Gear wave corrugation order spectrum extraction method based on coordinate system measurement method

Abstract

This invention discloses a method for extracting the order spectrum of gear waviness based on coordinate system measurement, belonging to the field of gear precision measurement and data processing technology. This method uses coordinate system measurement to obtain the coordinate points of the gear tooth profile around its entire length. A complete closed profile is formed through segmented splicing and overlapping elimination. Based on the closed profile, the number of teeth and basic parameters such as the addendum circle, dedendum circle, and base circle are autonomously identified. A theoretical involute curve is established and aligned with the measured tooth profile, and the normal deviation is calculated. High-order features are extracted through low-order feature separation, mapped to the gear's angular domain, and subjected to Fourier analysis to obtain the gear waviness order spectrum, identifying the principal and ghost orders. Simultaneously, the correspondence between high-order features and tooth number and tooth surface profile is preserved, enabling the localization of problematic tooth surfaces. This invention does not rely on generating measurement and dedicated analysis software, is applicable to various measurement devices, and can extract the order spectrum and locate abnormal tooth surfaces with fewer sampling points, significantly improving detection efficiency and versatility.

Description

Technical Field

[0001] This invention belongs to the field of gear precision measurement and data processing technology, specifically a method for extracting gear waviness order spectrum based on coordinate system measurement. Background Technology

[0002] As electric drive systems develop towards higher speeds, lower noise levels, and higher consistency, noise, vibration, and acoustic roughness issues in gear transmission systems are receiving increasing attention. Tooth surface waviness, as a periodic geometric error situated between macroscopic tooth profile errors and microscopic roughness, induces periodic excitations during gear meshing and may manifest as noise or vibration components of a specific order. Therefore, tooth surface waviness and its order characteristics have become crucial bases for gear noise analysis, gear inspection and evaluation, and machining quality control.

[0003] Existing methods for detecting and analyzing gear waviness typically rely on the output of precision gear measurement centers and their accompanying analysis software. One type of method is based on measurement results obtained through generating tooth profile measurement, representing the measurement data in the tooth profile or tooth direction as one-dimensional position coordinates and their corresponding tooth profile deviation, normal deviation, amplitude, or waviness curves. Filtering, stitching, Fourier transform, or order analysis are then performed on these data. This type of method utilizes the deviation or waviness curves output by the gear measurement center, but it places high demands on the generating measurement capabilities of the measuring equipment, the accuracy of motion control, and the data processing capabilities of the accompanying measurement software.

[0004] Another type of method, while further utilizing tooth surface waviness spectrum, dominant frequency, ghost frequency, and other results for noise assessment, anomaly identification, or machining condition analysis, typically still presupposes the prior acquisition of tooth profile deviation, normal deviation, tooth surface waviness, or tooth surface waviness signals. In other words, existing methods often use deviation curves, amplitude curves, or waviness curves as input data, paying less attention to how to autonomously construct tooth profile evaluation benchmarks, extract tooth profile deviations or normal deviations, and further obtain the gear's whole-circumference waviness order spectrum when the measuring equipment can only provide tooth profile measurement results under coordinate system measurement methods.

[0005] In practical engineering applications, not all measuring devices have the capability to measure tooth profiles, nor can all measuring systems directly output tooth profile deviation, normal deviation, or waviness curves. Compared to the generating tooth profile measurement method, the coordinate system measurement method has wider equipment adaptability. Many types of measuring devices (such as gear measuring centers, coordinate measuring machines, white light interferometers, laser confocal measuring instruments, and ultra-depth-of-field measuring instruments) can obtain the coordinate information of the tooth profile measurement results. If the gear waviness order spectrum can be extracted based on the tooth profile measurement results under the coordinate system measurement method, the dependence on specific high-precision gear measuring centers and their dedicated analysis software can be reduced, improving the versatility and general applicability of the gear waviness analysis method.

[0006] Furthermore, existing gear waviness analysis methods typically require a high density of measurement points to ensure the accuracy of spectral analysis. Some schemes require a large number of sampling points on a single tooth surface, resulting in long measurement times, which is detrimental to batch inspection and rapid quality evaluation. For gear waviness order spectrum extraction, if the principal order, ghost order, and their amplitudes can be reliably identified even with fewer effective sampling points, the amount of measurement data and measurement time can be significantly reduced, thereby improving inspection efficiency.

