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

Abstract

An efficient analysis method for tooth surface error low-order abnormal frequency components comprises the steps that measuring point distribution track parameters are solved through grinding process parameters and a tooth surface grinding contact track, and the value range of measuring point distribution track coordinates is obtained; on the basis of the distribution track of the measuring points, calculating the radius coordinates of the measuring points according to the intersection state of the section curve of the middle position of the tooth width and the distribution track of the measuring points, and calculating the axial position coordinates of the measuring points according to the intersection state of the intersection curve of the reference circle and the tooth surface and the distribution track of the measuring points to obtain the accurate positions of the measuring points on the tooth surface; accurate analysis of tooth surface error low-order frequency is realized, so that the problems of long error measurement time, high analysis cost and the like in the existing tooth surface low-order frequency component analysis process are solved; the invention further comprises a system, equipment and a medium for implementing the method.

Description

Technical Field

[0001] The present invention relates to the technical field of high-precision gear error measurement and data analysis, and in particular to a method for efficiently analyzing low-order abnormal frequency components of tooth surface errors. Background Art

[0002] High-precision gears are core components of high-performance transmission systems and are widely used in aerospace, new energy vehicles, consumer electronics, medical devices, and other fields. Gear precision directly impacts the noise level and lifespan of high-performance transmission systems and equipment. With increasing demands for equipment noise and lifespan, various abnormal frequency components caused by processed tooth surface waviness and abnormal topography have become a significant factor restricting gear performance. Low-order frequency components are particularly prone to causing transmission system vibration. In current production processes, the various frequency components of high-precision gear tooth surface errors are primarily determined through order analysis. This involves measuring the profile and tooth profile error data of all tooth surfaces using equipment such as gear testers. The measured data is then filtered, spliced, and spectrally analyzed using specialized processing methods to determine the frequency distribution of the profile and tooth profile errors. Furthermore, through comparative analysis, abnormal frequency components such as ghost orders are identified. The core of this analysis lies in the processing and analysis of tooth surface error data. Gear testers from manufacturers such as Klingelnberg and Gleason offer specialized tooth surface error order analysis modules such as Advanced Waviness Analysis to accomplish this. In theoretical research, the reference "G. Gravel, Analysis of Ripple on Noisy Gears [J]. Gear Solution, 2013, 1; 39-47" proposes sequentially decomposing the harmonic components of tooth surface error using sinusoidal fitting to obtain all the spectral characteristics of the tooth surface error. The reference "Ma Zhiwei, Meng Jing, Liu Yanan, et al., Principles of Tooth Surface Waviness Formation and Detection Analysis [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. While this method can accurately predict all integer and non-integer frequency components, it requires measuring the tooth profile and tooth guide errors of all tooth surfaces, which requires a large amount of data and is time-consuming. With the rapid development of new energy vehicles and other fields, the requirements for tooth surface accuracy and the number of gears are increasing. This severely limits the applicability of this method in large-scale production sites, increasing production cycle time and costs. Summary of the Invention

[0003] In response to the deficiencies in the prior art, the present invention provides an efficient analysis method for low-order abnormal frequency components of tooth surface errors. The measuring point distribution trajectory parameters are solved by grinding process parameters and tooth surface grinding contact trajectory to obtain the value range of the measuring point distribution trajectory coordinates. On the basis of the above-mentioned measuring point distribution trajectory, the measuring point radius coordinates are calculated according to the intersection state of the truncation curve at the middle position of the tooth width and the measuring point distribution trajectory, and the measuring point axial position coordinates are calculated according to the intersection state of the intersection curve of the pitch circle and the tooth surface and the measuring point distribution trajectory to obtain the accurate position of the measuring point on the tooth surface, thereby realizing accurate analysis of the low-order frequencies of the tooth surface errors, thereby solving the problems of long error measurement time and high analysis cost in the existing analysis process of low-order frequency components of the tooth surface.

