Gear and its anti-adjustment correction method for tooth surface machining

Abstract

The present invention discloses a reverse adjustment and correction method for gear tooth surface machining, which includes the following steps: Step 1: Calculate the parameters of the machine tool moving axes: 11) Taking the relative position relationship between the tool and the gear tooth surface as the research object, obtain the first coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system; taking the machine tool moving axes as the research object, obtain the second coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system; 12) The first coordinate transformation matrix is equal to the second coordinate transformation matrix, solve to obtain the parameters of the machine tool moving axes, and deduce the theoretical tooth surface equation of the gear based on the obtained parameters of the machine tool moving axes; Step 2: Measure the tooth surface error; Step 3: Perform high-order reverse adjustment and correction on the machine tool moving axes based on the gear tooth surface error: 31) Represent the machine tool moving axes in the form of a high-order polynomial, obtain the deviation between the corrected tooth surface and the theoretical tooth surface, and establish an objective function for reducing the tooth surface error; 32) Solve the reverse adjustment and correction objective function. The present invention also discloses a gear.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear processing, and specifically relates to a gear and a reverse adjustment and correction method for tooth surface machining thereof. Background Art

[0002] The numerically controlled worm wheel gear grinding machine is a special machine tool for precision machining of the hard tooth surface of face gears, which directly determines the tooth surface accuracy of face gears, and further affects the overall performance of the whole machine using face gear transmission. Improving the grinding accuracy of face gears will greatly increase the popularization and application of face gears, which is of great significance to the entire face gear tooth manufacturing industry. However, during the face gear grinding process, there are many moving axes involved in the grinding linkage of the worm wheel gear grinding machine, and the machining accuracy is jointly affected by quasi-static geometric errors, dynamically changing thermal errors, and force-induced deformation errors, etc. However, the cost and difficulty of identifying, tracing, and compensating the geometric errors of the gear grinding machine, as well as the thermal errors and force-induced deformations during the grinding process, are extremely high.

[0003] In order to improve the grinding accuracy of face gears, the prior art mainly conducts research from two aspects. One is to identify, trace, and compensate the geometric errors of the numerically controlled gear grinding machine, or to identify and compensate the geometric errors of the machine tool that have a greater impact on the tooth surface accuracy during the face gear grinding process; the other is to perform reverse adjustment and correction on the tooth surface, but it is only applicable to the tooth surface of face gears using the dish-shaped wheel gear grinding method. Identifying and compensating the geometric errors of the machine tool do not fully consider the influence of the thermo-mechanical coupling effect on the tooth surface accuracy during the grinding process, and there is currently no reverse adjustment and correction method for the face gear worm wheel gear grinding method with high efficiency. In the prior art, improving the grinding accuracy of face gears mostly uses the method of multiple iterations, which seriously depends on the operator's experience, greatly reduces the grinding efficiency and the qualified rate is not high. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a gear and a reverse adjustment and correction method for tooth surface machining thereof, which perform high-order reverse adjustment on the machine tool motion cycle based on the measurement results of tooth surface errors, thereby reducing tooth surface errors and improving machining accuracy.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention first proposes a reverse adjustment and correction method for gear tooth surface machining, including the following steps:

[0007] Step 1: Calculate the parameters of the machine tool motion axes

[0008] 11) Taking the relative position relationship between the tool and the gear tooth surface as the research object, transform the tool tooth surface equation along the transformation from the tool coordinate system to the workpiece coordinate system to obtain the gear tooth surface equation and the first coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system;

[0009] Taking the machine tool moving axis as the research object, the second coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system is obtained;

[0010] 12) The first coordinate transformation matrix is equal to the second coordinate transformation matrix. Solve to obtain the machine tool moving axis parameters, and deduce the theoretical tooth surface equation of the gear from the obtained machine tool moving axis parameters;

[0011] Step 2: Measure the tooth surface error;

[0012] Step 3: Perform high-order inverse adjustment correction on the machine tool moving axis based on the gear tooth surface error

[0013] 31) Express the machine tool moving axis in the form of a high-order polynomial, obtain the deviation between the corrected tooth surface and the theoretical tooth surface, and establish an objective function for reducing the tooth surface error;

[0014] 32) Solve the inverse adjustment correction objective function.

