Abstract:
A grinding machine, includes a pivotable tool spindle with a workpiece spindle adapted to receive a gearwheel workpiece and for rotationally driving the gearwheel workpiece about a workpiece spindle axis, wherein the tool spindle
       is configured to receive a grinding tool and rotationally drive the grinding tool about a tool spindle axis, and   is carried by a pivot axis in such a way that the tool spindle together with the grinding tool can be pivoted about the pivot axis, and   wherein the pivot axis (A) intersects the workpiece spindle axis (C) in a common plane projection, and wherein the pivot axis is offset laterally relative to the workpiece spindle axis and does not intersect the workpiece spindle axis.

Description:
[0001]    This application claims priority under 35 U.S. C. §§119(a)-(d) to German patent application no. 10 2016 006 070.0 filed May. 19, 2016 which is hereby expressly incorporated by reference as part of the present disclosure. 
       FIELD OF INVENTION 
       [0002]    The present invention relates to grinding machines fitted with a pivotable tool spindle. At least some grinding machines are concerned whose tool spindle is fitted with a grinding screw for grinding gearwheel workpieces. 
       BACKGROUND 
       [0003]      FIG. 1  shows a schematic view of a portion of a prior art grinding machine. In  FIG. 1  a pivotable tool spindle  120  can be seen in a horizontal position. The tool spindle  120  here comprises a spindle housing  121  and a spindle motor, which is hidden in the interior. Attached to the tool spindle  120  is a grinding worm  20 , which can be rotatably driven about a tool spindle axis B by means of the spindle motor. In order to enable the pivoting of the tool spindle  120 , a pivot axis A is provided, which in this case stands perpendicularly to the drawing plane. Such a grinding machine, which is equipped with a pivotable tool spindle  120 , typically comprises a pivot plate, indicated by a dashed circle K in  FIG. 1 . The pivot plate can be rotated about the pivot axis A in the drawing plane. The pivot axis A is located at the center of the circle K. The pivotable tool spindle  120  is arranged, for example, on a machine stand  101 , which can be seen in outlines in the background of  FIG. 1 . 
         [0004]    The workpiece to be ground is not shown in  FIG. 1 , but the position of the vertically extending workpiece spindle axis C is shown, which intersects with the pivot axis A in the prior art, i.e. in  FIG. 1 . The workpiece typically sits on a workpiece spindle (not shown), which can be rotationally driven around the workpiece spindle axis C. 
         [0005]    In order to intercept unequal torques which act on the tool spindle  120  in this known configuration, the pivot plate, or the pivot axis A, can be mechanically clamped during the grinding of the workpiece. In this case, the pivot axis A can be used only as a setting axis. This means that the pivot axis A cannot be used dynamically, but only statically. 
         [0006]    If one wishes to use the pivot axis A as a moving axis during grinding, mechanical clamping is not useful. In this case, a drive motor is required which keeps the pivot axis A in position and can also move it dynamically. The size of the drive motor depends on the torque to be applied. This temporary retaining can be effected, for example, in such a way that the drive motor, which serves to pivot the pivot plate, predetermines a correspondingly large holding current. However, the predetermination of a holding current increases the power consumption of the grinding machine. 
       SUMMARY 
       [0007]    It is the object of some of the embodiments of the invention to provide a technical approach for operating a grinding machine which allows the pivot axis to be operated dynamically. In addition, the grinding machine should be economical to purchase and operate. 
         [0008]    The object is achieved according to some of the embodiments of the invention by a grinding machine with a pivotable tool spindle according to claim  1 . 
         [0009]    Some embodiments of the invention are based on the approach of changing the overall constellation of the grinding machine in such a way that the pivot axis, which is used for pivoting the tool spindle, is arranged laterally offset with respect to the workpiece spindle axis. 
         [0010]    In addition, a constellation might be selected in which the pivot axis for pivoting the tool spindle lies in the region of the mass center point of the combination of tool spindle and tool. 
         [0011]    These two aspects are combined with one another in at least some embodiments in such a way that the pivot axis is arranged laterally offset with respect to the workpiece spindle axis, and that the pivot axis lies in the region of the center of mass of the combination of the tool spindle and the tool. 
