A multi-axis linkage multi-point following tooth surface topology modification method

Abstract

The present application relates to gear processing technical field, disclose a kind of multi-axis linkage multi-point following's gear face topology modification method, by multi-axis linkage numerical control system control grinding wheel and gear implementation, the multi-axis linkage numerical control system at least include X, Y, Z three linear coordinate axes, A, C two rotary coordinate axes;The grinding wheel does helical motion along the gear axial direction, while doing parabolic motion along the gear radial direction;Including the following steps, establish the mathematical model of gear tooth surface and grinding wheel profile;According to the intersection of normal on helical gear spiral tooth surface and grinding wheel axis, obtain all the contact points of helical gear and grinding wheel, and then get contact line, again the contact line is rotated around grinding wheel axis to obtain grinding wheel profile.It has beneficial effects: by setting reverse interference compensation, after single tooth profile processing, grinding wheel is modified, determine whether there is processing interference, when there is processing interference, start reverse compensation, reduce processing interference, improve gear precision.

Description

Technical Field

[0001] This invention relates to the field of gear machining technology, and in particular to a method for tooth surface topology modification using multi-axis linkage and multi-point following. Background Technology

[0002] Tooth surface modification, also known as gear tooth profile modification, refers to the deliberate, minute alteration of the gear tooth surface to deviate from the theoretical tooth surface. Depending on the modification location, gear tooth modification can be divided into profile modification and tooth direction modification. Profile modification includes edge trimming, root trimming, and root hollowing. Its function is to reduce engagement and disengagement impacts, alleviate dynamic loads, eliminate positive base pitch errors during meshing, improve load distribution, and reduce impact vibrations. Tooth direction modification includes tooth tip thinning, helix angle adjustment, drum-shaped trimming, and curved surface trimming. Its function is to ensure uniform load distribution along the tooth width direction under load; that is, the modification curve must compensate for meshing tooth direction errors, avoid edge point contact, and reduce edge contact.

[0003] In existing technologies, there are two main methods for gear shaping: one is to shape the cutting tool used to process the gear into a specific shape; the other is to control the movement of the cutting tool and the gear itself to achieve gear shaping. With the advancement of science and technology, multi-axis CNC machine tools are machine tools used to process complex curved surfaces. They utilize computer control to move and position the machine tool simultaneously in multiple directions, thereby completing more complex machining tasks and workpiece shapes.

[0004] However, existing technical solutions are not applicable to the precision and complex machining of gears. Summary of the Invention

[0005] To overcome the problems existing in the prior art, this invention proposes a multi-axis linkage and multi-point following tooth surface topology modification method, the detailed technical solution of which is as follows:

[0006] A multi-axis linkage and multi-point following tooth surface topology modification method is implemented by controlling a grinding wheel and a gear with a multi-axis linkage CNC system. The multi-axis linkage CNC system includes at least three linear coordinate axes (X, Y, Z) and two rotary coordinate axes (A, C). The grinding wheel performs helical motion along the axial direction of the gear and parabolic motion along the radial direction of the gear.

[0007] Includes the following steps:

[0008] S01, Establish a mathematical model of the gear tooth surface and the sand profile; Based on the intersection of the normal on the helical gear tooth surface and the grinding wheel axis, find all the contact points between the helical gear and the grinding wheel, and then obtain the contact line. Then, rotate the contact line around the grinding wheel axis to obtain the sand profile.

[0009] S02, the gear tooth surface is meshed, and the gear is indexed while rotating along the C-axis. The grinding wheel is fed along the radial X-axis of the gear. The geometric center of the grinding wheel is kept collinear with the center of the gear tooth groove. The C-axis, X-axis, and Z-axis are linked to detect the tooth direction and tooth profile of the gear, obtaining the tooth surface area. The sand profile is obtained based on the tooth surface area and the mathematical model in S01. The motion equations of the workpiece rotation angle and the servo axis are established using the sand profile and gear parameters. The unit normal vector of the tooth surface is calculated using the sand profile, and the tooth surface equation and the unit normal vector equation of the tooth surface are solved to obtain the meshing multi-point topological surface of the tooth surface and the sand profile. The machining of the meshing multi-point topological surface is carried out by fine-tuning the motion parameters of the servo axis.