[0007] Meanwhile, although the integer waviness order spectrum of a gear can reflect the overall waviness order characteristics of the tested gear, in actual inspection and analysis, obtaining only the integer order spectrum is sometimes insufficient to meet the needs of quality traceability and processing guidance. When abnormal main or ghost orders appear in the order spectrum, if it is not possible to further determine which teeth or tooth surfaces the abnormal waviness mainly originates from, it is difficult to conduct targeted re-inspection, quality judgment, or processing status analysis of the tested gear. Therefore, if it is possible to further locate the problematic tooth surfaces causing the waviness difference while extracting the gear waviness order spectrum, the pertinence of gear inspection and analysis can be improved, and more direct data can be provided for gear processing adjustment and quality improvement.

[0008] Therefore, there is an urgent need for a gear waviness order spectrum extraction method based on coordinate system measurement. This method should be able to autonomously construct evaluation benchmarks and extract deviations from tooth profile measurement results, even when the measurement results do not directly contain tooth profile deviations, normal deviations, or waviness curves. Furthermore, it should reconstruct the deviation signals of multiple teeth into a closed-loop error signal within one revolution of the gear, thereby obtaining the gear waviness order spectrum, principal order, ghost order, and their amplitudes. It should also be able to locate the problematic tooth surfaces causing waviness differences. This method should break free from the dependence on generating tooth profile measurement methods and dedicated measurement software, improve the efficiency of gear waviness order analysis with fewer sampling points, and provide a basis for gear inspection analysis and gear machining guidance. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a gear waviness order spectrum extraction method based on coordinate system measurement, which aims to solve the problems of existing gear waviness analysis relying on generating measurement and dedicated software, being unable to autonomously extract deviations from coordinate information, having low measurement efficiency, and being unable to locate problematic tooth surfaces; by autonomously constructing a tooth profile reference, extracting tooth profile deviations, reconstructing closure error signals, obtaining the order spectrum and locating abnormal tooth surfaces, the invention improves versatility and detection efficiency.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A method for extracting the order spectrum of gear waviness based on coordinate system measurement includes the following steps: S1: Use the coordinate system measurement method to obtain the tooth profile measurement results of the gear under test for one revolution, and export them as a data file containing the coordinate information of the measurement points; S2: Read and uniformly parse the data file, and uniformly represent the tooth profile measurement results under different formats as a tooth profile measurement result set, the tooth profile measurement result set including several measurement subsets corresponding to segmented measurements; S3: Preprocess the set of tooth profile measurement results. The preprocessing includes identifying and removing duplicate measurement parts between adjacent measurement subsets and duplicate measurement parts at the beginning and end closing positions. Then, the processed measurement subsets are spliced ​​together in sequence to form a complete closed profile of the gear. S4: Identify the tooth tip and determine the number of teeth based on the closed contour; S5: Based on the closed profile analysis, the addendum circle diameter and the root circle diameter are obtained; S6: Based on the number of teeth, the addendum circle diameter, the dedendum circle diameter, and the closed profile, calculate the basic parameters of the gear, which include at least the base circle diameter, the pitch circle diameter, the module, and the pressure angle. S7: Based on the closed profile and the polar angle of each effective tooth tip peak point, the closed profile is divided into the left tooth profile data and the right tooth profile data of each tooth; S8: Based on the tooth tip circle radius, tooth root circle radius, base circle radius and total tooth height, radially truncate the left and right tooth profile data of each tooth to extract the working tooth surface data; S9: Establish the theoretical involute based on the basic parameters, align the working tooth surface measurement data with the theoretical involute, and determine the starting angle of the theoretical involute of the left and right tooth profiles of each tooth; S10: Calculate the normal deviation of the working tooth surface measurement point relative to the theoretical involute based on the starting angle of the theoretical involute; S11: Perform a low-order fitting on the normal deviation to obtain a low-order feature that slowly changes along the arc length of the base circle. S12: Remove the low-order features from the normal deviation to obtain the high-order features; S13: Map the higher-order features to the gear one-turn angle domain, and calculate the influence of each higher-order feature on gear vibration to obtain the vibration influence signal of higher-order features in the gear one-turn angle domain; S14: Perform Fourier analysis on the high-order characteristic vibration influence signal to obtain the gear waviness order spectrum, and identify the principal order, ghost order and their amplitudes from it; S15: Based on the correspondence between the higher-order characteristic vibration influence signal and the tooth number, tooth surface side and working tooth surface position, locate the problematic tooth surface that causes abnormal waviness.