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

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

[0006] Step A: Calculate the measurement point distribution trajectory parameters through the grinding process parameters and the tooth surface grinding contact trajectory;

[0007] Step B: Based on the measurement point distribution trajectory parameters, the measurement point radius coordinates are calculated according to the intersection of the truncation curve at the middle position of the tooth width and the measurement point distribution trajectory to determine the tooth surface error measurement point position;

[0008] Step C: Obtain the length error variation of all tooth surface measurement points according to the coordinates of the tooth surface error measurement points;

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

[0010] The step A is specifically as follows:

[0011] 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 track 2. There are multiple contact tracks 2 on the tooth surface, and their axial spacing is . The axial feed rate is d. z =f z Z / n w Z w , take the top of the head as the z coordinate starting point z = 0, the coordinates of each point j on the i-th contact track 2i (x 2ij ,y 2ij ,z 2ij ) is calculated through meshing analysis of the gear and worm grinding wheel. The radius of each point j on the contact trajectory 2i is Radius R on contact track 2i 2ij and z coordinate z 2ij The value ranges are [min(R 2ij),max(R 2ij )] and [min(z 2ij ),max(z 2ij )]; the middle track 3 is between two adjacent contact tracks, representing the residual height of the grinding wheel between adjacent contact tracks on the right tooth surface 112; the coordinates (x 3ij ,y 3ij ,z 3ij ) According to 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 coordinate z 3ij 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 truncation of the middle position of the tooth width is the truncation curve 4 at the middle position of the tooth width, and the z coordinate of each point on it is 0.5H; the intersection line of the pitch circle and the right tooth surface 112 is the intersection curve 5 of the pitch circle and the tooth surface, and the radius of each point on it is 0.5d; when grinding, the first tooth 11 is processed from top to bottom, according to the head amount z1 and the axial feed amount f z The coordinates of each point j on the first intermediate trajectory (x 31j ,y 31j ,z 31j ), the range of z coordinate is [min(z 31j ),max(z 31j )]; then, the minimum and maximum values ​​of the z coordinate on the i-th intermediate track 3i are and

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

[0013] The step B is specifically as follows:

[0014] On tooth 1k (k = 1, ..., Z), check the relationship between the z coordinate range of each intermediate track and the z coordinate of the truncated curve 4 at the middle position of the tooth width in turn; when the z coordinate of the i-th intermediate track 3i satisfies When , the truncated curve 4 at the middle position of the tooth width and the middle track 3 have an intersection point, and the above 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 tracks 3, when the value range of the z coordinate of any intermediate track 3i does not meet When the truncated curve 4 at the middle position of the tooth width does not intersect with the middle track 3, the intersection of the intersection curve 5 of the pitch circle and the tooth surface and the middle track 3 is selected as the measuring point during calculation. At this time, the measuring point radius The z coordinate is

[0016] The step C is specifically as follows:

[0017] After the gear 1 is mounted on the testing equipment, the probe 6 is moved radially along the gear to the measuring point P. m Radius Move along the gear axis to the measuring point P m The z coordinate of At , rotate the gear 1 so that the right tooth surface 112 of the first tooth 11 contacts the probe 6, and obtain the measuring point P on the right tooth surface 112 m The actual length L m,1 , measuring point P m Actual and theoretical values ​​of the extension Subtract the length error LE m,1 Then, rotate gear 1 around the z axis by i-1 (i=2,…,Z) pitch angles, and repeat the above process to measure the measuring points P on the right tooth surface of all teeth. m The length error LE m,i ;

[0018] Take the measuring point P on the right tooth surface 112 of the first tooth 11 m The length error LE m,1 Based on, calculate the measuring point P on the right tooth surface 1i2 of the i-th tooth 1i m The length error change is expressed as ΔL mi =LEm,i -LE m,i-1 , we can get the variation law of the length error with the number of teeth; with the pitch angle θ zi =(i-1)2π / Z is a variable, and for all the measuring points P on the right tooth surface m The length error variation is fitted, and the expression between the length error variation and the pitch angle is obtained as ΔL m =f(θ z );

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

[0020] The step D is specifically as follows:

[0021] According to the working speed set in the gear grinding working condition, calculate the time data t=θ corresponding to the pitch angle sequence zi / n; The frequency spectrum of all tooth surface length error variations obtained by Fourier transform is: After Fourier transform, the frequency sequence is converted into a frequency multiple sequence of XN(ΔL m )=60X(ΔL m ) / n; According to the spectrum of the length error variation and the rotation frequency multiple sequence, the low-order spectrum 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 includes a processor capable of running the efficient analysis method of low-order abnormal frequency components of tooth surface errors.

