4.1. CHARACTERIZATION. CLASSIFI CATION. RANGE OF UTILISATION The couplings establish a permanent or intermitte nt link between two consecutive… [608336]

4. COUPLINGS (CUPLAJE)

4.1. CHARACTERIZATION. CLASSIFI CATION. RANGE OF UTILISATION

The couplings establish a permanent or intermitte nt link between two consecutive elements of a
kinematic chain, in order to transmit torque and rotation, usually without modifying the transmitting
law.
Excepting their main function of transmitting the load (torque) and the rotation, the couplings can
perform other functions too, like:
ƒ compensating the deviations of the elements li nked by the coupling, which are due to errors of
manufacturing and assembling;
ƒ connecting some shafts with parallel or concurrent axes;
ƒ protecting the transmission from shocks and vibrations ;
ƒ limiting the transmitted load;
ƒ limiting the rotations;
ƒ disconnecting the transmission when the direction of rotation is changed;
ƒ commended disengaged of the link between the elements.
Due to the great diversity of couplings types existing in practice, a generally accepted
classification is hard to be performed. Because of this reason, classifi cation criteria w ith a high degree
of generality are: the physical process of transmitting the load – mechanical (direct contact or friction),
hydraulic, or electric; the continu ity of transmitting the load – perman ent or intermitent; the possibility
of compensating the deviations wh en assembling the coupling or dur ing it’s functioning – fixed or
mobile; the shape of friction surfac es – plane, conical, cylindrical; the way of building the commands ;
the way of limiting the load and the rotations; the one-way transmission of the motion,etc.
One of the most used classifi cations, based on some of the criter ia presented above, is shown in
fig. 4.1.
The classification of couplings in mechanical hydraulic and elec tromagnetic couplings, take into
consideration the phenomena us ed to transmit the load.
The permanent couplings make a permanent link between the shafts. The interruption of the link
can be done only by disassembling the coupling.
The fixed permanent couplings make a link be tween two in-line shafts , without compensating
their position deviations and without absorbing the shocks and the vibr ations from the transmission.
The mobile permanent couplings have the supplem entary function of comp ensating the deviations
of the shafts or of linking shafts with parallel or concurrent axes. Th e rigid mobile permanent
couplings don’t damp the shocks or vibrations, while the elastic permanent couplings have this
function too.
The intermittent couplings make the connection between two sh afts, which can be interrupted
using an external command or automatically – when an overload appears, when the speed decreases or
when the direction of rotation changes.
For any transmission, no matter how complex it is, a corresponding coupling can be chosen or it
can use a combined coupling that fulfills all th e functional conditions im posed to the coupling.

4.2. THE CALCULUS LOAD

During functioning, a complex system of loads acts on the coupling. Ex cept to the torque, that has
to be transmitted, on the coupling also act :
ƒ internal loads, due to the inertia of the elements;
ƒ shock or vibrating loads, due to the working conditions of the transmission;
ƒ overloads, due to the enforced deformation of the elements; usually as a result of the
deviations of the shafts;
ƒ supplementary loads, due to friction between the mobile elements of the coupling .
These loads are depending on a complex system
of factors and makes very difficult the establish of
the torque that must be use for the coupling dimensioning.

Fig. 4.2 General variation of the transmitted
torque In fig. 4.2 is shown the general variation of the transmitted torque, during functioning . The characteristic points and stages of the transmitted torque variation are: a – the starting shock; b –
passing in the stationary regime; c – the stationary regime; d – the stopping shock. In the couplings design the torque used fo r dimensioning is called
calculus torque and is established with the relation
, (4.1) tn s tcM K M=
where Ks is a coefficient bigger than one, cal led safety coefficient of overload, and Mtn is the nominal
transmitted torque, established depending of the power of the electric engine P, in kW and the nominal
functioning rotation of the coupling n, in rot/min, with the relation
[] . mm N 10 55 , 96
nPMtn⋅ = (4.2)
The coefficient Ks is determined using the experimental data and is usually obtained as a product
of factors for which the values are shown in st andards or in the manufacturer’s cathalogues. The
factors are taking into cons ideration the type of the driving machine, the type of the driven machine
(the working conditions) and the functioning regime of the transmission.
The couplings can be choosen from standard s or from the cathal ogues of specialized
manufacturers, depending on the given torque Mt cat , following the condition Mt cat ≥ M tc .