[0015] Furthermore, in step 11), during the tooth surface machining process, the gear rotates at a constant speed The tool rotates around the axis at a ratio of the transmission ratio In addition, it linearly feeds l along the direction at an angle λ with its X-axis w ; Specifically, the first coordinate transformation matrix is:

[0016]

[0017] Among them, represents the first coordinate transformation matrix; represents the transformation matrix of the gear rotating around the axis ; M 20s0 (l w ) represents the transformation matrix of the tool linearly feeding l along the direction at an angle λ with its X-axis w ; M s0w0 represents the auxiliary matrix; represents the transformation matrix of the tool rotating around the axis ;

[0018] If the machine tool has three linear axes and three rotational axes, then the second coordinate transformation matrix is:

[0019]

[0020] Among them, T x , T y and T z respectively represent the moving distances of the three linear axes during the tooth surface machining process; and respectively represent the rotation angles of the three rotational axes during the tooth surface machining process; represents the second coordinate transformation matrix; Indicates that the gear rotates about the C axis transformation matrix; M f0g (T x ,T z ) indicates that the cutting tool moves along the X and Z axes by T x ,T z transformation matrix; Indicates that the cutting tool rotates about the A axis transformation matrix; M ec0 (T y ) indicates that the cutting tool moves along the Y axis by T y transformation matrix; Indicates that the cutting tool rotates about the B axis transformation matrix.

[0021] Furthermore, in step 12), let:

[0022] M fc = M 2w

[0023] The obtained machine tool motion axis parameters are:

[0024]

[0025] where i w2 represents the transmission ratio between the cutting tool and the gear; E 2s represents an inherent constant related to the gear radius and is also the termination position of the linear feed of the cutting tool; K1 and K2 are both machine tool inherent constants;

[0026] The theoretical tooth surface equation of the gear is derived based on the machine tool motion axis parameters as:

[0027]

[0028] where r f represents the gear tooth surface equation; represents the meshing equation between the cutting tool and the gear during rotation; represents the meshing equation between the cutting tool and the gear during movement; r w is the cutting tool tooth surface equation; u r , both represent the variables of the cutting tool equation.

[0029] Furthermore, in step two, the measuring points on the tooth surface are divided by the measuring point division method of Gleason, and the tooth surface error is measured using a tooth surface coordinate measuring instrument.

[0030] Furthermore, in step 31), the machine tool motion axes are expressed in the form of high-order polynomials:

[0031]

[0032] Among them, C a , C b and C c respectively represent the motion expressions of the A, B, and C axes; C x , C y and C z respectively represent the motion expressions of the X, Y, and Z axes; dC0 to dC6 represent the coefficients of each term of the high-order expression of the C-axis motion; dX0 to dX6 represent the coefficients of each term of the high-order expression of the X-axis motion; dY0 to dY6 represent the coefficients of each term of the high-order expression of the Y-axis motion; dZ0 to dZ6 represent the coefficients of each term of the high-order expression of the Z-axis motion; represents the i-th power of the gear rotation angle; represents the i-th power of the distance moved by the tool in the Y direction; i = 1, 2,..., 6;

[0033] The high-order polynomial coefficients of the machine tool motion axes are represented by a matrix as:

[0034] ξ = [ξ1, ξ2,..., ξ m T = [dC0, dC1,..., dC6,..., dZ0, dZ1,..., dZ6] T

[0035] Among them, ξ represents the high-order polynomial coefficient matrix of the machine tool motion axes; ξ j represents the j-th term of the high-order polynomial coefficient matrix of the modified tooth surface, j = 1, 2,..., m, and m represents the number of polynomial coefficients;

[0036] The deviation between the modified tooth surface and the theoretical tooth surface is obtained as:

[0037]

[0038] Among them, δ 2q (ξ j ) represents the deviation between the modified tooth surface and the theoretical tooth surface with respect to ξ j ; represents the tooth surface after modification with respect to ξ j ; represents the theoretical tooth surface; represents the j-th term of the high-order polynomial coefficients of the theoretical tooth surface; represents the normal vector of the theoretical tooth surface;

[0039] Then the objective function for reducing the tooth surface error is:

[0040]

[0041] Among them, n represents the total number of measurement points.

