Tooth profile slope deviation correction method for powerful tooth turning machining

Abstract

The invention relates to the technical field of gear machining, in particular to a powerful gear turning machining tooth profile slope deviation correction method which comprises the steps that a tooth profile slope deviation calculation formula containing the tool pose parameter adjustment amount is established; establishing a mapping relational expression between the matrix of the cutter pose parameter adjustment amount and the matrix of the tooth profile slope deviation; solving a polynomial coefficient in the mapping relational expression; setting a calculation error threshold value of the tooth profile slope deviation; the actually detected tooth profile slope deviation is input, and the corrected value of the tool pose parameter is obtained through back calculation; and the corrected value of the tool pose parameter is input into machine tool operation software, and after gear turning machining is completed, correction of the tooth profile slope deviation is achieved. Compared with a traditional correction method of multiple adjustment-trial cutting-detection feedback, the method is not limited by a machine tool structure, the operation process is simple and convenient, and the tooth profile slope error caused by the tool installation parameter error or the tool regrinding error can be corrected only by adjusting the tool installation parameter for one time.

Description

Technical Field

[0001] This invention relates to the field of gear machining technology, and in particular to a method for correcting the deviation of tooth profile slope in high-power gear turning. Background Technology

[0002] Gears are key basic components in many industries, and their machining technology is crucial to ensuring gear transmission performance. High-power gear turning is an emerging gear machining process with significant advantages such as high efficiency, high precision, and environmentally friendly dry cutting. It has become the preferred process for machining automotive transmission gears and precision reducer gears for robots.

[0003] In the gear machining process on heavy-duty gear turning machines, thermal and force-induced errors of the machine tool, as well as manufacturing and installation errors of the cutting tools, can lead to deviations in the machined gear tooth surface. Tooth profile slope deviation, as an important indicator of gear accuracy, is used to evaluate the average degree of inclination between the actual machined tooth profile and the theoretical tooth profile within the evaluation range. Typically, tooth profile slope deviation is influenced by the coupling effect of various machine tool and cutting tool errors, which greatly complicates the tracing and correction of this deviation. Although some companies can reduce tooth profile slope deviation by repeatedly adjusting the gear turning tool installation parameters, performing trial cuts, and detecting feedback, this trial-cutting method is somewhat blind, has low machine tool adjustment efficiency, and yields unsatisfactory correction results. Therefore, how to quickly correct tooth profile slope deviation based on the technical principles of gear turning machines is a key problem that urgently needs to be solved in gear turning technology. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for correcting tooth profile slope deviation in high-power gear turning based on adjusting tool installation parameters. This method can quickly correct tooth profile slope deviation in gear turning. Compared with the traditional trial-cut adjustment method, this invention has the advantages of high adjustment efficiency and high accuracy.

[0005] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0006] A method for correcting the slope deviation of tooth profile in high-strength gear machining includes:

[0007] S1: Establish a calculation formula for the tooth profile slope deviation δ, which includes the tool pose parameter adjustment amount. The tool pose parameter adjustment amount includes: the tool mounting axis angle adjustment amount ΔΣ, and the offset distance ΔY of the tool rotation center along the Y-axis of the machine tool. The calculation formula is as follows:

[0008] δ=M w-S1 M S1-S2 M S2-t r t -M w-S1 M′ S1-S2 MS2-t r t

[0009] Where, r t M is the matrix of tool cutting edge data points. w-S1 Let M be the spatial transformation matrix from the stationary coordinate system of the gear to the moving coordinate system of the gear. S2-t Let M be the spatial transformation matrix from the tool's moving coordinate system to the tool's stationary coordinate system. S1-S2 Let M′ be the spatial transformation matrix from the gear moving coordinate system to the tool moving coordinate system. S1-S2 This is the spatial transformation matrix from the gear static coordinate system to the tool static coordinate system, which includes tool pose parameter adjustments.

