Efficient analysis method for low-order abnormal frequency components of tooth surface error

Abstract

The application discloses a high-efficiency analysis method for low-order abnormal frequency components of tooth surface error, and solves point distribution trajectory parameters through grinding process parameters and tooth surface grinding contact trajectories to obtain the value range of the coordinates of the point distribution trajectory; on the basis of the point distribution trajectory, the intersection state of the tooth width middle position section curve and the point distribution trajectory is used to calculate the radius coordinate of the point, the intersection state of the intersection curve of the reference circle and the tooth surface and the point distribution trajectory is used to calculate the axial position coordinate of the point, the accurate position of the point on the tooth surface is obtained, the accurate analysis of the low-order frequency of the tooth surface error is realized, and the problems of long error measurement time and high analysis cost in the analysis process of the low-order frequency components of the tooth surface are solved; the application further discloses a system, equipment and medium for realizing the method.

Description

Technical Field

[0001] This invention relates to the field of high-precision gear error measurement and data analysis technology, and in particular to an efficient analysis method for low-order abnormal frequency components of tooth surface error. Background Technology

[0002] High-precision gears are core components of high-performance transmission systems, widely used in aerospace, new energy vehicles, consumer electronics, and medical devices. The precision of gears directly affects the noise level and lifespan of high-performance transmission systems and equipment. With increasing demands for noise levels and lifespan, various abnormal frequency components caused by post-processing tooth surface ripples and abnormal morphologies have become significant factors restricting gear performance, with low-order frequency components more likely to cause vibrations in the transmission system. In current production processes, the various frequency components of high-precision gear tooth surface errors are mainly obtained through order analysis. Gear testing equipment is used to measure the tooth profile and tooth direction error data of all tooth surfaces. Dedicated processing methods are then used to filter, stitch, and perform spectral analysis on the measured data to obtain the frequency distribution of tooth profile and tooth direction errors. Furthermore, comparative analysis reveals abnormal frequency components such as ghost orders. The core of this analysis is the processing and analysis of tooth surface error data. Gear testing instruments from manufacturers such as Klingelnberg and Gleason offer dedicated tooth surface error order analysis modules, such as Advanced Waviness Analysis, to accomplish this task. In terms of theoretical research, the reference "G. Gravel, Analysis of ripple on noisy gears[J]. Gear Solution, 2013, 1; 39-47." proposes to sequentially fit and decompose the harmonic components of different frequencies in the tooth surface error using a sine function, thereby obtaining all the spectral characteristics of the tooth surface error. The reference "Ma Zhiwei, Meng Jing, Liu Yanan, et al., Formation principle and detection analysis of tooth surface waviness[J], Equipment Manufacturing Technology, 2023, 6: 188-190" proposes a simple and effective data concatenation method based on the principles of external circular waviness and gear meshing, and identifies frequency characteristics through Fourier transform. Although the above methods can accurately predict all integer and non-integer multiple frequency components, they require measuring the tooth profile and tooth direction errors of all tooth surfaces, resulting in a large amount of measurement data and long time consumption. With the rapid development of new energy vehicles and other fields, the requirements for tooth surface accuracy and the number of gears are increasing, severely limiting the application of the above methods in large-scale production sites and increasing production cycles and costs. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides an efficient analysis method for low-order abnormal frequency components of tooth surface errors. The method solves for the measurement point distribution trajectory parameters by using grinding process parameters and the tooth surface grinding contact trajectory, obtaining the range of coordinate values ​​for the measurement point distribution trajectory. Based on the aforementioned measurement point distribution trajectory, the radius coordinates of the measurement points are calculated according to the intersection state of the cross-sectional curve at the midpoint of the tooth width with the measurement point distribution trajectory. The axial position coordinates of the measurement points are calculated according to the intersection state of the curve intersecting the pitch circle and the tooth surface with the measurement point distribution trajectory, thus obtaining the accurate position of the measurement points on the tooth surface. This achieves accurate analysis of low-order frequencies of tooth surface errors, solving the problems of long error measurement time and high analysis costs in existing low-order frequency component analysis processes.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] An efficient method for analyzing low-order abnormal frequency components of tooth surface errors includes the following steps:

[0006] Step A: Solve for the measurement point distribution trajectory parameters using grinding process parameters and tooth surface grinding contact trajectory;

[0007] Step B: Based on the measurement point distribution trajectory parameters, calculate the radius coordinates of the measurement points according to the intersection state of the cross-section curve at the midpoint of the tooth width and the measurement point distribution trajectory, and determine the position of the tooth surface error measurement point;

[0008] Step C: Based on the coordinates of the tooth surface error measurement points, obtain the change in elongation error for all tooth surface measurement points;

[0009] Step D: Use Fourier transform on the variation of the elongation error at all tooth surface measurement points to obtain the spectral characteristic curve of the tooth surface error data, and then use frequency domain analysis to obtain the abnormal low-order frequency components of the tooth surface error.

