GEARWHEEL, METHOD FOR PRODUCING A GEARWHEEL, AND METHOD FOR MEASURING A GEARWHEEL

Abstract

A gearwheel, wherein the gearwheel has a setpoint geometry, wherein the gearwheel has a modification superimposed on the setpoint geometry in the form of a pitch and/or topography changing from tooth to tooth, wherein a variation of the pitch and/or topography specified by the modification, observed over a total number of teeth of the gearwheel, corresponds to a superposition of at least two harmonic functions, which differ from one another in one parameter or in multiple parameters, such as their amplitude, frequency, or phase shift.

Claims

1. A gearwheel, wherein the gearwheel has a setpoint geometry, wherein the gearwheel has a modification superimposed on the setpoint geometry in the form of a pitch and/or topography changing from tooth to tooth, wherein a variation of the pitch and/or topography specified by the modification, observed over a total number of teeth of the gearwheel corresponds to a superposition of at least two harmonic functions, which differ from one another in one parameter or in multiple parameters, such as their amplitude, frequency, or phase shift.

2. The gearwheel according to claim 1, wherein the modification is specified in that a deviation is assigned to each tooth as a function value of the superimposed harmonic function.

3. The gearwheel according to claim 2, wherein the superimposed harmonic functions are sine functions, wherein the deviation is assigned to each tooth as a function value f(x) according to the following rule: $f\left(x\right)=K_{\max }*{.Math.}_{i=1}^n{A}_i*\sin \left(2*\pi *\left({\varphi }_i+{\omega }_i\frac{\left(x-1\right)}{Z}\right)\right),$ wherein K.sub.max corresponds to a maximum deviation of a toothing parameter or a process parameter, wherein “i” corresponds to a running index, wherein “n” corresponds to a number of the specified superimposed sine functions, wherein the variable “Z” corresponds to the total number of teeth of the gearwheel, wherein the variable “A” corresponds to a specified amplitude of a respective “i”-th sine function, wherein the variable “ϕ.sub.i”: corresponds to a specified phase shift of a respective “i”-th sine function, wherein the variable “ω.sub.i” corresponds to a specified frequency of a respective “i”-th sine function, and wherein the variable “x” is a natural number with x=1 to x=Z, wherein “x” corresponds to a number of a relevant tooth increasing from 1 to Z, and wherein the teeth are continuously numbered successively clockwise or counterclockwise.

4. The gearwheel according to claim 1, wherein the variation of the pitch and/or topography specified by the modification, observed over the total number of teeth of the gearwheel, corresponds to a superposition of precisely three sine functions.

5. The gearwheel according to claim 1, wherein a deviation from the setpoint geometry, resulting due to the modification superimposed on the setpoint geometry and averaged over two or more teeth of the gearwheel, corresponds to less than 30% of a total amplitude of the superposition of the at least two harmonic functions.

6. The gearwheel according to claim 1, wherein the frequency of the respective harmonic function, which corresponds to a number of cycles of the respective harmonic function observed over the total number of teeth, is less than the total number of teeth of the gearwheel.

7. The gearwheel according to claim 1, wherein the amplitudes of the superimposed harmonic functions cancel out for at least one tooth of the gearwheel or for precisely one tooth of the gearwheel and the modification for this tooth of the gearwheel is zero.

8. The gearwheel according to claim 1, wherein the setpoint geometry has toothing modifications, such as recesses, crowning, or the like and/or the gearwheel is a bevel gear in particular is a bevel gear produced by single indexing.

9. A method for producing a gearwheel, the method including the following steps: specifying a setpoint geometry of the gearwheel, specifying a modification superimposed on the setpoint geometry in the form of a pitch and/or topography changing from tooth to tooth, and producing the gearwheel by means of a gear cutting machine, wherein a variation of the pitch and/or topography specified by the modification, observed over a total number of teeth of the gearwheel, corresponds to a superposition of at least two harmonic functions which differ from one another in one parameter or in multiple parameters, such as their amplitude, frequency, or phase shift.

