Detection method and equipment for gear tooth surface ripple texture direction

Abstract

The invention relates to a gear tooth surface corrugation texture direction detection method and device, and belongs to the technical field of gear measurement. According to the to-be-detected tooth surface corrugation degree information, sine wave fitting of the tooth width middle position is carried out, and a multi-stage sine wave fitting model is established; taking each level of sine wave at the middle position of the tooth width obtained by fitting the multi-level sine wave fitting model as a fitting substrate; calling a multi-stage sine wave fitting model, fitting waviness information of other tooth width positions of the tooth surface into multi-stage sine wave composition with the same frequency as a fitting base, and obtaining sine wave composition of all tooth width positions of the tooth surface; calculating the direction angle of each sine wave according to the phase difference between the sine waves with the same frequency at all tooth width positions; calculating a corresponding weight according to the amplitude of each sine wave; based on the direction angles and the weights of all the sine waves, the direction of the tooth surface corrugation texture is obtained, the overall corrugation texture trend direction can be accurately determined, and the estimation accuracy of the gear noise performance is improved.

Description

Technical Field

[0001] This invention relates to a method and equipment for detecting the direction of ripple texture on gear tooth surfaces, belonging to the field of gear measurement technology. Background Technology

[0002] With the innovation of the automotive industry, electric vehicles have become the future development trend. Because electric vehicles lack engine noise masking, the noise of their transmission systems is more prominent, becoming one of the urgent problems to be solved. However, their direct-drive motor operation results in the transmission gears operating at high speeds. The goal of low noise at high speeds places more stringent requirements on the machining accuracy of the gears, especially the tooth surface morphology.

[0003] Among the many surface morphology factors affecting gear noise, tooth surface waviness plays a crucial role. As a periodic surface defect situated between macroscopic geometric errors and microscopic roughness, waviness's periodic deviation disrupts the smoothness of the meshing process. Ideally, gear meshing should maintain a smooth and seamless transmission. However, waviness on the tooth surface disrupts this ideal profile. When waviness-laden tooth surfaces mesh, the waviness texture significantly impacts the meshing process, with the degree of influence closely related to the direction of the waviness texture.

[0004] If the tooth surface ripple direction is parallel to the meshing contact line (or contact area, i.e., perpendicular to the contact trace), the crests and troughs of the ripples will cause periodic fluctuations in the position of the meshing contact point and the actual contact line length. This periodic disturbance results in unpleasant mid-to-high frequency noise (odd harmonic components above the meshing frequency) during meshing. Therefore, even a small ripple amplitude can generate significant high-frequency noise excitation. Although the tooth surface ripple direction has a significant impact on NVH performance, currently available domestic gear measuring equipment is only equipped with the function of detecting the tooth surface ripple direction. Therefore, achieving effective detection and evaluation of the tooth surface ripple direction is one of the keys to reducing noise in electric vehicle drive systems.

[0005] In the prior art, Chinese invention patent application CN119714158A discloses a method and system for detecting helical gears based on waviness information. The method includes: Step 1, extracting the waviness information of the entire helical gear; Step 2, processing the waviness information to obtain a spectrum; and Step 3, calculating the waviness angle on any single tooth of the helical gear. Step 4: Based on the angle of the corrugation on a single tooth. The first step involves using a spectrum diagram to determine if a gear is qualified. Step two includes: S201, fitting the tooth profile waviness curve B1 and the tooth direction waviness curve B2 using a fitting model to generate corresponding sine curves Q1 and Q2. Specifically, based on the core idea of ​​Fourier analysis, an initial fitting model is set, and the parameters in the initial fitting model are optimized using a grid search method to obtain the sine curve Q1 for the tooth profile waviness curve B1 and the sine curve Q2 for the tooth direction waviness curve B2. S202, order analysis is performed on Q1 and Q2 to generate corresponding spectrum diagrams pic1 and pic2; where the horizontal axis of pic1 and pic2 represents the order and the vertical axis represents the amplitude. It is evident that although an initial fitting model is set based on Fourier analysis, the grid search method is used during the initial fitting model construction process by setting a reasonable range for the initial prediction parameters. However, in cases of complex data composition, the grid search method consumes significant computational resources, which is not suitable for gear tooth surfaces with a large number of inspection requirements in practical application scenarios. Summary of the Invention

[0006] The purpose of this invention is to provide a method and device for detecting the direction of wavy texture on gear tooth surfaces, which fully considers the complexity of the periodic wavy texture of gears, accurately determines the overall trend direction, and achieves accurate detection of gear quality.

[0007] To achieve the above objectives, the present invention proposes a method for detecting the direction of ripple texture on gear tooth surfaces, comprising the following steps:

[0008] 1) Based on the waviness information of the tooth surface to be detected, a sine wave fitting is performed at the middle position of the tooth width to obtain a multi-level sine wave fitting result at the middle position of the tooth width; the multi-level sine wave fitting result is used as the fitting basis to establish a multi-level sine wave fitting model.

[0009] 2) Call the multi-level sine wave fitting model to fit the waviness information of the remaining tooth width positions on the tooth surface into a sine wave with the same frequency as the fitting base, and obtain the sine wave composition of all tooth width positions on the tooth surface.

