Method and system for creating a tooth base contour

Abstract

A method for creating a tooth root contour (1) comprising determining (S10) tooth root contour reference data, wherein the tooth root contour reference data describe at least one tooth root contour reference (2) for a workpiece; and determining (S20) tool data based on the tooth root contour reference data, wherein the tool data describe at least one tool geometry with which a tooth root contour (1) can be produced that partially corresponds to the tooth root contour reference (2); wherein the tool(s) is / are standard milling cutter(s).

Description

[0001] The present invention relates to a method and in particular a system for creating a tooth root contour, in particular a rolled one.

[0002] Reference is made to DE 747 715 A, the non-patent literature by Schossig, HP: "The Easy Way to Good Teeth - Milling High-Quality Gears on Standard Machines." WORKSHOP AND OPERATION. Munich: Carl Hanser Verlag, 2007. pp. 28 to 32. - ISBN 0043-2792; and CH 251 949 A.

[0003] The object of the present invention is in particular to simplify the creation of a tooth root contour, in particular to make it more efficient and / or more universal, in particular to improve the creation.

[0004] This object is achieved by a method having the features of claim 1. Claims 6 and 7 protect a system, computer program, or computer program product for implementing a method described herein. The subclaims relate to advantageous developments.

[0005] According to one embodiment of the present invention, a method for creating a tooth root contour is provided. In one embodiment, the method for creating and / or producing a tooth root contour is implemented on a universal machine. In one embodiment, the method for creating a tooth root contour is implemented using, in particular, conventional, standard tools and / or standard milling cutters. In one embodiment, the method comprises determining tooth root contour reference data, wherein the tooth root contour reference data describe at least one tooth root contour reference for a workpiece, in particular one to be machined. In one embodiment, the tooth root contour reference data describe a tooth root contour reference that can be produced from the workpiece.In one embodiment, the method comprises determining tool data based on the tooth root contour reference data, wherein the tool data describe at least one tool geometry with which a tooth root contour can be produced which corresponds, at least substantially and / or partially, to the tooth root contour reference, wherein a or the tool is in particular a standard milling cutter or wherein the tools are standard milling cutters.

[0006] In one embodiment, the tool data describe at least one tool geometry of a standard milling cutter, which in particular corresponds to the tooth root contour

[0007] reference data is / are compatible and / or for which a compatibility was or is determined in particular by determining the compatibility of the tool geometry with the workpiece and / or the tooth root contour reference data, wherein the determination of the compatibility, in one embodiment, comprises checking the tool geometry(s), in particular at least one dimension of the tool described by the tool data, and at least one dimension of the tooth root contour reference in an at least substantially identical dimensional direction or effective direction of the tool to be checked, in particular in the circumferential direction. In one embodiment, the determination of the compatibility comprises checking the tool geometry or size with respect to the distance between the 30° tangents of the two opposite tooth flanks.

[0008] Advantageously, in one embodiment, this makes it possible to create a tooth root contour using standard tools or standard milling cutters, in particular to make it possible for a tooth root contour to be created using at least one standard milling cutter.

[0009] In one embodiment, the method comprises, in particular, the upstream creation of a preliminary toothing and / or roughing. In one embodiment, the method comprises, in particular, the downstream finishing of the created and / or manufactured tooth root contour. This advantageously simplifies the creation of a tooth root contour.

[0010] According to the invention, the method comprises determining tooth root contour data based on the determined tool data and the determined tooth root contour reference data, wherein the tooth root contour data represent at least one tooth root contour that can be created in particular using one and / or more tool geometries described by the determined tool data or that is designed to be created with the determined tool geometries. In one embodiment, the determination of tooth root contour data, in particular for a plurality of described tool geometries, comprises determining a sequence by means of which the tooth root contour can be produced and / or for whose sequence compatibility was or could be determined. In one embodiment, the method comprises creating and / or producing the tooth root contour, in particular based on the tooth root contour data.

[0011] The term "creation" as used herein should be understood in particular as digital creation, in particular in the sense of "planning" and / or "visualizing," in particular "predicting success," and / or physical creation. In one embodiment, the creation of a tooth root contour comprises manufacturing the tooth root contour, in particular on a universal machine, further in particular on a 5-axis universal machine, in particular with the standard tool(s) or standard milling cutter(s).

[0012] The term "standard tool" as used herein should be understood in particular as a tool that is independent of the workpiece and / or product to be created and / or manufactured. In one embodiment, the term "standard tool" should not be understood in particular as a form milling cutter that is designed, at least essentially, to create and / or produce a tooth root contour reference.

