Method for grinding a gear by grinding a worm in a grinding machine
By adjusting the meshing geometry between the gear and the grinding worm, the problem of the larger contour formation area in the prior art is solved, and the contour formation area is minimized and processing productivity is improved.
Patent Information
- Application Number
- CN202080051552.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2019-07-17
- Filing Date
- 2020-07-02
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2040-07-02
AI Technical Summary
In hard finishing of gears, it is difficult for the prior art to achieve a minimum profile formation area, which affects processing productivity.
By calculating and adjusting the meshing geometry between the gear and the grinding worm, especially changing the meshing ratio between the abrasive surface and the gear of the grinding worm, the intersection position of the meshing line is ensured, so that the contour formation area of the grinding worm is minimized, thereby Improve productivity in grinding operations.
Optimization of the contact line between the workpiece and the tool is achieved, reducing the size of the profile formation area, improving productivity of the machining process, and allowing better tool utilization.
Smart Images
Figure CN114423555B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a method for grinding a gear by worm grinding in a grinding machine, wherein the tooth flank of the gear is ground together with the abrasive surface of the profile of the grinding worm, the gear having a rotation axis, the grinding worm having a rotation axis, and the tooth ring of the gear to be ground having a base circle diameter, a root circle diameter and a tip circle diameter. Background Art
[0002] In the mass or large-scale production of gears, in particular in their hard finishing, dressable grinding worms are often used as grinding tools. The grinding worms are usually dressed by diamond rollers in order to shape the gear profile to be ground in the grinding worm. In addition, the use of diamond rollers is necessary to regenerate the wear profile after grinding multiple workpieces. In the process, the action angle of the dressing roller is usually made equal to the action angle of the gear device to be processed. In addition, it is usually checked whether the correspondingly dressed grinding worm reliably reaches the available root circle or root shape circle of the gear device. If this is not the case, the action angle of the dressing roller is changed accordingly. In addition, the action angle of the grinding worm has an influence on the so-called profile forming area (i.e., the minimum width of the grinding worm required to form the ring gear profile). The size of the profile forming area significantly affects the productivity of the entire machining process. A general method is described in EP 0 278 512 A1. DE 10 2014 009 868 A1, EP 2 848 348 A2 and GB 669 122 A describe other similar solutions. Summary of the invention
[0003] The invention is based on the object of further developing a method of the type mentioned above in such a way that grinding can be carried out with the smallest possible profiling zone, for which purpose in particular the geometry of the meshing between the gear arrangement to be ground and the grinding worm is changed. This can increase the productivity of the grinding operation by increasing the number of components to be ground between two dressing operations.
[0004] The object solution of the present invention provides a method, which comprises the following steps:
[0005] a) calculating the engagement ratio between the abrasive surface of the profile of the grinding worm and the tooth surface of the gear when the gear and the grinding worm are meshed for grinding, wherein a cross section is considered along a plane including the rotation axis of the grinding worm and perpendicular to the rotation axis of the gear; the calculation comprising:
[0006] a1) determining a first meshing line generated by contact points between two consecutive abrasive surfaces and two consecutive tooth surfaces;
[0007] a2) determining a second meshing line generated by contact points between two consecutive abrasive surfaces opposite to the abrasive surface and two consecutive tooth surfaces opposite to the tooth surface;
[0008] a3) determining the intersection point of the first and second meshing lines;
[0009] a4) determining a line passing through the intersection point and tangent to the base circle diameter of the gear ring of the gear;
[0010] a5) determining the intersection point of the line with the root circle diameter and determining the intersection point of the line with the tip circle diameter;
[0011] a6) determining a line resulting from the intersection of said plane with a second plane containing said axis of rotation of said gear, said second plane being perpendicular to said plane and containing said point of intersection of said first and second meshing lines;
[0012] a7) determining the distance between the line of intersection of the line with the root circle diameter and the line of intersection of the plane;
[0013] a8) determining the distance between the intersection of said line with said top circle diameter and said line of intersection of said plane;
[0014] b) By changing the base diameter (d b ) is tangent to the line (13) so that the distances (a1, a2) are equal (a 1opt =a 2opt ), determining a change in the geometry of the meshing ratio compared to the geometry determined according to step a);
[0015] c) Geometric profile of the grinding worm (2) with the meshing ratio produced when the distances (a1, a2) are equal;
[0016] d) Grinding the gear with the grinding worm profiled according to step c).
