Technical area of the invention [0001] The subject of the invention is a method for semi-completing power skiving of a toothing or another periodical structure and an according power skiving tool for performing a semi-completing power skiving method.

Background of the invention, state of the art

[0002] There are numerous methods for the manufacturing of gear wheels. In the chip-producing soft pre-machining, one distinguishes hobbing, gear shaping, generating planing and skiving (resp. hop peeling). The hobbing and skiving are so- called continuous methods, as shall be explained in the following.

[0003] In the chip-producing manufacturing of gear wheels, one distinguishes between the intermitted indexing process or single indexing process and the continuous method, which partly also called continuous indexing process or face hobbing . [0004] In the continuous method, for example, a tool comprising according cutters is applied in order to cut the flanks of a work piece. The work piece is cut ready in one clamping continuously, i.e. in an uninterrupted process. The continuous method is based on complex coupled movement sequences, in which the tool and the work piece to be machined perform a continuous indexing movement relative to each other. The indexing movement results from the driving in coordination resp. the coupledly driving of plural axle drives of an according machine.

[0005] In the single indexing process, one tooth gap is machined, then for example a relative movement of the tool and a so-called indexing movement (indexing rotation), in which the work piece rotates relative to the tool, are carried out, before then the next tooth gap is machined. In this way, a gear wheel is manufactured step by step.

[0006] The initially mentioned gear shaping method may be described or represented by a cylinder gear transmission, because the intersection angle (also called intersection angle of axes) between the rotation axis Rl of the shaping tool 1 and the rotation axis R2 of the work piece 2 amounts to zero degree, as represented schematically in Fig . 1. The two rotation axes Rl and R2 run parallel, if the intersection angle of axes amounts to zero degree. The work piece 2 and the shaping tool 1 rotate continuously about their rotation axes R2 respectively Rl . In addition to the rotational movement, the shaping tool 1 carries out a stroke movement, which is referenced in Fig . 1 by the double arrow s _hx , and removes chips from the work piece 2 during this stroke movement.

[0007] Some time ago a method has been taken up anew, which is called (power) skiving . The basics are aged approximately 100 years. A first patent application with the number DE 243514 on this subject dates back to the year 1910 and has been released in the year 1912. After the original considerations and investigations of the initial years, the power skiving was no longer pursued further seriously. Hitherto, complex processes, which were partly empirical, were necessary in order to find a suitable tool geometry for the power skiving method. [0008] About in the middle of the nineteen eighties, the power skiving has been taken up anew. It was not until the present-day simulation methods and the modern CNC-controls of the machines, that the principle of power skiving could be implemented as a productive, reproducible and robust method . The high durability of present-day tool materials, the enormous high static and dynamical rigidity and the high performance of the synchronous running of the modern machines come in addition .

[0009] As shown in Fig . 2A, during the power skiving, an intersection angle of axes ∑ between the rotation axis Rl of the skiving tool 10 (also called skiving wheel) and the rotation axis R2 of the work piece 20 is prescribed, which is different from zero. The resulting relative movement between the power skiving tool 10 and the work piece 20 is a helical movement, which can be decomposed into a rotational portion (rotatory portion) and an advance portion (translational portion) . A generation helical type gear transmission can be considered as a drive technology-specific analogon, wherein the rotational portion corresponds to the rolling and the advance portion corresponds to the gliding of the flanks. The greater the absolute value of the intersection angle of axes ∑, the more the translational movement portion required for the machining of the work piece 20 increases. It causes namely a movement component of the flank cutting edges of the power skiving tool 10 in the direction of the tooth flanks of the work piece 20. Thus, during power skiving, the gliding portion of the combing relative movement of the mutually engaging gear wheels of the equivalent helical gear is utilized to carry out the cutting movement. In the power skiving, only a slow axial feed motion (also called axial feed) parallel to the rotation axis R2 of the work piece 20 is required and the so-called shaping (resp. pushing) movement, which is typical for the gear shaping, is dispensed with . Thus, also a return stroke movement does not occur in power skiving .

[0010] The cutting speed in power skiving is influenced directly by the rotational speed of the power skiving tool 10 resp. the work piece 20 and the utilized intersection angle of axes ∑ between the rotation axes Rl and R2. The intersection angle of axes ∑ and thus the gliding portion should be selected such that for a given rotational speed an optimum cutting speed is achieved for the machining of the material.

[0011] The movement sequences and further details of an established power skiving method can be taken from the schematic representation in Fig . 2A that has already been mentioned . Fig . 2A shows the power skiving of an outer toothing on a cylindrical work piece 20. The work piece 20 and the tool 10 (here a cylindrical power skiving tool 10) rotate in opposite directions, as can be recognized in Fig . 2A on the basis of the angular speeds coi and co ₂ . The cylindrical tool 10 is tilted away from the work piece 20 for generating kinematic rake angles. [0012] In addition, there are further relative motions. The axial feed motion Sax as mentioned already is required in order to work the total toothing width of the work piece 20 with the tool 10. The axial feed motion causes a displacement of the tool 10 with respect to the work piece 20 in a direction parallel to the work piece rotation axis R2. The direction of this motion of the tool 10 is indicated in fig. 2A by s _ax . In case a helical gearing is desired on the work piece 20 (i.e. helix angle β ₂ ≠0), a differential feed motion s _D is superimposed on the axial feed motion s _ax , which corresponds to an additional rotation of the work piece 20 about the work piece rotation axis R2, as indicated in fig. 2A. The differential feed motion s _D and the axial feed motion s _ax are adjusted at the calculation point AP such that the resulting feed of the tool 10 with respect to the work piece 20 occurs in the direction of the toothing gap to be generated. A radial feed s _rad can be applied additionally, for example in order to influence the convexity of the toothing of the work piece 20.

[0013] In power skiving, the vector of the cutting speed v _c results substantially as the difference of the two velocity vectors ν _γ and v ₂ of the rotation axes Rl, R2 of the tool 10 and the work piece 20, which [velocity vectors] are tilted with respect to each other by the effective intersection angle of axes ∑ _e ff. The symbol ν _γ is the velocity vector at the periphery of the tool and v ₂ is the velocity vector at the periphery of the work piece 20. The cutting speed v _c of the power skiving process may thus be changed by the intersection angle of axes∑ and the rotation speed in the equivalent helical gear. In the power skiving method, the axial feed motion s _ax , which is relatively slow as already mentioned, has only a small influence on the cutting speed v _c , which can be neglected . Therefore, the axial feed motion s _ax is not taken into account in the vector diagram comprising the vectors v v ₂ and v _c in Fig . 2.

