Finishing wheel and honing wheel design method for improving contact line stability in gear honing machining process

Abstract

The invention relates to the technical field of mechanical manufacturing and machining, in particular to a dressing wheel and honing wheel design method for improving contact line stability in the gear honing machining process. Based on workpiece gear parameters, a left and right tooth surface mathematical model is established, a honing process space coordinate conversion relation is established, a conjugate meshing relational expression is derived by combining the relative slip speed of meshing contact points and a normal vector, and a tooth surface contact line model is established; and the calculation modeling of the two-dimensional projection of the left and right tooth surface contact lines, the projection intersection point position and the variation under the same rotation angle is realized. And a honing wheel dressing contact line model under dressing wheels with different tooth numbers and a tooth surface contact line intersection projection model in the dressing and honing process under the tooth number difference are established. A honing wheel and variable tooth number dressing wheel design method is provided, and geometric and technological parameters of the honing wheel and the variable tooth number dressing wheel are determined; and a trimming and honing two-degree-of-freedom conjugate meshing relation and a modified tooth surface numerical model are constructed and verified, discretization and point cloud processing are conducted on the model, high-precision tooth surface point cloud is obtained, and accurate machining of a trimming wheel and a honing wheel is guided.

Description

Technical Field

[0001] This invention relates to the field of mechanical manufacturing and processing technology, and more specifically to a design method for dressing wheels and honing wheels to improve the stability of the contact line during honing. Background Technology

[0002] As a core component of mechanical transmission systems, the final machining quality of gears directly determines the service performance, reliability, and transmission efficiency of equipment. Currently, high-precision fields such as new energy vehicles and aerospace place stringent demands on transmission systems, requiring high speeds, high power density, ultra-low noise, and long lifespans. This poses unprecedented challenges to gear precision machining technology. In the gear manufacturing process, precision machining is the final crucial step in achieving high precision and performance. Internal gear honing, as one of the most popular gear hardening surface finishing technologies in recent years, not only significantly improves tooth surface roughness and enhances geometric accuracy, but also effectively reduces transmission noise by generating a "fishbone-like" texture structure conducive to oil film formation and inducing residual compressive stress. It plays a particularly crucial role in suppressing "ghost noise" caused by "tooth surface waviness."

[0003] However, as the manufacturing industry shifts towards a flexible production model of multiple varieties and small batches, the limitations of traditional gear honing processes are becoming increasingly apparent. Traditional processes typically use a dressing wheel with the same number of teeth as the workpiece for honing wheel dressing. While this facilitates line contact meshing, it suffers from problems such as periodic recurrence of machining errors, concentrated tool wear, and limited adaptability, making it difficult to economically and efficiently address the machining needs of gears with varying tooth counts. Therefore, if a single dressing wheel with a specific number of teeth could be used for honing gears with different tooth counts, machining costs could be significantly reduced and tool configuration simplified. This would be particularly suitable for honing small-module and low-tooth-count gears, and would be of great significance for improving the performance of electric vehicle gear transmission systems.

[0004] Currently, the design methods for dressing wheels and honing wheels in high-power gear honing processes still have the following limitations: First, the honing wheel parameters have not been systematically designed from the perspective of tooth surface contact state; second, there is a lack of in-depth research on the changes in tooth surface contact state under the difference in the number of teeth between the dressing wheel and the workpiece gear. Existing methods are mostly based on analysis using dressing wheels with the same parameters as the workpiece gear, resulting in an unclear understanding of the material removal mechanism in gear honing; third, the differences in the influence of dressing amount and dressing method on the contact state of the honing wheel tooth surface during dressing and honing processes under the difference in the number of teeth are not fully considered, as well as the resulting deviations in the geometric shape of the workpiece tooth surface. Specifically: Regarding the design of honing wheels and dressing wheels: CN113102842B "A design method for a high-power honing wheel" and CN116511617A "A design method for a high-power honing diamond dressing gear" only calculate the gear parameters of the honing wheel and dressing wheel based on the selected workpiece gear parameters, process parameters, and shaping requirements, without considering the impact of the number of teeth and helix angle of the honing wheel on the meshing contact state and changes of the tooth surface, as well as the verification of tool design parameters; CN118492524A "A method for reducing The "Optimized Design Method of Superhard Abrasive Dressing Wheel for High-Efficiency Honing" utilizes the honing machining principle, the spatial curved surface meshing principle, and workpiece gear parameters to optimize the design of the superhard abrasive dressing wheel, but it does not consider the design accuracy of the dressing wheel. CN117444554A "A Honing Wheel and Its Design Method, Herringbone Gear and Its Machining Method" designs and verifies the parameters of a honing wheel for herringbone gears, but mainly focuses on the relationship between the width of the herringbone gear relief groove and the honing wheel design parameters, without discussing the selection of honing wheel parameters. CN121256952A "A Design Method of Complex Shape Dressing Wheel and Honing Wheel for Internal Meshing High-Efficiency Honing" considers the complex shape requirements of the dressing wheel in its design of the dressing wheel and honing wheel, but it only verifies the tooth surface point cloud design based on given initial parameters, without considering the selection of initial parameters for the honing wheel and dressing wheel, or the influence of parameters on the contact state or tooth surface accuracy.

[0005] Regarding honing wheel dressing: CN117548746A "A method for dressing a honing wheel with variable shaft angle in an internal meshing high-power honing machine" considers the dressing amount and multi-axis linkage mode to establish a honing wheel dressing model with shaft angle, ensuring that the tooth surface texture is constant before and after dressing, but it does not consider the change of the contact line of the honing wheel before and after dressing. CN119457274B, "A Diamond Tool for Dressing Internal Meshing Honing Wheels and Its Application Method," considers the preparation and application methods of dressing wheels, realizing the dressing of honing wheels with different tooth profile requirements, but does not mention the influence of the dressing method. CN108723509A, "A Honing Wheel Dressing Method for High-Force Honing of CNC Internal Gear Honing Wheels," considers the variation law of shaft intersection angle with the dressing amount in the variable shaft intersection angle process and considers the stability of the tooth surface contact state, but does not conduct in-depth research on the change of tooth surface contact state under the difference in the number of teeth between the dressing wheel and the workpiece gear.