[0042] ​Further, in step 32), the Gauss-Newton method, the L-M method (Levenberg-Marquardt method), or the Dog-Leg method is used to solve the anti-adjustment correction objective function.

[0043] Further, the L-M method is used to solve the anti-adjustment correction objective function, and the solution of its Jacobian matrix is as follows:

[0044]

[0045] where J k (ξ (k) ) represents the Jacobian matrix; represents the deviation between the tooth surface after the k-th correction and the theoretical tooth surface, q = 1, 2,..., n.

[0046] The present invention also provides a gear manufactured by using the above-described anti-adjustment correction method for gear tooth surface machining.

[0047] Further, the gear is a face gear or a cylindrical gear.

[0048] The beneficial effects of the present invention are as follows:

[0049] The principle of the anti-adjustment correction method for gear tooth surface machining of the present invention is as follows: First, the motion axis parameters based on the machine tool structure are deduced, and the three-dimensional coordinates of the theoretical tooth surface and the measurement points are calculated; then, a high-order polynomial of the machine tool motion axis is constructed, the deviation between the gear tooth surface and the theoretical tooth surface is deduced, and an anti-adjustment correction objective function of the machine tool motion axis is established; finally, based on the gear tooth surface deviation actually measured by a three-coordinate measuring machine, the anti-adjustment correction of the motion axis is transformed into a non-linear least squares problem, and the coefficients of the high-order polynomial after the anti-adjustment correction of the machine tool motion axis are obtained by solving; it can realize the anti-adjustment correction of tooth surface machining and improve the tooth surface accuracy; moreover, the anti-adjustment correction method for gear tooth surface machining of the present invention can be applied to the anti-adjustment correction of the machine tool motion axis in the hobbing and worm grinding processes of face gears and cylindrical gears, and has the remarkable advantages of fast and stable solution speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] To make the objectives, technical solutions, and beneficial effects of the present invention clearer, the following drawings are provided for illustration:

[0051] Figure 1 It is a diagram of the relative position relationship between a face gear and a worm grinding wheel;

[0052] Figure 2 It is the motion axis coordinate system of a worm grinding machine;

[0053] Figure 3 It is the tooth surface measurement point on a plane;

[0054] Figure 4are the three-dimensional spatial coordinates of the measuring points on the tooth surface of the face gear on the tooth surface;

[0055] Figure 5 is the physical diagram of the tooth surface error measured by a coordinate measuring instrument; (a) cylindrical gear; (b) face gear;

[0056] Figure 6 is the tooth surface deviation obtained by measuring the face gear;

[0057] Figure 7 are the tooth surface deviations after correction before and after the tooth surface correction of the face gear; (a) before correction; (b) after correction. Specific Embodiment

[0058] The following further describes the present invention in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the exemplified embodiments are not intended to limit the present invention.

[0059] The gear tooth surface machining reverse adjustment and correction method of the present invention can be applied to the reverse adjustment and correction of the machine tool motion axes during the hobbing and worm grinding of face gears and cylindrical gears. In this embodiment, the most complex machining method: the worm grinding of face gears will be taken as an example to detail the specific implementation of the gear tooth surface machining reverse adjustment and correction method of the present invention. The reverse adjustment and correction of the other three machining methods can refer to this machining method to adjust the machine tool motion axes during the machining process to improve the tooth surface machining accuracy.