[0024] A device comprising:

[0025] Memory: a computer program for storing the method for efficiently analyzing low-order abnormal frequency components of tooth surface errors;

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

[0027] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a method for efficiently analyzing 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. The present invention realizes the premise of tooth surface error measurement point planning through the measurement point distribution trajectory on the tooth surface in step A and the coordinate position calculation in step B. The number of measurement points is far less than that of the existing tooth surface error order analysis method, which is conducive to solving the problem of long tooth surface error measurement time and greatly improving the detection efficiency of gear accuracy on the production site.

[0030] 2. Step D of the present invention achieves accurate prediction of the low-order spectral components of the tooth surface error through measurement point error data measurement plan planning and frequency domain feature analysis, which is conducive to solving the problems of existing tooth surface low-order frequency component detection process relying on expensive imported software, unavailable original data, and high analysis cost.

[0031] In summary, the present invention obtains the variation of the length error by measuring the applied position of the measuring point, and obtains the low-order spectrum distribution of the tooth surface error by using the frequency domain variation of the length error. The present invention has high analysis efficiency, strong versatility, and a wide range of applications. It can be applied to the precision detection of different types of gears during and after machining, and provides means and tools for error analysis in the large-scale production process of gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of gear structure and tooth distribution.

[0033] Figure 2 Schematic diagram of tooth surface error measurement point trajectory.

[0034] Figure 3 This is a schematic diagram of the tooth surface error measurement point distribution of the present invention, where: Figure 3 (a) is the intersection of the truncated curve 4 at the middle position of the tooth width and the middle trajectory 3. Figure 3 (b) in the figure shows that there is no intersection between the truncated curve 4 at the middle position of the tooth width and the middle trajectory 3.

[0035] Figure 4 Schematic diagram of the tooth surface error measurement system.

[0036] Figure 5 Schematic diagram of the variation of the length error with the number of teeth.

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

[0038] Figure 7 This is the result of tooth surface error order analysis of a commercial gear tester.

[0039] In the figure: 1-gear; 11-first tooth; 12-second tooth; 13-third tooth; 111-left tooth surface; 112-right tooth surface; 2-contact trajectory; 3-middle trajectory; 4-truncation curve at the middle position of the tooth width; 5-intersection curve of the pitch circle and the tooth surface; 6-probe. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present 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 only used to explain the present invention and are not intended to limit the present invention.

[0041] The structure of the gear 1 analyzed by the present invention is as follows Figure 1 As shown in the figure, 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), such as the first tooth 11, the second tooth 12, the third tooth 13, etc.; each tooth has a left tooth surface 111 and a right tooth surface 112; when gear 1 is ground, the upper head is z1, and the axial feed is f z .

[0042] Based on the above-mentioned gear 1, an efficient analysis method of low-order abnormal frequency components of tooth surface error of the present invention includes the following steps:

[0043] Step A: Calculate the measurement point distribution trajectory parameters through the grinding process parameters and the tooth surface grinding contact trajectory.