         [0012]    At least some embodiments in which the pivot axis directly or indirectly carries a shift axis have an asymmetric shift path of the shift axis. 
         [0013]    The grinding machine of some of the embodiments comprises a pivotable tool spindle and is provided with a workpiece spindle adapted to receive a gearwheel workpiece and to rotationally drive the gearwheel workpiece about a workpiece spindle axis. The tool spindle is designed/configured for accommodating a grinding tool and for rotationally driving the grinding tool about a tool spindle axis and is supported by a pivot axis such that the tool spindle together with the grinding tool can be pivoted about the pivot axis. In at least some embodiments, the pivot axis can carry a shift axis directly or indirectly. However, embodiments are also possible which operate without an actual shift axis. In such embodiments, the shift movement parallel to the tool rotation axis is typically generated by the superimposed movement of other linear axes. In this case, the pivot axis is supported directly or indirectly by one or more linear axes. 
         [0014]    The grinding machine of some of the embodiments is wherein the pivot axis is offset laterally relative to the workpiece spindle axis and therefore the pivot axis and the workpiece spindle axis do not intersect. 
         [0015]    The fact that the pivot axis and the workpiece spindle axis do not intersect can also be expressed as follows. The pivot axis and the workpiece spindle axis cross each other in the three-dimensional space and they only intersect when the pivot axis is projected into the plane of the workpiece-spindle axis planes. 
         [0016]    The tool spindle, including the grinding tool in some of the embodiments, has a center of mass which lies directly in the region of the pivot axis. If the pivot apparatus of the pivot axis does not support a shift axis, then the center of mass is a static point that is fixed with respect to the tool spindle, including the grinding tool. If the pivot apparatus of the pivot axis carries a shift axis, then the center of mass is a point which can shift depending on the shift position of the tool spindle and the grinding tool. 
         [0017]    If the center of mass is directly in the region of the pivot axis, a balanced constellation of the tool spindle and the tool is obtained. A balanced constellation is designated as an arrangement in which the pivot axis lies exactly in the central center of mass of the pivot apparatus, including the tool spindle and the grinding tool, or the pivot axis lies directly in the region of the center of mass. 
         [0018]    It is a significant advantage of some of the embodiments that the drive of the pivot axis can be dimensioned smaller than before, since it is only necessary to compensate for smaller torques. The drive of the pivot axis can be designed smaller, which leads to an improved energy efficiency of the machine. 
         [0019]    It is a further advantage of some of the embodiments that, due to the balanced constellation of the tool spindle and tool, no holding forces or smaller holding forces are required for holding the pivot axis. The balanced constellation of some of the embodiments provides an additional degree of freedom which makes it possible to carry out pivoting movements at any time, wherein the corresponding drive can be smaller-dimensioned than in previous solutions. At least some embodiments of the invention thus make possible the transition from a machining approach that has hitherto been static in nature to a dynamic machining approach. 
         [0020]    Some of the embodiments can be used for example in gear grinding machines. 
         [0021]    Some of the embodiments can be used above all in gear grinding machines which are designed for the grinding machining of straight and helical teeth. In particular, this concerns grinding machines which are designed for continuous rolling or profile grinding. 
         [0022]    Some of the embodiments can be used above all in gear grinding machines which are designed for the grinding machining of workpieces which are arranged in the gear grinding machine on a workpiece spindle with a vertical axis of rotation and which comprise a tool spindle with a grinding tool (in at least some embodiments with a grinding worm) which can be pivoted about a pivot axis standing perpendicularly to the workpiece spindle axis. 
         [0023]    It is a further advantage of some of the embodiments that the machine width can be provided with a smaller dimension if the tool spindle with a grinding tool is arranged offset to the left for example. This is because the relatively long end of the grinding spindle, or the housing of the grinding spindle, protrudes less far above the carriage of the shift axis. 
         [0024]    The shift axis is arranged symmetrically to the workpiece spindle axis in at least some embodiments. 
         [0025]    The carriage width of the shift axis can be reduced in at least some embodiments. 
         [0026]    The carriage width, or the shift path of the shift axis, can be asymmetric in at least some embodiments. 