[0010] S2: Establish the mapping relationship between the matrix of tool pose parameter adjustment and the matrix of tooth profile slope deviation:

[0011] [B]·[ρ]=[F]

[0012] In this matrix, [B] is a j×6 matrix, where each column represents the element of each term in the polynomial with respect to ΔΣ and ΔY, and the j rows represent the number of different combinations of ΔΣ and ΔY values; matrix [ρ] is a 6×1 matrix containing the coefficients of the 6 polynomials to be solved; and matrix [F] is a j×1 matrix representing the tooth profile slope deviation values ​​corresponding to different combinations of ΔΣ and ΔY values.

[0013] S3: Solve for the polynomial coefficients in the mapping relation;

[0014] S4: Set the calculation error threshold for tooth profile slope deviation;

[0015] S5: Input the actual detected tooth profile slope deviation, and calculate the correction value of the tool pose parameter based on the mathematical expressions in steps S2 and S3.

[0016] S6: Input the correction value of the tool pose parameter calculated in step S5 into the machine tool operation software. After the gear turning is completed, the tooth profile slope deviation can be corrected.

[0017] Furthermore, the directions of the machine tool coordinate axes are as follows: the X-axis direction of the machine tool is consistent with the center distance direction from the tool to the workpiece, the Z-axis direction of the machine tool is consistent with the rotation axis direction of the workpiece, and the Y-axis direction of the machine tool is perpendicular to both the X-axis and Z-axis of the machine tool.

[0018] Furthermore, the process of calculating the tooth profile slope deviation in step S2 includes: processing the tooth profiles on both sides of the gear into i discrete points, and using the tooth profile deviation calculation formula to sequentially calculate the set of tooth profile deviations [δ] for all discrete points within the evaluation height H range of the tooth profiles on both sides. L(i) ]、[δ R(i)], where the subscript "L" represents the left tooth profile and the subscript "R" represents the right tooth profile, and the set of tooth profile deviations on both sides are obtained by linear fitting using the least squares fitting method [δ] L(i) ]、[δ R(i) The slope of the obtained linear equation is the deviation of the tooth profile slope fhα on both sides. L fhα R .

[0019] Furthermore, the mapping relationship in step S2 is represented by a matrix as follows:

[0020]

[0021] Furthermore, the formula for solving the polynomial coefficients in step S3 is as follows:

[0022] [ρ]=([B] T [B]) -1 [B] T [F]

[0023] In the calculation formula, the superscript "T" represents the transpose matrix, and the superscript "-1" represents the inverse matrix.

[0024] Furthermore, the calculation error threshold for the tooth profile slope deviation in step S4 refers to the upper limit of the difference between the actual detected tooth profile slope deviation and the theoretically calculated tooth profile slope deviation, denoted as Δfhα. The maximum value of this calculation error threshold does not exceed the actual detected tooth profile slope deviation (fhα). L ',fhα R 30% of the maximum value in ').

[0025] Furthermore, the calculation process for the correction value of the tool pose parameters based on the actual detected tooth profile slope deviation in step S5 is as follows:

[0026] Based on the calculated polynomial coefficient matrix [ρ], input the actual detected tooth profile slope deviation (fhα). L ',fhα R Then, using the formula [B]·[ρ]=[F], the correction values ​​(ΔΣ', ΔY') of the tool pose parameters are calculated in reverse; then, the calculated correction values ​​(ΔΣ', ΔY') of the tool pose parameters are substituted into the calculation formula in step S1 to obtain the theoretically calculated tooth profile slope deviation (fhα). L fhα R By comparing the actual measured deviation of the tooth profile slope with the theoretically calculated deviation, the difference in the calculation error of the tooth profile slope deviation (Δfhα) is obtained. L ,Δfhα R If the absolute value of the difference in the calculation error of the tooth profile slope deviation is (|Δfhα)L |、|Δfhα R If all values ​​are less than the set error threshold Δfhα for the tooth profile slope deviation, the final corrected values ​​of the tool pose parameters (ΔΣ', ΔY') are obtained; otherwise, return to step S4 to increase the error threshold for the tooth profile slope deviation and repeat the calculation process of step S5.

