Title:
Cable damper
Kind Code:
A1


Abstract:
Damping arrangement for damping vibrations of cables or ropes, for vibration damping in carrier cables of bridges in particular, with at least one elastic element (5 to 8, 21) for reduction of vibration energy by elastic deformation, wherein said elastic element (5 to 8, 21) is arranged between a plurality of cables (17, 18, 19) to be dampened, in particular, however, between two cables (17, 18) or between said cable (1) to be dampened and a support element (9), as well as a carrier cable arrangement with at least one cable and at least one corresponding damping arrangement.



Inventors:
Petersen, Christian (Ottobrunn, DE)
Application Number:
10/298018
Publication Date:
05/22/2003
Filing Date:
11/15/2002
Assignee:
PETERSEN CHRISTIAN
Primary Class:
International Classes:
E01D19/16; (IPC1-7): E01D19/16
View Patent Images:
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Primary Examiner:
HARTMANN, GARY S
Attorney, Agent or Firm:
PEARNE & GORDON LLP (CLEVELAND, OH, US)
Claims:

What is claimed:



1. A damping arrangement for damping vibrations of cables or ropes, for vibration damping in carrier cables of bridges in particular, with at least one elastic element (5 to 8, 21) for reduction of vibration energy by elastic deformation, wherein said elastic element (5 to 8, 21) is arranged between a plurality of cables (17, 18, 19) to be dampened, at least, however, between two cables (17, 18) or between said cable (1) to be dampened and a support element (9, 25, 26).

2. The damping arrangement as defined in claim 1, wherein said elastic element (21) is arranged in direct contact with said cables (17, 18, 19) and keeps those at a defined distance.

3. The damping arrangement as defined in claim 1 or 2, wherein said damping arrangement in addition includes at least one armoring (20) holding said cables (17, 18, 19) in contact with said elastic element (21).

4. The damping arrangement as defined in one of claims 1 to 3, wherein the distance of said cables (17, 18, 19) is dimensioned by said elastic element (21) such that in case of wind loads an aeration which reduces vibration of said cables (17, 18, 19) is effected in the area not facing the wind.

5. The damping arrangement as defined in claim 1, wherein said support element (9, 25, 26) is arranged in the vicinity of said anchoring point of said cable (1).

6. The damping arrangement as defined in claim 1 or 5, wherein said support element (9) is built at least as part of a protective tube (10) for said anchoring point of said cable (1).

7. The damping arrangement as defined in claim 1 or 5, wherein said support element is embodied as lever (26) resistant to deflection in particular or as anchoring element (25), wherein said lever (26) or said anchoring element (25) are arranged at a point or constructional element stationary with respect to said cable (1), at the bridge deck or a bridge support in particular, namely in particular in the plane of said cable, extending perpendicularly to said bridge deck or said bridge support.

8. The damping arrangement as defined in one of claims 1, 5, 6 or 7, wherein for defined arrangement of said elastic elements (5 to 8) between support element (9, 25, 26) and cable (1) or between cables (17, 18) to be dampened a holding arrangement (22, 22′) is provided for, including holding elements (2 to 4), holding disks or plates in particular, between which said elastic elements (5 to 8) are received.

9. The damping arrangement as defined in claim 8, wherein of said two holding elements (2, 4; 3, 4) of said holding arrangement, which hold between them at least one elastic element (6, 7; 5, 8), one is effective connection with a cable (1, 17) and the other is in effective connection with at least one other cable (countercable) (18) or a support element (9, 25, 26), and namely such that said at least one elastic element (5, 8) during occurrence of cable vibration to be dampened essentially experiences a thrust distortion.

10. The damping arrangement as defined in claim 9, wherein for generation of said effective connection between said cable (1, 17, 18) to be dampened and said holding element (2 to 4) at least one transfer element (24 27) is provided for.

11. The damping arrangement as defined in claim 8 or 9, wherein said holding elements (2 to 4) are formed as annular disks mounted with their outer circumference to said support element (9) and with said inner circumference are solidly connected to said cable (1).

12. The damping arrangement as defined in one of claims 8 to 11, wherein said elastic element (5 to 8) at each of its ends which are arranged on said holding elements (2 to 4) comprises a mounting disk (23) stationarily received in said holding elements (2 to 4) or connected thereto).