[0060] Specifically, the gear tooth surface machining reverse adjustment and correction method of this embodiment includes the following steps:

[0061] Step 1: Calculate the parameters of the machine tool motion axes

[0062] 11) Taking the relative position relationship between the tool and the gear tooth surface as the research object, the tooth surface equation of the tool is transformed along the transformation from the tool coordinate system to the workpiece coordinate system to obtain the tooth surface equation of the gear and the first coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system.

[0063] The relative position relationship between the face gear and the worm grinding wheel is as Figure 1 shown, and the coordinate systems S2 and S w are fixedly connected to the face gear and the worm grinding wheel respectively. During the gear grinding process, the face gear rotates at a constant speed and the worm grinding wheel rotates around the axis at a transmission ratio in addition to moving linearly in the direction at an angle λ to its X-axis by a distance l w . Specifically, the first coordinate transformation matrix is:

[0064]

[0065] Among them, Represents the first coordinate transformation matrix; Represents the rotation of the gear around the axis transformation matrix; M 20s0 (l w ) represents the linear feed of the tool along the direction at an angle λ to its X-axis by l w transformation matrix; M s0w0 Represents the auxiliary matrix; Represents the rotation of the tool around the axis transformation matrix;

[0066] Taking the machine tool motion axes as the research object, the second coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system is obtained. As Figure 2 shown, it is the motion axis coordinate system of the face gear worm grinding machine. This grinding machine has three linear axes (X, Y, Z) and three rotational axes (A, B, C). During the gear grinding process, the corresponding moving distances (T x , T y , T z ) and the rotational angles Coordinate system S f and S c are the workpiece (face gear) and tool (worm grinding wheel) coordinate systems respectively. Coordinate systems S g and S e are the auxiliary coordinate systems. K1 and K2 are both machine tool inherent constants. The face gear is installed on the C-axis of the machine tool, and the worm grinding wheel is installed on the B-axis of the machine tool. Then the second coordinate transformation matrix is:

[0067]

[0068] Among them, T x , T y and T z respectively represent the moving distances of the three linear axes during the tooth surface machining process; and respectively represent the rotational angles of the three rotational axes during the tooth surface machining process; Represents the second coordinate transformation matrix; Represents the rotation of the gear around the C-axis transformation matrix; M f0g (T x , T z ) represents the transformation matrix when the tool moves along the X and Z axes by T x , T z respectively; Represents the rotation of the tool around the A-axis transformation matrix; M ec (T y ) represents the transformation matrix when the tool moves along the Y-axis by T y ; Represents the rotation of the tool around the B-axis Transformation matrix

[0069] 12) The first coordinate transformation matrix is equal to the second coordinate transformation matrix. Solve to obtain the parameters of the machine tool's moving axes, and deduce the theoretical tooth surface equation of the gear from the obtained parameters of the machine tool's moving axes. That is, let:

[0070] M fc = M 2w

[0071] The obtained parameters of the machine tool's moving axes are:

[0072]

[0073] where i w2 represents the tool and gear transmission ratio; E 2s represents an inherent constant related to the gear radius and is also the termination position of the linear feed of the tool; K1 and K2 are both inherent constants of the machine tool;

[0074] The theoretical tooth surface equation of the gear deduced from the parameters of the machine tool's moving axes is:

[0075]

[0076] where r f represents the gear tooth surface equation; represents the meshing equation between the tool and the gear during tool rotation; represents the meshing equation between the tool and the gear during tool movement; r w is the tool tooth surface equation; u r , both represent the variables of the tool equation.