     
    
     
       DRAWINGS 
         [0027]      FIG. 1  shows a schematic front view of a tool spindle with grinding worm, as used in prior art grinding machines; 
           [0028]      FIG. 2A  shows a schematic front view of a tool spindle with grinding worm, which according to a first embodiment is pivotally mounted with its center of mass directly in the region of a pivot axis, and in which the workpiece spindle axis is offset laterally relative to the pivot axis, juxtaposed, for reference, a schematic front view of the tool spindle (with grinding worm) of  FIG. 1 ; 
           [0029]      FIG. 2B  shows a schematic front view of a tool spindle with grinding worm, which according to a second embodiment comprises a shift axis, wherein, in the situation shown, the tool spindle with grinding worm sits at a right end of the shift axis; 
           [0030]      FIG. 2C  shows a schematic front view of the second embodiment of  FIG. 2B , wherein, in the situation shown, the tool spindle with grinding worm sits approximately at the center of the shift axis; 
           [0031]      FIG. 2D  shows a schematic front view of the second embodiment of  FIG. 2B , wherein, in the situation shown, the tool spindle with grinding worm sits at a left end of the shift axis; 
           [0032]      FIG. 3A  shows a schematic front view of a tool spindle with grinding worm, which according to a third embodiment of the invention comprises a shift axis, wherein a gearwheel workpiece is shown below the grinding worm; 
           [0033]      FIG. 3B  shows a schematic front view of the tool spindle with grinding worm according to  FIG. 3A , wherein exemplary details of the shift axis are shown; 
           [0034]      FIG. 4  shows a schematic front view of a grinding machine of an embodiment; 
           [0035]      FIG. 5A  shows a schematic diagram in which the torque of the pivot axis of a conventional machine constellation is plotted over the shift path of the shift axis; 
           [0036]      FIG. 5B  shows a schematic diagram in which the torque of the pivot axis of a machine constellation according to at least some embodiments of the invention is plotted over the shift path of the shift axis. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0037]    Within the scope of the present description, terms are used which are also used in relevant publications and patents. It should be noted, however, that the use of these terms is intended only for better understanding. The inventive concepts are not to be limited by the specific choice of the terms. At least some embodiments of the invention can be transferred without further ado to other conceptual systems and/or subject areas. In other areas, the terms can be applied mutatis mutandis. 
         [0038]    On the basis of the initially described  FIG. 1 , it can be seen that the center of mass MP does not coincide with the passage point of the pivot axis A in prior art machines. Since the spindle motor and the spindle housing  121  are relatively heavy, the center of mass MP, as indicated in  FIG. 1 , can lie for example to the right of the passage point of the pivot axis A. In addition, the pivot axis A and the workpiece spindle axis C intersect. 
         [0039]    The concept of the center of mass MP as used herein refers to the point in which the weight of those parts of the tool spindle  120 , together with the tool  20 , which are to the right of the center of mass MP are the same as the weight of those parts of the tool spindle  120 , together with tool  20 , which are to the left of the center of mass MP. The center of mass MP is thus the mean value weighted by the mass of the positions of all mass points of the tool spindle  120  together with the tool  20 . 
         [0040]    In other words, the tool spindle  120  together with the tool  20  is in an exactly balanced state when an axis perpendicular to the drawing plane of  FIG. 1  is passed through the center of mass MP and when the tool spindle  120  together with the tool  20  remains in this position. 
         [0041]    If a pivoting table  122  is used as a pivoting device which carries a shift axis and a tool spindle  120  together with a tool  20 , the center of mass MP is the mean value weighted with the mass of the positions of all mass points of the pivoting table  122 , the shift axis, the tool spindle  120  and the tool  20 . 
         [0042]    A first example of an embodiment will now be described with reference to  FIG. 2A  by means of a first exemplary embodiment. In this first embodiment, the pivot axis A, or a pivot plate (not shown here) of the pivot axis A, carries only a tool spindle  120  and a tool  20 . 
         [0043]    The two steps which led to the constellation according to at least some embodiments of the invention are explained with reference to  FIG. 2A .  FIG. 2A  shows an exemplary constellation according to at least some embodiments of the invention, in which the pivot axis A has its passage through the tool spindle  120  together with the tool  20  exactly in the center of mass MP. In this ideal case, the following statement applies: 
         [0044]    A=MP. 