[0027] The beneficial effects of this invention are:

[0028] 1) Compared with the traditional correction method of multiple adjustments, trial cuts and detection feedback, the tooth profile slope deviation correction method of the present invention does not require operators to repeatedly try and find the pattern. It only requires adjusting the tool installation parameters once to effectively correct the tooth profile slope deviation in gear turning.

[0029] 2) The tooth profile slope deviation correction method of the present invention can not only correct the tooth profile slope deviation caused by the error of the tool installation parameters, but also correct the principle error caused by the regrinding of the conical turning tool, and can further improve the service life of the conical turning tool.

[0030] 3) The tooth profile slope deviation correction method of the present invention is not limited by the machine tool structure, the operation process is simple, and it can reduce the adjustment time of the gear turning machine tool and improve the processing efficiency of the gear turning machine tool. Attached Figure Description

[0031] Figure 1 This is a flowchart of the high-power gear turning tooth profile slope deviation correction method according to an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of a typical vertical high-strength gear turning machine tool according to an embodiment of the present invention;

[0033] Figure 3 This is a kinematic model for gear machining according to an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0035] The gear to be machined is an internal meshing spur gear with involute tooth profile. Its main parameters are: number of teeth z. w =54, modulus m n =2mm, pressure angle α n =20°, tooth tip circle diameter d a1 =114.5mm, tooth root circle diameter d f1 =105mm, span M=103.066mm, measuring rod diameter dp =3.75mm.

[0036] The main parameters of a gear cutting tool are: number of teeth z t =31, helix angle β w =20° (right-hand rotation), front angle γ = 5°, back angle α e =7°, outer diameter d at =72.2mm.

[0037] The installation parameters for the gear cutting tool are: tool mounting axis angle Σ = 20°, tool mounting center distance a = 21.15mm.

[0038] like Figure 1 This is a flowchart of the high-power gear turning tooth profile slope deviation correction method according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a typical vertical high-strength gear turning machine. The three linear motion axes of the gear turning machine are defined as follows: the X-axis is aligned with the center distance between the tool and the workpiece; the Z-axis is aligned with the workpiece's rotation axis; and the Y-axis is perpendicular to both the X-axis and Z-axis.

[0039] The method for correcting the tooth profile slope deviation in high-strength gear machining includes the following steps:

[0040] S1: Establish a calculation formula for the tooth profile slope deviation δ, which includes the tool pose parameter adjustment. According to the principle of heavy-duty gear turning, the tool pose parameter adjustment includes: the tool mounting axis angle adjustment ΔΣ and the offset distance ΔY of the tool rotation center along the Y-axis of the machine tool. The calculation formula is as follows:

[0041] δ=M w-S1 M S1-S2 M S2-t r t -M w-S1 M′ S1-S2 M S2-t r t

[0042] Where, r t This is a matrix of tool cutting edge data points. For example... Figure 3 It is a kinematic model for gear machining, matrix M w-S1 To transfer from the gear's static coordinate system O1-x1y1z1 to the gear's moving coordinate system O w -x w y w z w The spatial transformation matrix, matrix M S2-t To move from the tool's coordinate system O t -x t y t z tThe spatial transformation matrix M from the tool static coordinate system O2-x2y2z2 is given by matrix M. S1-S2 Let M′ be the spatial transformation matrix from the gear static coordinate system O1-x1y1z1 to the tool static coordinate system O2-x2y2z2. S1-S2 The spatial transformation matrix from the gear static coordinate system O1-x1y1z1 to the tool static coordinate system O2-x2y2z2, including tool pose parameter adjustment;

[0043] In this embodiment, if a set of tool pose parameter adjustment amounts (ΔΣ=-0.3°, ΔY=0.4mm) are input, the tooth profile containing the tool pose parameter adjustment amounts will produce a tooth profile deviation δ compared to the theoretical tooth profile. In the above matrix, Let be the rotation angle from the stationary coordinate system of the gear to the moving coordinate system of the gear. Let denoted as the rotation angle from the tool's moving coordinate system to the tool's stationary coordinate system, 'a' be the tool mounting center distance, and 'Σ' be the intersection angle of the tool mounting axis.