[0006] Therefore, how to provide a design method for dressing wheels and honing wheels to improve the stability of the contact line during the honing process is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a design method for dressing wheels and honing wheels to improve the stability of the contact line during honing, aiming to solve the above-mentioned technical problems.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A method for designing dressing wheels and honing wheels to improve contact line stability during gear honing includes the following steps: S1. Based on the known gear parameters of the workpiece, establish a mathematical model of the left and right tooth surfaces of the workpiece gear to be honed, establish the spatial coordinate transformation relationship of the honing process, obtain the conjugate meshing relationship of the honing process based on the relative sliding velocity and normal vector at the meshing contact point on the tooth surface, and establish a mathematical model of the contact line of the left and right tooth surfaces of the workpiece gear. Using the contact line model of the left and right tooth surfaces of the workpiece gear, project the contact lines of the left and right tooth surfaces of the workpiece gear at the same rotation angle onto a two-dimensional plane, and establish a mathematical model for calculating the position and variation of the projection intersection point. S2. Establish a contact line model of the dressing process on the tooth surface of the honing wheel under different tooth count dressing wheels, and establish a projection model of the tooth surface contact line and its intersection point of the honing wheel during the dressing process and honing process under the difference in tooth count between the dressing wheel and the workpiece gear. S3. Based on the variation law of the dressing and honing contact line in S1 and S2, a design method for honing wheel and variable tooth number dressing wheel oriented towards contact line stability is constructed, and the geometric parameters and process parameters of dressing wheel, honing wheel, workpiece gear are obtained based on the method. S4. Establish the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the dressing and honing process. Based on the geometric parameters and process parameters of the dressing wheel, honing wheel, and workpiece gear in S3, construct the numerical model of the modified tooth surface of the dressing wheel, honing wheel, and workpiece gear, and verify the model. S5. Discretize and process the numerical model of the tooth surface to obtain a high-precision tooth surface point cloud of the target dressing wheel and honing wheel. Based on the high-precision tooth surface point cloud, perform precise machining of the dressing wheel and honing wheel.

[0009] Furthermore, the workpiece gear parameters include: Normal Module Normal pressure angle Number of teeth z, tooth width b, helix angle displacement coefficient Lead p, base circle helix angle Base circle diameter Pitch circle diameter d, addendum circle diameter Root circle diameter half angle of base circle tooth groove ; Specifically: (1), (2), (3), (4), (5), (6), (7), (8).

[0010] Furthermore, in step S1, establishing the mathematical model of the left and right tooth surfaces of the honing workpiece gear based on the known workpiece gear parameters specifically involves: Based on the gear meshing principle, the mathematical model of the left and right tooth surfaces of the honed workpiece gear is represented as follows: (9), (10) The normal vector corresponding to the tooth surface is represented as follows: (11), (12).

[0011] Furthermore, in S1, the spatial coordinate transformation relationship of the honing process is established. Based on the relative sliding velocity and normal vector at the meshing contact point on the tooth surface, the conjugate meshing relationship of the honing process is obtained, and the mathematical model of the contact line between the left and right tooth surfaces of the workpiece gear is established as follows: During honing, the honing wheel and the workpiece gear form a conjugate meshing relationship. That is, the honing wheel tooth surface and the workpiece tooth surface are in contact with each other while rotating around their respective centers of rotation, and the two tooth surfaces do not separate. Their relative motion lies within the tangent plane of the contact point between the two tooth surfaces and is perpendicular to the normal vectors of the two tooth surfaces. Using the fixed coordinate system of the workpiece gear as the analysis reference, the contact point Q between the honing wheel tooth surface and the workpiece tooth surface satisfies... ; The relative sliding velocity of the meshing contact point Q on the tooth surface is expressed as: (13) The contact point normal vector is represented as: (14) The conjugate meshing relationship is then expressed as: (15) in, Let Q be the position of the contact point in the workpiece gear reference coordinate system. , The rotational angular velocity of the honing wheel and the workpiece gear; Therefore, when the rotation angle of the workpiece gear is a certain value, there is only one honing contact line on the left and right tooth surfaces of the meshing workpiece gear, and this contact line is a set of contact points that satisfy the conjugate meshing relationship. The mathematical model of the contact line on the left and right tooth surfaces is expressed as follows: (16).

[0012] Furthermore, in S1, the contact line model of the left and right tooth surfaces of the workpiece gear is used to project the contact lines of the left and right tooth surfaces of the workpiece gear at the same rotation angle onto a two-dimensional plane, and a mathematical model for calculating the position and variation of the projection intersection is established as follows: Based on the workpiece tooth surface contact line model, a mathematical model is established for the position of the intersection point of the projections of the contact lines with the same rotation angle on the left and right tooth surfaces of the workpiece gear: (17) The change in the position of the intersection point directly corresponds to the change in the deflection of the honing wheel: (18).

[0013] Furthermore, the contact line model for the dressing process on the honing wheel tooth surface under different tooth counts in S2 is specifically as follows: Determine the maximum boundary for the number of teeth on the dressing wheel. The number of teeth on the workpiece gear is used as the minimum boundary for the number of teeth on the dressing wheel. , (19); While increasing the number of teeth, adjust the displacement coefficient: (20) (twenty one); The adjusted contact line on the honing wheel tooth surface is as follows: (twenty two).

[0014] Furthermore, the projection model of the tooth surface contact line and its intersection point of the honing wheel during the dressing and honing processes, under the difference in the number of teeth between the dressing wheel and the workpiece gear in S2, is specifically as follows: When the honing wheel rotates... When the angle between the dressing gear and the workpiece gear is a certain value, , If the value is also fixed, then there is only one dressing contact line and one honing contact line participating in the meshing on the honing wheel tooth surface. When the number of teeth is the same, the two coincide, while when the number of teeth is different, the two will form an intersecting relationship and intersect at a point, and this point is the contact point that simultaneously satisfies the conjugate meshing relationship between the dressing and honing processes. The honing contact line on the honing wheel tooth surface is: (twenty three); The mathematical model for the intersection location is: (twenty four); Similarly, the honing wheel tooth surface Convert to a two-dimensional plane Then the projection position and change of the intersection point are: (25), (26).

[0015] Furthermore, S3 specifically refers to: By increasing the gear ratio and helix angle, the meshing geometry is optimized, thereby constraining the migration of the contact line towards the tooth tip. Choose a larger number of teeth within the allowable range to improve the durability of the dressing wheel, and adjust the displacement coefficient accordingly. By adjusting the shaft angle between the dressing wheel shaft and the honing wheel shaft during the dressing process to compensate for changes in the contact state caused by the dressing amount, the geometric positional relationship between the honing wheel and the dressing wheel is determined. Based on the change in the dressing amount, the appropriate shaft angle for dressing can be calculated, and the corresponding adjustment of the honing wheel helix angle can be made. (27).

[0016] Furthermore, the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the dressing process are established. Based on the geometric and process parameters of the dressing wheel and honing wheel selected by S3, a numerical model of the tooth surface of the dressing wheel and honing wheel is established as follows: A numerical model of the dressing wheel tooth surface was established based on the dressing wheel's geometric parameters. (28) (29) in, , For tooth profile and tooth-direction bulging modification amount, , These are the superimposed curves for tooth profile and tooth direction modification, respectively. , For the shape modification constant, , , The development angle is the position for tooth profile modification. To adjust the width of the gear teeth, For the involute tooth surface helical parameters; (30) (31), (32), in, Coordinate system arrive The transformation matrix; It's the top left corner. matrix; , These represent the rotation angles of the dressing wheel and honing wheel at any given moment; The axial stroke of the dressing wheel during the dressing process; , , For adjusting the transmission ratio, center distance, and shaft angle during the dressing process; , This refers to the number of teeth on the two gears. According to the spatial conjugate meshing theory of interleaved shaft gears, the dressing process satisfies the following set of meshing equations: (33), (34), By combining equations (30) and (34), the independent motion variables at any contact point on the tooth surface of the dressing wheel can be solved. , and the position vector of the honing wheel tooth surface With normal vector ; A calculation model for tooth surface deviation is established compared with the involute tooth surface of a standard internal gear with the same geometric parameters as the honing wheel. The normal deviation at any discrete point on the honing wheel tooth surface is calculated, and the deviation of the honing wheel tooth surface after dressing is predicted. (35), in, , For the position vector and normal vector of the involute tooth surface of a standard internal gear with the same geometric parameters as the honing wheel, This represents the deviation between the tooth surfaces of the two parts.

