Patent Publication Number: US-6908284-B2

Title: Fan attachment with dynamic out-of-balance equalization

Description:
BACKGROUND OF THE INVENTION 
   Due to environmental considerations, great efforts are being made to eliminate sources of noise in motor vehicles to the greatest extent possible. In addition to tires and internal combustion engines, other acoustic sources are add-on components of the internal combustion engine, e.g., engine cooling fans. With acoustic sources of this nature, a general distinction is made between airborne noise vibrations and the occurrence of structure-borne noise. The occurrence of structure-borne noise can be perceived in the form of inertial force-excited vertical vibrations in the steering wheel of a motor vehicle. 
   PRIOR ART 
   With engine cooling fans that are common today, a compensation of the static imbalance is usually carried out so that the permissible limit values can be met. In the case of fans, which often have a flat design, a compensation of the dynamic imbalance (couple imbalance) is not possible at all or only at great expense, since the measurement itself causes problems due to the low flat clearance, and it would not be possible to securely attach the correction masses required to compensate the couple imbalance to the labile fan blades. As a result, it is accepted practice for engine cooling fans to be delivered with non-defined dynamic imbalance. Depending on the respective installation situation in the vehicle, the structure-borne noise produced by the dynamic imbalance can result in complaints about vibrations perceived in the passenger compartment. The remaining remedies, such as installing damping elements in the transmission path, or reworking plastic fans in order to reduce their imbalance present upon delivery, are costly and they do not necessarily result in a satisfactory reduction of vibrations. 
   The inertial forces—static and dynamic imbalances—are caused by inhomogeneous distributions of mass of the rotating rotor/armature assemblies and fans, and by tolerances of form and position relative to the rotation axis of the drive. Tolerances of form and position cause the rotation axis and main axis of inertia to no longer coincide. A parallel displacement between rotation axis and main axis of inertia, e.g., of a cooling fan having a fan wheel mounted on the armature or rotor shaft results in a static imbalance, while a main axis of inertia tilted relative to the rotation axis can produce a centrifugal moment, the effects of which are comparable to a couple imbalance or dynamic imbalance. 
   ADVANTAGES OF THE INVENTION 
   The advantages of the means for attaining the object of the invention proposed according to the invention are seen mainly in the fact that a soft connection of the axial fan to the armature or rotor of an electrical drive permits the axial fan to orient itself in the direction of the rotation axis as rotational speed increases. As a result, the disturbance variable, i.e., the imbalance moment, is automatically reduced by the rotation of the axial fan as the rotational speed increases. The influence of tolerances of form of the axial fan wheel drops off substantially with regard to the dynamic centrifugal moment, since a self-orientation of the axial fan wheel with regard to the rotation axis takes place. As a result, tolerances of form and position of the axial fan wheel are automatically compensated as well with regard to the dynamic imbalance. 
   Since the dynamic imbalance of an axial fan is clearly dominated by the dynamic imbalance of the axial fan wheel, a two-plane imbalance compensation with the armature and rotor of the electrical drive can be foregone. This, in turn, presents an opportunity for substantial savings, since the processing steps required to obtain two-plan imbalance compensation can now be eliminated entirely. The armature balancing can be foregone entirely, if necessary, by limiting the imbalance compensation to a purely static balancing of an axial fan on the axial fan wheel. 
   Due to the soft embodiment of the hub of the axial fan wheel, and/or the connection point of the axial fan wheel with the armature or the rotor shaft, the installation of additional damping systems that take up precious space can be foregone. The modifications of the hub of the axial fan wheel with regard to increasing flexural softness can also be carried out in simple fashion and very cost-effectively within the framework of reworking of engine cooling fans that have already been delivered. 

