components. There are several known techniques of changing friction conditions. Rolling friction bearings in u-joints greatly reduce fricrion forces. However, they do not perform well for small-amplitude reciproca lmotions. In many applications, shafts connected by u-joints are installed with an artificial 2-3° initial misalignment to prevent jamming of the rolling bodies.Another possible option is using hydrostatic lubrication. This technique is widely used for rectilinear guide ways, journal and thrust bearings, screw and worm mechanisms, etc. However, this technique seems impractical for rotating systems with high loading intensity (and thu s high required oil pressures).Replacement of sliding and rolling friction by elastically deformable connections can resolve the above problems. Figure 5 shows a "K" or "Kudnaverz" coupling made from a strong, flexible material (polyurethane) connected with the hubs by two "tongues" each. If the connected shafts have a radial offset, it is compensated by bending of the tongues, thus behaving like an Oldham coupling with elastic connections between the intermediate member and the hubs. If the connected shafts each have an angular misalignment, the middle membrane behaves as a "cross," while twisting deformations of the tongues create kinematics of a u-joint. As a result, this coupling can compensate large radial misalignments (~2.4 mm for a coupling with external diameter of= 55 mm), as well as angular misalignment s of , ±10 degrees. The torque ratings of such couplings are obviously quite low; e.g., a coupling with outside diameter= 55 mm has a rated torque= 4.5 N-m.Since displacements in the sliding connections a-b and c-d in Figure 3a are small (equal to the magnitude of the shaft misalignment), the Oldham coupling is a good candidate for application of the thin-layered rubber metal laminates (Ref. 1). Some of the advantages of using laminates are their very high compressive strength, up to 100,000 psi (700 MPa), and insensitivity of their shear stiffness to the compressive force. This property allows the preloading of the flexible element without increasing deformation losses.Figure 6 (from Ref 2) shows such an application. Hubs 101 and 102 have slots 106 and 107, respectively, whose axes are orthogonal. The intermediate disc can be assembled from two identical halves 103a and 103b. Slots 108a and 108b in the respective halves are also orthogonally oriented. Holders 105 are fastened to slots 108 in the intermediate disc and are connected to slots 106 and 107 via thin-layered rubber-metal laminated elements 111 and 112 as detailed in Figure 6b. These elements are preloaded by sides 125 of holders 105, which spread out by moving preloading roller 118 radially toward the center.This design provides for all kinematic advantages of the Oldham coupling without creating the above-listed problems associated with conventional Oldham couplings. The backlash is totally eliminated since the coupling is pre1oaded. For the same rated torque, the coupling is much smaller than the conventional one due to the high load carrying capacity of the laminates and the absence of stress concentrations like ones shown in Figure 4b. The intermediate disc (the heaviest part of the coupling) can be made from a light, strong material, such as aluminum, since it is not exposed to contact loading. This makes the coupling suitable for high speed applications.The misalignment compensation stiffness and the rated torque can be varied by proportioning the laminated elements (their overall dimensions, thickness and number of rubber layers, erc.). The loads on the connected shafts are greatly reduced and are not dependent on the transmined torque since the shear stiffness of the laminate does not depend on the compression load. To derive an expression for efficiency of the Oldham coupling with laminated connections, let the shear stiffness of the connection between one hub and the intermediate member be denoted by ksh and the relative energy dissipation in the rubber for one cycle of shear deformation by Ψ. Then, maximum potential energy in the connection (at maximum shear) is equal toand energy dissipated per cycle of deformation isEach of the two connections experiences two deformation cycles per revolution; thus the total energy dissipated per revolution of the coupling isTotal energy transmitted through the coupling per revolution is equal towhere Pis tangential force reduced to the external diameterandis the transmitted torque. Efficiency of a coupling is therefore equal towhere β is the loss factor of th e rubber.For the experimentally tested coupling (= 0.12 m), the parameters are: a laminate with rubber layers 2 mm in thickness; ψ = 0.2;= 1.8 x 105 N/m;= 150 N-m;= 0.001 m; thus η = 1 - (0.2 x 1.8 x 105 x 10-6)/150π = 1 - 0.75 x 10-4 = 0.999925, or the losses at full torque are reduced 200 times as compared to the conventional coupling.Test results for the conventional and modified Oldham couplings having= 0.12 m have shown th at the maximum transmited torque was the same, but there was a 3.5 times reduction in the radial force transmitted to the shaft bearings with a modified coupling. Actually, the coupling showed the lowest radial force for a given misalignment compared with any commercially available compensating coupling, including couplings with rubber elements. In addition to this, the noise level at the coupling was reduced by 13 dBA to= 83 dBA. Using ultra thin-layered laminates for the same coupling would further increase its rating by at least one order of magnirude, and may even require a redesign of the shafts to accommodate such a high transmitted load in a very small coupling.U-joints transmit rotation between two shafts whose axes are intersecting but not coaxial (Fig. 3c). A u-joint also has an intermediate member ("spider" or "cross") with four protruding pins ("trunnions") whose intersecting axes are located in one plane at 90° to each other. As in th e O ldham coupling, two trunnionshaving the same axis aremovably engaged with journals machined in the hub ("yoke") mounted on one shaft, and the other two trunnions, with the yoke attached to the other connected shaft. However, while the motions between the intermediate member and the hubs in the Oldham coupling are translational, in the u-joint these motions are revolute. This design is conducive to using rolling friction bearings, but the small reciprocating travel regime under heavy loads requires derating of the bearings.A typical embodiment of th e u-joint with thin-layered rubber-metal bearings (Ref. 3) is illustrated in Figure 7 for a large-size joint. Figure 7 shows two basic units (out of four constituting the universal joint): yoke-trunnion-elastomeric bearing sleeve (parts 31,33 and 35 respectively) and yoke-trunnion-elastomeric bearing sleeve (parts 32, 34 and 35, respectively). Sleeves (35) comprise rubber-metal laminates (37) having sleeve-like rubber layers (38). Separating them and bonded to them are sleeve-like thin, reinforcing, intermediate metal layers (39) and inner (40) and outer (41) sleeve-like material layers bonded to the extreme inner and outer sleeve-like rubber layers. The inner and outer metal layers of the laminated bearing sleeve aremade thicker than the intermediate metal layers, since they determine the overall shape of elastomeric bearing sleeves.The inner surface of the inner layer (40) is made tapered and conforming with the tapered outer surfaces of trunnions 33 and 34. The outer surface of the outer layer (41) is made cylindrical and conforming with the internal cylindrical surface of th e bore in yoke 31. Each bearing sleeve (35) is kept in place by a cover (44) abutting the end surface (43) of the outer metal layer (41). The cover is fastened to the outer metal layer and to the yoke by bolts. A threaded hole is provided in the center of the cover.Before assembly, the wall thickness of the elastomeric bearing sleeve (a sum of total thickness of rubber layers, intermediate merallayers and inner and outer metal layers) is larger than th e annular space between the inside surface of the bore in the yoke (31) and the respective outside surface of the trunnion (33). The difference between the wall thickness of th e bearing sleeve and th e available annular space is equal to the specified preloading compression deformation of the elastomeric bearing sleeve. To perform assembly