[0017] Furthermore, the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the honing process are established. Based on the workpiece gear parameters and the numerical model of the honing wheel tooth profile, the numerical model of the workpiece gear tooth profile is specifically established as follows: The position vector and normal vector of the gear tooth surface are expressed as follows: (36) (37) (38) in, Is the coordinate system to arrive Transformation matrix; yes Top left corner matrix; , These represent the rotation angles of the workpiece gear and the honing wheel at any given moment; This refers to the axial stroke of the honing wheel during the machining process. , , The transmission ratio, center distance, and shaft angle during the machining process are also considered. Similarly, the machining process must also satisfy the spatial conjugate meshing theory of interlaced shaft gears: (39) (40), Based on equations (36)-(40), the independent motion variables at any contact point on the tooth surface are obtained. , and the workpiece gear tooth surface position vector With normal vector .

[0018] This invention discloses a design method for dressing wheels and honing wheels to improve the contact line stability during gear honing. Compared with the prior art, this invention realizes the design and machining accuracy verification of dressing tools in high-power gear honing processes, effectively suppresses contact state fluctuations caused by tool parameters and dressing amounts, significantly improves the service life of honing wheels, and enhances the honing accuracy stability and consistency of workpiece gears, thereby helping to reduce production costs and improve economic benefits. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 This is a diagram showing the conjugate meshing relationship of tooth surface contact points during the honing process involved in this invention.

[0021] Figure 2 This is a schematic diagram illustrating the three-dimensional tooth surface projection transformation and intersection point position variation involved in this invention.

[0022] Figure 3 The diagram shows the projection distribution of the contact lines of the left and right tooth surfaces of the workpiece gear on a two-dimensional plane, as described in this invention. (a) represents the initial state, (b) represents a 5mm trimming amount, and (c) represents a 10mm trimming amount.

[0023] Figure 4This diagram illustrates the influence of the gear ratio and helix angle on the projection distribution of the contact lines on the left and right tooth surfaces of the workpiece gear when the rotation angle is 0°. (a) shows the distribution of the contact lines corresponding to a honing wheel with 121 teeth and a helix angle of 26.8° under a 5mm dressing adjustment; (b) shows the distribution of the contact lines corresponding to a honing wheel with 121 teeth and a helix angle of 30.8° under a 5mm dressing adjustment; (c) shows the distribution of the contact lines corresponding to a honing wheel with 83 teeth and a helix angle of 26.8° under a 5mm dressing adjustment; and (d) shows the distribution of the contact lines corresponding to a honing wheel with 83 teeth and a helix angle of 30.8° under a 5mm dressing adjustment.

[0024] Figure 5 This invention relates to the influence of the gear ratio and shaft angle (helix angle) on the position of the intersection point of the projection of the contact lines on the left and right tooth surfaces of the workpiece gear.

[0025] Figure 6 The diagram shows the changes in the trimmed contact line before and after adjustment, as described in this invention. (a) shows the changes in the trimmed contact line before adjusting the displacement coefficient, and (b) shows the changes in the trimmed contact line after adjusting the displacement coefficient.

[0026] Figure 7 This is a diagram showing the variation of the position of the projection intersection point before and after adjustment with the gear ratio, as involved in this invention.

[0027] Figure 8 This is a diagram showing the contact line distribution of the honing wheel tooth surface dressing and honing involved in this invention. Among them, (a) shows the cross-distribution of contact lines when the number of teeth on the dressing wheel is 37, (b) shows the cross-distribution of contact lines when the number of teeth on the dressing wheel is 49, and (c) shows the cross-distribution of contact lines when the number of teeth on the dressing wheel is 61.

[0028] Figure 9 This diagram shows the distribution of contact lines and intersection points of honing wheel tooth surface dressing and honing under the fixed shaft angle dressing method involved in this invention.

[0029] Figure 10 This is a diagram showing how the axial angle involved in this invention changes as the center distance increases.

[0030] Figure 11 This diagram shows the distribution of contact lines and intersection points of honing wheel tooth surface dressing and honing under the variable shaft angle dressing method involved in this invention.

[0031] Figure 12This diagram illustrates the tooth surface deviations of the dressing wheel, honing wheel, and workpiece gear under different dressing wheel tooth counts as described in this invention. (a) shows the tooth surface modification amount when the dressing wheel has 26 teeth; (b) shows the tooth surface modification amount when the dressing wheel has 37 teeth; (c) shows the tooth surface deviation amount when the honing wheel has 121 teeth after dressing (a); (d) shows the tooth surface deviation amount when the honing wheel has 121 teeth after dressing (b); (e) shows the tooth surface deviation amount when the workpiece gear has 26 teeth after honing (c); and (f) shows the tooth surface deviation amount when the workpiece gear has 26 teeth after honing (d).

[0032] Figure 13 This is a three-dimensional solid model of the variable tooth number dressing wheel involved in this invention.

[0033] Figure 14 This is a three-dimensional solid model of the variable number of teeth honing wheel involved in this invention.

[0034] Figure 15 This is a schematic diagram of the process for constructing a model of a dressing wheel and a honing wheel to improve contact line stability, as described in this invention. Detailed Implementation

[0035] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] This embodiment focuses on the design of parameters for a dressing wheel and honing wheel with variable tooth count in the internal meshing high-strength honing process for a certain type of new energy vehicle gearbox. The workpiece gear parameters are shown in Table 1. The steps of this implementation are as follows: Table 1 Parameters of workpiece gears and honing wheels

[0037] Step 1: Based on the known gear parameters of the workpiece, establish a mathematical model of the left and right tooth surfaces of the gear to be honed; establish the spatial coordinate transformation relationship of the honing process, analyze the relative sliding velocity and normal vector at the meshing contact point on the tooth surface, and derive the conjugate meshing relationship; establish a mathematical model of the contact line of the left and right tooth surfaces of the workpiece gear, propose an analysis method for converting the three-dimensional helical tooth surface projection into a two-dimensional plane, project the contact line of the left and right tooth surfaces of the workpiece gear at the same rotation angle onto a two-dimensional plane, and establish a mathematical model for calculating the position and variation of the projection intersection point.

[0038] The specific steps in Step One include: 1.1 The workpiece gear parameters include the normal module. Normal pressure angle Number of teeth z, tooth width b, helix angle displacement coefficient Lead p, base circle helix angle Base circle diameter Pitch circle diameter d, addendum circle diameter Root circle diameter half angle of base circle tooth groove ; The basic relevant parameters are calculated as follows: (1), (2), (3), (4), (5), (6), (7), (8).

