Rapid detection method for tooth surface waviness of involute helical gear based on wavelet transformation

Abstract

The invention discloses an involute helical gear tooth surface waviness rapid detection method based on wavelet transformation, relates to the technical field of gear measurement and evaluation, and aims to solve the problems of low efficiency, insufficient anti-interference capability and limited extraction precision in existing tooth surface waviness detection. High-density data sampling is carried out on a specified tooth surface of an involute helical gear, a multi-scale characteristic decomposition signal of wavelet transform is utilized, a tooth surface waviness signal is separated from complex morphology characteristic components, and in combination with a threshold optimization algorithm, detail characteristics of waviness are effectively reserved, and meanwhile interference of non-correlation signals is restrained. In addition, efficient data processing and real-time waviness feature extraction are realized by designing a rapid analysis process and an automatic parameter adjustment mechanism. The method is suitable for gear quality detection in a batch production environment, and provides a reliable basis for defect diagnosis and optimization in a gear manufacturing process. Compared with a traditional detection method, the method has remarkable advantages in the aspects of detection precision, stability and speed.

Description

Technical Field

[0001] The present invention relates to the technical field of gear measurement and evaluation, in particular to a rapid detection method for tooth surface waviness of an involute helical gear based on wavelet transformation. Background Art

[0002] High-speed transmission gears are critical components in the machinery and automotive industries, and transmission noise is an increasing concern for high-quality production. Accurately measuring tooth surface waviness is crucial for improving gear processing quality and optimizing manufacturing processes. Traditional waviness detection methods typically rely on Fourier transforms or filtering techniques. However, due to the non-stationary nature and complex spectral distribution of tooth surface waviness signals, these methods have limitations in extracting local features and suppressing noise.

[0003] Tooth surface waviness refers to the periodic wavy appearance on the tooth surface due to various reasons (such as machine tool vibration, tool wear, improper cutting parameters, etc.) during the machining of gears or other mechanical parts. Tooth surface waviness is an important performance indicator for producing high-quality gears. Therefore, a set of efficient and accurate tooth surface waviness detection methods is needed to help improve production processes and enhance the level of high-speed and low-noise gear production. Summary of the Invention

[0004] In order to overcome the above-mentioned defects in the prior art, the present invention provides a rapid detection method for the waviness of the tooth surface of involute helical gears based on wavelet transform, aiming to solve the problems of low efficiency, insufficient anti-interference ability and limited extraction accuracy in the existing tooth surface waviness detection.

[0005] To achieve the above object, the present invention adopts the following technical solutions, including:

[0006] A rapid detection method for the waviness of the tooth surface of an involute helical gear based on wavelet transform includes the following steps:

[0007] S1, select the teeth to be measured according to the number of teeth on the gear;

[0008] S2, on the selected tooth, use the gear measurement center to obtain the tooth surface morphology data of each tooth, including tooth profile data and tooth direction data, that is, the morphology data along the tooth profile direction and tooth direction direction respectively;

[0009] S3, removing the modification amount and low-order DC components from the acquired tooth surface topography data to obtain corrected tooth surface topography data;

[0010] S4, performing wavelet analysis on the corrected tooth surface topography data to extract the wavelet components of each frequency band;

[0011] S5, according to the frequency range of the tooth surface waviness, extract the wavelet components of the corresponding frequency band, perform spectrum analysis on the extracted results, and obtain a spectrum diagram.

[0012] Preferably, the specific method of step S4 is as follows:

[0013] S41, converting the horizontal coordinate of the corrected tooth profile data into the corresponding involute length;

[0014] S42, calculating the tooth profile overlap ratio and the tooth direction overlap ratio, determining the total length of the horizontal coordinate and the position of each segment of data according to the overlap ratio, and performing coordinate adjustment;

[0015] The overlap ratio is calculated as:

[0016]

[0017] Among them, R p is the tooth profile overlap ratio, θ is the corresponding angle of a single tooth, z is the number of teeth, r a is the radius of the tooth tip circle, r f is the tooth root radius, r b is the base circle radius; R h is the tooth overlap ratio, L is the sum of the leads, β is the pitch circle helix angle, and b is the tooth width;

[0018] S43, normalizing the tooth surface topography data after coordinate adjustment in step S42, using the normalized data as input data for wavelet analysis, and calculating the number of wavelet decomposition layers J according to the length of the input data and the desired target resolution;

[0019] S44, performing J-layer wavelet decomposition on the input data to obtain wavelet components of different frequency bands.