[0013] Advantageously, in one embodiment, this allows for the creation of a tooth root contour that can be manufactured more efficiently, particularly using simpler means, in particular a universal machine and / or a ("universal") tool or (standard) tool or standard milling cutter. Furthermore, this advantageously allows for the creation and / or production of a tooth root, in particular a gearing, more cost-effectively.

[0014] The term "universal machine," as used herein, is to be understood in particular as a machine or multi-purpose machine that, in contrast to a special-purpose or single-purpose machine, is versatile in its use, particularly with regard to its application and / or performance. Universal machines are typically used in workshop production, individual production, and small-batch production, or are designed for this purpose.

[0015] According to the invention, the method, in particular the determination of tooth root contour data, comprises determining at least one tool position, path data, and / or process data, in particular based on the tool data and / or the tooth root contour reference data. In one embodiment, a tooth root contour can be determined, in particular created, and further in particular, at least substantially produced, based on or based on the tool position, the path data, and / or the process data.

[0016] The term "tool position," as used herein, is to be understood in particular as a position of the tool in the x and / or y direction, in particular in an xy surface, which is furthermore in particular at, at least substantially, a right angle to the axis of rotation of the tooth (root) contour, furthermore in particular with respect to an xy position of the tooth root contour reference, in particular in accordance with a common standard, such as in particular ISO 6336-3, in particular such that a zero position of the x direction is located on the axis of symmetry of the tooth root. Advantageously, in one embodiment, in particular with the aid of the tool data, a section of a tooth root contour or a tooth root contour can be determined that is or can be created by a tool geometry at and / or at the tool position.

[0017] The term "path data" as used herein is to be understood in particular as data that describe at least one path of the tool for creating and / or producing the tooth root contour, in particular the entirety of the path(s) used to create and / or produce the tooth root contour, in particular based on the determined tooth root contour data, wherein the path data in particular has at least one determined tool position, further in particular all determined tool positions.

[0018] The term “process data”, as used herein, is to be understood in particular as data which, in particular in addition to the path data, describe further data and / or parameters which are necessary or required for the setup / adjustment of a machine, in particular a universal machine, into which the standard tool or the standard milling cutter(s) can be clamped or which is set up for this purpose and / or which can be used or are used for this purpose.

[0019] In one embodiment, this advantageously makes it possible to keep manufacturing costs within an economic framework, in particular to estimate whether creation and / or production based on the tooth root contour reference data and / or the tool data, in particular with regard to the workpiece which is to have the manufactured tooth root contour, can be carried out economically and / or efficiently.

[0020] In one embodiment, the determination of tooth root contour data comprises determining a maximum deviation from the determined tooth root contour reference data. In one embodiment, a deviation of the tooth root contour data is smaller than a predetermined maximum deviation and / or a predetermined deviation, in particular such that a tooth root contour reference described by the tooth root contour reference data is not exceeded or has been exceeded, in particular the tooth root contour reference is not, at least substantially, intersected in a partial section and / or in a predetermined partial section by the tooth root contour represented by the tooth root contour data. In one embodiment, the determination of the tooth root contour data comprises determining an interference contour which can arise or can arise in particular due to the tool position(s), path data and / or process data.arises, wherein in one embodiment a check, in particular with the aid of a simulation, of the functionality of the tooth root contour is determined and, if non-functionality is determined, at least one tool position, a (tool) path described by the path data and / or process data are changed, in particular in such a way that the determined interference contour is, at least substantially, removed and / or reduced in such a way that functionality of the tooth root contour can be or is guaranteed. In one embodiment, the determination of the tooth root contour data additionally or alternatively comprises determining a tooth root load-bearing capacity, in particular with the aid of a simulation, wherein if a predetermined tooth root load-bearing capacity is not achieved oris, at least one tool position, a (tool) path described by the path data and / or process data are changed, in particular in such a way that the predetermined tooth root load-bearing capacity is at least substantially reached or exceeded. In one embodiment, the determination of the tooth root contour data additionally or alternatively comprises determining a (resulting) roughness, in particular a roughness and / or surface roughness that can arise or arises during production and / or a (resulting) hill (see explanations below), in particular with the aid of a simulation. If, in one embodiment, the determined roughness shows that in particular oil and / or lubricant cannot run off, in particular from the created and / or manufactured orIn one embodiment, at least one tool position, a (tool) path described by the path data, and / or process data are changed, in particular such that the tooth root contour has a roughness from which oil and / or lubricant can run off. In one embodiment, the type of oil and / or lubricant to be used is taken into account. In one embodiment, a further tool position is added for this case and / or a (tool) path is changed or supplemented, in particular by a (further) tool position.