[0011] Furthermore, in step S3, for the first... A subset of measurements ,when When, take the previous measurement subset. The endpoint in the interval is taken as the end point of the previous measurement subset, and is denoted as:

[0012] in: For the first The endpoint of a measurement subset; For the first The last measurement point in the measurement subset; For the first The number of measurement points in each measurement subset; and The first The x and y coordinates of the endpoints in each measurement subset in the measurement coordinate system; Calculate the first Geometric distances from each measurement point in the measurement subset to the endpoint:

[0013] in: For the first The measurement subset of the first From the measurement point to the... Geometric distance between the endpoints of each measurement subset; and The first The measurement subset of the first The x and y coordinates of each measurement point in the measurement coordinate system; For the first The number of measurement points in each measurement subset; Determine the first The sequence number of the measurement point closest to the end point in the measurement subset:

[0014] in: For the first The measurement subset and the first The sequence number of the nearest measurement point to the end point of each measurement subset; Let the minimum distance be:

[0015] in: For the first The measurement subset and the first Minimum geometric distance between subsets of measurements; For the first The measurement subset of the first From the measurement point to the... Geometric distance between the endpoints of each measurement subset; Setting overlap judgment tolerance :when and When an overlapping region is determined, the first one is removed. In the measurement subset, from the first measurement point to the... The overlapping portion of the measurement points is retained. From the first measurement point to the last measurement point, we obtain the trimmed first measurement point. A subset of measurements:

[0016] in: For the first The measurement subset obtained after trimming the measurement subset; For the first The first measurement subset There are 10 measurement points.

[0017] Furthermore, in step S3, the method for eliminating repeated measurements at the beginning and end of the closed position is as follows: Take the starting point of the first measurement subset:

[0018] in: This marks the starting point of the first measurement subset; This refers to the first measurement point in the first measurement subset; and Let x and y be the x and y coordinates of the first measurement point in the first measurement subset in the measurement coordinate system. Calculate the geometric distance from each measurement point in the last measurement subset to the starting point of the first measurement subset:

[0019] in: For the last measurement subset The geometric distance from each measurement point to the starting point of the first measurement subset; This represents the number of measurement points in the last measurement subset after overlapping and cropping of adjacent measurement subsets. and For the last measurement subset The x and y coordinates of each measurement point in the measurement coordinate system; Determine the index of the measurement point in the last measurement subset that is closest to the starting point of the first measurement subset:

[0020] Let the minimum distance be:

[0021] in: This is the minimum geometric distance between the last measurement subset and the starting point of the first measurement subset; For the last measurement subset The geometric distance from each measurement point to the starting point of the first measurement subset; when and When an overlapping region is determined, the last measurement subset is removed from the first measurement. The overlapping portion from the first measurement point to the last measurement point is retained, and the overlap from the first measurement point to the last measurement point is retained. Using 1 measurement point, we obtain the last measurement subset after closed clipping:

[0022] in: This is the last subset of measurements after removing the closed overlapping region at the tail; For the last measurement subset, the first One measurement point; Tolerance for overlap determination.

[0023] Furthermore, in step S4, the method for identifying tooth tips and determining the number of teeth based on closed contours is as follows: For closed contour point array Coordinate centering is performed, and the center coordinates are estimated using the bounding box method. :

[0024] in: and These are the center x-coordinate and center y-coordinate estimated from the closed bounding box, respectively. A point array representing the complete closed contour of a gear's revolution; For the first closed contour One measurement point; This represents the total number of measurement points in the closed contour. Sequentially number the measurement points in the closed contour point column; and The first one in the closed contour The x and y coordinates of each measurement point in the measurement coordinate system; Convert each measurement point in the closed contour point list to centered coordinates:

[0025] in: and The first The x and y coordinates of each measurement point after centering; Calculate the polar radius of each measurement point relative to the center point:

[0026] in: For the first The polar radius of each measurement point relative to the center point; The high percentile value of the extreme diameter sequence is taken as the preliminary estimate of the tooth tip radius, and the low percentile value of the extreme diameter sequence is taken as the preliminary estimate of the tooth root radius.