operation, the tapered bearing sleeve is inserted into the wider opening of the tapered annular space between the internal surface of the bore and the external surface of the trunnion and pressed into this space by a punch shaped to contact simultaneously both end surfaces. Wedge action of the tapered connection between the conforming inner surface of metal layer 40 and outer surface of trunnion33 results in expansion of metal layer 40, in compression (preloading) of rubber layers and in gradual full insertion of the bearing sleeve into the annular space between the yoke and trunnion. The simultaneous contact between the pressing punch and both end surfaces of inner metal layer 40 and outer metal layer 41 assures insertion of the bearing sleeve without inducing axial shear deformation inside the bearing sleeve, which can cause distortion or even damage of the bearing sleeve.To disassemble the connection, bolts attaching the cover to the yoke are removed, and then a bolt is threaded into a hold until contacting the end surface of the trunnion. The further threading of the bolt pushes the outside cover together with the outer metal layer of the bearing sleeve, to which the cover is attached by bolts. The initial movement causes shear deformation in the rubber layers until disassembly protrusions engage with the inner metal layer, thus resulting in a uniform extraction of the bearing sleeve.It is highly beneficial that u-joints with the rubber-metal laminated bearings do not need sealing devices and are not sensitive to environmental contamination (dirt, erc.).The efficiency analysis for such u-joints is very similar to the analysis for the modified Oldham coupling. The efficiency of the joint iswhereis the torsional stiffness of the connection between the intermediate member and one yoke. It can be compared with efficiency of a conventional u-joint whereis the effective diameter of the trunnion bearing, 2R is the distance between centers of the opposite trunnion bearings, and µ is the friction coefficient in the bearings.A comparison of Equations 7 and 14 with Equations 12 and 13, respectively, shows that while efficiencies of conventional Oldham couplings and u-joints for a given e, α are constant, efficiency of the modified designs using rubber-metal laminated connections increases with increasing load (when the energy losses are of the greatest importance). The losses in an elastic Oldham coupling and u-joint at the rated torque can be 1-2 decimal orders of magnitude lower than the losses for conventional units. Due to high allowable compression loads on the laminate (in this case, high radial loads), the elastic Oldham couplings and u-joints can be made smaller than the conventional units with sliding or rolling friction bearings for a given rated torque. The laminates are preloaded to eliminate backlash, to enhance uniformity of stress distribution along the load-transmitting areas of the connections, and to increase torsional stiffness. Since there is no acrual sliding between the contacting surfaces, the expensive surface preparation necessary in conventional Oldham couplings and u-joinrs (heat treatment, high-finish machining, erc.) is not required. The modified Oldham coupling in Figure 6 and the u-joint in Figure 7 can transmit very high rorques while effectively compensating large radial and angular misalignments, respectively, and having no backlash since their laminated flexible elements arepreloaded. However, for small-rated torques, there are very effective and inexpensive alternatives to these designs whose kinematics are similar. These alternatives are also backlash-free.One is a Kudriavetz coupling, shown in Figure 5. Another alternative is a modified spider or jaw coupling whose cross section by the mid-plane of the six-legged spider is shown in Figure 8 (Ref 4). In this design the elastomeric spider of the conventional jaw coupling shown in Figure 10a is replaced with a rigid spider (9, 11) carrying tubular sleeves or coil springs (10) supported by spider pins (11) and serving as flexible elements radially compressed between cams (6 and 7) protruding from the respective hubs. If the number of spider legs is four, at 900 to each other, then the hubs have relative angular mobiliry, and the coupling becomes a u-joint with angular mobiliry greater than 10°, but with much higher rated torque than an equivalent size Kudnavetz coupling.Purely misalignmenr compensating couplings described in this section have their torsional and compensating properties decoupled by introduction of the intermediate member. Popular bellows couplings have high torsional stiffness and much lower compensating stiffness, but their torsional and compensating properties are not decoupled, so they are representatives of the "combination purpose couplings" group, which will be discussed in detail in Part II of this article, which will appear next issue.1. Rivin, E.I.1999, Marcel Dekker, Inc., NY.2. "Torsionally Rigid Misalignment Compensating Coupling," U.S. Patent 5,595,540.3. "Universal Cardan Joint with Elastomeric Bearings,"U.S. Patent 6,926,611.4. "Spider Coupling," lJ.S. Patent 6,733,393.5. "Torsional Connection with ,Radially Spaced Multiple :Flexible Elements," U.S. Patent 5,630,758.6. Rivin, E.I. "Shaped Elastomeric Components for Vibration Control Devices,"1999, Vol. 33, No. 7, pp. 18-23.This article has been reproduced with the permission of Power Transmission Engineering.
Gear-couplings are the king of coupling types. They can do things that many other couplings cannot do, can only do with difficulty or with expensive modifications and de-rating. Gear couplings are more power intensive, offer more modifications, and a wider size, torque bore range than any other type, and can perform at extremely high speeds. Gear couplings have axial slide capability, low speed high torque capability, shifter capability and spindle capability not found in other couplings. They are easily modified for shear pin service, floating shaft type, vertical type, insulated type, limited end float, and can have a brake drum or disc added. While those latter items may be available on other couplings, it is usually easier and less costly to modify the gear coupling. With all these advantages the gear coupling is used on twice as many applications versus the nearest competitor type.
Gear couplings can also perform at extremely high rates of speed. As implied by the name, gear couplings use the meshing of gear teeth to transmit the torque and to provide for misalignment. External gear teeth are cut on the circumference of the hub. Both toothed hubs fit inside the ends of a tubular sleeve that has matching gear teeth cut around its interior circumference, with each tooth extending axially the full length of the sleeve. Hub and sleeve teeth mesh, so torque transfers from the driving hub’s teeth to the sleeve teeth and back to the driven hub’s teeth.
Gear couplings achieve their misalignment capability through backlash in the teeth, crowning on the tooth surfaces, and major diameter fit. Backlash is the looseness-of-fit that results from gear teeth being narrower than the gaps between the teeth. In addition to contributing to the misalignment capabilities, the backlash provides space for the lubricant. The loose fit provides misalignment capability by allowing the sleeve to shift off-axis without binding against the hub teeth. Some gear couplings have more backlash than others. Those with the least (roughly one-half of the backlash present in those with the most) are known as “minimum backlash” couplings. Some users prefer this type, most prefer normal backlash. Crowning, or curving the surface of the hub teeth, further enhances this capability. The crowning can include tip crowns, flank crowns, and chamfers on the sharp edges. This also helps improve tooth life by broadening the contact area along the “pitch line” (where the teeth mate and transfer torque), thereby reducing the pressure of torque forces. In addition, it prevents the sharp squared edges of the tooth from digging in and locking the coupling. Vari-Crown, which varies the curvature radius along the tooth flank, maintains greater contact area between teeth during misalignment compared with standard crowning, and reduces those stresses that cause wear. Note that crowning applies to hub teeth only; sleeve teeth are straight except for a chamfer on the minor diameter edge.