[0010] S03: After machining the gear tooth profile once with the grinding wheel, the grinding wheel is dressed. The theoretical cross-section of the helical surface is calculated based on the input parameters. The actual cross-section of the gear's helical surface is obtained based on the detection. The points of the theoretical cross-section and the points of the actual cross-section are compared in a one-to-one correspondence, and the distance between the two points is calculated. When the distance between the two points is greater than a set threshold, reverse compensation is activated. A virtual compensation point is generated on the extension line from the point of the actual cross-section to the corresponding point of the theoretical cross-section. The distance from the virtual compensation point to the point of the theoretical cross-section is equal to the distance from the point of the actual cross-section to the corresponding point of the theoretical cross-section. The newly formed tool point is calculated using the virtual compensation point as the new initial calculation point. The grinding wheel is dressed according to the tool point. The grinding wheel profile is recalculated based on the dressed grinding wheel, and then the gear tooth profile is machined.

[0011] Furthermore, in S01, the grinding wheel and the gear are absolutely offset, and an O-shaped gap is established on the grinding wheel. c X c Y c Z c The tool coordinate system is established on the gear, and the OX coordinate system is created. w Y w Z w Establish the workpiece coordinate system and the transformation formula between the tool coordinate system and the workpiece coordinate system; based on the intersection of the normals of the grinding wheel axis and the gear helical tooth surface, solve to obtain the contact line equation, and then rotate the contact line around the grinding wheel axis to obtain the grinding profile.

[0012] Furthermore, the motion equations of the workpiece rotation angle and the servo axis are as follows:

[0013] In the formula, φ1 is the workpiece rotation angle, γ m d is a constant; f and d w δ, u1, and σ1 are the root circle diameter and pitch circle diameter of the gear, respectively; d1 is the grinding wheel diameter; β is the helix angle of the gear; δ, u1, and σ1 are gear parameters.

[0014] Furthermore, in S02, based on the sand profile equation, the modified tooth surface equation and the tooth surface unit normal vector equation are obtained through the positional relationship and meshing equation between the grinding wheel and the gear, thereby obtaining the meshing multi-point topological surface of the tooth surface and the sand profile.

[0015] Furthermore, the multi-axis linkage CNC system includes two grinding wheels, which simultaneously grind the gear.

[0016] According to any of the above embodiments, the present invention has at least the following beneficial effects: In the present invention, a mathematical model of the gear tooth surface and the sand profile is first established to ensure the stability of continuous processing;

[0017] Then, by meshing the gear tooth surface, the sand profile is calculated using the meshed tooth surface region, and finally the motion equation of the servo shaft and the meshing multi-point topology are obtained. The meshing multi-point topology of this tooth surface region is then machined by fine-tuning the motion parameters.

[0018] Finally, by setting up reverse interference compensation, the grinding wheel is dressed after machining a single tooth profile to determine whether there is machining interference. When machining interference exists, reverse compensation is activated, which reduces machining interference and improves gear precision.

[0019] The multi-axis forming gear grinding CNC servo system of the present invention has high stability, can meet the diverse sand dressing requirements of grinding machines with different structures, and the error is controllable. Attached Figure Description

[0020] Figure 1 This is a coordinate diagram of the workpiece coordinate system and the grinding wheel coordinate system of the present invention.

[0021] Figure 2 This is a schematic diagram of the tooth profile modification of the present invention.

[0022] Figure 3 This is a schematic diagram of the gear tooth surface grid distribution of the present invention.

[0023] Figure 4 This is a schematic diagram of the coordinate system for the bilateral grinding process of this invention.

[0024] Figure 5 This is a schematic diagram of the interference amount for different grinding wheel radii according to the present invention.

[0025] Figure 6 This is a schematic diagram of the grinding wheel interference of the present invention.

[0026] Figure 7 This is a schematic diagram of the interference compensation of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0028] During gear machining, the tooth surface deviates from the actual involute curve. To provide smooth operation and account for shaft angular errors, this deviation needs to be corrected. Topological modification can be divided into profile modification and tooth direction modification. Profile modification can be achieved through grinding wheel modification, while tooth direction modification requires the shape of the grinding wheel to change with the width of the gear, which is usually only achieved by changing the way the grinding wheel moves relative to the gear.

[0029] A multi-axis linkage and multi-point following tooth surface topology modification method specifically includes the following steps:

[0030] 1. Establish a mathematical model of the workpiece tooth surface and the sand profile. Based on the intersection of the normal on the helical gear tooth surface and the grinding wheel axis, find all the contact points between the helical gear and the grinding wheel, and then obtain the contact line. Then, rotate the contact line around the grinding wheel axis to obtain the sand profile.