         [0045]    More generally, the passage of the pivot axis A can lie directly in the region of the central center of mass in at least some embodiments. Therefore the more general statement applies: 
         [0046]    A˜MP. 
         [0047]    It can be recognized with respect to  FIG. 2A  that the position of the tool spindle  120  relative to the position of the pivoting table or the pivot axis A is displaced with the balanced bearing of the tool spindle  120  together with the tool  20 . The position of the pivoting table is indicated here by a dashed circle K, as also in  FIG. 1 . 
         [0048]    Furthermore, if possible, the tool  20  should be arranged centrally with respect to the workpiece  10  to be ground, so that all regions of the workpiece  10  can be easily reached and machined with all regions of the tool  20 . Therefore, an axis offset ΔA 2  is provided as described below. 
         [0049]    The offset between the conventional position of the tool spindle  120  in  FIG. 1  and the new position of the tool spindle  120  in  FIG. 2A  is designated by the reference symbol ΔA 1  and is indicated by a block arrow. In the constellations shown in  FIGS. 1 and 2A , the position of the machine stand  101  and the position of the pivot axis A together with pivot plates (indicated by the circle K) remain the same. In  FIG. 2A , only the tool spindle  120  together with the tool  20  has been shifted relative to the position of the pivot axis A by ΔA 1  and the position of the workpiece spindle axis C by ΔA 2  to the left. The displacement of the workpiece spindle axis C relative to the position of the pivot axis A is described in the following. ΔA 1  can be equal to ΔA 2  in at least some embodiments. However, ΔA 1  and ΔA 2  can also have different values in at least some embodiments. 
         [0050]    Instead of selecting an overall constellation, in which the pivot axis A and the workpiece spindle axis C continue to intersect (as shown in  FIG. 2A ), the workpiece spindle axis C is assigned a different position relative to the pivot axis A according to at least some embodiments of the invention. 
         [0051]    According to at least some embodiments of the invention, an overall constellation is provided for at least some embodiments in which the pivot axis A has a lateral offset ΔA 2  relative to the workpiece spindle axis C, as can be clearly seen in  FIG. 2A  and in  FIG. 3A .  FIGS. 2A to 2D  and  FIG. 3A  clearly show that the pivot axis A and the workpiece spindle axis C cross each other but do not intersect. In embodiments with a shift axis Sh which carries a pivot axis A, this statement applies primarily to a basic or zero position. Depending on the shift path Shw of the shift axis Sh, the corresponding machine can temporarily assume a position at which the pivot axis A and the workpiece spindle axis C intersect. 
         [0052]    However, the pivot axis A and the workpiece spindle axis C always intersect in a common plane projection. The plane projection mentioned here stands perpendicularly to the drawing plane. The corresponding plane can be the plane, for example, in which the workpiece spindle axis C lies. 
         [0053]    In at least some embodiments, the pivot axis A extends perpendicularly to the workpiece spindle axis C in the mentioned plane projection, as can be seen in  FIGS. 2A to 2D, 3A  and  FIG. 4 . These two axes A and C can, however, also extend obliquely with respect to each other in a common plane projection in at least some embodiments. 
         [0054]    In at least some embodiments, in order to enable a grinding machining of a gearwheel workpiece  10  (a straight spur gear  10  is shown by way of example in  FIG. 3A ), the grinding machine  100  is designed to carry out several movements in a three-dimensional space in a controlled manner. 
         [0055]    Therefore, a shift axis Sh is used in at least some embodiments, which is designed for the transverse displacement of the tool spindle  120  together with the grinding tool  20  in a vertical plane which stands perpendicularly to the pivot axis A. The transverse displacement is performed along a shift path Shw. In the representations of  FIGS. 2A-2D, 3A, 3B and 4 , said vertical plane extends in parallel to the drawing plane. 
         [0056]    In  FIGS. 2B-2D , a linear carriage  124  of the shift axis can be seen in outlines in three different shift positions. A linear carriage  124  can also be seen in  FIG. 3A .  FIG. 3B  shows details of an exemplary shift axis Sh. In the embodiments shown in  FIGS. 2B-2D, 3A and 3B , as well as in  FIG. 4 , the shift axis Sh sits on a pivot plate  122 , which is rotatably mounted about the pivot axis A. In at least some embodiments, the pivot plate  122  lies concentrically in relation to the pivot axis A. 
