Method for producing a toothing, machine tool for producing such a toothing, combination of a workpiece and a tool, and use of a tool in order to produce a toothing

Abstract

The invention relates to a method for producing a toothing, such as a notched toothing or a circular arc toothing, on a workpiece using a tool which comprises at least one tooth with a cutting edge which has a contour that at least partly corresponds to the positive mold of the toothing to be produced. The tool axis and the workpiece axis are parallel to each other during the production of the toothing, and the tool and the workpiece are rotated relative to each other in opposite directions in order to roll the tool and the workpiece over each other during the production of the toothing. The invention additionally relates to a combination of a workpiece and a tool, to a machine tool, in particular a milling machine, for producing a toothing, such as a notched toothing or a circular arc toothing, on a workpiece, and to the use of a tool in order to produce a toothing, such as a notched toothing or a circular arc toothing, on a workpiece.

Description

[0001] Method for producing a gear, machine tool for producing such a gear, combination of workpiece and tool and use of a tool for producing a gear

[0002] Description

[0003] The invention relates to a method for producing a gearing, a machine tool for producing such a gearing, a combination of workpiece and tool and the use of a tool for producing such a gearing, in detail according to the features of the independent claims.

[0004] Several processes are already known from the state of the art for the machining of gears using tools.

[0005] In polygon turning—also known as gear skiving or hobbing—the workpiece and tool roll against each other. The rotational axis is at an angle to the rotational axis of the workpiece throughout the entire machining process. The tool comprises a relatively complex negative form of the gear to be milled. It therefore has essentially as many teeth as the finished gear. Different tools must therefore be in stock for different pitches and gear diameters. This process is particularly suitable for producing peripheral gears.

[0006] In polygonal turning or fly-tooth milling, the two axes of rotation are at an angle to each other during machining. The tool does not necessarily have to have the entire negative shape of the gear to be produced. Furthermore, significantly fewer teeth on the tool are sufficient. This process is used for the production of axial gears. In both of the aforementioned processes, all teeth across the entire circumference of the workpiece are produced with a full rotation of the workpiece along the width of the tool.

[0007] In another process, gear shaping, the shaping tool—which only produces one and the same tooth at a time—moves back and forth parallel to the workpiece's rotational axis. Therefore, the tool does not roll on the workpiece during this shaping motion. Only by further indexing the workpiece by the tooth pitch is the next tooth cut out of the workpiece. Based on the existing processes, there is still a need to improve the manufacturing process, in particular to reduce machining time, increase the accuracy of the gearing to be produced, and to specify a tool that can be used for multiple pitches or gear diameters.

[0008] The object of the present invention is to provide a method for producing a gear, a machine tool for producing such a gear, a combination of workpiece and tool as well as the use of a tool for producing such a gear, which are improved compared to the prior art.

[0009] The object is achieved by a method for producing a gearing, a machine tool for producing such a gearing, a combination of workpiece and tool, and the use of a tool for producing such a gearing according to the independent claims. The dependent claims describe particularly useful embodiments of the invention.

[0010] In a method according to the invention for producing a toothing, such as serrations or circular arc toothing, on a workpiece by means of a tool, the at least one tooth comprises a cutting edge which has a contour which corresponds at least partially to the positive shape of the toothing to be produced, wherein the tool axis and the workpiece axis are parallel to one another during the production of the toothing and the tool and the workpiece are driven in rotation in opposite directions to one another in order to roll on one another during the production of the toothing.

[0011] In other words, the contour of the cutting edge corresponds to the negative form of the gear to be produced. The negative form (contour of the cutting edge) and the positive form (manufactured gear) are complementary to each other. The term "during production" refers to the time during which the tool and workpiece are in mesh, i.e., rolling against each other.

[0012] The term "tool axis" or "workpiece axis" refers to the respective rotational or rotary axis of the respective tool or workpiece. These rotational or rotary axes can also be corresponding axes of symmetry.

