A design method of complex modification dressing wheel and honing wheel for internal meshing strong force gear honing

Abstract

This application discloses a design method for complex profile dressing wheels and honing wheels used in high-power gear honing with internal meshing, relating to the field of mechanical manufacturing technology. The method establishes a numerical model of the dressing wheel tooth surface, determines whether the profile modification amount of the numerical model meets the profile modification requirements; if so, it establishes the spatial coordinate transformation relationship and conjugate meshing equation between the dressing wheel and the honing wheel, and, combined with the numerical model of the dressing wheel tooth surface, establishes a numerical model of the honing wheel tooth surface; based on the spatial coordinate transformation relationship between the workpiece gear and the honing wheel, and the numerical model of the honing wheel tooth surface, it establishes a numerical model of the complex profile workpiece gear tooth surface, and determines whether the profile modification amount of the numerical model meets the profile modification requirements; if so, it establishes a three-dimensional solid model of the dressing wheel and a three-dimensional solid model of the honing wheel based on the numerical models of the dressing wheel and honing wheel tooth surfaces, respectively. This application enables the precise design and verification of complex profile dressing wheels and honing wheels used in high-power gear honing.

Description

Technical Field

[0001] This application relates to the field of mechanical manufacturing technology, and in particular to a design method for a complex profile dressing wheel and honing wheel for internal meshing high-strength honing. Background Technology

[0002] With the increasing demands for high precision, high speed, and low noise in new energy vehicles, automotive transmission gears require gears with higher precision and lower surface roughness. However, traditional gear grinding processes suffer from high costs and low efficiency, shaving cannot machine hard tooth surfaces, and ordinary honing has limited correction capabilities. Therefore, a high-efficiency, high-precision finishing method suitable for hard-tooth-surface gears is needed: internal meshing high-strength honing. The main processing methods of internal meshing high-strength honing include: first, using a dressing wheel with tooth profiles similar to the workpiece gear to dress the honing wheel, and then using the dressed honing wheel to machine the workpiece gear; second, using a specially designed dressing tool to dress the honing wheel, and then using the dressed honing wheel to machine the workpiece gear. The first method is lower in cost and is widely used in the mass production of gears. Furthermore, complex modification of gear tooth profiles and directions has become the most effective way to reduce vibration and noise in gear transmission systems.

[0003] However, the existing design and verification methods for complex profile dressing wheels and honing wheels used in internal meshing high-strength honing have the following defects: 1) The actual machining of high-strength honing includes two processes: dressing the honing wheel with the dressing wheel and machining the workpiece gear with the honing wheel. However, there is currently no collaborative design and verification study of dressing wheels and honing wheels for high-strength honing, which makes it impossible to fully prove the design accuracy of the two types of tools; 2) The design and verification study of complex profile tooth surface parameters of dressing wheels and honing wheels for high-strength honing have not been fully discussed, which means that the actual machining process needs to be adjusted in conjunction with the multi-axis linkage function of the honing machine tool, which requires high precision control of the machine tool. Summary of the Invention

[0004] The purpose of this application is to provide a design method for complex profile dressing wheels and honing wheels for internal meshing high-strength honing, which can realize the precise design and verification of complex profile dressing wheels and honing wheels for high-strength honing.

[0005] To achieve the above objectives, this application provides the following solution: This application provides a design method for complex profile dressing wheels and honing wheels for internal meshing high-strength honing, including: Based on the machining requirements of gears in complex workpieces, determine the design parameters of the dressing wheel; Establish a numerical model for the dressed gear tooth surface; Based on the design parameters of the dressing wheel, determine whether the dressing amount of the numerical model of the dressing wheel tooth surface meets the dressing requirements; When the shaping amount of the numerical model of the dressing wheel tooth surface meets the shaping requirements, the spatial coordinate transformation relationship between the dressing wheel and the honing wheel is established. Determine the conjugate meshing equations for the dressing wheel and the honing wheel; Based on the conjugate meshing equation of the dressing wheel and the honing wheel, the spatial coordinate transformation relationship between the dressing wheel and the honing wheel, and the numerical model of the dressing wheel tooth surface, a numerical model of the honing wheel tooth surface is established. Establish the spatial coordinate transformation relationship between the workpiece gear and the honing wheel; Based on the spatial coordinate transformation relationship between the workpiece gear and the honing wheel and the numerical model of the honing wheel tooth surface, a numerical model of the gear tooth surface of a complex modified workpiece is established. Based on the design parameters of the gear of the complex modified workpiece, determine whether the modification amount of the numerical model of the gear tooth surface of the complex modified workpiece meets the modification requirements. When the modification amount of the numerical model of the gear tooth surface of the complex modified workpiece meets the modification requirements, a three-dimensional solid model of the dressing wheel and a three-dimensional solid model of the honing wheel are established respectively based on the numerical model of the dressing wheel tooth surface and the numerical model of the honing wheel tooth surface.

[0006] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a design method for complex profile dressing wheels and honing wheels for internal meshing high-strength honing. First, a numerical model of the dressing wheel tooth surface is established, and the modification amount of the numerical model is determined to meet the modification requirements, verifying the correctness of the parameters of the complex profile dressing wheel. Then, a numerical model of the honing wheel tooth surface is established, followed by a numerical model of the gear tooth surface of the complex profile workpiece. The modification amount of the numerical model of the gear tooth surface of the complex profile workpiece is determined to meet the modification requirements, verifying the correctness of the parameters of the complex profile honing wheel. Finally, based on the verified numerical models of the dressing wheel and honing wheel, a three-dimensional solid model is drawn, achieving precise design and verification of the complex profile dressing wheel and honing wheel for high-strength honing. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 A flowchart illustrating a design method for a complex profile dressing wheel and honing wheel for internal meshing high-strength honing, provided for embodiments of this application; Figure 2 This is a schematic diagram of the superimposed curve for secondary tooth profile modification provided in the embodiments of this application; Figure 3 This is a schematic diagram of the tooth profile of a gear with secondary tooth profile modification provided in an embodiment of this application; Figure 4 This is a schematic diagram of the superimposed curve for secondary tooth profile modification provided in the embodiments of this application; Figure 5 This is a schematic diagram of the axial cross-section of the tooth of the tooth-direction modified gear provided in the embodiments of this application; Figure 6 This is a schematic diagram of the calculation of additional angles for tooth profile modification provided in an embodiment of this application; Figure 7 A schematic diagram illustrating the principle of a design method for a complex profile dressing wheel and honing wheel for high-power internal meshing honing, provided in an embodiment of this application; Figure 8 A schematic diagram of the spatial coordinate system provided for an embodiment of this application; Figure 9 A schematic diagram of a single tooth surface of a complex shaping and trimming wheel provided in an embodiment of this application; Figure 10 A schematic diagram of the full tooth surface of a complex shaping and dressing wheel provided in an embodiment of this application; Figure 11 A schematic diagram of a single tooth surface of a complex-shaped honing wheel provided in an embodiment of this application; Figure 12 A schematic diagram of the full tooth surface of a complex-shaped honing wheel provided for an embodiment of this application; Figure 13 A comparative schematic diagram of the modified tooth surface of the complex modified wheel provided in the embodiments of this application; Figure 14 A comparative schematic diagram of the modified tooth surfaces of a complex modified workpiece gear provided in an embodiment of this application; Figure 15 A schematic diagram of a three-dimensional solid model of a complex shaping and trimming wheel provided in an embodiment of this application; Figure 16 A schematic diagram of a three-dimensional solid model of a complex honing wheel provided in an embodiment of this application. Detailed Implementation

