Face gear addendum fillet grinding method

Abstract

The invention discloses a face gear addendum fillet grinding machining method, and relates to the technical field of gear machining. The theoretical tooth surface of a worm grinding wheel is obtained through calculation of the tooth surface of a generating gear; the theoretical machining path of the diamond roller is obtained through calculation of the theoretical tooth surface of the worm grinding wheel; designing a tooth crest fillet surface of the face gear, and calculating to obtain a tooth crest fillet surface equation of the face gear; adjusting the worm grinding wheel according to the addendum fillet surface of the face gear, calculating to obtain the actual tooth surface of the worm grinding wheel, adjusting the diamond roller according to the actual tooth surface of the worm grinding wheel, and calculating to obtain the actual machining path of the diamond roller; and then a diamond roller is used for dressing the worm grinding wheel according to the actual machining path, then the dressed worm grinding wheel is used for grinding the face gear, and the face gear with the addendum fillet is obtained. According to the face gear addendum fillet grinding machining method, the machining efficiency is improved while the face gear addendum fillet machining precision is guaranteed.

Description

Technical Field

[0001] The invention relates to the technical field of gear processing, and in particular to a method for grinding a tooth top fillet of a face gear. Background Art

[0002] Face gears are usually meshed with involute cylindrical gears. Face gear transmission has a more compact structure than bevel gear transmission.

[0003] During the face gear processing, the tooth top of the face gear needs to be chamfered, which is an indispensable process. Generally, the chamfering is performed after the opposite gear is ground. After the opposite gear is chamfered, the face gear can reduce stress concentration during the transmission process and improve meshing stability.

[0004] In the related art, the accuracy of chamfering of the surface gear is unstable, and there are also problems such as low processing efficiency resulting in long processing time. Summary of the invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention provides a method for grinding the tooth top fillet of a face gear, which improves the processing efficiency while ensuring the processing accuracy of the tooth top fillet of the face gear.

[0006] According to the method for grinding the tooth top fillet of a face gear according to an embodiment of the present invention, a face gear is ground using a worm grinding wheel, comprising step S1, obtaining a theoretical tooth surface of the worm grinding wheel by calculating the tooth surface of the generated gear; Step S2, calculating the theoretical processing path of the diamond roller by the theoretical tooth surface of the worm grinding wheel, and the diamond roller is used for processing and dressing the worm grinding wheel; Step S3, designing the tooth addendum fillet surface of the face gear, and calculating and obtaining the tooth addendum fillet surface equation of the face gear; Step S4, adjusting the worm grinding wheel according to the tooth top fillet surface of the face gear, calculating the actual tooth surface of the worm grinding wheel, and adjusting the diamond roller according to the actual tooth surface of the worm grinding wheel, calculating the actual processing path of the diamond roller; Step S5, the diamond roller trims the worm grinding wheel according to the actual processing path, and then uses the trimmed worm grinding wheel to grind the face gear to obtain a face gear with a tooth top fillet.

[0007] The method for grinding the tooth top fillet of a face gear according to an embodiment of the present invention has at least the following beneficial effects: a worm grinding wheel is used to grind the facing gear; before the grinding, a series of calculations are performed to obtain the actual processing path of the diamond roller; after the diamond roller has trimmed the worm grinding wheel according to the actual processing path, the worm grinding wheel can grind the facing gear to directly obtain a face gear with a tooth top fillet, that is, the worm grinding wheel completes the processing of the tooth top fillet while grinding the facing gear, and there is no need to perform chamfering on the tooth top of the facing gear separately, thereby reducing one process step, and improving the processing efficiency while ensuring the processing accuracy of the tooth top fillet of the face gear.

[0008] According to some embodiments of the present invention, in step S3, the tooth top fillet surface of the face gear is obtained by enveloping a sphere, the sphere is tangent to the tooth top surface of the face gear and the tooth profile surface of the face gear, and the sphere rolls along the tooth width direction of the face gear for enveloping.

