Field of the invention
[0001] The invention relates to an elevator and its traction sheave. The elevator is meant
for transporting passengers and/or goods.
Background of the invention
[0002] Modern elevators usually have a drive machine which drives the elevator car under
control of an elevator control system. The drive machine typically comprises a motor
and a traction sheave engaging an elevator roping which is connected to the car. Thus,
the driving force is transmitted from the motor to the car via the roping.
[0003] Important factors affecting the traction, when produced by frictional engagement,
are the material pair of the rope and the traction sheave as well as lubrication between
them. The elevator ropes are normally made of steel wires twisted together. The traction
sheaves have a continuous circumferencial traction surface for transmitting tractive
force to the rope which is set to pass against it. For the purpose of reducing internal
friction and wear the ropes have lubricant in them. A problem with these types of
known elevators is that the lubricant easily escapes the rope under pressure caused
by the rope tension and contact with the traction sheave. At the point of the traction
sheave this reduces friction and therefore the force transmitting ability via the
rope-sheave contact. Especially, a thick lubricant layer between the traction sheave
and the rope could cause slipping. Accordingly, too thick layer of lubricant is harmful.
On the other hand it is found out that total elimination of the lubricant layer increases
wear of the outermost wires, because of the unavoidable occurrence of slipping between
the outermost rope wires and the tractions sheave. This slipping is caused largely
by dimension changes occurring in the rope when it passes around the traction sheave.
These dimensional changes in of the rope are caused for instance by the rope bending,
low elastic coefficient of the rope and non-constant forces affecting the rope during
its passage around the traction sheave.
[0004] The traction forces transmitted via frictional engagement between the ropes and the
traction sheave depend strongly on the normal forces between the ropes and the sheave.
These forces have in the prior art been increased by forming the rope grooves of the
traction sheave undercut, i.e. in the form allowing the rope to rest supported by
the groove walls and not on the groove bottom. High normal forces have resulted in
increased traction but in these solutions it has been difficulties in providing a
lubricant layer between the rope and the sheave which reduces rope wear yet does not
harm the frictional engagement.
Brief description of the invention
[0005] The object of the invention is, inter alia, to solve previously described drawbacks
of known solutions and problems discussed later in the description of the invention.
An object of the invention is to introduce an elevator and its traction sheave structure
with improved friction properties. An object of the invention is furthermore to introduce
an elevator and its traction sheave structure where lubricant layer between the rope
and the traction sheave traction surface can be controlled. Embodiments are presented,
inter alia, where a lubricant layer can be maintained with high surface pressures.
In particular, the thickness of the lubricant layer can be controlled to be more stable.
In this way, a strong frictional contact between the rope and the sheave can be achieved,
yet being able to provide lubricant between them in such a way that rope wear is not
excessive. It is also introduced a method of forming a circumferential traction surface
of a traction sheave which method provides improved friction properties for an elevator
traction sheave.
[0006] It is brought forward a new elevator, which comprises an elevator car, a traction
sheave for driving elevator hoisting ropes, at least one metal wire hoisting rope
for transmitting force between the elevator car and the traction sheave, having metal
wires forming at least part of the outer surface of the rope. The traction sheave
comprises a metallic circumferential traction surface per each of said at least one
rope for transmitting tractive force to the rope, which is set to pass against the
circumferential traction surface. The circumferential traction surface comprises recesses
spaced apart in circumferential direction of the traction sheave. In this way, the
surface pressure between the rope wire and the traction surface is adjusted high and
thereby to generate high friction. Preferably, the rope has lubrication inside it.
Thus, internal wear of the rope is reduced, as well as wear of the areas of the traction
sheave and the wires contacting each other. The recesses facilitate formation and
maintaining of a thin lubricant film in the contact area between the wires and the
traction surface. Thus normal forces can be increased and the interplay between the
traction surface and the lubricant inside the rope allows reduced wear yet without
losing traction.
[0007] In a preferred embodiment the recesses have a length in circumferential direction
which is less than the diameter of said metal wires forming at least part of the outer
surface of the rope. In this way the shear forces caused by the hard metallic recess
edges on the wire are substantially reduced.
[0008] In a preferred embodiment the recesses have a length in circumferential direction
which is less than 1 mm. The recesses are thus short in circumferential direction.
In this way the shear forces caused by the hard metallic recess edge are reduced.