[0039] 1.2 Based on the known gear parameters of the workpiece, establish mathematical models of the left and right tooth surfaces of the gear to be honed. Details are as follows: During the honing process, the honing wheel maintains line contact with the workpiece gear to remove the tooth surface material. Therefore, it is only necessary to ensure that a contact line appears within the effective tooth surface of the workpiece gear. Referring to the gear meshing principle, the mathematical model of the left and right tooth surfaces of the honed workpiece gear can be expressed as equations (9)-(10). The normal vectors corresponding to the tooth surfaces are shown in equations (11)-(12).

[0040] (9), (10) (11), (12).

[0041] 1.3 Establish the spatial coordinate transformation relationship during the honing process, analyze the relative sliding velocity and normal vector at the meshing contact point on the tooth surface, derive the conjugate meshing relationship during the honing process, and establish a mathematical model of the contact line between the left and right tooth surfaces of the workpiece gear. Specifically: In actual gear honing, when both the honing wheel and the workpiece gear have standard involute helical surfaces, a correct meshing relationship cannot be formed. Generally, a diamond dressing wheel (with the same parameters as the workpiece gear) is used to dress the honing wheel's tooth surface to the envelope of the workpiece's tooth surface, thus achieving correct workpiece tooth surface machining. Therefore, during honing, the honing wheel and the workpiece gear form a conjugate meshing relationship, meaning that the honing wheel's tooth surface and the workpiece's tooth surface are in contact with each other while rotating around their respective centers of rotation, and the two tooth surfaces do not separate. Their relative motion lies within the tangential plane of the contact point between the two tooth surfaces and is perpendicular to the normal vectors of the two tooth surfaces. Figure 1 As shown. Select the fixed coordinate system of the workpiece gear. For analytical reference, the contact point Q between the honing wheel tooth surface and the workpiece tooth surface must satisfy the following condition: .

[0042] The relative sliding velocity of the meshing contact point Q on the tooth surface can be expressed as equation (13), and the contact point normal vector can be expressed as equation (14). Then, the conjugate meshing relationship can be expressed as shown in equation (15). Wherein, Let the contact point Q be in the workpiece gear reference coordinate system. Location, , The rotational angular velocity of the honing wheel and the workpiece gear.

[0043] (13) (14) (15) Therefore, when the workpiece gear rotation angle When the value is certain, there is only one honing contact line on the left and right tooth surfaces of the meshing workpiece gear, and this contact line is a set of contact points that satisfy the conjugate meshing relationship. The mathematical model of the contact line on the left and right tooth surfaces can be expressed as equation (16).

[0044] (16).

[0045] 1.4 Using the contact line model of the left and right tooth surfaces of the workpiece gear, an analytical method is proposed to convert the projection of the three-dimensional helical tooth surface into a two-dimensional plane. The contact lines of the left and right tooth surfaces of the workpiece gear at the same rotation angle are projected onto the two-dimensional plane, and a mathematical model is established to calculate the position and variation of the projection intersection point. The details are as follows: As the honing wheel wears down and undergoes single radial dressing, the center distance between the workpiece gear and the honing wheel increases, causing changes in the distribution of the contact lines on the left and right tooth surfaces. This results in changes in the deflection of the honing wheel, which in turn significantly affects the workpiece's tooth profile accuracy. This deflection change can be reflected by the spatial relative displacement of the contact lines on the left and right tooth surfaces at the same angular position. However, directly observing the three-dimensional changes in the contact lines on the left and right tooth surfaces of the workpiece has a limited perspective, making it difficult to accurately capture their relative relationship. Therefore, to facilitate the description and analysis of the specific changes in the contact line state, the three-dimensional helical tooth surface of the workpiece gear is converted into a two-dimensional plane. This allows the contact lines on the left and right tooth surfaces to be projected onto the new two-dimensional plane, forming a projection intersection point. Figure 2 The diagram shows the transformation representation of the contact line projection and its intersection position. Based on the workpiece tooth surface contact line model (16), a mathematical model (17) is established for the intersection position of the projection of the contact lines with the same rotation angle on the left and right tooth surfaces of the workpiece gear. Then, the change in the intersection position (18) directly corresponds to the change in the honing wheel deflection.

[0046] (17) (18).

[0047] Based on the content described in step one, using the honing wheel and workpiece gear parameters in Table 1, calculate the honing contact line distribution on the left and right tooth surfaces of the workpiece gear, and project it onto a two-dimensional plane as shown below. Figure 3 As shown in (a), the contact lines on the left and right tooth surfaces are symmetrically distributed in the tooth width direction, and the contact lines with the same rotation angle form a projection intersection point in the tooth surface. However, as the honing wheel is continuously dressed, the meshing center distance between the workpiece gear and the honing wheel increases, and the distribution of the contact line state changes accordingly. Figure 3 (b) and (c) show the projected distribution of the contact lines on the left and right tooth surfaces of the workpiece gear when the dressing amount is 5 mm and 10 mm. As the dressing amount increases, the contact lines on the left and right tooth surfaces will move along the tooth root towards the tooth tip, and the change will become larger and larger.

[0048] Given the workpiece gear parameters, the variation in the position of the projected intersection point is actually determined by the number of teeth on the honing wheel, the helix angle, and the dressing amount. Taking the variation in the position of the contact line and the projected intersection point of the left and right tooth surfaces when the workpiece rotation angle is 0° as the object, Figure 4 The effects of different honing wheel tooth counts and helix angles on the position of the intersection point when the dressing amount is 5mm are presented. Figure 5 Further analysis reveals the influence of the gear ratio and shaft intersection angle on the position variation of the intersection point under this dressing amount. The analysis results show that as the number of teeth and helix angle of the honing wheel increase, the gear ratio and shaft intersection angle increase, while the position variation of the contact lines and projected intersection points of the left and right tooth surfaces along the tooth profile direction decreases. This reduces the variation in honing wheel deflection, thereby ensuring the stability of the workpiece tooth profile machining accuracy.

[0049] Step 2: Establish a tooth surface contact line model of the honing wheel during the dressing and honing processes, under the difference in the number of teeth between the dressing wheel and the workpiece gear, project and transform it to a two-dimensional plane, and establish a mathematical model for calculating the position and variation of the contact line intersection.

[0050] 2.1 Establish a contact line model of the dressing process on the tooth surface of the honing wheel under dressing wheels with different numbers of teeth. Specifically: There are two basic requirements for the design of the number of teeth on the dressing wheel: firstly, the designed number of teeth should not have a common factor with the number of teeth on the honing wheel and the workpiece gear; secondly, interference between the dressing wheel and the honing wheel during the dressing process should be avoided. The maximum boundary of the number of teeth on the dressing wheel can be determined using equation (19). The number of teeth on the workpiece gear is used as the minimum boundary for the number of teeth on the dressing wheel. .