[0009] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0010] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0011] Chinese patent application CN116511617A, entitled "A Design Method for High-Power Honing Diamond Dressing Gears," proposes to achieve precise design of diamond dressing wheels by utilizing workpiece gear design parameters, shaping requirements, and diamond particle size, but it does not conduct design verification research on honing wheels that directly machine workpiece gears; Chinese patent application CN118492524A, entitled "A Cost-Reducing and Efficiency-Enhancing Optimization Design Method for High-Power Honing Superhard Abrasive Dressing Wheels," proposes to achieve optimized design of superhard abrasive dressing wheels by utilizing honing machining principles, spatial curved surface meshing principles, and relevant workpiece gear parameters, but it does not consider the design accuracy of the dressing wheel; Chinese patent CN113102842A, "A Design Method for a Honing Wheel for High-Power Honing," proposes to determine the design parameters of the honing wheel using the gear parameters of the workpiece and to establish a three-dimensional solid model of the honing wheel. However, it only realizes the design of the grooving parameters of the honing wheel and does not conduct precise design and verification of the complex tooth surface modification of the honing wheel from the entire process of high-power honing dressing and shaping. Chinese patent application CN117444554A, "A Honing Wheel and Its Design Method, Herringbone Gear and Its Machining Method," designs and verifies the parameters of the honing wheel for herringbone gears, but mainly focuses on the relationship between the width of the herringbone gear relief groove and the design parameters of the honing wheel, without discussing its tooth surface modification parameters.

[0012] As can be seen from the above summary of existing methods, the existing design methods for high-power honing dressing wheels and honing wheels do not yet consider how to design and verify complex-shaped dressing wheels and honing wheels.

[0013] To overcome the shortcomings of existing methods, in an exemplary embodiment, such as Figure 1 As shown, this application provides a design method for a complex profile dressing wheel and honing wheel for internal meshing high-strength honing, including the following steps 101 to 110. Wherein: Step 101: Determine the design parameters of the dressing wheel based on the machining requirements of the complex-shaped workpiece gear.

[0014] Step 102: Establish a numerical model of the dressed gear tooth surface.

[0015] Step 103: Based on the design parameters of the dressing wheel, determine whether the dressing amount of the numerical model of the dressing wheel tooth surface meets the dressing requirements.

[0016] Step 104: When the shaping amount of the numerical model of the dressing wheel tooth surface meets the shaping requirements, establish the spatial coordinate transformation relationship between the dressing wheel and the honing wheel.

[0017] Step 105: Determine the conjugate meshing equation of the dressing wheel and the honing wheel.

[0018] Step 106: Based on the conjugate meshing equation of the dressing wheel and the honing wheel, the spatial coordinate transformation relationship between the dressing wheel and the honing wheel, and the numerical model of the dressing wheel tooth surface, establish the numerical model of the honing wheel tooth surface.

[0019] Step 107: Establish the spatial coordinate transformation relationship between the workpiece gear and the honing wheel.

[0020] Step 108: Based on the spatial coordinate transformation relationship between the workpiece gear and the honing wheel and the numerical model of the honing wheel tooth surface, establish a numerical model of the tooth surface of the complex modified workpiece gear.

[0021] Step 109: Based on the design parameters of the gear tooth surface of the complex modified workpiece, determine whether the modification amount of the numerical model of the gear tooth surface of the complex modified workpiece meets the modification requirements.

[0022] Step 110: When the modification amount of the numerical model of the gear tooth surface of the complex modified workpiece meets the modification requirements, establish a three-dimensional solid model of the dressing wheel and a three-dimensional solid model of the honing wheel according to the numerical model of the dressing wheel tooth surface and the numerical model of the honing wheel tooth surface, respectively.

[0023] By implementing steps 101 to 110 above, the precise design and verification of the complex shaping dressing wheel and honing wheel for high-power gear honing were achieved, ensuring that the precision machining requirements of complex gear workpieces are met.

[0024] In another exemplary embodiment of this application, the relevant parameters of the complex dressing wheel and honing wheel are designed and calculated based on the tooth parameters, installation and fixing method, dressing requirements, abrasive particle size, tooth surface morphology, and other requirements of the workpiece gear. These relevant parameters include normal module, tooth pressure angle, number of teeth on the dressing wheel and honing wheel, tooth width, helix angle, tooth profile dressing amount and range, tooth direction dressing amount and range, pitch circle radius, addendum circle radius, dedendum circle radius, effective addendum circle radius, effective dedendum circle radius, center distance, and shaft angle. The calculation of these relevant parameters refers to existing standard involute gear parameter calculation data.

[0025] In another exemplary embodiment of this application, step 102, which establishes the numerical model of the trimmed gear tooth surface, can be replaced by steps 201 to 205: Step 201: Based on the involute formation mechanism, establish the standard involute tooth surface vector equation of the dressing wheel as follows: ; In the formula, The standard involute development angle, θ For the incremental helix angle of the involute helical gear, For the reason and θ The vector equation for the standard involute tooth surface of the controlled dressing wheel. The radius of the base circle, The starting angle of the involute. p For the parameters of the helix, and , To adjust the involute base circle helix angle in the direction of the gear tooth profile. To dress the standard tooth surface of the wheel x coordinate, To dress the standard tooth surface of the wheel y coordinate, To dress the standard tooth surface of the wheel z coordinate.