[0077] Step 2: Measure the tooth surface error

[0078] In this embodiment, the Gleason measurement point division method is used to divide measurement points on the tooth surface, and the tooth surface error is measured using a tooth surface three-coordinate measuring instrument. Specifically, as Figure 3 shown, the tooth surface points of the face gear obtained by solving are shrunk according to the Gleason measurement point division rule. Among them, the shrinkage in the tooth length direction is 10% of the entire tooth length, and the shrinkage in the tooth height direction is 5% of the entire tooth height. At the same time, it should be noted that the shrunk measurement points should avoid the tooth surface chamfer and the tooth groove width at the measurement points near the tooth root should be greater than the diameter of the measuring ball. The tooth surface points of the face gear in the plane projection are:

[0079]

[0080] where X represents the x coordinate of the tooth surface point after projection; Z represents the z coordinate of the tooth surface point after projection; x f represents the x coordinate of the spatial tooth surface point; y frepresents the y coordinate of the spatial tooth surface point; z f Represents the z coordinate of the spatial tooth surface point.

[0081] The process of measuring point planning is:

[0082] (1) Project the face gear tooth surface points onto the plane;

[0083] (2) The tooth surface points are contracted according to the Gleason rule to obtain the contracted tooth surface points, which are the measuring points on the plane;

[0084] (3) Based on the plane coordinates of the measuring point, the above two equations can be combined to solve the three-dimensional coordinates of the measuring point on the tooth surface. The measured point on the tooth surface of the face gear after solution is as follows: Figure 4 shown.

[0085] Specifically, a three-coordinate measuring machine is used to measure the tooth surface errors of cylindrical gears and face gears. Figure 5 (a) and 5(b).

[0086] Step 3: High-order anti-adjustment correction of machine tool motion axis based on gear tooth surface error

[0087] Based on the calculated parameters of the machine tool motion axis, the face gear is ground with a worm grinding wheel. Due to the combined influence of errors such as machine tool geometric error, thermal error and force-induced deformation error, there is a certain deviation between the face gear tooth surface obtained by grinding and the theoretical tooth surface, making it difficult for the face gear tooth surface to meet the accuracy requirements. Based on the deviation between the actual tooth surface of the face gear and the theoretical tooth surface obtained by measurement, the gear tooth surface processing back-adjustment correction method of this embodiment is used to reduce the tooth surface deviation of the face gear after grinding and improve the tooth surface accuracy. The essence of the back-adjustment correction is to perform back-adjustment correction on the machine tool motion axis so that the corrected tooth surface produces a topological tooth surface with a direction opposite to the actual grinding tooth surface deviation relative to the theoretical tooth surface, thereby reducing the deviation between the tooth surface processed by the machine tool motion axis after correction and the theoretical tooth surface, and meeting the tooth surface accuracy requirements.

[0088] 31) The machine tool motion axis is expressed as a high-order polynomial form, the deviation between the corrected tooth surface and the theoretical tooth surface is obtained, and the objective function for reducing the tooth surface error is established.

[0089] Specifically, during the grinding process, the A axis remains stationary, while the B and C axes rotate with a strict transmission ratio. The machine tool motion axis is expressed as a high-order polynomial:

[0090]

[0091] Among them, C a , C b and C c Represent the motion expressions of A, B and C axes respectively; C x , C y and Cz respectively represent the motion expressions of the X, Y, and Z axes; dC0 to dC6 represent the coefficients of each term of the high-order expression of the C-axis motion; dX0 to dX6 represent the coefficients of each term of the high-order expression of the X-axis motion; dY0 to dY6 represent the coefficients of each term of the high-order expression of the Y-axis motion; dZ0 to dZ6 represent the coefficients of each term of the high-order expression of the Z-axis motion; represents the i-th power of the rotation angle of the gear; represents the i-th power of the moving distance of the tool in the Y direction; i = 1, 2,..., 6;

[0092] The high-order polynomial coefficients of the machine tool motion axes are represented by a matrix as:

[0093] ξ = [ξ1, ξ2,..., ξ m T = [dC0, dC1,..., dC6,..., dZ0, dZ1,..., dZ6] T

[0094] where ξ represents the high-order polynomial coefficient matrix of the machine tool motion axes; ξ j represents the j-th term of the high-order polynomial coefficient matrix of the modified tooth surface, j = 1, 2,..., m, and m represents the number of polynomial coefficients;

[0095] The deviation between the modified tooth surface and the theoretical tooth surface is obtained as:

[0096]

[0097] where δ 2q (ξ j ) represents the deviation between the modified tooth surface and the theoretical tooth surface with respect to ξ j ; represents the tooth surface after modification with respect to ξ j ; represents the theoretical tooth surface; represents the j-th term of the high-order polynomial coefficients of the theoretical tooth surface; represents the normal vector of the theoretical tooth surface;

[0098] Then the objective function for reducing the tooth surface error is:

[0099]

[0100] where n represents the total number of measurement points.

