Face gear tooth tip rounding grinding method

Abstract

The application discloses a face gear tooth addendum corner grinding processing method and relates to the technical field of gear processing. The theoretical tooth surface of a worm grinding wheel is calculated through the tooth surface of a profiled gear; the theoretical processing path of a diamond roller is calculated through the theoretical tooth surface of the worm grinding wheel; the tooth addendum corner surface of the face gear is designed, and the tooth addendum corner surface equation of the face gear is calculated; the worm grinding wheel is adjusted according to the tooth addendum corner surface of the face gear, the actual tooth surface of the worm grinding wheel is calculated, the diamond roller is adjusted according to the actual tooth surface of the worm grinding wheel, and the actual processing path of the diamond roller is calculated; the worm grinding wheel is trimmed according to the actual processing path by using the diamond roller, the face gear is ground by using the trimmed worm grinding wheel, and the face gear with the tooth addendum corner is obtained. The face gear tooth addendum corner grinding processing method can ensure the processing precision of the face gear tooth addendum corner and improve the processing efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear machining, in particular to a face gear tooth tip fillet grinding machining method. BACKGROUND

[0002] The face gear is generally meshed with the involute cylindrical gear for transmission. The face gear transmission has a more compact structure compared with the bevel gear transmission.

[0003] In the face gear machining process, the tooth tip of the face gear needs to be rounded and processed, which is an indispensable process. Generally, after the face gear is ground, the rounding process is performed. After the face gear is rounded, the face gear can reduce stress concentration and improve meshing stability during transmission.

[0004] In the related art, the precision of rounding the face gear is unstable, and the long processing time caused by low processing efficiency also exists. SUMMARY

[0005] The present application aims to at least solve one of the technical problems existing in the prior art. To this end, the present application provides a face gear tooth tip fillet grinding machining method, which ensures the precision of face gear tooth tip fillet machining while improving the processing efficiency.

[0006] According to the face gear tooth tip fillet grinding machining method of the embodiment of the present application, the worm grinding wheel is used for grinding the face gear, including the following steps.

[0007] Step S2, the theoretical machining path of the diamond roller is calculated based on the theoretical tooth surface of the worm grinding wheel, and the diamond roller is used for machining and trimming the worm grinding wheel.

[0008] Step S3, the tooth tip fillet surface of the face gear is designed, and the tooth tip fillet surface equation of the face gear is calculated.

[0009] Step S4, the worm grinding wheel is adjusted according to the tooth tip fillet surface of the face gear, the actual tooth surface of the worm grinding wheel is calculated, and the diamond roller is adjusted according to the actual tooth surface of the worm grinding wheel, and the actual machining path of the diamond roller is calculated.

[0010] Step S5, the diamond roller trims the worm grinding wheel according to the actual machining path, and then the worm grinding wheel is used for grinding the face gear, and the face gear with tooth tip fillet is obtained.

[0011] According to the face gear tooth addendum corner grinding processing method, the worm grinding wheel is used to grind the face gear, before the grinding processing, the actual processing path of the diamond roller is obtained through a series of calculations, after the worm grinding wheel is modified according to the actual processing path, the face gear is ground by the worm grinding wheel, and the face gear with the tooth addendum corner can be directly obtained, that is, the worm grinding wheel completes the processing of the tooth addendum corner while grinding the face gear, and the face gear tooth addendum corner processing is not needed to be processed separately, one process is reduced, the processing efficiency is improved while the face gear tooth addendum corner processing precision is ensured.

[0012] According to some embodiments of the present application, in step S3, the face gear tooth addendum corner surface is obtained by a spherical ball envelope, the spherical ball is tangent to the face gear tooth surface and the face gear tooth profile surface, and the spherical ball rolls in the tooth width direction of the face gear to perform the envelope.

[0013] According to some embodiments of the present application, in step S4, the difference between the face gear tooth addendum corner surface and the theoretical tooth surface of the face gear is established, the actual tooth surface of the worm grinding wheel is calculated according to the difference, and the actual processing path of the diamond roller is calculated according to the actual tooth surface of the worm grinding wheel.