[0044] The grinding condition sets the grinding wheel speed to n and the number of heads to Zw. 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 the gear 1 forms a contact track 2. There are multiple contact tracks 2 on the tooth surface, and their axial spacing is . The axial feed rate is d z =f z Z / n w Z w The upper part of the head is taken as the starting point of z coordinate z=0, and the coordinates of each point j on the i-th contact track 2i (x 2ij ,y 2ij ,z 2ij ) is calculated through meshing analysis of the gear and worm grinding wheel. The radius of each point j on the contact trajectory 2i is Radius R on contact track 2i 2ij and z coordinate z 2ij The value ranges are [min(R 2ij ),max(R 2ij )] and [min(z 2ij ),max(z 2ij )]. The middle track 3 is between two adjacent contact tracks, representing the residual height of the grinding wheel between adjacent contact tracks on the right tooth surface 112. The coordinates (x 3ij ,y 3ij ,z 3ij) According to 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 calculated by using polynomials, spline curves and other methods. 3ij and z coordinate z 3ij Fitting, when the variable is 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 truncation of the middle position of the tooth width is the truncation curve 4 at the middle position of the tooth width, and the z coordinate of each point on it is 0.5H. The intersection line of the pitch circle and the right tooth surface 112 is the intersection curve 5 of the pitch circle and the tooth surface, and the radius of each point on it is 0.5d. When grinding, the first tooth 11 is processed from top to bottom, according to the head amount z1 and the axial feed amount f z The coordinates of each point j on the first intermediate trajectory (x 31j ,y 31j ,z 31j ), the range of z coordinate is [min(z 31j ),max(z 31j )]. Then, the minimum and maximum values ​​of the z coordinate on the i-th intermediate track 3i are and

[0045] For other teeth 1k (k=2,…,Z), the contact track 2 on the tooth surface has an axial distance from the contact track on the first tooth 11, and the axial distance is d zT =f z / n w Z w Then, the minimum and maximum values ​​of the z coordinate on the ith intermediate track 3i on the tooth surface of tooth 1k are and

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

[0047] On tooth 1k (k = 1, ..., Z), for all intermediate tracks 3, check the relationship between the value range of the z coordinate of each intermediate track and the z coordinate of the truncated curve 4 at the middle position of the tooth width. When the z coordinate of the i-th intermediate track 3i satisfies When , the truncated curve 4 at the middle position of the tooth width and the middle track 3 have an intersection. When calculating, the above intersection is selected as the measuring point. The measuring point position is as follows: Figure 3 (a). At this time, the z coordinate of the measuring point Measuring point radius for

[0048] For all intermediate tracks 3, when the value range of the z coordinate of any intermediate track 3i does not meet When , the truncated curve 4 indicating the middle position of the tooth width does not intersect with the middle track 3. When calculating, the intersection of the intersecting curve 5 between the pitch circle and the tooth surface and the middle track 3 is selected as the measuring point. The measuring point position is as follows: Figure 3 (b) shows that. At this time, the measuring point radius

[0049] The z coordinate is

[0050] Step C: Obtain the length error variation of all tooth surface measurement points according to the coordinates of the tooth surface error measurement points;

[0051] Measuring point P on right tooth surface 112 m The error data measurement method is as follows Figure 4 As shown, the gear 1 is mounted on a precision testing device such as a gear tester through a fixture, and the probe 6 is moved along the radial direction of the gear to the measuring point P. m Radius Move along the gear axis to the measuring point P m The z coordinate of Rotate the gear 1 so that the right tooth surface 112 of the first tooth 11 contacts the probe 6, and obtain the measuring point P on the right tooth surface 112. m The actual length L m,1 , and the measuring point P m Theoretical Development Measuring point P m The actual value of the extension is subtracted from the theoretical value to obtain the measuring point P m The length error LE m,1 Measuring point P on the right tooth surface 112 of the first tooth 11 mAfter the length error measurement is completed, the gear 1 is rotated around the z axis by i-1 (i=2,…,Z) pitch angles, and the above process is repeated to measure the measuring point P on the right tooth surface of all teeth. m The length error LE m,i .

[0052] Take the measuring point P on the right tooth surface 112 of the first tooth 11 m The length error LE m,1 Based on the second tooth 12 right tooth surface 122 measuring point P m The length error change is expressed as ΔL m2 =LE m,2 -LE m,1 Similarly, the measuring point P on the right tooth surface 1i2 of the i-th tooth 1i is m The length error change is expressed as ΔL mi =LE m,i -LE m,i-1 Then we can get the variation law of the length error with the number of teeth ( Figure 5 ). With the pitch angle θ zi =(i-1)2π / Z is a variable, and polynomials, spline curves and other curves are used to calculate the measuring points P on the right tooth surface of all teeth. m The length error variation is fitted, and the expression between the length error variation and the pitch angle is obtained as ΔL m =f(θ z ).