[0014] The power skiving of an outer toothing of a work piece 20 using a conical power skiving tool 10 is shown in Fig . 2B. In Fig. 2B again, the intersection angle of axes∑, the vector of the cutting speed v _c , the velocity vectors v _x at the periphery of the tool 10 and v ₂ at the periphery of the work piece 20 as well as the cant angle 6i of the tool 10 and the cant angle β ₂ of the work piece 20 is shown. Here, the cant angle β ₂ is different from zero. The tooth head of the tool 10 is referenced with the reference sign 4 in Fig . 2B. The tooth breast is referenced with the reference sign 5 in Fig . 2B. The two rotation axes Rl and R2 do not intersect, but are arranged skew (resp. skew-whiff) with respect to each other. For a conical power skiving tool 10, the calculation point AP is hitherto usually chosen on the joint plumb of the two rotation axes Rl and R2, because a tilting of the power skiving tool 10 for providing of end relieve angles is not necessary. The pitch circles of the equivalent helical generation gear contact each other in this calculation point AP.

[0015] In power skiving, a tool 10 comes to application, which comprises at least one geometrically determined cutting edge. The flank cutting edge/flank cutting edges are not shown in Fig . 2A and Fig . 2B. The shape and arrangement of the flank cutting edges belong to those aspects, which must be taken into account for a concrete layout in practice.

[0016] In addition, the tool itself has a great importance in power skiving . In the example shown in Fig. 2A, the power skiving tool 10 has the shape of a straight-toothed spur wheel. The outer contour of the base body in Fig. 2A is cylindrical. However, it can also be tapered (also called conical), as shown in Fig. 2B.

[0017] It is known (refer e.g. to the publication DE 3915976 Al) that one can pursue a so-called semi-completing approach in power skiving. An approach is referred to as a semi-completing method, in which the right flanks and the left flanks of the work piece are finished in separated machining steps. Here, in a first step, only the geometries of the right or the left flanks are finished and the left resp. right flanks are pre-machined, if necessary. Then, in a second step, after the machine setting has been changed, the flanks which have not been finished in the first step are finished in a second step. Thereby, beside the desired flank geometry, also the desired gap width is achieved . One reason for the application of a semi- completing method is seen hitherto in that the geometry of the flanks can be designed more freely. That is to say, so-called "flank modifications" are possible more easily than in the completing method, in which the right and left flanks are finished simultaneously in one machining step. In addition, in the semi-completing method, also the tooth thickness can be corrected easily by changing the gap width by means of a rotation of the work piece.

[0018] The semi-completing method is originally known from the grinding in a single indexing process of toothings that have been pre-milled in the Zyclo-Palloid® method.

[0019] Proprietary investigations of the power skiving method have shown that a significant wear of the power skiving tool can occur, depending on the design of the power skiving tools 10. More precise considerations show that during power skiving, the chipping conditions on the running-in flank cutting edges eF and on the running-out flank cutting edges aF can be strongly different from each other, as is explained on the basis of the Figures 3A and 3B. Fig . 3A shows a schematic representation of a skiving wheel 10 having a conical outer contour in engagement with a straight-toothed inner toothing of a work piece 20 during power skiving in a projection of intersection of axes. A positive intersection angle of axes∑ has been prescribed. For reasons of clarity, only one cutting tooth 23 of a skiving wheel 10 and one tooth gap 21 of the work piece 20 are shown. Fig . 3A shows in a snap-shot recording how the cutting tooth 23 works itself through the material of the work piece 20. A portion of a tooth gap 21 has been generated already up to the actual point in time of the manufacturing. The constructive rake angles can be seen on the cutting tooth 23. The cutting face 22 of the cutting tooth 23 is formed without pitch angle (stair angle). During power skiving, the chip-forming conditions change continuously during the taking-off of each single chip. In particular, the chip- forming conditions are different at the flank cutting edges of the cutting tooth 23 for the running-in tooth flank eF and the running-out tooth flank aF. To some extent, the chip-forming conditions may even be strongly different.

[0020] Fig . 3B shows details of the point in time of manufacturing shown in Fig . 3A in an enlarged schematic representation . On the basis of Fig . 3B, the different effective chipping angles at the running-in tooth flank eF and the running- out tooth flank aF can be recognized . The chip angle at the running-out tooth flank aF is negative and the chip angle at the running-in tooth flank eF is positive. The cutting direction SR at the calculation point AP is also indicated in Fig . 3B. [0021] More detailed considerations have shown that during power skiving, the positive effective chip angle at the running-in tooth flank eF typically decreases only moderately during the taking-off of a single chip. On the other hand, the negative effective chip angle at the running-out tooth flank aF typically falls significantly during the taking-off of a single chip. Similarly as for the effective face chip angle at the cutting tooth 23, strongly negative effective chip angles (of up to - 60°) may occur.

[0022] These differences of the chip-forming conditions at the running-in tooth flanks eF and the running-out tooth flanks aF do not only lead to a varyingly different wear at the power skiving tool, but they may also have an influence on the quality of the generated tooth flanks.

[0023] The tilting of the chip surface 22 by means of a stair angle (also called chip surface tilt angle) would enable to balance the effective chip angles between running-in tooth flanks eF and running-out tooth flanks aF at the beginning of the taking-off of each single chip. For example, the chip surface 22 can be oriented perpendicular to the cutting direction SR in the calculation point AP. Then, the effective chip angles are approximately 0° at the beginning of the taking-off of each single chip on all parts of the flank cutting edges. These angles may also be designed slightly positive by an additional calotte grinding . However, the problematic peculiarity of the method of power skiving remains maintained, that the effective chip angle at the running-out tooth flank AF falls off significantly stronger than at the running-in tooth flank eF. [0024] In addition, it is characteristic for the power skiving that the portion of the chip taken off at the running-in tooth flank turns out to be thinner than the portion of the chip taken off at the running-out tooth flank aF. Also this peculiarity of the method of power skiving is problematic. [0025] The different chip-forming conditions at the running-in and running-out tooth flank eF and aF result in a different quality of the generated tooth flanks, where appropriate, as well as in a different load of the corresponding flank cutting edges at the power skiving tool 10.

[0026] Therefore, solutions are searched for which enable to design the surface quality of the right and left tooth flanks as equal as possible and thereby to improve them.

[0027] In addition, solutions are searched for which enable to reduce the wear of the power skiving tools, respectively to improve the tool life of the power skiving tools. The power skiving method becomes more economic by a reduced wear, since the manufacturing costs for toothing work pieces are substantially influenced by the lifetime of the tools.

[0028] It is thus an object of the present invention to provide a power skiving method and a power skiving tool for power skiving machining the tooth flanks of a toothed wheel or another periodical structure, which is characterized by an improvement of the surface quality of the tooth flanks.

[0029] According to the present invention, this object is solved by a method that is called here the semi-completing power skiving method comprising a readjustment of the intersection angle of axes. Thereby, the freedom in the design of the cutting process, more precisely of the chip-forming conditions, is the focus of the solution according to the invention.