[0027] in: This is a preliminary estimate of the tooth tip radius; This is a preliminary estimate of the tooth root radius; This indicates taking the 99.5 percentile value of the polar radius sequence; This indicates taking the 0.5 percentile value of the polar radius sequence; Determine the minimum protrusion threshold for the peak tooth tip:

[0028] in: The minimum protrusion threshold of the tooth tip peak; Peak prominence coefficient; Based on polarity sequence Peak identification will be performed if the local peak condition is met and the peak prominence is not less than [value missing]. The measurement points are determined as candidate tooth tip peak points, forming a set of candidate tooth tip peak points:

[0029] in: This is the set of candidate tooth tip peak points; For the first One candidate tooth tip peak point; These are the measurement points corresponding to the closed contour; For the first The measurement point number of each candidate tooth tip peak point in the closed profile point column; The number of candidate tooth tip peak points; Calculate the polar angle corresponding to the peak point of each candidate tooth tip:

[0030] in: For the first The polar angle corresponding to the peak point of each candidate tooth tip; and The first The x and y coordinates of the centered peak points of each candidate tooth tip; Sort by polar angle from smallest to largest:

[0031] in: For the sorted number The polar angle corresponding to the peak point of each candidate tooth tip; Calculate the polar angle interval between adjacent candidate tooth tip peak points :

[0032] in: The polar angle interval between adjacent candidate tooth tip peak points; For candidate tooth tip peak points that are adjacent at the beginning and end, their polar angle interval is: :

[0033] Set deduplication angle threshold When the polar angle interval is less than or equal to If one is selected, retain one; otherwise, retain the peak points at the apex of different teeth. After deduplication, the set of valid peak points at the apex of teeth is obtained.

[0034] in: The set of effective tooth tip peak points; For the first One effective tooth tip peak point; This represents the number of effective tooth tip peak points after deduplication. The number of effective tooth tip peak points is the number of teeth of the gear being tested.

[0035] in: The number of teeth on the gear being tested; Represents the set of effective tooth tip peak points The number of elements in the middle.

[0036] Furthermore, in step S5, the method for analyzing and obtaining the addendum circle diameter and the dedendum circle diameter is as follows: The polar radii of all measurement points are arranged into a polar radii sequence:

[0037] in: This is the sequence of extreme diameters corresponding to the closed profile of the gear. For the first The polar radius of each measurement point relative to the center point; This represents the total number of measurement points in the closed contour. Take the high percentile value of the polar diameter sequence as the estimated value of the tooth tip circle radius:

[0038] in: The radius of the tooth tip circle; Represents the polar radius sequence The 99.5 percentile value; Take the lower percentile value as the estimated value of the tooth root circle radius:

[0039] in: The radius of the tooth root circle; Represents the polar radius sequence The 0.5 percentile value; Calculate the tip circle diameter Root circle diameter .