This has also the benefit that when the rope contains lubricant, the recesses do not
receive it too easily. Thereby, the small length of the individual recesses facilitates
maintaining the lubricant film thin. This aim is also facilitated by the small length
of the recesses because thus they can be positioned densely. Resistance from receiving
lubricant excessively facilitates in forming a uniform thin film of lubricant in the
contact area between the wires and the traction surface when the rope has lubrication
inside it. In a preferred embodiment the recesses have a depth which is less than
1 mm. This limits them from receiving lubricant excessively thereby further facilitating
maintaining the lubricant film thin.
[0009] In a preferred embodiment the recesses have a cross section area in the transverse
direction relative to the traction sheave circumferential direction less than 1.5
square millimeters. The recesses are thus small in volume or at least their ability
to receive rapid volume flow is limited. This limits their ability to receive lubricant
which facilitates the forming of a thin film of lubricant in the contact area between
the wires and the traction surface.
[0010] In a preferred embodiment each of the recesses extends into the traction surface
material and has a bottom and walls surrounding an inside space open towards the rope
direction. Accordingly, the inside space is closed in all lateral directions. In this
way it can receive a limited volume of lubricant. This makes it more suitable for
returning the lubricant back in contact with the rope, and limiting it from receiving
excessive amount of lubricant. Also, the lubricant leakage far away from the wires
is reduced. For example, in this way, in case of an undercut rope groove, the lubricant
does not escape to groove bottom nor spray radially away from the traction sheave
due to its rotation.
[0011] In a preferred embodiment the number of recesses per meter is more than 300. The
recess area can thus be formed vast, however evenly distributed. In this way, the
normal forces can be increased to improve friction. Also, a formation of thin film
can be facilitated for the rope with lubrication inside it.
[0012] In a preferred embodiment, said metal wires are steel wires. Preferably, the metallic
circumferencial traction surface is made of steel or cast iron. In this way, the material
pair is well suitable for long-term elevator use.
[0013] In a preferred embodiment the traction sheave comprises a circumferencial groove
for each of said at least one rope, the groove(s) having said recessed circumferential
traction surface(s) for transmitting tractive force to the rope which is set to pass
in the groove against the circumferential traction surface. The groove provides guidance
for the ropes so the rope passes in a controlled manner against a desired traction
surface. Preferably, each groove comprises sidewalls each sidewall having a recessed
circumferential traction surface as above defined. Recesses provide an improvement
in friction properties as above defined.
[0014] In a preferred embodiment the groove(s) is/are undercut groove(s). In this way, more
contact pressure is directed to the sidewalls of the groove as the rope to rests supported
by the groove walls and not on the groove bottom. In this way, the forces can be increased
and the traction improved. Furthermore, in this way proportion of unrecessed traction
surface can be reduced.
[0015] In a preferred embodiment the recesses are round. This facilitates simple adjusting
of their volumes and consequently their ability to receive lubricant. In this way
the behavior between the recess and the wires is insensitive to the direction of the
wire. The number and density of the recesses can also be very high in this way which
facilitates formation thin of a uniformly thin lubricant film.
[0016] In a preferred embodiment said wires form cords and said wires are arranged in spiral
in their cords and the cords are arranged in spiral in the rope and the spiral direction
of the cords is opposite relative to the spiral direction of the wires. In this way,
the direction of the wire can be simply arranged to meet the recesses at least substantially
in the length-direction of the rope.
[0017] In a preferred embodiment the recesses are line-shaped in direction transverse to
the circumferential direction of the traction sheave. In this way, vast recess area
can be formed with a simple method, e.g. by cutting the surface with linear movement
of the cutting means.
[0018] Preferably, the recesses are distributed along the whole length of the circumference
to form a circular array of recesses. In this way, the whole length of the circumference
provides the benefits as disclosed.
[0019] It is also brought forward a new method of forming a circumferential traction surface
of a traction sheave for an elevator, which circumferential traction surface is, when
being rotated, suitable for transmitting tractive force to a rope, which is set to
pass against the circumferential traction surface, in which method
- a traction sheave body with a metallic circumferential surface is provided, and
- recesses are formed on said circumferential surface, which recesses are spaced apart
in circumferential direction of the traction sheave.
With this method, friction properties of a traction sheave can be improved considerably.
