Spiral bevel gear grinding tooth surface error multi-stage correction method

Abstract

The invention discloses a spiral bevel gear grinding tooth surface error multi-stage correction method which comprises the following steps: acquiring a cutter equation to obtain a cutter high-order equation; calculating a five-axis linkage equation to obtain a five-axis linkage high-order equation; obtaining a tooth surface measurement error value; an L-M algorithm is utilized, a tooth surface measurement error value and an adjustment coefficient initial value are input, whether the tooth surface measurement error value is larger than a preset value or not is judged, if yes, machining initial position correction is executed firstly, then small-error tooth surface error correction is executed, and if not, small-error tooth surface error correction is executed; the machining initial position correction comprises the following steps: taking a machining initial position error as an adjustment coefficient, carrying out L-M reverse adjustment calculation, and correcting a five-axis linkage high-order equation; the small-error tooth surface error correction comprises the following steps: screening high-order coefficients participating in reverse adjustment in a five-axis linkage high-order equation and a tool high-order equation, carrying out L-M reverse adjustment calculation, and correcting to obtain a final five-axis linkage high-order equation and a final tool high-order equation. The method is high in correction capability and high in efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of gear processing, and in particular to a multi-stage correction method for tooth surface errors of spiral bevel gear grinding. Background Art

[0002] The tooth surface geometry of spiral bevel gears is complex, and their high-precision manufacturing has always been a key issue in production. Five-axis CNC machine tools replace the complex mechanical adjustment parameters of traditional machine tools through flexible multi-axis linkage, and can equivalently implement any processing method of traditional machine tools. Five-axis CNC machine tools have higher precision and efficiency during the processing process and can achieve high-precision manufacturing of complex tooth surfaces. Although multi-axis CNC machine tools have begun to be widely used in the manufacture of spiral bevel gears, most of these machines use complex mechanical adjustment card parameters to achieve tooth surface processing and counter-adjustment. In addition, the traditional adjustment card parameter counter-adjustment method of tooth surface has few adjustment parameters, so the correction capability is also limited. The adjustment of each parameter requires multiple tests and measurements. The whole process is time-consuming and the production efficiency is low, which cannot give full play to the flexibility of five-axis machine tools. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention proposes a multi-stage correction method for spiral bevel gear grinding tooth surface errors, which has strong correction capability and high efficiency.

[0004] The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to an embodiment of the present invention comprises the following steps:

[0005] Determine the design parameters of spiral bevel gear tooth surfaces;

[0006] Establishing a tool model, obtaining a tool equation, and changing the tool equation into a high-order surface form to obtain a tool high-order equation;

[0007] Establishing a five-axis machine tool kinematic chain, calculating a five-axis linkage equation, and performing a high-order expansion on the five-axis linkage equation to obtain a five-axis linkage high-order equation;

[0008] Establishing a tooth surface error model and obtaining a tooth surface measurement error value, wherein the tooth surface measurement error value represents the tooth surface error caused by machining;

[0009] Using the LM algorithm, the tooth surface measurement error value and the initial value of the adjustment coefficient are input to determine whether the tooth surface measurement error value is greater than a preset value. If so, the initial position correction is performed first, and then the tooth surface error correction of the small error is performed. If not, the tooth surface error correction of the small error is performed directly.

[0010] The processing initial position correction includes: using the processing initial position error as the adjustment coefficient, performing LM back-adjustment calculation to obtain the corrected adjustment coefficient, correcting the five-axis linkage high-order equation based on the corrected adjustment coefficient, and then correcting the tooth surface measurement error value based on the corrected five-axis linkage high-order equation;

[0011] The tooth surface error correction of small errors includes: analyzing the main tooth surface error forms, screening the high-order coefficients involved in the counter-adjustment in the five-axis linkage high-order equation and the tool high-order equation, using the high-order coefficients involved in the counter-adjustment as the adjustment coefficients, performing the LM counter-adjustment calculation, and obtaining the corrected adjustment coefficients. Based on the corrected adjustment coefficients, the final five-axis linkage high-order equations and the tool high-order equations are corrected.

[0012] The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to the embodiment of the present invention has at least the following beneficial effects:

[0013] In this embodiment, the tool equation and the five-axis linkage equation are expanded to a high order, thereby improving the degree of freedom and correction capability of the counter-adjustment; the initial processing position is corrected based on the LM algorithm, and an error analysis is performed; based on the error analysis results, the tool path and tool surface of the high-order free surface are reconstructed to achieve the counter-adjustment correction of the tooth surface error, thereby improving the accuracy of the correction; and based on the LM algorithm, the five-axis linkage high-order equation and the tool high-order equation are directly corrected, and after correction, processing can be directly performed based on the corrected equation without further conversion, with strong correction capability and high efficiency.

[0014] According to some embodiments of the present invention, if the tool is a curved tool, the tool equation is expressed as:

[0015]

[0016] If the tool is a linear tool, the tool equation is expressed as:

[0017]

[0018] Where r(S,θ) is the blade equation, n(S,θ) and n(θ) are the normal vectors, R is the grinding wheel radius, and P w is the tool tip distance, r c is the trimming radius, α is the pressure angle, S is the tool profile length, and θ is the tool phase angle.