[0030] That is to say, the object is solved according to the present invention by a skiving method, which is based on the principle of the semi-completing method, which however works with a first intersection angle of axes in a first power skiving machining of a work piece and with a second intersection angle of axes in a second power skiving machining of the work piece, wherein the two intersection angles of axes differ significantly. As a result of this approach, optimum resp. improved chip-forming conditions are ensured for the manufacturing of both tooth flanks of a work piece. That is, optimized chip-forming conditions are prescribed for each tooth flank, so as to improve the surface quality of the tooth flanks.

[0031] It is characterizing for the method and the use of the invention that in the manufacturing of a toothing, for example, the right and left tooth flanks are power-skived with different machine settings, though with the same tool, continuously by use of a semi-completing approach. Here, the generation of tooth flanks with good surface quality is of primary concern, which is achieved by the control of the cutting conditions, or stated more precisely of the chip-forming conditions, at the tooth flanks.

[0032] Thus, according to the invention, a semi-completing power skiving method for an individual, i.e. flank-specific optimization of the chip-forming conditions, is concerned . That is to say, a method is concerned, in which aspects of the semi-completing are applied to a continuous power skiving method, wherein the chip-forming conditions are preferably optimized by an interim re-adjustment of the intersection angle of axes.

[0033] The semi-completing power skiving method according to the invention can be applied in relation with the manufacturing of rotationally symmetrical periodical structures, such as toothings and so on.

[0034] In the semi-completing power skiving method, a particularly designed tool comes to application, which is called power skiving tool herein.

[0035] In the power skiving according to the invention, the rotation axis of the tool is always set skew-whiff with respect to the rotation axis of the work piece, i.e. the intersection angle of axes ∑ is always unequal to zero. Preferably, for work pieces which are to be manufactured straight-toothedwith straight tooth, the first intersection angle of axes and the second intersection angle of axes are substantially symmetrical with respect to an axis of symmetry, which runs parallel to the work piece rotation axis, because the straight-toothing is a particular case of the helical toothing . For helical toothings, somewhat different conditions apply, as will be explained later.

[0036] According to the invention, a properly designed power skiving tool comes to application, which can be employed under two significantly different intersection angles of axes, wherein it has to be taken into account in the design that for a given tool diameter of the power skiving tool there are two intersection angles of axes, which satisfy the conditions of the cutting direction for the power skiving .

[0037] According to the invention, a method and a power skiving tool for power skiving at least one work piece with a rotationally symmetrical periodical structure by use of the power skiving tool is concerned . The following steps are performed, wherein the sequence of the steps may also be different: providing a work piece and a power skiving tool,

approaching a first relative position with a first intersection angle of axes of the power skiving tool with respect to the work piece,

performing a first skiving machining (also called first machining phase) of the work piece, wherein during the first skiving machining including maintaining the first intersection angle of axes, either all the right or all the left flanks of the periodical structure of the work piece are finished and the respective other flanks are pre-machined, where appropriate (depending on whether a skiving machining from a massive part or a hard machining is concerned),

approaching a second relative position with a second intersection angle of axes of the power skiving tool with respect to the work piece, wherein the second intersection angle of axes differs significantly from the first intersection angle of axes,

performing a second skiving machining (also called second machining phase) of the work piece, wherein during the second skiving machining including maintaining the second intersection angle of axes, those flanks of the periodical structure of the work piece are finished, which have not yet been machined or only pre-machined previously during the first power skiving machining (depending on whether a skiving machining out of massive substance or a hard machining is concerned).

[0038] For straight-toothed work pieces, the amount of the first intersection angle of axes and the amount of the second intersection angle of axes are preferably equal, i.e. the first intersection angle of axes and the second intersection angle of axes differ only by the sign.

[0039] For helically toothed work pieces, the amount of the first intersection angle of axes and the amount of the second intersection angle of axes are preferably different, i.e. the signs of the two intersection angles of axes may be equal or unequal.

[0040] According to the invention, also a reversal of the rotating direction is carried out together with the re-adjustment of the intersection angle of axes, when the first and the second intersection angle of axes have different signs. [0041] It is to be noted here, that the rotationally symmetrical periodical structures of the work pieces do not necessarily have to have symmetrical teeth resp. symmetrical tooth gaps, grooves or rills. In the following, for reasons of simplicity, work pieces having symmetrical teeth are shown and described . However, the invention may also be applied to asymmetrical structures. [0042] The invention can be applied both for the machining of outer and inner periodical structures and in particular also for the machining of outer as well as inner toothings.

[0043] It is characteristic for the power skiving according to the invention in all embodiments that the relative courses of motion (called relative motions) between work piece and tool are prescribed and executed such that material is continuously taken off from the work piece until the teeth or the other periodical structures are formed (in the case of soft machining from massive material) or are finished (in the case of hard machining). [0044] The invention is suitalbe among others for the pre-toothing, i.e. for the machining out of massive material. In the pre-toothing according to the invention, for example left flanks are only pre-machined and right flanks are finished during the first power skiving machining including maintaining the first intersection angle of axes, and only the left flanks are finished during the second power skiving machining including maintaining the second intersection angle of axes. Or left flanks are finished and right flanks are only pre-machined during the first power skiving machining including maintaining the first intersection angle of axes, and only the right tooth flanks are finished during the second power skiving machining including maintaining the second intersection angle of axes.

[0045] The method according to the invention is particularly suitable for the hard machining, because only left or right flanks are machined there in each machining phase, and thus the possibilities for optimization are greater than for the pre-toothing. In the hard machining according to the invention, e.g . only left flanks are machined during the first power skiving machining including maintaining the first intersection angle of axes and only right flanks are machined during the second power skiving machining including maintaining the second intersection angle of axes. Or only right flanks are machined during the first power skiving machining including maintaining the first intersection angle of axes and only left flanks are machined during the second power skiving machining including maintaining the second intersection angle of axes.

[0046] The power skiving according to the invention concerns a continuous chip-forming method.

[0047] According to the invention, in each machining phase, a radial motion can be superimposed on the relative feed motion of the power skiving tool, in order to influence e.g . the convexity of the teeth, according to the technical teaching of the German patent application DE 3915976 Al .

[0048] During the power skiving, the rotating tool performs an axial feed motion with respect to the rotating work piece in the direction of the work piece rotation axis, wherein this axial feed motion runs concordant or opposite to the cutting direction. [0049] For all embodiments, the tools according to the invention may be designed as so-called full (resp. integral) tools, i.e. tools are concerned which are formed substantially integrally. For the full tools, the cutting teeth are an integral element of the tool . [0050] For all embodiments of the invention, cutter head tools (herein called bar cutter tools) are particularly preferred, which have a disk-like, ring-like or plate-like cutter head base body, which is equipped with cutter inserts preferably in the form of bar cutters. Embodiments of the invention are also possible, which are designed as cutter plate tools, which have a disk-like, ring-like or plate-like cutter head base body, which is equipped with cutter plates.

[0051] The method according to the invention cannot only be performed by use of outer tools, but also by use of inner tools.