The normal forces can be increased and the interplay between the traction surface
and the lubricant inside the rope can be made better so that wear can be reduced without
losing traction.
[0020] In a preferred embodiment after the traction sheave body is provided, a circumferential
groove is formed on traction sheave body, which has the circumferencial surface on
which the recesses are later formed. In this way, rope guidance is additionally achieved.
The groove form also supports the effect of the recesses. With this process plural
grooves are preferably formed which are at later stage recessed. The circumferencial
surface on which the recesses are later formed is preferably a sidewall of the groove.
[0021] In a preferred embodiment the recesses are formed by removing material from the circumferencial
surface with laser or water-jet. These are methods which can provide an accurate result.
However, the most preferred method utilizes laser which can produce most easily accurate
and very small recesses into a curved shaped as that of a traction sheave, especially
when the surface is that of a sidewall of a groove. The laser may, for example, be
so called Nd:YAG laser which can efficiently produce the recesses in said metallic
surface.
[0022] It is also brought forward a new traction sheave for an elevator, which comprises
a metallic circumferential traction surface for a rope for transmitting tractive force
to a rope, which is set to pass against the circumferential traction surface. The
circumferential traction surface comprises recesses spaced apart in circumferential
direction of the traction sheave. The recesses are preferably as defined above or
elsewhere in the application.
[0023] In a preferred embodiment the traction sheave is obtained by the method as defined
above or elsewhere in the application.
[0024] The elevator as described anywhere above is preferably, but not necessarily, installed
inside a building. It is preferably of the type where the car is arranged to serve
two or more landings. Then, the car preferably responds to calls from landing and/or
destination commands from inside the car so as to serve persons on the landing(s)
and/or inside the elevator car. Preferably, the car has an interior space suitable
for receiving a passenger or passengers, and the car can be provided with a door for
forming a closed interior space. In this way, it is well suitable for serving passengers.
Brief description of the drawings
[0025] In the following, the present invention will be described in more detail by way of
example and with reference to the attached drawings, in which
Figure 1 illustrates schematically an elevator according to an embodiment of the invention.
Figure 2 illustrates a cross section of the rope and the traction surface cut along
the centerline of the rope at the point of contact between a wire of the rope and
the traction surface.
Figures 3 illustrates the recesses as viewed from the direction of the rope according
to a first preferred embodiment.
Figures 4 illustrates the recesses as viewed from the direction of the rope according
to a second preferred embodiment.
Figure 5 illustrates a cross section of the rope and a part of the traction sheave
as viewed in circumferential direction of the traction sheave.
Figure 6 illustrates a cross section of the rope and the traction sheave as viewed
in circumferential direction of the traction sheave.
Figure 7 illustrates a preferred structure for the rope.
Figure 8 illustrates a method of forming the circumferential traction surface of the
traction sheave.
Detailed description
[0026] Figure 1 illustrates an elevator according to a preferred embodiment. The elevator
comprises a hoistway S, an elevator car 1 and a counterweight CW vertically movable
in the hoistway S, and a drive machine which drives the elevator car under control
of an elevator control system (not shown). The drive machine comprises a motor M and
a traction sheave 2 engaging elevator ropes 3 with friction, which ropes 3 are connected
to the car 1. Thus, driving force can be transmitted from the motor to the car 1 via
the traction sheave 2 and the ropes 3. The ropes 3 connect the elevator car 1 and
the counterweight 2 and pass around the traction sheave 2. The traction sheave 2 comprises
a metallic circumferencial traction surface 4, 4' per each of said at least one rope
for transmitting tractive force to the rope 3 which is set to pass against the circumferential
traction surface 4, 4'. The hoisting ropes 3 are metal wire ropes. Thus, they have
metal wires w forming at least part of the outer surface of the rope 3. In particular,
the metal wire ropes are preferably steel wire ropes. The traction surface 4, 4' and
a wire w are presented in Figure 2 which illustrates a cross section cut along the
centerline of the rope 3 at the point of contact between a wire w and the traction
surface 4, 4'. The traction surface is circumferential with a great radius compared
to the wire dimensions, so the curved shape does not show in Figure 2. The circumferential
traction surface 4, 4' comprises recesses r, r', which are spaced apart in circumferential
direction x of the traction sheave 2 which direction also corresponds to that of the
rope 3 passing along the circumferential traction surface. In this way, the surface
pressure between the rope wire w and the traction surface is adjusted higher and thus
to be more preferable with regard to friction. At the area of the recesses, no contact
takes place between the rope and the traction sheave 2. This increases the support
forces at the areas between the recesses r, r'. These areas between the recesses r,
r' support the rope 3, in particular the outer wires thereof, with direct contact
apart from the possible lubricant layer therebetween. The recesses r, r' are very
short in circumferential direction. In this way the shear forces caused by the hard
metallic recess edges are substantially reduced. A generally advantageous length I
for the recesses r, r' circumferential direction is less than 1 mm, which is suitable
for improving friction of most elevator ropes with reasonable disadvantages caused
by shear forces affecting the rope. However, it is particularily preferable, that
the recesses r, r' have a length in circumferential direction which is less than the
diameter t of said metal wires w, which form part of the outer surface of the rope
3. In this way the shear forces caused by the hard metallic recess edge are substantially
reduced.