[0014] According to some embodiments of the present application, the diamond roller is a conical diamond roller.

[0015] According to some embodiments of the present application, when the worm grinding wheel grinds the face gear, the worm grinding wheel and the face gear rotate according to a set transmission ratio, and the worm grinding wheel further feeds in the radial direction of the face gear.

[0016] According to some embodiments of the present application, the rotational motion of the worm grinding wheel and the radial feeding of the worm grinding wheel are independently performed.

[0017] According to some embodiments of the present application, the theoretical tooth surface equation of the face gear is r2, and satisfies the equation:

[0018] ,

[0019] In the formula, M 2w is a coordinate transformation matrix, represents the engagement equation when the rotational parameters of the worm grinding wheel are unchanged and the feeding parameters are changed, represents the engagement equation when the feeding parameters of the worm grinding wheel are unchanged and the rotational parameters are changed, represents the relative speed when the worm grinding wheel feeding parameter E 2s is unchanged and the rotational parameter φ w is changed, φ represents the rotation parameter of the worm grinding wheel w E represents the feed parameter 2s the relative velocity under the condition of the change of the feed parameter.

[0020] According to some embodiments of the present application, the tooth surface of the worm grinding wheel is obtained from the generating gear envelope.

[0021] According to some embodiments of the present application, the worm grinding wheel rotates at an angular velocity of ω w the generating gear rotates at an angular velocity of ω s the generating gear is a involute profile, and the tooth surface equation of the generating gear is:

[0022] ,

[0023] wherein, r bs R is the base circle radius of the involute of the generating gear, θ 0s θ is the angle parameter of the intersection point of the involute and the base circle, θ s φ is the sum of the pressure angle and the spread angle of a point on the involute, u s β is the tooth direction parameter.

[0024] According to some embodiments of the present application, the generating gear envelope is extended by extending the starting circle of the involute of the generating gear, and the boundary of the generating gear is calculated to extend the theoretical tooth surface of the face gear.

[0025] Additional aspects and advantages of the present application will be given, partially in the following description, partially become obvious from the following description, or be understood by practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0026] The present application will be further described below in conjunction with the drawings and embodiments, wherein:

[0027] Figure 1 Fig. 1 is a schematic diagram of the involute profile of the generating gear of the embodiment of the present application;

[0028] Figure 2 Fig. 2 is a schematic diagram of the envelope of the generating gear, the face gear and the worm grinding wheel of the embodiment of the present application;

[0029] Figure 3 Fig. 3 is a front view of the diamond roller of the embodiment of the present application;

[0030] Figure 4 Fig. 4 is a side view of the diamond roller of the embodiment of the present application;

[0031] Figure 5 Fig. 1 is a schematic diagram of a mathematical model of a diamond roller dressing worm grinding wheel according to an embodiment of the present application;

[0032] Figure 6 Fig. 2 is a schematic diagram of a tooth addendum corner of a spherical enveloping face gear according to an embodiment of the present application;

[0033] Figure 7 Fig. 3 is a schematic diagram of mathematical modeling of a tooth addendum corner of a face gear according to an embodiment of the present application;

[0034] Figure 8 Fig. 4 is a schematic diagram of an extension boundary of a tooth addendum corner of a face gear according to an embodiment of the present application.

[0035] Reference Signs:

[0036] Formed gear 100, worm grinding wheel 200, face gear 300, diamond roller 400, spherical ball 500. DETAILED DESCRIPTION

[0037] Embodiments of the present application are described in detail below with reference to the attached drawings, wherein the same or similar components have the same or similar designations throughout the several figures of the drawings and any description set forth herein. The embodiments described below are presented by way of example only and are not intended to limit the present application as described herein.

[0038] In the description of the present application, it is to be understood that the relative or positional description, such as upper, lower, etc., is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0039] In the description of the present application, the plural refers to two or more. If there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the sequence of technical features indicated.

[0040] In the description of the present application, unless otherwise explicitly limited, the words such as setting, installing, connecting, etc. should be broadly understood, and the person skilled in the art can reasonably determine the specific meaning of the above words in the present application in combination with the specific content of the technical solution.