10. The method according to claim 9, wherein the manufacturing of each gap of the gearwheel is carried out using gap-specific machine settings, in order to manufacture the setpoint geometry having the superimposed modification, wherein the gearwheel is in particular a bevel gear that is produced in the single indexing method; or the gearwheel is a bevel gear that is produced in the single indexing method, wherein a design parameter of a virtual gear cutting machine, such as a radial for influencing the spiral angle or the like, which are converted into manufacturing parameters of the gear cutting machine, is varied specifically by gap in order to manufacture the setpoint geometry having the superimposed modification; or a manufacturing parameter of the gear cutting machine, such as a movement of a linear axis or a workpiece axis, is varied specifically by gap in order to manufacture the setpoint geometry having the superimposed modification.

11. The method according to claim 9, wherein the modification is specified in that a deviation is assigned to each tooth as a function value of the superimposed harmonic function, the superimposed harmonic functions are sine functions, wherein the deviation is assigned to each tooth as a function value f(x) according to the following rule: $f\left(x\right)=K_{\max }*{.Math.}_{i=1}^n{A}_i*\sin \left(2*\pi *\left({\varphi }_i+{\omega }_i\frac{\left(x-1\right)}{Z}\right)\right),$ wherein K.sub.max, corresponds to a maximum deviation of a toothing parameter or a process parameter, wherein “i” corresponds to a running index, wherein “n” corresponds to a number of the specified superimposed sine functions, wherein the variable “Z” corresponds to the total number of teeth of the gearwheel, wherein the variable “A.sub.i” corresponds to a specified amplitude of a respective “i”-th sine function, wherein the variable “ϕ.sub.i” corresponds to a specified phase shift of a respective “i”-th sine function, wherein the variable “ω.sub.i” corresponds to a specified frequency of a respective “i”-th sine function, and wherein the variable “x” is a natural number with x=1 to x=Z, wherein “x” corresponds to a number of a relevant tooth increasing from 1 to Z, and wherein the teeth are continuously numbered successively clockwise or counterclockwise.

12. The method according to claim 9, wherein the variation of the pitch and/or topography specified by the modification, observed over the total number of teeth of the gearwheel, corresponds to a superposition of precisely three sine functions.

13. A method, having the following steps: providing a gearwheel, wherein the gearwheel is designed according to claim 1, and measuring the gearwheel by means of a toothing measuring machine, wherein deviations of the gearwheel from the setpoint geometry are ascertained, wherein the modification superimposed on the setpoint geometry is not part of the setpoint geometry.

14. The method according to claim 13, wherein a number of teeth are measured on the gearwheel which is less than the total number of teeth of the gearwheel, wherein an average deviation from the setpoint geometry is determined on the basis of the measured teeth.

15. The method according to claim 14, wherein corrections for a grinding method of the gearwheel are determined on the basis of the average deviations.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The disclosure is described in more detail hereinafter on the basis of a drawing illustrating exemplary embodiments. In the schematic figures:

[0043] FIG. 1 shows a spur gear according to the disclosure in a side view;

[0044] FIG. 2 shows an illustration of a variation of a pitch of the gearwheel from FIG. 1 viewed over a total number of teeth of the gearwheel;

[0045] FIG. 3 shows a further illustration of the function underlying the variation of the pitch of the gearwheel from FIG. 2;

[0046] FIG. 4 shows an illustration of a variation of a pitch of a further gearwheel viewed over a total number of teeth of the further gearwheel;

[0047] FIG. 5 shows a further illustration of the function underlying the variation of the pitch of the gearwheel according to FIG. 4;

[0048] FIG. 6 shows a bevel gear according to the disclosure in a perspective view from above;

[0049] FIG. 7 shows a detail enlargement of the bevel gear from FIG. 6;

[0050] FIG. 8 shows a flow chart of a method according to the disclosure;