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

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

[0055] According to the working speed set in the gear grinding working condition, the time data corresponding to the pitch angle sequence is t=θ zi / n. All measuring points P on the teeth m The length error variation data ΔL m Based on the frequency resolution, the variation of the span error is discretized, and the spectrum of the variation of the 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 gets the frequency multiple sequence as XN(ΔL m )=60X(ΔL m) / n. Based on the spectrum of the length error variation and the frequency multiple sequence, the low-order spectrum characteristics of the tooth surface error data can be 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.

[0056] The present invention also includes:

[0057] A system includes a processor capable of running the efficient analysis method of low-order abnormal frequency components of tooth surface errors.

[0058] A device comprising:

[0059] Memory: a computer program for storing the method for efficiently analyzing low-order abnormal frequency components of tooth surface errors;

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

[0061] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a method for efficiently analyzing low-order abnormal frequency components of tooth surface errors.

[0062] Application examples:

[0063] The gear tooth surface data of Z=18 were measured and analyzed using a commercial gear tester and the method of the present invention. After measuring the right tooth surface with the commercial gear tester, an abnormal frequency of order 12 was found through order analysis, with an amplitude of 0.052 ( Figure 6 The analysis results of the method of the present invention also found that there is an abnormal frequency of order 12 on the right tooth surface, with an amplitude of 0.051 ( Figure 7 ), with an error of less than 2%, demonstrating the effectiveness and accuracy of the proposed method in identifying abnormal frequencies. Furthermore, commercial gear testers measure and analyze each tooth individually, typically requiring thousands of data points. However, the proposed method only requires Z data points, significantly reducing analysis efficiency.

Claims

1. An efficient analysis method for low-order abnormal frequency components of tooth surface errors, characterized by: The following steps are involved: Step A: Calculate the measurement point distribution trajectory parameters through the grinding process parameters and the tooth surface grinding contact trajectory; Step B: Based on the measurement point distribution trajectory parameters, the measurement point radius coordinates are calculated according to the intersection of the truncation curve at the middle position of the tooth width and the measurement point distribution trajectory to determine the tooth surface error measurement point position; Step C: Obtain the length error variation of all tooth surface measurement points according to the coordinates of the tooth surface error measurement points; Step D: Use Fourier transform to obtain the tooth surface error data spectrum characteristic curve for the length error variation of all tooth surface measurement points, and then use the frequency domain analysis method to obtain the abnormal low-order frequency components of the tooth surface error.