[0052] The method of the present invention may also be combined with an alternating semi-completing power skiving approach, which is known from the European patent application EP 11181521.3 having the title "SEMI-COMPLETING POWER SKIVING METHOD AND DEVICE COMPRISING AN ACCORDING POWER SKIVING TOOL FOR PERFORMING A SEMI-COMPLETING POWER SKIVING METHOD", which has been filed in the European Patent Office on September 15, 2011. [0053] The invention offers a series of advantages with respect to the conventional semi-completing power skiving, which are mentioned in summary in the following :

- balanced and improved surface quality of the tooth flanks due to the possibility to optimize the cutting conditions separately.

[0054] In particular in the hard machining, depending on the implementation of the method according to the invention, also the following advantages may result:

- longer lifetime of the tools;

- lower piece cost of the tools;

- reduced failure of the tool;

- better cost effectiveness. [0055] The method according to the invention can be performed both in relation with a dry and also a wet machining .

DRAWINGS [0056] Further details and advantages of the invention are described in the following on the basis of embodiment examples and with reference to the drawings. In all schematic drawings, for reason of simplicity of the representation, the work piece and the power skiving tool are reduced to the situation at the pitch circle (resp. on the work piece at the pitch cylinder) . The represented relations also hold for the total toothing with one tooth height.

FIG. 1 shows a schematic representation of a shaping wheel having a cylindrical outer contour in engagement with an outer-toothed work piece during gear shaping ;

FIG. 2A shows a schematic representation of a straight-toothed skiving wheel having a cylindrical outer contour in engagement with an outer- toothed work piece during power skiving;

FIG. 2B shows a schematic representation of a helically toothed skiving wheel having a conical outer contour in engagement with an outer-toothed work piece during power skiving in a projection of intersection of axes; FIG. 3A shows a schematic representation of a skiving wheel having a conical outer contour in engagement with a straight-toothed inner toothing of a work piece during power skiving in a projection of intersection of axes, wherein only one cutting tooth of the skiving wheel is shown;

FIG. 3B shows details of Fig . 3A in a schematic representation, wherein the different effective chip angles at the running-in and the running-out tooth flank can be recognized;

FIG. 4A shows a schematic representation of a skiving wheel having a conical outer contour in engagement with a straight-toothed inner toothing of a first work piece during power skiving in a projection of intersection of axes, wherein only one cutting tooth of the skiving wheel is shown and a positive intersection angle of axes of approximately +25 degrees has been prescribed here; shows a schematic representation in a situation that is mirror- symmetrical to Fig . 4A, with a skiving wheel having a conical outer contour in engagement with a straight-toothed inner toothing of a second work piece during power skiving in a projection of intersection of axes, wherein only one cutting tooth of the skiving wheel is shown and a negative intersection angle of axes of approximately -25 degrees has been prescribed; shows a schematic representation of a graphical superimposition of the two mirrored skiving wheels of Fig . 4A and Fig . 4B, wherein for machining the respective running-in tooth flanks the flank cutting edges have now been combined to one unified cutting tooth (here bordered by a bolt type line); shows a schematic representation of the unified cutting tooth of Fig. 5A in a front view; shows a schematic representation of the graphical superimposition of the flank cutting edges of Fig. 5A, wherein now the width of the face cutting edge of the unified cutting tooth (here bordered by a bold type line) has been reduced, in order to enable a use of this skiving wheel according to the invention in relation with the semi-completing machining according to the invention; shows a schematic representation of the cutting tooth of Fig. 5C in a front view;

FIG. 6A shows a schematic representation of a first method step according to the invention (also called first power skiving machining), wherein a skiving wheel according to the invention manufactures a first tooth gap out of massive material with a positive first intersection angle of axes, wherein the right running-in tooth flank of the first tooth gap is finished with the corresponding flank cutting edge and the left running- out tooth flank is pre-machined with the corresponding flank cutting edge here; shows a schematic representation of a second method step according to the invention (also called second power skiving machining), wherein the skiving wheel of Fig. 6A according to the invention further machines the first tooth gap with a negative second intersection angle of axes, wherein the left running-in tooth flank of the first tooth gap is finished with the corresponding flank cutting edge, while the other flank cutting edge performs a blank cut here; shows a strongly schematized and not proportional cross-sectional representation of the first method step according to the invention of Fig . 6A; shows a strongly schematized and not proportional cross-sectional representation of the second method step according to the invention of Fig . 6B; shows a schematic representation of a further method step according to the invention (again called first power skiving machining), wherein a skiving wheel according to the invention manufactures a helically toothed tooth gap out of massive material with a positive first intersection angle of axes; shows a schematic representation of a further method step according to the invention (again called second power skiving machining), wherein the skiving wheel according to the invention of Fig. 7A further machines the first helically toothed tooth gap with a positive second intersection angle of axis, wherein the running-in tooth flank of the first tooth gap is finished here with the corresponding flank cutting edge, while the other flank cutting edge performs a blank cut; FIG. 8A shows a perspective representation of a cylindrical outer-toothed work piece and a disk-shaped power skiving tool during the semi-completing power skiving according to the invention;

FIG. 8B shows an enlarged detail of the cylindrical outer-toothed work piece and the disk-shaped power skiving tool of Fig . 8A viewed from the rear side in a moment, in which both flank cutting edges of each cutter head machine the left and right flanks of an according tooth gap;

FIG. 8C shows an enlarged detail of the cylinder-shaped outer-toothed work piece and the disk-shaped power skiving tool of Fig. 8A viewed from the rear side in a moment, in which only one of the flank cutting edges of each cutter head machines a flank of an according tooth gap and the other flank cutting edge performs a blank cut.

DETAILED DESCRIPTION

[0057] In relation with the present description, terms are used which also find use in relevant publications and patents. It is noted however, that the use of these terms shall merely serve a better comprehension. The inventive idea and the scope of the patent claims shall not be limited in their interpretation by the specific selection of the terms. The invention can be transferred without further ado to other systems of terminology and/or technical areas. In other technical areas, the terms are to be employed analogously.

[0058] Rotational-symmetric periodic structures are for example gear wheels having an inner and/or outer toothing . However, for example, also brake discs, clutch or gear transmission elements, and so on may be concerned. The power skiving tools are particularly suitable for the manufacturing of pinion shafts, worms, ring gears, toothed wheel pumps, ring joint hubs (ring joints are employed for example in the motor vehicle sector for transmitting the force from a differential gear to a vehicle wheel), spline shaft joints, sliding collars, belt pulleys, and so on. Herein, the periodic structures are also called periodically repeating structures. [0059] In the following, mention is made primarily of gear wheels, teeth and tooth gaps. However, as mentioned above, the invention can, also be transferred to other construction parts with other periodic structures. In this case, these other construction parts do not concern tooth gaps, but for example grooves or channels. [0060] Since the invention concerns essentially the intersection angle of axes ∑ described already initially, a definition of this angle∑ and the sign is given in the following. projection of The consideration of work piece and power skiving tool along intersection of the joint plumb of the rotation axes Rl and R2 from the rotation axes axis R2 in the direction of the toothing is called projection of intersection of axes. The Figures 2B, 3A, 4A, 4B, 6A, 6B, 7A, 7B show projections of intersection of axes.

intersection The intersection angle of axes∑ is with respect to its amount angle of axes the smaller one of the angles that is embraced by the two

rotation axes Rl and R2. It becomes visible in the projection of intersection of axes. The following holds:

-90° <∑ < 90°,∑≠0°.