13. The damping arrangement as defined in claim 12, wherein said mounting disk (23) is vulcanized or glued to said elastic element (5 to 8).

14. The damping arrangement as defined in one of claims 8 to 13, wherein said holding elements (2 to 4) are fixed to said cable (1, 17, 18), support element (9, 25, 26) and/or transfer element (24, 27) by positive lock, press lock or material lock, by welding, glueing or by pressure seat in particular.

15. The damping arrangement as defined in one of the preceding claims, wherein said elastic elements (5 to 8, 21) are made out of elastomere material, silicone rubber or butyl rubber in particular.

16. The damping arrangement as defined in one of the preceding claims, wherein said damping arrangement includes a casing (29) or a cover.

17. The damping arrangement as defined in one of the preceding claims, wherein the damping effect essentially is caused by an elastic thrust distortion of said elastic elements (5 to 8, 21).

18. A carrier cable arrangement with at least one cable (1, 17 to 19) and at least one damping arrangement as defined in one of claims 1 to 17, with several damping arrangements as defined in claims 1 to 4 or 15 to 17 in particular or at least one damping arrangement as defined in one of the claims 1 or 5 to 17.

Description:

BACKGROUND OF THE INVENTION

[0001] The present invention relates to a damping arrangement for damping the vibrations of ropes or cables, for vibration damping in supporting cables of bridges in particular, as well as a corresponding carrier cable arrangement.

[0002] In bridge construction it. is known e.g. to use carrier cables for supporting bridge sections. Said carrier cables which either can be built as individual cables or as train of cables can be stimulated to vibrate by wind load, by a corresponding traffic load of the bridges or by other influences, e.g. seismic loads. Such vibrations in addition to a possible irritation of the users may result in that such a bridge can no longer be used, in the worst case that such a bridge is destroyed. Therefore, it is necessary to provide for suitable measurements for limiting or avoiding corresponding vibration of the carrier cables.

[0003] For this purpose, the state of art knows several measurements. Beside a mutual coupling of individual parts or cables arranged far away from one another, of the bridge which coupling causes an in total rigid bracing, first of all also due to the low expense and better esthetic impression the application of shock absorber elements, like e.g. hydraulic or friction members, on the cable ends in vicinity of the anchoring positions of the cables is made use of. Said shock absorber elements then mostly are extended in spread arrangement from the cable to be dampened in downward direction to the bridge deck and are anchored there. This causes a very high space requirement so that the bridge in total has to be embodied larger this representing a substantial expense. In addition, the shock absorber elements on basis of hydraulic or friction elements include high wear and in operation are susceptible to corrosion e.g.

SUMMARY OF THE INVENTION

[0004] It is, therefore, the main object of the present invention to make available damping being as simple as possible but also being efficient, of vibrations in cables or ropes, carrier cables of bridges in particular, permitting simple manufacture in particular and also subsequent equipment of the damping arrangement as well as permitting setting of damping answering the demands. In addition, the damping arrangement also is to be room-saving.

[0005] This object is solved by a damping arrangement showing the features of claim 1 as well as a carrier rope arrangement as defined in claim 18. Further preferred embodiments are subject of the depending claims 2 to 17.

[0006] The basic idea of the present invention lies in that elastic elements are provided for, which can absorb vibration energy by elastic deformation. In accordance with the present invention the elastic elements are arranged either between the cables to be dampened or between the cable to be dampened and a support element. In this way, in case of a movement of the cable in relation to a fixed point or a relative movement of the cables with respect to one another a deformation of the elastic elements is caused so that by the elastic deformation energy is absorbed. Herein, it is advantageous for a particularly efficient damping, if the elastic elements due to the vibration to be dampened are subjected to a thrust distortion essentially. According to a further aspect of the invention the damping arrangements in accordance with the present invention are constructed such that this requirement is met.

[0007] In a preferred embodiment in a carrier cable arrangement with several cables at least one, preferably however a plurality of elastic elements, is arranged in direct contact between said cables so that said cables are held at a defined distance. This on one hand has the effect that when said train is bent or displaced with respect to one another a thrust distortion of the elastic element or elements is caused, which again results in an elastic deformation of the elastic element. On the other hand, by the defined mutual distance between the cables it is effected that in case of a wind load an aeration of the side not facing the wind is rendered possible so that Karman transverse vibrations or galloping vibrations, respectively, can be avoided.