2. The efficient analysis method of low-order abnormal frequency components of tooth surface errors according to claim 1 is characterized in that: The step A is specifically as follows: 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 track (2). There are multiple contact tracks (2) on the tooth surface, and the axial spacing is d. The axial feed rate is d. z =f z Z / n w Z w , take the top of the head as the z coordinate starting point z = 0, the coordinates of each point j on the i-th contact track 2i (x 2ij ,y 2ij ,z 2ij ) is calculated through meshing analysis of the gear and worm grinding wheel. The radius of each point j on the contact trajectory 2i is Radius R on contact track 2i 2ij and z coordinate z 2ij The value ranges are [min(R 2ij ),max(R 2ij )] and [min(z 2ij ),max(z 2ij )]; the middle track (3) between two adjacent contact tracks represents the residual height of the grinding wheel between adjacent contact tracks on the right tooth surface 112; the coordinates (x 3ij ,y 3ij ,z 3ij ) According to 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 coordinate z 3ij 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 truncation of the middle position of the tooth width is the truncation curve (4) at the middle position of the tooth width, and the z coordinate of each point on it is 0.5H; the intersection line of the pitch circle and the right tooth surface (112) is the intersection curve (5) of the pitch circle and the tooth surface, and the radius of each point on it is 0.5d; when grinding, the first tooth (11) is processed from top to bottom, according to the head amount z1 and the axial feed amount f z The coordinates of each point j on the first intermediate trajectory (x 31j ,y 31j ,z 31j ), the range of z coordinate is [min(z 31j ),max(z 31j )]; then, the minimum and maximum values ​​of the z coordinate on the i-th intermediate track 3i are and For other teeth 1k (k=2,…,Z), there is an axial distance between the contact track (2) on the tooth surface and the contact track on the first tooth (11), and the axial distance is d zT =f z / n w Z w Then, the minimum and maximum values ​​of the z coordinate on the i-th intermediate track 3i on the tooth surface of tooth 1k are and 3. The efficient analysis method of low-order abnormal frequency components of tooth surface errors according to claim 2 is characterized in that: The step B is specifically as follows: On tooth 1k (k = 1, ..., Z), check the relationship between the range of the z coordinate of each intermediate track and the z coordinate of the truncated curve (4) at the middle position of the tooth width in turn; when the z coordinate of the i-th intermediate track 3i satisfies When , the truncated curve (4) indicating the middle position of the tooth width and the middle track (3) have an intersection point, and the above intersection point is selected as the measuring point during calculation; at this time, the z coordinate of the measuring point Measuring point radius for For all intermediate trajectories (3), when the value range of the z coordinate of any intermediate trajectory 3i does not satisfy When the truncated curve (4) indicating the middle position of the tooth width does not intersect with the middle track (3), the intersection of the intersection curve (5) of the pitch circle and the tooth surface and the middle track (3) is selected as the measuring point during calculation. At this time, the measuring point radius The z coordinate is 4. The efficient analysis method for low-order abnormal frequency components of tooth surface errors according to claim 3 is characterized in that: The step C is specifically as follows: After the gear (1) is mounted on the testing device, the probe (6) is moved radially along the gear to the measuring point P. m Radius Move along the gear axis to the measuring point P m The z coordinate of At , rotate the gear 1 so that the right tooth surface (112) of the first tooth (11) contacts the probe (6), and obtain the measuring point P on the right tooth surface (112). m The actual length L m,1 , measuring point P m Actual and theoretical values ​​of the extension Subtract the length error LE m,1 Then, rotate the gear (1) around the z axis by i-1 (i=2,…,Z) pitch angles, and repeat the above process to measure the measuring points P on the right tooth surface of all teeth. m The length error LE m,i ; Take the measuring point P on the right tooth surface (112) of the first tooth (11) m The length error LE m,1 Based on, calculate the measuring point P on the right tooth surface 1i2 of the i-th tooth 1i m The length error change is expressed as ΔL mi =LE m,i -LE m,i-1 , we can get the variation law of the length error with the number of teeth; with the pitch angle θ zi =(i-1)2π / Z is a variable, and the measuring point P on the right tooth surface of all teeth m The length error variation is fitted, and the expression between the length error variation and the pitch angle is obtained as ΔL m =f(θ z ); Based on the same method as above, the extension errors and error variations of the measuring points on the right tooth surface (112) and the left tooth surface (111) of all teeth 1k (k=1,…,Z) of gear 1 are obtained.

5. The efficient analysis method of low-order abnormal frequency components of tooth surface errors according to claim 4 is characterized in that: The step D is specifically as follows: According to the working speed set in the gear grinding working condition, calculate the time data t=θ corresponding to the pitch angle sequence zi / n; The frequency spectrum of all tooth surface length error variations obtained by Fourier transform is: After Fourier transform, the frequency sequence is converted into a frequency multiple sequence of XN(ΔL m )=60X(ΔL m ) / n; According to the spectrum of the length error variation and the rotation frequency multiple sequence, the low-order spectrum 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.

6. A system, characterized in that: The invention comprises a processor capable of running the efficient analysis method of low-order abnormal frequency components of tooth surface errors as described in any one of claims 1 to 5.

7. A device, characterized in that include: Memory: a computer program for storing the method for efficiently analyzing low-order abnormal frequency components of tooth surface errors according to any one of claims 1 to 5; Processor: used to implement an efficient analysis method for low-order abnormal frequency components of tooth surface errors 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, and when the computer program is executed by a processor, the method for efficiently analyzing low-order abnormal frequency components of tooth surface errors according to any one of claims 1 to 5 is implemented.

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