[0026] Step 202: Determine the normal vector of any point on the standard involute tooth surface of the dressing wheel. The vector equation is: ; In the formula, This refers to the normal vector at any point on the standard involute tooth surface of the dressing wheel. For any point normal vector along The components of the axis; For any point normal vector along The components of the axis; For any point normal vector along The components of the axis.

[0027] As can be seen from steps 201 and 202, the standard involute tooth surface vector equation and normal vector equation of the external helical gear are established based on the involute formation mechanism.

[0028] Step 203: Based on the standard involute tooth surface vector equation of the dressing wheel and the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, construct the functional mapping relationship of the normal modification amount of any point on the tooth profile with respect to the tooth surface equation.

[0029] (1) The relationship between the normal modification amount between any point on the modified tooth profile curve and the corresponding point on the standard involute tooth profile curve before modification is as follows: like Figure 2 As shown, the superimposed curve for quadratic tooth profile modification is a commonly used method in actual tooth profile modification. Its modification amount variation trend is consistent with the corresponding quadratic curve equation, showing a trend of maximum modification amount on both sides and zero modification amount in the middle along the involute, resulting in a tooth profile exhibiting the target bulge shape, such as... Figure 3 As shown. The equation for the superimposed curve of the secondary tooth profile modification is as follows: ; In the formula, The equation for the superimposed curves for tooth profile modification. This represents the maximum amount of modification at the tooth tip and root on the tooth profile curve.L The standard involute curve shaping length. This is the standard involute length parameter, used to determine the position of any point on the standard involute curve.

[0030] (2) Establish standard involute length parameters about The relationship between them is as follows: The expression for the standard involute length parameter can be obtained from the relationship between the arc length of a plane curve and the curve length of a plane curve: ; In the formula, These are the initial position parameters for a standard involute.

[0031] (3) Based on the equation of the superimposed curve of the quadratic tooth profile modification and the expression of the standard involute length parameter, determine the functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation. The functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation includes the tooth surface vector equation of the dressing wheel corresponding to the tooth profile and the normal vector equation of any point on the tooth surface corresponding to the tooth profile. The functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation is the numerical model of the dressing wheel tooth surface with the same profile as the workpiece gear.

[0032] The vector equation for the dressing wheel tooth surface corresponding to the tooth profile is: ; In the formula, This is the vector equation for the tooth surface of the dressing wheel corresponding to the tooth profile. The expression is derived by combining the equation of the superimposed curve for the secondary tooth profile modification and the expression of the standard involute length parameter.

[0033] The normal vector equation for any point on the tooth surface corresponding to the tooth profile is: ; In the formula, Let be the normal vector equation for any point on the tooth surface corresponding to the tooth profile. for about The derivative of .

[0034] Step 204: Based on the standard involute tooth surface vector equation of the dressing wheel and the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, construct the functional mapping relationship of the normal modification amount of any point on the tooth surface with respect to the tooth surface equation.

[0035] (1) The relationship between the normal modification amount between any point on the tooth surface after tooth modification and the corresponding point on the standard helical involute tooth surface before modification is as follows: like Figure 4As shown, the superimposed curve for quadratic tooth profile modification is a commonly used method in actual tooth profile modification. Its modification amount variation trend is consistent with the corresponding quadratic curve equation, showing a trend of maximum modification amount on both sides and zero modification amount in the middle along the helical axis, resulting in a tooth profile exhibiting the target bulge shape, such as... Figure 5 As shown. The equation for the superimposed curve of the secondary tooth profile modification is as follows: ; In the formula, This is the superposition amount of secondary tooth profile modification. This represents the maximum amount of shaping at the two end faces of the tooth. The length of the tooth profile is adjusted upwards. This is the tooth-up profile length parameter, used to determine the position of any point on the surface of a standard helical involute tooth.

[0036] (2) Establish the superposition amount of secondary tooth profile modification The relationship between the helical axes is as follows: In tooth profile modification, for a standard helical involute gear, the modified gear end section is rotated by a corresponding additional angle around the base circle center compared to its original shape, such as... Figure 6 As shown. Meanwhile, since the tooth profile modification amount is much smaller than the length of the involute, and the length of the involute is much smaller than the base circle radius of the gear, for ease of calculation, the relationship between the superimposed secondary tooth profile modification amount and the helical axis is as follows: ; In the formula, This refers to the additional angle by which the end section of the modified gear rotates around the center of the base circle compared to its original shape.

[0037] (3) Based on the standard involute tooth surface vector equation of the dressing wheel, the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, and the relationship between the superimposed amount of the second tooth profile modification and the helical axis, determine the functional mapping relationship of the normal profile modification amount of any point on the tooth surface with respect to the tooth surface equation; the functional mapping relationship of the normal profile modification amount of any point on the tooth surface with respect to the tooth surface equation includes the corresponding dressing wheel tooth surface vector equation and the corresponding normal vector equation of any point on the tooth surface. The functional mapping relationship of the normal profile modification amount of any point on the tooth surface with respect to the tooth surface equation is also a numerical model of the dressing wheel tooth surface with the same profile as the workpiece gear.

[0038] The corresponding dressing wheel tooth surface vector equation is: ; In the formula, The vector equation for the tooth surface of the dressing wheel corresponding to the tooth direction.

[0039] The equation of the normal vector at any point on the corresponding tooth surface is: ; In the formula, Let be the normal vector equation for any point on the corresponding tooth surface.

[0040] Step 205: Determine the numerical model of the dressing wheel tooth surface based on the functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation and the functional mapping relationship of the normal modification amount at any point on the tooth surface with respect to the tooth surface equation.

[0041] For example, the numerical model of the dressing wheel tooth surface includes: the vector equation of the dressing wheel tooth surface having the same tooth surface shape as the workpiece gear, and the vector equation of the normal vector of any point on the tooth surface having the same tooth surface shape as the workpiece gear.