[0009] According to some embodiments of the present invention, in step S4, the difference between the tooth top fillet surface of the face gear and the theoretical tooth surface of the face gear is established, the actual tooth surface of the worm grinding wheel is calculated based on the difference, and then the actual processing path of the diamond roller is calculated based on the actual tooth surface of the worm grinding wheel.

[0010] According to some embodiments of the present invention, the diamond roller is a conical diamond roller.

[0011] According to some embodiments of the present invention, when the worm grinding wheel is grinding the face gear, the worm grinding wheel and the face gear both rotate according to a set transmission ratio, and the worm grinding wheel also feeds in the radial direction of the face gear.

[0012] According to some embodiments of the present invention, the rotational movement of the worm grinding wheel and the radial feeding of the worm grinding wheel are performed independently of each other.

[0013] According to some embodiments of the present invention, the theoretical tooth surface equation of the face gear is r 2 , and satisfy the equation: , Where M 2w is the coordinate transformation matrix, It represents the meshing equation when the rotation parameters of the worm wheel remain unchanged and the feed parameters change. It represents the meshing equation when the feed parameter of the worm wheel remains unchanged but the rotation parameter changes. Indicates that when the worm wheel feed parameter E 2s The rotation parameter φ remains unchanged w The relative speed under changing conditions, Indicates when the worm wheel rotates parameter φ w The feed parameter E remains unchanged 2s Relative speed under changing conditions.

[0014] According to some embodiments of the present invention, the tooth surface of the worm grinding wheel is obtained by enveloping the shaping gear.

[0015] According to some embodiments of the present invention, the worm grinding wheel is ω w The angular velocity of the gear is ω s The gear is rotated at an angular velocity, the profile of the gear is an involute profile, and the tooth surface equation of the gear is: , In the formula, r bs is the base circle radius of the involute of the gear, θ 0s is the angle parameter of the intersection of the involute and the base circle, θ s is the sum of the development angle and the pressure angle at a point on the involute, u s is the tooth direction parameter.

[0016] According to some embodiments of the present invention, the involute starting circle of the shaping gear is extended, and the boundary of the shaping gear is calculated to extend the theoretical tooth surface of the face gear.

[0017] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments, wherein: Figure 1 Schematic diagram of the involute tooth profile of the shaping gear according to an embodiment of the present invention; Figure 2 It is a schematic diagram of the envelope of the profile gear, the face gear and the worm grinding wheel according to an embodiment of the present invention; Figure 3 The figure is a formal diagram of a diamond roller according to an embodiment of the present invention; Figure 4 It is a side view of a diamond roller according to an embodiment of the present invention; Figure 5 Schematic diagram of a mathematical model of a diamond roller dressing worm grinding wheel according to an embodiment of the present invention; Figure 6 A schematic diagram of the tooth top fillet of a spherical envelope surface gear according to an embodiment of the present invention; Figure 7 It is a schematic diagram of mathematical modeling of the tooth top fillet of the face gear according to an embodiment of the present invention; Figure 8 Schematic diagram of the extension boundary of the tooth top fillet of the face gear according to an embodiment of the present invention.

[0019] Figure Number: The forming gear 100, the worm grinding wheel 200, the face gear 300, the diamond roller 400, and the ball 500. DETAILED DESCRIPTION

[0020] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0021] In the description of the present invention, it should be understood that descriptions involving orientation, such as orientation or positional relationship indicated as up, down, etc., are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0022] In the description of the present invention, "a plurality" means more than two. If there is a description of "first" or "second", it is only used for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0023] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0024] As described in the background technology, in the process of chamfering the tooth top of the opposite gear, a special processing tool can be used to chamfer the tooth top of the opposite gear using an industrial robot or a five-axis CNC machining center. In this method, the tooth top of the opposite gear is generally chamfered after the grinding process of the face gear is completed. The grinding process and the chamfering process of the face gear are performed on different equipment or work platforms, so the face gear needs to be repositioned, which is cumbersome and takes a long time to process. For example, the face gear processing tool is modified to obtain a special processing tool, and then the chamfering process is performed on the face gear, which increases the tool cost. In the process of grinding the tooth top of the opposite gear by connecting a grinding wheel to the end of the mechanical arm of the industrial robot, the face gear needs to be disassembled and installed, the positioning of the face gear is difficult, and the precision of the processed tooth top fillet is not high. When the face gear is CNC milled by a five-axis CNC machining center, the face gear also has the difficulty of positioning when disassembling and installing, and the precision of the processed tooth top fillet is not high.