[0017] The calculation is preferably performed analytically based on the geometrical relationships of the gear arrangement (see the description of the example, in particular according to Figure 4 ).
[0018] Regarding the above step b), according to another iterative numerical embodiment of the present invention, the following sub-steps are provided:
[0019] b1) recalculating the engagement ratio according to step a), changing the position of the line passing through the intersection point and tangent to the base circle diameter (changing the angle α existing between the line as the intersection of the planes and the perpendicular to the line passing through the intersection point and tangent to the base circle diameter by a given angular difference Δα), determining the distances and comparing the determined distances with one another;
[0020] b2) Repeating step b1) by incrementally changing the position of the lines until the distances are equal.
[0021] When performing step b2) above, the position of the line can be changed stepwise between an initial value and a final value, and then the geometry is determined in which the distances have a minimum deviation from each other. When performing step b2) above, for this purpose, the position of the line can be changed stepwise by a predetermined angular change.
[0022] Therefore, the root circle diameter is preferably the available root circle diameter, and the tip circle diameter is preferably the available tip circle diameter.
[0023] However, the root circle diameter may also be the formed root circle diameter and the tip circle diameter may be the formed tip circle diameter.
[0024] A special embodiment of the invention provides for modifying the profiling of the grinding worm after the above-mentioned step b) has been carried out and before the above-mentioned step c) has been carried out. The background for such a measure is the situation in which there is a toothed ring in which the explained optimization is not possible, because due to an unfavorable toothed ring geometry, the grinding worm cannot reach the profiled root circle or the available root circle, or the root circle rounding radius cannot be completely formed in the toothed ring. This is the case with the advantageous use of the aforementioned modification step, according to which the initially calculated optimal action angle on the grinding worm is calculated iteratively or analytically before the profiling of the grinding worm, until the aforementioned restrictions no longer exist. The new action angle on the grinding worm determined in this way is no longer optimal in the sense of the explained adjustment of the meshing line, but is still more favorable than the nominal action angle (on which the original calculation was based). In this way, a higher productivity can be achieved in any case.
[0025] Therefore, the profiling of the ground worm can be carried out according to the above step c) by manufacturing a worm steel basic body and covering the worm steel basic body with an abrasive layer.
[0026] However, it is alternatively and preferably provided that the profiling of the grinding worm is carried out according to step c) above by providing a dressable grinding worm having said geometry. According to one possibility, a dressing roller corresponding to said geometry can be produced for profiling the grinding worm, with which the grinding worm is dressed; alternatively, it is also possible that the profiling of the grinding worm is carried out with a numerically controlled dressing device, which generates the geometry of the abrasive surface of the grinding worm.
[0027] The invention also comprises a dressing roller for dressing a grinding worm produced according to the above method.
[0028] The invention therefore proposes to specifically modify the meshing conditions between the workpiece to be ground, i.e. the gearing, and the grinding worm. This adaptation is carried out by analyzing the geometry of the gearing during the meshing, i.e. the contact, between the grinding tool and the gearing. This contact usually takes place via a meshing line which extends in the normal direction of the involute tooth flank and the worm surface (abrasive surface of the profile of the grinding worm). The meshing lines of the left and right flanks intersect at the pitch diameter, thereby forming a tip meshing zone and a root meshing zone which are strongly dependent on the (given) profile displacement of the gear. The projection of the meshing zone forms the profile forming zone (see Figure 4 ), which is responsible for forming the entire ring gear contour.
[0029] Since the profile modification factor is usually not equal to zero, the tip portion and the root portion of the contact portion differ from each other. The profile forming area is always defined by the larger ratio. In the best case according to the invention, in which the ratios are equal, the profile forming area assumes the smallest possible value. According to the invention, the best case is achieved if the action angle of the grinding worm is specifically defined so that the meshing zones of the left and right flanks are "shifted" towards each other and the tip portion and the root portion are therefore equal.
[0030] Therefore, it is conceivable that the meshing relationship between the abrasive surface of the profile of the grinding worm and the tooth surface of the gear is first calculated, thereby determining the size of the initially existing profile forming area.