   
     SUMMARY OF THE DRAWINGS 
     The invention will be described hereinbelow with reference to drawings. 
       FIG. 1  shows an axial fan wheel, the main axis of inertia of which is tilted relative to the rotation axis, 
       FIG. 2  shows the inclination of the axial fan wheel on a substitute model of the axial fan wheel, 
       FIG. 3  shows the inclination δ of the axial fan at rotational speed ω=0, 
       FIG. 4  shows the forces and moments acting on the substitute model of the axial fan, and 
       FIG. 5  is the side view of an axial fan with electrical drive, and 
       FIG. 6  is the top view of the hub of the axial fan wheel according to the depiction in  FIG. 5 , 
       FIG. 7  shows a further exemplary embodiment of a flexurally soft mounting of an axial fan wheel on a drive, 
       FIG. 8  shows a third exemplary embodiment of a flexurally soft coupling of an axial fan wheel to a drive, 
       FIG. 9A  shows a fourth exemplary embodiment of a flexurally soft coupling of an axial fan wheel to a drive with range of displacement, and 
       FIG. 9B  shows the coupling point of axial fan wheel and drive according to the depiction in  FIG. 9  as a detail shown in an enlarged view. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1  shows an axial fan wheel, the main axis of inertia of which is tilted relative to the rotation axis. 
   An axial fan wheel  1  comprises fan blades  2  and  3  essentially situated on its outer circumferential region, which said fan blades are mounted on the circumference of a hub region  4 . An axial fan wheel  1  according to the depiction in  FIG. 1  is preferably manufactured as a plastic injection-molded part. An axial fan wheel of this type is supported on an armature or rotor shaft of an electrical drive not shown in  FIG. 1 , and it is set in rotation via the electrical drive. The axial fan wheel  1  has a main axis of inertia labelled “x—x” in the depiction according to FIG.  1 . Another axis of inertia, labelled “y—y”, extends at a right angle to said main axis of inertia. 
   A rotation axis coordinate system  8 , characterized by the rotation axis ξ—ξ and the axis η—η extending at a right angle thereto, is displaced relative to the aforementioned axes of inertia x—x and y—y. The rotation axis coordinate system  8  is tilted slightly compared to the coordinate system formed by the axes of inertia. The rotation axis ξ—ξ is turnably supported in bearings, one of which is designed as a fixed bearing  5  that absorbs axial and radial forces, and the other bearing  6  of which is designed as a movable bearing capable only of absorbing radial forces and permitting an axial displacement of the rotation axis ξ—ξ of the axial fan wheel  1 . 
   The center of gravity, in which the axes of inertia x—x and y—y of the axial fan wheel  1  intersect, is labelled with reference numeral  7 . ω represents the angular velocity at which the axial fan wheel—driven by an electrical drive not shown here—rotates around the rotation axis ξ—ξ. 
     FIG. 2  shows the inclination of an axial fan wheel with reference to a substitute model of an axial fan wheel. 
   According to the depiction shown as a model in  FIG. 2 , the axial fan  1  is idealized as a rigid disk, while its region of connection to the rotation axis ξ—ξ is modelled as an axially-acting spring arrangement  9  and  10 . 
   According to the depiction in  FIG. 2 , the imbalance moment J ξη ·ω 2  is directed in such a manner that the fan&#39;s main axis of inertia x—x is brought into overlap with the rotation axis ξ—ξ, so that the torque delivered by the electrical drive not shown here can be utilized by the embodiment of the connection of the fan modelled as a rigid disk to its hub region in order to reduce the dynamic imbalance given by the centrifugal moment J ξη ·ω 2 . In the case of the modelled depiction according to  FIG. 2 , the rotation axis ξ—ξ is supported in a fixed bearing  5  and in a movable bearing  6 . 
   The axial force F Ax  ( 11 ) acts on the fixed bearing  5  in the axial direction, and the radial force F Ay  ( 12 ) acts on the fixed bearing  5  in the radial direction. In contrast, the movable bearing  6  only absorbs forces in the radial direction, characterized by F By  ( 13 ). The angle between the main axis of inertia x—x of the axial fan wheel  1  and its rotation axis ξ—ξ is labelled with δ. 
   The inclination δ of the axial fan wheel at rotational speed ω=0 is shown in the depiction according to FIG.  3 . 
   In the case of an axial fan wheel, centrifugal moments produce considerable forces and moments depending on the rotational speed. With a maximum centrifugal moment of 45000 gmm 2 , for example, the imbalance moment characterized as follows acts on the axial fan wheel  1  at a speed of 2500 rpm: 
       M   =         J     ξ   ⁢           ⁢   η       ·     ω   2       =       45000   ⁢           ⁢       gmm   2     ·       (         2500   ·   2     ⁢           ⁢   π     60     )     2       ⁢     s     -   2         =     3.08   ⁢           ⁢   Nm             
 