While the hub and sleeve teeth are cut to fit loosely side to side, they are cut to fit closely where the tip diameter of the hub teeth meet the root diameter of the gaps between the sleeve teeth. That is called a major diameter fit. When the coupling is not rotating, those two surfaces rest upon each other if it is a horizontal installation. Minor diameter fits (where the tips of the sleeve teeth meet the root diameter of the hub teeth) are purposely avoided, because a close fit here would preclude suitable misalignment capability and torque transmission capability.
It was noted earlier that gear couplings are power intensive. That means more torque transmitted per pound of coupling weight and per cubic inch of space consumed than other couplings. In many cases the gear coupling has more torque capability than the shaft can transmit. The resulting relatively small size of the gear coupling allows the addition of attachments without having the coupling grow to impracticable proportions. It also allows the OEM designer more latitude to locate the coupling in small, out-of-the-way places with confidence that it will be reliable. Gear couplings eventually wear, but rarely to a catastrophic failure. They can be sized to make sure that wear life is consistent with the rest of the machine design.
Coupling Configuration
Sleeve Alternatives
Gear coupling sleeves can be a single piece, termed a “continuous sleeve”, or can be split laterally (radially) into two half sleeves, one on each hub. The split version is termed a “flanged sleeve”, because each half has a flanged end, drilled for bolt holes, which allows them to be bolted together.
Because the continuous sleeve needs neither flanges nor bolts, it provides the advantage of making the coupling lighter and smaller in diameter than comparably rated flange types. With that comes lower inertia values, which helps lighten motor load during start-up. Bolt stress, which can be a weak point in some applications, is eliminated. The absence of bolts is an advantage in high-speed applications, because bolts add potential points of unbalance and bolted connections can be another point of non-concentricity.
When two halves of a flanged sleeve are bolted together, the bolting becomes an important part of the power transmission path. Best designs have the power transmitted across the face by friction, in which case the bolts simply provide enough clamping force to provide face friction. Other designs could allow the bolts to carry the load in shear, but those are in the minority. Both cases require a proper analysis of the multiple loads on the bolts. In addition the bolt bodies may provide the centering action to pilot the two halves of the coupling.
Bolts can either be exposed, or shrouded for safety reasons. However, with the advent of OSHA coupling-guard requirements, shrouding becomes unnecessary. The two types also have different windage loss and that affects high speed applications. Windage losses cause a heat generation inside the coupling guard. Note that flange bolts are specially made for their purpose, and should never be replaced with common hardware-store bolts. Flanged sleeve gear couplings built to American Gear Manufacturers Association (AGMA) dimensional standards will mate half-for-half with all other gear couplings made to those same standards.
While AGMA standards are U.S. based, many European manufacturers build to match the dimensions. However, matching dimensions include the interface only, such as outside flange diameter, number of boltholes, bolt hole size, bolt circle, and flange thickness. Although length-through-bore of the hub is often identical as well, torque and bore capability are likely to be different and should be compared carefully.
Flex Planes and Misalignment Capability
Planes of flexibility (“flex planes”) are those pivot points along the shaft-to-shaft connection where rigid components engage but can move independently of each other The standard gear coupling (two toothed hubs engaging opposite ends of the same rigid sleeve) has two flex planes, one at each hub-to-sleeve gear mesh. When both flex planes work together in series, flexing in the same direction, they give the gear coupling an angular misalignment capability of up to 1½° at each flex plane.
This standard configuration is called “full flex” or “double engagement” coupling.
The full-flex gear coupling, with two flex planes in series flexing in opposite directions, allows for parallel (radial) misalignment of 0.055 to 0.165 inches in standard models with short sleeves. The longer the sleeve (i.e. the greater the axial distance from one flex plane to the other), the greater the parallel misalignment. The greatest parallel capability results from floating shaft, spacer and spindle versions, described later, which greatly lengthen the distance between flex planes.
Gear couplings can be configured with only one flex plane, for applications where parallel misalignment capability is unwanted. In flanged type couplings, this is accomplished by using a single-piece flanged hub with no teeth, as the rigid half, bolted to a flexible half that uses a standard flanged sleeve with teeth and a standard hub with crowned teeth. These are called “flex-rigid”, “single-engagement” or sometimes “half couplings”. In continuous-sleeve couplings, a flex-rigid configuration is accomplished by mating the sleeve at the rigid end with a hub having straight teeth that fits into the sleeve like a spline shaft into a spline hub. While the full flex design is the most popular in gear couplings, flex rigid designs are often useful in systems with three bearings or floating shafts. Sometimes one flex-rigid coupling is used in series with another flex-rigid coupling at a distance to allow much more parallel misalignment.
While gear couplings will normally provide from ½° to 1½° of angular misalignment per flex half, they can be designed for up to 6° with reduced load capability and with accommodating grease seals.
Axial Displacement
Gear couplings naturally accommodate axial (in-out) shaft movement better than other competing designs, because their hub teeth easily slide along their sleeve teeth with no effect on coupling operation or torque load capability. Axial movement often results from thermal expansion/contraction of the shaft, as in hot applications, or a rotor seeking its magnetic centers (floating rotor). Thrust bearings can limit or prevent shaft movement at the coupling end, but if positioned at the far end of the machine, they can force the shaft movement back toward the coupling. The amount of axial displacement the gear coupling can handle depends primarily on the length of the sleeve, and specials are available for long sliding application.
The Gear Coupling Tooth
The gear coupling tooth has evolved over many years. The first gear couplings had straight teeth, and depended purely on backlash to achieve misalignment. Later improvements included tooth crowning that increased misalignment capability and coupling life. The original tooth form followed the spur gear form with modification. Various pressure angles were used that walked the line between life and strength. The 40° pressure angle tooth was chosen for strength. It proved to have problems with wear life and with reactionary loading on the machinery. Eventually the 20° pressure angle tooth became the standard, and it still is the standard. Some 25° teeth are used to achieve added strength for special designs. The additional strength of today’s materials alleviates the need for 40° teeth and still provides low sliding friction.
The gear coupling tooth, like the spline tooth, is not a full height tooth. Where the spline is 50% height, the gear coupling tooth is about 80%. Gear coupling teeth do not need full height because the torque load is carried at the pitch line of the tooth and many teeth are in contact with each other in the hub and the sleeve to carry the load. The number of teeth in contact is a function of the true form of the teeth. If all teeth in the hub and sleeve are identical the maximum number will be in contact. As the teeth wear into place the more teeth come into contact. Therefore initial tooth wear makes the coupling stronger, but can increase the friction loading too.
The strength of the gear tooth is the subject of many questions in determining the amount of load to be carried. The tooth is the strongest of all the elements of a gear coupling. The tooth strength is calculated as a bending moment at the root of the tooth, the shear strength at the pitch line, and the Hertzian loading at the contact surface. All of these forces act concurrently.
The most likely failure mode of a gear coupling tooth is that which comes from wear rather than any other factor. As the teeth wear, they move from being the strongest element to being the weakest element.
Severe misalignment that causes a lock up of the teeth will also result in premature failure. Most other loading on the coupling will not result in failed teeth.