[0051] FIG. 9 shows a gear cutting machine;

[0052] FIG. 10 shows a bevel gear with a bar cutter head;

[0053] FIG. 11 shows a bevel gear with a bar cutter head and a virtual crown gear;

[0054] FIG. 12 shows a bevel gear with a tool having parameters of a virtual gear cutting machine;

[0055] FIG. 13 shows the bevel gear from FIG. 12 with the tool and with further parameters of the virtual gear cutting machine;

[0056] FIG. 14 shows a toothing measuring machine; and

[0057] FIG. 15 shows a flow chart of a further method according to the disclosure.

DETAILED DESCRIPTION OF THE DRAWINGS

[0058] FIG. 1 shows a gearwheel 100 having twelve teeth 105, which are continuously numbered successively counterclockwise from 1 to 12. The gearwheel 100 is a spur gear. The gearwheel has a setpoint geometry, which specifies the shape of right flanks 110 and left flanks 120 and a setpoint pitch P.sub.SOLL on the pitch circle D.

[0059] The gearwheel 100 has a modification superimposed on the setpoint geometry in the form of a pitch P.sub.MOD changing from tooth to tooth, which can also be designated in the present case as a modified pitch or noise-optimized pitch.

[0060] The variation of the pitch P.sub.MOD specified by the modification corresponds in the present case, viewed over a total number of teeth Z=12 of the gearwheel 100, to a superposition of precisely three sine functions (FIG. 2).

[0061] The superimposed harmonic functions are three sine functions in the present example, wherein the deviation is assigned to each tooth as a function value f(x) according to the following general rule

[00002]$f\left(x\right)=K_{\max }*A_1*\sin \left(2*\pi *\left({\varphi }_1+{\omega }_1\frac{\left(x-1\right)}{Z}\right)\right)+K_{\max }*A_2*\sin \left(2*\pi *\left({\varphi }_2+{\omega }_2\frac{\left(x-1\right)}{Z}\right)\right)+K_{\max }*A_3*\sin \left(2*\pi *\left({\varphi }_3+{\omega }_3\frac{\left(x-1\right)}{Z}\right)\right),$

wherein the following numeric values are used in the present example according to FIG. 2

[00003]$f\left(x\right)=0.015\mathrm{mm}*0.4*\sin \left(2*\pi *\left(0.11+2*\frac{\left(x-1\right)}{12}\right)\right)+0.015\mathrm{mm}*0.3*\sin \left(2*\pi *\left(0.66+5*\frac{\left(x-1\right)}{12}\right)\right)+0.015\mathrm{mm}*0.3*\sin \left(2*\pi *\left(0+11*\frac{\left(x-1\right)}{12}\right)\right),$

wherein for the first sine function the amplitude A.sub.1=0.4, the frequency ω.sub.1=2, and the phase shift ϕ.sub.1=0.11 are specified, wherein for the second sine function the amplitude A.sub.2=0.3, the frequency ω.sub.2=5, and the phase shift ϕ.sub.2=0.66 are specified, and wherein for the third sine function the amplitude A.sub.3=0.3, the frequency ω.sub.3=11, and the phase shift ϕ.sub.3=0 are specified. K.sub.max corresponds in this example to a pitch error of at most 0.015 mm, which is proportionally superimposed on the teeth 105 of the gearwheel 100 by means of the sine functions.

[0062] The following deviations f(x) result therefrom for each tooth 1 to 12 (see FIG. 2):