[0010] 3) Calculate the direction angle of each sine wave based on the phase difference between sine waves of the same frequency at all tooth width positions; calculate the corresponding weight based on the amplitude of each sine wave; and obtain the direction of the tooth surface ripple texture based on the direction angle and weight of all sine waves.

[0011] Further, in step 1), based on the waviness information of the tooth surface to be detected, a sine wave fitting is performed at the mid-position of the tooth width. The multi-level sine wave fitting results at the mid-position of the tooth width are obtained through the following steps:

[0012] 11) Call the Fourier transform algorithm to perform spectral transformation on the tooth surface waviness information to be detected, and obtain the spectral transformed tooth surface waviness information;

[0013] 12) Perform sine wave decomposition on the tooth surface waviness information after spectrum conversion, and decompose the tooth surface waviness information into several sine waves to be fitted;

[0014] 13) Fit the sine wave to be fitted at the midpoint of the tooth width to generate a multi-level sine wave fitting result at the midpoint of the tooth width.

[0015] Furthermore, the tooth surface waviness information after spectral conversion is decomposed into sinusoidal waves through the following steps, decomposing the tooth surface waviness information into several sinusoidal waves to be fitted:

[0016] 121) Based on the spectral results of the tooth surface waviness information, select the frequency corresponding to the largest amplitude value in the spectral results as the initial frequency, and determine the initial sine wave based on the initial frequency;

[0017] 122) Using a nonlinear least squares optimization algorithm, for the tooth surface waviness information, the frequency and amplitude of an initial sine wave are used as initial values ​​to iteratively search for the minimum residual and its corresponding frequency and eigenvalue; based on the frequency and eigenvalue corresponding to the minimum residual, the sine wave with the largest amplitude in the tooth surface waviness information is obtained; during the iterative search process, the current sine wave is determined based on the current search frequency and eigenvalue; the tooth surface waviness information after removing the current sine wave is set as the current residual; the minimum residual is the residual with the smallest value among all residuals during the iterative search process;

[0018] 123) When the minimum residual does not reach the preset convergence accuracy requirement, the minimum residual is replaced with the tooth surface waviness information in step 121), and steps 121) to 123) are continued until the minimum residual reaches the preset convergence accuracy requirement, and all the obtained maximum amplitude sine waves are determined as the several sine waves to be fitted.

[0019] Furthermore, in step 13), during the fitting process of the sine wave to be fitted at the midpoint of the tooth width, the multi-level sine wave fitting model is constructed based on the frequency information of the sine wave to be fitted at the preset midpoint of the tooth width.

[0020] Further, step 2) includes:

[0021] Determine the sine wave to be fitted corresponding to the waviness information at the remaining tooth width positions;

[0022] Based on the multi-level sine wave fitting model, the amplitude and phase of the sine wave to be fitted at the frequency of the fitting substrate at the remaining tooth width positions are calculated to obtain the multi-level sine wave composition at the remaining tooth width positions. Based on the multi-level sine wave composition at the middle position of the tooth width and the multi-level sine wave composition at the remaining tooth width positions, the multi-level sine wave composition at all tooth width positions of the tooth surface is obtained to characterize the tooth surface ripple texture.

[0023] Furthermore, the fitting formula for the sine wave to be fitted at the remaining tooth width positions using the multi-level sine wave fitting model is as follows:

[0024]

[0025] The amplitude is calculated using the following formula:

[0026] ;

[0027] The phase is calculated using the following formula:

[0028] ;

[0029] Among them, F wi This represents the final fitting result for each tooth width position; a it b it These are the quantities used in the fitting process, for ease of calculating phase and amplitude; f t A represents the t-th sine wave frequency in the multi-level sine wave fitting model. itmax This represents the amplitude of the t-th sine wave in the fitting result of the i-th tooth profile; Let t be the phase of the sine wave in the fitting result of the i-th tooth profile.

[0030] Further, in step 3), based on the phase difference between sine waves of the same frequency at all tooth width positions, the direction angle of each sine wave is calculated using the following method:

[0031] Using the tooth width position and its corresponding sine wave phase as variables, a linear regression fitting is performed to obtain an approximate linear relationship model between tooth width and phase; based on the approximate linear relationship model between tooth width and phase, the phase difference caused by the change in tooth width length is calculated; and based on the phase difference caused by all changes in tooth width length, the direction angle of each sine wave is obtained.

[0032] Furthermore, the orientation angle is calculated using the following formula:

[0033] ;

[0034] in, For each sine wave, the direction angle is denoted as ; This represents the change in tooth width. Indicates the wavelengths corresponding to different frequency components; t represents the phase difference; t is the index of the sine wave included in the multi-level sine wave fitting model.

[0035] Further, in step 3), the corresponding weights are calculated based on the amplitude of each sine wave using the following formula:

[0036] ;

[0037] in, As weight; The amplitude; t represents the sum of squares of the amplitudes of all sine waves on the tooth surface; t is the index of the sine waves included in the multi-level sine wave fitting model.

[0038] On the other hand, the present invention also proposes a detection device for the direction of gear tooth surface ripple texture, including a processor, the processor being used to execute the above-mentioned detection method for the direction of gear tooth surface ripple texture.