[0044] Furthermore, the tooth profiles on both sides of the gear are processed into i discrete points, and the tooth profile deviation set [δ] of all discrete points within the evaluation height H of the tooth profiles on both sides is calculated sequentially using the tooth profile deviation calculation formula. L(i) ]、[δ R(i) ], where the subscript "L" represents the left tooth profile and the subscript "R" represents the right tooth profile. The set of tooth profile deviations on both sides are obtained by linear fitting using the least squares fitting method [δ]. L(i) ]、[δ R(i) The slope of the linear equation obtained is the deviation fhα of the tooth profile slope on both sides. L =5.8mm, fhα R =18.7mm.

[0045] S2: Establish the mapping relationship between the matrix of tool pose parameter adjustment and the matrix of tooth profile slope deviation;

[0046] Using the general mathematical expression of the polynomial response surface model, the mathematical expressions for the tool pose parameter adjustment and the tooth profile slope deviation are established as follows:

[0047] fhα=ρ1+ρ2ΔΣ+ρ3ΔY+ρ4ΔΣ 2 +ρ5ΔY 2 +ρ6ΔΣΔY

[0048] Since, according to the calculation formula in step S1, by inputting a set of tool pose parameter adjustment amounts (ΔΣ=-0.3°, ΔY=0.4mm), the deviation value of the tooth profile slope on both sides (fhα) can be obtained. L =5.8μm, fhαR =18.7μm). When a series of tool mounting axis intersection adjustment amounts ΔΣ are input. (j) and a series of tool offset distances ΔY (j) The cross-combination matrix [ΔΣ] (j) ΔY (j) ], where the range of the tool mounting axis angle adjustment is ΔΣ (j) The range of the tool offset distance ΔY is ∈[-0.5°, 0.5°]. (j) If ∈[-1mm, 1mm], then the matrix [fhα] formed by the deviation of the tooth profile slope on both sides can be obtained. L(j) ]、[fhα R(j) Therefore, the mapping relationship between the matrix of tool pose parameter adjustment and the matrix of tooth profile slope deviation in step S2 is expressed as a matrix:

[0049]

[0050] To facilitate the description of the calculation process, the above mapping relationship is simplified as follows:

[0051] [B]·[ρ]=[F]

[0052] Among them, matrix [B] is a j×6 matrix, each column represents the element of each term in the polynomial with respect to ΔΣ and ΔY, and the j rows represent the number of different combinations of ΔΣ and ΔY values; matrix [ρ] is a 6×1 matrix containing the coefficients of the 6 polynomials to be solved; matrix [F] is a j×1 matrix, representing the tooth profile slope deviation value corresponding to different combinations of ΔΣ and ΔY values.

[0053] S3: Solve for the polynomial coefficients in the mapping relation;

[0054] Furthermore, the formula for calculating the polynomial coefficients in step S3 is as follows:

[0055] [ρ]=([B] T [B]) -1 [B] T [F]

[0056] In the calculation formula, the superscript "T" represents the transpose matrix, and the superscript "-1" represents the inverse matrix.

[0057] Table 1 shows the polynomial coefficients ρ corresponding to the tooth profiles on both sides.

[0058]

[0059] S4: Set the calculation error threshold for tooth profile slope deviation;

[0060] Since the mapping relationship established in step S2 is an approximate statistical model, and solving the polynomial coefficients in this mathematical expression in step S3 is a process of finding the best approximate solution for an overdetermined system, the actual calculated tooth profile slope deviation will have a certain calculation error. To improve computational efficiency, a calculation error threshold Δfhα for the tooth profile slope deviation needs to be set. This threshold refers to the upper limit of the difference between the actual detected tooth profile slope deviation and the theoretically calculated tooth profile slope deviation, and the specific value is set to 1.5 μm.