[0019] According to some embodiments of the present invention, the tool high-order equation is expressed as:

[0020]

[0021] Among them, r0~r6 are high-order coefficients of tool profile.

[0022] According to some embodiments of the present invention, calculating the five-axis linkage equation includes:

[0023] Obtain the machine tool motion processing parameters in the adjustment card design parameters, perform equivalent conversion calculations on the tool spacing center and tool vector between the traditional machine tool motion chain and the five-axis machine tool motion chain, obtain the five-axis linkage equation, and solve the five-axis linkage equation as follows:

[0024]

[0025] The five-axis linkage equation represents the motion of the machine tool's two rotation axes, B and A, and three linear axes, X, Y, and Z. xw 、n yw 、n zw is the tool vector calculated based on the design parameters of the adjustment card, x jw 、y jw 、z jw It is the position of the tool center calculated according to the design parameters of the adjustment card, Z J is the clamping height of the cutter head, X P It is the X-direction offset from the A-axis turntable center to the B-axis rotation center when A=0, and Z P is the height of the turntable plane from the center of the B axis when A=0, X J is the workpiece fixture height.

[0026] According to some embodiments of the present invention, performing a high-order expansion on the five-axis linkage equation to obtain a five-axis linkage high-order equation includes:

[0027] For the five-axis linkage equation, the rocker angle Performing high-order expansion on the variables, the five-axis linkage high-order equation is obtained as follows:

[0028]

[0029] Among them, a b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 、a z0 ~a z6 are the high-order coefficients of the motion equations for the five axes.

[0030] According to some embodiments of the present invention, establishing a tooth surface error model and obtaining a tooth surface measurement error value includes:

[0031] The design parameters of the tool and the spiral bevel gear are obtained, and 5×9 theoretical tooth surface points are calculated based on the tool equation, the five-axis linkage high-order equation, the five-axis machine tool kinematic chain, the meshing principle and the tooth surface projection principle. A tooth surface error model can be established by introducing error amounts into the high-order coefficients in the five-axis linkage high-order equation in the derivation process to obtain error tooth surface points. Based on on-machine measurement technology, the actual tooth surface is measured along the normal vector direction of the theoretical tooth surface point to obtain a measurement point, and the distance between the measurement point and the theoretical tooth surface point is the tooth surface measurement error value.

[0032] According to some embodiments of the present invention, the LM back-modulation calculation includes:

[0033] (1) Calculating the sensitivity matrix of the adjustment coefficient to the error;

[0034] (2) calculating the change value of the adjustment coefficient according to the sensitivity matrix, and calculating the approximation error value after adding the change value of the adjustment coefficient;

[0035] (3) Determine whether the change value of the adjustment coefficient is less than the set iteration accuracy. If yes, exit the loop and output the corrected adjustment coefficient. If no, execute step (4).

[0036] (4) Determine whether the square of the optimization target decreases; if not, abandon the change value of the adjustment coefficient at this time, increase the damping factor, and repeat step (2); if yes, reduce the damping factor, enter the next cycle according to the adjustment coefficient at this time, and execute step (1);

[0037] The optimization target is a value obtained by subtracting the approximation error value from the tooth surface measurement error value.

[0038] According to some embodiments of the present invention, the modifying the five-axis linkage high-order equation based on the modified adjustment coefficient includes:

[0039] The corrected adjustment coefficient is subtracted from the five-axis linkage high-order equation to obtain the corrected five-axis linkage high-order equation.

[0040] According to some embodiments of the present invention, analyzing the main tooth surface error forms and screening the high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation include:

[0041] Perform sensitivity analysis on tooth surface errors, introduce small perturbations to the high-order coefficients in the five-axis linkage high-order equation and the high-order coefficients in the tool high-order equation, record the difference surface point sets generated by the transformation of each high-order coefficient, perform fourth-order surface fitting on the difference surface point sets, and analyze the main tooth surface error forms and the resulting error amounts;

[0042] The tooth surface measurement error value is fitted with a fourth-order surface, the tooth surface error form is analyzed, and matched with the existing difference surface sensitivity analysis data results, thereby screening the high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation.

[0043] According to some embodiments of the present invention, the final five-axis linkage high-order equation and the tool high-order equation are corrected based on the corrected adjustment coefficient, including:

[0044] The corrected adjustment coefficients are subtracted from the high-order coefficients involved in the inverse adjustment in the five-axis linkage high-order equation and the tool high-order equation to obtain the final five-axis linkage high-order equation and the tool high-order equation.