[0027] It is preferable, that each of said ropes 3 has lubrication inside it, which is in
contact at least with the metal wires w. Thus, it can lubricate the wires w, and also
escape from within the rope 3 to the contact area between the wires w and the traction
sheave traction surface 4, 4. Thus, the wear of the wires w, as well as wear of the
traction surface 4,4' is reduced. The recesses can each receive lubricant leaking
from between the rope and the sheave. The recesses can store lubricant and return
it into contact with the rope. The shortness of the recesses r, r', as earlier specified,
has also the benefit that it makes it possible that the recesses can be positioned
densely. This leads to that a thin film of lubricant can be uniformly produced. In
practice, an advantageous lubricant flow to form a uniform lubricant film can in this
way be enabled.
[0028] The recesses r, r' have a small cross section area in the transverse direction relative
to the circumferential direction x. In other words, the length I times the depth d
is small. This leads to small capacity to receive lubricant. In this way they do not
receive easily excessively easily the lubricant, and can return some lubricant back
to contact with the rope. It is advantageous that the recesses have a cross section
area in the transverse direction relative to the circumferential direction less than
1.5 square millimeter. It is preferable that the recesses have a depth d which is
less than 1 mm. In this way, some wear tolerance can be still maintained but the volume
of the recess is not excessive in terms of its capability to return lubricant to contact
with the rope 3. Accordingly, the recesses are so small that they do not swallow all
the lubricant.
[0029] Figures 3 and 4 illustrate traction surfaces 4 and 4' with alternative shapes for
the recesses r, r' as seen in the direction of normal of the traction surface 4,4'.
In the figure arrow x illustrates the circumferencial direction of the traction sheave
2. In the embodiment as illustrated in Figure 3, the recesses are round. In the embodiment
as illustrated in Figure 4, the recesses are line-shaped in direction transverse to
the circumferential direction x of the traction sheave 2.
[0030] Figure 5 illustrates a preferred embodiment where the traction sheave 2 comprises
a circumferencial groove 5 for the rope 3, the groove 5 having a recessed circumferential
traction surface 4, 4' for transmitting tractive force to the rope 3 which is set
to pass in the groove 5 against the circumferential traction surface 4, 4'. In particular,
the groove 5 comprises sidewalls each having a recessed circumferential traction surface
4, 4' of the like as earlier specified. The sidewalls face the rope at an inclined
angle which increases the support forces on the rope resting on the sidewalls. The
groove 5 is in this case an undercut groove. If is preferable, but not necessary,
that the traction surface 4, 4' is curved at least substantially with the same radius
as the radius of the rope. In this way, the high contact pressure can be divided to
the rope surface more evenly. Also, this facilitates more even wear of the rope 3.
Figure 6 illustrates a preferred embodiment where the traction sheave 2 comprises
plurality of said circumferential grooves 5 for plurality of ropes 3, each groove
being as described in connection with Figure 5.
[0031] The recess r, r' are short but they should be densely distributed along the circumference
of the traction sheave 2. In this way, the effect of increasing the normal force is
considerable and the ability to stabilize the lubricant layer thickness is considerable
(in case lubricant is used). Good results are achieved when the number of recesses
per meter is more than 300.