[0025] In other chamfering processes, a special chamfering machine is manually operated to perform tooth top chamfering on the face gear. In this type of processing method, the manual processing efficiency is low, the processing time is long, and the chamfering accuracy of the face gear is unstable.

[0026] A method for grinding a face gear tooth top fillet according to an embodiment of the present invention uses a worm grinding wheel pair and includes step S1, obtaining a theoretical tooth surface of the worm grinding wheel by calculating the tooth surface of the generated gear; Step S2, obtaining a theoretical processing path of a diamond roller by calculating the theoretical tooth surface of the worm grinding wheel, and the diamond roller is used to process and dress the worm grinding wheel; Step S3, designing the tooth addendum fillet surface of the face gear, and calculating the tooth addendum fillet surface equation of the face gear; Step S4, adjusting the worm grinding wheel according to the tooth top fillet surface of the face gear, calculating the actual tooth surface of the worm grinding wheel, and adjusting the diamond roller according to the actual tooth surface of the worm grinding wheel, calculating the actual processing path of the diamond roller; Step S5, the diamond roller is used to dress the worm grinding wheel according to the actual processing path, and then the dressed worm grinding wheel is used to grind the face gear to obtain a face gear with a tooth top fillet.

[0027] The opposite gear is ground using a worm grinding wheel. Before the grinding process, a series of calculations are performed to obtain the actual processing path of the diamond roller. After the diamond roller has trimmed the worm grinding wheel according to the actual processing path, the worm grinding wheel can directly obtain a face gear with a tooth top fillet by grinding the opposite gear. That is, the worm grinding wheel completes the processing of the tooth top fillet while grinding the opposite gear. There is no need to perform chamfering on the tooth top of the opposite gear separately, which reduces one process step and improves the processing efficiency while ensuring the processing accuracy of the tooth top fillet of the face gear.

[0028] It can be understood that in step S3, the tooth top fillet surface of the face gear is obtained by enveloping a sphere, the sphere is tangent to the tooth top surface of the face gear and the tooth profile surface of the face gear, and the sphere rolls along the tooth width direction of the face gear to envelop.

[0029] It can be understood that in step S4, the difference between the tooth top fillet surface of the face gear and the theoretical tooth surface of the face gear is established, the actual tooth surface of the worm grinding wheel is calculated based on the difference, and then the actual processing path of the diamond roller is calculated based on the actual tooth surface of the worm grinding wheel.

[0030] It can be understood that the diamond roller is preferably a conical diamond roller.

[0031] It can be understood that when the worm grinding wheel is grinding the face gear, both the worm grinding wheel and the face gear rotate according to a set transmission ratio, and the worm grinding wheel is also fed in the radial direction of the face gear.

[0032] Preferably, the rotational movement of the grinding worm and the radial feed of the grinding worm are performed independently of each other.

[0033] It can be understood that the tooth surface of the worm grinding wheel is obtained by enveloping the profile gear.

[0034] It can be understood that the involute starting circle of the shaping gear is extended, the boundary of the shaping gear is calculated, and the theoretical tooth surface of the opposite gear is extended, so that a complete tooth top fillet surface can be machined.