[0061] S5: Input the actual detected tooth profile slope deviation, and calculate the correction value of the tool pose parameter based on the mathematical expressions in steps S2 and S3.

[0062] Since the polynomial coefficient matrix [ρ] has already been solved, the actual detected tooth profile slope deviation (fhα) is input. L =10μm, fhα R If ΔΣ' = -5μm, then according to the formula [B]·[ρ] = [F], the correction values ​​of the tool pose parameters (ΔΣ' = 0.08°, ΔY' = 0.58mm) can be calculated. Substituting the calculated correction values ​​of the tool pose parameters (ΔΣ' = 0.08°, ΔY' = 0.58mm) into the calculation formula in step S1, the theoretically calculated tooth profile slope deviation (fhα) is obtained. L =9.8μm, fhα R = -5.1μm). By comparing the actual detected tooth profile slope deviation with the theoretically calculated tooth profile slope deviation, the difference in the calculation error of the tooth profile slope deviation (Δfhα) is obtained. L = -0.2μm, Δfhα R =0.1μm). Because the absolute value of the difference in the calculation error of the tooth profile slope deviation (|Δfhα) L |=0.2μm、|Δfhα R The values ​​of |=0.1μm) are all less than the set error threshold for calculating the tooth profile slope deviation Δfhα=1.5μm, thus obtaining the final corrected values ​​of the tool pose parameters (ΔΣ'=0.08°, ΔY'=0.58mm).

[0063] As can be seen from the above calculation process, compared with the traditional correction method of multiple adjustments, trial cuts, and feedback, the tooth profile slope deviation correction method of the present invention does not require operators to repeatedly try and find the pattern. It only requires calculating the correct tool installation parameter adjustment amount according to the calculation method, and adjusting the tool installation parameters only once on the machine tool, which can effectively correct the tooth profile slope deviation in gear turning.

[0064] S6: Input the correction value of the tool pose parameter calculated in step S5 into the machine tool operation software. After the gear turning is completed, the tooth profile slope deviation can be corrected.

[0065] The tooth profile slope deviation correction method of the present invention can not only correct tooth profile slope deviations caused by tool installation parameter errors, but also correct fundamental errors caused by regrinding of conical turning tools, thereby further improving the service life of conical turning tools. Furthermore, the tooth profile slope deviation correction method of the present invention is not limited by machine tool structure, the operation process is simple, it can reduce the adjustment time of the turning machine tool, and improve the processing efficiency of the turning machine tool.

[0066] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for correcting the slope deviation of tooth profile in high-power gear turning, characterized in that, include: S1: Establish a calculation formula for the tooth profile slope deviation δ, which includes the tool pose parameter adjustment amount. The tool pose parameter adjustment amount includes: the tool mounting axis angle adjustment amount ΔΣ, and the offset distance ΔY of the tool rotation center along the Y-axis of the machine tool. The calculation formula is as follows: δ=M w-S1 M S1-S2 M S2-t r t -M w-S1 M′ S1-S2 M S2-t r t Where, r t M is the matrix of tool cutting edge data points. w-S1 Let M be the spatial transformation matrix from the stationary coordinate system of the gear to the moving coordinate system of the gear. S2-t Let M be the spatial transformation matrix from the tool's moving coordinate system to its stationary coordinate system. S1-S2 Let M′ be the spatial transformation matrix from the gear moving coordinate system to the tool moving coordinate system. S1-S2 This is the spatial transformation matrix from the gear static coordinate system to the tool static coordinate system, which includes tool pose parameter adjustments. S2: Establish the mapping relationship between the matrix of tool pose parameter adjustment and the matrix of tooth profile slope deviation: [B]·[ρ]=[F] In this matrix, [B] is a j×6 matrix, where each column represents the element of each term in the polynomial with respect to ΔΣ and ΔY, and the j rows represent the number of different combinations of ΔΣ and ΔY values; matrix [ρ] is a 6×1 matrix containing the coefficients of the 6 polynomials to be solved; and matrix [F] is a j×1 matrix representing the tooth profile slope deviation values ​​corresponding to different combinations of ΔΣ and ΔY values. S3: Solve for the polynomial coefficients in the mapping relation; S4: Set the calculation error threshold for tooth profile slope deviation; S5: Input the actual detected tooth profile slope deviation, and calculate the correction value of the tool pose parameter based on the mathematical expressions in steps S2 and S3. S6: Input the correction value of the tool pose parameter calculated in step S5 into the machine tool operation software. After the gear turning is completed, the tooth profile slope deviation can be corrected.