[0010] Step A specifically involves:

[0011] During grinding, the contact point between the grinding wheel and the right tooth surface 112 of the first tooth 11 of gear 1 forms a contact trajectory 2. Multiple contact trajectories 2 exist on the tooth surface, with an axial spacing equal to the axial feed rate d. z =f z Z / n w Z w Taking the upper part of the protrusion as the starting point of the z-coordinate z = 0, the coordinates (x, y) of each point j on the i-th contact trajectory 2i are... 2ij ,y 2ij ,z 2ij The radius of each point j on the contact trajectory 2i is calculated through meshing analysis of the gear and worm wheel. Radius R on contact trajectory 2i 2ij and z coordinates 2ij The range of values ​​for are respectively [min(R) 2ij),max(R 2ij )] and [min(z 2ij ),max(z 2ij [); The intermediate trajectory 3 is between two adjacent contact trajectories, representing the residual height of the grinding wheel between adjacent contact trajectories on the right tooth surface 112; the coordinates (x, y) of each point j on the i-th intermediate trajectory 3i. 3ij ,y 3ij ,z 3ij Based on the coordinates of the two adjacent contact trajectories 2, we have x 3ij =0.5(x 2ij +x 2(i+1)j ), y 3ij =0.5(y) 2ij +y 2(i+1)j ) and z 3ij =0.5(z) 2ij +z 2(i+1)j The radius of each point j on the intermediate trajectory 3i is... The radius R of each point on the intermediate trajectory 3i 3ij and z coordinates 3ij To perform data fitting, when the variable is the z-coordinate z 3ij The coordinate relationship expression of the intermediate trajectory 3i is R 3ij =f1(z 3ij When the variable is radius R 3ij The coordinate relationship expression of the intermediate trajectory 3i is z 3ij =f2(R 3ij On the right tooth surface 112, the cross-section at the midpoint of the tooth width is curve 4, with the z-coordinate of each point on it being 0.5H; the intersection of the pitch circle and the right tooth surface 112 is curve 5, with the radius of each point on it being 0.5d; during grinding, the first tooth 11 is machined from top to bottom, based on the lead-out amount z1 and the axial feed rate f. z The coordinates (x, y) of each point j on the first intermediate trajectory are obtained through meshing analysis of the gear and worm wheel. 31j ,y 31j ,z 31j The range of values ​​for the z-coordinate is [min(z)]. 31j ),max(z 31j Then, the minimum and maximum values ​​of the z-coordinates on the i-th intermediate trajectory 3i are respectively and

[0012] For the other teeth 1k (k=2,…,Z), there is an axial distance d between the contact trajectory 2 on the tooth surface and the contact trajectory on the first tooth 11. zT =f z / n w Zw Then, the minimum and maximum values ​​of the z-coordinates on the i-th intermediate trajectory 3i on tooth 1k are respectively and

[0013] Step B specifically involves:

[0014] On tooth 1k (k=1,…,Z), sequentially check the relationship between the range of z-coordinates of each intermediate trajectory and the z-coordinate of the cross-section curve 4 at the midpoint of the tooth width; when the z-coordinate of the i-th intermediate trajectory 3i satisfies At this point, the cross-shaped curve 4, representing the midpoint of the tooth width, intersects with the midpoint trajectory 3. This intersection point is selected as the measuring point during calculation. At this time, the z-coordinate of the measuring point... Measuring point radius for

[0015] For all intermediate trajectories 3, when the range of z-coordinate values ​​for any intermediate trajectory 3i does not satisfy... At this point, the cross-shaped curve 4, representing the midpoint of the tooth width, does not intersect with the midpoint trajectory 3. Therefore, the intersection point of the curve 5, representing the intersection of the pitch circle and the tooth surface, and the midpoint trajectory 3 is selected as the measuring point. In this case, the radius of the measuring point... The z-coordinate is

