Design method of diamond roller for worm grinding wheel dressing

Abstract

The application discloses a design method of a diamond roller for dressing a worm grinding wheel, and first, a modified involute gear tooth profile curve is designed through a quadratic curve splicing method, and a modified involute tooth surface equation is obtained based on a modified involute principle; then, a meshing coordinate system based on an imaginary rack method is established, an imaginary rack tooth surface equation is obtained by meshing the modified involute tooth surface equation, and further, a worm grinding wheel tooth surface equation is obtained by twice meshing the imaginary rack tooth surface equation; finally, a diamond roller dressing worm grinding wheel coordinate system is established, and a diamond roller profile is obtained based on a contact line principle and the worm tooth surface equation in step B; the application solves the problems of easy concave profile and low precision in the process of designing the diamond roller for the multi-section complex modified gear for new energy vehicles, realizes accurate solution of the diamond roller profile, and improves the reliability of diamond roller design and processing.

Description

Technical Field

[0001] This invention belongs to the field of gear grinding technology, and specifically relates to a design method for a diamond roller for dressing worm gear grinding wheels. Background Technology

[0002] The new energy vehicle industry is driving the development of gear transmissions towards ultra-high speeds, with gears reaching a maximum service speed of 20,000~30,000 r / min. To effectively mitigate the impact, vibration, and noise generated on gear tooth surfaces during high-speed meshing, the most effective method is to modify the gear tooth profile. Compared to the traditional "drum-shaped" profile modification, the tooth profile modification of gears used in new energy vehicles is more complex, often involving two or three stages. This involves considering the edge modification of the tooth tip and root, in addition to the drum-shaped modification, further increasing the difficulty of gear manufacturing.

[0003] Worm wheel grinding has become the most widely used finishing process for hardened gear teeth in China due to its high processing efficiency and quality. It involves first dressing the worm wheel with diamond rollers, and then using the dressed worm wheel to perform continuous generating grinding on the gear teeth. The shape and precision of the machined gear teeth are entirely determined by the design and manufacturing precision of the diamond roller profile.

[0004] The design of a diamond roller for dressing worm gear grinding wheels can be divided into three steps:

[0005] 1) Based on the tooth profile modification requirements of the target gear, design the tooth profile modification curve and establish the modified tooth surface of the target gear;

[0006] 2) Based on the modified tooth surface of the target gear, and using the principles of gear meshing and spatial coordinate transformation, calculate the equation of the tooth surface of the worm grinding wheel;

[0007] 3) Calculate the rolling profile using the worm gear tooth surface equation.

[0008] Currently, the main problems with solving the diamond rolling profile for worm wheel dressing are as follows:

[0009] 1) The approximate design of gear tooth profile modification curves by fitting high-order functions not only fails to meet the multi-segment modification requirements of new energy vehicles, but also results in an uneven curve transition.

[0010] 2) The diamond rolling profile obtained by the two-parameter envelope method is prone to concavity, and the tooth profile of the machined gear is not qualified.

[0011] 3) Approximating the axial or normal profile of the worm wheel as the profile of the diamond grinding wheel has a certain deviation and is not accurate enough.

[0012] Therefore, for different gear tooth profile modification requirements, especially multi-segment modification, it is necessary to develop a design method for diamond rolling profiles suitable for worm gear grinding wheels. Summary of the Invention

[0013] The purpose of this invention is to address the shortcomings of the prior art by providing a design method for diamond rollers used in worm gear dressing, solving the problems that traditional design methods cannot meet the needs of multi-segment dressing, and that the roller profile is prone to concavity and inaccurate roller profile calculation.

[0014] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0015] A design method for a diamond roller for dressing worm gear grinding wheels includes the following steps:

[0016] Step A: Complete the design of the involute gear tooth profile modification curve by splicing quadratic curves. Based on the principle of involute modification, obtain the equation of the modified involute tooth surface.