   According to the depiction shown in  FIG. 3 , the moment acts in the direction of the arrow on an axis of the axial fan wheel—modelled as a rigid disk—extending at a right angle to the plane of the drawing. As a result of this moment, the axial fan wheel  1  is displaced by the angle α into the position labelled with δ−α and with  1 ′. As a result, the main axis of inertia x—x of the axial fan wheel  1  moves closer to the position of the rotation axis ξ—ξ, around which the axial fan wheel  1  rotates at the angular velocity ω. Based on the calculation shown hereinabove, it become clear that the re-alignment of the main axis of inertia x—x with the position of the rotation axis ξ—ξ increases as rotational speed increases, since said rotational speed is squared in the moment calculation. This means that, as rotational speed increases, the angle α increases and, as a result, the inclination δ at ω=0 is reduced continually until, in the ideal case, the angle δ−α equals zero. In this case, the main axis of inertia x—x of the axial fan wheel  1  coincides with its rotation axis ξ—ξ. 
   The forces  15  labelled with F c  act on the hub region  4  of the axial fan wheel  1  modelled as a rigid disk. Said forces act on the rotation axis ξ—ξ of the axial fan wheel  1  around the lever arm a—also labelled with reference numeral  14 —and counteract the moment produced by the centrifugal moment J ξη ·ω 2 . As rotational speed increases, the axial fan wheel  1  is pushed in the direction of the rotation axis ξ—ξ as a result of the centrifugal moment J ξη ·ω 2 . It follows from this that, when the hub region is designed to be as flexurally soft as possible, that is, with a flexurally soft connection of the hub region  4 , 27 of the axial fan wheel  1  with its rotation axis ξ—ξ, the imbalance moment that occurs and that decreases with the rotational speed can be utilized to re-align the main axis of inertia x—x of the axial fan wheel  1  in the rotation axis ξ—ξ of said axial fan wheel with tilting at ω=0. 
     FIG. 4  shows the forces and moments acting on the substitute model of the axial fan. 
   The inclination of the axial fan wheel  1  modelled as a rigid disk  1  that occurs at a given speed ω≠0 is characterized by δ minus α. To obtain re-alignment, that is, to make the main axis of inertia x—x coincide with the rotation axis ξ—ξ, the centrifugal moment J ξη ·ω 2  is utilized by the soft connection of the hub region  5  to the rotation axis ξ—ξ as rotational speed increases. In order to obtain a return of the axial fan wheel  1  modelled as a rigid disk in the depiction according to  FIG. 4  to an angular position in which the angle difference δ−α equals zero, a connection of the hub region  4  to the rotation axis ξ—ξ should be designed that is as flexurally soft as possible and enables a self-orientation of the axial fan wheel  1 . 
   The moment relationship for the axial fan wheel  1  that occurs as far as the axial fan wheel  1  is concerned is:
 
Σ M= 0, that is, J ξη ·ω 2 ·ω 2   =F   c   ·a. 
 