TABLE-US-00001 Tooth [00004]$\begin{array}{c}\underset{i=1}{\overset{n}{.Math.}}{A}_i*\\ \sin \left(2*\pi *\left({\varphi }_i+{\omega }_i\frac{\left(x-1\right)}{Z}\right)\right)\end{array}$ [00005]$\begin{array}{c}{K}_{\max }*\underset{i=1}{\overset{n}{.Math.}}{A}_i*\\ \sin \left(2*\pi *\left({\varphi }_i+{\omega }_i\frac{\left(x-1\right)}{Z}\right)\right)\end{array}$  1 0.002 0.00003 mm  2 0.235 0.00353 mm  3 0.046 0.00069 mm  4 −0.522   −0.00783 mm    5 0.088 0.00011 mm  6 −0.127   −0.00191 mm    7 0.161 0.00242 mm  8 0.47  0.00705 mm  9 −0.26    −0.00390 mm   10 0.022 0.00033 mm 11 −0.261   −0.00392 mm   12 −0.288   −0.00432 mm  

[0063] A deviation from the setpoint geometry, which results due to the modification superimposed on the setpoint geometry and is averaged over three or four teeth 105 of the gearwheel 100, is less than 25% of the total amplitude of the superposition of the sine functions. Three or four teeth are typically observed here, which have a spacing of two or three teeth from one another, i.e., are arranged distributed over the circumference of the gearwheel.

[0064] In FIG. 3, the function f(x) has been shown for function values from x=1 to x=75, in order to better illustrate the superimposed harmonic sine functions. The illustration of FIG. 2 is therefore a detail II from FIG. 3.

[0065] In the above-mentioned example, a gearwheel having an even number of teeth is shown. The described procedure may be transferred as desired to gearwheels having an odd number of teeth and higher number of teeth.

[0066] The example of FIG. 4 relates to a bevel gear having 21 teeth, wherein each tooth is assigned the deviation as the function value f(x) according to the following general rule

[00006]$f\left(x\right)=K_{\max }*A_1*\sin \left(2*\pi *\left({\varphi }_1+{\omega }_1\frac{\left(x-1\right)}{Z}\right)\right)+K_{\max }*A_2*\sin \left(2*\pi *\left({\varphi }_2+{\omega }_2\frac{\left(x-1\right)}{Z}\right)\right)+K_{\max }*A_3*\sin \left(2*\pi *\left({\varphi }_3+{\omega }_3\frac{\left(x-1\right)}{Z}\right)\right),$

for which the following numeric values are used in the present example according to FIG. 4

[00007]$f\left(x\right)=0.1°*0.4*\sin \left(2*\pi *\left(0.11+2*\frac{\left(x-1\right)}{21}\right)\right)+0.1°*0.3*\sin \left(2*\pi *\left(0.66+5*\frac{\left(x-1\right)}{21}\right)\right)+0.1°*0.3*\sin \left(2*\pi *\left(0+19*\frac{\left(x-1\right)}{21}\right)\right),$

wherein for the first sine function the amplitude A.sub.1=0.4, the frequency ω.sub.1=2, and the phase shift ϕ.sub.1=0.11 are specified, wherein for the second sine function the amplitude A.sub.2=0.3, the frequency ω.sub.2=5, and the phase shift ϕ.sub.2=0.66 are specified, and wherein for the third sine function the amplitude A.sub.3=0.3, the frequency ω.sub.3=11, and the phase shift ϕ.sub.3=0 are specified. K.sub.max corresponds in this example to a spiral angle deviation of an average spiral angle β.sub.m of at most 0.1°, which is superimposed by means of the sine functions on the teeth of the gearwheel. The following deviations f(x) in [° ] result therefrom for each tooth 1 to 21, (see FIG. 4):

TABLE-US-00002 tooth [00008]$\begin{array}{c}\underset{i=1}{\overset{n}{.Math.}}{A}_i*\\ \sin \left(2*\pi *\left({\varphi }_i+{\omega }_i\frac{\left(x-1\right)}{Z}\right)\right)\end{array}$ [00009]$\begin{array}{c}{K}_{\max }*\underset{i=1}{\overset{n}{.Math.}}{A}_i*\\ \sin \left(2*\pi *\left({\varphi }_i+{\omega }_i\frac{\left(x-1\right)}{Z}\right)\right)\end{array}$  1 0.002 0.0002°  2 0.036 0.0036°  3 0.327 0.0327°  4 0.164 0.0164°  5 −0.376   −0.0376°    6 −0.493   −0.0493°    7 −0.075   −0.0075°    8 0.131 0.0131°  9 −0.108   −0.0108°   10 −0.131   −0.0131°   11 0.318 0.0318° 12 0.541 0.0541° 13 0.133 0.0133° 14 −0.273   −0.0273°   15 −0.133   −0.0133°   16 0.072 0.0072° 17 −0.196   −0.0196°   18 −0.482   −0.0482°   19 −0.165   −0.0165°   20 0.360 0.0360° 21 0.347 0.0347°