[0017] The equation for the modified involute tooth surface is as follows (1):

[0018] (1);

[0019] in, The standard involute end face tooth profile equation.

[0020] The equation for the involute end face tooth profile is as follows;

[0021] To generate the coordinate transformation matrix of the involute tooth surface,

[0022] The equation for the modified involute tooth surface of a cylindrical gear is the gear tooth surface equation.

[0023] It equals the sum of the expansion angle and the pressure angle;

[0024] For involute shaping, and Functional relationship;

[0025] Step B: Establish a meshing coordinate system based on the hypothetical rack method. The hypothetical rack tooth surface equation is obtained by meshing solution of the modified involute tooth surface equation in Step A. Then, the worm grinding wheel tooth surface equation is obtained by secondary meshing solution of the hypothetical rack tooth surface equation.

[0026] Among them, the meshing coordinate system of the imaginary rack method is established based on the pairwise meshing relationship between the gear, rack and worm grinding wheel;

[0027] The tooth surface equation of the imaginary rack is obtained by coordinate transformation and meshing principle based on the meshing relationship between the imaginary rack and the gear, as shown in equation (4).

[0028] ;

[0029] In the formula, This refers to the angle through which the gear rotates during the meshing motion. This represents the distance the hypothetical rack moves during meshing. This is the distance from the imaginary point of meshing between the rack and gear to the center of rotation of the gear.

[0030] For gear-fixed coordinate system to the gear fixed coordinate system The coordinate transformation matrix;

[0031] Fixed coordinate system for gears To the rack-and-pinion coordinate system The coordinate transformation matrix;

[0032] This represents the imaginary rack and gear in the rack-fixed coordinate system. The relative velocity vector at the lower engagement point;

[0033] This represents the imaginary rack and gear in the rack-fixed coordinate system. The normal vector at the lower engagement point;

[0034] Based on the hypothetical meshing relationship between the rack and the worm grinding wheel, and using coordinate transformation and the meshing principle, the equation of the tooth surface of the worm grinding wheel is solved within the end face of the worm grinding wheel, as shown in equation (7).

[0035] ;

[0036] in, Equation for gear tooth surface In the fixed coordinate system of the worm gear grinding wheel The envelope formed below;

[0037] This refers to the angle through which the worm gear grinding wheel rotates during its meshing motion. The angle between the shafts of the worm gear and the gear;

[0038] Fixed coordinate system for worm gear grinding wheel To the fixed coordinate system of the worm gear grinding wheel The transformation matrix;

[0039] Fixed coordinate system for rack To the fixed coordinate system of the worm gear grinding wheel The transformation matrix;

[0040] and Represent the imaginary rack and worm wheel in the fixed coordinate system of the worm wheel. The relative velocity and normal vector at the lower engagement point;

[0041] It is obtained by calculating the velocity vector of the rack and worm grinding wheel at the meshing point;

[0042] Step C: Establish the coordinate system of the diamond roller dressing worm wheel. Based on the contact line principle, calculate the diamond roller profile from the worm tooth surface equation in step B.

[0043] In step A, when the tooth profile modification curve is a two-segment curve, in equation (1) The design can be completed using equation (2).

[0044] (2);

[0045] When the tooth profile modification curve is a three-segment curve, in equation (1) Use equation (3) to complete the design.

[0046] (3);

[0047] In equations (2) and (3), , The parameters of the parabola equation are... , , The parameters are the circle equation parameters; SAP and EAP are the endpoints of the tooth profile evaluation interval. , The segmentation position of the tooth profile shaping curve;

[0048] After completing the design of the tooth profile modification curve, the equation of the modified involute tooth surface can be obtained according to equation (1).

[0049] In step B, It is calculated by the velocity vector of the rack and gear at the meshing point;

[0050] The coordinate transformation of the normal vector of the gear at that point is obtained, and the calculation is shown in equation (5).

[0051] (5).

[0052] In step B, when Solve equations (4) and (5) simultaneously to obtain the hypothetical rack tooth profile equation.