The intersection angle of axes∑ carries a sign. Without restriction of the generality, the sign is defined in the projection of intersection of axes as follows: The intersection angle of axes ∑ is positive, if the projected rotation axis Rl about the intersection point of axes is rotated mathematically negatively about the amount |∑| with respect to the projected rotation axis

R2. Otherwise it is negative. A situation with a positive first intersection angle of axes Σ ¹ is shown e.g . in Fig . 6A and a situation with a negative second intersection angle of axes∑ ² is shown e.g. in Fig . 6B.

effective The effective intersection angle of axes∑ _eff is the angle intersection

embraced by the two velocity vectors ^Vz and ^Vl according to : angle of axes

cos(∑ _e// ) = ^{2 1}

NN . According to the invention the following holds :

-90° < ∑eff < 90°, ∑eff ≠ 0°.

The effective intersection angle of axes ∑ _e ff carries a sign just as the intersection angle of axes∑. The sign of the intersection angle of axes ∑ _e ff is equal to the sign of the intersection angle of axes∑.

For untilted ( S =0°) power skiving tools, the effective

intersection angle of axes ∑ _eff is equal to the intersection angle of axes ∑. Generally, the following holds : cos∑ = cos∑ _e - cosS with the tilt angle δ .

[0061] The invention is based on working with two intersection angles of axes (herein called first intersection angle of axes Σ ¹ and second intersection angle of axes∑ ² ), which differ significantly. According to the invention, for all embodiments, the amount of the difference of the intersection angles of axes is preferably at least 5 degree and particularly preferably more than 10 degree.

[0062] In the following, mention is also made of a "skew-whiff" position of the two rotation axes Rl and R2, if the intersection angle of axes∑ is different from zero. Since according to the invention the intersection angle of axes ∑ is always different from zero, the two rotation axes Rl and R2 are positioned skew-whiff in all embodiments.

[0063] Basic aspects of the method according to the invention are described in the following with reference to the strongly schematized representations of Figures 4A, 4B as well as Figures 5A, 5B, 5C, 5D. These figures serve primarily for the derivation of the inventive solutions and are to be understood as strongly schematized representations.

[0064] In order that the cutting direction SR (see e.g . Fig . 3), i.e. the vector v _c of the cutting direction, at the calculation point AP, points in the direction of the gap 21 to be generated, the inclination angle β _χ and the diameter of the pitch circle d _wl of the power skiving tool must obey the condition d _w2 ^■ n ₂ ^■ cosy¾ = d _wl ^■ n _x ^■ cos^ for a fixed transmission ratio i = n ₂ /n _l . Herein, the diameter d _w2 of the pitch circle and the inclination angle β ₂ of the work piece are to be considered as given . The following possibilities, which differ only by the sign, result for the inclination angle β _χ for a fixed diameter d _wl of the pitch circle : β\ and β = -β\ . In addition, the condition ∑ _eff = β ₂ + β _γ must be fulfilled with the effective intersection angle of axes ∑ _eff , so that the cutting direction SR points in the direction of the gap (compare Fig . 3B) . Fitting with β\ and β _χ , there are thus two possible effective intersection angles of axes ∑ ^l _eff and ∑ ² _eff , for which a machining of the work piece 20 may be carried out respectively with a power skiving tool 10 and the same diameter d _wl of the pitch circle. However, the respective conventional tools differ with respect to the inclination angle β _χ as well as the profile. Two intersection angles of axes ∑ ^l _eff and ∑ _e ² _ff are mathematically associated with the two effective intersection angles of axes Σ ¹ and ∑ ² .

[0065] For β ₂ = 0° , thus for a straight-toothed work piece, ∑ _ff = -∑] _ff . holds.

Thus, a mirror-symmetrical special case is on hand here, as shown in the two subsequent schematic representations of the Figures 4A and 4B. Both representations in the Figures 4A and 4B also hold for: β ₂ = 0° , δ = 0° , ∑ « ±25° .

[0066] Fig . 4A shows a schematic representation of a skiving wheel 10.1 having a conical outer contour in engagement with a straight-toothed inner toothing of a first work piece 20.1 during power skiving in a projection of intersection of axes. A first, here positive intersection angle of axes Σ ¹ of approx. +25 degree has been given here. For clarity, only one cutting tooth 23.1 of the skiving wheel 10.1 and one tooth gap 21 of the work piece 20.1 are shown . Fig . 4A shows in a snap-shot, how the cutting tooth 23.1 works through the material of the work piece 20.1. A portion of a tooth gap 21.1 has been generated already up to the actual point in time of manufacturing . The constructive rake angles resulting from the conical basic shape of the skiving wheel 10.1, can be recognized at the cutting tooth 23.1. [0067] Fig . 4B shows a schematic representation of a situation that is mirror- symmetrical with respect to that of Fig . 4A, that is a skiving wheel 10.1 having a conical outer contour in engagement with a straight-toothed inner toothing of a second work piece 20.1 during power skiving in a projection of intersection of axes. A second, here negative intersection angle of axes∑ ² of approx. -25 degree has been given here. The second work piece 20.2 corresponds to the first work piece 20.1. It is thus possible to manufacture the same work pieces 20.1., 20.2 with the two skiving wheels 10.1 and 10.2, if one manufactures the first work piece 20.1 with the first intersection angle of axes Σ ¹ (refer to Fig. 4A) and the second work piece 20.2 with the second intersection angle of axes∑ ² (refer to Fig. 4B). [0068] For clarity, also in Fig. 4B only one cutting tooth 23.2 of the skiving wheel 10.2 and one tooth gap 21.2 of the work piece 20.2 are shown. Fig. 4B shows in a snap-shot, how the cutting tooth 23.2 works through the material of the work piece 20.2. A portion of a tooth gap 21.2 has been manufactured up to the actual point in time of manufacturing . The constructive rake angles at the cutting tooth 23.2 resulting from the conical basic shape of the skiving wheel 10.2 can be recognized .

[0069] In a comparison of the Figures 4A and 4B one recognizes that in Fig . 4A the right flank cutting edge of the cutting tooth 23.1 is employed for machining the running-in tooth flank eF and in Fig . 4B the left flank cutting edge of the cutting tooth 23.2 is used for machining the running-in flank eF with the respective better effective cutting angle.