[0020] Preferably, in step S43, the number of layers of wavelet decomposition is calculated as follows:

[0021] J=log2(N)-log2(H)

[0022] Among them, J is the number of layers of wavelet decomposition, N is the length of input data, and H is the target resolution.

[0023] Preferably, in step S44, the wavelet decomposition is specifically as follows:

[0024]

[0025] Among them, y norm [n] represents the input data, that is, the normalized data, n represents the nth point, y norm [n] is the normalized vertical coordinate value of the nth point; A J is the J-th layer approximation coefficient, D j is the detail coefficient of the jth layer.

[0026] Preferably, in step S43, the normalization process is specifically as follows:

[0027]

[0028] Among them, y norm [n] represents the normalized data, y[n] represents the tooth surface topography data after coordinate adjustment in step S42; n represents the nth point, y[n] is the ordinate value of the nth point, y norm [n] is the normalized vertical coordinate value of the nth point; y max 、y min These are the maximum and minimum values in the tooth surface topography data after the coordinate adjustment in step S42.

[0029] Preferably, in step S5, the detail coefficient of the corresponding layer is selected according to the frequency range of the tooth surface waviness, and the waviness signal is reconstructed. The wavelet component corresponding to the selected detail coefficient is converted back to the time domain signal through inverse wavelet transform, and the waviness is denormalized and converted into frequency domain data to obtain the gear spectrum diagram.

[0030] Preferably, in step S3, a polynomial fitting method is used to perform curve fitting on the tooth surface topography data obtained in step S2, and the fitting formula is as follows:

[0031] f(x)=a0+a1x+a2x 2 +…+a n x m

[0032] Where x is the measured length corresponding to the tooth surface topography data, the ordinate f(x) is the normal deviation at x; m ≥ 2; after fitting, the fitting curve is subtracted from the original data to obtain the corrected data with the modification amount and low-order DC components removed, that is, the corrected tooth surface topography data.

[0033] Preferably, in step S2, the measurement position of the tooth profile data is selected as the middle position of the tooth width; the measurement position of the tooth direction data is selected as the pitch circle diameter position.

[0034] Preferably, in step S1, the tooth at the starting position, the tooth at the quarter position, the tooth at the half position, the tooth at the three quarter position and three teeth at any other position are selected as the teeth to be measured.

[0035] The present invention also provides a computer program product, which includes a computer program / instruction, which, when executed by a processor, implements the above-mentioned rapid detection method for the waviness of the tooth surface of an involute helical gear based on wavelet transform.

[0036] The advantages of the present invention are:

[0037] (1) The present invention aims to solve the problems of low efficiency, insufficient anti-interference ability and limited extraction accuracy in existing tooth surface waviness detection. By performing high-density data sampling on the specified tooth surface of the involute helical gear, the signal is decomposed using the multi-scale characteristics of the wavelet transform, and the tooth surface waviness signal is separated from the complex morphological feature components. Combined with the threshold optimization algorithm, the detailed features of the waviness are effectively retained while suppressing the interference of non-related signals. The present invention is suitable for gear quality detection in a mass production environment and provides a reliable basis for defect diagnosis and optimization in the gear manufacturing process. Compared with traditional detection methods, the present invention has significant advantages in detection accuracy, stability and speed.

[0038] (2) The present invention selects skipped teeth based on the proportional relationship of the number of gear teeth, which can effectively cover the different positions and characteristics of the gear tooth surface, and the measured data is representative and comprehensive. This skipped tooth detection method can significantly improve measurement efficiency, avoid the high cost and tedious operation of tooth-by-tooth measurement, and reduce the data processing pressure caused by measurement redundancy. The present invention realizes efficient data processing and real-time waviness feature extraction by designing a fast analysis process and an automatic parameter adjustment mechanism.

[0039] (3) The present invention employs a wavelet-based analysis scheme to decompose tooth surface topography data in the frequency domain and accurately extract the waviness component. Wavelet analysis can flexibly switch between the time and frequency domains and has multi-resolution characteristics, making it suitable for separating low-frequency trends and high-frequency details in tooth surface texture. Compared to traditional Fourier analysis methods, wavelet analysis has higher accuracy and robustness when processing non-stationary signals and can more intuitively reflect the characteristics of tooth surface topography.