[0021] This advantageously makes it possible, in one embodiment, to create a tooth root contour that has a (high) similarity to the tooth root contour reference, in particular, has at least comparable strengths, and can be created and / or manufactured more efficiently. Advantageously, in one embodiment, a tooth root contour can be created and / or manufactured while maintaining functionality, in particular more cost-effectively.

[0022] In one embodiment, determining tooth root contour data comprises optimizing the at least one tool position and / or optimizing the path data and / or increasing a number of tool positions. In one embodiment, the optimization has a minimum number of tool positions as a target variable. In one embodiment, the optimization comprises increasing the number of tool positions based on the determined maximum deviation from the determined tooth root contour reference data, in particular if the determined, in particular maximum, deviation is greater than a predetermined (limit) deviation. In one embodiment, the optimization comprises calculating the path data, in particular if a determined, in particular maximum, deviation is smaller than a predetermined (limit) deviation.

[0023] In one embodiment, the determination of tooth root contour data, in particular the determination of at least one tool position, path data, and / or process data, comprises optimizing the number of path data, in particular minimizing the number of path data. In one embodiment, the number of path data is limited to a maximum of seven, or a maximum of six, or a maximum of five paths, and / or at least two paths, or at least three paths, in particular per tooth flank or twice as many per tooth gap. In particular, the determination of at least one tool position, path data, and / or process data comprises an optimization taking into account the minimum and / or maximum number of path data.

[0024] In one embodiment, this makes it possible to create and / or manufacture the created tooth root contour more efficiently, in particular in such a way that no special machine is required, and in particular can be carried out on a universal machine, in particular any desired one. In one embodiment, this advantageously makes it possible to plan and / or carry out a process for creating and / or manufacturing more cost-effectively. In one embodiment, this advantageously makes it possible to reduce, in particular eliminate, the influence of a tooth root contour deviating from the tooth root contour reference on the tooth root load-bearing capacity, and in particular the created and / or manufactured tooth root contour has, at least substantially, the same strength as the tooth root contour reference.

[0025] According to the invention, the determination of the tooth root contour data and / or the optimization of the at least one tool position comprises a check as to whether the 30° tangent of the described tooth root contour reference is intersected by the represented tooth root contour and, based on the check, the at least one determined tool position, the path data and / or the process data is / are changed, in particular when the 30° tangent is intersected, so that, in one embodiment, an at least substantially undisturbed radius contour is present in the region of the 30° tangent.

[0026] In one embodiment, in particular for each tooth root contour created, a path, in particular an optimized or optimal path, can thereby advantageously be determined for the corresponding tool, or a path, in particular an optimized or optimal path is determined, further in particular a strength of the tooth root can thereby advantageously be guaranteed, at least substantially.

[0027] In one embodiment, the tool data describe a tool geometry of a standard tool, in particular a side milling cutter, in particular an end milling cutter, and more particularly a ball-end milling cutter. In one embodiment, the tool data describe a tool geometry of a milling cutter that is at least partially and / or sectionally convex or spherically shaped. In one embodiment, the tool geometry is a geometry of a standard tool, in particular an end milling cutter, and more particularly a ball-end milling cutter.

[0028] The term "geometry" in relation to tools as used herein should be understood in particular as dimension(s), tolerance(s), and / or cutting edge dimensions, such as cutting edge length, cutting edge diameter, and / or cutting edge angle. In one embodiment, the geometry comprises the removed and / or removed volume.

[0029] Advantageously, in one embodiment, this makes it possible for a tooth root contour to be created using standard tools or standard milling cutters.

[0030] In one embodiment, the tooth root contour reference data describe a tip circle of the (reference) gearing; a (reference) involute of the preliminary gearing and / or the final gearing; and / or a reference contour that can be produced by hobbing, in particular a reference contour according to ISO 6336-3.

[0031] Advantageously, this makes it possible for the tooth root contour to be created or to be created on the basis of a reference contour, in particular a conventional or common one, and in particular for a load-bearing capacity of the created tooth root contour to be achieved or to be ensured, which is at least substantially comparable to the load-bearing capacity of the reference.