Lubricant must always be available in the tooth mesh. The lack of lubricant will, of course, cause the coupling to fail almost instantly. The gear coupling is fitted together so as to prevent the lubricant from leaking. Most gear couplings are lubricated with grease. The sleeve to hub interface at the boundaries will need elastomer O-rings, gaskets, or labyrinths to prevent grease leakage. (Note that O-ring material might limit the coupling’s ambient temperature capability.) When oil lubrication is used, it is usually a continuous flow through the tooth mesh, but can be a batch lube in some applications. Oil lubrication is a special case.
Misalignment may allow grease to leak out the seal surface, or some modifications may need a wiper seal rather than an O-ring. One type of flange coupling uses a high misalignment seal with more flex than the regular seal. The seals can be held in place by several means. The Oring is the simplest; it fits into a groove in the sleeve.
The continuous sleeve coupling seal is held in place by a spiral ring. The seal has stiffeners molded into the inside face. It is a U or C shape that stays closed under load. It also provides the movement limit for the coupling and is actually rated to withstand an axial force.
Sometimes the seal holder is bolted to the coupling sleeve. This is always the case on couplings larger than size 9. It makes the assembly of the coupling to the shaft easier, and makes replacement of seals easier. The couplings with bolt on seal carriers are designated heavy duty (HD). Flange series couplings size 7 through 9 can be either the “HD” version or the plain version.
Remember that the coupling grease is not ordinary grease but is specially formulated so the oils do not separate from the soaps. The result is that the lubricant is contained within the needed space and sludge is not allowed to accumulate. Oil and soaps separate in ordinary lubricants because of centrifugal forces on the heavier particles. Use only coupling grease for best results.
Variations to Gear Couplings
1. Fill the Space between Shafts
Couplings often must fill a space between shafts as one of their primary attributes. It would seem a simple enough task, but not all couplings offer flexibility doing that job. This is another reason why the gear coupling is very popular.
2. “BSE” Dimension
The distance between shaft ends (BSE) will vary with different machine systems to accommodate design standards, product line alternatives,different motor frames and maintenance needs. The “BSE” dimension is important for all couplings. Gear couplings have the advantage of allowing a variable “BSE”. That variation can be achieved by machining the hub face or can be achieved by reversing one or both of the hubs. An infinite number of possibilities can be obtained from catalog minimum to catalog maximum. Note this gap (BSE) does not always affect the distance between flex planes unless the hubs are reversed. A combination of facing and reversing is possible too. All couplings have a certain “BSE” dimension variability, but few are able to tolerate as great a variance as gear couplings can.
3. Spacer Couplings
Spacer couplings consist of two flexible hub and sleeve assemblies i.e. a half coupling on both the driving and driven shafts. These are connected by a tubular center section of various lengths that can easily be removed to allow space for removal of the hub or other components on one side of the system without disturbing the hub or component mountings on the other side. The tubular center section can have flanged ends for bolting to hub flanged sleeves, or toothed ends that mate with hubs using continuous sleeves. Spacers are built to the standards of the rotating machinery builders. Pumps have several standard spacers such as 3½ inches, 7 inches and others. Compressors could have a different set of standard spacers. Spacers can serve to separate the flex planes and can be part of the torsional tuning of a coupling.
They have practical limits on length in regard to cost, weight and critical speed. The flanged hollow tube is machined to varying tolerances depending on speed and balance. As the tube gets longer, deflection of the unsupported center section forces the cylinder walls to be made thicker. As the walls get thicker the cost grows more and so does the weight. The weight then reduces the critical speed. That is a cross combination of events that eventually makes the spacer a poor choice. When the spacer becomes impractical, the next step is to use a floating shaft coupling to achieve the necessary spacing.
4. Floating Shafts
Floating shaft couplings consist of flex rigid couplings on both driving and driven shafts connected by a piece of solid shafting between the couplings. Usually the coupling hubs on the equipment ends are rigid while the two center hubs connected to the floating shaft are flexible.
While these two can be used to provide service spacing, the primary reason for a long floating shaft is to allow for greater radial misalignment between shafts. The secondary reason is to reach a long distance between the driver and the rotating equipment. Weight and critical speed are important considerations for floating shafts. They are found on bridge cranes and steel rolling mills.
The couplings and center shaft are designed as a unit to suit their specific application. The parameters include the usual torque and bore, but must include length and speed because, as in any spacer, critical speed and deflection are interrelated. These issues may require a larger diameter center shaft to reduce deflection. In that case the rigid hubs are on the floating shaft, taking advantage of the rigid hub’s greater bore capability, to accommodate the oversized center shaft.
Otherwise, the center shaft may need to be necked down (reduced) to fit a flex coupling hub. The rigid hub could also be placed on the outside to fit a shaft that is made larger than is necessary to carry torque, as would be the case with bending problems. The center shaft would be smaller to carry torque only and thus fit the flex hub. When the flex hub is on the center shaft it is called a marine style coupling. When the flex hub is on the equipment shaft it is called a reduced moment style. The floating shaft designer must always balance the effects of weight (which causes deflection) and diameter (which determines torque capacity and resists deflection but increases weight and cost).
5. Limited End Float Couplings
Gear couplings can be modified to allow shaft growth in the axial direction or to limit movement in the axial direction. Limiting the movement calls for a plate and possibly a button to be inserted between the coupling halves. As the shaft tries to move in the axial direction, it is stopped after moving a predetermined distance.
These are called limited end float couplings. They are necessary with sleeve bearing motors, a design commonly found in larger sizes of 200 horsepower or more. The same plates and
buttons are used on vertical couplings as explained below.
6. Sliders
In addition to thermal growth, gear couplings can be arranged to slide great distances. Extra long sleeves enable the hub to slide 10 inches or more, either at rest or while in operation, to serve applications where equipment must be temporarily removed from the system and the coupling is the most suitable point of movement. Refiners, Jordan machines, and roll winders found in paper mills utilize this sliding capability. The Jordan coupling is a special variation that can move its hub relative to its shaft with a clamping mechanism.
Two dimensions are important when considering the slider coupling. One is the minimum BSE and the other is the total amount of slide. Those are in addition to the usual gear coupling requirements. If a Jordan is involved the amount of clamping movement is necessary to know.
7. Spindle Couplings
Spindle couplings are special floating shaft gear couplings that are used in rolling mills. They are designed for high torque, shock loads, and high angular misalignment. They have replaceable wear parts and customized accessories. Spindle couplings also have some slide capability to adjust to the installation or operational requirements of rolling mills. The spindle coupling uses the continuous sleeve principal to reduce the overall outer diameter.
8. Insulating Couplings
For more information, please visit Half Gear Couplings Manufacturer in China.
Gear couplings can also be equipped to block galvanic (electrical) currents, which can cause pitting and corrosion at the close running fits of gear teeth and other mechanical components. One half of the coupling is electrically insulated from the other half by adding insulating plates and bushings. It is not necessarily a high voltage insulator as found in wiring systems.