[0031] A modified geometry is then determined in which the above distances (a1 and a2) become equal. Said geometry is then used as the basis for the manufacturing process.
[0032] The determination of the modified geometry can be done analytically by considering the corresponding geometrical relationships (starting from step a above), and from said determination the required situation of equal distances (a1=a2) is given (see the more detailed description below). Figure 4 ).
[0033] However, it is also possible to determine the geometry of the above requirements with equal distances numerically (iteratively): the engagement ratio is then recalculated, the geometry is thereby changed and the size of the profile forming zone is again determined. The calculation steps are then repeated with an incrementally varying geometry until the profile forming zone is minimized. The profiling of the grinding worm is then carried out with the geometry thus obtained (i.e. with the minimal profile forming zone). The gear is thus ground together with the grinding worm profiled in this way.
[0034] With such a defined contouring zone, the highest productivity of the machining process can be achieved.
[0035] Therefore, the proposed procedure leads to an optimization or reduction of the contact line between the workpiece and the tool.
[0036] Thus, by using a grinding worm when grinding a gear, the resulting grinding process is utilized.
[0037] The proposed method thus allows a better tool utilization by selectively modifying the resulting geometry of the grinding worm and in particular allows a minimized profiling zone. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] Examples of embodiments of the invention are shown in the drawings.
[0039] Figure 1 A perspective view showing a gear being hard finished with a grinding worm,
[0040] Figure 2 The meshing relationship between the gear teeth and the grinding worm according to the prior art is schematically shown.
[0041] Figure 3 The figure schematically shows the meshing relationship between the gear teeth and the grinding worm according to one embodiment of the present invention.
[0042] Figure 4 The geometrical relationship of the meshing between the gear arrangement and the grinding worm is schematically shown, showing the change from the prior art to the technical solution according to the present invention. DETAILED DESCRIPTION
[0043] Figure 1 First, the basic process of grinding the teeth of the gear 1 with the grinding worm 2 is shown. The gear 1 rotates about the rotation axis a, while the grinding worm 2 rotates about the rotation axis b, with a given engagement between the gear 1 and the grinding worm 2. The abrasive surface of the grinding worm 2 wears the tolerances on the tooth flanks of the toothed ring of the gear 1.
[0044] The profiling of the grinding surface of the grinding worm 2 is carried out according to the method described below.
[0045] To this end, the usual prior art procedure is first Figure 2 It shows:
[0046] The gear 1 meshes with the grinding worm 2 , and specifically, the tooth surface of the gear 1 to be ground meshes with the abrasive surface of the grinding worm 2 . Figure 2 (as well as Figure 3 ) is a section taken along a first plane E1 containing the rotation axis b of the grinding worm 2 and perpendicular to the rotation axis a of the gear 1. Figure 2 and 3 The drawing plane in FIG. 1 is a second plane E2 which contains the rotation axis a of the gear wheel 1 and is perpendicular to the plane E1 .
[0047] The first contact point S1 and the second pitch point S2 with the first abrasive surface 3 and the second abrasive surface 5 of the grinding worm 2 result in meshing of the first tooth surface 7 and the second tooth surface 9 of the gear 1. Accordingly, the third contact point S3 and the fourth contact point S4 are formed on the mating tooth surfaces, i.e., between the third tooth surface 8 and the fourth tooth surface 10 and the third abrasive surface 4 and the fourth abrasive surface 6.
[0048] The first meshing line 11 can be defined by the first contact point S1 and the second contact point S2, and the second meshing line 12 can also be defined by the third contact point S3 and the fourth contact point S4. Their intersection is the first intersection S5, which provides the pitch circle diameter d0 of the gear ring of the gear 1 (see Figure 4 ). A second line 14 may be drawn through the first intersection point S5, which is generated by the intersection of the first plane E1 and the second plane E2.
[0049] According to the existing technology, Figure 2 As shown, the grinding worm 2 is profiled to the final meshing situation. For example, a diamond dressing roller is manufactured, which corresponds to the geometry of the gear 1 to be ground and then generates the profile of the abrasive surface that meshes with the grinding worm 2.
[0050] See also Figure 4 It can be seen that the tangent line passing through the first intersection point S5 can be applied to the base circle diameter d of the gear teeth of gear 1. b ; This line is represented as the first line 13.