[0070] Now, the invention is based on the insight to unify the two tools 10.1 and 10.2 represented in the Figures 4A and 4B in first instance in a virtual power skiving tool 100.1, as shown strongly schematized in Figures 5A and 5B. The Figures 5A and 5B show an intermediate step for defining a power skiving tool 100.2 that is suitable for the power skiving method according to the invention (see Figures 5C and 5D). The virtual power skiving tool 100.1 is "generated" by a graphical resp. numerical superposition of the two tools 10.1 and 10.2. Quasi thereby, the unification of two portions of tools of the cutting teeth 23.1 and 23.2 is formed, whereby the flank cutting edges which are used for machining the running- in flanks eF are taken over. The resulting cutting tooth 23.3 is represented in Fig . 5A by a trapezoid that is encircled by a bold type line. An according front view of the resulting cutting tooth 23.3 is shown in fig. 5B, wherein the final flank cutting edges are represented by a bold type line.

[0071] Now, according to the invention, such a power skiving tool 100.1 is to be applied in the context of a semi-completing power skiving method, since only those flanks are finished therewith, for which the respective optimum intersection angle of axes is used . The tool 100.1 according to Figures 5A and 5B is not only suitable for semi-completing power skiving, since the cutting tooth 23.3 has a width that corresponds to the gap width of the tooth gap

[0072] In order to enable a semi-completing machining, thus the width of the cutting tooth 23.3 must be reduced, which is explained by means of the Figures 5C and 5D. The Figures 5C and 5D show a further step for defining a suitable power skiving tool 100.2 for the power skiving method according to the invention. The power skiving tool 100.2 is derived from the tool 100.1 of Figures 5A and 5B by reducing the width of the head cutting edge. By reducing the front cutting edge, one cutting tooth 23.4 results. The according trapezoid encircled by a bold type line no longer fills the borderlines which have been obtained by the superposition of the two tools 10.1, 10.2 and their cutting teeth 23.1, 23.2. An according front view of the resulting cutting tooth 23.4 is shown in Fig. 5D. The cutting tooth 23.4 is somewhat "slimmer" than the cutting tooth 23.3 in Fig. 5B.

[0073] The basic principle of the method according to the invention for semi- completing power skiving of a work piece 50.1 is shown and described now by means of the Figures 6A to 6D, wherein the tool has a rotationally symmetrical periodical structure which is finished or at which such a structure is to be manufactured from solid material. A special power skiving tool 100.3 is applied in the method according to the invention, which has been calculated and manufactured by means of the steps described previously (refer to Figures 5A to 5D).

[0074] The method according to the invention comprises at least the following steps, wherein these steps must not necessarily be performed in the sequence mentioned :

- providing the work piece 50.1,

- providing the power skiving tool 100.3, which has plural cutting teeth 111 and one rotation axis Rl . Only one cutting tooth 111 is shown in the Figures 6A to 6D.

- Approaching a first relative position RPl with a first intersection angle of axes Σ ¹ of the power skiving tool 100.3 with respect to the work piece 50.1. In the example shown in Fig . 6A and in the example shown in Fig. 7A, the first intersection angle of axes Σ ¹ is positive respectively.

- Starting from the first relative position RPl, a first power skiving machining of the work piece 50.1 is performed, wherein the first intersection angle of axes Σ ¹ is maintained during the first power skiving machining . In Fig. 6A, a position is shown which has been reached starting from the first relative position RPl . In the first relative position RPl, the power skiving tool 100.3 is still outside of the work piece 50.1 and then typically starts a feed motion, in which the position shown in Fig. 6A is passed once. During this first power skiving machining, either all right flanks (generally referred to by 54) or all left flanks (generally referred to by 53) of the periodical structure of the tool 50.1 is finished and the respective other flanks 53, 54 are pre-machined, or an empty cut is performed at the respective other flanks 53, 54. In Figures 6A and 6C, a situation is shown, in which the left flanks are pre-machined (as indicated by the reference numeral 53v, wherein the v stands for pre-machined) and the right flanks are finished (as indicated by the reference numeral 54f, wherein the f stands for finished).

- Now, after all tooth gaps 52 have continuously undergone the first power skiving machining, a second relative position RP2 is approached and thereby a second intersection angle of axes ∑ ² of the power skiving tool 100.3 is adjusted with respect to the work piece 50.1. The second intersection angle of axes∑ ² differs significantly from the first intersection angle of axes Σ ¹ . In the example shown in Fig. 6B, the second intersection angle of axes∑ ² is negative, wherein∑ ² =-∑ ¹ . In the example shown in Fig. 7B, the second intersection angle of axes∑ ² is positive just as the first intersection angle of axes Σ ¹ , however its amount is significantly greater.

- Starting from the second relative position RP2, a second power skiving machining of the work piece 50.1 is carried out, wherein the second intersection angle of axes∑ ² is maintained during the second power skiving machining . In Fig. 6B a position is shown, that has been reached starting from the second relative position RP2. In the second relative position RP2, the power skiving tool 100.3 is still outside of the work piece 50.1 and then typically starts a feed motion, in which the position shown in Fig . 6B is passed once. During the second power skiving machining, those flanks of the periodical structure of the work piece 50.1 are finished (here the left flanks 53), which have only been pre-machined or not yet machined during the first power skiving machining. By means of the Figures 6B and 6D one can recognize that after the first power skiving machining the tooth gap 52 has a gap width that is smaller than after the second power skiving machining . It can be recognized well in Fig . 6B how the cutting tooth 111 pushes from the upside downwards through the gap 52 that has been pre-machined already during the first power skiving machining . Above the work piece 100.3, the gap 52 is already finished and is thus bordered by the finishingly machined flanks 53f and 54f. Below the tool 100.3, the gap 52 is not yet finished and is thus bordered by the pre-machined flank 53v and the finishingly machined flank 54f [0075] According to the invention, each of the cutting teeth 111 comprises a first flank cutting edge 113 for cutting the right flanks 54, a second flank cutting edge 112 for cutting the left flanks 53 and a front cutting edge 114, which is arranged in a transition area between the first flank cutting edge 113 and the second flank cutting edge 112 and which machines the base 55 of the tooth. [0076] Here, at various positions, mention is made of a first relative position RPl and a second relative position RP2. In addition, the approaching of these relative positions RPl or RP2 is described. These two relative positions RPl and RP2 differ in any case by the intersection angles of axes Σ ¹ and∑ ² . In addition, the two relative positions RP1 and RP2 may also differ by other setting values (as e.g . the rotation direction etc.). In the respective relative positions RP1 or RP2, the power skiving tool 100.3 or 100.4 is still located outside of the work piece 50.1 or 50.2.