         [0057]    In at least some embodiments, the shift axis Sh is designed as a linear carriage  124 , which can comprise two linear guides  123  for example, as indicated in  FIG. 3B . Details of a shift axis Sh and such linear carriages  124  are well known and thus no further details are given here. 
         [0058]    In addition to the transverse displacement along the shift path Shw, which is made possible here by means of the shift axis Sh, further controlled movements in the three-dimensional space are typically required. In principle, this involves relative movements of the grinding tool  20  with respect to the gearwheel workpiece  10 . It is irrelevant for at least some embodiments of the invention whether, for example, the grinding tool  20  is moved and the gearwheel workpiece  10  is rotationally driven only about the workpiece spindle axis C, or whether the also gearwheel workpiece  10  can carry out (linear) movements for example. 
         [0059]    A preferred constellation of a grinding machine  100  of an embodiment is shown in  FIG. 4 . As already described above, the grinding machine  100  of some embodiments comprises a tool spindle  120 , which is arranged in at least some embodiments in relation to the pivot axis A in such a way that the pivot axis A penetrates the tool spindle  120  directly in the region of the center of mass MP. In each case, the pivot axis A has a relative lateral offset against the position of the workpiece spindle axis C. As already mentioned above, in at least some embodiments a pivot plate  122  can be used, which carries a linear carriage  124 . The linear carriage  124  is part of the shift axis Sh. 
         [0060]    In addition, in at least some embodiments, the grinding machine  100  can have three further axes X, Y, Z which are designed as linear axes. 
         [0061]    A first of these further axes, referred to here as a Y-axis, extends in the example shown parallel to the workpiece spindle axis C, as shown in  FIG. 4 . This Y-axis can be arranged, for example, on a machine stand  101  of the grinding machine  100 . In  FIG. 4 , it can be seen that the Y-axis can comprise two linear guides  102  for example. The Y-axis on the machine stand  101  carries the pivot axis A here and the pivot axis A again carries the shift axis Sh as well as the tool spindle  120  together with the tool  20 . Details of such a linear Y-axis are well known and no further details are given here. 
         [0062]    The Y-axis is used to perform a stroke (grinding stroke parallel to the C-axis). The Y-axis can be integrated in at least some embodiments into the machine stand  101 , which also carries the tool spindle  120 , as shown in  FIG. 4 . However, the Y-axis can also be arranged in at least some embodiments in the region of the workpiece spindle  110  in order to allow displacing the workpiece spindle  110  together with the gearwheel workpiece  10  parallel to the C-axis. 
         [0063]    A second one of these further axes, referred to here as the Z-axis, extends, for example, parallel to the pivot axis A. In the representation of  FIG. 4 , the corresponding Z-axis stands perpendicularly to the drawing plane. This Z-axis can, for example, enable a radial feed movement of the machine stand  101  with respect to the gearwheel workpiece  10 . In  FIG. 4 , it can be seen that the Z-axis can comprise two linear guides  103  for example. Details of such a linear Z-axis are well-known and no further details are given here. 
         [0064]    The X-axis of such a grinding machine  100  can extend parallel to the drawing plane. In the illustrated snapshot, the tool spindle axis B lies parallel to the X-axis. If the shift axis Sh is located on the pivot plate  122 , as shown in  FIG. 4  by way of example, then the X-axis is not absolutely necessary. The linear movement parallel to the X-axis can be realised, for example, by the linear movement of the workpiece spindle  110  or by the linear movement of the machine stand  101  relative to the workpiece spindle  110 . Such arrangements are also well known. 
         [0065]    The three further axes X, Y, Z form a Cartesian coordinate system in at least some embodiments, as shown in  FIG. 4 . 
         [0066]    Depending on the embodiment, the pivot axis A, or the pivot plate  122 , can carry a plurality of components. In the embodiments according to  FIGS. 2B to 2D, 3A, 3B  and according to  FIG. 4 , the pivot plate  122  carries, for example, the components of the shift axis Sh and the tool spindle  120  together with the tool  20 . In this case, in at least some embodiments, care is taken that the specification of the exactly balanced arrangement or the nearly balanced arrangement of the pivot axis A involves all components which are supported by the pivot plate  122 , i.e. the components of the shift axis Sh are also taken into account in determining the center of mass MP. Since the tool spindle  120  together with the tool  20  can be displaced along the shift axis Sh, the center of mass MP also shifts. This will be explained below with reference to  FIGS. 2B to 2D . 