[0035] In some embodiments, the steps of the face gear tooth top fillet grinding method are explained and described in more detail. The tooth surface of the worm grinding wheel is obtained by enveloping the profile gear. ω w The angular velocity of the gear rotates along its own axis and generates a shape ω s As an example, the angular velocity of the rotation along its own axis is Figure 1 As shown in the figure, the profile of the gear is a standard involute profile, and the tooth surface equation of the gear can be expressed as: (1), In the formula, r bs is the base circle radius of the involute of the gear, θ 0s is the angle parameter of the intersection of the involute and the base circle, θ s is the sum of the development angle and the pressure angle at a point on the involute, u s is the tooth direction parameter. According to the tooth surface equation of the gear, the unit normal vector of the gear can be calculated as: (2), Based on the meshing relationship between the worm grinding wheel and the shaping gear, the worm grinding wheel and the shaping gear are internally meshed. The tooth surface equation of the worm grinding wheel is derived from the tooth surface equation of the shaping gear through coordinate transformation and meshing principle. The tooth surface r of the worm grinding wheel w It can be expressed as: (3), Where M ws is the coordinate transformation matrix, v s is the relative speed between the forming gear and the worm wheel.

[0036] In the process of grinding the face gear with a worm grinding wheel, the development process of the worm grinding wheel mainly includes two movements. The first aspect is that the worm grinding wheel rotates around its own axis, and the face gear also rotates around its own axis at the same time, and the worm grinding wheel and the face gear rotate according to the designed transmission ratio; the second aspect is that the worm grinding wheel can also be fed radially along the face gear. It should be understood that the rotation of the worm grinding wheel and the face gear and the radial feeding of the worm grinding wheel along the face gear are two independent movements, that is, the rotation angle of the worm grinding wheel and the face gear has nothing to do with the feeding position of the worm grinding wheel. Therefore, when the worm grinding wheel and the face gear rotate, the worm grinding wheel can envelop the contour of the face gear, and when the worm grinding wheel is fed radially along the face gear, the worm grinding wheel can gradually envelop the tooth profile of the face gear in the entire tooth length direction. The superposition of the two movements completes the process of the worm grinding wheel developing the processed face gear. For example Figure 2 The position relationship shown.

[0037] Based on the above process, it can be understood that the theoretical tooth surface equation of the face gear is r 2 , and satisfy the equation: (4), Where M 2w is the coordinate transformation matrix, It represents the meshing equation when the rotation parameters of the worm wheel remain unchanged and the feed parameters change. It represents the meshing equation when the feed parameter of the worm wheel remains unchanged but the rotation parameter changes. Indicates that when the worm wheel feed parameter E 2s The rotation parameter φ remains unchanged w The relative speed under changing conditions, Indicates when the worm wheel rotates parameter φ w The feed parameter E remains unchanged 2s Relative speed under changing conditions.

[0038] In the movement of diamond roller dressing worm grinding wheel, diamond roller with standard cone surface is generally used, such as Figure 3 and Figure 4 The diamond roller of the structure shown in FIG. The maximum outer radius of the diamond roller is R g , the half cone angle is a g , half of the top thickness is s , the straight line parameters are t , the rotation parameter is θ g , the coordinate vector and normal vector of the surface point of the diamond roller in the coordinate system can be expressed as: (5), (6), It should be understood that in some embodiments, it is possible to establish Figure 5 The coordinate system of the dressing motion between the diamond roller and the worm grinding wheel is shown in Figure 1. w and S g They are respectively connected to the worm grinding wheel and the diamond roller. c is a global fixed coordinate system, and the rotation angle of the worm wheel along its own axis is φ a , the worm wheel rotation angle is φ w , φ w is the generation motion parameter in the worm wheel surface equation, and is also the angle at which the worm wheel rotates along its own axis; the worm wheel rotation angle is φ w1 , φ w1 It is the rotation angle parameter of the relative motion between the diamond roller and the worm grinding wheel. Through coordinate transformation, the coordinate vector and normal vector of the diamond roller and the worm grinding wheel can be converted to the global fixed coordinate system S c Next, the equation is: (7), The coordinate transformation matrix M cg 、M ca 、M ab 、M bw It can be expressed as: (8), (9), (10), (11), Since the surfaces of the diamond roller and the worm grinding wheel must be tangent at a certain point when the diamond roller is dressing the worm grinding wheel, the following equation can be derived: (12), Then solve the above equations and discretize φ a Numerical, Solved y , z , φ b It can be known that the diamond roller can dress one spiral line on the tooth surface of the worm grinding wheel each time, and can dress multiple spiral lines by repeating it many times, that is, multiple spiral lines constitute the curved surface of the worm grinding wheel.