[0031] When the tool surface is a rotating surface, there exists a contact line between the workpiece helical tooth surface and the tool surface conjugate to this surface. The normal to a point on this contact line intersects the tool axis. Based on this principle, by using the condition that the normal on the helical tooth surface of the helical gear intersects the grinding wheel axis, all contact points between the helical gear and the grinding wheel can be determined, thus obtaining the contact line. Then, by rotating this contact line around the grinding wheel axis, the grinding profile can be obtained.

[0032] The grinding wheel used as the cutting tool is absolutely offset from the gear to be machined to ensure the stability of continuous machining of the helical surface. The positional relationship between the forming tool and the workpiece is as follows: Figure 1 As shown, in Figure 1 Chinese: OX w Y w Z w For the workpiece coordinate system, O c X c Y c Z c Let X be the tool coordinate system; ∑ be the angle between the tool axis and the workpiece axis; α be the center moment between the forming tool and the workpiece; X be the workpiece coordinate system. w Shaft and forming tool X c The axes coincide, but the directions are opposite.

[0033] Based on the coordinate position relationship diagram, we obtain the coordinates from O. c X c Y cZ c To OX w Y w Z w The transformation relationship formula is: x = α - X; y = -Ycos∑ - Zsin∑; Equation (1)

[0034] z = -Ysin∑ - Zcos∑.

[0035] In equation (1): x, y and z are the coordinates of points in the workpiece coordinate system; X, Y and Z are the coordinates of points in the tool coordinate system.

[0036] Establishing the workpiece coordinate system OX w Y w Z w Then, assume X w OY w There is a smooth curve r(t) on the coordinate plane.

[0037] r(t)={x(t),y(t)},t∈[t,t2] , formula (2)

[0038] In the formula, x(t) and y(t) represent the coordinate components of the curve on the x-axis and y-axis of the workpiece coordinate system, respectively. Assuming the curve undergoes helical motion with a lead of h along the positive Zw axis, a helical surface R(θ,t) can be obtained in the workpiece coordinate system.

[0039] R(θ,t)={x(t)cosθ-y(t)sinθ,x(t)sinθ+y(t)cosθ,pθ}, equation (3)

[0040] In the formula: θ is the curve rotation angle parameter, and p is the helical parameter. Here, only the right-hand helical case is considered. The normal n at any point on the helical surface can be obtained using the formula.

[0041] Establish a forming tool coordinate system OcXcYcZc. Draw a radial vector R from the tool coordinate origin to points on the helical surface. Then, the contact line condition on the helical surface can be expressed as:

[0042] (k'×R)·n=0. Equation (4)

[0043] In the formula, k' is the tool axis.

[0044] Considering the relationship between the workpiece coordinate system and the forming tool coordinate system, the simplified formula is...

[0045] -(ycos∑+xsin∑)n1+n2(xa)cos∑+n3(ax)sin∑=0, equation (5)

[0046] In the formula, n1, n2, and n3 are the coordinate components of the normal to any point on the helical surface, respectively.

[0047] By combining equations (3) and (5), we can obtain the contact line equation of the helical surface in the workpiece coordinate system.

[0048] -(ycos ∑+xsin∑)[p(x'(t)sinθ+y'(t)cosθ)]-

[0049] [p(x'(t)cosθ-y'(t)sinθ)](xa)cos ∑+

[0050] {[p(x'(t)sinθ+y'(t)cosθ)]y(t)-[p(x'(t)

[0051] cos0-y'(t)sinθ)]}x(t) / p(ax)sinx=0, equation (6)

[0052] In the formula, θ and t satisfy equation (3).

[0053] By rotating the contact line around the forming tool axis, the tool rotation surface can be obtained. The contact line can then be transformed to the tool coordinate system O using coordinate transformation formula (1). c X c Y c Z c Then the axial section of the forming tool's rotating surface can be expressed as:

[0054] ,

[0055] Z=Z, Equation (7).

[0056] 2. Tooth Surface Modification. The tooth surface modification amount is allocated using mesh coordinates to ensure a specified modification amount is obtained at a designated location. First, the gear tooth surface is divided into meshed regions. Based on the detection of tooth surface regions 1, 3, and 7 after grinding, the corresponding tooth surface regions are obtained. Then, the sand profile is obtained based on these tooth surface regions. The servo axis motion equation and meshing multi-point topology are obtained from the sand profile. By fine-tuning the servo axis motion parameters, the meshing multi-point topology machining of the corresponding regions is carried out.