[0039] The beneficial effects of this invention are as follows: Based on the waviness information of the tooth surface to be detected, a sine wave is fitted at the mid-tooth width position to obtain a multi-level sine wave fitting result at the mid-tooth width position; the multi-level sine wave fitting result is used as the fitting base to establish a multi-level sine wave fitting model; the multi-level sine wave fitting model is called to fit the waviness information of the remaining tooth width positions of the tooth surface into a sine wave with the same frequency as the fitting base, thus obtaining a sine wave composition for all tooth width positions of the tooth surface; the direction angle of each sine wave is calculated based on the phase difference between the sine waves of the same frequency at all tooth width positions; the corresponding weight is calculated based on the amplitude of each sine wave; based on the direction angle and weight of all sine waves, the direction of the tooth surface waviness texture is obtained. This fully considers the complexity of the periodic waviness texture of the gear, accurately determines the overall trend direction, and enables the prediction of gear noise performance during the measurement stage, thereby helping manufacturers control noise from the source. In addition, it can be used as a monitoring tool to adjust the machining process parameters and cutting tools in a timely manner based on the measurement results, so as to ensure the quality of the machined tooth surface morphology and provide assistance for the precision control of the entire life cycle of gear machining inspection. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating a method for detecting the direction of ripple texture on gear tooth surfaces proposed in this invention.

[0041] Figure 2 This is a schematic diagram of the measurement trajectory when the gear tooth surface ripple texture direction detection method proposed in this invention is used to obtain tooth surface measurement information in actual application scenario 1;

[0042] Figure 3 This is a schematic diagram of the fitting result of the gear tooth surface ripple texture direction detection method proposed in this invention at the middle position of the tooth width in actual application scenario 1;

[0043] Figure 4 This is a schematic diagram of the tooth profile fitting results at other positions on the tooth surface in actual application scenario 1, based on the detection method for the direction of ripple texture on the gear tooth surface proposed in this invention.

[0044] Figure 5 This is a schematic diagram illustrating the direction angle calculation principle of the gear tooth surface ripple texture direction detection method proposed in this invention in practical application scenario 1;

[0045] Figure 6 This is a schematic diagram of the texture direction angles of the left and right tooth surfaces calculated in actual application scenario 1 using the gear tooth surface ripple texture direction detection method proposed in this invention.

[0046] Figure 7 This is a schematic diagram of the meshing contact line principle on the internal tooth surface of a gear in the prior art;

[0047] Figure 8 This is a flowchart illustrating the detection method for the direction of ripple texture on gear tooth surface proposed in this invention in practical application scenario 2. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0049] The inventive concept of this invention is as follows: In order to accurately detect the direction of the waviness texture on the tooth surface, a multi-level sine wave fitting model is established by fitting and decomposing the waviness curve at the middle position of the tooth width, thereby obtaining a set of sine wave fitting bases to process the waviness at other tooth width positions on the same tooth surface, improving the accuracy of sine wave fitting of waviness information and the accuracy of phase difference calculation between each sine wave, so as to accurately detect the direction of the waviness texture on the gear tooth surface, fully considering the complexity of the periodic waviness texture of the gear, and at the same time, by judging the texture direction angle, a preliminary assessment of the gear noise performance can be achieved, providing a new idea for the control of gear noise performance.

[0050] Detailed implementation method 1:

[0051] like Figure 1 The diagram shown is a flowchart illustrating a method for detecting the direction of ripple texture on a gear tooth surface proposed in this invention. The method includes steps S11, S12, and S13, specifically:

[0052] Step S11: Based on the tooth surface waviness information to be detected, a sine wave fitting is performed at the mid-tooth width position to obtain a multi-level sine wave fitting result for the mid-tooth width position. The multi-level sine wave fitting result is used as the fitting basis to establish a multi-level sine wave fitting model. Here, during the sine wave fitting process at the mid-tooth width position, a Fourier transform algorithm is called to perform a spectral transformation on the tooth surface waviness information to be detected, obtaining the spectrally transformed tooth surface waviness information. The spectrally transformed tooth surface waviness information is then decomposed into several sine waves to be fitted, wherein the several sine waves to be fitted obtained here are several sine waves with different frequencies. The sine waves constituting the mid-tooth width position are fitted to generate the multi-level sine wave fitting result for the mid-tooth width position. The mid-tooth width position refers to a pre-defined mid-tooth width range based on gear specifications or industrial requirements.

[0053] Meanwhile, the tooth surface waviness information to be detected in step S11 is obtained by the following method: measuring the shape information of the tooth surface based on the gear measurement center; performing detrending term processing on the measured tooth surface information to remove information such as bulging amount in the measurement information that affects the acquisition of tooth surface waviness information; and using wavelet decomposition algorithm to extract waviness information from the measurement data to obtain the tooth surface waviness information to be detected.