[0032] The method a circumferential traction surface 4,4' of a traction sheave 2 for an
elevator is formed forming, which circumferential traction surface 4,4' is, when being
rotated, suitable for transmitting tractive force to a rope 3, which is set to pass
against the circumferential traction surface (4,4'). The method comprises a step of
providing a traction sheave body b with a metallic circumferential surface and a step
of forming recesses r, r' on said circumferential surface, which recesses r, r' are
spaced apart in circumferential direction x of the traction sheave 2. The recesses
r, r' as well as the traction sheave material are preferably as defined elsewhere
in the application. In the method after the traction sheave body b is provided, a
circumferential groove is formed on the traction sheave body b, which has the circumferential
surface on which the recesses r, r' are later formed. In the step of forming the groove,
the groove can be formed by machining (e.g. by rotary cutting method) the traction
sheave body b to have said circumferential surface on which the recesses are to be
formed. Each groove comprises sidewalls each sidewall having a circumferential surface
on which recesses r or r' are to be formed in the later step. Figure 8 illustrates
an embodiment of the method step where recesses r, r' are formed. In the method the
recesses are formed with device C. In this case the recesses are formed by removing
material from the circumferential surface with laser beam(s). Accordingly, device
C is a device for laser cutting. In practise, it may be so called Nd:YAG type of laser
device, which enables very accurate removal of material by evaporizing. The actual
laser cutting of the plural recesses r, r' can be carried out by rotating the sheave
body b stepwise around. Thus device C need not move substantially. Alternatively the
recesses could be formed by removing material from the circumferencial surface with
water jet(s). Accordingly, device C could in this alternative solution be a device
for water-jet cutting. The outcome of this method is disclosed in Figures 2-6. As
illustrated in Figure 6, the traction sheave is preferably prepared to have plurality
of said grooves 5 each having side walls which each have a recessed traction surface
4, 4'.
[0033] The traction sheave for an elevator, which comprises a metallic circumferencial traction
surface 4, 4' for at least one rope 3 for transmitting tractive force to a rope 3,
which is set to pass against the circumferential traction surface 4, 4'. The circumferential
traction surface 4, 4' comprises recesses r, r' spaced apart in circumferential direction
x of the traction sheave 2. The structure of the traction sheave is illustrated in
the Figures 1-6 and 8 and described elsewhere in the application. The traction sheave
is preferably obtained by the method as described earlier.
[0034] As mentioned earlier, it is preferable that the recesses r, r' have a length in circumferential
direction which is less than the diameter t of said metal wires w forming at least
part of the outer surface of the rope. One well working solution has the rope(s) 3
with outer wire w from 0.2 mm to 0.3 mm in diameter t and the traction sheave with
recesses r, r' from 0.05 mm to 0.2 mm long. For example, the wire can be 0.2 mm in
diameter t and the recess 0.1 mm long.
[0035] The metallic circumferencial traction surface is may be made for example of steel
or cast iron. These materials can be machined relatively easily and accurately with
laser or water jet or other means as mentioned. In any case, the traction sheave traction
surface is preferably made of metal, which has hardness from 450 HV to 1200 HV. In
this way, the recesses r, r' do not wear down quickly and the properties regarding
lubricant storage are maintained long enough to give the traction sheave 2 a life-time
required for long-term use of the elevator.
[0036] Each of said ropes 3 is preferably essentially round in its cross section. Figure
7 illustrates a preferred structure for the rope 3. The outer wires w may be wound
to form cords c surrounding the core of the rope 3. The core may be made of metal,
for example from corresponding metal wires as aforementioned outer wires w. Without
departing from the idea of the invention, the core of the rope 3 may be also from
other material than metal. Likewise, the outer wires w may be arranged to form cords
of different structure or amount than what is disclosed in Figure 7. It is preferable
that the rope 3 is a twisted wire rope. This type of metal ropes are common in elevators.
The spiral configuration of the wires leads to that the wires are often not totally
parallel with the circumference of the traction sheave, however the angle of the wires
relative to the longitudinal axis of the rope does not with most ropes harm the functioning
of the idea. It is preferable that the spiral of wires w in their cords c have opposite
spiral direction than the cords c in the rope. In this way the outer wires w can be
arranged to meet the recesses essentially in length-direction.
[0037] In the Figures only a portion of the traction sheave surface is illustrated. The
recess pattern, however continues completely around the traction sheave. Accordingly,
the recesses r, r' are distributed along the whole length of the circumference to
form a circular array of recesses r, r'.