   If this relationship is fulfilled, the axial fan wheel  1  rights itself in its rotation around the rotation axis ξ—ξ in such a manner that the rotation axis ξ—ξ and the main axis of inertia x—x of the axial fan wheel  1  coincide. The axial and radial forces acting on the bearings  5  and  6  of the rotation axis ξ—ξ through the axial fan wheel  1  are characterized with the reference numerals  11 ,  12  and  13  in the depiction according to FIG.  4 . 
   The depiction according to  FIG. 5  is the side view of an axial fan with electrical drive. 
   According to the side view in  FIG. 5 , the axial fan wheel  1  comprises a number of fan blades  2  and  3  in its outer circumferential region, which said fan blades are integrally molded on the circumference of a hub region  4 . In the center of the hub region  4 , the axial fan wheel  1  is interconnected with a driven shaft  20  of an electrical drive  21 . The electrical drive  21  is accommodated in a housing  22  and partially extends into the pot-shaped hub region  4  of the axial fan wheel  1  in order to shorten the axial length of the fan arrangement according to the depiction in  FIG. 5. A  disk  23  composed of flexurally soft, elastic material can be mounted on the driven shaft  20  of the electrical drive  21 , which said disk is interconnected with a region  27 —that is turned inwardly in the shape of a plate or well—of the hub region  4  of the axial fan wheel  1 . Fastening screws  24  serve to interconnect the elastic disk  23  mounted on the driven shaft  20  of the electrical drive  21  with the well-shaped hub plate  27  of the hub region  4 . The fastening screws  24  can be equipped with spring elements  30  in order to increase the flexural softness of the connection between the elastic disk  23  and hub plate  27  in the hub region  4  of the axial fan wheel  1 . The spring elements  30  can be provided on the fastening screws  24  either in the region of the hub plate  27  turned inwardly in the manner of a well, or between the fastening screws  24  and the elastic disk  23 . 
   Retaining devices are labelled with reference numeral  25 ; they can be used to fasten the housing  22  of the electrical drive  21  to a radiator assembly in the engine compartment of a motor vehicle. 
   A balancing weight is labelled with reference numeral  26 ; it is accommodated on a fan blade  3  on the circumference of the hub region  4  of the axial fan wheel  1  according to the depiction in  FIG. 5  in order to statically balance the axial fan wheel  1 . 
   Hub and disk bores  28  are formed in the hub and disk at the connection of the hub plate  27 —turned inward in the manner of a well—in the hub region  4  of the axial fan wheel  1  and the elastic disk  23 , which said bores accommodate the fastening screws  24  with optional spring elements  30  accommodated on them. The hub bores  28  are arranged on a divided circle of hub bores  29 , which is shown in  FIG. 6  in greater detail. 
   The depiction according to  FIG. 6  shows the top view of the hub of the axial fan wheel according to FIG.  5 . 
   The pot-shaped hub region  4  of the axial fan wheel according to the depiction in  FIG. 5  comprises slits  31  extending in the radial direction that are offset here by 120° relative to each other on the circumference of the hub region. The slits  31  are designed with a length  32  that exceeds the respective slit width  33  by a multifold amount. In addition to the radial slits  31  arranged here offset at a 120° angle relative to each other, the hub region  4  of an axial fan wheel  1  can also be developed with 4, 5, 6 or an even higher number of radial slits  31 . Forming the radial slits  31  in the wall of the hub region  4  that lies in the plane of the drawing of the depiction according to  FIG. 6  enables a self-alignment of the axial fan wheel  1  by the centrifugal moment J ξη ·ω 2  to be achieved in which the main axis of inertia x—x of the axial fan wheel  1  coincides with its rotation axis ξ—ξ. Next to a formation of radial slits  31  in the hub region  4  of the axial fan wheel  1 , the hub bores  28  in the hub region  4  mentioned hereinabove in conjunction with  FIG. 5  can be formed on a divided circle of screw connections  29 , the diameter of which is less than half the diameter of the hub region  4  of the axial fan wheel  1 . The further the hub bores  2 —only three of which are arranged on the divided circle of screw connections  29  in the depiction according to FIG.  6 —are located in the direction of the bore  34  that is penetrated by the driven shaft  20  of the electrical drive  21 , the greater the flexural softness that occurs in the hub region  4  of the axial fan wheel  1 , and, when the axial fan wheel  1  rotates around the rotation axis ξ—ξ at angular velocity c, said flexural softness promotes self-alignment and compensation of tolerances of form and position of the axial fan wheel  1  produced using a plastic injection-molding procedure. 