[0057] When using form grinding, the grinding wheel spirals upwards along the workpiece's axial direction while simultaneously undergoing a parabolic motion along its radial direction, thus shaping the workpiece in the tooth width and tooth direction. Given the gear end section profile, the grinding profile can be solved using coordinate transformations and the contact equation between the grinding wheel and the workpiece. During form grinding, a family of contact lines exists on the workpiece's tooth surface. This family of contact lines is the collection of contact lines between the grinding wheel and the workpiece at every instant, forming the workpiece's tooth surface. The grinding profile can be solved using appropriate coordinate transformations. Conversely, when the grinding profile equation is known, the equation of the shaped tooth surface can also be obtained through the positional relationship and meshing equation between the grinding wheel and the workpiece.

[0058] like Figure 2 As shown, the workpiece gear is indexed while rotating along the C-axis, and the grinding wheel is fed along the radial X-axis of the workpiece. The C, X, and Z axes are linked to flexibly control the positional relationship between the gear and the grinding wheel in space, thus completing the tooth profile machining. During grinding wheel dressing, the Y and Z axes are linked to maintain a certain accuracy in the grinding profile. During machine measurement, the CNC system controls the linkage of the C, X, and Z axes to detect the tooth direction and profile, and obtain the tooth surface area. Based on the mathematical model and the tooth surface area, the grinding profile is obtained, denoted as r(u,θ), and the grinding profile is transformed from the workpiece coordinate system to the tool coordinate system. The corresponding equation is:

[0059]

[0060]

[0061] During form grinding, the geometric center of the control grinding wheel and the center of the gear tooth groove are always aligned. Therefore, the C-axis rotation angle is opposite to the workpiece rotation angle, and similarly, the A-axis rotation angle is opposite to the workpiece helix angle. The tooth surface equation can be obtained from the sand profile through coordinate transformation, and similarly, the sand profile can be obtained from the tooth surface equation through coordinate transformation. Since the corresponding angle and position parameters in the above equations can be obtained, the motion equations of each servo axis during CNC form grinding of the workpiece can be obtained, specifically:

[0062]

[0063] In the formula, φ1 is the workpiece rotation angle, and γ m It is a constant;

[0064] d f and d w δ, u1, and σ1 are the root circle diameter and pitch circle diameter of the gear, respectively; d1 is the grinding wheel diameter; β is the helix angle of the gear; δ, u1, and σ1 are gear parameters.

[0065] After coordinate transformation, the modified tooth surface vector (u, θ, q) is obtained from the sand profile, where u and θ are tooth surface parameters, and q is a motion parameter. The unit normal vector of the tooth surface in the coordinate system allows for the calculation of the tooth surface equation and the unit normal vector equation, thus yielding the meshing multi-point topological surface of the tooth surface and the sand profile. By fine-tuning the motion parameters of the servo axis, the machining of the meshing multi-point topological surface is carried out.

[0066] 3. Double-sided grinding

[0067] During grinding, the grinding wheel moves in a spiral motion along the workpiece axis and a parabolic motion along the radial direction. Compared to standard helical gear grinding, the grinding wheel adds a parabolic motion along the workpiece radial direction. A schematic diagram of the grinding wheel's motion along the tooth direction during helical gear modification is shown below. Figure 4As shown. Workpiece coordinate system O h X h Y h Z h Fixedly connected to the fixed frame of the gear mounting rotary table, the workpiece coordinate system O h X h Y h Z h It is fixedly connected to the workpiece, and the coordinate axis Z1 passes through the center of the rotary table and the workpiece axis. Grinding wheel coordinate system O c X c Y c Z c Relative to coordinate system O h X h Y h Z h The motion is when the workpiece coordinate system O h X h Y h Z h When it rotates around the Z1 axis through an angle φ1, its coordinate origin is along the Z... a Move a distance L1 = p1φ1 in the direction, and simultaneously move along X h Move a distance α in the positive direction x .