[0053] because The hypothetical rack tooth profile equation can then be described as follows: ;

[0054] The hypothetical rack tooth profile equation Fixed coordinate system by rack Transform to rack fixed coordinate system Down, Let be the transformation matrix.

[0055] (6).

[0056] If we assume that the rack, gear, and worm wheel mesh in pairs at the same meshing point, and that all three have the same normal vector at that point, then in the calculation, we only need to transform the normal vector of the gear at the meshing point in equation (5) to the fixed coordinate system of the worm wheel. Download now;

[0057] (8);

[0058] Solve the equations of (7) and (8) simultaneously to obtain the equation of the worm gear grinding wheel tooth surface. .

[0059] In step C, any point on the contact line If there is a common normal vector, and the relative velocity of the point is perpendicular to the normal vector, then the contact line condition is:

[0060] ;

[0061] In the formula, For the helical parameters;

[0062] For common normal vectors, It is the relative velocity;

[0063] and Each is any point In the coordinate system of the worm gear grinding wheel and diamond roller coordinate system The radius vector in the middle;

[0064] and These are the rotational speeds of the worm wheel and the diamond roller about their respective axes of rotation in their respective coordinate systems;

[0065] For the worm gear grinding wheel coordinate system middle The direction of the axis is the unit vector. Diamond roller coordinate system middle The direction unit vector of the axis.

[0066] The common normal vector Using step B Please provide a solution.

[0067] The tooth surface of the worm gear grinding wheel is an involute helical surface, and any point within the tooth surface satisfies involute helical motion. Therefore: .

[0068] Equation (9) can then be written as:

[0069] .

[0070] The For any point In the diamond roller coordinate system The lower radius vector can be obtained from the equation of the worm gear grinding wheel tooth surface. The coordinate transformation is performed, as shown in equation (11).

[0071] (11);

[0072] In the formula, For the worm gear grinding wheel coordinate system To the diamond roller coordinate system The coordinate transformation matrix;

[0073] By combining equations (10) and (11), the contact line when the tooth surface of the worm grinding wheel and the rotating surface of the diamond roller make relative motion can be obtained.

[0074] The beneficial effects of this invention are:

[0075] (1) This invention discloses a design method for a diamond roller for dressing a worm gear. An imaginary rack is added between the two meshing tooth surfaces of the worm gear and the gear, such that the rack's tooth surface satisfies a conjugate meshing relationship with both the worm gear tooth surface and the helical gear tooth surface. The diamond roller profile is designed using this imaginary rack. First, the involute gear tooth profile modification curve is designed using a quadratic curve splicing method. Based on the involute modification principle, the equation for the modified involute tooth surface is obtained. Then, a meshing coordinate system based on the imaginary rack method is established, and the modification... The involute tooth surface equation is solved by meshing to obtain the hypothetical rack tooth surface equation. Further, the worm gear tooth surface equation is obtained by a second meshing solution using the hypothetical rack tooth surface equation. Finally, a coordinate system for dressing the worm gear is established using a diamond roller. Based on the contact line principle, the diamond roller profile is obtained from the worm tooth surface equation obtained in step B. This invention solves the problems of easy concave profile and low precision in the design of diamond rollers for multi-segment complex profiled gears used in new energy vehicles, achieving accurate solution of the diamond roller profile and improving the reliability of diamond roller design and processing.

[0076] (2) It can be used for different gear tooth profile modification requirements, especially multi-segment modification. It is suitable for high-precision design of diamond rolling profile for worm gear grinding wheels. It solves the problems of traditional inability to design multi-segment modification, easy concave rolling profile, and inaccurate rolling profile solution, as well as the problem of inaccurate tooth profile modification curve design in the existing diamond rolling profile solution process for worm gear grinding wheel dressing. It has high engineering application value.