[0016] Step C specifically involves:

[0017] After gear 1 is installed on the testing equipment, the probe 6 is moved radially along the gear to the measuring point P. m radius At that point, it moves along the gear axis to measuring point P. m z-coordinate At this point, rotating gear 1 causes the right tooth surface 112 of the first tooth 11 to contact the probe 6, thus obtaining the measuring point P on the right tooth surface 112. m Actual span L m,1 Measurement point P m Actual and theoretical values ​​of the span Subtraction yields its expansion error LE m,1 Then, rotate gear 1 around the z-axis by i-1 (i = 2, ..., Z) tooth pitch angles, and repeat the above process to measure the measuring point P on the right tooth surface of all teeth. m Elongation error LE m,i ;

[0018] Measurement point P on the right tooth surface 112 of the first tooth 11 m Elongation error LE m,1 Based on this, calculate the measurement point P on the right tooth surface 1i2 of the i-th tooth 1i. m The change in the span error is expressed as ΔL mi =LEm,i -LE m,i-1 The variation law of the expansion error with the number of teeth was obtained; the tooth pitch angle θ was used as the basis for this variation. zi = (i-1)2π / Z is a variable, and the measurement point P is on the right tooth surface of all teeth. m By fitting the change in the expansion error, the expression for the relationship between the change in the expansion error and the tooth pitch angle is obtained as ΔL. m =f(θ) z );

[0019] Based on the same method, the elongation error and error change of the measuring points on the right tooth surface 112 and left tooth surface 111 of all teeth 1k (k=1,…,Z) of gear 1 are obtained.

[0020] Step D specifically involves:

[0021] Based on the working speed set for gear grinding conditions, calculate the time data t = θ corresponding to the tooth pitch angle sequence. zi / n; The spectrum of all tooth surface elongation error variations is obtained through Fourier transform. After Fourier transform, the frequency sequence is converted into a frequency conversion multiple sequence XN(ΔL) m )=60X(ΔL m ) / n; Based on the spectrum of the change in the length extension error and the frequency multiple sequence, the low-order spectral characteristic curve of the tooth surface error data is obtained. According to the amplitude variation law of the characteristic curve and the given amplitude range, the abnormal low-order frequency components can be obtained.

[0022] The present invention also includes:

[0023] A system, including a processor, is provided to run the aforementioned efficient analysis method for low-order abnormal frequency components of tooth surface errors.

[0024] An apparatus comprising:

[0025] Memory: A computer program for storing the efficient analysis method for low-order abnormal frequency components of tooth surface error described above;

[0026] Processor: Used to implement the efficient analysis method for low-order abnormal frequency components of tooth surface error when executing the computer program.

[0027] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the efficient analysis method for low-order abnormal frequency components of tooth surface errors.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. This invention realizes the premise of tooth surface error measurement point planning by calculating the distribution trajectory of measurement points on the tooth surface in step A and the coordinate position in step B. The number of measurement points is much smaller than that of existing tooth surface error order analysis methods, which helps to solve the problem of long measurement time of existing tooth surface error and greatly improves the detection efficiency of gear accuracy on the production site.

[0030] 2. Step D of this invention achieves accurate prediction of low-order spectral components of tooth surface error through measurement point error data planning and frequency domain feature analysis. This helps to solve the problems of relying on expensive imported software, inability to obtain raw data, and high analysis costs in the existing detection process of low-order frequency components of tooth surface.

[0031] In summary, this invention obtains the change in elongation error by measuring the position of the measuring point, and uses the frequency domain change of the change in elongation error to obtain the low-order spectral distribution of the tooth surface error. It has high analysis efficiency, strong versatility, and wide applicability. It can be applied to the accuracy detection of different types of gears during and after processing, providing a means and tool for error analysis in the large-scale production process of gears. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the gear structure and tooth distribution.

[0033] Figure 2 This is a schematic diagram of the trajectory of the tooth surface error measurement points.

[0034] Figure 3 This is a schematic diagram of the tooth surface error measurement point distribution according to the present invention, wherein... Figure 3 (a) shows the case where the cross-shaped curve 4 at the midpoint of the tooth width intersects with the midpoint trajectory 3. Figure 3 (b) in the figure represents the case where the cross-shaped curve 4 at the middle position of the tooth width does not intersect with the middle trajectory 3.