[0068] During double-sided grinding along the tooth direction on a CNC profile grinding machine, the grinding wheel also needs to move in two directions: the X-axis and the Z-axis. In the X-axis direction, the grinding wheel completes a radial feed motion along the workpiece while simultaneously incorporating a parabolic motion to achieve tooth profile shaping. In the Z-axis direction, similar to grinding standard cylindrical helical gears, the grinding wheel completes a helical motion along the workpiece axis to ensure grinding along the entire tooth width. The motion equations of the grinding wheel in the x and c directions during profile shaping can be expressed as follows:

[0069] Cx(φ1)=(d f +d w ) / 2-α x

[0070] Cz(φ1)=P1φ1=(d1ctgβ / 2)·φ1

[0071] From the formula, we can obtain α. x The magnitude of the normal profile modification amount in bidirectional grinding is extracted and assigned to achieve bidirectional grinding.

[0072] 4. Gear trimming.

[0073] In CNC gear grinding, the tooth profile is modified by dressing the grinding wheel.

[0074] Grinding wheel dressing, also known as wheel dressing, is called bypass machining or self-cutting machining in system operation. The value of gears is determined by their precision. In the process from wheel dressing to grinding, the precision of each step is intricately linked. Different machine tool structures and different grinding wheel materials are suited to different wheel dressing methods. In this invention, wheel dressing employs a method based on helical surface forming machining compensation and interference reduction.

[0075] After machining a gear tooth profile, the grinding wheel is dressed. Different dressing methods and techniques will produce different interference amounts. During the dressing process, the grinding wheel diameter will decrease, such as... Figure 5 As shown, the interference amount changes with the diameter of the grinding wheel. When the diameter of the grinding wheel is less than a certain value, the interference phenomenon disappears. In order to ensure that the interference error remains at the same level in each grinding operation, it is necessary to recalculate the interference compensation amount and the grinding profile based on the dressing amount of the grinding wheel.

[0076] Analysis of the interference mechanism in helical surface forming processes reveals that when a disc grinding wheel is used to machine a helical surface, an excess portion is removed at the edge of the workpiece's cross-section, resulting in interference. The essence of this interference is that the grinding wheel radius is not the minimum distance from any point on the helical surface to the tool center. Therefore, with parameters such as the angle between the grinding wheel axis and the workpiece axis remaining constant, the interference between the grinding wheel and the helical surface gradually decreases as the radius of the forming grinding wheel's cross-section decreases. When the grinding wheel's cross-section radius is less than a certain value, the interference disappears. However, when a given grinding wheel diameter is used to calculate the forming grinding wheel's cross-section using the previously described method, interference may still occur when machining a helical surface with that cross-section.

[0077] like Figure 6 As shown, since the rotating surface of the grinding wheel is tangent to the helical surface of the workpiece, in any section perpendicular to the axis of the grinding wheel, the cross-section of the grinding wheel will necessarily be tangent to the cross-section of the helical surface. There are two types of tangency: such as... Figure 6 As shown in A1, the arc of the grinding wheel's cross-section is outside the workpiece; in this case, no interference will occur. Figure 6 As shown in A2, the arc of the grinding wheel is within the workpiece solid. Figure 6 In A1, the workpiece profile is tangent to the forming grinding wheel profile at point C. At this point, the grinding wheel arc is outside the workpiece solid and will not cause interference. Figure 6 In A2, the workpiece profile is tangent to the profile of the forming grinding wheel at C2. At this time, the arc of the grinding wheel is inside the workpiece body, and during machining, the part that should not be cut off will inevitably be cut off, thus causing interference.

[0078] When machining interference occurs, the reverse error principle compensation is activated to perform sand repair. Different structures require the use of corresponding compensation data, and the corresponding threshold settings vary depending on the grinding wheel material and structure.

[0079] There is an error between the theoretical helical surface profile and the actual helical surface profile machined by the forming grinding wheel. The theoretical helical surface profile of the gear can be obtained using the previous mathematical model and corresponding parameters. The actual helical surface profile can be obtained by inspecting the gear. The theoretical and actual helical surface profiles are discretized to obtain multiple discrete points. These discrete points are then compared with the discrete points on the actual helical surface profile in a one-to-one correspondence, and the distance between the two discrete points is defined as the interference error. When the interference error exceeds a set threshold, machining interference is considered to have occurred.

[0080] like Figure 7 As shown, in the region where the theoretical and actual cross-sections of the helical surface interfere, P1 is a point on the actual cross-section of the helical surface actually machined by the forming tool, and its relationship with the corresponding theoretical cross-section point P is... c The distance ε1 is the forming interference error at point P. To eliminate error ε1, at point P... c A new calculation point P2 is generated relative to point P1, serving as the virtual workpiece profile point. Using this virtual point as the new initial calculation point, a new forming tool point is calculated. It is expected that the interference error of the workpiece profile point P3 produced by the forming tool formed by this new forming tool point will be within acceptable limits. Because the compensation amount is the inverse value of the interference error, this method has been verified to enable diverse sand dressing on gear grinding machines with different structures, and the error is controllable.