[0042] The vector equation for the tooth surface of the dressing wheel, which has the same tooth surface shape as the workpiece gear, is: ; In the formula, The vector equation for the dressing wheel tooth surface with the same tooth surface shape as the workpiece gear. This refers to the additional angle by which the modified gear end section rotates around the center of the base circle compared to its original shape. The expression is derived by combining the equation of the superimposed curve for the secondary tooth profile modification and the expression of the standard involute length parameter.

[0043] The normal vector equation for any point on the tooth surface with the same tooth shape as the workpiece gear is: ; In the formula, Let the normal vector equation be given for any point on the tooth surface that has the same tooth surface shape as the workpiece gear. for about The derivative of .

[0044] In another exemplary embodiment of this application, the numerical model of the complex modified gear tooth surface is discretized, and the normal deviation at any discrete point on the tooth surface is calculated to verify whether the modification range trend and the maximum modification amount meet the modification requirements. Then, step 103 can be replaced by steps 301 to 305: Step 301: Discretize the tooth surface of the dressing wheel along the tooth profile direction and the tooth width direction.

[0045] The tooth surface of the dressing wheel is discretized into a grid along the tooth profile and tooth width directions, which can be divided into 5×9 grids.

[0046] Step 302: Based on the design parameters of the dressing wheel, use the numerical model of the dressing wheel tooth surface to determine the position vector of any discrete point on the tooth surface of the dressing wheel after shaping.

[0047] Step 303: Based on the position vector of any discrete point on the modified tooth surface, use the formula... Determine the normal deviation at discrete points on the dressing wheel.

[0048] In the formula, To adjust the discrete points on the wheel ( i , j Normal deviation at point ) Discrete points on the tooth surface after modification ( i , j The position vector of ) and These are discrete points on the surface of a standard helical involute tooth. i , j The position vector and normal vector of ).

[0049] Step 304: If the normal deviation at discrete points on the dressing wheel is less than or equal to a preset deviation threshold, then the dressing amount of the numerical model of the dressing wheel tooth surface is determined to meet the dressing requirements. For example, the preset deviation threshold is 0.1 μm.

[0050] Step 305: If the normal deviation at the discrete point on the dressing wheel is greater than the preset deviation threshold, then it is determined that the dressing amount of the numerical model of the dressing wheel tooth surface does not meet the dressing requirements.

[0051] like Figure 7 As shown, when the amount of modification in the numerical model of the dressed wheel tooth surface does not meet the modification requirements, the installation method (center distance, shaft angle and displacement coefficient, etc.), modification superposition curve, abrasive characteristics and other related physical quantities in S1 are changed, and the numerical model of the dressed wheel tooth surface is re-established. The purpose is to make the generated complex modified dressed wheel tooth surface numerical model meet the preset modification requirements.

[0052] In another exemplary embodiment of this application, the above step 104, which establishes the spatial coordinate transformation relationship between the dressing wheel and the honing wheel, can be replaced by the following steps 401 to 405: Step 401: Establish the fixed reference coordinate system of the dressing wheel, the fixed reference coordinate system of the honing wheel, the motion coordinate system of the dressing wheel, and the motion coordinate system of the honing wheel respectively.

[0053] In the internal meshing high-strength honing process, the relative motion between the internal gear honing tool (referred to as the honing wheel) and the dressing wheel can be considered as the meshing motion of a pair of internal meshing interlocking gear pairs, such as... Figure 8 As shown, a fixed reference coordinate system is established for the dressing wheel. Honing wheel fixed reference coordinate system Adjusting the coordinate system of the wheel motion Heheng grinding wheel motion coordinate system .in dCenter distance, included axis angle . The helix angle of the honing wheel. The helix angle of the honing wheel.

[0054] Step 402: Determine the first transformation matrix between the fixed reference coordinate system and the moving coordinate system of the dressing wheel as follows: ; In the formula, This is the first transformation matrix. This is the transpose of the first transformation matrix. Time period t Internal trim wheel angle.

[0055] Step 403: Determine the second transformation matrix between the fixed reference coordinate system and the moving coordinate system of the honing wheel as follows: ; In the formula, This is the second transformation matrix. This is the transpose of the second transformation matrix. Time period t Internal honing wheel rotation angle.

[0056] Step 404: Determine the third transformation matrix between the fixed reference coordinate system of the dressing wheel and the fixed reference coordinate system of the honing wheel as follows: ; In the formula, This is the third transformation matrix. This is the transpose of the third transformation matrix. The center distance, The angle between the axes is denoted by .

[0057] Step 405: Based on the first transformation matrix, the second transformation matrix, and the third transformation matrix, determine the transformation matrix between the dressing wheel motion coordinate system and the honing wheel motion coordinate system as follows: ; In the formula, To adjust the transformation matrix between the grinding wheel's motion coordinate system and the honing wheel's motion coordinate system, for transpose, To adjust the wheel angle, The honing wheel rotation angle.

[0058] In another exemplary embodiment of this application, the above-described step 105, which determines the conjugate meshing equation between the dressing wheel and the honing wheel, can be replaced by the following steps 501 to 506: Step 501: Using the angular velocity and position vector of the dressing wheel, the meshing point on the dressing wheel tooth surface in the fixed reference coordinate system of the dressing wheel can be calculated. The relative velocity in the reference coordinate system of the dressing wheel is determined by the following expression: ; In the formula, To determine the relative velocity of the meshing point on the dressing wheel tooth surface in the fixed reference coordinate system of the dressing wheel. To adjust the wheel angular velocity (rad / s), To adjust the position vector of the dressing wheel at the meshing point, The standard involute development angle, θ For the incremental helix angle of the involute helical gear, Time period t Internal trim wheel angle. , , Transformation matrix The top left corner 3×3 submatrix.

[0059] Step 502: Using the angular velocity and position vector of the honing wheel, the meshing point on the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel can be calculated. The relative velocity in the coordinate system is determined by the relative velocity of the meshing point on the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel. ; In the formula, Let be the relative velocity of the meshing point on the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel. The angular velocity of the honing wheel (rad / s) This is the position vector of the honing wheel at the meshing point. , , Transformation matrix The top left corner 3×3 submatrix.