[0008] For guaranteeing the contact of the cables with the elastic element or elements, it is advantageous at least in the region of the elastic elements to provide for at least one, preferably however several, two armoring in particular which embraces the elastic element and the cables and thus keeps them together.

[0009] For protecting the damping arrangements with the elastic elements and the armoring against atmospheric influences and, in particular, for maintaining the frictional contact of the cables with the elastic elements in defined manner, it is further advantageous to provide for a casing or a cover in the damping arrangement at least in the area of the elastic elements.

[0010] In an alternative embodiment of said damping arrangement at least one, preferably however several elastic elements are arranged between the cable to be dampened and a support element which preferably is fixed in the vicinity of an anchoring point of the cable. Herein, it proved to be particularly sensible to form said support element as part of a protective tube which usually is provided for close to the anchoring point to protect the cable against damages by atmospheric influences or by vandalism.

[0011] Preferably, the support element can be built as deflection-resistant lever or as anchor member. The lever or anchor element then form a stationary reference point for the swinging cable which is to be dampened. For this reason it is advantageous when using a lever, if the latter is built particularly resistant to deflection.

[0012] When using a lever as support element the stationary reference point by which a damping of the swinging cable can be achieved via the elastic element is brought into direct vicinity of the cable to be dampened so that the elastic elements can be arranged in simple manner. In the alternative embodiment in which the support element is formed by an anchor element, e.g. on the bridge deck, the distance between the cable to be dampened and the anchor point in most cases must be bridged by a transfer element which transmits the vibrations of the cable to the elastic elements which are arranged on the anchor element acting as support element.

[0013] For mounting the elastic elements which can be selected in all embodiments in their number and material selection in accordance with the damping requirements in a defined or alternative manner, respectively, between the support element and the cable or between all cables, it is advantageous to provide for a holding arrangement with holding members which on one hand are connected to the support element and on the other hand to the cable or—in case of coupled cables—to those. The arrangement and embodiment of the holding elements of the holding arrangement therein preferably is to be chosen such that in case of occurrence of the cable vibration to be dampened the elastic elements arranged in said holding arrangement are subjected to a thrust distortion in particular, as thereby a particularly safe and efficient damping is achieved.

[0014] In case that the distance between the cables to be coupled or between the cable to be dampened and the corresponding holding element in the holding arrangement is too large for permitting a direct connection, in advantageous manner connection of the holding elements can be realized via corresponding transfer elements as well, which can correspondingly transmit the vibration to be dampened then.

[0015] In a preferred embodiment, the holding elements preferably are built as annular disks as they then can in simple manner be connected to the support element which advantageously is formed as tube coaxial to the cable, and the cable.

[0016] In order to achieve a solid connection of the elastic elements to the holding elements and/or the holding arrangement, respectively, and for in particular avoid lifting of the elastic elements from the holding elements, it is advantageous to stationarily connect the elastic elements to the holding elements. For this purpose it turned out to be advantageous to provide the elastic elements with an assembling disk which can be vulcanized to or glued to the elastic element or the end of the elastic element, respectively, which is to be connected to the holding element.

[0017] Fixation of the holding elements to the cables, the support elements or the transfer elements can be effect by any form of positive lock, frictional lock or material lock. Herein, however, welding, glueing and positive arrangement, by pressure seat on the cable in particular, proved to be most suitable.

[0018] The elastic elements preferably are made from an elastomere material, butyl or silicone rubber in particular, since the latter is particularly characterized by its low dependence on temperature of its material properties. Furthereon, the elastic elements provide the advantage that they are not susceptible to corrosion and they show their effect in any direction.

[0019] It is particularly advantageous in the damping arrangement in accordance with the present invention that a simple assembly and inspection of the damping arrangement is rendered possible and simple exchange in particular, of the elastic elements is given so that perhaps also reaction is possible on changed damping requirements by exchange of the elastic elements. In addition, the damping arrangement in accordance with the present invention to a great extent is free of wear and does not include corrosion problems. The demands for a room-saving embodiment have been accounted for, too, particularly if thinking of the embodiments in which a lever or an anchoring point are used as support element in the cable plane directly below the cable to be dampened so that a spread anchoring of the cables can be done without.