[0054] Step S12: Call the multi-level sine wave fitting model to fit the waviness information of the remaining tooth width positions on the tooth surface into a sine wave with the same frequency as the fitting base, thus obtaining the sine wave composition of all tooth width positions on the tooth surface. Here, in the fitting process of actual application scenarios, in order to facilitate the subsequent calculation of amplitude and phase of the fitting results, it is preferable that the multi-level sine wave fitting model uses the following fitting equation to decompose the sine wave to be fitted corresponding to the waviness information of the remaining tooth width positions into the form shown below. Specifically, the fitting equation is:

[0055] ;

[0056] Where i=1…k is the number of corresponding measurement paths on the tooth surface; m represents the number of sine waves contained in the fitting base; f t It is a set of known results; , To fit the intermediate values ​​of the sine wave, the final amplitude and phase can be calculated based on these two parameters. During the fitting process, the waviness information at the remaining tooth width positions is calculated, corresponding to the frequency of the sine wave to be fitted at the frequency of the fitting substrate. , And then according to , The amplitude and phase information of the corresponding frequency components are obtained. Finally, the tooth waviness of the remaining tooth width positions after fitting can be expressed as follows:

[0057] ;

[0058] in, ; Let be the amplitude of the t-th sine wave in the fitting result of the i-th tooth profile; f represents the phase of the t-th sine wave in the fitting result of the i-th tooth profile; t t is the frequency of the t-th sine wave in the tooth profile fitting result (i.e., the t-th sine wave frequency in the multi-level sine wave fitting model); i=1…k is the number of corresponding measurement paths on the tooth surface; t is the index of the sine wave included in the multi-level sine wave fitting model.

[0059] Step S13: Calculate the direction angle of each sine wave based on the phase difference between sine waves of the same frequency at all tooth width positions; calculate the corresponding weight based on the amplitude of each sine wave; and obtain the direction of the tooth surface ripple texture based on the direction angles and weights of all sine waves. Here, the amplitude of the sine wave is proportional to its corresponding texture angle weight. The direction of the tooth surface ripple texture is calculated using the following formula:

[0060] ;

[0061] in, The direction of the tooth surface wavy texture; Let be the texture angle of the t-th sine wave; is the texture angle weight of the t-th sine wave; t is the index of the sine waves included in the multi-level sine wave fitting model.

[0062] The direction angle of each sine wave is calculated using the following formula:

[0063] ;

[0064] in, For each sine wave, the direction angle is denoted as ; This represents the change in tooth width. Indicates the wavelengths corresponding to different frequency components; t represents the phase difference; t is the index of the sine wave included in the multi-level sine wave fitting model.

[0065] The weights corresponding to each sine wave are calculated using the following formula:

[0066] ;

[0067] in, As weight; The amplitude; t represents the sum of squares of the amplitudes of all sine waves on the tooth surface; t is the index of the sine waves included in the multi-level sine wave fitting model.

[0068] Through the above steps S11-S13, a sinusoidal fitting base is constructed based on the waviness curve fitting in the middle of the tooth width, thereby processing the waviness at the remaining tooth widths on the same tooth surface, which facilitates the calculation of the phase difference; in the process of phase difference calculation, the overall trend of the waviness texture of the tooth surface is characterized by calculating the texture angle weight.

[0069] Method Detailed Implementation 2:

[0070] In practical application scenario 1, the specific steps of the gear tooth surface ripple texture detection method proposed in this invention are as follows:

[0071] Step 1: Obtaining Tooth Surface Measurement Information

[0072] Error topology information of the tooth surface is obtained based on the gear measurement center. Therefore, a topology plan is developed on the tooth surface as follows: Figure 2 The diagram shows the measurement trajectory when measuring information on the tooth surface. Multiple tooth profiles (15 or more) are measured at equal intervals in the tooth width direction to obtain tooth surface deviation information. The measured tooth profile information is then used to form the error tooth surface.

[0073] Step 2: Detrending Processing of Tooth Profile Information

[0074] Information such as bulge and modification amounts included in the measured tooth profile information is defined as trend terms. To avoid the influence of trend terms on the acquisition of tooth surface waviness information, they are removed from the measurement information. The trend term components in the tooth profile measurement information are fitted using a least-squares quadratic polynomial, and the fitting results are removed from the measurement data to obtain pure tooth profile deviation information.

[0075] Step 3: Extraction of waviness information

[0076] To obtain the direction of the waviness texture on the tooth surface, waviness information needs to be extracted from the tooth profile deviation. Waviness information, along with roughness and shape error, constitutes the tooth profile deviation, and these three are defined by wavelength. Waviness belongs to the low-frequency range. Wavelet decomposition algorithm is used for extraction. First, an appropriate number of decomposition levels is selected. According to GB / Z18620.4-2008 (Test Specification for Cylindrical Gears Part 4: Inspection of Surface Structure and Tooth Contact Spots), the boundary wavelengths between gear surface waviness and roughness / shape error are... , To decompose the three error components in as much detail as possible, we selected... The number of boundary layers was calculated as follows:

[0077] ;

[0078] In the formula, Fs The sampling frequency during measurement; The wavelength is the dividing line between waviness and shape error. Using wavelet functions and scaling functions, the original tooth profile deviation information is decomposed into low-frequency approximate signals and high-frequency detail signals. The low-frequency approximate signal is used as the input for the next decomposition layer. This decomposition process is repeated until the required number of decomposition layers is reached, ultimately obtaining P. max Layer detail information and one layer approximation information. Combined with the sampling frequency F s Based on the frequency band separation characteristics achieved by wavelet decomposition, information with wavelengths conforming to waviness characteristics is selected for reconstruction processing to finally obtain the tooth surface waviness information. (That is, the waviness information of the tooth surface to be detected).