[0013] By means of the present invention, periodically recurring structures (in this case: gear teeth) can be produced. This is achieved by machining parallel to the axis with a counter-rotating workpiece and tool. The resulting tool movement corresponds to the mathematical shape of a cycloid as soon as the circle that defines the circumference of the workpiece is unfolded as a line. The cycloid can be an extended or twisted cycloid (which forms "loops" and points of intersection with itself) because the cutting edge(s) lie on a larger outer diameter than the tool shank. However, because in the cycloid both circles roll onto one another (onto the outer circumference), i.e. the outer diameter of the cutting edge(s) - also called the tool radius - and the outer diameter of the workpiece, the cycloid is strictly speaking an epicycloid, and accordingly an extended or twisted cycloid.An intertwined epicycloid that forms "loops" and intersections with itself. These occur when the outer diameter of the tool, including the cutting edge(s), is larger than the outer diameter of the workpiece. The parameters of the cycloid or epicycloid are selected so that the number of loops or intersections corresponds to the number of tooth gaps. Since the cutting edge(s) of the tool move periodically along the epicycloid, thus removing the tooth gap from the tooth tip of two directly adjacent teeth, the tooth gap approximately takes on the part of the shape of the intertwined epicycloid that forms the "loop." Since this part is round, circular arc gearing can be produced in this way.

[0014] The shape of the cycloid is designed to approximate the desired tooth shape, or more precisely, the tooth gap shape, as closely as possible in the cutting edge engagement area. The control variables are the center distance and the tool radius. Additionally, the profile diameter and profile center distance can be influenced by the following measures: the selection of the technological parameters (feed, chip thickness) and the resulting machining forces, the selection of the tool radius, and the variation of the axis intersection angle up to ±10°. The tool angles a and y should be selected so that favorable machining conditions prevail both at the cutting edge entry and exit.

[0015] In particular, the tooth shape can comprise a circular arc with any number of teeth, any pitch circle and circular arc diameter, which is determined by the tool and also by the speed ratio i.

[0016] The speed ratio i between workpiece n? and tool no can be: no Z 2 l = — = - n2 z0 where n2 is the speed of the workpiece, no is the speed of the tool, z? is the number of teeth of the gearing to be produced on the workpiece and zo is the number of teeth on the tool and the number of teeth zo of the tool is selected such that the greatest common divisor of Z2 and zo is not greater than 1. The speed ratio i between tool and workpiece is therefore coupled to the negative theoretical ratio of the number of teeth between the two rolling partners, tool and workpiece. Therefore, the tool does not have to have all of the teeth that are on the gearing to be produced; only a subset of them can be attached to the workpiece. Preferably, the greatest common divisor should be exactly 1. This means that 29 teeth could be provided on the tool, for example, and 30 teeth would then be produced on the workpiece.One could also say that the above definition, that the greatest common factor of z? and zo should not be greater than 1 number of teeth on the tool, is identical to the definition that the number of teeth on the tool should always differ from the number of teeth on the gear to be produced on the workpiece, in particular by one, namely that zo is always one less than Z2. Thus, the tool could always have one fewer tooth than the number of teeth on the gear to be produced on the workpiece. This applies insofar as just one gear can be produced with the tool: For example, at least one tooth on the tool is needed to produce two gears on the workpiece.

[0017] During the toothing process, the tool is preferably moved relative to the workpiece—or vice versa—along an axis parallel to the workpiece's longitudinal axis to produce the desired toothing length, so that the tool, with the outer contour of the cutting edge, is moved linearly along the tooth flank to be produced and parallel to the tooth gap base. One could also say that the distance between the tool and the workpiece remains constant during the toothing process, i.e., when the cutting edge moves into and out of the workpiece.