BRIEF DESCRIPTION OF DRAWINGS

[0020] Further particulars, advantages and features of the present invention will become obvious from the following detailed description of the embodiments by means of the attached drawing. The purely schematic drawing herein shows in

[0021] FIG. 1 a longitudinal section through a damping arrangement with a cable;

[0022] FIG. 2 a cross sectional view of the outer annular disk of FIG. 1;

[0023] FIG. 3 a cross sectional view of the inner annular disk of FIG. 1;

[0024] FIG. 4 a lateral view of a further damping arrangement;

[0025] FIG. 5 a cross-sectional view of the damping arrangement of FIG. 4;

[0026] FIG. 6 a schematic view of the aeration effect of the damping arrangement of FIG. 4 in case of lateral wind load;

[0027] FIG. 7 a longitudinal sectional view of a damping arrangement similar to FIG. 1 which, however, is arranged between to cables to be dampened;

[0028] FIG. 8 a longitudinal sectional view of the embodiment of FIG. 7, in which the damping arrangement of FIG. 7, however, is arranged by transfer elements on the sides;

[0029] FIG. 9 a series of partial views showing the arrangement of a damping arrangement under FIG. 1 or FIG. 7 using levers and transfer elements;

[0030] FIG. 10 a sectional view of a damping arrangement in accordance with FIG. 1 in which the arrangement of the elastic elements is modified;

[0031] FIG. 11 a further view of the damping arrangement of FIG. 10;

[0032] FIG. 12 a cross-sectional view of an embodiment of the damping arrangement under FIG. 7 in case of arrangement on the bridge deck using a transfer element;

[0033] FIG. 13 a lateral view of the embodiment under FIG. 12;

[0034] FIG. 14 a three-dimensional view of a casing for the embodiment of FIG. 12;

[0035] FIG. 15 a cross-sectional view of a damping arrangement under FIG. 12, however, with several elastic elements; and in

[0036] FIG. 16 a lateral view of the embodiment of FIG. 15.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT

[0037] In FIG. 1 a longitudinal section of a first embodiment of a damping arrangement in accordance with the present invention is shown, in which via an accurately fitting sleeve 11 an annular disk 4 comprising in total (see FIG. 3) on both sides six recesses for accommodating elastic elements 5, 6, 7 and 8 is arranged on a cable 1. Said elastic elements 5 to 8 in the damping arrangement of FIG. 1 in addition are held in two outer annular disks 2 and 3 which on their insides also comprise 6 recesses 13 (see FIG. 2) which can engage into said elastic elements 5 to 8. Said outer annular disks 2 and 3 are solidly connected to a support element 9 in form of a tubular section by glueing or welding, said support element again in the shown embodiment being arranged in a protective tube 10 protecting said cable 1 in the vicinity of the anchoring point against external influences. Said annular disks 2 to 4 together form the holding arrangement 22. By the arrangement shown in FIG. 1, of said elastic elements 5 to 8 vibrations in any direction can be absorbed by the elastic deformation of said elastic elements, the concentrical arrangement of the holding arrangement and said protective tube 10 serving as support element, around said cable 1 essentially a load of said elastic elements 5 to 8 by thrust distortion being guaranteed. By the arrangement of the damping arrangement in said protective tube 10 all parts are protected against weather and installation or removal, respectively, of said damping arrangement or said elastic elements, respectively, is easily to be managed. In this way by the selection of the number and of the material properties of said elastic elements 5 to 8 the damping effect of said damping arrangement can be easily adjusted in accordance with the demands.

[0038] FIG. 2 shows the inner side of an outer annular disk 2 or 3 in cross-sectional view. Here, said recesses 13 for accommodation of said elastic elements 5 to 8 can be clearly seen, those being uniformly arranged over the circumference of said annular disk. Said elastic elements 5 to 8 can either be inserted into said recesses 13 directly or via mounting disks provided for on said elastic elements, said mounting disks being vulcanized or glued to said elastic elements. For more simple manufacture and assembly said annular disk can be of multiple-part construction, two-part construction in particular. The cable passage 12 in correspondence with the embodiment of FIG. 1 is somewhat larger than the diameter of said cable 1 so that said cable 1 can move in said cable passage 12 without contact to said annular disks 2 or 3.