[0060] Step 503: Using the meshing point on the dressing wheel tooth surface as a fixed reference coordinate system for the dressing wheel. The relative velocity and the meshing point on the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel The relative velocity at the meshing point can be obtained by subtracting the relative velocities on the dressing wheel and honing wheel tooth surfaces. Then, based on the expression for the relative velocity at the meshing point on the dressing wheel tooth surface and the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel, the formula can be used... The expression for the relative velocity at the meshing point is obtained; where, The relative velocity is at the meshing point.

[0061] Step 504: Apply the formula Substituting these values ​​into the expression for the relative velocity at the engagement point, we obtain the final expression for the relative velocity at the engagement point; where, To adjust the number of teeth, The number of teeth on the honing wheel. .

[0062] Dressing wheel angular velocity With the angular velocity of the honing wheel The ratio is equal to the adjustment wheel angle within a certain time period. Size and honing wheel rotation angle The ratio of the size is equal to the inverse ratio of the number of teeth on the dressing wheel to the number of teeth on the honing wheel.

[0063] Step 505: Based on the principle of conjugate tooth surface meshing, the conjugate meshing equation between the dressing wheel and the honing wheel is determined as follows: ; In the formula, Let be the normal vector of the meshing point in the fixed reference coordinate system of the dressing wheel. .

[0064] Step 506: The conjugate meshing equation of the dressing wheel and the honing wheel is denoted as: .

[0065] In another exemplary embodiment of this application, the numerical model of the honing wheel tooth surface is as follows: ; In the formula, This is the normal vector at the meshing point of the numerical model of the honing wheel tooth surface. The standard involute development angle, θ For the incremental helix angle of the involute helical gear, Time period t Internal trim wheel angle, This is a simplified form of the transformation matrix between the dressing wheel's motion coordinate system and the honing wheel's motion coordinate system. for The top left 3×3 submatrix To adjust the normal vector at the meshing point of the numerical model of the gear tooth surface. These are the coordinates of the meshing point in the numerical model of the honing wheel tooth surface. To adjust the coordinates of the meshing point in the numerical model of the gear tooth surface, The equation for the conjugate meshing of the dressing wheel and the honing wheel.

[0066] In another exemplary embodiment of this application, since the established complex shaping and dressing wheel is exactly the same as the theoretical workpiece gear, the spatial conjugate tooth surface meshing relationship between the workpiece gear and the complex shaping and honing wheel is exactly the same as the spatial conjugate tooth surface meshing relationship between the complex shaping and dressing wheel and the honing wheel. That is, the second envelope is the reverse process of the first envelope, and its derivation process is the same, so it will not be described again.

[0067] Establish the spatial coordinate transformation relationship between the workpiece gear and the complex honing wheel. Specifically: .

[0068] , and This represents the spatial transformation matrix when the workpiece gear meshes with the honing wheel. Since the workpiece gear and the dressing wheel are exactly the same, these four quantities are the same as those mentioned above. , , , same.

[0069] Based on the principle of spatial conjugate tooth surface meshing, the conjugate meshing equation between the workpiece gear and the complex profile honing wheel is derived. The details are as follows: .

[0070] Using the numerical model of the tooth surface of a complex honing wheel, a numerical model of the gear tooth surface of a complex modified workpiece is established as follows: ; In the formula, This represents the normal vector at the meshing point of the numerical model of the gear tooth surface of a complex modified workpiece. The standard involute development angle, θ For the incremental helix angle of the involute helical gear, Time period t Internal workpiece gear rotation angle, This is the transformation matrix between the honing wheel's motion coordinate system and the workpiece gear's motion coordinate system. for The top left 3×3 submatrix This is the normal vector at the meshing point of the numerical model of the honing wheel tooth surface. The coordinates of the meshing point in the numerical model of the gear tooth surface of a complex modified workpiece. These are the coordinates of the meshing point in the numerical model of the honing wheel tooth surface. This is the equation for the conjugate meshing of the workpiece gear and the honing wheel.

[0071] In another exemplary embodiment of this application, the numerical model of the gear tooth surface of the complex modified workpiece is discretized, and the normal deviation at any discrete point on the tooth surface is calculated to verify whether the modification range trend and the maximum modification amount meet the modification requirements. This verification is the same as steps 301-305. If the modification requirements are met, it means that the numerical model of the complex modified honing wheel tooth surface formed by the first envelope in step two meets the actual processing requirements, that is, the accurate design and verification of the complex modified honing wheel is achieved.

[0072] Normal deviation at any discrete point on the gear tooth surface of a complex modified workpiece The calculation method is as follows: ; In the formula, Used to determine the position parameters at any discrete point on the tooth surface. This represents the position vector of any point on the tooth surface after modification. and This represents the position vector and normal vector of any point on the surface of a standard helical involute tooth.

[0073] like Figure 7 As shown, when the shaping requirements are not met, the conjugate meshing equation between the dressing wheel and the honing wheel in S2 is changed (mainly adjusting the center distance, additional installation angle, and axial stroke speed), so that the numerical model of the tooth surface of the complex shaping honing wheel can be derived from the spatial coordinate transformation relationship between the shaping honing wheel and the workpiece gear in S3, so that the numerical model of the tooth surface of the complex shaping workpiece gear that meets the final design shaping requirements can be derived.

[0074] In another exemplary embodiment of this application, step 110 described above can be replaced by steps 601 to 603: Step 601: After performing tooth surface discretization processing on the numerical model of the dressing wheel tooth surface and the numerical model of the honing wheel tooth surface, the tooth surface point cloud of the dressing wheel and the tooth surface point cloud of the honing wheel are obtained.

[0075] The point cloud processing software, such as Cloud Compare, is used to adjust the data to obtain a high-precision point cloud of the tooth surface of the target complex shaping and honing wheel.

[0076] Step 602: Based on the actual required width for machining the complex profile honing wheel, adjust and truncate the obtained point cloud of the complex profile honing wheel tooth surface to obtain the point cloud data of the target complex profile honing wheel tooth surface. Then, obtain the midpoint position of the tooth length. Z Using the coordinate system and the width of the honing wheel, the tooth length is determined. Z To coordinate range The point cloud of the honing wheel tooth surface is obtained; among which, Midpoint of tooth length ZTo coordinates, This refers to the width of the honing wheel.

[0077] Step 603: Import the point cloud data of the dressing wheel tooth surface and the honing wheel tooth surface into the 3D solid design software, and establish the 3D solid model of the dressing wheel and the 3D solid model of the honing wheel respectively.