   A further possibility for obtaining a flexurally soft connection of the hub region  4  with the driven shaft  20  of an electrical drive  21  is to reduce the material strength in the hub region  4  in the region of the hub plate  27  turned inwardly in the manner of a well. Furthermore, a flexurally softer connection of the hub region  4  to the driven shaft  20  of the electrical drive  21  can be obtained by forming spring elements on the spring elements  24  that interconnect the elastic disk  23  and the hub plate  27 —turned inwardly in the manner of a well—of the hub region  4 , which said spring elements produce spring moments F c ·a depending on the displacement that counteract the centrifugal moment J ξη  that increases as rotational speed increases. If the two moments mentioned hereinabove are in equilibrium, the axial fan wheel  1  is aligned in such a manner that its main axis of inertia x—x coincides with the rotation axis ξ—ξ, and no vibrations can be transmitted by means of structure-borne noise to other components in the engine compartment of a motor vehicle, or to the passenger compartment of a motor vehicle. 
     FIG. 7  shows a further exemplary embodiment, according to the invention, of a flexurally soft mounting of an axial fan wheel on a drive. 
   According to the depiction in  FIG. 7 , an elastic driver  23  and a hub plate  27  of the axial fan wheel  1  interconnected with the elastic driver  23  are mounted on the armature shaft  20  of an electrical drive not shown here. In the exemplary embodiment according to  FIG. 7 , the elastic driver  23  is provided with a profile  50  configured in the shape of an “S” that extends on the elastic driver  23  in its radial direction. The hub plate  27  of the axial fan wheel  1  is screwed together via fastening screws  24  on fixing threads of the elastic driver  23  in the region of the divided circle of screw connections  29 . A spacer bush  37  is installed between the screw heads of the fastening screws  24  and the transversely-extending end surface of the driver  23  composed of elastic material. Said spacer bush rests with a bearing surface  39  on the flat end face of the driver  23  composed of elastic material. A circumferential recess  35  is accommodated on the hub plate  27  in the region of the spacer bush  37 , in which an elastic element is recessed. As depicted in  FIG. 7 , for example, the elastic element  36  can be accommodated as an O-ring that encircles the spacer bush  37 . In its non-deformed state, that is, in its non-loaded state, the O-ring recessed in the circumferential recess  35  permits a displacement “s” that is identified in the depiction according to  FIG. 7  with reference numeral  38 . This means that the hub plate  27  of the axial fan wheel can move around the tilt angle δ sketched in  FIG. 7  due to the fact that the spacer element  36  recessed in the recess  35  creates a flexurally soft connection between the elastic driver  23  and the hub plate  27  of the axial fan wheel  1 . 
     FIG. 8  shows a third exemplary embodiment of a flexurally soft connection of an axial fan wheel to a drive. 
   The depiction according to  FIG. 8  also shows a driver  23  composed of elastic material and provided with an S-shaped profile, and a hub plate  27  interconnected with said driver via fastening screws  24 . In deviation from the exemplary embodiment shown in  FIG. 7 , the third exemplary embodiment shown according to  FIG. 8 , a corrugated washer  40  composed of metallic material is recessed in the circumferential recess  35  on the hub plate  27  of the axial fan wheel. The corrugated washer  30  composed of metallic material and recessed in the circumferential recess  35  also enables a flexurally soft connection of the hub plate  27  of the axial fan wheel  1  to the driver  23  composed of elastic material. The depiction according to  FIG. 8  shows that a displacement path “s” exists as a