Modification for Special Needs
Vertical Couplings
Both continuous sleeve and flanged sleeve gear couplings can operate in the vertical position with the addition of a vertical kit, which is a limited end float plate or plate-and-button that supports the loose weights above the coupling. The button is rounded to allow the load to transfer under misalignment. Therefore, load is transferred to the lower shaft and ultimately supported by a thrust bearing in that equipment. Since a gear coupling is normally a shrink or interference fit, the upper hub is fixed to the shaft as is the lower one. In a vertical-floating shaft coupling, where both outer hubs are rigid and inner hubs are flexible, the entire center rotor is loose weight that needs to be supported by a plate in the upper coupling and a plate and button in the lower coupling.
A special vertical coupling is the rigid adjustable pump coupling. This coupling is designed for use with vertical circulating pumps that need clearance adjustments in the impeller. As indicated in the coupling name, it is a rigid coupling with no teeth in either half, with no provision for misalignment. The entire rotor weight is hung from the motor or driver bearings. Special designs of hanging load gear couplings can provide misalignment capability.
Other Gear Coupling Special Configurations
Gear couplings can be configured to do special jobs. Possibilities include the shear pin, cutout shifter, and brake coupling. Shear pin couplings disconnect when subjected to predetermined torque overloads thus protecting other equipment. Torque overloads could come from stalls or cyclic overloads.
Cutout couplings allow the driving/driven halves to be disengaged without disassembling the coupling. They use a special sleeve in which the teeth are interrupted at one end by a flat-bottomed annular groove. When the sleeve is shifted axially to align the groove with the teeth of one hub that hub spins freely, disengaged from the torque transmission path. A cutout pin (set screw) holds the sleeve in engaged or disengaged positions. They can be used on a dual drive machine to isolate the unused driver, or for a turning gear that rotates heavy equipment when it is off line, and helps prevent a permanent set in the shaft. Automatic cutout is available for temporary disconnect “on the fly” to allow adjustment of relative position between driving/driven halves.
Brake Drums and Brake Discs
Gear couplings are easily modified for the attachment of a brake, which saves system space by eliminating a separate brake. In other situations putting the brake at the coupling prevents the high cyclic torque from reaching low torque shafts. Brake wheel couplings are often attached near the gearbox shaft since high gear inertia is in the box. The brake drum or disk is a piece of metal, machined to standard brake sizes and clamped between the coupling’s bolted flanged sleeves, requiring longer bolts. The coupling manufacturer does not include the brake and actuator.
Whenever a brake is installed in the system, it flags the need to check the stopping torque requirements. Stopping torque, like starting torque, depends on the amount of time that is available to stop or start. See the section on torque for a torque formula.
Moderate and High Speed Applications
As noted earlier, gear couplings are capable of very high speeds and high torque together. The limits have always been the need for lubrication of the mating gear surfaces and the need for balance. While high speeds increase the wear rate and can be the cause of high stresses within the coupling, the bigger issue is balance. Couplings operating at high RPM or high rim speed will cause vibration problems if they are not in balance.
Balance
A full discussion of balance will be found in another section of this handbook so only a few issues that relate specifically to gear couplings will be referenced here. Balance concerns itself with how the weight of the rotating mass or inertia is positioned or displaced relative to the center of rotation. If that weight is perfectly distributed around the center of rotation, the coupling is in balance. Since nothing is perfect in couplings, there is always a potential unbalance.
Coupling balance is achieved through design, manufacturing and remedial balancing machines. Off center bores, out of round circumferences, non-parallel sides, or even loose fits lead to mass displacement. In castings some of the potential unbalance could come from voids or air space internal to the casting. When a coupling consists of an assembly, the component design and the assembly process can result in an unbalance condition.
If the hub OD is not perfectly concentric with the hub bore the center of mass and center of rotation will be different. This means the gear teeth must be carefully cut with a pitch diameter concentric with the bore. That is controlled by the arbor or mandrel used on the hobbing machine and the concentricity of the pilot bore. The hub face must be perpendicular to the bore or to the hub OD. If it is not it becomes a trapezoid. Trapezoidal hubs have poor weight distribution and therefore unbalance.
Sleeves must likewise be concentric with the hub bore at the pitch diameter, the OD and at the pilot fits if any exist. Flanged sleeves must have a concentric bolt circle as well as a proper hole size and location. Flange-to-flange alignment before bolting will have a big effect on the balance of the assembled coupling.
Once the equipment is designed and the tolerances are established, it is possible to calculate the mass displacement of each component. The mass displacement of each component is added algebraically by a method that is called the square root of the sum of the squares. The total mass displacement can then be called the potential unbalance of the coupling. That total unbalance of the coupling could then be compared to recognized standards to see if it is acceptable. Refer to AGMA standard 9000-C90 for more on this subject.
Component & Assembly Balancing
It is unlikely that calculation of the mass displacement would be sufficient to satisfy a high-speed specification. That leads to the next process. Each component or piece of the coupling could be subjected to a balancing procedure on a balancing machine. Single-plane or two-plane balancing is also a consideration. If the coupling’s width-to-diameter ratio is 1:1, or greater in diameter, single-plane balancing is sufficient. If width (axial dimension) is greater, two-plane balancing is needed. (See chapter on balancing for more information.) Machine balancing results in adding or subtracting weight from the piece to counter the unbalanced weight and lessen the unbalance. The remaining unbalance of the part while on the balance machine is called the residual unbalance. The coupling can be assembled after component balancing and left at that potential unbalance. The total unbalance of the assembly at that point would depend on the distribution of the individual high points within the assembly. The worst case would be to end up with all heavy points in one quadrant.
For further reduction of unbalance, the coupling could be assembled and returned to the balance machine, again with corrective adding or subtracting of weight. The result would be called an assembly balanced coupling. With these, all individual pieces are match marked before the coupling is disassembled so they can be reassembled exactly the same way on the users equipment.
A gear coupling is not easily assembly balanced. First the coupling must be assembled with tight fits between the hub teeth and sleeve teeth so that loose parts will not fool the balancing machine. After the coupling is balanced, the teeth are relieved so the coupling can be installed in a system with possible misalignment.
The final balance, after the coupling is removed from the machine, will be affected by the concentricity run-out and bearing surfaces of the mandrels, arbors and mounting devices of the balance machine. The coupling, unlike machinery rotors, is not balanced on its own shaft. A half coupling might be balanced on the equipment rotor, but then the two half couplings from the two different rotors must be joined together. Why should one worry so much about balance? The balance is critical on high-speed applications to prevent destructive vibration. Different applications have different definitions of high or low speed, but generally for couplings, anything greater than 3000 RPM is high speed.
High Speed Gear Couplings
Most high-speed gear couplings are spacer types, that would acknowledge the need for maintenance on the connected equipment. Two important attributes of high-speed couplings are lightweight and low inertia. If the coupling is to be accelerated from zero to 10,000 or 15,000 rpm the torque required to reach those speeds quickly is substantial if inertia is allowed to be too high. High-speed machines are sensitive to overhung weights too. Everything is built for speed, which means small, light and precise.