[0051] (19); When a dressing gear with a different number of teeth than the workpiece is used, the contact state during the dressing process will differ. That is, when the number of teeth is different, but the module, pressure angle, and helix angle are the same, the dressing contact line at the same rotation angle on the honing wheel tooth surface will change along the tooth profile direction, causing the honing wheel tooth surface to deviate from the ideal geometry after dressing. Analysis shows that changing only the number of teeth of the dressing gear will cause the axis of the dressing and honing processes to be inconsistent, which leads to a large change in the dressing contact line. Therefore, this study proposes a dressing gear design method that increases the number of teeth while appropriately adjusting the displacement coefficient, which can effectively suppress the change in dressing contact line caused by the difference in the number of teeth. The calculation formulas are (20) and (21). Then the dressing contact line on the honing wheel tooth surface after adjustment is formula (22).

[0052] (20) (twenty one); (twenty two).

[0053] 2.2 Establish a projection model of the tooth surface contact line and its intersection point of the honing wheel during the dressing and honing processes, under the condition of the difference in the number of teeth between the dressing wheel and the workpiece gear. Specifically: When the honing wheel rotates... When the angle between the dressing gear and the workpiece gear is a certain value, , This is also determined. Therefore, on the honing wheel tooth surface, only one dressing contact line and one honing contact line participate in meshing. When the number of teeth is the same, they coincide; when the number of teeth differs, they will form an intersecting relationship and intersect at a point, which is the contact point that simultaneously satisfies the conjugate meshing relationship between the dressing and honing processes. The honing contact line on the honing wheel tooth surface is given by equation (23), and the mathematical model for the intersection point is given by equation (24). Similarly, the honing wheel tooth surface... Convert to a two-dimensional plane Then the projection position and change of the intersection point are given by equation (25) - (26).

[0054] (twenty three); (twenty four); (25), (26).

[0055] Based on the information provided in step two, using the parameters in Table 1, the range of variation in the number of teeth on the dressing gear is calculated to be [26, 61]. Taking the changes in the contact line when the honing wheel rotation angle is 0° as an example, the changes in the contact line before and after adjustment are shown below. Figure 6 As shown in (a) and (b), the variation of the position of the projection intersection point with the gear ratio is as follows: Figure 7 As shown, when the number of teeth on the dressing gear is 61, the change in the position of the projected intersection point decreases from 0.258 mm to 0.011 mm, proving that the design method of adjusting the displacement coefficient of the variable number of teeth dressing gear is significantly effective.

[0056] At the same time, using the parameters in Table 1, Figure 8 The distribution of the dressing and honing contact lines on the left tooth surface of the honing wheel in its initial state is shown. As the number of teeth on the dressing wheel increases, the contact lines at the same rotation angle become more inclined in the tooth profile direction and more dispersed in the tooth direction, resulting in an intersection of the two contact lines. With increasing absolute value of the rotation angle, the difference between the two contact lines increases, leading to greater differences in material removal. This results in tooth profile errors on the workpiece tooth surface due to variations in the pressure angle along the tooth profile direction, and tooth direction errors along the lead direction due to residual unremoved tooth surface material at both ends of the tooth width. When the honing wheel rotation angle is 0°, the two contact lines intersect at a point where the material removal amounts from both processes are consistent. Therefore, these errors will cause a concave deviation on the workpiece tooth surface. This geometric deviation increases with the degree of difference in the number of teeth.

[0057] Furthermore, when there is a difference in the number of teeth between the dressing gear and the workpiece gear, the contact line should be kept stable during repeated dressing with the honing wheel to ensure the stability of machining accuracy. This study focuses on the changes in the position of the dressing and honing contact line and intersection points on the left tooth surface with a honing wheel rotation angle of 0°. Figure 9 The distribution of two contact lines and the change of intersection point positions on the honing wheel tooth surface are given when the dressing amount is 0, 0.2, and 0.4 mm. As the dressing amount increases, the contact lines and intersection points move along the tooth root and one end of the tooth width of the honing wheel, causing the material removal on the tooth surface to tilt to one side from the relatively symmetrical direction of the tooth width. The difference in the amount of material removed on both sides increases, resulting in a deviation in the geometric shape of the tilted workpiece tooth surface.

[0058] Using the results of single radial dressing under different tooth counts as a control, Figure 10 The variation of the shaft intersection angle with the trimming amount is shown. When the trimming amount is 5mm, the shaft intersection angle only needs to be adjusted to 0.987°, and the variation is small, indicating that the method has good operability and application potential in practical engineering. Figure 11 This paper demonstrates the distribution of the contact line and its intersection points on the honing wheel tooth surface using the variable shaft angle dressing method with dressing amounts of 0.2 mm and 0.4 mm. The results show that by dynamically adjusting the shaft angle, this method effectively suppresses the offset of the contact line and its intersection points, significantly mitigating the deterioration trend of the workpiece tooth surface accuracy. This not only maintains the consistency of tooth surface material removal and enhances the stability of machining accuracy, but also reduces wear caused by the asymmetrical meshing between the dressing gear and the honing wheel, thus helping to extend the service life of the honing wheel.

[0059] Step three, based on the variation law of the dressing and honing contact line in steps one and two, proposes a design method for honing wheels and variable tooth number dressing wheels aimed at stabilizing the contact line. Furthermore, it studies and proposes a variable shaft angle dressing method to ensure contact line stability under tooth number differences.

[0060] A honing wheel design method considering the stability of the contact line on the workpiece tooth surface under repeated dressing is proposed. Details are as follows: High-precision, long-life honing wheels can significantly improve economic efficiency in the mass production of automotive gears. The distribution of the contact lines on the left and right tooth surfaces of the workpiece gear and the dressing amount of the honing wheel have a significant impact on the tooth profile accuracy of the honed workpiece gear. In the initial design of the honing wheel, the contact lines of the left and right tooth surfaces with the same rotation angle should be made almost symmetrical in the tooth profile direction. This symmetrical structure results in minimal change in the honing wheel deflection in the initial state. The central part of the gear tooth surface is clamped between the left and right tooth surfaces of the working gear for machining, and the left and right tooth surfaces can provide sufficient surface pressure for tooth surface material removal. This leads to a slower change in the machining accuracy of the workpiece gear tooth profile and better quality. However, as the dressing amount increases, the contact line on the workpiece tooth surface will shift along the tooth profile direction, disrupting the symmetry in that direction. This results in the honing wheel deflection after dressing being less than in the initial honing state. The honing process will then proceed without support on one side of the tooth surface, leading to inconsistent surface pressure on both sides. This results in increased honing removal at the tooth tip on one side and decreased removal at the tooth root on the other, causing changes in the gear tooth profile accuracy. Therefore, to effectively suppress the offset of the contact line in the tooth profile direction caused by the dressing amount, referring to step one, the meshing geometry can be optimized by appropriately increasing the gear ratio and helix angle. This constrains the migration of the contact line towards the tooth tip, helping to maintain the workpiece tooth surface accuracy over longer machining cycles.