[0045] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0047] Figure 1 Schematic diagram of the tool shape according to an embodiment of the present invention;

[0048] Figure 2 is a simplified structural diagram of a five-axis machine tool according to an embodiment of the present invention;

[0049] Figure 3 Schematic diagram of a kinematic chain of a five-axis machine tool according to an embodiment of the present invention;

[0050] Figure 4 is a schematic diagram of a tooth surface error model according to an embodiment of the present invention;

[0051] Figure 5 1 is a schematic diagram of the process of high-order multi-stage tooth surface anti-adjustment according to an embodiment of the present invention;

[0052] Figure 6 Schematic diagram of a difference surface of a fourth-order fitting according to an embodiment of the present invention;

[0053] Figure 7 Schematic diagram of the effect of LM calculation approximating the error tooth surface, where (a) is the original error convex difference surface, (b) is the convex difference surface generated by LM calculation adjusting parameters, and (c) is the difference surface of the two convex error difference surfaces. DETAILED DESCRIPTION

[0054] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0055] In the description of the present invention, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0056] In the description of the present invention, "a plurality" refers to more than two. The use of "first" or "second" is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of the indicated technical features, or implicitly indicating the order of the indicated technical features.

[0057] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0058] Reference below Figures 1 to 7 A multi-stage correction method for tooth surface errors of spiral bevel gear grinding according to an embodiment of the present invention is described.

[0059] In order to better describe the multi-stage correction method for the tooth surface error of spiral bevel gear grinding according to an embodiment of the present invention, the LM algorithm is first described. The LM algorithm is an optimization algorithm for nonlinear least squares problems that combines the advantages of gradient descent and Gauss-Newton method. It searches for the minimum value of the objective function through the Jacobian matrix and iterative process, where the adjustment of the parameter λ (i.e., the damping factor) affects the behavior of the algorithm. During the iterative process, the Jacobian matrix is calculated and the parameter vector is adjusted until the convergence condition is reached. The LM algorithm is suitable for scenarios that solve nonlinear optimization problems.

[0060] The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to an embodiment of the present invention includes but is not limited to the following steps:

[0061] Step 1: Determine the design parameters of the spiral bevel gear tooth surface.

[0062] Step 2: Establish a tool model, obtain the tool equation, and then change the tool equation into a high-order surface form to obtain the tool high-order equation; it should be noted that during the back-adjustment correction, the tool can be modified to back-adjust the tooth surface error. Changing the tool equation into a high-order surface form can obtain a higher degree of freedom and improve the back-adjustment correction capability.

[0063] Step 3: According to the structure of the five-axis machine tool, establish the five-axis machine tool kinematic chain, and calculate the five-axis linkage equation based on the parameters of step 1, and then perform high-order expansion of the five-axis linkage equation to obtain the five-axis linkage high-order equation; It should be noted that, for example Figure 2 As shown, the five-axis machine tool has five axes, two rotary axes B and A, and three linear axes X, Y, and Z. The five-axis linkage equation represents the motion of the five axes of the machine tool, that is, the path of the tool.

[0064] Step 4: Establish the tooth surface error model and obtain the tooth surface measurement error value e m , tooth surface measurement error value e m Indicates the tooth surface error caused by machining.

[0065] Step 5: Perform high-order multi-level anti-adjustment on the tooth surface. The specific steps are as follows:

[0066] Using the LM algorithm, input the tooth surface measurement error value e m And the initial value of the adjustment coefficient x0, judge whether the tooth surface error is large, that is, the tooth surface measurement error value e m Is it greater than the preset value? If so, the initial position correction is performed first, and then the tooth surface error correction with small errors is performed. If not, the tooth surface error correction with small errors is performed directly. In this embodiment, the preset value is 10 times the single-point target error.

[0067] The initial processing position correction includes: taking the initial processing position error as the adjustment coefficient x (i.e. Figure 5 Select the five-axis 0-order coefficient correction in the LM, perform LM back-adjustment calculation, and obtain the corrected adjustment coefficient x. Based on the corrected adjustment coefficient x, correct the five-axis linkage high-order equation. Then, based on the corrected five-axis linkage high-order equation, calculate the tooth surface measurement error value e. m Correction; It should be noted that after the five-axis linkage high-order equation is corrected for processing, the corresponding processing error will also change, so it is necessary to measure the tooth surface error value e m Re-measure and obtain the new tooth surface measurement error value e m Obviously, if the initial position of the machining is corrected, the tooth surface measurement error value e m When it is greater than the preset value, the subsequent calculation should be based on the five-axis linkage high-order equation after the initial position correction, the tooth surface error model and the tooth surface measurement error value e m As the basis.

[0068] The tooth surface error correction of small errors includes: analyzing the main tooth surface error forms, screening the high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation, using the high-order coefficients involved in the anti-adjustment as the adjustment coefficient x, performing LM anti-adjustment calculation, and obtaining the corrected adjustment coefficient x. Based on the corrected adjustment coefficient x, the final five-axis linkage high-order equation and tool high-order equation are corrected to complete the correction and reconstruction of the tool path and tool surface. Subsequent processing is based on the final five-axis linkage high-order equation and tool high-order equation, and the anti-adjustment correction of the tooth surface error is completed.