[0039] Similar to the representation of FIG. 2, in FIG. 3 a lateral view of the centric annular disk 4 is shown which in the shown embodiment also is made in two-part construction. Of course, said annular disk as well as the two-part annular disks 2 and 3 also comprises corresponding means for connecting the parts of said annular disks, which, however, for sake of simplicity, are not shown. In correspondence with said recesses 13 at said outer annular disks 2 and 3 said annular disk 4 comprises recesses 14 which, however, are provided for on two sides. Said annular disk 4 provided for accurately fitting arrangement on said cable 1, correspondingly comprises a cable passage 15 on whose margin 16 said sleeve 11 is arranged by which said annular disk 4 is fixed on said cable 1 with accurate fit or press fit.

[0040] Another embodiment of said damping arrangement is shown in FIG. 4 showing a lateral view of a train out of several cables 17 to 19 (19 not shown). As can be better seen in the cross-sectional view in FIG. 5, said train in total includes 3 cables 17 to 19, between which said elastic element 21 is arranged such that said cables 17 to 19 mutually show a given distance. For keeping said cables 17 to 19 in contact with said elastic element 21, an armoring 20 is provided for which is arranged in the area of said elastic element 21 around said train of cables 17 to 19. As can be seen in FIG. 4, preferably for each damping arrangement two armoring 20 are provided for. Along the entire train usually a plurality of said damping elements shown in FIGS. 4 and 5 are provided for. Said damping arrangements under FIGS. 4 and 5 on one hand have the effect that a bending of said train with cables 17 to 19 causes a mutual displacement of said cables, which again effects a thrust distortion of said elastic element which thus absorbs energy by elastic deformation. In addition, said plurality of damping arrangements along said cable train has the effect that said cables 17 to 19 are present at a given distance to one another so that in case of a wind load an aeration in the region not facing the wind behind said train results due to the slots between said cables, this resulting in that Karman transverse vibrations and galloping vibrations can be avoided.

[0041] This is schematically shown in FIG. 6 in which the direction of wind is shown by the arrows and the turbulences in the region not facing the wind behind said train of cables 17 to 19 are indicated schematically.

[0042] A further embodiment of a damping arrangement in accordance with the invention is shown in FIG. 7. The damping arrangement 22′ shown here in its construction essentially corresponds to said damping arrangement 22 of FIG. 1. However, it differs from said damping arrangement of FIG. 1 in such way that said damping arrangement is not arranged in coaxial relation to the cable to be dampened and a support element but rather is arranged between two cables 17 and 18 to be dampened. For this reason, said holding elements 2 to 4 no longer need to be built as annular disks but can have any suitable shape, can be formed plate-like or rod-like in particular. Said holding elements 2 to 4 in the shown embodiment of FIG. 7 are directly connected to said cables 17 and 18, where all suitable possibilities of connection, like flange connection, can be chosen.

[0043] Between said holding elements 2 to 4, connected to different cables also in said damping arrangement 22′ elastic elements 5 and 6 are provided for, wherein independently from the shown embodiment starting with one elastic element any number of elastic elements is possible.

[0044] The arrangement of said elastic elements 5 and 6 in said holding elements 2 to 4 represents a further difference of said damping arrangement 22′ to said damping arrangement 22 of FIG. 1. In the embodiment of FIG. 7 said elastic elements 5 and 6 on their ends by which they are received in said holding elements 2 to 4, comprise mounting disks or plates 23 solidly received or clamped, respectively, in said holding elements 2 to 4. This provides—as compared to the embodiment of FIG. 1—the advantage that by said elastic elements 5 and 6 in case of a load of said damping arrangement 22′ in direction of the cable axis avoid lifting of said elastic elements 5 and 6 from said holding elements 2 and 4 and a possible jamming caused thereby, within said damping arrangement is avoided. The stationary clamping of said mounting plates 23 can be realized in any manner common to the man skilled in the art. An embodiment is shown in FIG. 10 and will be described lateron.

[0045] At first, however, indication is made to FIG. 8 showing a further embodiment of the arrangement of said damping arrangement 22′ between two cables 17 and 18. Beside the direct mounting of said holding elements 2 to 4 at said cables 17 and 18 namely also in case of cables being arranged with a larger distance to one another, the arrangement of said damping arrangement 22′ via transfer elements 24 is possible. Said transfer elements 24 which in most simple case consist of rods 24 mounted to said cables 17 and 18 using collars 29, for transmission of vibrations are connected to said corresponding holding elements 2 to 4.