[0038] Alternatively, some other methods for forming the recesses can be used. For example,
the recesses can be formed by sandblasting or by etching.
[0039] The recesses r, r' are preferably in the form of blind holes extending into the traction
surface material. That is, they have a bottom and walls and an inside space open towards
the rope 3.
[0040] It is to be understood that the above description and the accompanying Figures are
only intended to illustrate the present invention. It will be apparent to a person
skilled in the art that the inventive concept can be implemented in various ways.
The invention and its embodiments are not limited to the examples described above
but may vary within the scope of the claims.
1. An elevator comprising
- an elevator car (1),
- a traction sheave (2) for driving elevator hoisting ropes (3),
- at least one metal wire hoisting rope (3) for transmitting force between the elevator
car (1) and the traction sheave (2), having metal wires (w) forming at least part
of the outer surface of the rope (3),
wherein the traction sheave (2) comprises a metallic circumferential traction surface
(4, 4') for each of said at least one rope for transmitting tractive force to the
rope (3) which is set to pass against the circumferential traction surface (4, 4'),
characterized in that the circumferential traction surface (4, 4') comprises recesses (r, r') spaced apart
in circumferential direction (x) of the traction sheave (2).
2. An elevator according to claim 1, characterized in that the recesses (r, r') have a length in circumferential direction which is less than
the diameter of said metal wires (w) forming at least part of the outer surface of
the rope (3).
3. An elevator according to any one of the preceding claims, characterized in that each of the recesses (r, r') has a length in circumferential direction which is less
than 1 mm.
4. An elevator according to any one of the preceding claims, characterized in that the rope (3) has lubrication inside it.
5. An elevator according to any one of the preceding claims, characterized in that each of the recesses (r, r') extends into the traction surface material and has a
bottom and walls surrounding an inside space.
6. An elevator according to any one of the preceding claims, characterized in that each of the recesses has a cross section area in the transverse direction relative
to the circumferential direction less than 1.5 square millimeters.
7. An elevator according to any one of the preceding claims, characterized in that each of the recesses has a depth (d) which is less than 1 mm.
8. An elevator according to any one of the preceding claims, characterized in that the number of recesses per meter is more than 300.
9. An elevator according to any one of the preceding claims, characterized in that said metal wires (w) are steel wires.
10. An elevator according to any one of the preceding claims, characterized in that the traction sheave (2) comprises a circumferencial groove (5) for each of said at
least one rope (3), each groove (5) having a recessed circumferential traction surface
(4, 4') as defined for transmitting tractive force to the rope (3) which is set to
pass in the groove (5) against the circumferential traction surface (4, 4').
11. An elevator according to any claim 10, characterized in that each groove (5) comprises sidewalls, each sidewall having a recessed circumferential
traction surface (4, 4') as defined.
12. An elevator according to any one of the preceding claims 10-11, characterized in that each groove (5) is an undercut groove.
13. An elevator according to any one of the preceding claims, characterized in that the recesses (r, r') are round or line-shaped.
14. Method of forming a circumferential traction surface (4,4') of a traction sheave (2)
for an elevator, which circumferential traction surface (4,4') is, when being rotated,
suitable for transmitting tractive force to a rope (3), which is set to pass against
the circumferential traction surface (4,4'), in which method
- a traction sheave body with a metallic circumferencial surface is provided, and
- recesses (r, r') are formed on said circumferencial surface, which recesses (r,
r') are spaced apart in circumferential direction (x) of the traction sheave (2).
15. A method according to any one of the preceding claims, characterized in that in the method after the traction sheave body (b) is provided, a circumferential groove
(5) is formed on traction sheave body (b), which circumferential groove (5) has the
circumferencial surface on which the recesses (r, r') are later formed.
16. A method according to any one of the preceding claims, characterized in that the recesses (r, r') are formed by removing material from the circumferencial surface
with a laser.
17. A traction sheave for an elevator, which comprises a metallic circumferencial traction
surface (4, 4') for at least one rope (3) for transmitting tractive force to a rope
(3), which is set to pass against the circumferential traction surface (4, 4'), characterized in that the circumferential traction surface (4, 4') comprises recesses (r, r') spaced apart
in circumferential direction (x) of the traction sheave (2).