4.3. PERMANENT COUPLINGS

4.3.1. Steady permanent couplings

The steady permanent couplings establish a perm anent and rigid link between two collinear shafts,
in order to transmit a torque and the rotation motion. The misalignment of the shafts must lie within
the limits 0,002… 0,05 mm, so that the coupling doe sn’t create overloads in the shafts and their
bearings. Such couplings are used for connecting long shafts made of several parts which work at low
speeds ( n < 250 rot/min) and are also used at transmissions with low moments of inertia imposed by
the working regime.

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4.3.1.1. Sleeve Couplings (Cuplaje cu man șon)

The sleeve couplings can be found in constructions with a sleeve made of one or two parts.
The couplings with single sleeve are made under the shape of a bushing assembled on the two
shaft ends. The assemblies can be made with cylindrical pins, tapered pi ns, straight keys, disk keys or
splines. At the assemblies with strai ght keys or with splines, the bushing must be axialy fixed in one of
the shafts, the most used solution bei ng with screw sets (see. fig. 4.3, c și d).
The calculus of these couplings involve dime nsioning the assemblies bushing – shaft ends and
checking the bushing for torsion, th e calculus being made with the calculus torque. The relation for
bushing checking is
()attc
pt
td DD M
WMτ ≤− π= = τ4 416, (4.3)
where D and d are the characteristic diameters of the bushing (see. fig. 4.3), and τat – the allowable
torsion strength for the bushing material. The exterior diameter of the sleeve is constructively adopted
depending on the shaft end diameter D = (1,4…1,8) d. The upper values of the interval are
recommended for sleeves made of cast-iron, and the lower ones for sleeves made of steel. This type of couplings is rarely used because of its large axial dimensions and because of hard mounting, needing
axial displacements for at least one of the shafts
The couplings with two-parts sleeve are like the ones with single sl eeve, the difference being that
the sleeve is divided with an axial plan .The two parts of the sleeve are assembled with screws on the
shaft ends. The load is transmitted by friction between the liner and the shaft ends, but there might also
be assemblies with straight keys between the shaf ts ends and the sleeve. The standards give two
b a
c d
Fig. 4.3 Single Sleeve Couplings
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constructive types of coupli ng with divided liner : for horizontal shafts (fig . 4.4, a) and for vertical
shafts (fig. 4.4, b) – but in this case the parallel keys, that are used for safety, have a cotter .

a b
Fig. 4.3 Couplings with two-parts sleeve
The calculus of these couplings consists of check ing the screws, after the constructive dimensions
are choosen from standards.
The use of these couplings is no wider than that of the couplings with a single sleeve, although for
mounting it is not necessary the axial displacement of the shafts.