We mentioned that high-speed couplings are precision made to tight tolerances. They are also made with ground bores, body fitted bolts and reamed holes in the flanges. Since the couplings are highly stressed the materials are magnetic particle inspected to make sure of the integrity of the piece. The material may be standard 4140 steel, but it often has papers to prove its strength and chemical composition. Hubs are attached to the shaft by hydraulic fits on a taper in the really high-speed units. That eliminates keys and keyways that could affect the balance. Other methods might include an integral flange on the rotor that bolts up to a marine style spacer coupling.
Sometimes the need for maintainability or rigidity forces the coupling to be a marine type of spacer coupling. Marine style refers to the tooth location not the application. In a marine type unit the gear teeth are on the spacer section not the hub section. This increases the overhung moment so a trade off is being made.
Materials for High Speed Units
While balance is most important to high speed gear couplings, it must also be noted that high speed has the potential for high wear of the teeth. For that reason extreme high-speed units utilize hardened teeth to extend the coupling life. However, this requires material that will be compatible with induction hardening, carbonization, or nitride hardening. The hardened tooth must retain its strength to carry the torque. Iron carbides and carbon or other nitrides provide the surface hardness. While AISI 1045 carbon steel is the most popular for gear couplings, AISI 4140 high alloy steel is used on high-speed units. Coupling materials and hardening will be discussed more thoroughly a bit later in this chapter.
Lubrication of High Speed Units
High-speed couplings are lubricated with oil rather than grease. The oil, which is circulated through filters and coolers, is sprayed into the sleeve on one side of the teeth and drained from the sleeve on the other side of the teeth. Circulating oil has the advantage of constant renewal, but even with the circulation it is necessary to prevent sludge build-up in the coupling. Sludge will prevent oil from reaching the necessary surfaces that need lubrication. Anti-sludge features in a coupling prevent the build up by putting drains and dams in the passages.
Grease-lubricated high-speed couplings are limited in their application possibilities. Even though grease labeled as “coupling type”, will resist separation of soaps and oils, it is not enough for the true high-speed application. Another problem with grease is temperature build up. Oil that is circulating is also cooled. Grease that is static would heat up from the rubbing friction at the high speeds.
Mounting the Gear Coupling in a Shaft System
Metric Versus English Units
The metric and English systems of size and tolerance were developed without a desire to interchange with each other. Simple conversions are not satisfactory because different bore dimensions are used, along with different tolerances and different formulas defining tight and loose fits. Metric bores are defined in ISO standards while English bores are defined in AGMA and ANSI standards. Those standards are also summarized in coupling manufacturers’ catalogs.
Hub to Shaft Interface
There are several methods to fasten the hub to the shaft. In all cases the objective is to have a joint that facilitates the transfer of torque from shaft to hub, is easy to install or remove, and does not make the alignment more difficult.
Clearance or Loose Fits
Loose fits are easiest to manufacture and to install. But, loose fits are not the first choice for gear couplings, except low torque applications or some nylon sleeve applications. The loose fit does not provide sufficient restraint for the forces found in gear couplings, so interference fits are used. Loose or clearance fit hubs use a keyway and a loose fit key to transmit torque, with a setscrew to hold the hub tight to the shaft and key to prevent wobble and fretting wear. The key and setscrew also help if some cyclic loading is present. Since that is the only means of transferring the torque, the length through bore for clearance fits is longer than that of other fits. The preferred length is 1.25 to 1.5 times the diameter of the bore. Keyways on clearance fit bores are a square cross section. Key sizes are matched to shaft sizes to ensure sufficient surface is available for the torque transfer. The key also has a loose fit within the keyway.
Interference (or Shrink) Fits
The interference or shrink fit is the hub mounting choice in the majority of gear couplings. It utilizes a hub bore diameter that is slightly smaller than the shaft diameter under all tolerance combinations. There are many combinations to the amount of interference, but a popular number is .0005 inches per inch of shaft diameter.
The interference fit installation is accomplished by heating the hub to the point where it expands enough to fit over the shaft. Heating can be done in ovens, oil baths or by induction. The induction method is popular as a hub removal method too. A temperature of 300° F to 350° F is sufficient to do the job. Excess heat may change the metallurgical properties of the hub, and excess shrink or interference may split the hub.
The interference fit hub has a straight bore with a keyway so the friction between shaft and hub and the key are not used to transmit torque. The key is the main means of torque transfer, and may be either a loose or interference fit. Again a square key is used, and most times a radius is included in the keyway and on the key to reduce stress concentrations.
Reduced keys, known as shallow, half height or rectangular keys can be used to allow greater shaft diameters within the hub limits. All are wider than they are tall. Metric keys are of the reduced or rectangular key variety. When using reduced keys, torque capability must be carefully assessed. On large couplings and shafts two half-height keys are sometimes used to strengthen torque transmission. Interference fit hubs use a 1 to 1 ratio between the hub contact length and the shaft diameter. That ratio may vary in applications prone to high cyclic loads or sudden peaks in the torque from transitory conditions.
Tapers and Mill Motor Bores
Two types of taper bores are also common on gear couplings. One type is the tapered and keyed mill motor bore. This hub fits a standard mill motor shaft that has a like taper. As the hub slides up the shaft it forms a tight fit with the shaft. A shaft end nut is used to hold it in place. This method achieves good torque transfer, with a tight fit. It is an easy assembly or disassembly feature. Tapered shafts of this type can be used with machinery other than mill motors.
Another type of taper bore is the shallow taper hydraulic type. In this type there is no key. The hub is expanded by hydraulic pressure and pushed up the shaft to a predetermined point. When the pressure is removed, the hub shrinks to the shaft. The shaft can have a nut or plate attached to the end for retention of the hub. Removal also is accomplished by hydraulic pressure. The hubs have oil grooves machined in the bore to facilitate the application of oil pressure. Taper bore shaft hub combinations require a very complete match between the hub and shaft. The contact area of the hub bore to a gage acting as a shaft is measured in the manufacturing of the hubs to make sure a proper fit will be obtained when the hub is mounted on the shaft. Standards have been established to use as a guide for percentage of contact.
Shrink fit and hydraulic fit hubs are the choice for the heavy torque applications. One of the weak points in the power transmission train is the interface between hub and shaft. It is also the place where cyclic loads and peak loads can cause slippage or fretting damage. The tightness of the fit contributes to a more secure connection for torque transmission.
Sleeve to Sleeve Interface
Interchangeability
Gear couplings from size 1 to size 9 will match up half for half with other flange type gear couplings made to AGMA standard dimensions. However, while the dimensional standard ensures compatibility of the face to face match between sleeve flanges, it does not assure matching torque capability or bore. This should always be checked. When a labyrinth seal coupling is matched to an O-ring-sealed coupling, the bore capability and torque may both be different despite the fact that their flanges match and bolt together.
Bolts and Torque
Flange bolting is important to coupling reliability, as bolting can be a potential weak point. Most designs use a friction basis for transferring the load across the face to face match of the two coupling halves. Bolts are designed for tension loading, and primarily serve the purpose of clamping the two flanges together to enable face friction to transfer torque. In fact, the maximum outer diameter of the flange on flanged sleeve couplings is partially determined by the needs of space for bolts and surface for friction. Although friction is the main means of torque transfer, if the coupling is overloaded to the point of overcoming friction, it becomes a shear load on the bolts before becoming a coupling failure. Since the bolts are loaded by several types of forces one must be sure the bolt threads are not in the shear plane between the flanges.