[0040] Furthermore, in step S6, the method for calculating the basic parameters of the gear is as follows: Calculate the total height of the teeth Set the radial safety factor Determine the lower boundary radius of the initial tooth profile region. and upper boundary radius ;in: and These are the addendum circle radius and the dedendum circle radius, respectively. Gradient calculations are performed on the closed contour point sequence to obtain the local tangential variation. , Calculate the modulus of the local tangential change. ;in: and They represent the first The changes in the abscissa and ordinate at each measurement point along the sequence of measurement points; This represents the gradient operation along the sequence of measurement points; and The first The x and y coordinates of each measurement point after centering; For the first Local tangential change modulus at each measurement point; Calculate the estimated local normal value for each measurement point. ;in: For the first Local normal estimates corresponding to each measurement point; Determine the set of measurement points to participate in the statistical estimation of the base circle. The base circle radius is obtained by taking the median of the local normal estimates for each point within the set. and base circle diameter ;in: For the first The polar radius of each measurement point relative to the center point; This represents the total number of measurement points in the closed contour. This indicates taking the median; Correct the effective lower boundary radius based on the base circle radius. ,in: The effective tooth profile region is obtained by considering the safety margin above the base circle. ;in: This represents the safety margin above the base circle; This is the set of measurement point numbers corresponding to the corrected effective tooth profile region. Calculate the geometric polar angle of the measurement point Direction discrimination quantity Pressure angle auxiliary amount Involute function value Base circle development angle ;in: For the first Geometric polar angles of each measurement point; For the first The direction discrimination of each measurement point is used to distinguish the rising and falling sides of the tooth profile; For the first The pressure angle auxiliary quantity corresponding to each measurement point; The radius of the base circle; For the first The involute function values ​​corresponding to each measurement point; For the first The base circle unfolding angle corresponding to each measurement point; Determine the tooth pitch angle based on the number of teeth z. Polar angle of the first effective tooth tip peak point For reference, the measurement points are assigned to the corresponding teeth to obtain the effective measurement point set for the left and right tooth surfaces; The average development angle of the base circle of the left and right tooth surfaces of each tooth is calculated using the complex mean method, and the pressure angle is solved based on the virtual common normal method. ,make ,in: The target involute function value is calculated from the equivalent base circle tooth thickness angle. Calculate the modulus Pitch circle diameter ;in: Modulus; z is the base circle diameter; z is the number of teeth; The pressure angle; It is the pitch circle diameter.

[0041] Furthermore, in step S7, the method for splitting the closed contour into left tooth profile data and right tooth profile data is as follows: The first The polar angle of the effective tooth tip peak point is denoted as For the first closed contour Calculate the relative polar angle of each measurement point. ;in: , The number of teeth on the gear being tested; For the first The measurement point relative to the first The relative polar angle of each effective tooth tip peak point; For the first Geometric polar angles of each measurement point; Will satisfy The measurement points were assigned to the first One tooth; when When the left tooth profile measurement point is marked, The measurement points for the right tooth profile were marked, and the data for the left tooth profile were obtained by sorting them according to their relative polar angles. and right tooth profile data .

[0042] Furthermore, in step S8, the method for extracting the working tooth surface data is as follows: Setting the root safety margin factor and tooth tip safety margin factor Determine the lower boundary radius of the evaluation for the working tooth surface. And assess the upper boundary radius ;in: The radius of the tooth tip circle; The radius of the base circle; The radius of the tooth root circle; Full tooth height; For left tooth profile data Calculate the polar diameter at each measurement point. , retain satisfaction The measurement points are used as the working tooth surface data of the left tooth profile. ; For right tooth profile data Calculate the polar diameter at each measurement point. , retain satisfaction The measurement points are used as the working tooth surface data of the right tooth profile. .

[0043] Furthermore, in step S9, the method for establishing the theoretical involute and performing alignment is as follows: For the working tooth surface data of the left tooth profile Calculate the theoretical involute starting angle of the left tooth profile:

[0044] in: For the first The theoretical involute starting angle corresponding to the left tooth profile of each tooth; For the first The number of measurement points in the working tooth surface data of the left tooth profile of each tooth; For the first The first tooth on the left working tooth surface Polar angles at each measurement point; For the first The first tooth on the left working tooth surface The pressure angle auxiliary quantity corresponding to each measurement point; For the first The first tooth on the left working tooth surface The involute function values ​​corresponding to each measurement point; Establish the involute polar angle equation for the left tooth profile theory:

[0045]

[0046] in: For the first The theoretical involute of the left tooth profile of a single tooth is at a radius... The polar angle at that location; For the radius on the theoretical involute The corresponding pressure angle auxiliary value; The radius of the base circle; Let be the radius of any point on the theoretical involute line relative to the center of the gear; The coordinate equation of the left tooth profile involute is obtained as follows:

[0047] in: and The first The theoretical involute of the left tooth profile of a single tooth is at a radius... The x and y coordinates of the location; Data for the working tooth surface of the right tooth profile Calculate the theoretical involute starting angle of the right tooth profile:

[0048] in: For the first The theoretical involute starting angle corresponding to the right tooth profile of each tooth; For the first The number of measurement points in the working tooth surface data of the right tooth profile of each tooth; For the first The right tooth profile working surface of the first tooth Polar angles at each measurement point; For the first The right tooth profile working surface of the first tooth The pressure angle auxiliary quantity corresponding to each measurement point; For the first The right tooth profile working surface of the first tooth The involute function values ​​corresponding to each measurement point; Establish the involute polar angle equation for the right tooth profile theory:

[0049] in: For the first The theoretical involute of the right tooth profile of a single tooth has a radius of... The polar angle at that location; Get the first The coordinate equation of the theoretical involute of the right tooth profile of each tooth:

[0050] in: and The first The theoretical involute of the right tooth profile of a single tooth has a radius of... The x-coordinate and y-coordinate of the location.