[0077] In addition, the following lines have been drawn in order to make visible the relative positions of the power skiving tool 100.3 and the work piece 50.1 in the Figures 6C and 6D. The symbol ML represents the centre line of the cutting tooth 111. For tools 100.3 which are designed for toothing straight-toothed work pieces 50.1, the centre line ML corresponds to the centre line of the cutting tooth 111. The virtual centre of the gap of the tooth gap 52 to be machined is indicated by the line LM . A bold dotted line shows in schematized form those sections (flanks) of the cutting tooth 111, which take off material at the work piece 50.1 in the moment shown. In Fig. 6C, material is taken off by the two flank cutting edges 112 and 113 at the tooth flanks 53v, 54f as well as by the complete front cutting edge, as is shown by the mentioned bold type dotted line. In Fig. 6D, material is taken off only by the left flank cutting edge 113 at the tooth flank 53v as well as material at the base 55 of the tooth by the complete front cutting edge, as shown by the mentioned bold type dotted line.

[0078] In all embodiments, the front cutting edge 114 has a width that is smaller than the gap width at the base 55 of the tooth of the gap 52 to be machined at the work piece 50.1, as has been explained by means of Fig . 5C.

[0079] In the machining of straight-toothed work pieces 50.1 according to the principle shown in the Figures 6A to 6D, a reversal of the rotation direction for the work piece 50.1 and the tool 100.3 is necessary in relation with the re-adjustment of the intersection angle of axes from Σ ¹ to∑ ² , since the intersection angles of axes Σ ¹ and∑ ² differ by the sign in the example shown. That is to say, the work piece 50.1 and the tool 100.3 rotate oppositely as compared to previously after the reversal of the rotation direction. In the Figures 6A and 6B, the reversal of the rotation direction is represented by differently oriented angular velocities coi and co ₂ . The reversal of the rotation direction is defined by the equivalent gear which plays an important role in the definition of the geometrical relationships [0080] If the signs of the intersection of axes Σ ¹ and ∑ ² are the same, no reversal of the rotation direction is required .

[0081] According to the invention, during the first power skiving machining, the first power skiving tool 100.3 is rotated in a first rotation direction with the angular velocity <¾ about the rotation axis Rl and the work piece 50.1 is rotated in a second rotation direction with the angular velocity ω ₂ about the work piece rotation axis R2 by CNC-controlled drives (not shown) . After the reversal of the rotation direction, in the second power skiving machining, the power skiving tool 100.3 is rotated in a direction (angular velocity -<¾) opposite to the first rotation direction about the rotation axis Rl and the work piece 50.1 is rotated in a direction about the work piece rotation axis R2 (angular velocity -ω ₂ ) opposite to the second rotation direction by the CNC-controlled drives.

[0082] According to the invention, a transition from the first relative position RP1 to the second relative position RP2 is carried out at least by the re-adjustment of the intersection angle of axes∑ from the first intersection angle of axes Σ ¹ to the second intersection angle of axes∑ ² .

[0083] According to the invention, the following (detailed) steps are carried out respectively during the first power skiving machining and the second power skiving machining of the work piece 50.1 : - rotating the power skiving tool 100.3 about the rotation axis Rl of the power skiving tool 100.3,

- (using the CNC control) coupledly rotating the work piece 50.1 about the work piece rotation axis R2, and

- performing an axial feed motion VB (VB is shown in Fig . 8A) of the power skiving tool 100.3 with respect to the work piece 50.1 in a direction parallel to the work piece rotation axis R2.

[0084] Up to here, the invention has been described on the basis of a straight-toothed work piece 50.1. For straight-toothed work pieces 50.1, in all embodiments, one can work with the same angular velocities coi and co ₂ for the same cutting speeds respectively in the first power skiving machining and the second power skiving machining, as can be taken from the Figures 6A and 6B and the equations presented herein .

[0085] The situation for helical toothings can be derived from the special case of straight-toothing .

[0086] In the machining of helically toothed work pieces with a sufficiently large inclination angle β _χ , the two intersection angles of axes Σ ¹ and ∑ ² may - but do not have to - be chosen such that the mentioned reversal of the rotation direction is not required, which is an advantage, because a gain in time can be achieved thereby, for example. To this end, the two intersection angles of axes Σ ¹ and∑ ² , which differ significantly, must have the same sign, as has been mentioned already. [0087] In this case, the tool profile of the power skiving tool 100.4 is typically asymmetrical . In addition, for helically toothed work pieces 50.2, for equal cutting speeds, one has to work with different rotation speeds respectively angular velocities in the first power skiving machining and the second power skiving machining . A tooth flank is finished in this case as a running-in flank eF, the other tooth flank is finished as a running-out flank aF.

[0088] Now, by means of the Figures 7A and 7B, the basic principle of the method according to the invention for power skiving a helically toothed work piece 50.2 with a large inclination angle is shown and described, wherein the work piece has a rotationally symmetrical periodic structure which is finished, or in which such a structure is to be machined from solid material . In the method according to the invention, a special power skiving tool 100.4 is used, which has been calculated and manufactured on the basis of the steps described previously (refer to Figures 5A to 5D) . For small inclination angles, one even has to work with a reversal of the rotation direction .

[0089] The method according to the invention comprises at least the following steps, whereby these steps do not necessarily have to be carried out in the sequence mentioned : providing the work piece 50.2,

providing the power skiving tool 100.4, which has plural helically toothed cutting teeth 111 and a rotation axis Rl . In the figs. 7 A and 7B, only one cutting tooth 111 is shown respectively.

Approaching a first relative position RPl (shown in Fig. 7A) with a first intersection angle of axes Σ ¹ of the power skiving tool 100.4 with respect to the work piece 50.2 (it is to be taken into account that the relative position RPl does not have to correspond to the relative position RPl according to Fig. 6A or 6C. Also the intersection angles of axes Σ ¹ may differ by the amount and/or the sign). In the example shown in Fig. 7A, the first intersection angle of axes Σ ¹ is positive.

Starting from the first relative position RPl, a first power skiving machining of the work piece 50.2 is carried out, wherein the first intersection angle of axes Σ ¹ is maintained during the first power skiving machining. During this first power skiving machining, either all right flanks (generally referenced by 54) or all left flanks (generally referenced by 53) of the periodical structure of the work piece 50.2 are finished and the respective other flanks 53, 54 are pre-machined in the example shown. In fig . 7A a situation is shown in which the left flanks are finished with a positive effective cutting angle (as indicated by the reference numeral 53f) and the right flanks are pre-machined (as indicated by the reference numeral 54v).

After all the tooth gaps 52 have continuously undergone the first power skiving machining, a second relative position RP2 (see Fig. 7B) is approached and a second intersection angle of axes∑ ² of the power skiving tool 100.4 with respect to the work piece 50.2 is adjusted . In the example shown in Fig . 7B, the second intersection angle of axes∑ ² is positive just as the first intersection angle of axes Σ ¹ , however its amount is significantly greater (it is to be observed that the relative position RP2 does not have to correspond to the relative position RP2 according to Figures 6B or 6D here. Also the intersection angles of axes∑ ² may differ by the amount and/or the sign).