[0067] In FIG. 5, the function f(x) has been shown for function values from x=1 to x=75, in order to better illustrate the superimposed harmonic sine functions. The illustration of FIG. 4 is therefore a detail IV from FIG. 4.

[0068] All numeric values are to be understood solely as an example to illustrate the procedure according to the disclosure.

[0069] A deviation from the setpoint geometry, which results due to the modification superimposed on the setpoint geometry and is averaged over three or four teeth of the gearwheel according to the example of FIG. 4, is less than 25% of the total amplitude of the superposition of the sine functions. Three or four teeth are typically observed, which have a spacing of five or six teeth to one another, i.e., are arranged distributed over the circumference.

[0070] For the preceding examples, the frequency of a respective harmonic function, which corresponds to a number of cycles of the respective harmonic function observed over the total number of teeth, is less than the total number of teeth of the respective gearwheel.

[0071] For the preceding examples, the amplitudes of the superimposed harmonic functions cancel out for the tooth 1 of the respective gearwheel and the modification for this tooth of the gearwheel is essentially zero.

[0072] The above-described modification can be used for a bevel gear 400 (FIG. 6). The bevel gear 400 has teeth 410 and gaps 413 having concave flanks 411 and convex flanks 412. A pitch P.sub.SOLL provided according to the setpoint geometry of the bevel gear and a modified pitch P.sub.MOD, which results from the noise-optimized setpoint geometry of the bevel gear, are shown in an exemplary and schematic manner fora tooth of the bevel gear.

[0073] The modification can be specified for the bevel gear 400 in the form of a pitch and topography changing from tooth to tooth. In particular, it can be provided that a variation of the pitch and topography specified by the modification, observed over the total number of teeth of the bevel gear 400, corresponds to a superposition of at least two harmonic functions, which differ from one another in one parameter or in multiple parameters, such as their amplitude, frequency, or phase shift.

[0074] According to the disclosure, a method for producing a gearwheel 100, 400 can be specified (FIG. 8), having the method steps: (A) specifying a setpoint geometry of the gearwheel; (B) specifying a modification superimposed on the setpoint geometry in the form of a pitch and/or topography changing from tooth to tooth, wherein a variation of the pitch and/or topography specified by the modification, observed over a total number of teeth of the gearwheel, corresponds to a superposition of at least two harmonic functions, which differ from one another in one parameter or in multiple parameters, such as their amplitude, frequency, or phase shift; (C) producing the gearwheel by means of a gear cutting machine 500 (FIG. 9).

[0075] FIG. 9 shows by way of example a gear cutting machine 500 for producing bevel gear teeth. Such a gear cutting machine 500 has movement axes in the form of three linear axes X, Y, Z, an axis A for rotationally driving the one tool 520 for the bevel gear production, such as a bar cutter head or the like, an axis B for rotationally moving the bevel gear workpiece 400, and a pivot axis C for inclining the workpiece 400 relative to the tool 520. The tool 520 is held on a tool spindle 510 and the workpiece 400 is held on a workpiece spindle 530.

[0076] FIG. 10 shows the bar cutter head 520 having bar cutters 521 and the bevel gear 400.