Other specifications could allow body fit bolts to carry the load in shear, although from an engineering standpoint the concept of carrying load on bolts in shear is not favored. The body fit bolt has a tight fit to the bolt holes that keep the two halves concentric. To carry that method to the extreme one would drill and ream the boltholes at assembly and then match mark the two coupling halves.
Bolting will also affect and be affected by balance requirements. Balanced couplings may require weigh-balanced bolts. In addition, bolting can provide a means of piloting the two half couplings. To use the bolts as a pilot, the boltholes must be drilled to a close tolerance or line reamed at assembly.
Remember that the continuous sleeve coupling is not affected by any of the issues associated with bolting. The continuous sleeve coupling provides a bolt-free method of transferring torque through a continuous cylinder of metal with the additional advantage of a smaller outside diameter.
Alignment
Although alignment is covered in another section of this handbook, the gear coupling has some special alignment considerations that should be noted here. As mentioned in the bolting section, it is necessary for the two halves of flanged type to have some sort of piloting for best alignment practice. That can be achieved by piloted bolts or better achieved by pilot rings or rabbet fits. The alignment needs depend on the connected machinery and the speed of operation. High-speed operation always needs close alignment. Always refer to the machinery specification’s first, not the coupling specifications, when setting the alignment parameters. Since continuous sleeve couplings do not have bolts, alignment is done hub face to hub face.
Indexing Couplings
Once in a while there is a call for an “indexing” coupling. That type of coupling aligns two shafts in a rotational circular position that is the same each time. To accomplish that, the hub keyway is cut to be in line with a tooth or a space. The second hub is cut the same way. If it is a continuous-sleeve coupling, the continuous sleeve might be marked to identify the same tooth or space on both ends of the sleeve. The procedure on flanged sleeve couplings is more complex. In addition to the keyway meeting the hub tooth or space, a bolthole on the flange also must be lined up with a tooth or space. The mating flange must be drilled the same way so that when it is assembled the unit will be aligned or indexed. Of course, to make this work, the shaft keyway must also be aligned with a significant part of the machinery. Indexing is done to a specified tolerance on the location of that alignment.
Additional indexing is accomplished with floating shaft couplings when the coupling on each end of the unit has a different number of teeth. The indexing can then have a number of set points equal to the product of the two numbers of teeth.
Selecting Gear Couplings
Gear coupling selection parameters include two very important items and many more secondary items. The most important items are the bore and torque capabilities, in that order. Bore refers to the nominal shaft size where the coupling will be used. Torque in this case refers to the normal operating torque that the coupling must transmit. The secondary items can include a whole host of things like speed, misalignment, weight, spacer length, inertia, etc.
Bore and Torque: First Pass Selection
The gear coupling size in most cases will be determined by the nominal shaft size. The nominal shaft size is a mixed number of units and fractions that represent a specific diameter of shafting. The actual shaft is the decimal equivalent of that number plus .000 minus .0005 or .001 inches. Nominal sizes are not just any number, but are chosen from a list of preferred numbers. Preferred numbers can also be metric in origin. This is part of our discussion is limited to inch numbers. That nominal number would also be the coupling bore with the actual size as a function of the class of fit.
Gear couplings typically use interference fits, so the coupling bore usually is smaller than the shaft size. The amount of interference varies by the designer’s requirements, but a value of .0005 inches per inch of bore diameter is often used. For details on shaft size for interference or clearance fits refer to AGMA 9002-A86. That is an inch series document; if metric is of interest, refer to “Preferred Metric Limits and Fits” ANSI B4.2 1978 reaffirmed 1984.
If the nominal shaft size is equal to or less than the published coupling bore capability, the gear coupling is usually okay for the service. “If it fits it is okay” is the gear coupling motto. For example smooth running, 1800 RPM, machinery without high starting torque or stopping requirements can use bore size to select the coupling.
The second step in gear coupling selection is to check the torque requirement of the application vs. the torque rating of the coupling. Normal operating torque is used unless a peak or cyclic torque is known. If the application calls for peak torque or cyclic torque, more care must be taken. The application description is also important to see if further investigation is needed. At this point, the nominal torque requirements of the system times an application factor that could be used to select the coupling.
The normal or continuous operating torque of the system is that torque value that is required for design point operation on a continuous basis. Coupling ratings are sometimes listed as HP per 100 RPM, but torque and horsepower can be derived from one another if the speed in RPM is also known.
Service Factors
Service factors (sometimes called Application Factors) are applied to the normal torque to account for variations that are typical of specific applications. They are based on a combination of empirical data and experience, and provide a quick reference to guide selection of a coupling for torque, and perhaps life, without going into the details of the application. Service Factor tables usually are provided in coupling catalogs, and will be different for different types of couplings. Another source of Service Factors (application factors) is AGMA standard 922-A96. Factors of Safety and Service Factors should not be confused with each other or interchanged. The former is for design work and the latter is for applications work.
Stretching the Bore
This subject is included to highlight the fact that it is not recommended. Never exceed the bore associated with the coupling size and the key type. Square keys have a maximum bore, rectangular keys have another and metric has its own. Do not mix them. When extra shrink is requested, or an over bore is requested for low torque applications, engineering should review the application. The gear coupling is the most power intensive coupling as it is designed, but the shaft to hub connection can be the weak point of the coupling. Stretching the limits can result in machinery failure as well as coupling failure.
Other Considerations
Bigger Than Size 7
There are several magic numbers when it comes to gear couplings. One is the size cut-off between big and small. That number is arbitrarily set at 7, but could be 9. The AGMA dimensional interchange goes to size 9 for gear couplings, but once the size rises to 7 and above, the number of applications become very limited. A size 7 gear coupling has a bore capability of nine or more inches (depends on key size too) and a torque of one million inch pounds. That torque corresponds to 16,000 horsepower at 1,000 RPM. Not many applications go that far and when they do the situation is special or low speed. Generally, big gear couplings are used on very low RPM and very high torque applications such as those found in the steel and aluminum rolling mills, crushers, rubber processors or mine concentrators.
For an idea of how big the gear couplings can be made, the catalogs will show gear couplings up to size 30. Loosely, the number equates to half the pitch diameter for flanged sleeve couplings. That means the coupling overall diameter will exceed sixty inches. Continuous sleeve coupling numbers are roughly equal to the maximum bore.
When the coupling size reaches the double-digit numbers, the torque rating is nebulous. Couplings are often re-rated based on improved materials, heat treating, and hardening. In reality the user and designer are trading wear life for torque rating. The torque rating can be used as a peak load or cyclic high and not always as the normal operating torque.
Not many modifications are made to these large coupling sizes. At this size, added functions are too expensive to build into the coupling and may be available as a separate device. Torque limiters fall in the latter category as they replace shear pins. The weight of the coupling and the other pieces of the rotating system also may preclude the desire for modifications. We should point out that large coupling bores are not always the ordinary bore and keyway because they may have special shapes and non-standard dimensions.