[0041] As described in the background, in the machining process of rounding the tooth top of the face gear, a special machining tool can be used to round the face gear by using an industrial robot and a five-axis numerical control machining center. In such a method, the face gear is generally rounded after grinding. The grinding and rounding of the face gear are performed on different devices or work platforms, so the face gear needs to be repositioned, which is complicated and time-consuming. For example, the face gear machining tool is modified to obtain a special machining tool, and the face gear is rounded, which additionally increases the cost of the tool. In the grinding process of the tooth top of the face gear, the face gear needs to be disassembled and installed, and the positioning of the face gear is difficult, and the precision of the rounded tooth top is not high. The face gear is also disassembled and installed for positioning in the numerical control milling of the face gear by using a five-axis numerical control machining center, and the precision of the rounded tooth top is not high.

[0042] In other rounding processes, the face gear is rounded by manually operating a special chamfering machine. In such a machining method, the manual processing efficiency is low, the processing time is long, and the rounding precision of the face gear is unstable.

[0043] The face gear tooth top rounding grinding method of one embodiment of the application uses a worm wheel to include steps S1, the theoretical tooth surface of the worm wheel is calculated by the tooth surface of the generated gear;

[0044] Step S2, the theoretical machining path of the diamond roller is calculated by the theoretical tooth surface of the worm wheel, and the diamond roller is used to machine the worm wheel;

[0045] Step S3, the tooth top rounding surface of the face gear is designed, and the tooth top rounding surface equation of the face gear is calculated;

[0046] Step S4, the worm wheel is adjusted according to the tooth top rounding surface of the face gear, the actual tooth surface of the worm wheel is calculated, and the diamond roller is adjusted according to the actual tooth surface of the worm wheel, and the actual machining path of the diamond roller is calculated;

[0047] Step S5, the diamond roller is machined according to the actual machining path, and the worm wheel is machined according to the actual machining path, and the face gear is machined by using the machined worm wheel, and the face gear with the tooth top rounding is obtained.

[0048] The face gear is ground by the worm grinding wheel. Before the grinding, the actual machining path of the diamond roller is obtained through a series of calculations. After the worm grinding wheel is modified according to the actual machining path, the face gear is ground by the worm grinding wheel, so that the face gear with the addendum corner can be directly obtained, that is, the worm grinding wheel completes the machining of the addendum corner while grinding the face gear, and the machining of the addendum corner of the face gear is not needed, so that one process is reduced, and the machining efficiency is improved while the machining precision of the addendum corner of the face gear is ensured.

[0049] It can be understood that in step S3, the addendum corner surface of the face gear is obtained by a spherical ball envelope, the spherical ball is tangent to the addendum 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 perform the envelope.

[0050] It can be understood that in step S4, the difference between the addendum corner 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 according to the difference, and the actual machining path of the diamond roller is calculated according to the actual tooth surface of the worm grinding wheel.

[0051] It can be understood that the diamond roller is preferably a conical diamond roller.

[0052] It can be understood that when the worm grinding wheel grinds the face gear, the worm grinding wheel and the face gear rotate according to the set transmission ratio, and the worm grinding wheel also feeds along the radial direction of the face gear.

[0053] Preferably, the rotational motion of the worm grinding wheel and the radial feeding of the worm grinding wheel are independently performed.

[0054] It can be understood that the tooth surface of the worm grinding wheel is obtained by an envelope of the generating gear.

[0055] It can be understood that the boundary of the generating gear is calculated by extending the starting circle of the involute of the generating gear, so as to extend the theoretical tooth surface of the face gear, so that the complete addendum corner surface can be machined.