         [0067]      FIG. 2B  shows a schematic front view of a tool spindle  120  with a grinding worm  20 , which according to this second embodiment of the invention comprises a shift axis Sh. In the illustrated situation, the tool spindle  120  sits with a grinding worm  20  at a right end of the shift axis Sh. The arrow denoted by Sh in  FIG. 2B  indicates that when the shift axis Sh is actuated the tool spindle  120  with the grinding worm  20  can only be displaced to the left out of this end position. 
         [0068]      FIG. 2C  again shows the second embodiment. In the illustrated situation, the tool spindle  120  with the grinding worm  20  sits approximately at the center of the shift axis Sh. The double arrow in  FIG. 2C , designated with Sh, indicates that the tool spindle  120  with the grinding worm  20  can be moved out of this central position to the right and left by actuating the shift axis Sh. 
         [0069]      FIG. 2D  also shows the second embodiment. In the illustrated situation, the tool spindle  120  sits with a grinding worm  20  at a left end of the shift axis Sh. The arrow denoted by Sh in  FIG. 2D  indicates that the tool spindle  120  with the grinding worm  20  can only be displaced to the right from this end position when the shift axis Sh is actuated. 
         [0070]    In the comparison of  FIGS. 2B to 2D  it can be seen that the center of mass MP is displaced during the displacement of the tool spindle  120  together with the tool  20 . In  FIG. 2B , the center of mass MP is located to the right of the passage of the pivot axis A. In  FIG. 2C , the center of mass MP is located very close to the passage of the pivot axis A and in FIG.  2 D the center of mass MP is located to the left of the passage of the pivot axis A. The center of mass MP shifts not necessarily symmetrically to the passage of the pivot axis A. In practice, a range for the displacement of the center of mass MP is usually obtained which is asymmetrical to the pivot axis A. 
         [0071]    If, on the other hand, the axis Sh (in this case, the axis Sh is not a shift axis in the actual sense but a linear axis) carries the pivot plate  122  together with the tool spindle  120  and the tool  20 , the components of the axis Sh do not need to be considered in the determination of the center of mass MP. In this case, the corresponding center of mass MP is also referred to as a static center of mass MP.  FIG. 2A  shows an embodiment with a static center of mass MP. 
         [0072]    In embodiments with a static center of mass MP, it can be advantageous to combine the passage of the pivot axis A in the design of the machine  100  with the center of mass MP, as already described. In embodiments with a moving center of mass MP, it can be advantageous to lay the passage of the pivot axis A into the displacement range of the center of mass MP when designing the machine  100 , as shown in  FIGS. 2B to 2D . 
         [0073]    Since the pivot axis A according to at least some embodiments of the invention does not intersect with the workpiece spindle axis C (except possibly in the mentioned temporary special case), a certain asymmetry of the tool spindle  120 , or of the tool  20 , relative to the workpiece spindle axis C is obtained. This asymmetry can be compensated for in at least some embodiments in such a way that the shift axis Sh is designed for the asymmetrical transverse displacement of the tool spindle  120  together with the grinding tool  20  with respect to the pivot axis A. If the shift axis Sh enables movements of ±150 mm for example in one embodiment of the prior art, the shift axis Sh can allow a movement of +150 mm to the left and a movement of −120 mm to the right in some embodiments. These are merely examples of numbers. 
         [0074]    Due to the balanced arrangement, the means for holding can be smaller in size because smaller torques are to be compensated. 
         [0075]    In order to illustrate the effect of at least some embodiments of the invention graphically, the numerical examples of a conventional machine constellation were compared with the numerical examples of a machine constellation according to embodiments of the invention in  FIGS. 5A and 5B .  FIG. 5A  shows a schematic diagram in which the torque DM of the pivot axis A of a conventional machine constellation (e.g. as shown in  FIG. 1 ), is plotted via the shift path Shw of the shift axis Sh. Due to the unbalanced constellation, in at least some embodiments, the drive motor of the pivot axis A is able to apply torques DM in the range from 1000 Nm to −200 Nm, i.e. the drive motor is dimensioned so that it can apply a maximum of 1000 Nm. 