[0077] (3) The secondary meshing calculation based on the hypothetical rack method can accurately solve the equation of the tooth surface of the worm grinding wheel, and obtain the profile of the diamond roller by solving the contact line between the diamond roller and the worm grinding wheel during the dressing process. The calculation results are more accurate and have higher precision.

[0078] (4) The method of splicing quadratic curves can effectively design highly accurate profile curves for multi-segment complex profile gears used in new energy vehicles, which can solve the problem of low accuracy of traditional high-order function fitting design.

[0079] (5) The diamond profile obtained by this method is strictly convex, which is convenient for finishing and processing and will not cause interference that affects manufacturing accuracy. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the hypothetical rack method of the present invention;

[0081] Figure 2 This is a schematic diagram of the involute shaping principle;

[0082] Figure 3 These are common profile modification curves for new energy vehicles;

[0083] Figure 4 It is a meshing coordinate system based on the hypothetical rack method;

[0084] Figure 5 It is the coordinate system for diamond roller dressing worm gear grinding wheels. Detailed Implementation

[0085] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification.

[0086] This invention provides a design method for a diamond roller for dressing worm gear grinding wheels, such as... Figures 1 to 5 As shown.

[0087] A design method for a diamond roller for dressing worm gear grinding wheels includes the following steps:

[0088] Step 1: Complete the design of the involute gear tooth profile modification curve by splicing quadratic curves. Based on the principle of involute modification, obtain the equation of the modified involute tooth surface.

[0089] A modified involute is formed by superimposing modification amounts along the direction of the theoretical involute's generation line, such as... Figure 2 As shown, the amount of shaping and the development angle of the involute. There is a one-to-one correspondence. (See diagram) Let the pressure angle be any point on the involute. Let be the radius of the base circle.

[0090] The equation for the modified involute tooth surface can be described as Equation (1):

[0091] (1);

[0092] In the formula, The standard involute end face tooth profile equation. The equation for the involute end face tooth profile is used for modification. To generate the coordinate transformation matrix of the involute tooth surface, The equation for the modified involute tooth surface of a cylindrical gear (hereinafter referred to as the gear tooth surface equation). It equals the sum of the expansion angle and the pressure angle. For involute shaping, and It is a functional relationship.

[0093] like Figure 3 As shown, the common tooth profile modification requirements for gears used in new energy vehicles are two-stage or three-stage. The tooth profile modification design parameters usually include the tooth profile bulge amount. Tooth profile tilt deviation Tooth tip and root trimming amount and For this type of profile modification curve, the present invention adopts a spliced ​​quadratic curve design. By controlling the tangency of the splicing position of the quadratic curves, the profile modification curve can be strictly convex outward without concavity inward. Among them, the bulging curve is designed using a circular equation, while the tooth tip modification curve and tooth root modification curve can be designed using a parabolic equation.

[0094] When the tooth profile modification curve is a two-segment curve, in equation (1) The design can be completed using equation (2). When the tooth profile modification curve is a three-segment curve, in equation (1) The design can be completed using formula (3).

[0095] (2);

[0096] (3);

[0097] In equations (2) and (3), , The parameters of the parabola equation are... , , These are the parameters for the circular equation. SAP and EAP are the endpoints of the tooth profile evaluation interval. , The segmentation positions of the tooth profile shaping curve.

[0098] After completing the design of the tooth profile modification curve, the equation of the modified involute tooth surface can be obtained by combining equation (1).

[0099] Step 2: Establish a meshing coordinate system based on the hypothetical rack method. The hypothetical rack tooth surface equation is obtained by meshing solution of the modified involute tooth surface equation in Step 1. Furthermore, the worm grinding wheel tooth surface equation is obtained by second meshing solution of the hypothetical rack tooth surface equation.