[0051] Furthermore, in step S10, the method for calculating the normal deviation is as follows: For the first tooth surface of the left tooth profile working tooth surface Calculate the polar angle of the base circle tangent point at each measurement point. Base circle unfolded arc length Tangent length and normal deviation ;in: For the first The left profile of the first tooth Polar angle of the base circle tangent point corresponding to each measurement point on the working tooth surface; For the first The first tooth on the left working tooth surface Polar angles at each measurement point; For the first The first tooth on the left working tooth surface The pressure angle auxiliary quantity corresponding to each measurement point; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; The radius of the base circle; For the first The left profile of the first tooth The tangent length from each measurement point on the working tooth surface to the corresponding tangent point on the base circle; For the first The left profile of the first tooth Extreme diameter of each measuring point on the working tooth surface; For the first The left profile of the first tooth Normal deviation of each measuring point on the working tooth surface, in units of ; For the first tooth surface of the right tooth profile working tooth surface Calculate the polar angle of the base circle tangent point at each measurement point. Base circle unfolded arc length Tangent length and normal deviation ;in: For the first The right profile of the first tooth Polar angle of the base circle tangent point corresponding to each measurement point on the working tooth surface; For the first The right tooth profile working surface of the first tooth Polar angles at each measurement point; For the first The right tooth profile working surface of the first tooth The pressure angle auxiliary quantity corresponding to each measurement point; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The right profile of the first tooth The tangent length from each measurement point on the working tooth surface to the corresponding tangent point on the base circle; For the first The right profile of the first tooth Extreme diameter of each measuring point on the working tooth surface; For the first The right profile of the first tooth Normal deviation of each measuring point on the working tooth surface, in units of ; The first The normal deviations of each tooth surface are sorted in ascending order of the base circle unfolded arc length to obtain the first tooth. Data set of deviations in the left profile of each tooth and the Data set of deviations in the right profile of each tooth ; Repeat the above calculation for all teeth to obtain the left tooth profile deviation data set. And right tooth profile deviation data set .

[0052] Furthermore, in step S11, the method for performing low-order fitting on the normal deviation is as follows: For the The left profile of each tooth, with low-order features represented as follows:

[0053] in: For the first The arc length of the left tooth profile of each tooth when unfolded on the base circle Low-order features at the location; , and The first The coefficients of the quadratic term, the coefficients of the linear term, and the constant term of the quadratic polynomial of the left tooth profile of each tooth are determined by the least squares method. Get the first Low-order eigenvalues ​​of the left tooth profile corresponding to each measurement point:

[0054] in: For the first The left profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point; Get the first The low-order feature data of the left tooth profile of each tooth are represented as follows:

[0055] in: For the first Low-order feature data of the left profile of each tooth; For the first The number of effective measurement points on the working tooth surface of the left tooth profile of each tooth; For the The low-order features of the right tooth profile of each tooth are represented as follows:

[0056] in: For the first The arc length of the right tooth profile of each tooth when unfolded on the base circle Low-order features at the location; , and The first The coefficients of the quadratic term, the coefficients of the linear term, and the constant term of the quadratic polynomial of the right tooth profile of each tooth are determined by the least squares method. Get the first Low-order eigenvalues ​​of the right tooth profile corresponding to each measurement point:

[0057] in: For the first The right profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; Get the first The low-order feature data of the right tooth profile of each tooth are represented as follows:

[0058] in: For the first Low-order feature data of the right tooth profile of each tooth; For the first The number of effective measurement points on the working tooth surface of the right tooth profile of each tooth; The above fitting was performed on all teeth to obtain the set of low-order feature data of the left tooth profile. and the set of low-order features of the right tooth profile .