[0079] Step 4. Decomposition of tooth surface ripple texture direction

[0080] The tooth surface waviness texture is decomposed into the superposition of multiple sinusoidal wave textures with different frequencies and directions. The directionality of a single sinusoidal wave texture is manifested in the phase change with the tooth width position at different tooth width sections. Therefore, its direction can be calculated based on the tooth width positions of each measured tooth profile and the phase difference between them. In order to obtain the sinusoidal decomposition results of the same frequency components of waviness at each tooth width position, the waviness curve in the middle of the tooth width is fitted and decomposed to establish a multi-level sinusoidal wave fitting model to obtain a set of sinusoidal wave fitting bases, thereby processing the waviness at other tooth widths on the same tooth surface and facilitating the calculation of phase differences. The specific steps are as follows:

[0081] Fast Fourier Transform (FFT) is performed on the tooth-shaped waviness information to obtain the spectral results of the waviness curve. Based on the spectral results, the frequency with the largest amplitude is selected as the initial value. An optimization method is then used to solve for the maximum amplitude sine wave contained in the waviness curve. The residual R0 is used as the initial value. er Using minimum as the objective function, we find the optimal frequency and amplitude, among other characteristic values. Specifically:

[0082] Let the frequency of the maximum amplitude obtained from the Fourier analysis be f0 (initial frequency). Then, the initial sine wave components can be expressed as follows:

[0083] ;

[0084] Where x represents the corresponding tooth profile extension; a and b are eigenvalues; f0 is the maximum amplitude frequency, based on the known waviness information (i.e., the tooth surface waviness information obtained in step 3). The values ​​of a and b are obtained by solving the least squares principle, thereby determining the initial sine wave F. 0max Therefore, F is calculated and removed. 0maxThe subsequent measurement data (i.e., the tooth surface waviness information obtained in step 3) The initial residuals of )

[0085] ;

[0086] Where r represents the waviness information (i.e., the tooth surface waviness information obtained in step 3). ).

[0087] However, since the accuracy of the results obtained from Fourier analysis is affected by the measurement length, in order to more accurately obtain the sine wave with the maximum amplitude contained in the waviness information, a nonlinear least squares optimization algorithm is adopted with the minimum residual obtained in each search as the optimization objective. This algorithm is used to obtain the original waviness information (i.e., the tooth surface waviness information). In the search around frequency f0, the minimum residual and its corresponding optimal frequency f1, as well as the corresponding a1 and b1 values, are obtained. From this, the original waviness information (i.e., the tooth surface waviness information obtained in step 3) can be obtained. The expression for the maximum amplitude sine wave contained in the ) is:

[0088] ;

[0089] in, ; F 1max Remove from the ripple information (i.e., remove the fitted F...) 1max The tooth surface waviness information obtained in step 3 (This will be eliminated during the process). F will be obtained. 1max Minimum residual R at time er `as the original information (i.e., to remove F) 1max Rear tooth surface waviness information The original waviness information is used as the basis for subsequent steps. This process is repeated, decomposing the original waviness information by determining the initial frequency based on the Fourier spectrum results, searching for the minimum residual and its corresponding optimal frequency and eigenvalue near the initial frequency, and then determining the maximum amplitude sine wave contained in the original waviness information. Each order of sine wave components is solved sequentially until the minimum residual reaches the preset convergence accuracy requirement, which is considered the completion of the decomposition of the tooth surface waviness (i.e., the "maximum amplitude sine wave" removed each time is taken as the waviness of each order on the tooth surface). The maximum amplitude sine wave removed each time is determined as the several sine waves to be fitted. If the number of sine waves obtained when the convergence accuracy requirement is reached is m, then the final fitting result of the waviness error curve can be expressed by the following formula:

[0090] ;

[0091] in, ; Let be the amplitude of the t-th sine wave in the fitting result of the i-th tooth profile; f represents the phase of the t-th sine wave in the fitting result of the i-th tooth profile; t t is the frequency of the t-th sine wave in the fitting result of the tooth profile; i=1…k is the number of corresponding measurement paths on the tooth surface; t=1…m is the index of the sine wave obtained by fitting decomposition on the tooth surface.