result of the corrugated washer  40  shown in the resting state between the flat surfaces of the hub plate  27  and the elastic driver  23 , which said displacement path is labelled with reference numeral  38  in the depiction according to  FIG. 8 , in analogous fashion to the depiction according to FIG.  7 . By means of the displacement “s”, it is ensured that the hub plate  27  with axial fan wheel  1  developed thereon can move by the amount represented by the angle δ, which ensures that the hub plate  27  can move relative to the elastic driver  23  mounted on the armature shaft  20 . The fastening screws  24 , with which the hub plate  27  of the axial fan wheel  1  is interconnected with the flat end face of the elastic driver  23 , are arranged in the divided circle of screw connections  29 . 
     FIG. 9A  shows a fourth exemplary embodiment of a flexurally soft connection of an axial fan wheel on the drive with a range of displacement. 
   The axial fan wheel  1  according to the depiction in  FIG. 9A  is mounted on the armature shaft  20  of an electrical drive  21  with a bush element  42  installed therebetween. The electrical drive  21  is mounted on a structural element of a vehicle via retaining elements  25  shown here in a schematic representation. The axial fan wheel  1  comprises fan blades  2  in which balancing weights  26  can be located. The retaining elements  25  are situated on the housing  22  of the electrical drive  21  at an angle of 120° relative to each other, for example. The hub plate  27  of the axial fan wheel  1  partially surrounds the electrical drive  21 . The region labeled with the letter Y in  FIG. 9A  is shown as an enlarged detail in the depiction according to FIG.  9 B. 
   In the depiction according to  FIG. 9B  it is clear that a bush element  42  is accommodated in the region of a bearing area  46  of the armature shaft  20  of the electrical drive  21 . The bush element  42  is pressed against a locating ring  47  by means of a tensioning element  43  also bearing against the armature shaft  20  in the region of an annular groove  45 . The locating ring  47  completely encircles the armature shaft  20  of the electrical drive  21 . The tensioning element  43 , which can be designed as a clamping disk, for example, bears with a shoulder against a flank of an annular groove  45  developed in the armature shaft  20 . while the shoulder of the tensioning element  43  extending further outward bears against the end face formed by the bush element  42  and the hub plate  27  of the axial fan wheel  1 . The hub plate  27  and the bush element  42  are interconnected via fastening screws  24 . The bush element  42  comprising a support  44  is placed by means of the tensioning element  43  in the axial direction against a bearing surface  49  on the locating ring  47 . As a result, the bush element  42  is secured in the axial direction. 
   The armature shaft  20  of the electrical drive  21  comprises a bearing area  46  on which the support  44  of the bush element  42  rests. The support  44  represents a tilting point of the bush element  42  tiltable in the radial direction and secured on the armature shaft  20  in the axial direction. Due to the fact that the bush element  42  can move relative to the bearing area  46  of the armature shaft  20 , an inclination of the hub plate  27 —and, therefore, the axial fan wheel  1 —mounted on the tiltably supported bush element  42  can take place within the range of the permitted tilting play. Dynamic imbalances that occur are automatically compensated by means of this seating of the bush element  42 , acted upon by a tensioning element  43  when the armature shaft  20  of the electrical drive  21  rotates. 
   The required tilt angle can be calculated from the expected dynamic imbalance of the fan. This explained briefly with reference to an example calculation. In the case of a fan with 25000 gmm 2  expected dynamic imbalance, the soft tilt angle required can be calculated using the equation 
               ⁢       U     d   ⁢           ⁢   yn       =             J   x     -     J   y       2     ·   2     ⁢           ⁢   sin   ⁢           ⁢   δ           
         From   ⁢           ⁢   this     ,       it   ⁢           ⁢     follows   :           ⁢     
     ⁢           ⁢   δ       =         1   2     ·   arcsi     ⁢           ⁢     n   (       2   ·     U     dy   ⁢           ⁢   n           Jx   -   Jy       )         ,       
 