4.3.1.2. Couplings with flanges (Cuplaje cu flan șe)

These couplings are made of two half couplings under the shape of two sl eeve flanges assembled
on shaft ends with straight keys and between them with screws .
Therea are two types of couplings with flanges: with screws mounted with clearance and with
fitted bolts.
The first type of coupling (fig. 4.5) transmits the torque through the friction between the half
couplings. The necessary compression force for
transmitting the load is achieved by clamping the screws at mounting . The condition to
transmit the calculus torque by the friction between the flanges is
20Dz F M Mf tcμ = ≤ , (4.4)
The force F0 which compresses the flanges,
corresponding for each screw results
.2
00D zMFtc
μ= (4.5)
In relations (4.4) and (4.5) Mf represents
the friction torque between the flanges, μ – the
friction coefficient between the flanges with
values μ = 0,2…0,3, z – the number of screws,
D – the diameter of screws arrangement . Fig. 4.5 Coupling with flanges and screws mounted
with clearance
The force F0 generates traction stress on the screw. Because, during mounting, the screw is also
loaded by the screwing torque, the dimensioning of the screws is performed with relation
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atFdσ π⋅=0
13 , 1 4, (4.6)
where d1 represents the necessary inner diameter of the thread of the screws, σat – the allowable
strength at traction.
For unloading the screws of this stress they can be mounted in bus hings (see. fig. 4.5, b), which
are assembled without clearance between the flanges.
The coupling with flanges and fitted bolts (fig.
4.6) uses, for connecting the flanges, fitted bolts, the
passing holes from the two flanges being precise.
The load is transmitted through direct contact between the flanges and the rod of the screws. The force for each screw is
D zMFtc2
1= , (4.7)
where z is the number of screws, and D – the
diameter of arranging for the screws.
The fitted bolts are checked at shearing stress with the relation

Fig. 4.6 Coupling with flanges and fitted bolts
,
42
01
af fDFτ ≤
π= τ (4.8)

and the crushing check being made with the relation
.
min 01
as sl DFσ ≤ = σ (4.9)
a
In relations (4.8) and (4.9) th e following notations are made: D0 –
the diameter of the rod; lmin = min ( l1, l2) – the minimum length of
contact between the screws and the flanges. The calculus corresponds to the assemblies with fitted bolts, with transversal load.
b

4.3.2. Rigid mobile permanent couplings
c
The name of these couplings comes from the rigid intermediary
element which makes the link between half couplings. These
couplings are meant to compensate position deviations without the
possibility of damping shocks and vibrations. The deviations represent
the differences with respect to th e normal position of the shaft ends
(fig. 4.7, a) and can be: axial (fig. 4. 7, b), radial(fig. 4.7, c), angular
(fig. 4.7, d) or combined (fig. 4.7, e). The rigid mobile permanent
couplings are classificated in function of the type of deviations that can
be compensated . d
e
Fig. 4.7 Deviations

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4.3.2.1. Rigid mobile permanent couplings for compensating axial deviations
The coupling with claws (fig. 4.8) is used for transmitting small torques, at lubricating pumps and
manually operated devices .
The coupling with transversal pin is made in one of the two variants shown in fig. 4.9. The
calculus of these couplings c onsist in checking th e pin for shearing and crushing stress.

Fig. 4.8 Coupling with claws
a
b
Fig. 4.10 Coupling with claws Fig. 4.9 Couplings with transversal pin
The claws coupling shown in fig. 4.10 is made of two identical half couplings 1 and 2, centered
on a ring 3. The load is transmitted through contact between the claws, which are stressed at crushing,
shearing and bending. This coupling transmits high torsion moments for shafts diameters in the range d = 30…140 mm and compensates
axial deviations Δl = 16…24 mm.

4.3.2.2. Permanent couplings for
compensating radial deviations (misalignements)
The Oldham coupling (fig. 4.11) is the
most spread type from this category of
couplings. It has several constructive solutions, different by the shape of their elements. The half couplings 1 and 2 are identical and the intermediary element connects them through conjugated shapes.
During functioning, at radial deviations of the
Fig. 4.11 Oldham Coupling
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shafts, the intermediary element has a planetary motion. The radial deviations can that can be taken are
ΔR = 0,04 D.
The functional surfaces ar e stressed at crushing.

4.3.2.3. Permanent couplings for compen sating angular deviations
This category of couplings
includes the so called cardan joints
which make the connection between shafts that have a variable position.
The main element of the coupling is
the cardan joint (fig. 4.12), that connects two concurrent shafts. This is
made of the pitchforks 1 and 2
assembled on the shaft ends – that are connected through the intermediary element 3 –under the shape of a cross in the case from fig .4.12. To link the two parallel shafts, two cardan joints are used (fig 4.13.) linked
by a shaft called cardan shaft, that has a variable length. The modification of the cardan shaft length
from fig.4.13. is obtained due to it’s construction from two parts, spline assembled. The calculus of the
cardan couplings is performed for the pitchforks, the cardan cross, the bearings between the pitchforks
and the screw assemblings.
Advanced solutions from this category are the Weiss and the Rzeppa [1,3], which use rolling elements, through which the synchronous tran smission of the movement is ensured.