[0100] like Figure 1 There is a pairwise meshing relationship between the working gear 3, the imaginary rack 2, and the worm grinding wheel 1. Based on this, the following is established: Figure 4 The meshing coordinate system shown is based on the hypothetical rack method. For the worm gear grinding wheel fixed coordinate system, it can be rotated around its axis. It rotates. A fixed coordinate system is established for the worm gear grinding wheel. This is a gear-fixed coordinate system, which can be rotated around its axis. It rotates. A fixed coordinate system is used for the gear. For a rack-and-pinion fixed coordinate system, it can be used along the coordinate axes. It performs translational motion. A fixed coordinate system is established for the rack. and These represent the angles that the worm gear and the gear rotate through during their meshing motion. This represents the distance the hypothetical rack moves during meshing. This is the distance from the imaginary point of meshing between the rack and gear to the center of rotation of the gear. The center distance between the worm grinding wheel and the gear. It is the angle between the shafts of the worm gear and the gear.

[0101] Based on the meshing relationship between the hypothetical rack and gear, the equation of the hypothetical rack's tooth surface is... It can be obtained through coordinate transformation and the meshing principle, as shown in equation (4).

[0102] ;

[0103] In the formula, For gear-fixed coordinate system to the gear fixed coordinate system The coordinate transformation matrix, Fixed coordinate system for gears To the rack-and-pinion coordinate system The coordinate transformation matrix. and Represent the hypothetical rack and gear in the rack-fixed coordinate system, respectively. The relative velocity vector and normal vector at the lower engagement point. It can be calculated from the velocity vectors of the rack and gear at the meshing point. The calculation is shown in equation (5), which is obtained by transforming the normal vector coordinates of the gear at that point.

[0104] (5);

[0105] make Solve the equations of the hypothetical rack tooth surface by combining (4) and (5). .because The equation of the hypothetical rack tooth profile can be written as: .

[0106] The hypothetical rack tooth profile equation Fixed coordinate system by rack Transform to rack fixed coordinate system Down. Let be the transformation matrix.

[0107] (6);

[0108] Based on the hypothetical meshing relationship between the rack and the worm grinding wheel, and using coordinate transformation and the meshing principle, the equation of the tooth surface of the worm grinding wheel is solved within the end face of the worm grinding wheel, as shown in equation (7).

[0109] ;

[0110] In the formula, Fixed coordinate system for rack To the fixed coordinate system of the worm gear grinding wheel The transformation matrix, Fixed coordinate system for worm gear grinding wheel To the fixed coordinate system of the worm gear grinding wheel The transformation matrix. and Represent the imaginary rack and worm wheel in the fixed coordinate system of the worm wheel. The relative velocity vector and normal vector at the lower engagement point. It can be calculated from the velocity vectors of the rack and worm wheel at the meshing point.

[0111] Since the hypothetical rack, gear, and worm wheel satisfy a pairwise meshing relationship at the same meshing point, their normal vectors at that meshing point are the same. In the calculation, it is only necessary to transform the normal vector of the gear at the meshing point in equation (5) to the fixed coordinate system of the worm wheel. Download it now.

[0112] (8);

[0113] Solve the equations of (7) and (8) simultaneously to obtain the equation of the worm gear grinding wheel tooth surface. .

[0114] Step 3: Establish the coordinate system of the diamond roller dressing worm wheel. Based on the contact line principle, obtain the diamond roller profile from the worm tooth surface equation in Step 2.

[0115] A worm gear is essentially a helical gear with an involute helical tooth surface. A diamond roller is a rotating surface; dressing a worm gear is equivalent to using a disc-shaped tool with a rotating surface to machine a workpiece with a helical surface. Based on the contact conditions, at any instant during relative motion, there is always a tangent contact line between their surfaces with a fixed spatial position.

[0116] Based on the process motion of dressing worm grinding wheels with diamond rollers, a system is established as follows: Figure 5 The coordinate system shown is used. Let the worm gear grinding wheel coordinate system be... middle , , The direction unit vector of the axis is , , Diamond roller coordinate system middle , , The direction unit vector of the axis is , , Their respective rotational speeds about the axis are and . The distance between their centers. Let be the angle between the axes of rotation of the two.