[0018] During the production of the gearing, the tool can be moved relative to the workpiece - or vice versa - simultaneously along a further, second axis that is perpendicular to the longitudinal axis of the workpiece in order to produce a conical gearing. When we talk about a conical gearing here, we mean that the workpiece can be conical, i.e. its outer diameter changes along the longitudinal axis of the workpiece. The workpiece is therefore conical or truncated cone-shaped, at least over part of its outer diameter. In order to always achieve the same gearing depth over the conical outer circumference, the gearing is also conical. Thus, the characteristic of the conical gearing requires a conical outer circumference of the workpiece while maintaining a constant tooth depth.In principle, it would also be conceivable for the workpiece to be cylindrical and the toothing to be conical, so that the depth changes over its course.

[0019] The toothing produced in this way can be a serrated toothing or a circular arc toothing.

[0020] The method is preferably used to produce external or peripheral gearing.

[0021] The present invention also relates to a tool according to the invention for producing a gear, such as serrations or circular arc gears on a workpiece, wherein the tool has at least one tooth with a cutting edge that comprises a contour that corresponds at least partially to the positive shape of the gear to be produced, the tool is designed as a peripheral milling cutter, so that the at least one tooth is directed away from the tool in the radial direction of the tool, the outer diameter of the at least one cutting edge is greater than the distance between two adjacent tooth flanks of the gear to be produced and the cutting edge has a length, a width and a height and the width is dimensioned such that it represents a fraction of the flank length of the gear to be produced in the workpiece.

[0022] The number of teeth zo of the tool can be calculated according to the following formula for the speed ratio i: no Z 2 l = — = - n2 z0 where n2 is the rotational speed of the workpiece, no is the rotational speed of the tool, z? is the number of teeth of the gearing to be produced on the workpiece and zo is the number of teeth on the tool, and the number of teeth zo of the tool is selected such that the greatest common divisor of Z2 and zo is not greater than 1.

[0023] Preferably, the tool has as many cutting edges as the number of teeth (and the number of tooth gaps) of the gear to be produced.

[0024] The invention also relates to a combination of a workpiece and a tool according to the invention.

[0025] The present invention also relates to a machine tool, in particular a milling machine, for producing gear teeth, such as serrations or circular arc gear teeth, on a workpiece, comprising a machine frame; a tool carrier mounted on the machine frame, in which a tool is received; a first drive device for rotating the tool in the tool carrier about a tool axis; a receiving device mounted on the machine frame for receiving a workpiece; a second drive device for rotating the receiving device about a workpiece axis; a translational drive device for generating a relative translational movement between the tool carrier and the receiving device along at least two axes;a control device configured to allow control of the relative linear movements between the tool carrier and the receiving device substantially simultaneously; wherein the tool is designed as a peripheral milling cutter, such that the at least one tooth is directed away from the tool in the radial direction of the tool; wherein the tool has at least one tooth with a cutting edge comprising a contour that corresponds at least partially to the positive shape of the gearing to be produced; wherein the outer diameter of the at least one cutting edge is greater than the distance between two adjacent tooth flanks of the gearing to be produced;wherein the control device is configured to move the tool through the area of ​​the gearing to be produced on the workpiece such that it is displaced overall along the tooth flanks to be machined at a constant distance from the tooth gap base and / or the tooth tip of the gearing to be produced; wherein the tool axis and the workpiece axis are parallel to one another during the production of the gearing, and the tool and the workpiece are driven in rotation in opposite directions to roll against one another during the production of the gearing.

[0026] In the machine tool, the control device can be set up in such a way that the tool is displaced relative to the workpiece - or vice versa - along an axis which runs parallel to the longitudinal axis of the workpiece during the production of the gearing in order to produce the desired length of the gearing, so that the tool is displaced with its outer diameter of the cutting edges linearly along the tooth flank to be produced parallel to the tooth gap base, wherein preferably the tool is displaced relative to the workpiece - or vice versa - simultaneously along a further, second axis which is perpendicular to the longitudinal axis of the workpiece during the production of the gearing in order to produce a conically running gearing.