[0069] It should be noted that a five-axis machine tool has five axes, such as Figure 2 As shown in the figure, each axis has an initial machining position error. This error is caused by manual installation and tool setting, and is the deviation between the initial theoretical machining coordinate system and the actual machining coordinate system. In this paper, the initial machining position errors of the B-axis, A-axis, X-axis, Y-axis, and Z-axis are represented by ΔB, ΔA, ΔX, ΔY, and ΔZ, respectively. In addition, small tooth surface error correction mainly corrects the combined errors caused by thermal errors and feed control errors during the machining process.

[0070] The multi-stage correction method for the tooth surface error of spiral bevel gear grinding in an embodiment of the present invention performs high-order expansion on the tool equation and the five-axis linkage equation, thereby improving the degree of freedom and correction capability of the counter-adjustment; based on the LM algorithm, the initial processing position is corrected, and error analysis is performed; based on the error analysis results, the tool path and tool surface of the high-order free surface are reconstructed to achieve the counter-adjustment correction of the tooth surface error, thereby improving the accuracy of the correction; and based on the LM algorithm, the five-axis linkage high-order equation and the tool high-order equation are directly corrected, and after correction, processing can be directly performed based on the corrected equation without further conversion, with strong correction capability and high efficiency.

[0071] In some embodiments of the present invention, if the tool is a curved tool, the tool equation is expressed as:

[0072]

[0073] If the tool is a linear tool, the tool equation is expressed as:

[0074]

[0075] Where r(S,θ) is the blade equation, n(S,θ) and n(θ) are the normal vectors, R is the grinding wheel radius, and P w is the tool tip distance, r c is the shaping radius, α is the pressure angle, S is the tool profile length, and θ is the tool phase angle; Figure 1An example of the tool's topography is shown in Figure 2. It should be noted that the tooth surface includes both concave and convex surfaces, and the pressure angle and trim radius values for concave and convex surfaces are different. When cutting concave surfaces, the outer cutting edge is used, and the addition and subtraction signs in the above equations are the upper ones. When cutting convex surfaces, the inner cutting edge is used, and the addition and subtraction signs in the above equations are the lower ones.

[0076] It is understandable that during the counter-adjustment correction, the tool can be modified to counter-adjust the tooth surface error. Therefore, in step 2, the tool equation is changed to a high-order surface form to obtain a high-order tool equation to obtain a higher degree of freedom. The tool high-order equation can be expressed as:

[0077]

[0078] Among them, r0~r6 are the high-order coefficients of the tool profile. In step 5, when performing small error tooth surface error correction, the high-order coefficients involved in the anti-adjustment in the tool high-order equation are screened from r0~r6; in addition, it should be noted that the tool equation for arc-type tools and linear tools is the same equation after being changed to the high-order surface form.

[0079] In some embodiments of the present invention, calculating the five-axis linkage equation specifically includes the following steps:

[0080] Get the machine tool motion processing parameters in the adjustment card design parameters, and combine the traditional machine tool motion chain with the five-axis machine tool motion chain (refer to Figure 3 As shown in the figure, perform equivalent conversion calculation of tool distance center and tool vector, calculate the five-axis linkage equation, and solve the five-axis linkage equation as follows:

[0081]

[0082] Among them, the five-axis linkage equation represents the movement of the machine tool's two rotary axes B and A and three linear axes X, Y, and Z. xw 、n yw 、n zw is the tool vector calculated based on the adjustment card design parameters, x jw 、y jw 、z jw It is the position of the tool center calculated according to the design parameters of the adjustment card, Z J is the clamping height of the cutter head, X P It is the X-direction offset from the A-axis turntable center to the B-axis rotation center when A=0, and Z P is the height of the turntable plane from the center of the B axis when A=0, X J is the workpiece fixture height.

[0083] Since the five axes in the above five-axis linkage equation are all cradle angles function of the angle, so the motion equation of each axis can be expressed as The high-order expansion is performed for the variables. Usually, the sixth order meets the requirements of the machining accuracy. Based on this, in some embodiments of the present invention, the five-axis linkage equation is expanded to obtain the five-axis linkage high-order equation, including the following steps: the five-axis linkage equation is expanded with the cradle angle Performing high-order expansion for the variables, the high-order equation of the five-axis linkage is obtained as follows:

[0084]

[0085] Among them, a b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 、a z0 ~a z6 are the high-order coefficients of the motion equations for the five axes.

[0086] In some embodiments of the present invention, in step 4, establishing a tooth surface error model and obtaining a tooth surface measurement error value specifically includes the following steps:

[0087] Obtain the design parameters of the tool and spiral bevel gear, and calculate the 5×9 theoretical tooth surface points (r1, r2, ..., r based on the tool equation, five-axis linkage high-order equation, five-axis machine tool kinematic chain, meshing principle and tooth surface projection principle. m ), by introducing the error amount into the high-order coefficients in the five-axis linkage high-order equation in the derivation process, the tooth surface error model can be established to obtain the error tooth surface point. The tooth surface error model is shown in the figure below. Figure 4 As shown in the figure; Based on the on-machine measurement technology, the actual tooth surface is measured along the normal vector direction of the theoretical tooth surface point to obtain the measurement points (P1, P2, ..., P m ), the distance between the measuring point and the theoretical tooth surface point is the tooth surface measurement error value (e1, e2,…, e m ), which is the tooth surface error caused by machining.