[0032] In one embodiment, the determination of the tooth root contour data and / or the optimization of the at least one tool position comprises a check as to whether the intersection point of the root form circle with the tooth root contour reference is at least substantially encompassed by the represented tooth root contour and, in one embodiment, based on the check, the at least one determined tool position, the path data and / or the process data is / are changed if this point is at least substantially not encompassed or would be or is located in the tooth gap during creation and / or manufacture.In one embodiment, determining the tooth root contour data comprises determining a tool position in which at least one radius of the tool geometry is formed, at least substantially, perpendicular to an intersection point of the root form circle and the tooth root contour reference and / or a predetermined distance to this intersection point is not undershot or exceeded, in particular the tooth root contour runs, at least substantially, through this intersection point.

[0033] Advantageously, in one embodiment, this makes it possible for the transition from the involute of the (created and / or manufactured) finished toothing to the tooth root or tooth root contour to be maintained or formed, in particular in accordance with standards.

[0034] In one embodiment, determining tooth root contour data comprises determining a hill between the paths or resulting cutting volumes, in particular a hill that exceeds a predetermined distance from the tooth root contour reference. In one embodiment, determining the hill comprises changing a tool position and / or changing the path data, in particular adding another path, in particular such that the hill is at least substantially removed and / or the predetermined distance is at least substantially maintained.

[0035] In one embodiment, the determination of the tooth root contour data comprises checking a safety factor, in particular such that a, in particular predetermined, safety factor can be or is maintained, in particular such that a ratio of a limit stress of the tooth root to a stress in the tooth root does not, at least substantially, exceed or fall below a, in particular usually, predetermined value and / or value range, further in particular according to a, in particular common standard, further in particular according to ISO 6336-3.

[0036] In one embodiment, the determination of tooth root contour data comprises determining a tooth root load-bearing capacity, in particular by means of FEM simulation, wherein the represented tooth root contour has a predetermined tooth root load-bearing capacity and / or does not fall below a required tooth root load-bearing capacity and wherein, in one embodiment, at least one of tool position, path data and / or process data is changed based on the determined tooth root load-bearing capacity, in particular if a predetermined tooth root load-bearing capacity is not achieved.

[0037] According to one embodiment of the invention, a system is provided for creating a tooth root contour, in particular on or using a universal machine, and / or for operating and / or monitoring a multi-axis machine, in particular a 5-axis universal machine. In one embodiment, the system is configured to carry out a method described herein. In one embodiment, the system and / or its means comprise means for determining tooth root contour reference data; means for determining tool data; and / or means for determining tooth root contour data. In one embodiment, the system is configured to create and / or produce a tooth root contour described herein, in particular based on determined tooth root contour data. In one embodiment, the system comprises at least one or precisely one multi-axis machine, in particular a 5-axis universal machine.In one embodiment, the system, in particular the multi-axis machine, is configured to be controlled based on the determined tooth root contour data. Control is understood here, in particular, to include closed-loop control.

[0038] In one embodiment, this can advantageously ensure and / or enable cost-effectiveness in the creation of tooth root contours with multi-axis machines, particularly 5-axis universal machines. In one embodiment, this can advantageously (further) reduce the number of milling and / or machining steps.

[0039] A system and / or means within the meaning of the present invention can be designed in hardware and / or software, in particular at least one, in particular digital, processing unit, in particular a microprocessor unit (CPU), graphics card (GPU) or the like, preferably connected to a memory and / or bus system for data or signals, and / or one or more programs or program modules. The processing unit can be designed to execute instructions implemented as a program stored in a memory system, to detect input signals from a data bus, and / or to output signals to a data bus. A memory system can have one or more, in particular different, storage media, in particular optical, magnetic, solid-state, and / or other non-volatile media. The program can be designed in such a way that it embodies the methods described here oris capable of carrying out, so that the processing unit can carry out the steps of such methods and thus in particular can operate or monitor the multi-axis machine, in particular the 5-axis universal machine.

[0040] In one embodiment, a computer program product can comprise, in particular be, a storage medium, in particular a computer-readable and / or non-volatile one, for storing a program or instructions or with a program or instructions stored thereon. In one embodiment, execution of this program or these instructions by a system or a controller, in particular a computer or an arrangement of multiple computers, causes the system or the controller, in particular the computer(s), to carry out a method described here or one or more of its steps, or the program or the instructions are configured to do so.

[0041] The terms "a" or "an" as used herein are defined as "one or more." The terms "another" and "another," and any other variations thereof, are defined as "at least one other."