[0092] Multiple sine waves of different frequencies that constitute the waviness information in the middle of the tooth width are used to retain only their frequency information (sin(2πf)). t (t=1…m)), construct the tooth surface fitting base, see Figure 3 This is a schematic diagram showing the fitting results of the gear tooth surface ripple texture direction detection method proposed in this invention at the mid-tooth width position in practical application scenario 1. The tooth profile ripple F at the remaining tooth widths on the same tooth surface is also shown using this set of bases. wi The line fitting is performed, and the fitting equation is expressed as follows:

[0093] ;

[0094] Where i=1…k is the number of corresponding measurement paths on the tooth surface; m represents the number of sine waves contained in the fitting base; f t This is a set of known results, specifically referring to the frequencies of various orders of sine waves obtained by fitting a sine wave at the midpoint of the tooth width. Here, since the sine wave results obtained by fitting at the midpoint of the tooth width are used as the fitting basis, a multi-level sine wave fitting model is established to fit the remaining tooth profile on the tooth surface. Therefore, f t It is a set of known results; , For eigenvalues, which are the same process quantities as those fitted to the middle of the tooth width, in order to facilitate the solution of amplitude and phase information, it is only necessary to calculate 'a' at the corresponding frequency. it b it According to a it b it The amplitude and phase information of the corresponding frequency components can then be calculated. The final tooth waviness after fitting can be expressed as follows:

[0095] ;

[0096] in, The amplitude; For phase; i=1…k is the number of corresponding measurement paths on the tooth surface; f t Let be the frequency of the t-th sine wave in the fitting result of the tooth profile; t=1…m are the indices of the sine waves obtained by fitting decomposition on the tooth surface. This has been verified, as shown below. Figure 4The diagram shows the tooth profile fitting results at other positions on the tooth surface in actual application scenario 1 of the gear tooth surface ripple texture direction detection method proposed in this invention. The fitting results of the ripple at other tooth widths on the same tooth surface all have good effects, and the same frequency components of the ripple curves at different tooth widths can be obtained.

[0097] Step 5. Solving for the direction and angle of the ripple texture.

[0098] This step calculates the texture direction of each frequency sinusoidal component that constitutes the tooth surface corrugation. Solving for the texture direction only requires calculating the phase difference between each frequency component at different tooth widths, and combining this with the tooth width position to obtain the corresponding direction angle (see...). Figure 5 The red ripples represent one of the sinusoidal wave components in the middle of the tooth width. When these ripples move along the black diagonal lines in the diagram, they form a ripple texture on the tooth surface. The direction angle of the texture... This is represented by a black diagonal line. The specific effect of moving along this black diagonal line at different tooth widths is that the phase of the sine wave changes, i.e., a phase difference is generated, as shown in the formula in the figure. When moving along the tooth width... At that time, the phase changed. The texture orientation angle can be calculated based on the relationship between phase and wavelength. ).

[0099] To facilitate the calculation of the texture orientation angle, linear regression fitting is performed using the tooth width position and the phase corresponding to the same frequency component at the same position as variables to obtain an approximate linear relationship between tooth width and phase. This allows for the calculation of the phase difference caused by a unit change in tooth width. The texture direction angle is calculated by processing multiple tooth profile errors measured on the tooth surface to obtain the waviness composition at each tooth width position. The fitting results at each tooth width position are all composed of the same set of sine waves (each sine wave in the set has a different frequency). Therefore, each frequency of sine wave represents a texture direction, and only sine waves with the same frequency can calculate the corresponding texture direction based on the phase difference. The formula for calculating the texture direction angle can be expressed as follows:

[0100] ;

[0101] in, For each sine wave, the direction angle is denoted as ; This represents the change in tooth width. Indicates the wavelengths corresponding to different frequency components; t = 1…m represents the phase difference of the sine waves of the same frequency at different tooth width positions; t = 1…m represents the index of the sine waves obtained by fitting decomposition on the tooth surface. This refers to the texture angles of each sinusoidal component obtained from the final solution.

[0102] The overall trend of the tooth surface wavy texture is characterized by a weighted approach. The weight of each component constituting the tooth surface wavy texture is calculated based on the significance of the fluctuations of each sinusoidal wave component, and then the texture angle representing the overall trend is calculated based on these weights. The formula for calculating the weighted angle is as follows:

[0103] ;

[0104] in, As weight; The amplitude; t = 1…m represents the sum of squares of the amplitudes of all sine waves on the tooth surface; t = 1…m represents the index of the sine waves obtained by fitting decomposition on the tooth surface.

[0105] Based on the direction angles and weights of all sine waves, the direction of the tooth surface corrugation texture is obtained using the following formula: ;

[0106] in, The direction of the tooth surface wavy texture; Let be the texture angle of the t-th sine wave; represents the texture angle weight of the t-th sine wave; t=1…m represents the index of the sine wave obtained by fitting decomposition on the tooth surface. For example... Figure 6 As shown, the tooth surface texture direction angle is obtained after steps 1-5 in this specific embodiment, where the direction angle of the left tooth surface is... , The direction angle of the right tooth surface is , ,in, The weighted angle, calculated based on the weights of each frequency component, is used to characterize the overall corrugation direction of the tooth surface. The direction of the sine wave with the largest amplitude among all frequency components.

[0107] Step 6. Prediction of gear noise performance

[0108] According to the meshing principle of involute cylindrical helical gears, when a pair of gears mesh, the meshing contact line of the meshing tooth surfaces is as follows: Figure 7 As shown, during meshing, the contact line can be considered as the intersection of the meshing tooth surfaces and the meshing plane. However, due to the influence of the helix angle, the contact line of involute helical gears appears as a slanted straight line on the meshing plane, and the angle between this straight line and the axis is the base circle helix angle. .