Fig. 4.12 Cardan Joint
Fig. 4.13 Cardan shaft Spline Assemling
4.3.2.4. Permanent couplings for compensating combined deviations
In this category of couplings ar e included the ones that have the po ssibility to compensate all types
of deviations (axial, radial and angular) separately or combined.
The toothed couplings are specific to this cate gory. In fig.4.14 is show n a toothed coupling made
of two identical half couplings 1 – under the shape of hubs with ex terior teeth – and two identical
sleeves 2 – with interior teeth assembled by sc rews and centered between them by the ring 4. The
centering of the hubs 1 with respect to the sleeve s 2 is achived through centering thresholds. For
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decreasing the wearing, the coupling can work with lubrication. The sealing is performed by “O” rings
mounted between the sleeves 2 and the hubs 1.
The load is transmitted through contact on the fla nks of the teeth, from the hub to the sleeve and
afterwards to the other hub. The co mpensation of the axial deviations is done by the axial displacement
of the hubs towards the conjugated sleeves (depending on the axial sp ace allowed by the construction
and especially depending on the width of the teeth from the sleeves). The compensation of the angular
and radial deviations is performed by leaning the hubs with respect to the sleev es, in opposite direction
for compensating the angular devia tions and in the same way for compensating the radial ones .
The shape of the teeth influences not only th e transmitting capacity of the load but also the
capacity of compensating the deviations. For a be tter capacity of compensating the deviations, the
teeth are made with a convex shape both on the flank and on the length (fig. 4.15).

Prag de
centrare Etanșare
(inel O)
Fig. 4.15 The shape of the
teeth
Fig. 4.14 Toothed coupling
The lubrication of the coupling, needed to decr ease the flank wear and increasing the reliability,
can be performed in one of the following ways:
• Lubrication with cosmol ene (unsoare consistent ă) – ensures the lubrication from the start and
doesn’t complicate the constr uction – is used at low speeds and high torques;
• The lubrication with oil bath – ensures a certain lubrication starting from a given speed when
the oil is centrifugated in the teeth area – is recommended at relatively small diameters and
low functioning temperatures;
• The lubrication with oil circulation is reco mmended at high temperatures and very high
rotations when the lubrication by an own oil bath would lead to the centrifugal compression of
the oil on the inner sides of the sleeves.
The toothed couplings are choosen from standards or from the catalogues of the manufacturing
companies, where can be found informations for establishing the capable torque of the toothed
couplings depending on the angle between the hubs and th e sleeves, needed to take over the deviations.
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The checking calculus of the toot hed coupling consists in compari ng the contact stress – from the
flank of the tooth – and the bending stresses – from the tooth base – with the allowable strengths. The
calculus relations take into account the fatigue character of both stresses. The constructive solutions of
the toothed couplings are various, having wide possibilities of adapting to the requests imposed to the
transmission.