[0027] Finally, the invention relates to the use of a tool for producing a gear, such as serrated gears or circular arc gears on a workpiece, wherein the tool is preferably designed according to the invention and has at least one tooth, with a cutting edge which comprises a contour which corresponds at least partially to the positive shape of the gear to be produced, the tool is designed as a peripheral milling cutter, so that the at least one tooth is directed away from the tool in the radial direction of the tool, the outer diameter of the at least one cutting edge is greater than the distance between two adjacent tooth flanks of the gear to be produced and the cutting edge has a length, a width and a height and the width is dimensioned such that it represents a fraction of the flank length of the gear to be produced in the workpiece.

[0028] The tool diameter (outer diameter of the cutting edge(s)) can preferably be selected so that it is larger than the outer diameter of the workpiece.

[0029] In principle, what has been said about the process also applies analogously to the tool, the combination of tool and workpiece, the machine tool and the use of the tool.

[0030] The advantages of the invention will now be explained in more detail with reference to a preferred embodiment and the figures.

[0031] It shows:

[0032] Fig. 1 shows a spatial representation of a combination of workpiece and tool according to a possible embodiment; Fig. 2 shows the resulting cutting edge movement in the workpiece coordinate system;

[0033] Fig. 3 is a schematic representation of a machine tool according to a possible embodiment;

[0034] Fig. 4 shows a schematic embodiment of a tool according to the invention;

[0035] Fig. 5 shows the cutting movement of a cutting edge of the tool on the workpiece.

[0036] Fig. 1 shows a spatial representation of a combination of a workpiece 7 and a tool 3 according to the invention according to a possible embodiment. More specifically, the representation shows the point in time at which the tool 3 has completely produced a toothing on the workpiece 7 and is now disengaged from the workpiece 7.

[0037] The tool 3 is designed here as a peripheral milling cutter, ie, it comprises a plurality of teeth 9 arranged radially to its shank and is intended to produce external toothing on the circumference of the workpiece 7. Each tooth 9 of the tool has a cutting edge 13, which is intended, for example, to produce toothing on the workpiece 7.

[0038] The number of teeth 9 of tool 3 can be determined based on the speed ratio i mentioned above. Thus, the number of teeth zo of tool 3 can be selected such that the greatest common factor of z? and zo is not greater than 1. In principle, it would be conceivable for tool 3 to comprise only a single tooth 9. In the embodiment shown in Fig. 1, the number of teeth corresponds to the number of tooth gaps of the gearing on workpiece 7.

[0039] Fig. 3 shows a schematic representation of the basic components of a machine tool according to the invention. This comprises a machine frame 1 and a holding device 6 mounted thereon for supporting the workpiece 7 to be machined. A rotary drive device 8 is assigned to the holding device 6 and / or the workpiece 7 in order to rotate the workpiece 7 and / or the holding device 6 about the workpiece axis 10 (in this case the C-axis). The machine frame 1 also carries a drive device 4 for rotating a tool carrier 2 containing the tool 3 about the tool axis 5. The drive device 4 and the tool carrier 2 are combined in this case to form a tool head. The tool head is movable relative to the workpiece along three mutually perpendicular axes X, Y, Z. For this purpose, at least one translational drive device 11 is provided.The tool head can be rotatable about the B-axis to generate a relative angular movement between the tool axis 5 and the workpiece axis 10. However, this is not necessary for the invention; it is sufficient if the B-axis is set so that it runs parallel to the workpiece axis 10. The machine tool here therefore comprises 5 axes, which can be controlled essentially simultaneously via a control device 12. The B-axis could also be omitted for the invention. The control device 12 is configured such that it can move the tool 3 through the area of ​​the gearing to be produced on the workpiece 7, so that it is displaced overall along the tooth flanks to be machined at a constant distance from the tooth gap base and / or the tooth tip of the gearing to be produced. This means that the tool axis 5 and the workpiece axis 10 remain parallel to one another during machining.