[0035] Figure 4 This is a schematic diagram of a tooth surface error measurement system.

[0036] Figure 5 This is a schematic diagram illustrating the variation of the length extension error with the number of teeth.

[0037] Figure 6 This is a diagram showing the results of the tooth surface error order analysis of the present invention.

[0038] Figure 7 This is a graph showing the results of the tooth surface error order analysis of a commercial gear testing instrument.

[0039] In the diagram: 1-Gear; 11-First tooth; 12-Second tooth; 13-Third tooth; 111-Left tooth surface; 112-Right tooth surface; 2-Contact trajectory; 3-Intermediate trajectory; 4-Cut curve at the middle position of the tooth width; 5-Intersection curve of the pitch circle and the tooth surface; 6-Probe. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] The structure of gear 1 analyzed in this invention is as follows: Figure 1 As shown, the number of teeth is Z, the tooth width is H, the pitch circle diameter is d, and the base circle radius is r. b Gear 1 is mainly composed of multiple teeth, such as tooth 1k (k = 1, ..., Z), for example, the first tooth 11, the second tooth 12, the third tooth 13, ...; each tooth includes a left tooth surface 111 and a right tooth surface 112; when gear 1 is ground, the upper overhang is z1, and the axial feed is f. z .

[0042] Based on the aforementioned gear 1, the present invention provides an efficient analysis method for low-order abnormal frequency components of tooth surface errors, comprising the following steps:

[0043] Step A: Solve for the measurement point distribution trajectory parameters using grinding process parameters and tooth surface grinding contact trajectory.

[0044] The grinding condition is set with the grinding wheel speed as n and the number of grinding heads as Zw. For example... Figure 2 As shown, during grinding, the contact point between the grinding wheel and the right tooth surface 112 of the first tooth 11 of gear 1 forms a contact trajectory 2. There are multiple contact trajectories 2 on the tooth surface, with an axial spacing equal to the axial feed rate d. z =f z Z / n w Z w Taking the upper part of the protrusion as the starting point of the z-coordinate z=0, the coordinates (x, y, z) of each point j on the i-th contact trajectory 2i are... 2ij ,y 2ij ,z 2ij The radius of each point j on the contact trajectory 2i is calculated through meshing analysis of the gear and worm wheel. Radius R on contact trajectory 2i 2ij and z coordinates 2ij The range of values ​​for are respectively [min(R) 2ij ),max(R 2ij )] and [min(z 2ij ),max(z 2ij The intermediate trajectory 3 is the distance between two adjacent contact trajectories, representing the residual height of the grinding wheel between adjacent contact trajectories on the right tooth surface 112. The coordinates (x, y) of each point j on the i-th intermediate trajectory 3i are... 3ij ,y 3ij ,z 3ijBased on the coordinates of the two adjacent contact trajectories 2, we have x 3ij =0.5(x 2ij +x 2(i+1)j ), y 3ij =0.5(y) 2ij +y 2(i+1)j ) and z 3ij =0.5(z) 2ij +z 2(i+1)j The radius of each point j on the intermediate trajectory 3i is... The radius R of each point on the intermediate trajectory 3i is determined using methods such as polynomials and spline curves. 3ij and z coordinates 3ij To perform fitting, when the variable is the z-coordinate z 3ij The coordinate relationship expression of the intermediate trajectory 3i is R 3ij =f1(z 3ij When the variable is radius R 3ij The coordinate relationship expression of the intermediate trajectory 3i is z 3ij =f2(R 3ij On the right tooth surface 112, the cross-section at the midpoint of the tooth width is curve 4, with the z-coordinate of each point on it being 0.5H. The intersection line between the pitch circle and the right tooth surface 112 is curve 5, with the radius of each point on it being 0.5d. During grinding, the first tooth 11 is machined from top to bottom, based on the lead-out amount z1 and the axial feed rate f. z The coordinates (x, y) of each point j on the first intermediate trajectory are obtained through meshing analysis of the gear and worm wheel. 31j ,y 31j ,z 31j The range of values ​​for the z-coordinate is [min(z)]. 31j ),max(z 31j Then, the minimum and maximum values ​​of the z-coordinates on the i-th intermediate trajectory 3i are respectively and

[0045] For the other teeth 1k (k=2,…,Z), there is an axial distance d between the contact trajectory 2 on the tooth surface and the contact trajectory on the first tooth 11. zT =f z / n w Z w Then, the minimum and maximum values ​​of the z-coordinates on the i-th intermediate trajectory 3i on tooth 1k are respectively... and

[0046] Step B: Based on the measurement point distribution trajectory parameters, calculate the radius coordinates of the measurement points according to the intersection state of the cross-section curve at the middle position of the tooth width and the measurement point distribution trajectory, and determine the position of the tooth surface error measurement point.