[0078] 3D solid design software such as UG.

[0079] Importing the 3D solid models of dressing wheels and honing wheels into CNC machine tools can be used for the precise machining of complex-shaped dressing wheels and honing wheels.

[0080] The following example focuses on the design of dressing wheels and honing wheels in the internal meshing high-strength honing process for a certain type of new energy transmission. The normal module is 1.5 mm, and the tooth pressure angle is 15°. ° The dressing gear has 53 teeth and a helix angle of 26°. ° Tooth width 28mm; the dressing length of the tooth profile is the effective involute range length, and the dressing amount is 0 on both sides of the standard involute. The maximum value in the middle is 2. The tooth profile modification length range is 80% of the tooth length, with the maximum modification amount on both sides being 13. The minimum value in the middle is 0. The remaining parts are not modified in terms of tooth profile and tooth direction; the honing wheel has 115 teeth and a helix angle of 39°. ° The tooth width is 19mm. The steps for this implementation case are as follows: 1. Calculate other parameters from the basic parameters of complex-shaped workpieces such as gears, honing wheels, and dressing wheels. Specifically, this includes: center distance. The angle between the axes is The pitch circle radius of the dressing wheel is The base circle radius is The radius of the tooth tip circle is The radius of the tooth root circle is The effective tip circle radius is The effective root circle radius is .

[0081] The range of involute increment angles for dressing the tooth surface can be calculated from the above parameters. The range of the spiral increment angle is And the effective tooth profile modification range of the involute is The range of minute additional rotation caused by the effective profile modification length and modification amount in the tooth direction is: .

[0082] Using the above parameters, a numerical model of the tooth surface of a complex profiled dressing wheel was designed and calculated. The correctness of the parameters was verified based on the tooth surface normal deviation. The tooth surfaces of individual teeth and the entire tooth surface of the complex profiled dressing wheel were plotted, as shown below. Figure 9 and Figure 10 As shown.

[0083] 2. Due to the symmetry of the left and right tooth surfaces of complex shaping and dressing wheels, the left tooth surface is used as the dividing line. Taking the mesh as an example, the actual shaping amount at 45 points was calculated, as shown in Tables 1 and 2. It can be seen that the shaping amount between the standard tooth surface and the actual shaped tooth surface of the dressing wheel is within an acceptable range, verifying the correctness of the parameters of the complex shaping dressing wheel. Therefore, the shaping method proposed in this invention is feasible.

[0084] Table 1 Actual tooth profile modification amount at 45 points on the left tooth surface of complex modified gear teeth ( )

[0085] Table 2 Actual tooth profile modification amount at 45 points on the left tooth surface of the complex profile modification wheel ( )

[0086] 3. Establish the spatial coordinate transformation relationship between the complex shaping and dressing wheel and the honing wheel using the corresponding parameters. Derive the conjugate meshing equation between the complex shaping and dressing wheel and the honing wheel using the relative velocity and normal vector at the meshing point, as shown below: Spatial coordinate transformation matrix: ; Relative velocity at the engagement point: ; Normal vector at the engagement point: ; Conjugate meshing equation: .

[0087] 4. Based on the verified numerical model of the complex profile honing wheel tooth surface and the conjugate meshing equation, the numerical model of the complex profile honing wheel tooth surface is derived. The tooth width of the honing wheel is then truncated according to actual machining requirements to obtain the numerical model of the target complex profile honing wheel tooth surface. The tooth surfaces of individual teeth and the entire tooth surface of the complex profile honing wheel are then drawn, as shown below. Figure 11 and Figure 12 As shown.

[0088] 5. The numerical model of the complex-shaped honing wheel tooth surface is transformed into the workpiece gear motion coordinate system using the principle of spatial conjugate meshing. The normal deviation between the complex-shaped honing wheel tooth surface and the theoretical standard tooth surface, and the normal deviation between the complex-shaped workpiece gear tooth surface obtained by honing and the theoretical standard tooth surface are calculated, as shown in Tables 3 and 4 below. The honing trends shown in Tables 3 and 4 are the same, and the difference in honing amount is almost zero, verifying the correctness of the parameters of the complex-shaped honing wheel. This indicates that the design method proposed in this invention meets the expected requirements of honing design (maximum tooth profile 2). Maximum tooth direction 13 ).

[0089] Table 3. Normal deviation of tooth surface at 45 points on the left tooth surface of complex profiled and dressed gears ( )

[0090] Table 4. Normal deviation of gear tooth surface at 45 points on the left tooth surface of complex modified workpieces ( )

[0091] Complex shaping and dressing wheel tooth surface, for example Figure 13 As shown, the modified tooth surface of a gear on a complex modified workpiece is, for example... Figure 14 As shown.

[0092] 6. Discretize the validated numerical models of complex shaping and honing wheels to generate high-precision point cloud models. Use the point cloud data to create 3D models in 3D solid modeling software and import them into CNC machine tools for precise machining of the complex shaping and honing wheels. The 3D solid models of the complex shaping and honing wheels are shown below. Figure 15 and Figure 16 As shown.

[0093] Based on the same inventive concept, this application also provides a complex shaping and honing wheel for internal meshing high-strength honing, obtained by employing the aforementioned design method for complex shaping and honing wheels for internal meshing high-strength honing. The solution provided by this complex shaping and honing wheel for internal meshing high-strength honing is similar to the solution described in the above method, and will not be repeated here.