Speed
Catalog ratings are often accompanied by speed limits in RPM. It is possible to increase the RPM limit by balancing the coupling to minimize vibration. Balancing combined with special manufacturing tolerances can increase the speed even more. However, a perfectly balanced coupling will eventually have a speed limit set by stress, friction between the teeth, and lubricant breakdown.
Misalignment
All couplings have a misalignment limit. The standard gear coupling is capable of 1½° angular misalignment per mesh. Specially designed gear couplings can push that limit to 6° or more, per mesh. However, high misalignment limits can reduce the torque capability of the coupling.
Misalignment accelerates tooth wear, because it causes the hub and sleeve to rub harder against each other. Sometimes high misalignment capability is sought for and limited to non-operational conditions, such as moving a shaft aside for maintenance.
Modifications used to achieve high misalignment capability in gear couplings include increases in backlash (tooth gap), additional crowning, 25° or more tooth pressure angles, hardened wear surfaces, modified grease seals, increased clearance between sleeve and hub (makes the teeth look taller), and a torque de-rating. High misalignment couplings may also have modifications to make coupling maintenance easier or less expensive such as replaceable wear surfaces.
Materials of Construction
Gear couplings are typically made of two common steels, AISI 1045 carbon steel, and AISI 4140-alloy steel. Alloy steel means elements other than carbon have been added to give additional properties to the steel.
Standard gear couplings use AISI 1045 steel. It can be bar stock or forging depending on the size and the component. Couplings needing higher strength or hardness for greater wear resistance are made from AISI 4140 which also can be bar stock or forging.
Gear couplings can be specified in 303 SS, but that is expensive and usually done only when required for the food processing or the pulp and paper industry.
Steel can be treated in many ways to improve hardness and strength. Hardness is the key to improving wear resistance for longer life under increased friction from high speed or misalignment, because gear couplings typically wear out under load rather than break. Strength provides resistance to the impact and cyclic loads.
The terms heat treatment, hardening, annealing, quenching and tempering are used in conjunction with the materials. Each of these terms represents a process that conditions the steel. Heat-treating is the general description that includes variations of all the others. Heat-treating does not have to mean hardening of the steel although it is usually taken in that context. Hardening of steel can mean in-depth hardened or surface hardened, which is also called casehardening. Hardness is measured in Brinnell units or Rockwell units, abbreviated as Bhn or Rc. The Rockwell Rc method of measurement is more popular on hardened surfaces of gear couplings while Bhn is used for overall hardness of a batch of steel.
For AISI 1045 steel, expected properties of strength for gear couplings would require a range of 190-260 Bhn. For AISI 4140 the range would extend up to 300 Bhn in the higher strength versions of the steel. The basic process in simple terms is that the steel is heated to a critical temperature held for a period of time and then rapidly cooled. After the rapid cooling the steel has a very hard structure that may need further tempering or annealing to trade hardness for strength. Rapid cooling is called quenching. Tempering or annealing is heating to a temperature and then cooling at a predetermined rate that is slower than a quench. The intent of these processes is to obtain a strong hard material that is ductile and tough.
For wear resistance we want to increase the surface hardness to 50 Rc or better. That requires an additional process known as hardening, case hardening, or nitriding. The process is to load the surface with iron carbides by exposure to carbon and heat or carbon nitrides and other nitrides by exposure to nitrogen and heat. The heat is provided by a heat treating furnace and the other elements are provided by the atmosphere in the case of nitriding or by packing the piece in carbon in the case of carburizing. The base steel has to be suitable for the process. In the case of nitriding the end product retains the original dimensions, but in the case of carburizing the end product grows and needs to be ground if the original dimensions are to be held. There are many methods, beyond these mentioned, which can harden steel surfaces. It is a complex subject. The process of hardening the surface of gear coupling teeth can extend the useful life of gear couplings.
Gear Coupling Applications
Reduced Moment, Three Bearing and Four Bearing Systems
The weight of the coupling and any reactionary forces all act at the center of the flex plane and cause a bending moment on the equipment shaft. When the coupling is placed close to a support bearing, the close support reduces that bending moment arm and the coupling can be called a “reduced moment” coupling. Reduced moments mean smaller loads and less wear on the equipment bearings. Placing the flex point close to a bearing also helps keep the system stable. Increasing the distance between flex point and bearing invites vibration, or wobble. For the most part, a three-bearing system has one bearing in the driven equipment and two bearings in the driver. The one-bearing side of the equipment is given a rigid half coupling without a flex plane. The two bearing side of the equipment, which is more stable, is given a flexible half coupling. With only one flex plane, this type of system can only have angular misalignment. Three bearing systems are commonly found in motor generator sets, and a long-shaft situation such as bridge crane traction drives.
The more common system is the four-bearing system with two bearings each in the driving and driven equipment. The system is more expensive and usually needs two flex planes because two bearings on each shaft make shaft locations rigid, usually in parallel misalignment.
Standard Couplings vs. Spacers
The simplest application for a coupling is a pump, compressor or centrifuge or the input side of a gearbox. These usually involve an electric motor drive mounted on the same base plate as the driven equipment. The coupling connects the two shafts and the most complicated issue is usually the BSE dimension. As the gear coupling has some range in BSE, the equipment designer can use a common size base plate for many different models of his equipment. The torque requirement of this type of rotating equipment is usually a smooth curve from zero to full speed and does not have any cyclic content. The coupling can be selected by torque and bore with a minimum service factor.
When the designer wants to make his equipment easier and cheaper to maintain, a spacer is installed between the two flex halves of the coupling. When the designer needs to span a long gap between driving and driven equipment (as when reaching up to a big-diameter roll, removing a large piece of equipment from an on-line position, or extending through a wall or bulkhead) a floating shaft is needed. This arrangement is often used with pinion stands, where the output is a double shaft that drives a meshing pair of rolls or mixers that are part of a large machine, such as a rolling mill.
Separating the Driver & Driven
Rotating equipment such as fans, pumps and compressors can have two separate drivers on the same piece of equipment. The drivers might be an electric motor for start-up and a steam turbine for running. That occurs on co-generation applications where steam is available and the operator wants to conserve electricity or use the electricity for other purposes.
Sometimes the equipment has an electric motor for normal purposes and some other device like an internal combustion engine for emergency operation. Other times the equipment sits idle but the driver runs. While these sound like applications for clutches, they also can be places where cut-out gear couplings might be the wiser choice. The gear coupling in many cases is less expensive and takes less space in the system than a clutch.
Save the Equipment from Torque
Rotating equipment shafts are often oversized because they are designed to limit deflection, which can lead to oversize couplings. Motors are sized as the next larger standard unit compared to the application requirements. Those issues plus a service factor can result in a drive system that has torque capability well in excess of the driven equipment needs. In such systems, torque spikes or overloads are easily passed to components that are not designed to withstand them and may be severely damaged. To prevent that, a torque limit device is installed in the drive train. The gear coupling, which probably is needed in the system for other reasons anyway, can provide the same protection at much lower cost than many devices sold as torque limiters, with the simple addition of a shear pin.
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