[0042] In one embodiment, one or more, in particular all, steps of the method are carried out completely or partially automatically, in particular by the controller or its means.

[0043] Further advantages and features emerge from the subclaims and the exemplary embodiments. The following shows, partly schematically: Fig. 1: shows schematically a flow chart to illustrate a preferred embodiment of the method according to the invention; Fig. 2: schematically shows a system according to an embodiment of the present invention; and Fig. 3: schematically a tooth root contour reference and a tooth root contour.

[0044] Fig. 1 schematically shows a flowchart to illustrate an embodiment of the method according to the invention. The method comprises determining tooth root contour reference data S10 and determining tool data S20. Furthermore, the method can comprise determining tooth root contour data S30. With the aid of the method, it can advantageously be determined more efficiently, in one embodiment, whether a tooth root contour reference 2 can be created and / or produced using the available tools or milling cutters, at least substantially, or whether a determined tooth root contour 1 can be produced more efficiently using the (available) standard milling cutters. The determination of tooth root contour data can comprise further steps, such as, for example, determining at least one tool position, path data and / or process data S40 and determining a maximum deviation S50. In embodiments, the method can comprise further steps, in particular those described herein.

[0045] Fig. 2 schematically shows an embodiment of a system 10 with means for determining tooth root contour reference data 11 and means for determining tool data 12. Furthermore, the system 10 can have means for determining tooth root contour data 13. The means 11, 12 and 13 can, in one embodiment, have at least one sensor and / or at least one digital processing unit, in particular a microprocessor. In one embodiment, the means and / or their means are an integral part of a machine, in particular a universal machine, and / or distributed over (at least) one IT system. The system 10 is, in one embodiment, configured to create a product with at least one tooth root contour 1 (as described herein) from a workpiece.

[0046] Fig. Figure 3 schematically shows a created tooth root contour 1, as well as a tooth root contour reference 2 and tool geometries. These are shown in a particularly commonly used xy coordinate system, with the axis of symmetry on the x-axis at zero. The tooth root contour reference 2 is, in one embodiment, designed according to a standard, in particular ISO 6336-3. Furthermore, Fig. 3 schematically shows tool positions W1, W2, W3 for one flank (in the illustration for the right flank). The tool has in the exemplary illustration of Fig. 3 has a circular (arc)-like cutting edge, the section of which is symbolically indicated by the three circles around the tool positions W1, W2 and W3. The tooth root contour 1 resulting from the use of the tool geometry and the determination of the tooth root contour data is similar to the tooth root contour reference 2. The tooth root contour 1 has deviations from the tooth root contour reference 2. These deviations can, in one embodiment, be reduced during or with the help of determining the tooth root contour data, in particular the tooth root contour 1 can be optimized. The resulting tooth root contour 1 of the Fig. 3 can be seen on the left side, which has the same tool positions in a mirrored manner (on the axis of symmetry) that result in the tooth root contour 1 on this corresponding flank. For the tool position W2, it can be seen that this does not intersect the 30° tangent, in particular, in one embodiment, is positioned such that the tool geometry touches the 30° tangent of the tooth root contour reference 2 at this point or the tool position is designed such that the 30° tangent is not intersected and in particular - if, in one embodiment, it is a particularly partially circular and / or circular tool geometry, in particular a cutting geometry - the radius (of this) is arranged perpendicular to the 30° tangent (of the tooth root contour reference 2).W3 is a particular example of how, in one embodiment, an excessive deviation from the tooth root contour reference 2, generated here by the tool positions W1 and W2, can be reduced. W3 is shown in . Fig. 3 is positioned in such a way that a hillock H between the cuts created by W1 and W2 can be or is removed and / or reduced. The resulting tooth root contour 1, as can be seen on the left-hand side, therefore does not have a hillock H that could in particular impair the functionality of the created and / or manufactured tooth root. In one embodiment, determining the tooth root contour data comprises determining path data that describe at least one tool path for creating and / or manufacturing the tooth root contour 1 (as described herein), which has at least one tool position W1, W2, W3, in particular all tool positions. The gear (to be manufactured) can have an allowance of a preliminary toothing VVZ or a dimension of a final toothing FVZ. In particular, in one embodiment, the method comprises a step for creating a preliminary toothing VVZ and / or a step for creating a final toothing FVZ.In one embodiment, the creation of the preliminary toothing VVZ and / or the finished toothing FVZ is independent of the creation of a tooth root contour 1, in particular of the determination of tooth root contour data. In one embodiment, at least one tool position is placed such that - if, in one embodiment, it is a, in particular partially, circular and / or circular tool geometry, in particular cutting geometry - the radius is arranged perpendicular to the intersection point of the root form circle FF with the tooth root contour reference 2 of the finished toothing (indicated by the dashed curve arranged essentially horizontally to the plane of the page). The tooth root contour 1 shown of the . Fig. 3 can therefore be manufactured with three tool positions W1, W2, W3 per flank.