[0047] On tooth 1k (k=1,…,Z), for all intermediate trajectories 3, sequentially check the relationship between the range of z-coordinate values ​​of each intermediate trajectory and the z-coordinate of the cross-section curve 4 at the midpoint of the tooth width. When the z-coordinate of the i-th intermediate trajectory 3i satisfies… At this point, the cross-shaped curve 4, representing the midpoint of the tooth width, intersects with the midpoint trajectory 3. During calculation, this intersection point is selected as the measuring point, and its location is as follows: Figure 3 As shown in (a). At this time, the z-coordinate of the measuring point... Measuring point radius for

[0048] For all intermediate trajectories 3, when the range of z-coordinate values ​​for any intermediate trajectory 3i does not satisfy... When the cross-shaped curve 4, representing the midpoint of the tooth width, does not intersect with the midpoint trajectory 3, the intersection point of the curve 5, representing the intersection of the pitch circle and the tooth surface, and the midpoint trajectory 3 is selected as the measuring point during calculation. The measuring point position is as follows: Figure 3 As shown in (b). At this time, the radius of the measuring point...

[0049] The z-coordinate is

[0050] Step C: Based on the coordinates of the tooth surface error measurement points, obtain the change in elongation error for all tooth surface measurement points;

[0051] Measuring point P on right tooth surface 112 m Error data measurement methods such as Figure 4 As shown, gear 1 is mounted on a precision testing device such as a gear testing instrument using a fixture, and the probe 6 is moved radially along the gear to the measuring point P. m radius At that point, it moves along the gear axis to measuring point P. m z-coordinate Rotating gear 1 causes the right tooth surface 112 of the first tooth 11 to contact the probe 6, thus obtaining the measuring point P on the right tooth surface 112. m Actual span L m,1 And measuring point P m Theoretical extension Measuring point P m The actual value of the span is subtracted from the theoretical value to obtain the measured value of point P. m Elongation error LE m,1 Measurement point P on the right tooth surface 112 of the first tooth 11. mAfter the expansion error measurement is completed, rotate gear 1 around the z-axis by i-1 (i=2,…,Z) tooth pitch angles, and repeat the above process to measure the measuring point P on the right tooth surface of all teeth. m Elongation error LE m,i .

[0052] Measurement point P on the right tooth surface 112 of the first tooth 11 m Elongation error LE m,1 Based on this, measuring point P on the right tooth surface 122 of the second tooth 12. m The change in the span error is expressed as ΔL m2 =LE m,2 -LE m,1 Similarly, we can obtain the measuring point P on the right tooth surface 1i2 of the i-th tooth 1i. m The change in the span error is expressed as ΔL mi =LE m,i -LE m,i-1 Therefore, the variation law of the expansion error with the number of teeth can be obtained ( Figure 5 ). With tooth pitch angle θ zi = (i-1)2π / Z is the variable. Polynomials, spline curves, and other curves are used to measure point P on the right tooth surface of all teeth. m By fitting the change in the expansion error, the expression for the relationship between the change in the expansion error and the tooth pitch angle is obtained as ΔL. m =f(θ) z ).

[0053] Using the same method and steps, the elongation error and error change of the measuring points on the right tooth surface 112 and left tooth surface 111 of all teeth 1k (k=1,…,Z) of gear 1 can be obtained.

[0054] Step D: Use Fourier transform on the variation of the elongation error at all tooth surface measurement points to obtain the spectral characteristic curve of the tooth surface error data, and then use frequency domain analysis to obtain the abnormal low-order frequency components of the tooth surface error.