[0040] To produce the gearing, the tool 3 is positioned with its tool axis 5 parallel to the workpiece axis 10, and the workpiece 7 is clamped in the holding fixture 6. The tool 3, the holding fixture 6, and thus the workpiece 7 are driven in opposite directions of rotation by the machine tool, more precisely by means of the rotary drive devices 4. For example, the tool 3 rotates counterclockwise about its tool axis 5, as indicated by the arrow in Fig. 1, whereas the workpiece 7 rotates clockwise about its workpiece axis 10. The tool 3 is advanced in the radial direction of the workpiece 7 with regard to the milling depth of the gearing (e.g., along the X and / or Y axis in Fig. 3) and then moves, as indicated by the double arrow, parallel to the workpiece axis 10 (along the Z axis in Fig. 3), i.e., parallel to the tooth gap base of the gearing to be produced.At the start of machining, tool 3, for example, during axial travel parallel to workpiece axis 10, strikes workpiece 7 with cutting edge 13 and begins to machine it. While workpiece 3 and tool 7 rotate, tool 3 is moved along the Z-axis until it exits workpiece 7 once the gear teeth have been completely produced. The tool can then be moved radially away from workpiece axis 10 along the X- and / or Y-axis. A movement along the X- and / or Y-axis with simultaneous axial movement of the Z-axis can also be used to produce conical gear teeth.

[0041] Due to the superposition of both rotations of workpiece 7 and tool 3, each cutting edge 13 of tool 3 executes part of a cycloid, more precisely an epicycloid Z, which corresponds to the positive shape of the tooth gap of the gearing. This is shown in more detail in Fig. 2. Thus, in principle, a tool 3 with only one tooth 9 would be necessary to produce the gearing shown in Fig. 2.

[0042] Regardless of the number of teeth, the contour of the cutting edge 13 can be selected such that it at least partially corresponds to the positive shape of the toothing to be produced, or more precisely, to the tooth gap to be created. As indicated in Fig. 1, the contour of tooth 9 or the cutting edge 13 could, for example, be approximately semicircular.

[0043] Fig. 5 shows the cutting edge movement of a cutting edge 13 of tool 3 on workpiece 7, of which the tip circle of the gear to be produced is indicated by the dashed arc. A portion of the epicycloid Z can be seen, here a twisted part ("loop" with an intersection point), which corresponds to the positive shape of the contour of a tooth gap on workpiece 7.

[0044] Independently of the embodiments shown, one could also say that the toothing produced is a serration or circular arc toothing, in which the tool and machining parameters are selected such that the rolling movement of tool 3 and workpiece 7 results in an intertwined epicycloid Z, the “loops” of which lie radially within the tip circle of the toothing to be produced, compare also Fig. 2.

[0045] In Fig. 5, the same cutting edge 13 is shown at three different moments (entry, middle, exit) while traversing the epicycloid Z. Here, the epicycloid Z is shown as a solid line, which represents the ideal or theoretical shape of the epicycloid Z. The dashed cycloid corresponds to the actual travel path of the cutting edge. For simplicity, the cutting edge is shown here as a triangle.

[0046] Cutting edge 13 thus plunges into workpiece 7 at the entry (right position), continues along the "loop" of epicycloid Z through the center (lower position) to the exit (left position), and transfers its movement along epicycloid Z as a positive form to workpiece 7, thereby creating the tooth gap base of the gearing. It can be seen that cutting edge 13 has different angles of attack at the entry (right position), approximately in the center (lower position), and at the exit (left position). These result from the two opposite rotations of tool 3 and workpiece 7.

[0047] Fig. 4 shows a schematic, three-dimensional representation of a possible embodiment of the tool 3, wherein only one tooth 9 with a cutting edge 13 is shown. Here it is indicated that the outer diameter A of the at least one cutting edge 13 is greater than the distance between two adjacent tooth flanks of the gearing to be produced, i.e. it is a peripheral and not an end mill. The cutting edge 13 has a length Ls, a width Bs (along the tool axis 5) and a height Hs (perpendicular to the tool axis 5). The width is dimensioned such that it corresponds to a fraction of the flank length F (see Fig. 1) of the gearing to be produced in the workpiece 7. The cutting edge 13 can therefore be made significantly shorter, which is particularly advantageous for the machining process and the forces acting on it.