4.3.3. Elastic permanent mobile couplings (Cuplaje elastice)

4.3.3.1. Characterization, functions
These couplings are currently named elastic couplings .
The intermediary element can be metallic or nonm etallic. This element takes part in transmitting
the torsion moment between the half coupli ngs, defining the coupli ng properties :
• damping the shocks and vibrations;
• the elastic compensation of the shafts deviations;
• modifying the eigenvalue of the mechanical syst em; in order to avoid the vibrations.
The functions fulfilled by these couplings are based on their characteristic elements .
The elastic characteristic of these
couplings is defined by the dependence
between the relative rotation angle ϕ o f
the two half couplings and the torque
transmitted by the coupling. The stiffness
of the coupling is given by the relationship:
No Damping With Damping
.ϕ=tMk (4.10)
a b
The elastic characteristic (fig .4.16, a)
can be linear – with constant stiffness – or nonlinear – with variable stiffness. Fig. 4.16 Elastic characteristics
The relative damping degree d is a characteristic of these couplings through which the capacity of
damping the shocks is defined. The damping appears when is a difference between loading and
unloading on the elastic characteristic (fig. 4.16, b) . The shocks are absorbed through the deformation
of the intermediary elastic element, transforming the energy of the shock in strain energy ( Le). A part
of this energy is transformed into heat, representing the friction work ( Lf) on the coupling. In this way,
only a part from the energy of the shock is given back to the system. The relative damping degree is
defined by the relationship

ef
LLd= (4.11)
and is directly proportio nal with the damping capacity of the coupling.
The high values of the damping capacity for shocks lead to a smooth functioning of the
transmissions that are equiped with this ki nd of couplings, even at variable loads .
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In the case of elastic couplings with damping it is also improved the behaviour in vibrating
regimes. Fig .4.17 show s the variation of the
vibrations amplitude aω depending on their
frequency ω, both of them being related to the
resonance values aω0, respectively ω0 . It can be
observed that in case of couplings with damping
the vibrations amplitude is limited. When
increasing the excitating frequency ω, the
amplitude of the vibrations aω increases on the
curve MAB, deeply decreases from point B to C
and continues to decrease on the curve CN .
When decreasing the excitating frequency ω,
the amplitude of the vibrations increases on the
curve NCD and then sharply from point D to A, from where starts to decrease on the curve AM.
Because increasing the damping degree leads to an incr ease in the mechanical work turned into heat, it
must be taken into account the limitation of the functio ning of these couplings at very repeated shocks
and on long periods of time in the resonance doma in, due to heating of the elastic element.
Area of
instability
Fig. 4.17 The resonance characteristic
The deformability of the elastic element determines the coupling capacity of taking over position
deviations. The deformability of this element depends on the coupling construction and on the material
the elastic element is made of. The reliability of the coupling is influenced by the size of the
deviations, the deformation of the elastic element in troducing additional forces in the elements of the
coupling, on the shafts a nd on the their bearings.

4.3.3.2. Elastic couplings with nonmet allic intermediary elements

The nonmetallic elements are usually made of r ubber. This material is recommended through its
properties: high elasticity, high damping capacity, constructive simpleness, low costs. The nonmetallic
elements lead to electrical insu lation of the connected shafts, but in comparison with the metallic
intermediary elements give to the coupling a smalle r reliability, the transmited torques being limited at
small – medium values.
Elastic coupling with bolts (Cuplajul elastic cu bol țuri) is manufactured in two standardized
options: N – normal (fig. 4.18, a) and B – with bushi ngs (fig. 4.18, b). The c oupling consists of: two
identical half couplings; the bol ts, alternating mounted on the tw o half couplings, and sustained
through the rubber sleeves into the conjugated half coupling. Theese couplings allow compensation of
misalignment ΔR = 0,3…0,6 mm, angular deviations Δα ≤ 10 and axial deviations Δl in the limits of
maintaining contact between the rubb er sleeves and the half couplings.
The load is transmitted through the contact be tween half couplings, bolts and rubber sleeves.
The calculus of the elastic couplings with bolts is performed taking into account the hypothesis of
uniform distribution of the load on the z bolts.
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a b
Fig. 4.18 Elastic coupling with bolts
The load on each bolt is
,2
11D zMFtc= (4.12)
where D1 is the arranging diameter of the bolts.
The checking calculus of the bolt for bending – c onsidering it embedded in the half coupling and
the load being applied with the maximum lever – is made with the relation '
bl
ai
bb
zi
idl F
WMσ ≤
π= = σ
323'
1 (4.13)
and the checking calculus of the elastic sleeve for crus hing – at contact with th e bolt – is made with the
relation
.1
as
b bsl dFσ ≤ = σ (4.14)
In the previous relations (4.12) and (4.13) the follo wing notations were used: db – the bolt
diameter; lb – the width of the sleeve; σ ai – the bolt allowable strength for bending σai = (0,25…0,4)
σ02; σas – the rubber allowable strength for crushing σas = 5…7 MPa.
The Periflex type elastic coupling (fig. 4.19) is one of the many types of elastic couplings with
rubber bandage. The Periflex coupling has in its co mponence the identical half couplings 1 and 2 the
rubber bandage with te xtile insertions 3, assemble d on the half coupligs with screws, with the help of
disks 4.
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This coupling is used for
compensating axial deviations Δl =
3…6 mm, radial deviations ΔR = 2…6
mm and angular deviations Δα =
2…6°. The large volume of the
intermediary rubber element ofers an increased damping capacity for shocks and vibrations.
The torque is transmitted by
friction from the rubber bandage, on
one hand, and the halfcouplings and
the disks on the other hand. The compressing force, needed to transmit the load by friction, is established by
tightening the screws. The condition of
transmitting the load through friction is