[0117] According to the contact wire principle, any point on the contact wire... If there is a common normal vector, and the relative velocity of the point is perpendicular to the normal vector, then the contact line condition is:

[0118] ;

[0119] In the formula, For the helical parameters. For the common normal vector, the method in step two can be used. Please provide a solution. and Each is any point In the coordinate system of the worm gear grinding wheel and diamond roller coordinate system The radius vector in the vector.

[0120] Given that the tooth surface of a worm gear grinding wheel is an involute helical surface, any point within its tooth surface satisfies involute helical motion, therefore... .

[0121] Then equation (9) can be written as:

[0122] .

[0123] because For any point In the diamond roller coordinate system The lower radius vector can be obtained from the equation of the worm gear grinding wheel tooth surface. It is obtained by performing coordinate transformation.

[0124] (11);

[0125] In the formula, For the worm gear grinding wheel coordinate system To the diamond roller coordinate system The coordinate transformation matrix.

[0126] By combining (10) and (11), the contact line when the tooth surface of the worm grinding wheel and the rotating surface of the diamond roller move relative to each other can be obtained.

[0127] Rotate the contact line around the axis of the diamond roller to obtain the rotating surface of the diamond roller. The cross-section of this rotating surface along the axis of rotation of the diamond roller is the profile of the diamond roller. The calculation method will not be described in detail here.

[0128] If this patent uses terms such as "first" and "second" to define components, those skilled in the art should know that the use of "first" and "second" is merely for the convenience of describing the invention and simplifying the description, and the above terms have no special meaning.

[0129] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claims. The scope of protection of this invention is defined by the appended claims and their equivalents.

[0130] In the description of this invention, it should be understood that the terms "front", "rear", "left", "right", "center", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only used to facilitate the description of this invention and to simplify the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this invention.

Claims

1. A design method for a diamond roller for dressing worm gear grinding wheels, characterized in that, Includes the following steps: Step A: Complete the design of the involute gear tooth profile modification curve by splicing quadratic curves. Based on the principle of involute modification, obtain the equation of the modified involute tooth surface. The equation for the modified involute tooth surface is as follows (1): (1)； in, The standard involute end face tooth profile equation. The equation for the involute end face tooth profile is as follows; To generate the coordinate transformation matrix of the involute tooth surface, The equation for the modified involute tooth surface of a cylindrical gear is the gear tooth surface equation. It equals the sum of the expansion angle and the pressure angle; For involute shaping, and Functional relationship; Step B: Establish a meshing coordinate system based on the hypothetical rack method. The hypothetical rack tooth surface equation is obtained by meshing solution of the modified involute tooth surface equation in Step A. Then, the worm grinding wheel tooth surface equation is obtained by secondary meshing solution of the hypothetical rack tooth surface equation. Among them, the meshing coordinate system of the imaginary rack method is established based on the pairwise meshing relationship between the gear, rack and worm grinding wheel; The tooth surface equation of the imaginary rack is obtained by coordinate transformation and meshing principle based on the meshing relationship between the imaginary rack and the gear, using equation (4). ； In the formula, This refers to the angle through which the gear rotates during the meshing process. This represents the distance the hypothetical rack moves during meshing. This is the distance from the imaginary point of meshing between the rack and gear to the center of rotation of the gear. For gear-fixed coordinate system to the gear fixed coordinate system The coordinate transformation matrix; Fixed coordinate system for gears To the rack-and-pinion coordinate system The coordinate transformation matrix; This represents the imaginary rack and gear in the rack-fixed coordinate system. The relative velocity vector at the lower engagement point; This represents the imaginary rack and gear in the rack-fixed coordinate system. The normal vector at the lower engagement point; Based on the hypothetical meshing relationship between the rack and the worm wheel, the equation of the tooth surface of the worm wheel is solved in the end face of the worm wheel using coordinate transformation and meshing principle, and is expressed as equation (7). ； in, Equation for gear tooth surface In the fixed coordinate system of the worm gear grinding wheel The envelope formed below; This refers to the angle through which the worm gear grinding wheel rotates during its meshing motion. The angle between the shafts of the worm gear and the gear; Fixed coordinate system for worm gear grinding wheel To the fixed coordinate system of the worm gear grinding wheel The transformation matrix; Fixed coordinate system for rack To the fixed coordinate system of the worm gear grinding wheel The transformation matrix; and Represent the imaginary rack and worm wheel in the fixed coordinate system of the worm wheel. The relative velocity and normal vector at the lower engagement point; It is obtained by calculating the velocity vector of the rack and worm grinding wheel at the meshing point; Step C: Establish the coordinate system of the diamond roller dressing worm wheel. Based on the contact line principle, calculate the diamond roller profile from the worm tooth surface equation in step B. In step A, when the tooth profile modification curve is a two-segment curve, in equation (1) Use equation (2) to complete the design. （2）； When the tooth profile modification curve is a three-segment curve, in equation (1) Use equation (3) to complete the design. （3）； In equations (2) and (3), , The parameters of the parabola equation are... , , The parameters are the circle equation parameters; SAP and EAP are the endpoints of the tooth profile evaluation interval. , The segmentation position of the tooth profile shaping curve; After completing the design of the tooth profile modification curve, the equation of the modified involute tooth surface can be obtained according to equation (1).

2. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 1, characterized in that: In step B, It is calculated by the velocity vector of the rack and gear at the meshing point; The coordinates of the normal vector of the gear at that point are obtained by transformation, and the calculation is shown in equation (5). （5）。 3. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 2, characterized in that: In step B, when Solve equations (4) and (5) simultaneously to obtain the hypothetical rack tooth profile equation. ; because The hypothetical rack tooth profile equation is described as follows: ; The hypothetical rack tooth profile equation Fixed coordinate system by rack Transform to rack fixed coordinate system Down, Let be the transformation matrix. （6）。 4. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 2, characterized in that: If we assume that the rack, gear, and worm wheel mesh in pairs at the same meshing point, and that all three have the same normal vector at that point, then in the calculation, we only need to transform the normal vector of the gear at the meshing point in equation (5) to the fixed coordinate system of the worm wheel. Download now; （8）； Solve the equations of (7) and (8) simultaneously to obtain the equation of the worm gear grinding wheel tooth surface. .

5. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 1, characterized in that: In step C, any point on the contact line If there is a common normal vector, and the relative velocity of the point is perpendicular to the normal vector, then the contact line condition is: ； In the formula, For the helical parameters; For common normal vectors, It is the relative velocity; and Each is any point In the coordinate system of the worm gear grinding wheel and diamond roller coordinate system The radius vector in the middle; and These are the rotational speeds of the worm wheel and the diamond roller about their respective axes of rotation in their respective coordinate systems; For the worm gear grinding wheel coordinate system middle The direction of the axis is the unit vector. Diamond roller coordinate system middle The direction unit vector of the axis.

6. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 5, characterized in that: The common normal vector Using step B Please provide a solution.

7. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 5, characterized in that: The tooth surface of the worm gear grinding wheel is an involute helical surface, and any point within the tooth surface satisfies involute helical motion. Therefore: ; Then equation (9) can be written as: 。 8. The design method of a diamond roller for dressing a worm gear grinding wheel according to claim 7, characterized in that: The For any point In the diamond roller coordinate system The lower radius vector is derived from the equation of the worm gear grinding wheel tooth surface. The coordinates are transformed and obtained using equation (11). （11）； In the formula, For the worm gear grinding wheel coordinate system To the diamond roller coordinate system The coordinate transformation matrix; By combining equations (10) and (11), the contact line when the tooth surface of the worm grinding wheel and the rotating surface of the diamond roller make relative motion can be obtained.

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