[0055] Based on the working speed set according to the gear grinding conditions, the time data corresponding to the tooth pitch angle sequence is t=θ zi / n. Using all tooth measurement points P m The data on the change in the span error ΔL m Based on this, the variation in span error is discretized according to frequency resolution, and the spectrum of the variation in span error is obtained by Fourier transform. After Fourier transform, the time series corresponds to the frequency change sequence X(ΔL) m (Unit: Hz), the frequency sequence yields the frequency conversion multiple sequence as XN(ΔL) m )=60X(ΔL mBased on the spectrum of the change in length error and the frequency multiple sequence, the low-order spectral characteristics of the tooth surface error data can be obtained. Based on the amplitude variation law of the characteristic curve and the given amplitude range, the abnormal low-order frequency components can be obtained.

[0056] The present invention also includes:

[0057] A system, including a processor, is provided to run the aforementioned efficient analysis method for low-order abnormal frequency components of tooth surface errors.

[0058] An apparatus comprising:

[0059] Memory: A computer program for storing the efficient analysis method for low-order abnormal frequency components of tooth surface error described above;

[0060] Processor: Used to implement the efficient analysis method for low-order abnormal frequency components of tooth surface error when executing the computer program.

[0061] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the efficient analysis method for low-order abnormal frequency components of tooth surface errors.

[0062] Application examples:

[0063] The gear tooth surface data with Z=18 were measured and analyzed using both a commercial gear testing instrument and the method of this invention. After measuring the right tooth surface with the commercial gear testing instrument, order analysis revealed an abnormal frequency of order 12 with an amplitude of 0.052 (…). Figure 6 The analysis results of the method of this invention also revealed an anomalous frequency of the 12th order on the right tooth surface, with an amplitude of 0.051. Figure 7 The error is less than 2%, demonstrating the effectiveness and accuracy of the method in identifying abnormal frequencies. Furthermore, commercial gear testing instruments measure each tooth individually and perform order analysis, typically requiring data from thousands of points, while the method of this invention only needs to measure data from Z points, significantly reducing analysis efficiency.

Claims

1. A highly efficient analysis method for low-order abnormal frequency components of tooth surface errors, characterized in that, Includes the following steps: Step A: Solve for the measurement point distribution trajectory parameters using grinding process parameters and tooth surface grinding contact trajectory; Step B: Based on the measurement point distribution trajectory parameters, calculate the radius coordinates of the measurement points according to the intersection state of the cross section curve at the middle position of the tooth width and the measurement point distribution trajectory, and determine the position of the tooth surface error measurement point; Step C: Based on the coordinates of the tooth surface error measurement points, obtain the change in elongation error for all tooth surface measurement points; Step D: Use Fourier transform on the variation of the elongation error at all tooth surface measurement points to obtain the spectral characteristic curve of the tooth surface error data, and then use frequency domain analysis to obtain the abnormal low-order frequency components of the tooth surface error.

2. The efficient analysis method for low-order abnormal frequency components of tooth surface error according to claim 1, characterized in that, Step A specifically involves: During grinding, the contact point between the grinding wheel and the right tooth surface (112) of the first tooth (11) of the gear (1) forms a contact trajectory (2). Multiple contact trajectories (2) exist on the tooth surface, with an axial spacing of [missing information]. The upper part of the protrusion is used as z Starting point of coordinates z =0,th i Contact trajectory 2 i above points j coordinates The contact trajectory 2 was calculated through meshing analysis of the gear and worm wheel. i above points j The radius is Contact trajectory 2 i upper radius and z coordinate The range of values ​​for are respectively and The intermediate trajectory (3) between two adjacent contact trajectories represents the residual height between adjacent contact trajectories of the grinding wheel on the right tooth surface (112); i 3 intermediate trajectories i above points j coordinates Based on the coordinates of the two adjacent contact trajectories (2), we have , and , intermediate trajectory 3 i above points j The radius is ; For the intermediate trajectory 3 i radius of each point and z coordinate Perform data fitting when the variable is z coordinate Intermediate trajectory 3 i The coordinate relationship expression is as follows When the variable is the radius Intermediate trajectory 3 i The coordinate relationship expression is as follows On the right tooth surface (112), the cross-section at the midpoint of the tooth width is the cross-section curve (4) at the midpoint of the tooth width, and the points on it... z The coordinate is 0.5 H The intersection line between the pitch circle and the right tooth surface (112) is the intersection curve (5) of the pitch circle and the tooth surface, with a radius of 0.5 at each point. d During grinding, the first tooth (11) is machined from top to bottom, depending on the amount of protrusion. z 1 and axial feed rate f z The points on the first intermediate trajectory were obtained through meshing analysis of gears and worm gear grinding wheels. j coordinates , z The range of coordinate values ​​is ; then, the first i 3 intermediate trajectories i superior z The minimum and maximum values ​​of the coordinates are respectively and ; For other teeth 1 k , k =2,…,Z, The contact trajectory (2) on the tooth surface has an axial distance from the contact trajectory on the first tooth (11), and this axial distance is 2,…,Z. So, tooth 1 k The first tooth surface i 3 intermediate trajectories i superior z The minimum and maximum values ​​of the coordinates are respectively and .