         [0076]    In  FIG. 5B  a corresponding schematic diagram of a machine constellation according to at least some embodiments of the invention (e.g. as shown in  FIG. 4 ) is plotted over the shift path Shw of the shift axis Sh. Due to the significantly better balanced constellation, in at least some embodiments, the drive motor of the pivot axis A is only be able to apply torques DM in the range of 700 Nm to −500 Nm, i.e. the drive motor is dimensioned such that it can apply a maximum of 700 Nm. 
         [0077]    In an ideally balanced constellation, the values of the positive and the negative torque DM are the same. In order to remain at similar numerical values as in  FIGS. 5A and 5B , in at least some embodiments, the torque of an ideally balanced constellation could be at ±600 Nm for example, i.e. the drive motor is dimensioned in such a way that it can apply a maximum of 600 Nm. 
         [0078]    The quality of the balancing can thus be defined for example via the torque values. The smaller the amount-related difference ΔDM of the torque values is, the better the constellation is balanced. At ΔDM=0, the constellation is ideally balanced. 
         [0079]    According to at least some embodiments of the invention, the center of mass MP is then directly in the region of the pivot axis A if at least one of the following conditions is fulfilled (the figures in brackets refer to the numerical example in  FIG. 5B ):
       B1. If the amount-related smaller value of the negative and of the positive torque (500 Nm is less than 700 Nm) deviates by less than 30% from the larger value (here 700 Nm). In the embodiment of  FIG. 5B , the 500 Nm are approximately 71.43% of the 700 Nm. The value which is smaller in respect of amount therefore deviates by less than 30% from the larger value and the condition B1 is considered fulfilled. In the embodiment of  FIG. 5A , these values deviate by 80% from each other and the condition B1 is far from being fulfilled.   B2. If the difference (700 Nm−500 Nm=200 Nm) of the absolute value of the positive torque (700 Nm) and the absolute value of the negative torque (|−500 Nm|=500 Nm) deviate by less than 20% of the sum (700 Nm+500 Nm=1200 Nm) of the absolute value of the negative torque (|−500 Nm|=500 Nm) and of the absolute value of the positive torque (700 Nm). In the embodiment of  FIG. 5B , this definition yields a value of approx. 16.67%. Since 16.67% is less than 20%, in the case of  FIG. 5B  the condition B2 is regarded as fulfilled. In the embodiment of  FIG. 5A , this definition yields a value of approximately 66.67% and the condition B2 is by no means fulfilled.   B3. If in a diagram in which the torque DM of the pivot axis A is plotted over the shift path Shw of the shift axis Sh, the course of the torque DM is symmetrical with respect to the axis which maps the shift path Shw, the condition B3 is fulfilled.   B4. If in a diagram in which the torque DM of the pivot axis A is plotted over the shift path Shw of the shift axis Sh, the course of the shift path Shw is symmetrical with respect to the axis which maps the torque DM, the condition B4 is fulfilled.       
 
         [0084]    In at least some embodiments, the conditions B1 and/or B2 are applied to constellations in which the pivot axis A does not carry a shift axis Sh (see  FIG. 2A  for example). 
         [0085]    In at least some embodiments, the conditions B2 and/or B3 and/or B4 are applied to constellations in which the pivot axis A carries a shift axis Sh (see  FIGS. 2B-2D, 3A, 3B, 4  for example). 
         [0086]    With respect to  FIG. 5B , it can be seen by way of example that the shift axis Sh can be designed for the asymmetrical transverse displacement of the tool spindle  120  together with the grinding tool  20  with respect to the pivot axis A. The shift path Shw goes significantly further into the negative range than in the positive range of the diagram (i.e. the shift axis Sh allows larger movements to the left than to the right). 
         [0087]    As may be recognized by those of ordinary skill in the pertinent art based on the teachings herein, numerous changes and modifications may be made to the above described and other embodiments of the present invention without departing from the spirit of the invention as defined in the claims. Accordingly, this detailed description of embodiments is to be taken in an illustrative, as opposed to a limiting sense.