with a fan diameter of 390 mm and a fan weight of 463 g: 
         Jx   -   Jy     =       m   ⁢       r   2     4       =       463   ⁢           ⁢   g   ⁢         195   2     ⁢           ⁢     mm   2       4       =       4401   ·     10     3   ⁢                 ⁢           ⁢     gmm   2               
         which   ⁢           ⁢   results   ⁢           ⁢     in   :     
     ⁢   δ       =           1   2     ·   arcsi     ⁢           ⁢     n   (       2   ·     U     dy   ⁢           ⁢   n           Jx   -   Jy       )       =         1   2     ·   arcsi     ⁢           ⁢     n   (         2   ·   25000     ⁢           ⁢     gmm   2           4401   ·     10   3       ⁢           ⁢     gmm   2         )             
 
   The calculated angle of 0.32° corresponds to a soft displacement of s=50·sin 0.32°=0.28 mm, assuming a divided circle of screw connections 29 of 50 mm. 
   Based on this example calculation for the given example and assuming the stated data, the displacement path “s” labelled with reference numeral  38  is approximately 3/10 mm. 
   
     
       
         
             
           
             
                 
             
             
               List of Reference Numerals 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
             
          
             
                 
                1 
               Axial fan wheel 
             
             
                 
                1&#39; 
               Axial fan wheel in rotation 
             
             
                 
                2 
               Fan blade 
             
             
                 
                3 
               Fan blade 
             
             
                 
                4 
               Hub region 
             
             
                 
                5 
               Fixed bearing 
             
             
                 
                6 
               Movable bearing 
             
             
                 
                7 
               Center of gravity 
             
             
                 
                8 
               Rotation axis coordinate system 
             
             
                 
                9 
               Spring element 
             
             
                 
               10 
               Spring element 
             
             
                 
               x—x 
               Fan axis (main axis of inertia) 
             
             
                 
               y—y 
               Fan vertical axis 
             
             
                 
               ξ—ξ 
               Rotation axis of axial fan wheel 
             
             
                 
               η—η 
               Tilt 
             
             
                 
               J ξη  * ω 2   
               Centrifugal moment 
             
             
                 
               ω 
               Angular velocity 
             
             
                 
               δ 
               Inclination at ω = 0 
             
             
                 
               α 
               Displacement at ω ≠ 0 
             
             
                 
               δ − α 
               Displacement difference 
             
             
                 
               11 
               Axial force component fixed bearing 5 
             
             
                 
               12 
               Radial force component fixed bearing 5 
             
             
                 
               13 
               Radial force component movable bearing 6 
             
             
                 
               14 
               Lever arm a 
             
             
                 
               15 
               Spring force F c   
             
             
                 
               20 
               Armature shaft 
             
             
                 
               21 
               Electrical drive 
             
             
                 
               22 
               Housing 
             
             
                 
               23 
               Elastic disk 
             
             
                 
               24 
               Fastening screw 
             
             
                 
               25 
               Retaining device 
             
             
                 
               26 
               Balancing weight 
             
             
                 
               27 
               Hub plate 
             
             
                 
               28 
               Hub bore 
             
             
                 
               29 
               Divided circle of screw connections 
             
             
                 
               30 
               Spring element 
             
             
                 
               31 
               Radial slit 
             
             
                 
               32 
               Length of slit 
             
             
                 
               33 
               Width of slit 
             
             
                 
               34 
               Bore 
             
             
                 
               35 
               Circumferential recess 
             
             
                 
               36 
               Spacer element 
             
             
                 
               37 
               Spacer bush 
             
             
                 
               38 
               Displacement s 
             
             
                 
               39 
               Bearing surface 
             
             
                 
               40 
               Corrugated washer 
             
             
                 
               41 
               Tilting play 
             
             
                 
               42 
               Bush element 
             
             
                 
               43 
               Tensioning element 
             
             
                 
               44 
               Support 
             
             
                 
               45 
               Annular groove 
             
             
                 
               46 
               Bearing area 
             
             
                 
               47 
               Locating ring 
             
             
                 
               48 
               Annular space 
             
             
                 
               49 
               Bearing surface of bush element 
             
             
                 
               50 
               S-shaped driver profile