[0047] One of the objectives is, in one embodiment, to be able to produce a tooth root contour 1 more efficiently, cost-effectively, and / or with less time, using standard tools and / or standard machines typically found in metal and / or plastic processing companies, or the like, in particular without relying on special tools and / or special machines. In particular, in one embodiment, at least one preform of the final tooth to be produced can be created and / or manufactured using the method described herein.

[0048] Although exemplary embodiments have been explained in the preceding description, it should be noted that numerous modifications are possible. Furthermore, it should be noted that the exemplary embodiments are merely examples and are not intended to limit the scope of protection, applications, or structure in any way. Rather, the preceding description provides the skilled person with a guide for implementing at least one exemplary embodiment, whereby various modifications, particularly with regard to the function and arrangement of the described components, can be made without departing from the scope of protection as it results from the claims and equivalent combinations of features. List of reference symbols 1 Tooth root contour 2 Tooth root contour reference 30° 30° tangent FF foot form circle FVZ finished gearing VVZ pre-toothing W1, W2, W3 tool position(s) H Hill S10 Determination of tooth root contour reference data S20 Determining tool data S30 Determination of tooth root contour data S40 Determination of at least one tool position, path data and / or process data S50 Determining a maximum deviation 10 systems 11 Means for determining tooth root contour reference data 12 Means of tool data 13 Means for determining tooth root contour data

Claims

[1] Method for creating a tooth root contour (1) comprising: Determining (S10) tooth root contour reference data, wherein the tooth root contour reference data describe at least one tooth root contour reference (2) for a workpiece; Determining (S20) tool data based on the tooth root contour reference data, wherein the tool data describe at least one tool geometry with which a tooth root contour (1) can be produced that partially corresponds to the tooth root contour reference (2); wherein the tool(s) is / are standard milling cutters; and Determining (S30) tooth root contour data based on the determined tool data and the determined tooth root contour reference data, wherein the tooth root contour data represent at least one tooth root contour (1) that can be created using one or more tool geometries described by the determined tool data; and wherein the determination (S30) of tooth root contour data further comprises determining at least one tool position, path data and / or process data, based on the tool data, for creating the determined tooth root contour (1); wherein the determination of tooth root contour data (S30) comprises a check as to whether the 30° tangent of the described tooth root contour reference (2) is intersected by the represented tooth root contour (1) and, based on the check, the at least one determined tool position, the path data and / or the process data is / are changed when the 30° tangent is intersected. [2] Method according to the preceding claim, characterized bythat the determination of tooth root contour data (S30) comprises determining a maximum deviation from the determined tooth root contour reference data and wherein a deviation of the tooth root contour data is smaller than the determined maximum deviation and / or does not exceed a predetermined deviation from the tooth root contour reference data. [3] Method according to one of the preceding claims, characterized by that the determination of tooth root contour data (S30) comprises optimizing the at least one tool position and / or optimizing the path data and / or minimizing a number of tool positions. [4] Method according to one of the preceding claims, characterized by that the tool geometry has a geometry of a standard tool, in particular a side milling cutter, in particular an end mill, in particular an at least partially convex or spherically shaped milling cutter, further in particular a ball milling cutter. [5] Method according to one of the preceding claims, characterized by that the tooth root contour reference data describe a tip circle of the gearing; an involute of the preliminary gearing and / or the finished gearing; and / or a reference contour that can be produced by hobbing. [6] System (10) for operating and / or monitoring a multi-axis machine, in particular a 5-axis universal machine, which is configured to carry out a method according to one of the preceding claims and / or comprises means (11) for determining (S10) tooth root contour reference data; and means (12) for determining (S20) tool data; in particular means (13) for determining (S30) tooth root contour data. [7] Computer program or computer program product, wherein the computer program or computer program product contains instructions, in particular stored on a computer-readable and / or non-volatile storage medium, which, when executed by one or more computers or a system according to claim 6, cause the computer(s) or the system to carry out a method according to one of claims 1 to 5.

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