[0059] Furthermore, in step S12, the method for obtaining higher-order features is as follows: For the The first tooth in the left profile of the tooth For each measurement point, the higher-order eigenvalues ​​are represented as:

[0060] in: For the first The left profile of the first tooth Higher-order eigenvalues ​​of each measurement point; For the first The left profile of the first tooth Normal deviation of each working tooth surface measurement point; For the first The left profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; No. The high-order feature data of the left profile of each tooth are represented as follows:

[0061] in: For the first High-order feature data of the left profile of each tooth; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The number of effective measurement points on the working tooth surface of the left tooth profile of each tooth; For the The first tooth in the right profile of the tooth For each measurement point, the higher-order eigenvalues ​​are represented as:

[0062] in: For the first The right profile of the first tooth Higher-order eigenvalues ​​of each measurement point; For the first The right profile of the first tooth Normal deviation of each working tooth surface measurement point; For the first The right profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; No. The high-order feature data of the right profile of each tooth are represented as follows:

[0063] in: For the first High-order feature data of the right tooth profile of each tooth; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The number of effective measurement points on the working tooth surface of the right tooth profile of each tooth; The above processing was performed on all teeth to obtain the high-order feature data sets of the left and right tooth profiles:

[0064]

[0065] in: This is the set of high-order feature data of the left tooth profile for all teeth; This is the set of high-order feature data of the right tooth profile for all teeth; The number of teeth on the gear being tested.

[0066] Furthermore, in step S14, the method for obtaining the gear waviness order spectrum is as follows: The vibration influence signal of the high-order characteristic feature in the gear's angular domain after equal-angle resampling is represented as follows:

[0067] in: For the first The higher-order characteristic vibration influence values ​​corresponding to each angle sampling position; For the first Each angle sampling position; This represents the number of resampling points within the angle domain of one revolution of the gear. Discrete Fourier transform of the high-order characteristic vibration influence signal in the angle domain:

[0068] in: For the first Complex coefficients of each Fourier component; The Fourier component index; The imaginary unit; No. The gear order corresponding to each Fourier component Amplitude ,Depend on Constructing the gear waviness order spectrum :

[0069] For the number of teeth is For the gear under test, the order corresponding to the number of teeth and its integer multiples is determined. Orders with significant amplitudes in the vicinity are identified as principal orders, and orders whose amplitudes reach a preset threshold outside of principal orders are identified as ghost orders; where: It is a positive integer.

[0070] Furthermore, in step S15, the method for locating the problematic tooth surface causing abnormal waviness is as follows: Combining the amplitude anomalies of the principal and ghost orders in the order spectrum, and the correspondence between the high-order characteristic vibration influence signal retained in step S13 and the tooth number, tooth surface side and working tooth surface position, observe the local high-order characteristic changes in the corresponding angle range of different teeth, trace back to the corresponding tooth and its tooth surface according to the angle position of the abnormal high-order characteristics, and output the tooth number of the suspected problem tooth and the abnormal tooth surface as the left tooth surface or the right tooth surface.

[0071] The beneficial effects of this invention are as follows: The present invention provides a method for extracting the order spectrum of gear waviness based on coordinate system measurement, which achieves the following technical effects.

[0072] (1) Breaking equipment dependence and improving versatility. The coordinate system measurement method is used to obtain tooth profile coordinate information, which does not require the equipment to have generating measurement capabilities; by reading data in multiple formats and uniformly parsing and automatically splicing closed profiles, it is compatible with various equipment such as gear measurement centers, coordinate measuring machines, and white light interferometers, thus getting rid of the dependence on specific high-precision gear measurement centers and their dedicated analysis software.

[0073] (2) Autonomously constructing a benchmark to achieve deviation extraction. The system autonomously identifies the number of teeth, addendum circle, and dedendum circle from the closed profile and calculates parameters such as base circle, module, and pressure angle. Without relying on external theoretical parameter input, it can establish a theoretical involute and align it with the measured tooth profile, thereby calculating the normal deviation. Even when the measuring equipment only outputs the original coordinate points, it can still obtain deviation data for waviness analysis.

[0074] (3) Significantly improve detection efficiency. By performing low-order fitting (such as a quadratic polynomial) on the normal deviation and removing it, high-order features are extracted; and the method of the present invention does not require high-density measurement points, and can reliably identify the principal order, ghost order and their amplitudes with fewer effective sampling points, greatly reducing the amount of measurement data and measurement time, and is suitable for batch detection and rapid quality evaluation.