[0061] A method for designing dressed gears that considers the stability of the dressed contact line under the condition of tooth number difference is proposed. The details are as follows: Adopting a dressing wheel design with a variable number of teeth is beneficial to improving the production flexibility of actual gear machining. However, while increasing the number of teeth on the dressing gear extends its service life, it also significantly alters the state of the dressing contact line. This change increases the difference between the dressing contact line and the honing contact line, thus affecting the uniformity of material removal from the workpiece tooth surface and the tooth profile accuracy. To mitigate the negative impact of tooth number differences, the meshing geometry can be compensated by reasonably adjusting the displacement coefficient, effectively reducing the difference between the two types of contact lines. Therefore, referring to step two, selecting a larger number of teeth within the allowable range to improve the durability of the dressing wheel, and simultaneously and reasonably adjusting the displacement coefficient, can maintain the stability of the dressing contact line, thereby achieving flexibility in the dressing wheel tooth number design without sacrificing the stability of dressing quality.

[0062] To address variations in the number of teeth, a variable shaft angle adjustment method is proposed to ensure consistent machining accuracy. Details are as follows: To avoid the deterioration of the gear tooth profile accuracy caused by single radial dressing of the honing wheel, a variable shaft angle dressing method can be adopted. This method adjusts the shaft angle between the dressing wheel shaft and the honing wheel shaft during the dressing process to compensate for the change in contact state caused by the dressing amount, thereby maintaining stable contact on the workpiece tooth surface and effectively improving the problem of uneven material removal during honing. The geometric positional relationship between the honing wheel and the dressing wheel can be determined by equations (20), (21), and (27). Therefore, the appropriate shaft angle for dressing can be calculated according to the change in dressing amount, that is, the corresponding adjustment of the helix angle of the honing wheel can be achieved.

[0063] (27).

[0064] Referring to the design method in step three, a machining case study (workpiece gear parameters are shown in Table 1) will be used to illustrate this. The design of the honing wheel parameters is based on... Figure 5 Based on the analysis results, the goal is to control the variation of the contact line projection intersection point to be less than 1 mm under a dressing amount of 5 mm. Taking into account the size limitations of the honing machine tool and the range of tooth number variation of the dressing gear, the initial tooth number of the honing wheel is determined to be 121 (tooth ratio greater than 4.5), the helix angle is 30.847° (axis intersection angle is 7°), and the maximum outer diameter is 270 mm. At the same time, two sets of dressing gears with variable tooth numbers were designed for comparison: (1) with 26 teeth and a displacement coefficient of 0.4, which is consistent with the parameters of the workpiece gear; (2) with 37 teeth and a displacement coefficient of 0.365, which can control the variation of the dressing contact line to within 3 μm. However, it is worth noting that the difference in tooth number will cause the workpiece tooth surface to have a concave deviation and reduce the actual bulging amount. This effect can be compensated by increasing the dressing amount of the dressing gear in advance. The specific parameters of the workpiece gear, honing wheel and dressing gear are shown in Table 2, and the corresponding dressing and processing parameters are shown in Table 3.

[0065] Table 2. Selected tool parameters and dressing amount under tooth number differences

[0066] Table 3 Transmission parameters during the dressing and machining processes

[0067] Step four: Establish the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the dressing and honing processes. Using the geometric parameters and process parameters of the dressing wheel, honing wheel, and workpiece gear selected in step three, derive the numerical model of the modified tooth surface of the dressing wheel, honing wheel, and workpiece gear, and perform deviation prediction to verify whether the parameter design is reasonable.

[0068] 4.1 Establish the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship for the dressing process. Using the geometric and process parameters of the dressing wheel and honing wheel selected in step three, establish a numerical model of the tooth surface of the dressing wheel and honing wheel. Specifically: (1) First, a numerical model of the dressing wheel tooth surface is established using the geometric parameters of the dressing wheel, as shown below.

[0069] (28) (29) in, , For tooth profile and tooth-direction bulging modification amount, , These are the superimposed curves for tooth profile and tooth direction modification, respectively. , For the shape modification constant, , , The development angle is the position for tooth profile modification. To adjust the width of the gear teeth, For the involute tooth surface helical parameters; (2) Establish the spatial coordinate relationship between the dressing gear and the honing wheel during the dressing process. Coordinate system and They are rigidly connected to the dressing gear and the honing wheel, respectively. , , , This serves as an auxiliary coordinate system. Therefore, the position vector of the honing wheel tooth surface... With normal vector As shown in equations (30)-(31).

[0070] (30) (31), (32), in, Coordinate system arrive The transformation matrix; It's the top left corner. matrix; , These represent the rotation angles of the dressing wheel and honing wheel at any given moment; The axial stroke of the dressing wheel during the dressing process; , , For adjusting the transmission ratio, center distance, and shaft angle during the dressing process; , This refers to the number of teeth on the two gears. According to the spatial conjugate meshing theory of interleaved shaft gears, the dressing process satisfies the following set of meshing equations: (33), (33), By combining equations (30) and (34), the independent motion variables at any contact point on the tooth surface of the dressing wheel can be solved. , and the position vector of the honing wheel tooth surface With normal vector ; (3) Establish a tooth surface deviation calculation model compared with the standard internal gear involute tooth surface with the same geometric parameters as the honing wheel, calculate the normal deviation at any discrete point on the honing wheel tooth surface, and realize the deviation prediction of the honing wheel tooth surface after honing wheel dressing. Specifically, as follows: The honing wheel tooth surface differs from the involute helical tooth surface of an internal gear. Based on the aforementioned mathematical model of the dressing process and the numerical model of the double-crown tooth surface of the dressing wheel, the calculation model for the torsional tooth surface deviation of the honing wheel can be expressed as equation (35). , For the position vector and normal vector of the involute tooth surface of a standard internal gear with the same geometric parameters as the honing wheel, This represents the deviation between the tooth surfaces of the two parts.

[0071] (35), 4.2 Establish the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship during the honing process. Using the workpiece gear parameters and the numerical model of the honing wheel tooth surface described in step 4.1, establish the numerical model of the workpiece gear tooth surface and perform deviation calculations to verify the rationality of the parameter design. Specifically: Establish the spatial motion coordinate relationship between the honing wheel and the workpiece gear, coordinate system and They are rigidly connected to the workpiece gear and the honing wheel, respectively. , , , The auxiliary coordinate system is used. Therefore, the position vector and normal vector of the workpiece gear tooth surface are shown in equations (36)-(37).

[0072] (36) (37) (38) in, Is the coordinate system to arrive Transformation matrix; yes Top left corner matrix; , These represent the rotation angles of the workpiece gear and the honing wheel at any given moment; This refers to the axial stroke of the honing wheel during the machining process. , , The transmission ratio, center distance, and shaft angle during the machining process are also considered. Similarly, the machining process must also satisfy the spatial conjugate meshing theory of interlaced shaft gears: (39) (40), Based on equations (36)-(40), the independent motion variables at any contact point on the tooth surface are obtained. , and the workpiece gear tooth surface position vector With normal vector .

[0073] To evaluate the degree of fit between the workpiece gear tooth surface and the ideal tooth surface generated by the two meshing envelopes, the normal deviation at each grid point can be calculated using equation (41), quantifying the geometric shape deviation between the actual tooth surface and the standard tooth surface. Wherein, , For the position vector and normal vector of the standard involute gear tooth surface with the same geometric parameters as the workpiece gear, This represents the deviation between the tooth surfaces of the two parts.