[0039] When designing the tooth tip fillet surface of the face gear, refer to Figure 6 As shown in FIG. 1 , a spherical ball can be used to be tangent to the tooth top surface of the face gear and the tooth profile surface of the face gear, and the spherical ball rolls along the tooth width direction of the face gear to envelop the tooth top fillet surface of the face gear. Figure 6 The structure shown and Figure 7 As shown, the spherical surface is in the coordinate system S f The following can be expressed as: (13), in φ and θ is the spherical parameter, r is the radius of the sphere, x b , y b , z b is the coordinate of the center of the sphere, in the coordinate system S f The following can be expressed: (14), Since the sphere and the tooth profile and tooth top surface of the face gear remain tangent, the contact equation can be expressed as: (15), Among them, P g is a point on the tooth profile of the face gear, n g is the normal vector of the point on the tooth profile surface of the face gear, P d is the point on the tooth top surface of the face gear, n d is the normal vector of the point on the tooth top surface of the face gear, P a , P c is a point on the surface of the sphere, P a , P c is the normal vector of the point on the surface of the sphere. There are 9 variables in the equation group (15), and 8 unknown quantities can be solved. The center of the discrete sphere is z b , we can solve the position where the ball and the face gear are in tangential contact, then the tooth top circle equation of the face gear is y It can be expressed as: (16), in φ y and θ y is the tooth tip fillet surface parameter of the face gear, which can be expressed as: (17).

[0040] The difference between the tooth top fillet surface of the face gear and the theoretical tooth surface of the face gear is established, and the actual tooth surface of the worm grinding wheel is calculated based on the difference, and then the actual processing path of the diamond roller is calculated based on the actual tooth surface of the worm grinding wheel. Specifically, the tooth top fillet surface of the face gear can be regarded as the error tooth surface, and the error value between the tooth top fillet of the face gear and the theoretical tooth surface is established, and then the tooth surface error of the face gear is converted to the tooth surface of the worm grinding wheel through formula calculation to obtain the actual tooth surface of the worm grinding wheel, and the processing path of the diamond roller is adjusted based on the actual tooth surface of the worm grinding wheel.

[0041] Theoretical tooth surface r of face gear 2 With the tooth tip fillet r y The error between d It can be expressed as: (18), The face gear and the worm wheel are in instantaneous point contact, and the tooth surface meshing points of the two are in a one-to-one correspondence. 2 ( u s , θ s ) and the tooth surface r of the worm wheel w ( u s , θ s ) is corresponding, then the actual tooth surface r of the worm grinding wheel wa It can be expressed as: (19), Adjust the machining path of the diamond roller according to the actual tooth surface of the worm grinding wheel, and adjust the actual tooth surface of the worm grinding wheel to wa Substitute the theoretical tooth surface r into formula (12) w , the actual tooth surface machining path of the diamond roller enveloping worm grinding wheel can be solved.

[0042] In order to machine the complete face gear tooth top fillet surface, refer to Figure 8 As shown in the figure, the theoretical tooth surface of the face gear needs to be extended on the original basis, that is, the involute starting circle of the shape-forming gear needs to be extended. Then the parameter value of the shape-forming gear boundary ( u sf , θ sf ) can be solved by the equation: (20), Among them, P f is the boundary point of the tooth profile extension on the face gear, which can be expressed as: (twenty one), Set the parameter value of the gear boundary ( u sf , θ sf ) into the gear equation, the boundary of the gear can be obtained.