Starting from the second relative position RP2, a second power skiving machining of the work piece 50.2 is carried out, wherein the second intersection angle of axes ∑ ² is maintained during the second power skiving machining . During the second power skiving machining, those flanks of the periodical structure of the work piece 50.2 are finished (here the left flanks 54), which have only been pre- machined or not yet machined during the first power skiving machining . By means of the Fig. 7B one can recognize that after the first power skiving machining, the tooth gap 52 has a gap width which is somewhat smaller than after the second power skiving machining .

[0090] In Fig . 7A, i.e. during the first power skiving machining of the work piece 50.2, the machining of the left tooth flank is carried out as a running-out flank aF with a positive effective cutting angle. In Fig. 7B, i.e. during the second power skiving machining of the work piece 50.2, the machining of the right tooth flank is carried out as a running-in flank eF with a positive effective cutting angle.

[0091] The principle shown in relation with the Figures 5A to 5D of superpositioning the cutting teeth and reducing of the front width of these cutting teeth can be applied analogously also to cutting teeth which are provided with a stair angle. For both relative positions, one thereby starts from cutting teeth, the cutting face of which is oriented approximately perpendicular to the tooth gap to be generated in the calculation point. In the unification of the cutting teeth, the cutting faces which embrace an angle may be connected with each other for example by rounding . That is to say, one obtains a cutting face that is domed in the direction of the width of the cutting tooth.

[0092] Preferably according to the invention, both tooth flanks of the tooth gaps of a spur toothing are finished as running-in flanks, as can be taken from the Figures 6A and 6B. Possibly, it is also conceivable to finish the two flanks as running-out flanks. The concrete implementation of the method according to the invention depends among others from the cutting conditions to be expected .

[0093] The power skiving method described may be applied dry or wet in all embodiments, whereby the use of the power skiving machining in the dry is preferred . [0094] The application spectrum of the power skiving method described is large and extends to the application in the machining of most different rotationally symmetrical periodical structures. [0095] The power skiving tools 100.3, 100.4 described are designed particularly for the power skiving of a work piece 50.1, 50.2, which has a rotationally symmetrical periodical structure. To this end, such a power skiving tool 100.3, 100.4 is used in a CNC-controlled power skiving machine that is programmed and equipped such that it is capable of performing the method described here.

[0096] Fig . 8A shows a perspective representation of a cylindrical outer- toothed work piece, which is referenced here with the reference numeral 50.1, and of a disk-shaped power skiving tool 100.5 in the semi-completing power skiving according to the invention. In the moment shown in fig. 8A, a first intersection angle of axes Σ ¹ is set, while a first power skiving machining of the work piece 50.1 is carried out. The power skiving tool 100.5 has a larger number of cutting teeth 111, which are all arranged on a lateral surface 102 of the power skiving tool 100.5 and which point substantially radially outwards. Each of the cutting teeth 111 has a first flank cutting edge 113 for cutting the right flanks 54, a second flank cutting edge 112 for cutting the left flanks 53 and a front cutting edge 114, which is arranged in a transition area between the first flank cutting edge 113 and the second flank cutting edge 112. [0097] Fig . 8B shows a magnification of a detail of the cylindrical outer- toothed work piece 50.1 and the disk-shaped power skiving tool 100.5 of Fig. 8A viewed from the rear side (respectively from the upper side when related to Fig . 8A) in a moment, in which both flank cutting edges 112, 113 of a cutting head 111 are machining the left flanks 53f and the right flanks 54v of a tooth gap 52. In the moment shown, a left flank 53f is finished and a right flank 54v is pre-machined.

[0098] Fig . 8C shows a magnification of a detail of the cylindrical outer- toothed work piece 50.1 and the disk-shaped power skiving tool 100.5 according to Fig. 8A viewed from the rear side (respectively from the upper side when related to Fig. 8A) in a moment, in which only one flank cutting edge 113 of a cutting head 111 machines a flank 54f of a tooth gap 52 and the other flank cutting edge 112 makes a dummy cut. The representations in Figures 8B and 8C differ in particular in that a first intersection angle of axes Σ ¹ is set in Fig. 8B and a second intersection angle of axes∑ ² is set in Fig . 8C.

[0099] In Fig . 8B (herein also called first power skiving machining) and in Fig. 8C (herein also called second power skiving machining), the viewing direction is the same (in both cases the head surface 56 of the cylindrical outer-toothed work piece 50.1 lies in the plane of the drawing). The rotation axis R2 is perpendicular to the plane of the drawing and the viewing direction runs parallel to the rotation axis R2. One views the tool 100.5 from the rear side (from the upper side when related to Fig . 8A), so that the very cutting faces are not visible, but the clearance surfaces of the cutting heads 111 are visible.

List of reference numerals: shaping wheel 1 work piece 2 tooth head 4 tooth breast 5 skiving tool 10

First skiving tool 10.1 Second skiving tool 10.2

(power-skived) work piece 20 first (power-skived) work piece 20.1 second (power-skived) work piece 20.2 tooth gap 21 cutting face 22 cutting tooth 23 cutting teeth 23.1, 23.2 resulting cutting tooth 23.3 exemplified cutting tooth of a skiving tool 23.4 according to the invention first skived straight-toothed work piece 50.1 second skived helically toothed work piece 50.2 tooth gap 52 left flank in general 53 left flank pre-machined 53v left flank finished 53f right flank in general 54 right flank pre-machined 54v right flank finished 54f base of tooth 55 front surface 56 skiving tool 100 skiving tool 100.1 skiving tool according to the invention 100.2 skiving tool according to the invention for a 100.3 straight-toothed work piece

skiving tool according to the invention for a 100.4 helically toothed work piece

skiving tool according to the invention for a 100.5 straight-toothed work piece

lateral surface 102

Cutting teeth / cutting heads 111

Second flank cutting edge / left flank cutting 112 edge

first flank cutting edge / right flank cutting edge 113 head cutting edge 114 running-out tooth flank aF calculation point AP inclination angle of the tool Bi inclination angle of the tool β\ A ² inclination angle of the work piece β ₂ tilt angle δ diameter of the pitch circle of the tool d _w i diameter of the pitch circle of the work piece d _w2 running-in tooth flank eF transmission ratio I virtual centre of gap LM centre line ML number of teeth of the tool nl number of teeth of the work piece n2 rotation axis of the tool (tool axis) Rl rotation axis of the work piece (work piece axis) first relative position RP1 second relative position RP2 stroke movement s _hx axial feed motion s _ax differential feed motion s _D radial feed motion s _rad cutting direction SR intersection angle of axes ∑ first intersection angle of axes Σ ¹ second intersection angle of axes ∑ ² effective intersection angle of axes ∑„ effective first and second intersection angle of y ¹ ∑ ² axes

feed movement VB amount of cutting speed v _c cutting speed vector v _c speed vector of skiving tool v _x speed vector of work piece v ₂ rotation speed about the axis Rl

rotation speed about the axis R2 ω ₂