2. The method for correcting the tooth profile slope deviation in high-strength gear machining according to claim 1, characterized in that, The directions of the machine tool coordinate axes are as follows: the X-axis of the machine tool is aligned with the center distance between the tool and the workpiece; the Z-axis of the machine tool is aligned with the rotation axis of the workpiece; and the Y-axis of the machine tool is perpendicular to both the X-axis and Z-axis of the machine tool.

3. The method for correcting the slope deviation of tooth profile in high-strength gear machining according to claim 1, characterized in that, The process of calculating the tooth profile slope deviation in step S2 includes: processing the tooth profiles on both sides of the gear into i discrete points, and using the tooth profile deviation calculation formula to sequentially calculate the set of tooth profile deviations [δ] for all discrete points within the evaluation height H of the tooth profiles on both sides. L(i) ]、[δ R(i) ], where the subscript "L" represents the left tooth profile and the subscript "R" represents the right tooth profile, and the set of tooth profile deviations on both sides are obtained by linear fitting using the least squares fitting method [δ] L(i) ]、[δ R(i) The slope of the obtained linear equation is the deviation of the tooth profile slope fhα on both sides. L fhα R .

4. The method for correcting the tooth profile slope deviation in high-strength gear machining according to claim 1, characterized in that, The mapping relationship in step S2 is represented by a matrix as follows:

5. The method for correcting the tooth profile slope deviation in high-strength gear machining according to claim 1, characterized in that, The formula for solving the polynomial coefficients in step S3 is as follows: [p]=([B] T [B]) -1 [B] T [F] In the calculation formula, the superscript "T" represents the transpose matrix, and the superscript "-1" represents the inverse matrix.

6. The method for correcting the tooth profile slope deviation in high-strength gear machining according to claim 1, characterized in that, In step S4, the calculation error threshold for the tooth profile slope deviation refers to the upper limit of the difference between the actual detected tooth profile slope deviation and the theoretically calculated tooth profile slope deviation, denoted as Δfhα. The maximum value of this calculation error threshold does not exceed the actual detected tooth profile slope deviation (fhα). L ',fhα R 30% of the maximum value in ').

7. The method for correcting the slope deviation of tooth profile in high-strength gear machining according to claim 1, characterized in that, The calculation process for the correction value of the tool pose parameter in step S5, based on the actual detected tooth profile slope deviation, is as follows: Based on the calculated polynomial coefficient matrix [ρ], input the actual detected tooth profile slope deviation (fhα). L ',fhα R Then, using the formula [B]·[ρ]=[F], the correction values ​​(ΔΣ', ΔY') of the tool pose parameters are calculated in reverse; then, the calculated correction values ​​(ΔΣ', ΔY') of the tool pose parameters are substituted into the calculation formula in step S1 to obtain the theoretically calculated tooth profile slope deviation (fhα). L fhα R By comparing the actual measured deviation of the tooth profile slope with the theoretically calculated deviation, the difference in the calculation error of the tooth profile slope deviation (Δfhα) is obtained. L ,Δfhα R If the absolute value of the difference in the calculation error of the tooth profile slope deviation is (|Δfhα) L |、|Δfhα R If all values ​​are less than the set error threshold Δfhα for the tooth profile slope deviation, the final corrected values ​​of the tool pose parameters (ΔΣ', ΔY') are obtained; otherwise, return to step S4 to increase the error threshold for the tooth profile slope deviation and repeat the calculation process of step S5.

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