[0048] Reference symbol

[0049] 1 machine frame

[0050] 2 tool carriers

[0051] 3 tools

[0052] 4 Drive device

[0053] 5 tool axis

[0054] 6 Mounting device

[0055] 7 Workpiece

[0056] 8 rotary drive device

[0057] 9 tooth

[0058] 10 Workpiece axis

[0059] 11 translational drive device

[0060] 12 Control device

[0061] 13 cutting edges

[0062] A outer diameter

[0063] B B-axis

[0064] B s Wide cutting edge

[0065] C C-axis

[0066] F flank length

[0067] H s Cutting edge height

[0068] Ls length cutting edge

[0069] X X-axis

[0070] Y Y-axis

[0071] Z Z-axis n0 tool speed n2 n2 workpiece speed

Claims

Claims 1. Method for producing a gear, such as serration or circular arc gear, on a workpiece (7) by means of a tool (3) which comprises at least one tooth (9) with a cutting edge (13) which has a contour which corresponds at least partially to the positive shape of the gear to be produced, wherein the tool axis (5) and the workpiece axis (10) are parallel to one another during the production of the gear and the tool (3) and the workpiece (7) are driven in rotation in opposite directions to one another in order to roll on one another during the production of the gear.

2. Method according to claim 1, characterized in that the speed ratio i between workpiece (7) n? and tool (3) no is: n0 Z 2 i = — = - n2 z0 where n2 is the rotational speed of the workpiece (7), no is the rotational speed of the tool (3), z? is the number of teeth of the gearing to be produced on the workpiece (7) and zo is the number of teeth on the tool (3), and the number of teeth zo of the tool (3) is selected such that the greatest common divisor of Z2 and zo is not greater than 1.

3. Method according to claim 1 or 2, characterized in that during the production of the gearing the tool (3) is displaced relative to the workpiece (7) - or vice versa - along an axis (Z) which runs parallel to the longitudinal axis of the workpiece (7) in order to produce the desired length of the gearing, so that the tool (3) with the outer contour of the cutting edge (13) is displaced linearly along the tooth flank to be produced and parallel to the tooth gap base.

4. Method according to claim 1 or 2, characterized in that the tool (3) is displaced during the production of the toothing relative to the workpiece (7) - or vice versa - simultaneously along a further, second axis (X, Y) which is perpendicular to the longitudinal axis of the workpiece (7) in order to produce a conically extending toothing.