[0101] 32) Solve the inverse adjustment correction objective function.

[0102] ​The high-order polynomial inverse adjustment correction objective function of the motion axes of a face gear hob-type grinding machine is a typical non-linear least squares problem. The solution methods include the Gauss-Newton method, the L-M method (Levenberg-Marquardt method), and the Dog-Leg method. Usually, the Gauss-Newton method converges relatively fast but is unstable. The L-M method is a damped Gauss-Newton method, and the Dog-Leg method uses a trust region instead of a damping term. Both methods have a relatively fast solution speed and good stability. In this embodiment, the L-M method is used to solve the inverse adjustment correction objective function, and its Jacobian matrix solution is as follows:

[0103]

[0104] Among them, J k (ξ (k) ) represents the Jacobian matrix; represents the deviation between the tooth surface after the k-th correction and the theoretical tooth surface, q = 1, 2,..., n.

[0105] The measuring points of the tooth surface of the face gear after grinding are measured by a coordinate measuring machine, and the measured tooth surface deviation is as Figure 6 shown. The standard gear of the face gear is projected, and the tooth surface deviation of the face gear measured by the coordinate measuring machine after grinding the worm grinding wheel is represented on this plane, as Figure 7 (a) shown. Based on the tooth surface deviation of the coordinate measuring machine, the inverse adjustment correction method is used to perform inverse adjustment correction on the motion axes of the machine tool during the grinding process, and the tooth surface deviation of the face gear obtained is as Figure 7 (b) shown.

[0106] In addition, the inverse adjustment correction method for gear tooth surface machining in this embodiment is also applicable to the inverse adjustment correction of the motion axes of the machine tool during the hobbing of cylindrical gears, the hob-type grinding of worm grinding wheels, and the hobbing of face gears. However, it is necessary to measure the machined tooth surface by the 45-point measurement method using a coordinate measuring machine. The number of measurement points can be increased as needed, but it is necessary to ensure that they are evenly distributed on the tooth surface. According to the measurement results, this method is used to perform inverse adjustment correction on the motion axes of the machine tool, thereby improving the tooth surface accuracy.

[0107] This embodiment also proposes a gear obtained by machining using the inverse adjustment correction method for gear tooth surface machining as described above. Specifically, the gear is a face gear or a cylindrical gear.