[0046] FIG. 9 in purely schematical way shows a plurality of different possibilities of use for a damping arrangement 22′ in accordance with the embodiment of FIG. 7. As can be seen in the partial pictures from left to right, said damping arrangement 22′ can be arranged at the cable 1 to be dampened directly, whereas the support point with respect to which the vibration is absorbed via said damping arrangement 22′ is formed by a lever 26 resistant to deflection, which e.g. is arranged in the anchoring ping 25 on said bridge deck. Herein, said lever 26 can be fixed in said anchoring point 25 with a great variety of angles with respect to said bridge deck, since a suitable adjustment with respect to said cable 1 to be dampened also is possible using said damping element 22′.

[0047] Beside the use of a lever 26 resistant to deflection for arrangement of said damping arrangement 22′ between a cable 1 to be dampened and a fixed point or support element, in addition a transfer element 27 can be provided for which transmits the vibrations of said part 1 onto said damping arrangement 22′. Correspondingly, said lever 26 resistant to deflection can also be done without completely and said damping arrangement can be provided for on said anchoring point 25 directly. The two last partial pictures of FIG. 9 then show further more complex manners of mounting, in which said lever 26 or said transfer element 27, respectively, show more complex forms as compared to the simple rods of the preceding embodiments.

[0048] The particularly preferred possibility of arranging said damping arrangement 22′ via a lever 26 or a transfer element 27 in such manner directly below said cable, i.e. in the cable plane perpendicular to said bridge deck is not shown in FIG. 9. As compared to the state of art where bracings of carrier cables of bridges usually are spread, i.e. in V shape, a direct mounting of said damping arrangement via a lever 26 resistant to deflection or a transfer element 27 directly below said cable 1 to be dampened is particularly room-saving, since then no additional room on said bridge deck is required.

[0049] FIG. 10 shows an embodiment of a damping arrangement 22 or 22′ in accordance with FIG. 1 or FIG. 7, respectively, in which said elastic elements 5 and 6 are solidly arranged in said receiving elements 2 to 4 using mounting plates 23. As can be seen in FIG. 10, e.g. said elastic element 5 is solidly clamped in said holding element 3 using a mounting plate 28 which can e.g. be screwed to said holding element 3, in a recess of said holding element 3 that a lifting of said mounting plate 23 from said holding element 3 is impossible.

[0050] As can be seen from the arrangement of said elastic element 6 on said holding element 2, by this manner of mounting also a particularly simple removal or exchange, respectively, of said elastic elements is possible. In said holding element 2 namely said mounting plate 28 is removed so that it can be seen that said elastic element 6 can easily be lifted from said holding element 2.

[0051] In the embodiment of FIG. 10 said holding element 4 is realized in two-part manner with the two parts 4a and 4b which can be mutually screwed such that two opposing elastic elements 5 and 6 simultaneously with one another are mounted in said holding element 4.

[0052] FIG. 11 shows the embodiment of FIG. 10 is general view and in correspondence with the application example of FIG. 1.

[0053] FIG. 12 shows a lateral cross-sectional view of said damping arrangement 22′ in a example of application in which said damping arrangement 22′ is arranged on an anchoring point 25 on said bridge deck directly, whereas the connection to the cable to be dampened is established by a transfer element 27.

[0054] In FIG. 13 the embodiment of FIG. 12 can be seen in a lateral view rotated by 90 degrees, wherein the arrangement of said mounting plates 23 can be seen in whose center the arrangement of said cylindrical elastic elements 5 and 7 is indicated.

[0055] FIG. 14 is a three-dimensional representation of the embodiment of FIGS. 12 and 13, wherein it can be seen here that the lower end of the ashlar transfer element 27 forms a casing 29 in which said damping arrangement 22′ is accommodated.

[0056] FIGS. 15 and 16 describe a further embodiment which is similar to the embodiment of FIGS. 12 and 13. Said damping arrangement shown in FIGS. 15 and 16, however, comprises not only four elastic elements 5 to 8, like in the embodiment of FIGS. 12 and 13, but in total 8 elastic elements. This makes obvious that by the damping arrangement in accordance with the present invention depending on the demand a correspondingly adapted damping can be realized.





 
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