[0088] It should be noted that the tooth surface includes concave and convex surfaces. The calculated 5×9 theoretical tooth surface points refer to 45 theoretical tooth surface points on the concave and convex surfaces, a total of 90 theoretical tooth surface points. The number of measurement points corresponds to the number of theoretical tooth surface points, so the tooth surface measurement error value e m A total of 90 items.

[0089] Reference Figure 5 As shown, in some embodiments of the present invention, the main tooth surface error forms are analyzed, and the high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation are screened, which specifically includes the following steps:

[0090] The sensitivity analysis of the tooth surface error is performed, that is, the sensitivity analysis of each high-order coefficient is performed. A small perturbation (0.01° for the rotation axis and 0.1mm for the linear axis and tool) is introduced to the high-order coefficients (35) in the five-axis linkage high-order equation and the high-order coefficients (7) in the tool high-order equation. The difference surface point set generated by the transformation of each high-order coefficient is recorded, and the fourth-order surface fitting is performed on the difference surface point set, for example Figure 6 As shown, the main tooth surface error forms and the resulting error amounts are analyzed;

[0091] Measuring error value of tooth surface e m (A total of 90 items) perform fourth-order surface fitting, analyze the tooth surface error form, and match it with the existing difference surface sensitivity analysis data results, thereby screening the high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation.

[0092] Reference Figure 5 As shown, in some embodiments of the present invention, LM back-regulation calculation includes the following steps:

[0093] (1) Calculate the sensitivity matrix of the adjustment coefficient x to the error;

[0094] (2) Calculate the adjustment coefficient change value Δx (Δx1, Δx2, Δx3, ..., Δx n , n is the number of coefficients involved in the reverse adjustment), and calculate the approximation error value e after adding the adjustment coefficient change value Δx;

[0095] (3) Determine whether the adjustment coefficient change value Δx is less than the set iteration accuracy. If so, it means that a very accurate parameter result has been iteratively calculated, so the loop is exited and the corrected adjustment coefficient x is output. If not, the result is still inaccurate, and the next step (4) is executed.

[0096] (4) Determine whether the square of the optimization target S becomes smaller, and adjust the iterative parameter (damping factor λ) for the next iteration. When λ is set relatively large, it is equivalent to gradient descent, which is suitable for the situation where the current estimated parameters are far from the optimal solution. When λ is set relatively small, it is equivalent to Gauss-Newton, which is suitable for the situation where the estimated parameters are close to the optimal solution. The optimization target is the tooth surface measurement error value e mThe value obtained by subtracting the approximation error value e; if the judgment result is no, it means that the current estimated parameters are far from the optimal solution, then the adjustment coefficient change value Δx at this time is abandoned, the damping factor λ is increased, and step (2) is repeated, and the loop is entered from step (2); if the judgment result is yes, it means that the iteration direction is correct and the optimization target is approaching 0, then the damping factor λ is reduced, and the next round of loop is entered according to the adjustment coefficient x obtained at this time, and step (1) is executed; until Δx in the loop is less than the set iteration accuracy, the loop is jumped out, and the correction value of the adjustment coefficient x of the approximation error surface is obtained. Figure 7 A schematic diagram of the effect of LM calculation approximating the error tooth surface is given, where (a) is the original error convex difference surface, (b) is the convex difference surface generated by LM calculation adjusting parameters, and (c) is the difference surface of the two convex error difference surfaces.

[0097] It should be noted that the adjustment coefficient x is a substitute value. When performing the initial position correction, the LM back-adjustment calculation is performed, and the initial position errors ΔB, ΔA, ΔX, ΔY and ΔZ are selected as the adjustment coefficient x for iterative calculation. When performing the tooth surface error correction of small errors, r0~r6, a are selected. b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 、a z0 ~a z6 The selected high-order coefficients involved in the back-adjustment are used as the adjustment coefficient x for iterative calculation. The calculation method and principle are the same, only the parameter represented by the adjustment coefficient x is different. In addition, if the initial position correction is performed first and then the tooth surface error correction of small errors is performed, then when the tooth surface error correction of small errors is performed, the tooth surface measurement error value e in the LM back-adjustment calculation will be m It is the corrected tooth surface measurement error value obtained by correcting the initial machining position.