5. Method according to one of claims 1 to 4, characterized in that the toothing produced is a serrated toothing or circular arc toothing. Method according to one of claims 1 to 5, characterized in that the method is used for producing external or circumferential gearing. Tool (3) for producing gearing, such as serrated gearing or circular arc gearing, on a workpiece (7), wherein the tool (3) has at least one tooth (9) with a cutting edge (13) comprising a contour that at least partially corresponds to the positive shape of the gearing to be produced, the tool (3) is designed as a circumferential milling cutter, such that the at least one tooth (9) is directed away from the tool (3) in the radial direction thereof, the outer diameter of the at least one cutting edge (13) is greater than the distance between two adjacent tooth flanks of the gearing to be produced, and the cutting edge (13) has a length (Ls), a width (Bs), and a height (Hs), and the width (Bs) is dimensioned such that it corresponds to a fraction of the flank length (F) of the gearing to be produced in the workpiece (7).Tool (3) according to claim 7, characterized in that the number of teeth zo of the tool (3) is determined according to the following formula of the speed ratio i: no. Z 2 l = — = - n2 z0 where n2 is the rotational speed of the workpiece (7), no is the rotational speed of the tool (3), z? is the number of teeth of the gearing to be produced on the workpiece (7), and zo is the number of teeth on the tool (3), and the number of teeth zo of the tool (3) is selected such that the greatest common divisor of Z2 and zo is not greater than 1, preferably exactly 1. Tool (3) according to claim 7 or 8, characterized in that the tool (3) has as many cutting edges (13) as the number of teeth of the gearing to be produced. Tool (3) according to one of claims 1 to 9, characterized in that the outer diameter of the cutting edge(s) (13) is greater than the outer diameter of the workpiece (7). Combination of workpiece (7) and tool (3) according to one of claims 7 to 10. Machine tool, in particular a milling machine, for producing a gearing, such as serrated gearing or circular arc gearing, on a workpiece (7), comprising a machine frame (1); a tool carrier (2) mounted on the machine frame (1), in which a tool (3) is received; a first drive device (4) for rotating the tool (3) in the tool carrier (2) about a tool axis (5); a receiving device (6) mounted on the machine frame (1) for receiving a workpiece (7); a second drive device (8) for rotating the receiving device about a workpiece axis (C); a translational drive device (11) for generating a relative translational movement between the tool carrier (2) and the receiving device (6) along at least two axes; a control device (12) configured to allow control of the relative linear movements between the tool carrier (2) and the receiving device (6) substantially simultaneously;wherein the tool is preferably manufactured according to one of claims 7 to 10, wherein the tool (3) is designed as a peripheral milling cutter, such that the at least one tooth (9) is directed away from the tool (3) in the radial direction thereof; wherein the tool (3) has at least one tooth (9) with a cutting edge (13) that comprises a contour that corresponds at least partially to the positive shape of the gearing to be produced; wherein the outer diameter (A) of the at least one cutting edge (13) is greater than the distance between two adjacent tooth flanks of the gearing to be produced, and preferably the cutting edge (13) has a length (Ls), a width (Bs), and a height (Hs), and the width (Bs) is dimensioned such that it corresponds to a fraction of the flank length (F) of the gearing to be produced in the workpiece (7);wherein the control device (12) is configured to move the tool (3) through the region of the toothing to be produced on the workpiece (7) in such a way that it is displaced overall along the tooth flanks to be machined at a constant distance from the tooth gap base and / or the tooth tip of the toothing to be produced; wherein; the tool axis (5) and the workpiece axis (10) are parallel to each other during the production of the gearing and the tool (3) and the workpiece (7) are driven in rotation in opposite directions to each other in order to roll on each other during the production of the gearing.Machine tool according to claim 12, characterized in that the control device (12) is set up such that the tool (3) is displaced relative to the workpiece (7) - or vice versa - along an axis (Z) which runs parallel to the longitudinal axis of the workpiece (7) during the production of the gearing in order to produce the desired length of the gearing, so that the tool (3) with its outer diameter of the cutting edge(s) (13) is displaced linearly along the tooth flank to be produced, parallel to the tooth gap base, wherein preferably the tool (3) is displaced relative to the workpiece (7) - or vice versa - simultaneously along a further, second axis (X, Y) which is perpendicular to the longitudinal axis of the workpiece (7) during the production of the gearing in order to produce a conically running gearing.Use of a tool (3) for producing a gear, such as serrated gearing or circular arc gearing, on a workpiece (7), wherein the tool (3) is preferably produced according to one of claims 7 to 10 and has at least one tooth (9) with a cutting edge (13) that comprises a contour that corresponds at least partially to the positive shape of the gear to be produced, the tool (3) is designed as a peripheral milling cutter, so that the at least one tooth (9) is directed away from the tool (3) in the radial direction thereof, the outer diameter of the at least one cutting edge (13) is greater than the distance between two adjacent tooth flanks of the gear to be produced, and the cutting edge (13) has a length, a width, and a height, and the width is dimensioned such that it represents a fraction of the flank length (F) of the gear to be produced in the workpiece (7).

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