[0043] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in the relevant technical field without departing from the purpose of the present invention.

Claims

1. A method for grinding the tooth top fillet of a face gear, using a worm grinding wheel to grind the face gear, characterized in that: include: Step S1, obtaining the theoretical tooth surface of the worm grinding wheel by calculating the tooth surface of the profiling gear; Step S2, calculating the theoretical processing path of the diamond roller by the theoretical tooth surface of the worm grinding wheel, and the diamond roller is used for processing and dressing the worm grinding wheel; Step S3, designing the tooth addendum fillet surface of the face gear, and calculating and obtaining the tooth addendum fillet surface equation of the face gear; Step S4, adjusting the worm grinding wheel according to the tooth top fillet surface of the face gear, calculating the actual tooth surface of the worm grinding wheel, and adjusting the diamond roller according to the actual tooth surface of the worm grinding wheel, calculating the actual processing path of the diamond roller; Step S5, the diamond roller trims the worm grinding wheel according to the actual processing path, and then uses the trimmed worm grinding wheel to grind the face gear to obtain a face gear with a tooth top fillet.

2. The method for grinding the tooth top fillet of a face gear according to claim 1, characterized in that: In step S3, the tooth top fillet surface of the face gear is obtained by enveloping a sphere, the sphere is tangent to the tooth top surface of the face gear and the tooth profile surface of the face gear, and the sphere rolls along the tooth width direction of the face gear to envelop.

3. The method for grinding the tooth top fillet of a face gear according to claim 1, characterized in that: In step S4, the difference between the tooth top fillet surface of the face gear and the theoretical tooth surface of the face gear is established, the actual tooth surface of the worm grinding wheel is calculated based on the difference, and then the actual processing path of the diamond roller is calculated based on the actual tooth surface of the worm grinding wheel.

4. The method for grinding the tooth tip fillet of a face gear according to any one of claims 1 to 3, characterized in that: The diamond roller is a conical diamond roller.

5. The method for grinding the tooth top fillet of a face gear according to claim 1, characterized in that: When the worm grinding wheel is grinding the face gear, the worm grinding wheel and the face gear both rotate according to a set transmission ratio, and the worm grinding wheel also feeds in the radial direction of the face gear.

6. The method for grinding the tooth top fillet of a face gear according to claim 5, characterized in that: The rotational movement of the worm grinding wheel and the radial feed of the worm grinding wheel are performed independently of each other.

7. The method for grinding the tooth top fillet of a face gear according to claim 6, characterized in that: The theoretical tooth surface equation of the face gear is r2, and satisfies the equation: ， Where M 2w is the coordinate transformation matrix, It represents the meshing equation when the rotation parameters of the worm wheel remain unchanged and the feed parameters change. It represents the meshing equation when the feed parameter of the worm wheel remains unchanged but the rotation parameter changes. Indicates that when the worm wheel feed parameter E 2s The rotation parameter φ remains unchanged w The relative speed under changing conditions, Indicates when the worm wheel rotates parameter φ w The feed parameter E remains unchanged 2s Relative speed under changing conditions.

8. The method for grinding the tooth top fillet of a face gear according to claim 1, characterized in that: The tooth surface of the worm grinding wheel is obtained by enveloping the shaping gear.

9. The method for grinding the tooth top fillet of a face gear according to claim 8, characterized in that: The worm grinding wheel ω w The angular velocity of the gear is ω s The gear is rotated at an angular velocity, the profile of the gear is an involute profile, and the tooth surface equation of the gear is: ， In the formula, r bs is the base circle radius of the involute of the gear, θ 0s is the angle parameter of the intersection of the involute and the base circle, θ s is the sum of the development angle and the pressure angle at a point on the involute, u s is the tooth direction parameter.

10. The method for grinding the tooth top fillet of a face gear according to claim 1, characterized in that: The involute starting circle of the shaping gear is extended, and the boundary of the shaping gear is calculated to extend the theoretical tooth surface of the face gear.

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