[0098] In some embodiments of the present invention, when performing the correction of the initial position of machining, the five-axis linkage high-order equation is corrected based on the corrected adjustment coefficient, including the steps of: subtracting the corrected adjustment coefficient from the five-axis linkage high-order equation to obtain the corrected five-axis linkage high-order equation, that is, subtracting the corrected adjustment coefficient x (i.e., ΔB, ΔA, ΔX, ΔY, and ΔZ) obtained by the current LM inverse adjustment calculation from the five-axis linkage high-order equation. Therefore, the five-axis linkage high-order equation after the correction of the initial position of machining can be expressed as:

[0099]

[0100] When performing the tooth surface error correction of small errors, the final five-axis linkage high-order equation and tool high-order equation are corrected based on the corrected adjustment coefficient, including the steps of: subtracting the corrected adjustment coefficient x obtained by the LM back-adjustment calculation from the high-order coefficients involved in the back-adjustment in the five-axis linkage high-order equation and the tool high-order equation, i.e., r0~r6, a b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 、a z0 ~a z6 The high-order coefficients that are screened out and participate in the anti-adjustment are correspondingly subtracted from the corrected adjustment coefficient x, and the other parameters remain unchanged to obtain the final five-axis linkage high-order equation and tool high-order equation.

[0101] Obviously, if the initial machining position correction is performed before the small error tooth surface error correction is performed, the five-axis linkage high-order equation after the initial machining position correction is used as the basis for the small error tooth surface error correction. If the small error tooth surface error correction is not performed directly, the five-axis linkage high-order equation obtained by performing a high-order expansion of the five-axis linkage equation is used as the basis; that is, in this embodiment, the subsequent steps are all calculated or analyzed based on the corrected values in the previous steps.

[0102] In order to facilitate the understanding of the content of the present invention, now according to the attached Figure 1-7 A multi-stage correction method for tooth surface error of spiral bevel gear grinding according to a specific embodiment of the present invention is described, and the specific steps are as follows:

[0103] Step 1: Determine the design parameters of the spiral bevel gear tooth surface.

[0104] Step 2: Establish a tool model and obtain the tool equation. If the tool is an arc-shaped tool, the tool equation is expressed as:

[0105]

[0106] If the tool is a linear tool, the tool equation is expressed as:

[0107]

[0108] Then the tool equation is changed into a high-order surface form, and the tool high-order equation (both tools with two morphologies are included) is obtained as follows:

[0109]

[0110] Step 3: Based on the five-axis machine tool structure, establish a five-axis machine tool kinematic chain. Then obtain the machine tool kinematic processing parameters in the adjustment card design parameters. Perform equivalent conversion calculations on the tool distance center and tool vector between the traditional machine tool kinematic chain and the five-axis machine tool kinematic chain. Calculate the five-axis linkage equation and solve it as follows:

[0111]

[0112] Then the five-axis linkage equation is converted into the rocking angle Performing high-order expansion for the variables, the high-order equation of the five-axis linkage is obtained as follows:

[0113]

[0114] Step 4: Obtain the design parameters of the tool and spiral bevel gear, and calculate the 5×9 theoretical tooth surface points (r1, r2, ..., r m ), 45 theoretical tooth surface points on each concave and convex surface, a total of 90 theoretical tooth surface points, by introducing the error amount into the high-order coefficients in the five-axis linkage high-order equation in the derivation process, the tooth surface error model can be established to obtain the error tooth surface points. The tooth surface error model is shown in the figure below. Figure 4 As shown in the figure; Based on the on-machine measurement technology, the actual tooth surface is measured along the normal vector direction of the theoretical tooth surface point to obtain the measurement points (P1, P2, ..., P m ), the distance between the measuring point and the theoretical tooth surface point is the tooth surface measurement error value (e1, e2,…, e m ), which is the tooth surface error caused by machining.

[0115] Step 5: Perform high-level multi-stage anti-adjustment on the tooth surface, refer to Figure 5 , the specific steps are as follows:

[0116] Using the LM algorithm, input the tooth surface measurement error value e m And the initial value of the adjustment coefficient x0, determine the tooth surface measurement error value e m Is it greater than 10 times the single-point target error? If so, perform the initial position correction first, and then perform the tooth surface error correction for small errors. If not, perform the tooth surface error correction for small errors directly.

[0117] The initial position correction process includes the following steps:

[0118] Taking the initial machining position error (ΔB, ΔA, ΔX, ΔY, and ΔZ) as the adjustment coefficient x, perform LM back-adjustment calculation to obtain the corrected adjustment coefficient x. Subtract the corrected adjustment coefficient x from the previously obtained five-axis linkage high-order equation to obtain the corrected five-axis linkage high-order equation, which is expressed as:

[0119]

[0120] Then the modified five-axis linkage high-order equation is used to perform gear grinding and measurement to obtain the new tooth surface measurement error value e m and the tooth surface measurement error value e m Updated to serve as the basis for subsequent calculations.