[0077] It can be provided that the manufacturing of each gap 413 of the bevel gear 400 is carried out using gap-specific machine settings, in order to manufacture the setpoint geometry with the superimposed modification, wherein the bevel gear 400 is produced in the single indexing method. In this case, the gear cutting machine 500 receives a complete gap-specific data set for each gap 413, which possibly comprises gap-specific settings, i.e., settings differing from gap to gap, for each of the machine axes.

[0078] Alternatively, you can be provided that a manufacturing parameter of the gear cutting machine 500, such as a movement of one of the linear axes X, Y, Z or the workpiece axis B or the pivot axis C is varied specifically by gap in order to manufacture the setpoint geometry having the superimposed modification. The modification can thus be applied to the bevel gear as a gap-specific function of a single machine axis, while the further machine axes are moved for all gaps in the same manner.

[0079] It can be provided that the bevel gear 400 is produced in the single indexing method, wherein a design parameter of a virtual gear cutting machine, such as a radial ϕ for influencing the spiral angle or the like, which are converted into manufacturing parameters of the gear cutting machine 500, is varied specifically by gap in order to manufacture the setpoint geometry having the superimposed modification.

[0080] The radial ϕ in bevel gear production designates the spacing of a cutterhead axis MK to a roller cradle axis WW or roller cradle WW, which coincides in the present case with a crown gear axis of a virtual crown gear P (FIG. 11). The tool WK maps a tooth of the virtual crown gear P during the production of a bevel gear K and is pivoted for this purpose around the roller cradle WW.

[0081] FIGS. 12 and 13 show design parameters of a virtual gear cutting machine, which are used to describe the movements between the bevel gear workpiece K and the tool WK. FIG. 12 shows a further schematic illustration of the bevel gear K, with the tool WK, the roller cradle axis WW, and the radial φ. Furthermore, a machining wheel rotational angle β, a pivot angle σ, a tilt angle τ, an axial offset η, and an average cradle angle α.sub.m are shown.

[0082] The illustration according to FIG. 13 schematically shows the bevel gear K, the tool WK, the roller cradle axis WW, a cradle angle α, the machining wheel rotational angle β, an element angle γ, a horizontal ε, a depth position λ, an installation dimension t.sub.B, an intersection point X, and a spacing mccp of a machine center to the intersection point.

[0083] On the basis of the above-mentioned design parameters of the virtual gear cutting machine, the relative movements between the tool and the workpiece can be described independently of the machine. A finished design carried out on the basis of the virtual gear cutting machine can then be converted specifically by machine into axial movements of machine axes of a gear cutting machine, such as the gear cutting machine 500.

[0084] The modification superimposed on the setpoint geometry in the form of a pitch and/or topography changing from tooth to tooth can already be taken into consideration during the design on the basis of the virtual gear cutting machine, and can be mapped by one or more of the above-mentioned parameters of the virtual gear cutting machine. The modification superimposed on the setpoint geometry in the form of a pitch and/or topography changing from tooth to tooth is already part of the machine data converted for the machine axes in this case.

[0085] Furthermore, a method is specified according to the disclosure (FIG. 15), having the following method steps: (a) providing a gearwheel 100, 400 according to the disclosure and (b) measuring the gearwheel 100, 400 by means of a toothing measuring machine 300 (FIG. 14), wherein deviations of the gearwheel 100, 400 from the setpoint geometry are ascertained, wherein the modification superimposed on the setpoint geometry is not part of the setpoint geometry.

[0086] A number of teeth is measured on the gearwheel 100, 400 which is less than the total number of teeth of the gearwheel 100, 400, wherein in particular less than half of the teeth of the gearwheel 100, 400 are measured and in the present case precisely three or four teeth of the gearwheel 100, 400 distributed around the circumference are measured. An average deviation from the setpoint geometry is determined on the basis of the measured teeth.

[0087] In a step (c) corrections for grinding method of the gearwheel 100, 400 are determined on the basis of the average deviations.

[0088] The toothing measuring machine 300 can include a tactile sensor 310 and/or an optical sensor 320 for toothing measurement.