[0056] In some embodiments, the steps of the face gear addendum corner grinding method are more specifically explained and described. The tooth surface of the worm grinding wheel is obtained by an envelope of the generating gear. The worm grinding wheel rotates along its own axis at an angular velocity of ω w , and the generating gear rotates along its own axis at an angular velocity of ω s . For example, referring to FIG. 1, the generating gear is a standard involute profile, and the tooth surface equation of the generating gear can be expressed as: Figure 1

[0057] (1), ​

[0058] wherein, r bs is the base circle radius of the generating gear, θ 0s is the angle parameter of the intersection point of the involute and the base circle, θ s is the sum of the angle of development and the pressure angle of a point on the involute, u s is the transverse direction parameter. According to the tooth surface equation of the generating gear, the unit normal vector of the generating gear can be calculated as:

[0059] (2),

[0060] Based on the meshing relationship between the worm grinding wheel and the generating gear, the worm grinding wheel and the generating gear are internally meshed, the tooth surface equation of the worm grinding wheel is derived from the tooth surface equation of the generating gear through coordinate transformation and meshing principle, and the tooth surface r w can be expressed as:

[0061] (3),

[0062] wherein, M ws is the coordinate transformation matrix, and v s is the relative speed of the generating gear and the worm grinding wheel.

[0063] In the process of grinding the face gear by the worm grinding wheel, the generating process of the worm grinding wheel mainly includes two movements. On the one hand, the worm grinding wheel rotates around its own axis, and at the same time, the face gear also rotates around its own axis, and the worm grinding wheel and the face gear rotate according to the designed transmission ratio. On the other hand, the worm grinding wheel can also feed along the radial direction of the face gear. It needs to be understood that the rotation of the worm grinding wheel and the face gear and the feeding of the worm grinding wheel along the radial direction of the face gear are two independent movements, that is, the rotation angle of the worm grinding wheel and the face gear is irrelevant to the feeding position of the worm grinding wheel. Therefore, when the worm grinding wheel and the face gear rotate, the worm grinding wheel can envelope the profile of the face gear, and when the worm grinding wheel feeds along the radial direction of the face gear, the worm grinding wheel can gradually envelope the tooth profile of the face gear in the whole tooth length direction. The superposition of the two movements completes the process of generating the face gear by the worm grinding wheel. For example Figure 2 the positional relationship shown.

[0064] Based on the above process, it can be understood that the theoretical tooth surface equation of the face gear is r2, and it satisfies the equation:

[0065] (4),

[0066] wherein, M 2w is the coordinate transformation matrix, The engagement equation when the rotation parameter of the worm grinding wheel is unchanged and the feed parameter is changed, The engagement equation when the feed parameter of the worm grinding wheel is unchanged and the rotation parameter is changed, The engagement equation when the feed parameter E 2s of the worm grinding wheel is unchanged and the rotation parameter φ w is changed, The engagement equation when the rotation parameter φ w of the worm grinding wheel is unchanged and the feed parameter E 2s is changed.

[0067] In the motion of dressing the worm grinding wheel with the diamond roller, the standard conical diamond roller is generally used, such as the diamond roller shown in the structures of Figure 3 and Figure 4 . In the structures, the maximum outer radius of the diamond roller is R g , the half-cone angle is a g , the half of the top thickness is s , the linear parameter is t , and the rotary parameter is θ g The coordinate vector and the normal vector of the curved surface point of the diamond roller in the coordinate system can be expressed as:

[0068] (5),

[0069] (6),

[0070] It is to be understood that in some embodiments, the coordinate system of the dressing motion between the diamond roller and the worm grinding wheel can be established as shown in Figure 5 . The coordinate systems S w and S g are fixed with the worm grinding wheel and the diamond roller, respectively. It is assumed that the coordinate system S c is a global fixed coordinate system, the worm grinding wheel has a rotation angle of φ a , the worm grinding wheel has a rotation angle of φ w , φ w is the generating motion parameter in the worm grinding wheel curved surface equation, and is also the angle of the worm grinding wheel rotating along its own axis; the worm grinding wheel has a rotation angle of φ w1 , φ w1 is the rotation angle parameter when the diamond roller and the worm grinding wheel relatively move. Through coordinate transformation, the coordinate vector and the normal vector of the diamond roller and the worm grinding wheel can be converted to the global fixed coordinate system S c , and the equation is:

[0071] (7),

[0072] The coordinate transformation matrix M cg , M ca , M ab , M bw may be expressed as:

[0073] (8),

[0074] (9),

[0075] (10),

[0076] (11),

[0077] Since the diamond roller and the curved surface of the worm grinding wheel are tangent at a certain point when the diamond roller is used to dress the worm grinding wheel, the following equation can be derived:

[0078] (12),

[0079] Solving the above equation set, the discrete φ a values are obtained. y , z , φ b It can be seen that the diamond roller can dress one helix on the tooth surface of the worm grinding wheel each time, and multiple helices can be dressed repeatedly, that is, multiple helices form the curved surface of the worm grinding wheel.

[0080] When designing the addendum corner surface of a face gear, referring to Figure 6 , a spherical ball can be used to be tangent to the addendum surface of the face gear and the tooth profile surface of the face gear, and the spherical ball is rolled along the tooth width direction of the face gear to obtain the addendum corner surface of the face gear. As shown in the structure Figure 6 and Figure 7 , the spherical surface in the coordinate system S f may be expressed as:

[0081] (13),

[0082] wherein φ and θ are spherical parameters, r is the radius of the spherical ball, x b , y b , zb For the spherical coordinates, in the coordinate system S f The following can be expressed:

[0083] (14),

[0084] Since the spherical ball is tangent to the tooth profile surface and the addendum surface of the face gear, the tangent equation can be expressed as:

[0085] (15),

[0086] Where P g is a point on the tooth profile surface 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 a point on the addendum surface of the face gear, n d is the normal vector of the point on the addendum surface of the face gear, P a , P c is a point on the surface of the spherical ball, P a , P c is the normal vector of the point on the surface of the spherical ball. There are 9 variables in equation set (15), which can solve 8 unknowns, and the z b The position of the spherical ball tangent to the face gear can be solved, and the addendum circle surface equation r y of the face gear can be expressed as:

[0087] (16),

[0088] Where φ y and θ y is the addendum circle corner surface parameter of the face gear, which can be expressed as:

[0089] (17).

[0090] The difference between the addendum circle corner 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 according to the difference. Then, the actual machining path of the diamond roller is calculated according to the actual tooth surface of the worm grinding wheel. Specifically, the addendum circle corner of the face gear can be regarded as an error tooth surface, and the error value between the addendum circle corner and the theoretical tooth surface of the face gear is established. Then, the tooth surface error of the face gear is converted to the tooth surface of the worm grinding wheel through formula calculation, and the actual tooth surface of the worm grinding wheel is obtained. The actual machining path of the diamond roller is adjusted based on the actual tooth surface of the worm grinding wheel.

[0091] The error y between the theoretical tooth surface r2 of the face gear and the addendum circle r d can be expressed as:

[0092] (18)

[0093] The face gear and the worm grinding wheel have instantaneous point contact, and the meshing points of their tooth surfaces have a one-to-one correspondence. The tooth surface r2 of the face gear... u s , θ s ) and the tooth surface r of the worm grinding wheel w ( u s , θ s If ) corresponds, then the actual tooth surface r of the worm grinding wheel wa It can be represented as:

[0094] (19)

[0095] Adjust the machining path of the diamond roller according to the actual tooth surface of the worm grinding wheel, so that the actual tooth surface r of the worm grinding wheel is... wa Substitute into formula (12) to replace the theoretical tooth surface r w This allows us to solve for the actual machining path of the diamond roller enveloping the worm gear grinding wheel's tooth surface.

[0096] To machine the complete tooth tip fillet surface of a face gear, refer to... Figure 8 As shown, the theoretical tooth surface of the face gear needs to be extended from the original, that is, the involute starting circle of the generative gear needs to be extended. Therefore, the parameter values ​​of the boundary of the generative gear ( u sf , θ sf It can be obtained by solving the equation:

[0097] (20)

[0098] Among them, P f For the boundary point of the tooth profile extension on the face gear, it can be represented as:

[0099] (twenty one),

[0100] The parameter values ​​of the production gear boundary ( u sf , θ sf Substituting into the equation of the generating gear, we can obtain the boundary of the generating gear.