[0108] The above-described embodiments are only preferred embodiments cited to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for reverse adjustment and correction of gear tooth surface machining, characterized in that: It includes the following steps: Step 1: Calculate the parameters of the machine tool's moving axes 11) Taking the relative position relationship between the cutting tool and the gear tooth surface as the research object, during the tooth surface machining process, the gear rotates at a constant speed , and the cutting tool rotates around the axis at the transmission ratio . In addition, it linearly feeds along the direction forming an angle with its X-axis ; Transform the cutting tool tooth surface equation along the transformation from the cutting tool coordinate system to the workpiece coordinate system to obtain the gear tooth surface equation and the first coordinate transformation matrix from the cutting tool coordinate system to the workpiece coordinate system; Taking the machine tool's moving axes as the research object, since the machine tool has three linear axes and three rotary axes, obtain the second coordinate transformation matrix from the tool coordinate system to the workpiece coordinate system; 12) Consider the inherent constants of the machine tool and , the first coordinate transformation matrix is equal to the second coordinate transformation matrix, solve to obtain the parameters of the machine tool's moving axes, and deduce the theoretical tooth surface equation of the gear from the obtained parameters of the machine tool's moving axes; Step 2: Measure the tooth surface error Divide the measurement points on the tooth surface according to Gleason's measurement point division method, and use a three-coordinate measuring instrument for the tooth surface to measure the tooth surface error; Step 3: Perform high-order inverse adjustment correction on the machine tool's moving axes based on the gear tooth surface error 31) Represent the machine tool's moving axis as a sixth-order polynomial form, and include the gear rotation angle and the moving distance of the tool in the Y direction For the two variables, obtain the deviation between the corrected tooth surface and the theoretical tooth surface, and establish an objective function to reduce the tooth surface error; 32) Use the L-M method to solve the inverse adjustment correction objective function; In step 11), the first coordinate transformation matrix is: Among them, represents the first coordinate transformation matrix; represents the transformation matrix of the gear rotating around the axis ; represents the linear feed of the cutting tool along the direction forming an angle with its X-axis ; represents the auxiliary matrix; represents the transformation matrix of the cutting tool rotating around the axis ; The second coordinate transformation matrix is: Among them, , and respectively represent the moving distances of three linear axes during the tooth surface machining process; , and respectively represent the rotation angles of three rotary axes during the tooth surface machining process; represents the second coordinate transformation matrix; represents the transformation matrix when the gear rotates around the C axis ; represents the transformation matrix when the cutting tool moves along the X and Z axes respectively ; represents the transformation matrix when the cutting tool rotates around the A axis ; represents the transformation matrix when the cutting tool moves along the Y axis ; represents the transformation matrix when the cutting tool rotates around the B axis ; In step 12), let: The obtained parameters of the machine tool's moving axes are: Among them, represents the tool and gear transmission ratio; represents an inherent constant related to the gear radius and is also the termination position of the linear feed of the tool; and are both inherent constants of the machine tool; The theoretical tooth surface equation of the gear deduced according to the parameters of the machine tool's moving axes is: Among them, represents the gear tooth surface equation; represents the meshing equation between the tool and the gear during tool rotation; represents the meshing equation between the tool and the gear during tool movement; is the tool tooth surface equation; and both represent the variables of the tool tooth surface equation; In step 31), the machine tool moving axes are expressed in the form of a high-order polynomial: Among them, , and represent the motion expressions of the A, B, and C axes respectively; , and represent the motion expressions of the X, Y, and Z axes respectively; ~ represent the coefficients of each term of the high-order expression of the C-axis motion; ~ represent the coefficients of each term of the high-order expression of the X-axis motion; ~ represent the coefficients of each term of the high-order expression of the Y-axis motion; ~ represent the coefficients of each term of the high-order expression of the Z-axis motion; represents the th power of the gear rotation angle; represents the th power of the distance the tool moves in the Y direction; ; Express the high-order polynomial coefficients of the machine tool's moving axes in matrix form as: Among them, represents the high-order polynomial coefficient matrix of the machine tool motion axis; represents the -th term of the high-order polynomial coefficient matrix of the modified tooth surface, , represents the number of polynomial coefficients; The deviation between the corrected tooth surface and the theoretical tooth surface is: Among them, represents the deviation between the corrected tooth surface and the theoretical tooth surface with respect to ; represents the tooth surface after correction with respect to ; represents the theoretical tooth surface; represents the -th term of the high-order polynomial coefficients of the theoretical tooth surface; represents the normal vector of the theoretical tooth surface; Then the objective function for reducing the tooth surface error is: Among them, represents the total number of measurement points.

2. The gear tooth surface machining reverse adjustment and correction method according to claim 1, characterized in that: Use the L-M method to solve the inverse adjustment correction objective function, and its Jacobian matrix solution is: Among them, represents the Jacobian matrix; represents the deviation between the tooth surface after the -th correction and the theoretical tooth surface.

3. A gear, characterized in that: It is processed by using the gear tooth surface machining inverse adjustment correction method as described in claim 1 or 2.

4. The gear according to claim 3, characterized in that: The gear is a face gear or a cylindrical gear.

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