[0051] The first line 13 intersects the available root circle diameter d of the gear teeth of the gear 1 at the second intersection point S6. Nf Similarly, the first line 13 at the third intersection S7 with the gear teeth of the gear 1 of the available top circle diameter d Na intersect.
[0052] The second intersection point S6 and the third intersection point S7 determined in this way allow the first distance a1 and the second distance a2 measured from the second line 14 to be determined.
[0053] As from Figure 4 Visible and as Figure 2 As also reflected in FIG. 1 , the tip engagement distance (the area of the first line 13 between the first intersection point S5 and the third intersection point S7) and the root engagement distance (the area of the first line 13 between the first intersection point S5 and the second intersection point S6) have different sizes. Therefore, Figure 2 A typical machining situation is shown without changing the engagement ratio on the grinding worm; the root and tip parts of the engagement between workpiece and tool are clearly different.
[0054] The contour forming area PAZ is twice the larger of the first distance a1 and the second distance a2, that is, Figure 4In the case shown, it is twice the first distance a1.
[0055] Figure 4 The method according to the invention is shown for moving from the explained meshing situation between the gear wheel 1 and the grinding worm 2 to an improved situation (a numerical iteration procedure is described here (using the angle difference Δα), wherein the calculation is performed in each case by changing the position of the first line 13; this represents an alternative to directly determining the desired final geometry):
[0056] As shown, perpendicular to the first line 13 (through the first intersection S5 and the base circle diameter d b The vertical line 14 (the tangent line) passes through the rotation axis a of the gear 1. Therefore, the vertical line and the second line 14 enclose an angle α.
[0057] In accordance with Figure 2 After the situation has been calculated, the calculation is now repeated step by step, changing the angle α; that is, it is changed by the given angle difference Δα, and it is determined for the new situation, resulting in how the size ratio of the distances a1 and a2 changes.
[0058] Continue calculating until you reach Figure 1 The condition shown, where the two distances a1 and a2 are equal: a1 opt =a2 opt For this case, the root and tip parts of the mesh are equal. This case corresponds to Figure 3 , where the resulting ratios are plotted.
[0059] In the optimal case where the two distances a1 and a2 are equal, the result is a minimum and therefore optimal contour formation zone PAZ opt ,like Figure 4 As shown; this is now equal to the distance a1 opt and a2 opt twice as much.
[0060] Because of PAZ opt The contouring area is now minimized, so only a smaller axial section of the worm needs to be ground to machine the workpiece. This means that for the same axial worm length, more workpieces can be machined between two dressing operations. The productivity of the method is thus increased.
[0061] The above calculation (see Figure 4 ) based on the available root circle diameter d Nf and available top circle diameter d Na However, it is also possible to base the profile on the root diameter d Ff and the forming top circle diameter d Fa The calculation is performed. The diameter is slightly lower or higher than the two available circles. Depending on which diameter is available as data input, these can be used in the calculation.
[0062] It should be noted that in the above process steps a1) and a2), the meshing line is determined by the contact points of two consecutive tooth surfaces between the gear and the tool. However, the number of simultaneous contact points between the tool and the tooth surface varies depending on the gear parameters.
[0063] The meshing line determined according to steps a1) and a2) ultimately corresponds to the first line 13, since said line is tangential to the base circle of the gear arrangement (which ultimately is the definition of the meshing line). However, the first line 13 is introduced as an independent element, since it is the line that changes during the further calculation process.
[0064] As mentioned above, in some gear transmission situations, the explained optimization (i.e. the change in the meshing angle that is ultimately made) is not feasible because
[0065] 1. Due to unfavorable gear ring geometry, the grinding worm cannot reach the profile root circle or the usable root circle, or
[0066] 2. The root fillet radius cannot be completely formed in the gear ring.
[0067] In this case, after the calculation (step a) and step b) according to claim 1) and before the profiling of the grinding worm (step c) according to claim 1), the calculated optimum pressure angle (a1) at the grinding worm must be recalculated iteratively or analytically. opt =a2 opt ), until the limitations (1 and / or 2) no longer exist. The new pressure angle thus determined at the grinding worm is no longer optimal in the sense of the explained line of action regulation (where a1 opt =a2 opt ), but still more favorable than the nominal pressure angle (starting from the original calculation of the nominal pressure angle). In any case, an increase in productivity is also achieved in this way.