Fig. 4.19 Periflex Coupling
,42 1
01 iD DF z M Mf tc+μ = ≤ (4.15)
where μ is the friction coefficient between the bandage and the half coupling or disk ; D and D1 2 – the
diameters of the friction surface; z – the number of screws; F01 – the compressing force of each screw;
i – the number of pairs of friction surfaces ( i = 2, for the construction from fig. 4.19).
From relation (4.15), the necessary compression force on each screw results
().4
2 101i D D zMFtc
+ μ= (4.16)
The screws are checked for traction, with an increased force equal with 1,3 F01 in order to take
into account the torsion stress – from mounting – produced by the scre wing torque, with the relation
,
43 , 1
2
101
at tdFσ ≤
π= σ (4.17)
where d1 is the interior diameter of the thread.
The rubber bandage is checked for crushing, with relation
()as s
D DF zσ ≤
−π= σ
2
12
201
4 (4.18)
and for shearing, in the cross section corresponding to the diameter D, with relation 2
.2
2
2aftc
fh DMτ ≤
π= τ (4.19)
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-14- In relations (4.18) and (4.19) the following notations are made: h – the thickness of the bandage;
σas – the rubber allowable strength for crushing, σ as = 5…7 MPa; τaf – the rubber allowable strength
for shearing, τaf = 0,3…0,5 MPa.
Due to the rotation speed, the rubber bandage is stressed to traction by th e centrifugal force, and
for this reason the peripheral functioning speed must be li mited to maximal values va = 17,5…20 m/s,
so that the allowable strength for traction σ
a – coupling with bolts and elastic disks (Hardy ty pe ), characterized by torsional elasticity and
high deformability ;
d – Vulkan coupling, with cross sectioned banda ge, easier to manufacture a nd with a capacity of
transmitting the load higher than that of a Periflex coupling . Other types of elastic couplings with nonmetallic intermediary elements are shown in fig 4.20 :
a b at = 0,5 MPa should not be exceeded.
b – coupling with rubber element stressed to to rsion, with high capacity of loading, but not
recommended for taking over variable cyclic loads and for functioning at high temperatures
,when the strength of the elastic element joint decreases ;
c – variant for the Periflex coupling ;

c d
Fig. 4.20 Elastic couplings with non metallic intermediary elements

Intermitent
Steady MECHANICAL COUPLINGS

HYDRAULIC ELECTROMAGNETIC
(with induction )
Hidrostatic
Hidrodynamic Mobile
Axial
adjustement
Radial
adjustement
Combined
adjustement With metallic
element
With non-metallic
element Transmitting the
load through
shape Transmitting the
load through
friction
Electromagnetic
command Rigid Elastic Commended Automated
Safety
Oneway
Centrifugal Angular
adjustement Permanent
Mechanical
command
Pneumatic
command Hidrodynamic
command

Fig. 1.1 The classification of couplings
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