[0081] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-axis linkage and multi-point following tooth surface topology modification method, implemented by a multi-axis linkage CNC system controlling a grinding wheel and gear, characterized in that, The multi-axis linkage CNC system includes at least three linear coordinate axes (X, Y, Z) and two rotary coordinate axes (A, C); the grinding wheel moves helically along the gear axis and parabolically along the gear radial direction. Includes the following steps: S01, Establish a mathematical model of the gear tooth surface and the sand profile; Based on the intersection of the normal on the gear helical tooth surface and the grinding wheel axis, find all the contact points between the gear and the grinding wheel, and then obtain the contact line. Then, rotate the contact line around the grinding wheel axis to obtain the sand profile. S02, the gear tooth surface is meshed, and the gear is indexed while rotating along the C-axis. The grinding wheel is fed along the radial X-axis of the gear. The geometric center of the grinding wheel is kept collinear with the center of the gear tooth groove. The C-axis, X-axis, and Z-axis are linked to detect the tooth direction and tooth profile of the gear, obtaining the tooth surface area. The sand profile is obtained based on the tooth surface area and the mathematical model in S01. The motion equations of the workpiece rotation angle and the servo axis are established using the sand profile and gear parameters. The unit normal vector of the tooth surface is calculated using the sand profile, and the tooth surface equation and the unit normal vector equation of the tooth surface are solved to obtain the meshing multi-point topological surface of the tooth surface and the sand profile. The machining of the meshing multi-point topological surface is carried out by fine-tuning the motion parameters of the servo axis. S03: After machining the gear tooth profile once with the grinding wheel, the grinding wheel is dressed. The theoretical cross-section of the helical surface is calculated based on the input parameters. The actual cross-section of the gear's helical surface is obtained based on the detection. The points of the theoretical cross-section and the points of the actual cross-section are compared in a one-to-one correspondence, and the distance between the two points is calculated. When the distance between the two points is greater than a set threshold, reverse compensation is activated. A virtual compensation point is generated on the extension line from the point of the actual cross-section to the corresponding point of the theoretical cross-section. The distance from the virtual compensation point to the point of the theoretical cross-section is equal to the distance from the point of the actual cross-section to the corresponding point of the theoretical cross-section. The newly formed tool point is calculated using the virtual compensation point as the new initial calculation point. The grinding wheel is dressed according to the tool point. The grinding wheel profile is recalculated based on the dressed grinding wheel, and then the gear tooth profile is machined.

2. The tooth surface topology modification method with multi-axis linkage and multi-point following according to claim 1, characterized in that, In S01, the grinding wheel and the gear are absolutely offset, and an O is established on the grinding wheel. c X c Y c Z c The tool coordinate system is established on the gear, and the OX coordinate system is created. w Y w Z w Establish the workpiece coordinate system and the transformation formula between the tool coordinate system and the workpiece coordinate system; based on the intersection of the normals of the grinding wheel axis and the gear helical tooth surface, solve to obtain the contact line equation, and then rotate the contact line around the grinding wheel axis to obtain the grinding profile.

3. The tooth surface topology modification method with multi-axis linkage and multi-point following according to claim 1, characterized in that, The motion equation of the workpiece rotation angle and the servo axis is as follows: In the formula, φ1 is the workpiece rotation angle, γ m d is a constant; f and d w δ, u1, and σ1 are the root circle diameter and pitch circle diameter of the gear, respectively; d1 is the grinding wheel diameter; β is the helix angle of the gear; δ, u1, and σ1 are gear parameters.

4. The tooth surface topology modification method with multi-axis linkage and multi-point following according to claim 1, characterized in that, In S02, based on the sand profile, the modified tooth surface equation and the unit normal vector equation of the tooth surface are obtained through the positional relationship and meshing equation between the grinding wheel and the gear, and then the meshing multi-point topological surface of the tooth surface and the sand profile is obtained.

5. The tooth surface topology modification method with multi-axis linkage and multi-point following according to claim 1, characterized in that, The multi-axis linkage CNC system includes two grinding wheels, which simultaneously grind the gear.

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