[0040] (4) As a multi-resolution analysis tool, wavelet transform has good localization characteristics in the time and frequency domains and can dynamically adapt to local changes in the signal, providing a new solution for tooth surface waviness detection. By selecting an appropriate mother wavelet, wavelet transform can perform multi-scale decomposition of the tooth surface signal, effectively separating high-frequency waviness from low-frequency errors and noise, and improving detection accuracy through threshold denoising technology, enabling accurate analysis of waviness. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The figure is a flow chart of a rapid detection method for the waviness of the tooth surface of involute helical gears based on wavelet transform.

[0042] Figure 2 Schematic diagram for removing the shaping amount and low-order components.

[0043] Figure 3 This is the tooth profile data diagram.

[0044] Figure 4 This is the tooth direction data diagram.

[0045] Figure 5 It is the tooth profile spectrum diagram.

[0046] Figure 6 It is the tooth direction spectrum diagram. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0048] This embodiment provides a method for quickly detecting the waviness of the tooth surface of an involute helical gear based on wavelet transform, and the steps are as follows:

[0049] S1. Select the gear to be measured according to the number of gear teeth.

[0050] The teeth to be measured are selected according to the number of teeth Z of the gear. In order to ensure that the selected measuring teeth are representative, they are usually selected according to the following ratio: the first tooth (the tooth at the starting position), Teeth (quarter position teeth), Teeth (middle teeth, i.e. teeth at half position), The tooth (the tooth at the three-quarter position) and the remaining three teeth at any position should be rounded to the nearest integer. For example, for a gear with Z = 27 teeth, after calculating the ratio, the 1st, 7th, 14th, and 21st teeth can be selected, along with any three teeth, such as the 4th, 11th, and 18th teeth. It should be noted that the three teeth can be adjusted based on experience or specific requirements, but the distribution should be as even as possible to cover the overall characteristics of the gear.

[0051] This method avoids the high cost of full-tooth measurement by selecting representative teeth from the integral gear, while ensuring the adequacy and accuracy of the measured data, providing a reliable basis for subsequent analysis.

[0052] All data must be rounded to ensure measurement consistency and accuracy. This selection method ensures that the measured data can fully reflect the overall characteristics of the gear.

[0053] S2, obtaining the tooth surface topography data of the tooth selected in step S1.

[0054] On the selected teeth, use the gear measurement center to obtain the tooth surface morphology data of each tooth one by one. For each selected tooth, it is necessary to measure the tooth profile data and tooth direction data separately, and ensure the accuracy of the measurement position. Specifically:

[0055] Tooth profile data is topographic information acquired along the tooth profile. The measurement location is chosen to be the middle of the tooth width. This is because the middle position better reflects the overall shape characteristics of the tooth profile while avoiding data errors caused by edge effects. For example, for a gear with a tooth width of 20 mm, the tooth profile should be measured at the center of the tooth width, 10 mm from the tooth edge.

[0056] Tooth profile data is topographic information acquired along the tooth profile direction, and the measurement location is usually selected at the pitch circle diameter. The pitch circle diameter location is highly representative and can reflect the transmission characteristics of the gear.

[0057] In practice, the stability of the measuring equipment and the consistency of the measurement path must be ensured. The tooth profile and tooth direction data collected for each tooth are used for subsequent analysis and processing. The data obtained through this method can reflect the overall topography of the tooth surface, laying the foundation for removing modification amounts and extracting waviness.

[0058] S3, for the tooth surface topography data obtained in step S2, removing the modification amount and the low-order DC component to obtain corrected tooth surface topography data.

[0059] The tooth surface profile data (raw data) obtained in step S2 may contain deviations (modification amounts) due to modification design or processing errors, as well as low-order DC components caused by installation eccentricity or other system factors. These components will interfere with subsequent analysis, so the raw data needs to be processed to remove these unnecessary effects. A polynomial fitting method is used to curve fit the raw data to approximately describe the overall trend of the tooth surface modification. Common methods are quadratic or cubic polynomial fitting:

[0060] f(x)=a0+a1x+a2x 2 +…+a n x m

[0061] In the formula, the value of m is selected according to actual needs (usually 2 or 3). After fitting, the original data is subtracted from the fitting curve to obtain the corrected data with the modification amount and low-order DC components removed, that is, the corrected tooth surface morphology data, such as Figure 2 As shown, Figure 2 In the figure, Initial Data, Fitted Curve, and Corrected Data represent the original data, fitted curve, and corrected data, respectively. The abscissa x is the measurement length corresponding to the tooth surface topography data, and the ordinate f(x) is the normal deviation at x.