[0101] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A face gear tooth addendum corner grinding method of grinding a face gear using a worm grinding wheel, characterized by, The application relates to a method for manufacturing a face gear with tooth tip rounding. The method comprises the following steps: S1, calculating a theoretical tooth surface of the worm grinding wheel through the tooth surface of a generating gear; S2, calculating a theoretical machining path of a diamond roller for machining and modifying the worm grinding wheel through the theoretical tooth surface of the worm grinding wheel; S3, designing a tooth tip rounding surface of the face gear, the tooth tip rounding surface of the face gear is obtained through a spherical envelope, the spherical surface is tangent to a tooth tip surface of the face gear and a tooth profile surface of the face gear, the spherical surface is rolled along the tooth width direction of the face gear to perform the envelope, and a tooth tip rounding surface equation of the face gear is calculated; S4, adjusting the worm grinding wheel according to the tooth tip rounding surface of the face gear, calculating an actual tooth surface of the worm grinding wheel, and adjusting the diamond roller according to the actual tooth surface of the worm grinding wheel, and calculating an actual machining path of the diamond roller; 2. The face gear addendum corner grinding method according to claim 1, characterized by, S5, the diamond roller modifies the worm grinding wheel according to the actual machining path, and the worm grinding wheel after modification is used to grind the face gear, so that the face gear with tooth tip rounding is obtained.

3. The face gear addendum corner grinding method according to any one of claims 1 to 2, characterized by, In step S4, a difference between the tooth tip rounding 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 according to the difference, and the actual machining path of the diamond roller is calculated according to the actual tooth surface of the worm grinding wheel.

4. The face gear addendum corner grinding method according to claim 1, characterized by, The diamond roller is a conical diamond roller.

5. The face gear addendum corner grinding method according to claim 4, characterized by, When the worm grinding wheel grinds the face gear, the worm grinding wheel and the face gear rotate according to a set transmission ratio, and the worm grinding wheel also feeds along the radial direction of the face gear.

6. The face gear addendum corner grinding method according to claim 5, characterized by, The rotational movement of the worm grinding wheel and the radial feeding of the worm grinding wheel are independent of each other. ， wherein M 2w is a coordinate transformation matrix, represents the engagement equation when the rotation parameter of the worm grinding wheel is constant and the feed parameter is changed, represents the engagement equation when the feed parameter of the worm grinding wheel is constant and the rotation parameter is changed, is a tooth surface equation of the worm grinding wheel, is a tooth surface normal vector of the worm grinding wheel, The theoretical tooth surface equation of the face gear is r2, and the equation is satisfied: s is a sum of an angle of development and a pressure angle of a point on an involute of the generated gear, u s is a transverse direction parameter of the generated gear, represents a relative velocity when the feed parameter E 2s of the worm grinding wheel is constant and the rotation parameter φ w is changed, represents a relative velocity when the rotation parameter φ w of the worm grinding wheel is constant and the feed parameter E 2s is changed.

7. The face gear addendum corner grinding method according to claim 1, characterized by, The tooth surface of the worm grinding wheel is obtained through the generating gear.

8. The face gear addendum corner grinding method according to claim 7, characterized by, The worm grinding wheel rotates at an angular velocity of The rotational movement of the worm grinding wheel and the radial feeding of the worm grinding wheel are independent of each other. w The profile gear rotates at an angular velocity of The theoretical tooth surface equation of the face gear is r2, and the equation is satisfied: s The profile gear is an involute profile, and a tooth surface equation of the profile gear is ， wherein r bs is the base circle radius of the involute gear, The tooth surface of the worm grinding wheel is obtained through the generating gear. 0s is the angle parameter of the involute and base circle intersection, The generating gear is extended, the boundary of the generating gear is calculated, and the theoretical tooth surface of the face gear is extended. s is the sum of the angle of development and the pressure angle at a point on the involute, u s is the transverse direction parameter.

9. The face gear addendum corner grinding method according to claim 1, characterized by, ​

Images