[0068] The following should also be noted: The "root circle diameter" is sometimes defined as the diameter at which the lowest point of the gear tooth backlash is located. The same applies to the "tip circle diameter", which often indicates or specifies the highest point of the gear tooth backlash. However, in the context of the present invention, the terms "root circle diameter" and "tip circle diameter" should be understood as the diameter at which the involute begins or ends.
Claims
1. A method for grinding a gear (1) in a grinding machine by means of a grinding worm (2), wherein: The tooth surface of the gear (1) is ground together with the abrasive surface of the profile of the grinding worm (2), the gear (1) having a gear rotation axis (a), the grinding worm (2) having a grinding worm rotation axis (b), and the gear ring of the gear (1) to be ground having a base circle diameter (d b ), root circle diameter (d f ) and the top circle diameter (d a ), It is characterized in that The method comprises the following steps: a) calculating the meshing ratio between the abrasive surface of the profile of the grinding worm (2) and the tooth surface of the gear (1) when the gear (1) and the grinding worm (2) are meshed for grinding, wherein a cross section is considered along a first plane (E1) including the rotation axis (b) of the grinding worm (2) and perpendicular to the rotation axis (a) of the gear (1); the calculation comprising: a1) determining a first meshing line (11) generated by contact points between two consecutive abrasive surfaces and two consecutive tooth surfaces; a2) determining a second meshing line (12) generated by contact points between two consecutive abrasive surfaces opposite to the abrasive surface of step a1) and two consecutive tooth surfaces opposite to the tooth surface of step a1); a3) determining a first intersection point (S5) of the first meshing line (11) and the second meshing line (12); a4) determining a base circle diameter (d ) of the gear ring that passes through the first intersection point (S5) and is equal to the base circle diameter (d ) of the gear (1) b ) the first line of tangency (13); a5) determining the first line (13) and the root circle diameter (d f ) and determine the second intersection point (S6) of the first line (13) and the top circle diameter (d a )’s third intersection point (S7); a6) determining a second line (14), the second line (14) being generated as the intersection of the first plane (E1) and a second plane (E2) containing the axis of rotation (a) of the gear (1), the second plane being perpendicular to the first plane (E1) and containing the first intersection point (S5) of the first meshing line (11) and the second meshing line (12); a7) Determine the first line (13) and the root circle diameter (d f ) and a second line (14) of intersection of the first plane (E1) and the second plane (E2); a8) determining the first line (13) and the top circle diameter (d a ) and the second line (14) of the intersection line of the first plane (E1) and the second plane (E2); b) By changing the base diameter (d b ) so that the first distance (a1) and the second distance (a2) are equal, determining a change in the geometry of the meshing ratio compared to that determined according to step a); c) a geometrical profile of the grinding worm (2) with respect to the meshing ratio produced when the first distance (a1) and the second distance (a2) are equal; d) Grinding the gear (1) using the grinding worm profiled according to step c).
2. The method according to claim 1, characterized in that The root circle diameter (d f ) is the available root circle diameter (d Nf ), the top circle diameter (d a ) is the available top circle diameter (d Na ).
3. The method according to claim 1, characterized in that The root circle diameter (d f ) is the diameter of the forming root circle (d Ff ), the top circle diameter (d a ) is the top diameter of the molding (d Fa ).
4. The method according to any one of claims 1 to 3, characterized in that After carrying out step b) according to claim 1 and before carrying out step c) according to claim 1 , the contour of the grinding worm ( 2 ) is modified.
5. The method according to claim 1, characterized in that According to step c) of claim 1, the profiling of the grinding worm (2) is performed by manufacturing a worm steel basic body and covering the worm steel basic body with an abrasive layer.
6. The method according to claim 1, characterized in that According to step c) of claim 1 , the profiling of the grinding worm ( 2 ) is carried out by providing a dressable grinding worm ( 2 ) with the described geometry.
7. The method according to claim 6, characterized in that In order to profile the grinding worm (2), a dressing roller is produced which corresponds to the geometry and with which the grinding worm (2) is dressed.
8. The method according to claim 6, characterized in that The contour shaping of the grinding worm (2) is carried out by a numerically controlled dressing device, which generates the geometric shape of the grinding surface of the grinding worm (2).