[0109] Therefore, when periodic wavy textures exist on the tooth surface, the direction of these textures significantly affects the meshing state during gear engagement. When the angle between the wavy texture direction and the meshing contact trace is the same or small, the meshing contact line periodically contacts the peaks and troughs of the periodic wavy textures on the tooth surface during meshing. This results in a harmonic higher than the meshing order being generated during meshing. This higher-order harmonic becomes the excitation source for noise generation, increasing the risk of noise during gear meshing. Therefore, measuring the texture direction angle allows for early assessment of the risk of noise generation, thus enabling the screening of noisy gears.

[0110] As can be seen, the gear tooth surface ripple texture direction detection method proposed in this invention achieves preliminary prediction of gear noise performance based on the tooth surface ripple texture direction. When the macroscopic error of the gear being tested meets the requirements, the tooth surface ripple texture direction is evaluated. If the overall trend direction of the tooth surface ripple texture (i.e., the weighted angle obtained after processing the tooth surface data) is close to the direction of the meshing contact line (the angle threshold range needs to be determined in conjunction with gear parameters and actual requirements), it indicates that the gear has a high risk of generating noise excitation when it participates in meshing. Therefore, to achieve early judgment of gears with severe noise, the processing technology needs to be adjusted. Further analysis combined with the tooth surface ripple detection results can more accurately analyze the noise situation.

[0111] By including the direction angle of tooth surface ripple texture as one of the evaluation criteria for tooth surface machining quality during the measurement stage, and combining it with ripple degree detection and analysis, it is possible to judge noisy gears during the measurement stage, which is of great significance for guiding gear production.

[0112] Method Detailed Implementation 3:

[0113] like Figure 8 The diagram illustrates the process of detecting the direction of gear tooth surface ripple texture proposed in this invention in practical application scenario 2. First, the shape information of the tooth surface is measured based on the gear measurement center. Then, the measured tooth surface information undergoes detrending processing to remove the influence of information such as bulge volume from the measurement information. A wavelet decomposition algorithm is used to extract ripple information from the measurement data, obtaining the ripple texture present on the tooth surface. A multi-level sine wave fitting model is established to decompose the tooth profile ripple at each tooth width in the form of sine wave combinations. The sine waves of each order fitted to the tooth profile at the middle of the tooth width are used as the fitting basis to process the remaining tooth profiles on the same tooth surface. The direction angle of each sine wave component is calculated based on the phase difference of the fitting results, and the weight is calculated based on the amplitude of each component. The weighted angle represents the overall trend of the tooth surface ripple texture direction. By judging the texture direction angle, a preliminary assessment of gear noise performance is achieved. This allows for the early screening of gears with poor noise performance during the measurement stage, providing a new approach to controlling gear noise performance.

[0114] On the other hand, the present invention also proposes a detection device for the direction of gear tooth surface ripple texture, including a processor, the processor being used to execute a detection method for the direction of gear tooth surface ripple texture as described above. Here, the specific implementation of the device is described in specific implementations 1-3 of the method, and will not be repeated here.

[0115] In summary, this invention proposes a method for detecting and characterizing the direction of tooth surface ripple texture based on the measurement center of a gear. It obtains tooth surface topological error data through precise measurement of the gear tooth surface. The measurement data is processed to remove the influence of factors such as bulging, thus obtaining the tooth profile deviation. Wavelet decomposition is used to extract the waviness information contained in the tooth profile deviation. A multi-level sine wave fitting model is employed to decompose the tooth surface ripple texture into multi-level sine wave textures, and the texture direction is calculated based on the relationship between phase and tooth width. The relationship between the tooth surface ripple texture direction and the meshing contact line is used to preliminarily determine the gear's noise performance. This method fully considers the complexity of the gear's periodic ripple texture, accurately determines the overall trend direction, and enables the prediction of gear noise performance during the measurement stage, thereby helping manufacturers control noise at its source. Furthermore, it can be used as a monitoring tool to adjust machining process parameters such as honing and grinding, as well as cutting tools, in a timely manner based on the measurement results, ensuring the quality of the machined tooth surface morphology and contributing to the precision control of the entire lifecycle of gear machining and inspection.

Claims

1. A method of detecting the direction of a gear tooth surface waviness texture, characterized by, The method comprises the following steps: 1) according to the tooth surface waviness information to be detected, performing sinusoidal wave fitting on the tooth width middle position to obtain a multi-stage sinusoidal wave fitting result of the tooth width middle position; taking the multi-stage sinusoidal wave fitting result as a fitting base, and establishing a multi-stage sinusoidal wave fitting model; 2) calling the multi-stage sinusoidal wave fitting model, fitting the waviness information of the remaining tooth width positions of the tooth surface into sinusoidal waves with the same frequency as the fitting base to obtain sinusoidal wave composition of all tooth width positions of the tooth surface; 3) according to the phase difference between the sinusoidal waves with the same frequency at all tooth width positions, calculating the directional angles of the sinusoidal waves; and according to the amplitude of each sinusoidal wave, calculating the corresponding weight; based on the directional angles and the weight of all sinusoidal waves, obtaining the tooth surface waviness texture direction.