[0062] S4, determine the data coordinates, perform wavelet analysis on the corrected tooth surface topography data, and extract the wavelet components of each frequency band.

[0063] After removing the distortion and low-order DC components, the next step is to integrate the data and determine its coordinates for wavelet analysis. This process includes confirming the data coordinates and designing the wavelet analysis scheme. The specific steps are as follows:

[0064] S41, Data Coordinate Confirmation: The tooth profile data measured by the gear measurement center uses the involute angle as the horizontal coordinate. This needs to be converted to the corresponding involute length as the horizontal coordinate for subsequent calculations. The tooth width data uses the tooth width as the horizontal coordinate.

[0065] S42, calculation of the overlap ratio of tooth profile data and tooth direction data: Since the sum of the corresponding span angles of the involute of each tooth on the tooth profile is greater than the angle of one rotation of the gear, the tooth profile data of adjacent teeth overlap; since the sum of the corresponding leads of each tooth on the tooth direction is greater than the gear tooth width, the tooth direction data of adjacent teeth overlap. The overlap ratio needs to be calculated to determine the length of the horizontal axis and the position corresponding to each data segment. The calculation formula is as follows:

[0066]

[0067] Among them, R p is the tooth profile overlap ratio, θ is the corresponding angle of a single tooth, z is the number of teeth, r a is the radius of the tooth tip circle, r f is the tooth root radius, r b is the base circle radius; R h is the tooth overlap ratio, L is the sum of the leads, β is the pitch circle helix angle, and b is the tooth width.

[0068] The total length of the horizontal coordinate and the position of each segment of data are calculated based on the overlap ratio, and the coordinates are adjusted to obtain the tooth surface morphology data after the coordinate adjustment. Figure 3 and Figure 4 As shown, Figure 3 and Figure 4 The tooth profile data and tooth direction data of each tooth are given in the figure. Figure 3 and Figure 4 The horizontal axis is the measured length corresponding to the calculated data, and the vertical axes are the corrected tooth profile and tooth direction deviation.

[0069] S43, Design Wavelet Analysis:

[0070] The tooth surface topography data after coordinate adjustment in step S42 is normalized to eliminate the influence of dimension. The formula is as follows:

[0071]

[0072] Among them, y norm[n] represents the normalized data, y[n] represents the tooth surface topography data after coordinate adjustment in step S42; n represents the nth point, y[n] is the vertical coordinate size of the nth point; y max 、y min These are the maximum and minimum values in the tooth surface topography data after the coordinate adjustment in step S42.

[0073] Daubechies5 is then selected as the wavelet basis function. Daubechies5 is sensitive to signal variations and has minimal edge effects, making it suitable for separating and extracting the tooth surface waviness component. The number of wavelet decomposition layers is directly related to the accuracy of the analysis and the effective separation of the target frequency band. Its calculation is based on the length of the normalized tooth surface topography data and the desired target resolution. The specific number of decomposition layers is calculated using the following formula:

[0074] J=log2(N)-log2(H)

[0075] Where J is the number of decomposition levels, N is the length of the input data, and H is the target resolution. This formula allows for flexible adjustment of the number of decomposition levels based on signal characteristics and analysis requirements to ensure that the extracted components have clear frequency separation.

[0076] S44, performing J-layer wavelet decomposition on the normalized tooth surface topography data to decompose wavelet components of different frequency bands.

[0077]

[0078] Among them, A J is the J-th layer approximation coefficient, D j is the detail coefficient of the jth layer.

[0079] In step S4, the distribution lengths of adjacent tooth measurement data within the full tooth data set are calculated based on the positional relationship of the measurement data. This is then combined with the number and specific locations of the selected measurement teeth to create a complete measurement data curve. Subsequently, a suitable multi-scale wavelet analysis scheme is designed to separate the characteristic information of the gear surface within different frequency ranges, facilitating the separation of texture and error components.

[0080] S5, according to the frequency range of the tooth surface waviness (wavelength between 0.1mm-1mm, frequency 1Hz-10Hz), select the detail coefficient of the corresponding layer, reconstruct the waviness signal, and convert the wavelet component corresponding to the selected detail coefficient back to the time domain signal through inverse wavelet transform. Denormalize and convert the waviness into frequency domain data, visualize it, and obtain the gear spectrum diagram.

[0081] Finally, the waviness signal extracted through the above steps can be used for further analysis. Its frequency domain representation clearly shows the amplitude distribution of different frequency components, such as Figure 5 and Figure 6 shown.