[0074] (41).

[0075] Based on the tooth surface simulation method established in step four, which involves "dressing gear → honing wheel → workpiece gear", the micro-geometric shape deviation of the tooth surface under different numbers of dressed gear teeth in Table 2 was quantitatively analyzed. The results are as follows: Figure 12 As shown in the figure. Simulation analysis results indicate that the meshing envelope process of the interleaved shaft gear pair produces honing wheel tooth surfaces with specific contact characteristics, which is fundamentally different from the tooth surfaces of internal gears. The fundamental reason is that the meshing geometry between the dressing gear and the honing wheel determines the topology of the honing wheel tooth surface. When the number of teeth on the dressing gear changes, the meshing geometry changes accordingly, leading to changes in the state of the dressing contact line, ultimately resulting in differences in the degree of twisting of the honing wheel tooth surface, exhibiting a significant offset in the tooth width direction. This difference in tooth surface twisting and offset under varying tooth numbers is the direct cause of the concave deviation on the workpiece tooth surface. Specifically, when honing wheel tooth surfaces with different degrees of twist mesh with the workpiece gear, the contact pressure and material removal rate distribution in the tooth width direction becomes uneven, resulting in relatively more material removal in the middle of the workpiece tooth surface and more residue at both ends, thus forming a concave deviation. This concave deviation has a smaller impact in the tooth profile direction but is significant in the tooth width direction, and is a key factor restricting the final machining accuracy and shaping accuracy of the gear.

[0076] Step 5: Discretize and perform point cloud processing on the numerical models of the modified tooth surfaces of the dressing wheel and honing wheel that have been verified. Adjust the point cloud data in point cloud processing software such as Cloud Compare to obtain high-precision tooth surface point clouds of the target dressing wheel and honing wheel. Then import the high-precision point cloud data into 3D solid design software such as UG to realize the establishment of 3D solid models of complex modified dressing wheels and honing wheels, and import them into CNC machine tools for precise machining of complex modified dressing wheels and honing wheels.

[0077] 5.1 The aforementioned verified numerical models of the tooth surface of the shaping and dressing wheel and the honing wheel are subjected to tooth surface discretization and point cloud processing. The point cloud processing software, such as Cloud Compare, is used to adjust the point cloud to obtain the high-precision tooth surface point cloud of the target shaping and dressing wheel and the honing wheel.

[0078] 5.2 Then, import the high-precision point cloud data of the tooth surface of the target shaping and honing wheel into 3D solid design software such as UG to realize the establishment of 3D solid models of the shaping and honing wheel and import them into CNC machine tools for precise machining of the shaping and honing wheel.

[0079] The validated numerical models of the variable-tooth-count dressing wheel and honing wheel were discretized to generate high-precision point cloud models. The point cloud data was then used to create 3D models in 3D solid modeling software and imported into CNC machine tools for the precise machining of complex-shaped dressing wheels and honing wheels. The 3D solid models of the variable-tooth-count dressing wheel and honing wheel are shown below. Figure 13 , 14 As shown.

[0080] This invention first establishes a mathematical model of the workpiece gear tooth surface and the honing conjugate meshing relationship based on the workpiece gear parameters, installation method, and shaping requirements, obtaining contact line models for the left and right tooth surfaces. Then, the contact line is projected onto a two-dimensional plane, and the influence of honing wheel parameters on the contact line and the intersection of the projection is analyzed. Next, a tooth surface contact line model of the honing wheel during the dressing and honing process is established under the difference in tooth count between the dressing wheel and the workpiece gear, clarifying that the difference in tooth count causes the contact line to intersect, and analyzing the influence of changes in the dressing wheel's tooth count on the contact line state. Secondly, based on the analysis of the influence of honing wheel and dressing wheel parameters on the contact line state, a parameter design method for the honing wheel and the variable tooth count dressing wheel is proposed. Thirdly, numerical models of the shaped tooth surfaces of the dressing wheel, honing wheel, and workpiece gear are established, and the shaped tooth surface of the dressing wheel, the shaped tooth surface of the honing wheel, the machining tooth surface of the workpiece gear, and the prediction and verification of the geometric shape deviations of their respective tooth surfaces are performed. Finally, the validated numerical model of the tooth surface is discretized to generate a point cloud. Through point cloud editing and 3D modeling, high-precision solid models of the dressing wheel and honing wheel are generated for CNC machining. This invention realizes the design and machining accuracy verification of the dressing tool in the high-power honing process, effectively suppressing contact state fluctuations caused by tool parameters and dressing amounts, significantly improving the service life of the honing wheel, and enhancing the honing accuracy stability and consistency of the workpiece gears. This helps reduce production costs and improve economic efficiency.

[0081] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0082] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for dressing wheels and honing wheels to improve the contact line stability during gear honing, characterized in that, Includes the following steps: S1. Based on the known gear parameters of the workpiece, establish a mathematical model of the left and right tooth surfaces of the workpiece gear to be honed, establish the spatial coordinate transformation relationship of the honing process, obtain the conjugate meshing relationship of the honing process based on the relative sliding velocity and normal vector at the meshing contact point on the tooth surface, and establish a mathematical model of the contact line of the left and right tooth surfaces of the workpiece gear. Using the contact line model of the left and right tooth surfaces of the workpiece gear, project the contact lines of the left and right tooth surfaces of the workpiece gear at the same rotation angle onto a two-dimensional plane, and establish a mathematical model for calculating the position and variation of the projection intersection point. S2. Establish a contact line model of the dressing process on the tooth surface of the honing wheel under different tooth count dressing wheels, and establish a projection model of the tooth surface contact line and its intersection point of the honing wheel during the dressing process and honing process under the difference in tooth count between the dressing wheel and the workpiece gear. S3. Based on the variation law of the dressing and honing contact line in S1 and S2, a design method for honing wheel and variable tooth number dressing wheel oriented towards contact line stability is constructed, and the geometric parameters and process parameters of dressing wheel, honing wheel, workpiece gear are obtained based on the method. S4. Establish the spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the dressing and honing process. Based on the geometric parameters and process parameters of the dressing wheel, honing wheel, and workpiece gear in S3, construct the numerical model of the modified tooth surface of the dressing wheel, honing wheel, and workpiece gear, and verify the model. S5. Discretize and process the numerical model of the tooth surface to obtain a high-precision tooth surface point cloud of the target dressing wheel and honing wheel. Based on the high-precision tooth surface point cloud, perform precise machining of the dressing wheel and honing wheel.

2. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, The parameters of the workpiece gear include: Normal Module Normal pressure angle Number of teeth z, tooth width b, helix angle displacement coefficient Lead p, base circle helix angle Base circle diameter Pitch circle diameter d, addendum circle diameter Root circle diameter half angle of base circle tooth groove ; Specifically: （1）， （2）， （3）， （4）， （5）， （6）， （7）， （8）。 3. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, In step S1, the mathematical model of the left and right tooth surfaces of the honing workpiece gear is established based on the known workpiece gear parameters as follows: Based on the gear meshing principle, the mathematical model of the left and right tooth surfaces of the honed workpiece gear is represented as follows: （9）， （10）， The normal vector corresponding to the tooth surface is represented as follows: （11）， （12）。 4. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, In S1, the spatial coordinate transformation relationship of the honing process is established. Based on the relative sliding velocity and normal vector at the meshing contact point on the tooth surface, the conjugate meshing relationship of the honing process is obtained, and the mathematical model of the contact line of the left and right tooth surfaces of the workpiece gear is established as follows: During the honing process, the honing wheel and the workpiece gear form a conjugate meshing relationship. That is, the honing wheel tooth surface and the workpiece tooth surface are in contact with each other while rotating around their respective rotation centers. The two tooth surfaces do not separate and their relative motion is in the tangent plane of the contact point between the two tooth surfaces and is perpendicular to the normal vector of the two tooth surfaces. The fixed coordinate system of the workpiece gear is selected as the analysis reference. The contact point Q between the honing wheel tooth surface and the workpiece tooth surface satisfies... ; The relative sliding velocity of the meshing contact point Q on the tooth surface is expressed as: （13）， The contact point normal vector is represented as: （14）， The conjugate meshing relationship is then expressed as: （15）， in, Let Q be the position of the contact point in the workpiece gear reference coordinate system. , The rotational angular velocity of the honing wheel and the workpiece gear; Therefore, when the rotation angle of the workpiece gear is a certain value, there is only one honing contact line on the left and right tooth surfaces of the meshing workpiece gear, and this contact line is a set of contact points that satisfy the conjugate meshing relationship. The mathematical model of the contact line on the left and right tooth surfaces is expressed as follows: （16）。 5. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, In step S1, the contact line model of the left and right tooth surfaces of the workpiece gear is used to project the contact lines of the left and right tooth surfaces of the workpiece gear at the same rotation angle onto a two-dimensional plane, and a mathematical model for calculating the position and variation of the projection intersection is established as follows: Based on the workpiece tooth surface contact line model, a mathematical model is established for the position of the intersection point of the projections of the contact lines with the same rotation angle on the left and right tooth surfaces of the workpiece gear: （17）， The change in the position of the intersection point directly corresponds to the change in the deflection of the honing wheel: （18）。 6. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, The contact line model established in S2 for the dressing process on the honing wheel tooth surface under different tooth count dressing wheels is as follows: Determine the maximum boundary for the number of teeth on the dressing wheel. The number of teeth on the workpiece gear is used as the minimum boundary for the number of teeth on the dressing wheel. , （19）； While increasing the number of teeth, adjust the displacement coefficient: （20）， （21）； The adjusted contact line on the honing wheel tooth surface is as follows: （22）。 7. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, The projection model of the tooth surface contact line and its intersection point of the honing wheel during the dressing and honing processes, under the difference in the number of teeth between the dressing wheel and the workpiece gear in S2, is specifically as follows: When the honing wheel rotates... When the angle between the dressing gear and the workpiece gear is a certain value, , If the value is also fixed, then there is only one dressing contact line and one honing contact line participating in the meshing on the honing wheel tooth surface. When the number of teeth is the same, the two coincide, while when the number of teeth is different, the two will form an intersecting relationship and intersect at a point, and this point is the contact point that simultaneously satisfies the conjugate meshing relationship between the dressing and honing processes. The honing contact line on the honing wheel tooth surface is: （23）； The mathematical model for the intersection location is: （24）； Similarly, the honing wheel tooth surface Convert to a two-dimensional plane Then the projection position and change of the intersection point are: （25）， （26）。 8. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, Specifically, S3 is: By increasing the gear ratio and helix angle, the meshing geometry is optimized, thereby constraining the migration of the contact line towards the tooth tip. Choose a larger number of teeth within the allowable range to improve the durability of the dressing wheel, and adjust the displacement coefficient accordingly. By adjusting the shaft angle between the dressing wheel shaft and the honing wheel shaft during the dressing process to compensate for changes in the contact state caused by the dressing amount, the geometric positional relationship between the honing wheel and the dressing wheel is determined. Based on the change in the dressing amount, the appropriate shaft angle for dressing can be calculated, and the corresponding adjustment of the honing wheel helix angle can be made. （27）。 9. The method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 1, characterized in that, The spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the dressing process are established. Based on the geometric and process parameters of the dressing wheel and honing wheel selected by S3, the numerical model of the tooth surface of the dressing wheel and honing wheel is established as follows: A numerical model of the dressing wheel tooth surface was established based on the dressing wheel's geometric parameters. （28）， （29）， in, , For tooth profile and tooth-direction bulging modification amount, , These are the superimposed curves for tooth profile and tooth direction modification, respectively. , For the shape modification constant, , , The development angle is the position for tooth profile modification. To adjust the width of the gear teeth, For the involute tooth surface helical parameters; （30）， （31）， （32）， in, Coordinate system arrive The transformation matrix; It's the top left corner. matrix; , These represent the rotation angles of the dressing wheel and honing wheel at any given moment; The axial stroke of the dressing wheel during the dressing process; , , For adjusting the transmission ratio, center distance, and shaft angle during the dressing process; , This refers to the number of teeth on the two gears. According to the spatial conjugate meshing theory of interleaved shaft gears, the dressing process satisfies the following set of meshing equations: （33）， （34）， By combining equations (30) and (34), the independent motion variables at any contact point on the tooth surface of the dressing wheel can be solved. , and the position vector of the honing wheel tooth surface With normal vector ; A calculation model for tooth surface deviation is established compared with the involute tooth surface of a standard internal gear with the same geometric parameters as the honing wheel. The normal deviation at any discrete point on the honing wheel tooth surface is calculated, and the deviation of the honing wheel tooth surface after dressing is predicted. （35）， in, , For the position vector and normal vector of the involute tooth surface of a standard internal gear with the same geometric parameters as the honing wheel, This represents the deviation between the tooth surfaces of the two parts.

10. A method for designing dressing wheels and honing wheels to improve contact line stability during honing as described in claim 9, characterized in that, The spatial coordinate transformation relationship and the two-degree-of-freedom conjugate meshing relationship of the honing process are established. Based on the workpiece gear parameters and the numerical model of the honing wheel tooth surface modification, the specific numerical model of the workpiece gear tooth surface modification is established as follows: The position vector and normal vector of the gear tooth surface are expressed as follows: （36）， （37）， （38） in, Is the coordinate system to arrive Transformation matrix; yes Top left corner matrix; , These represent the rotation angles of the workpiece gear and the honing wheel at any given moment; This refers to the axial stroke of the honing wheel during the machining process. , , The transmission ratio, center distance, and shaft angle during the machining process are also considered. Similarly, the machining process must also satisfy the spatial conjugate meshing theory of interlaced shaft gears: （39）， （40）， Based on equations (36)-(40), the independent motion variables at any contact point on the tooth surface are obtained. , and the workpiece gear tooth surface position vector With normal vector .

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