[0094] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0095] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0096] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0097] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A design method for a complex profile dressing wheel and honing wheel for internal meshing high-strength honing, characterized in that, include: Based on the machining requirements of gears in complex workpieces, determine the design parameters of the dressing wheel; Establish a numerical model for the dressed gear tooth surface; Based on the design parameters of the dressing wheel, determine whether the dressing amount of the numerical model of the dressing wheel tooth surface meets the dressing requirements; When the shaping amount of the numerical model of the dressing wheel tooth surface meets the shaping requirements, the spatial coordinate transformation relationship between the dressing wheel and the honing wheel is established. Determine the conjugate meshing equations for the dressing wheel and the honing wheel; Based on the conjugate meshing equation of the dressing wheel and the honing wheel, the spatial coordinate transformation relationship between the dressing wheel and the honing wheel, and the numerical model of the dressing wheel tooth surface, a numerical model of the honing wheel tooth surface is established. Establish the spatial coordinate transformation relationship between the workpiece gear and the honing wheel; Based on the spatial coordinate transformation relationship between the workpiece gear and the honing wheel and the numerical model of the honing wheel tooth surface, a numerical model of the gear tooth surface of a complex modified workpiece is established. Based on the design parameters of the gear of the complex modified workpiece, determine whether the modification amount of the numerical model of the gear tooth surface of the complex modified workpiece meets the modification requirements. When the modification amount of the numerical model of the gear tooth surface of the complex modified workpiece meets the modification requirements, a three-dimensional solid model of the dressing wheel and a three-dimensional solid model of the honing wheel are established respectively based on the numerical model of the dressing wheel tooth surface and the numerical model of the honing wheel tooth surface. Based on the numerical model of the dressing wheel tooth surface and the numerical model of the honing wheel tooth surface, a three-dimensional solid model of the dressing wheel and a three-dimensional solid model of the honing wheel are established respectively, specifically including: After performing tooth surface discretization processing on the numerical model of the dressing wheel tooth surface and the numerical model of the honing wheel tooth surface, the tooth surface point cloud of the dressing wheel and the tooth surface point cloud of the honing wheel are obtained. Obtain the Z-coordinate of the midpoint of the tooth length, and combine it with the honing wheel width to extract the Z-coordinate range of the tooth length. The point cloud of the honing wheel tooth surface is obtained; among which, The coordinate of the Z-axis is the position of the midpoint of the tooth length. The width of the honing wheel; Import the point cloud data of the dressing wheel tooth surface and the honing wheel tooth surface into the 3D solid design software to create 3D solid models of the dressing wheel and the honing wheel respectively.

2. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 1, characterized in that, Establishing a numerical model for the dressed gear tooth surface, specifically including: Based on the involute formation mechanism, the standard involute tooth surface vector equation of the dressing wheel is established as follows: In the formula, The standard involute development angle, θ For the incremental helix angle of the involute helical gear, For the reason and θ The vector equation for the standard involute tooth surface of the controlled dressing wheel. The radius of the base circle, The starting angle of the involute. p For the parameters of the helix, and , To adjust the involute base circle helix angle in the tooth profile direction; The normal vector equation for any point on the standard involute tooth surface of the dressing wheel is: In the formula, For any point on the standard involute tooth surface of the dressing wheel; Based on the standard involute tooth surface vector equation of the dressing wheel and the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, construct the functional mapping relationship of the normal modification amount of any point on the tooth profile with respect to the tooth surface equation. Based on the standard involute tooth surface vector equation of the dressing wheel and the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, construct the functional mapping relationship of the normal modification amount of any point on the tooth surface with respect to the tooth surface equation. Based on the functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation and the functional mapping relationship of the normal modification amount at any point on the tooth surface with respect to the tooth surface equation, the numerical model of the tooth surface of the dressing wheel is determined.

3. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 2, characterized in that, Based on the standard involute tooth surface vector equation of the dressing wheel and the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, a functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation is constructed, specifically including: The equation for the superposition curve of the second-order tooth profile modification is established as follows: In the formula, The equation for the superimposed curves for tooth profile modification. For standard involute length parameters, This represents the maximum amount of modification at the tooth tip and root on the tooth profile curve. L The standard involute curve shaping length; The expression for determining the standard involute length parameter is: In the formula, These are the initial position parameters for a standard involute. Based on the equation of the superimposed curve of the secondary tooth profile modification and the expression of the standard involute length parameter, the functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation is determined; the functional mapping relationship of the normal modification amount at any point on the tooth profile with respect to the tooth surface equation includes the tooth surface vector equation of the dressing wheel corresponding to the tooth profile and the normal vector equation of any point on the tooth surface corresponding to the tooth profile. The vector equation for the dressing wheel tooth surface corresponding to the tooth profile is: ； In the formula, This is the vector equation for the tooth surface of the dressing wheel corresponding to the tooth profile. The expression is derived by combining the equation of the superimposed curve for the secondary tooth profile modification and the expression of the standard involute length parameter. The normal vector equation for any point on the tooth surface corresponding to the tooth profile is: ； In the formula, Let be the normal vector equation for any point on the tooth surface corresponding to the tooth profile. for about The derivative of .

4. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 2, characterized in that, Based on the standard involute tooth surface vector equation of the dressing wheel and the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, a functional mapping relationship of the normal modification amount at any point on the tooth surface with respect to the tooth surface equation is constructed, specifically including: The equation for the superimposed curve of the secondary tooth profile modification is established as follows: In the formula, This is the superposition amount of secondary tooth profile modification. This refers to the tooth-upward profile length parameter. This represents the maximum amount of shaping at the two end faces of the tooth. The length of the tooth profile upwards. ; The relationship between the superposition of secondary tooth profile modifications and the helical axis is established as follows: In the formula, The additional angle by which the end section of the gear rotates around the center of the base circle compared to its original shape after modification; Based on the standard involute tooth surface vector equation of the dressing wheel, the normal vector equation of any point on the standard involute tooth surface of the dressing wheel, and the relationship between the superimposed amount of the second tooth profile modification and the helical axis, the functional mapping relationship of the normal profile modification amount of any point on the tooth surface with respect to the tooth surface equation is determined; the functional mapping relationship of the normal profile modification amount of any point on the tooth surface with respect to the tooth surface equation includes the corresponding dressing wheel tooth surface vector equation and the corresponding normal vector equation of any point on the tooth surface. The vector equation for the corresponding dressing wheel tooth surface is: ； In the formula, The vector equation for the tooth surface of the dressing wheel corresponding to the tooth direction; The equation of the normal vector at any point on the corresponding tooth surface is: ； In the formula, Let be the normal vector equation for any point on the corresponding tooth surface.

5. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 2, characterized in that, The numerical model of the dressing wheel tooth surface includes: the vector equation of the dressing wheel tooth surface with the same tooth surface shape as the workpiece gear, and the vector equation of the normal vector of any point on the tooth surface with the same tooth surface shape as the workpiece gear. The vector equation for the dressing wheel tooth surface, which has the same tooth surface shape as the workpiece gear, is: ； In the formula, The vector equation for the tooth surface of the dressing wheel that has the same tooth surface shape as the workpiece gear. This refers to the additional angle by which the modified gear end section rotates around the center of the base circle compared to its original shape. The expression is derived by combining the equation of the superimposed curve for the secondary tooth profile modification and the expression of the standard involute length parameter. The normal vector equation for any point on the tooth surface that has the same tooth surface shape as the workpiece gear is: ； In the formula, Let the normal vector equation be given for any point on the tooth surface that has the same tooth surface shape as the workpiece gear. for about The derivative of .

6. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 1, characterized in that, Based on the design parameters of the dressing wheel, determine whether the dressing amount of the numerical model of the dressing wheel tooth surface meets the dressing requirements, specifically including: Discretize the tooth surface of the dressing wheel along the tooth profile direction and the tooth width direction; Based on the design parameters of the dressing wheel, the position vector of any discrete point on the tooth surface of the dressing wheel after shaping is determined using the numerical model of the dressing wheel tooth surface. Based on the position vector of any discrete point on the modified tooth surface, the formula is used. Determine the normal deviation at discrete points on the dressing wheel; where, To adjust the discrete points on the wheel ( i , j Normal deviation at point ) Discrete points on the tooth surface after modification ( i , j The position vector of ) and These are discrete points on the surface of a standard helical involute tooth. i , j The position vector and normal vector of ) If the normal deviation at the discrete point on the dressing wheel is less than or equal to the preset deviation threshold, then the dressing amount of the numerical model of the dressing wheel tooth surface is determined to meet the dressing requirements. If the normal deviation at discrete points on the dressing wheel is greater than a preset deviation threshold, then the dressing amount of the numerical model of the dressing wheel tooth surface is determined to not meet the dressing requirements.

7. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 1, characterized in that, Establishing the spatial coordinate transformation relationship between the dressing wheel and the honing wheel specifically includes: Establish fixed reference coordinate systems for the dressing wheel, honing wheel, dressing wheel, and honing wheel respectively; The first transformation matrix between the fixed reference coordinate system and the moving coordinate system of the dressing wheel is determined as follows: In the formula, This is the first transformation matrix. This is the transpose of the first transformation matrix. Time period t Internal trim wheel angle; The second transformation matrix between the fixed reference coordinate system and the moving coordinate system of the honing wheel is determined as follows: In the formula, This is the second transformation matrix. This is the transpose of the second transformation matrix. Time period t Internal honing wheel rotation angle; The third transformation matrix between the fixed reference coordinate system of the dressing wheel and the fixed reference coordinate system of the honing wheel is determined as follows: In the formula, This is the third transformation matrix. This is the transpose of the third transformation matrix. The center distance, The included angle is the axis; Based on the first transformation matrix, the second transformation matrix, and the third transformation matrix, the transformation matrix between the dressing wheel motion coordinate system and the honing wheel motion coordinate system is determined as follows: In the formula, To adjust the transformation matrix between the grinding wheel's motion coordinate system and the honing wheel's motion coordinate system, for transpose, To adjust the wheel angle, The honing wheel rotation angle.

8. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 1, characterized in that, Determine the conjugate meshing equations for the dressing wheel and the honing wheel, specifically including: The expression for the relative velocity of the meshing point on the dressing wheel tooth surface in the fixed reference coordinate system of the dressing wheel is: In the formula, To determine the relative velocity of the meshing point on the dressing wheel tooth surface in the fixed reference coordinate system of the dressing wheel. To adjust the wheel angular velocity, To adjust the position vector of the dressing wheel at the meshing point, The standard involute development angle, θ For the incremental helix angle of the involute helical gear, Time period t Internal trim wheel angle; The expression for the relative velocity of the meshing point on the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel is determined as follows: In the formula, Let be the relative velocity of the meshing point on the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel. The angular velocity of the honing wheel, This is the position vector of the honing wheel at the meshing point; Based on the expression for the relative velocity of the meshing point on the dressing wheel tooth surface and the honing wheel tooth surface in the fixed reference coordinate system of the dressing wheel, using the formula... The expression for the relative velocity at the meshing point is obtained; where, The relative velocity at the point of engagement; Formula Substituting these values ​​into the expression for the relative velocity at the engagement point, we obtain the final expression for the relative velocity at the engagement point; where, To adjust the number of teeth, The number of teeth on the honing wheel; Based on the principle of conjugate tooth surface meshing, the conjugate meshing equation between the dressing wheel and the honing wheel is determined as follows: In the formula, This is the normal vector of the meshing point in the fixed reference coordinate system of the dressing wheel; The conjugate meshing equation of the dressing wheel and the honing wheel is denoted as: In the formula, The equation for the conjugate meshing of the dressing wheel and the honing wheel.

9. The design method for complex profile dressing wheel and honing wheel for internal meshing high-strength honing according to claim 1, characterized in that, The numerical model of the honing wheel tooth surface is as follows: ； In the formula, This is the normal vector at the meshing point of the numerical model of the honing wheel tooth surface. The standard involute development angle, θ For the incremental helix angle of the involute helical gear, Time period t Internal trim wheel angle, This is a simplified form of the transformation matrix between the dressing wheel's motion coordinate system and the honing wheel's motion coordinate system. for The top left 3×3 submatrix To adjust the normal vector at the meshing point of the numerical model of the gear tooth surface. These are the coordinates of the meshing point in the numerical model of the honing wheel tooth surface. To adjust the coordinates of the meshing point in the numerical model of the gear tooth surface, The equation for the conjugate meshing of the dressing wheel and the honing wheel; The numerical model of the gear tooth surface of the complex modified workpiece is as follows: ； In the formula, This represents the normal vector at the meshing point of the numerical model of the gear tooth surface of a complex modified workpiece. The standard involute development angle, θ For the incremental helix angle of the involute helical gear, Time period t Internal workpiece gear rotation angle, This is the transformation matrix between the honing wheel's motion coordinate system and the workpiece gear's motion coordinate system. for The top left 3×3 submatrix This is the normal vector at the meshing point of the numerical model of the honing wheel tooth surface. The coordinates of the meshing point in the numerical model of the gear tooth surface of a complex modified workpiece. These are the coordinates of the meshing point in the numerical model of the honing wheel tooth surface. This is the equation for the conjugate meshing of the workpiece gear and the honing wheel.

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