[0121] The correction of small tooth surface errors includes the following steps:

[0122] The sensitivity analysis of the tooth surface error is performed, that is, the sensitivity analysis of each high-order coefficient is performed. A small perturbation (0.01° for the rotation axis and 0.1mm for the linear axis and tool) is introduced to the high-order coefficients (35) in the five-axis linkage high-order equation and the high-order coefficients (7) in the tool high-order equation. The difference surface point set generated by the transformation of each high-order coefficient is recorded, and the fourth-order surface fitting is performed on the difference surface point set, for example Figure 6 As shown, the main tooth surface error forms and the resulting error amounts are analyzed;

[0123] Measuring error value of tooth surface e m (90 items in total) Perform fourth-order surface fitting, analyze the tooth surface error form, and match it with the existing difference surface sensitivity analysis data results to screen the latest five-axis linkage high-order equations and tool high-order equations for high-order coefficients involved in anti-tuning;

[0124] The selected high-order coefficients involved in the anti-adjustment are used as the adjustment coefficients x, and the LM anti-adjustment calculation is performed to obtain the corrected adjustment coefficient x. The corrected adjustment coefficient x obtained by the LM anti-adjustment calculation is subtracted from the high-order coefficients involved in the anti-adjustment in the latest five-axis linkage high-order equation and the tool high-order equation, i.e., r0~r6, a b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 、a z0 ~a z6 The corrected adjustment coefficient x is subtracted from the selected high-order coefficients involved in the anti-adjustment, and the other parameters remain unchanged to obtain the final five-axis linkage high-order equation and tool high-order equation; subsequent processing is based on the final five-axis linkage high-order equation and tool high-order equation, thus completing the anti-adjustment correction of the tooth surface error.

[0125] In addition, in step 5, the LM back-adjustment calculation includes the following steps:

[0126] (1) Calculate the sensitivity matrix of the adjustment coefficient x to the error;

[0127] (2) Calculate the adjustment coefficient change value Δx (Δx1, Δx2, Δx3, ..., Δx n , n is the number of coefficients involved in the reverse adjustment), and calculate the approximation error value e after adding the adjustment coefficient change value Δx;

[0128] (3) Determine whether the adjustment coefficient change value Δx is less than the set iteration accuracy. If so, it means that a very accurate parameter result has been iteratively calculated, so the loop is exited and the corrected adjustment coefficient x is output. If not, the result is still inaccurate, and the next step (4) is executed.

[0129] (4) Determine whether the square of the optimization target S becomes smaller. The optimization target is the tooth surface measurement error value e m The value obtained by subtracting the approximation error value e; if the judgment result is no, the adjustment coefficient change value Δx at this time is abandoned, the damping factor λ is increased, and step (2) is repeated, and the loop is entered from step (2); if the judgment result is yes, the damping factor λ is reduced at this time, and the next round of loop is entered according to the adjustment coefficient x obtained at this time, and step (1) is executed; until Δx in the loop is less than the set iterative accuracy, the loop is jumped out, and the corrected value of the adjustment coefficient x of the approximation error surface is obtained.

[0130] Among them, in the LM back-adjustment calculation, the adjustment coefficient x is a substitute value. When performing the initial position correction, the LM back-adjustment calculation is performed, and the initial position errors ΔB, ΔA, ΔX, ΔY and ΔZ are selected as the adjustment coefficient x for iterative calculation. When performing the tooth surface error correction of small errors, r0~r6, a are selected. b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 、a z0 ~a z6 The high-order coefficients selected for back-adjustment are used as adjustment coefficients x for iterative calculation. The calculation method and principle are the same, only the parameters represented by the adjustment coefficients x are different. In addition, if the initial position correction is performed first and then the tooth surface error correction for small errors is performed, then when the tooth surface error correction for small errors is performed, the tooth surface measurement error value e in the LM back-adjustment calculation is m It is the tooth surface measurement error value obtained by correcting the initial machining position.

[0131] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0132] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in the relevant technical field without departing from the scope of the present invention.

Claims

1. A multi-stage correction method for spiral bevel gear grinding tooth surface error, characterized in that: The steps include: Determine the design parameters of spiral bevel gear tooth surfaces; Establishing a tool model, obtaining a tool equation, and changing the tool equation into a high-order surface form to obtain a tool high-order equation; Establishing a five-axis machine tool kinematic chain, calculating a five-axis linkage equation, and performing a high-order expansion on the five-axis linkage equation to obtain a five-axis linkage high-order equation; Establishing a tooth surface error model and obtaining a tooth surface measurement error value, wherein the tooth surface measurement error value represents the tooth surface error caused by machining; Using the LM algorithm, the tooth surface measurement error value and the initial value of the adjustment coefficient are input to determine whether the tooth surface measurement error value is greater than a preset value. If so, the initial position correction is performed first, and then the tooth surface error correction of the small error is performed. If not, the tooth surface error correction of the small error is performed directly. The processing initial position correction includes: using the processing initial position error as the adjustment coefficient, performing LM back-adjustment calculation to obtain the corrected adjustment coefficient, correcting the five-axis linkage high-order equation based on the corrected adjustment coefficient, and then correcting the tooth surface measurement error value based on the corrected five-axis linkage high-order equation; The tooth surface error correction of small errors includes: analyzing the main tooth surface error forms, screening the high-order coefficients involved in the counter-adjustment in the five-axis linkage high-order equation and the tool high-order equation, using the high-order coefficients involved in the counter-adjustment as the adjustment coefficients, performing the LM counter-adjustment calculation, and obtaining the corrected adjustment coefficients. Based on the corrected adjustment coefficients, the final five-axis linkage high-order equations and the tool high-order equations are corrected.

2. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: If the tool is an arc-shaped tool, the tool equation is expressed as: If the tool is a linear tool, the tool equation is expressed as: Where r(S,θ) is the blade equation, n(S,θ) and n(θ) are the normal vectors, R is the grinding wheel radius, and P w is the tool tip distance, r c is the trimming radius, α is the pressure angle, S is the tool profile length, and θ is the tool phase angle.

3. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 2, characterized in that: The tool high-order equation is expressed as: Among them, r0~r6 are high-order coefficients of tool profile.

4. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: The calculation of the five-axis linkage equation includes: Obtain the machine tool motion processing parameters in the adjustment card design parameters, perform equivalent conversion calculations on the tool spacing center and tool vector between the traditional machine tool motion chain and the five-axis machine tool motion chain, obtain the five-axis linkage equation, and solve the five-axis linkage equation as follows: The five-axis linkage equation represents the motion of the machine tool's two rotation axes, B and A, and three linear axes, X, Y, and Z. xw 、n yw 、n zw is the tool vector calculated based on the design parameters of the adjustment card, x jw 、y jw 、z jw It is the position of the tool center calculated according to the design parameters of the adjustment card, Z J is the clamping height of the cutter head, X P It is the X-direction offset from the A-axis turntable center to the B-axis rotation center when A=0, and Z P is the height of the turntable plane from the center of the B axis when A=0, X J is the workpiece fixture height.

5. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 4, characterized in that: The five-axis linkage equation is expanded in a high-order manner to obtain a five-axis linkage high-order equation, including: For the five-axis linkage equation, the rocker angle Performing high-order expansion on the variables, the five-axis linkage high-order equation is obtained as follows: Among them, a b0 ~a b6 、a a0 ~a a6 、a x0 ~a x6 、a y0 ~a y6 a z0 ~a z6 are the high-order coefficients of the motion equations for the five axes.

6. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: The step of establishing a tooth surface error model and obtaining a tooth surface measurement error value includes: The design parameters of the tool and the spiral bevel gear are obtained, and 5×9 theoretical tooth surface points are calculated based on the tool equation, the five-axis linkage high-order equation, the five-axis machine tool kinematic chain, the meshing principle and the tooth surface projection principle. A tooth surface error model can be established by introducing error amounts into the high-order coefficients in the five-axis linkage high-order equation in the derivation process to obtain error tooth surface points. Based on on-machine measurement technology, the actual tooth surface is measured along the normal vector direction of the theoretical tooth surface point to obtain a measurement point, and the distance between the measurement point and the theoretical tooth surface point is the tooth surface measurement error value.

7. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: The LM back-adjustment calculation includes: (1) Calculating the sensitivity matrix of the adjustment coefficient to the error; (2) calculating the change value of the adjustment coefficient according to the sensitivity matrix, and calculating the approximation error value after adding the change value of the adjustment coefficient; (3) Determine whether the change value of the adjustment coefficient is less than the set iteration accuracy. If yes, exit the loop and output the corrected adjustment coefficient. If no, execute step (4). (4) Determine whether the square of the optimization target decreases; if not, abandon the change value of the adjustment coefficient at this time, increase the damping factor, and repeat step (2); if yes, reduce the damping factor, enter the next cycle according to the adjustment coefficient at this time, and execute step (1); The optimization target is a value obtained by subtracting the approximation error value from the tooth surface measurement error value.

8. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: The step of correcting the five-axis linkage high-order equation based on the corrected adjustment coefficient includes: The corrected adjustment coefficient is subtracted from the five-axis linkage high-order equation to obtain the corrected five-axis linkage high-order equation.

9. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: The analysis of the main tooth surface error forms and the screening of high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation include: Perform sensitivity analysis on tooth surface errors, introduce small perturbations to the high-order coefficients in the five-axis linkage high-order equation and the high-order coefficients in the tool high-order equation, record the difference surface point sets generated by the transformation of each high-order coefficient, perform fourth-order surface fitting on the difference surface point sets, and analyze the main tooth surface error forms and the resulting error amounts; The tooth surface measurement error value is fitted with a fourth-order surface, the tooth surface error form is analyzed, and matched with the existing difference surface sensitivity analysis data results, thereby screening the high-order coefficients involved in the anti-adjustment in the five-axis linkage high-order equation and the tool high-order equation.

10. The multi-stage correction method for spiral bevel gear grinding tooth surface errors according to claim 1, characterized in that: The final five-axis linkage high-order equation and the tool high-order equation are corrected based on the corrected adjustment coefficient, including: The corrected adjustment coefficients are subtracted from the high-order coefficients involved in the inverse adjustment in the five-axis linkage high-order equation and the tool high-order equation to obtain the final five-axis linkage high-order equation and the tool high-order equation.

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