3. The efficient analysis method for low-order abnormal frequency components of tooth surface error according to claim 2, characterized in that, Step B specifically involves: In tooth 1 k , k On the path =1,…,Z, check each intermediate trajectory sequentially. z The range of coordinate values ​​and the cross-sectional curve (4) at the midpoint of the tooth width. z The relationship between coordinates; when the first i 3 intermediate trajectories i of z Coordinates satisfy At this time, the cross-shaped curve (4) representing the middle position of the tooth width intersects with the middle trajectory (3), and the above intersection point is selected as the measuring point during calculation; at this time, the measuring point z coordinate Radius of measuring point for ; For all intermediate trajectories (3), when any intermediate trajectory 3 i of z The range of coordinate values ​​does not meet the requirements. When the cross-shaped curve (4) representing the middle position of the tooth width does not intersect with the middle trajectory (3), the intersection point of the curve (5) where the pitch circle intersects the tooth surface and the middle trajectory (3) is selected as the measuring point during calculation. At this time, the radius of the measuring point is... , z Coordinates are .

4. The efficient analysis method for low-order abnormal frequency components of tooth surface error according to claim 3, characterized in that, Step C specifically involves: After the gear (1) is installed on the testing equipment, the probe (6) is moved radially along the gear to the measuring point. P m radius At that location, move along the gear axis to the measuring point. P m of z coordinate At this point, the rotating gear (1) causes the right tooth surface (112) of the first tooth (11) to contact the probe (6), thus obtaining the measuring point on the right tooth surface (112). P m Actual exhibition length L m,1 measuring points P m Actual and theoretical values ​​of the span Subtraction yields its expansion error LE m,1 Then, rotate gear (1) around... z Axis rotation i -1 ( i =2,…,Z) tooth pitch angles, repeat the above process to measure the measuring points on the right tooth surface of all teeth. P m Elongation error LE m,i ; The measuring point on the right tooth surface (112) of the first tooth (11) P m Elongation error LE m,1 Based on this, calculate the first i 1 tooth i Right tooth surface 1 i 2 measuring points P m The change in the elongation error is expressed as The variation law of the expansion error with the number of teeth was obtained; the tooth pitch angle was used as the basis for this variation. As variables, measure points on the right tooth surface of all teeth. P m By fitting the change in the expansion error, the expression for the relationship between the change in the expansion error and the tooth pitch angle is obtained as follows: ; Based on the same method above, all teeth 1 of gear (1) are obtained. k , k =1,…,Z, the expansion error and error change of the measuring points on the right tooth surface (112) and the left tooth surface (111); 5. The efficient analysis method for low-order abnormal frequency components of tooth surface error according to claim 4, characterized in that, Step D specifically involves: Calculate the time data corresponding to the tooth pitch angle sequence based on the working speed set for the gear grinding conditions. The spectrum of all tooth surface elongation error variations was obtained through Fourier transform. After Fourier transform, the frequency sequence is converted into a frequency conversion multiple sequence. The low-order spectral characteristic curve of the tooth surface error data is obtained based on the spectrum of the change in the length extension error and the frequency multiple sequence. The abnormal low-order frequency components can be obtained based on the amplitude variation law of the characteristic curve and the given amplitude range.

6. A system, characterized in that, Includes a processor capable of running an efficient analysis method for low-order abnormal frequency components of tooth surface error as described in any one of claims 1 to 5.

7. A device, characterized in that, include: Memory: A computer program for storing the efficient analysis method of low-order abnormal frequency components of tooth surface error as described in any one of claims 1 to 5; Processor: Used to implement an efficient analysis method for low-order abnormal frequency components of tooth surface error according to any one of claims 1 to 5 when executing the computer program.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements an efficient analysis method for low-order abnormal frequency components of tooth surface errors as described in any one of claims 1 to 5.

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