2. The method of claim 1, wherein, In step 1), according to the tooth surface waviness information to be detected, the sinusoidal wave fitting on the tooth width middle position is performed, and the multi-stage sinusoidal wave fitting result of the tooth width middle position is obtained through the following steps: 11) calling a Fourier transform algorithm, performing frequency spectrum conversion on the tooth surface waviness information to be detected to obtain the tooth surface waviness information after frequency spectrum conversion; 12) performing sinusoidal wave decomposition on the tooth surface waviness information after frequency spectrum conversion, and decomposing the tooth surface waviness information into a plurality of to-be-fitted sinusoidal waves; 13) fitting the to-be-fitted sinusoidal waves constituting the tooth width middle position to generate the multi-stage sinusoidal wave fitting result of the tooth width middle position.

3. The method of claim 2, wherein, The tooth surface waviness information after frequency spectrum conversion is decomposed into a plurality of to-be-fitted sinusoidal waves through the following steps: 121) according to the frequency spectrum result of the tooth surface waviness information, selecting the frequency corresponding to the maximum amplitude in the frequency spectrum result as an initial frequency, and determining an initial sinusoidal wave based on the initial frequency; 122) calling a nonlinear least squares optimization algorithm, taking the frequency and amplitude of the initial sinusoidal wave as initial values, and iteratively searching for the minimum residual and the corresponding frequency and characteristic value of the tooth surface waviness information; according to the frequency and characteristic value corresponding to the minimum residual, obtaining the maximum amplitude sinusoidal wave in the tooth surface waviness information; in the iterative search process, according to the current searched frequency and characteristic value, determining the current sinusoidal wave; taking the tooth surface waviness information after eliminating the current sinusoidal wave as the current residual; the minimum residual is the residual with the smallest value among all residuals in the iterative search process; 123) when the minimum residual does not meet the preset convergence accuracy requirement, replacing the minimum residual with the tooth surface waviness information in step 121), and continuing to execute steps 121) to 123) until the minimum residual meets the preset convergence accuracy requirement, and determining all obtained maximum amplitude sinusoidal waves as the plurality of to-be-fitted sinusoidal waves.

4. The method of claim 2, wherein, In step 13), in the process of fitting the to-be-fitted sinusoidal waves constituting the tooth width middle position, the multi-stage sinusoidal wave fitting model is constructed according to the frequency information of the to-be-fitted sinusoidal waves constituting the tooth width middle position.

5. The method of claim 1, wherein, The step 2) comprises: determining the to-be-fitted sinusoidal wave corresponding to the waviness information of the remaining tooth width positions; Based on the multi-stage sinusoidal wave fitting model, the amplitude and phase corresponding to the fitting base frequency of the to-be-fitted sinusoidal wave at the remaining tooth width positions are calculated to obtain the multi-stage sinusoidal wave composition of the remaining tooth width positions; according to the multi-stage sinusoidal wave composition of the tooth width middle position and the multi-stage sinusoidal wave composition of the remaining tooth width positions, the multi-stage sinusoidal wave composition of all tooth width positions of the tooth surface is obtained to represent the tooth surface wave texture.

6. The method of claim 5, wherein, The fitting formula of the multi-stage sinusoidal wave fitting model for the to-be-fitted sinusoidal wave at the remaining tooth width positions is as follows: wherein the amplitude is calculated by the following equation: ； The phase is calculated by the following formula: ； Where, F wi represents the final fitting result of each tooth width position; a it , b it are the fitting solution process quantities, in order to facilitate the solution of phase and amplitude; f t is the frequency of the tth sinusoidal wave in the multi-stage sinusoidal wave fitting model; A itmax represents the amplitude of the tth sinusoidal wave in the fitting result of the ith tooth profile; is the phase of the tth sinusoidal wave in the fitting result of the ith tooth profile.

7. The method of claim 1, wherein, In step 3), the direction angle of each sinusoidal wave is calculated according to the phase difference between the sinusoidal waves at all tooth width positions with the same frequency by the following method: Taking the tooth width position and the corresponding phase in the sinusoidal wave as variables, linear regression fitting is performed to obtain an approximate linear relationship model between the tooth width and the phase; based on the approximate linear relationship model between the tooth width and the phase, the phase difference generated by the tooth width length change is calculated; according to the phase difference generated by the tooth width length change, the direction angle of each sinusoidal wave is obtained.

8. The method of claim 7, wherein, The direction angle is calculated by the following formula: ； wherein, is a direction angle of each sine wave; is a tooth width variation amount; denotes a wavelength corresponding to a different frequency component; is a phase difference; t is an index of a sine wave included in the multi-stage sine wave fitting model.

9. The method of claim 1, wherein, In step 3), the corresponding weight is calculated according to the amplitude of each sinusoidal wave by the following formula: ； wherein, is a weight; is an amplitude; is a sum of the square of the amplitudes of all sinusoidal waves on the tooth surface; t is an index of the sinusoidal wave contained in the multi-stage sinusoidal wave fitting model.

10. An apparatus for detecting the direction of a gear tooth surface waviness texture, characterized by, The processor is used to execute the gear tooth surface wave texture direction detection method according to any one of claims 1-9.

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