[0082] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A rapid detection method for the waviness of involute helical gear tooth surface based on wavelet transform, characterized in that: The following steps are involved: S1, select the teeth to be measured according to the number of teeth on the gear; S2, on the selected tooth, use the gear measurement center to obtain the tooth surface morphology data of each tooth, including tooth profile data and tooth direction data, that is, the morphology data along the tooth profile direction and tooth direction direction respectively; S3, removing the modification amount and low-order DC components from the acquired tooth surface topography data to obtain corrected tooth surface topography data; S4, performing wavelet analysis on the corrected tooth surface topography data to extract the wavelet components of each frequency band; S5, according to the frequency range of the tooth surface waviness, extract the wavelet components of the corresponding frequency band, perform spectrum analysis on the extracted results, and obtain a spectrum diagram.

2. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 1 is characterized in that: The specific method of step S4 is as follows: S41, converting the horizontal coordinate of the corrected tooth profile data into the corresponding involute length; S42, calculating the tooth profile overlap ratio and the tooth direction overlap ratio, determining the total length of the horizontal coordinate and the position of each segment of data according to the overlap ratio, and performing coordinate adjustment; The overlap ratio is calculated as: Among them, R p is the tooth profile overlap ratio, θ is the corresponding angle of a single tooth, z is the number of teeth, r a is the radius of the tooth tip circle, r f is the tooth root radius, r b is the base circle radius; R h is the tooth overlap ratio, L is the sum of the leads, β is the pitch circle helix angle, and b is the tooth width; S43, normalizing the tooth surface topography data after coordinate adjustment in step S42, using the normalized data as input data for wavelet analysis, and calculating the number of wavelet decomposition layers J according to the length of the input data and the desired target resolution; S44, performing J-layer wavelet decomposition on the input data to obtain wavelet components of different frequency bands.

3. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 2, characterized in that: In step S43, the number of layers of wavelet decomposition is calculated as follows: J=log2(N)-log2(H) Among them, J is the number of layers of wavelet decomposition, N is the length of input data, and H is the target resolution.

4. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 2, characterized in that: Step S44, wavelet decomposition is specifically as follows: Among them, y norm [n] represents the input data, that is, the normalized data, n represents the nth point, y norm [n is the normalized vertical coordinate value of the nth point; A J is the J-th layer approximation coefficient, D j is the detail coefficient of the jth layer.

5. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 2 or 4, characterized in that: In step S43, the normalization process is specifically as follows: Among them, y norm [n] represents the normalized data, y[n] represents the tooth surface topography data after coordinate adjustment in step S42; n represents the nth point, y[n] is the ordinate value of the nth point, y norm [n] is the normalized vertical coordinate value of the nth point; y max 、y min These are the maximum and minimum values in the tooth surface profile data after the coordinate adjustment in step S42.

6. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 4, characterized in that: In step S5, according to the frequency range of the tooth surface waviness, the detail coefficient of the corresponding layer is selected, the waviness signal is reconstructed, the wavelet component corresponding to the selected detail coefficient is converted back to the time domain signal through inverse wavelet transform, the waviness is denormalized and converted into frequency domain data to obtain the gear spectrum diagram.

7. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 1, characterized in that: In step S3, a polynomial fitting method is used to perform curve fitting on the tooth surface topography data obtained in step S2. The fitting formula is as follows: f(x)=a0+a1x+a2x 2 +…+a n x m Where x is the measured length corresponding to the tooth surface topography data, the ordinate f(x) is the normal deviation at x; m ≥ 2; after fitting, the fitting curve is subtracted from the original data to obtain the corrected data with the modification amount and low-order DC components removed, that is, the corrected tooth surface topography data.

8. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 1 is characterized in that: In step S2, the middle position of the tooth width is selected as the measurement position of the tooth profile data; the pitch circle diameter position is selected as the measurement position of the tooth direction data.

9. The rapid detection method of involute helical gear tooth surface waviness based on wavelet transform according to claim 1, characterized in that: In step S1 , the tooth at the starting position, the tooth at the quarter position, the tooth at the half position, the tooth at the three quarter position, and three teeth at any other position are selected as teeth to be measured.

10. A computer program product, characterized in that The invention comprises a computer program / instruction, which, when executed by a processor, realizes the rapid detection method of the tooth surface waviness of an involute helical gear based on wavelet transform according to any one of claims 1 to 9.

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