[0075] (4) Achieve precise positioning of problematic tooth surfaces. When mapping higher-order features to the gear's one-turn angle domain, the correspondence between higher-order features and tooth number and tooth surface side is preserved; when a major or ghost order with abnormal amplitude appears in the order spectrum, it can be traced back to the specific tooth and tooth surface, and the auxiliary positioning result of the problematic tooth surface is output, providing direct and quantifiable data basis for gear quality traceability, re-inspection and processing technology adjustment.

[0076] In summary, this invention forms a complete autonomous technology closed loop from data input, benchmark construction, deviation extraction, order analysis to problem localization, effectively solving the technical problems of existing methods such as strong dependence on generating measurement and dedicated software, low measurement efficiency, and inability to locate problem tooth surfaces. Attached Figure Description

[0077] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a flowchart of the gear waviness order spectrum extraction method based on coordinate system measurement method of the present invention; Figure 2 To plot the closed profile of the gear in the same two-dimensional coordinate system for each measurement subset; Figure 3 For gear parameter identification and estimation results; Figure 4 A split diagram of the tooth profile data; Figure 5 A schematic diagram for effective tooth profile extraction; Figure 6 A schematic diagram for calculating the theoretical position; Figure 7 The results are as follows: (a) shows the tooth profile error of the left tooth surface; (b) shows the tooth profile error of the right tooth surface. Figure 8 (a) Extraction of high-order errors; (b) Extraction of tooth profile error and low-order features of left tooth surface; (c) Extraction of tooth profile error and low-order features of right tooth surface; (d) Extraction of high-order features of left tooth surface; Figure 9 The higher-order error-angle domain is represented; (a) is the left tooth surface error angle domain diagram; (b) is the right tooth surface error angle domain diagram; Figure 10 The gear order spectrum; (a) right tooth profile order spectrum; (b) left tooth profile order spectrum; Figure 11 The diagram shows a tooth profile measurement method; (a) shows the tooth profile measurement of an external gear; (b) shows the tooth profile measurement in a coordinate system. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0079] This embodiment aims to propose a method for extracting the order spectrum of gear waviness based on coordinate system measurement. The method uses coordinate system measurement to measure one revolution of the gear and obtain the tooth profile measurement results. When the measurement results do not directly contain tooth profile deviation, normal deviation, or waviness curve, the gear waviness order spectrum is obtained through data reading, segment splicing, closed profile reconstruction, gear parameter identification and calculation, left and right tooth profile splitting, working tooth surface interception, theoretical involute establishment and alignment, normal deviation calculation, separation of low-order and high-order features, angular domain vibration influence analysis, and Fourier analysis. The method further locates the problematic tooth surface that causes waviness abnormality.

[0080] Specifically, such as Figure 1 As shown in the figure, the gear waviness order spectrum extraction method based on coordinate system measurement in this embodiment includes the following steps.

[0081] S1: Use the coordinate system measurement method to obtain the tooth profile measurement results of the gear being measured for one revolution, and export them as a data file containing the coordinate information of the measurement points.

[0082] This embodiment employs a coordinate system measurement method to measure one revolution of the gear under test, obtaining the tooth profile measurement results over the entire revolution, and exporting the measurement results as a data file. The data file includes the coordinate information of the measurement points in the measurement coordinate system, and the measurement results are not required to directly contain tooth profile deviation, normal deviation, amplitude curve, or waviness curve. Specifically, the data file format includes, but is not limited to, .DAT, .Mka, .txt, Excel files, or other data formats capable of recording the coordinate information of the measurement points. This step enables this embodiment to be adaptable to coordinate system measurement data exported from different measuring devices (such as gear measurement centers, coordinate measuring machines, white light interferometers, laser confocal measuring instruments, and ultra-depth-of-field measuring instruments) or different measuring software.

[0083] Specifically, in this embodiment, a gear is selected for testing and installed on a measuring device. A measuring coordinate system O-XY is established based on the installation position of the gear. A measuring section is selected on the gear, and the coordinate system measurement method is used to scan and measure the circumference of the gear within the measuring section to obtain the two-dimensional coordinates of each measuring point in the measuring coordinate system.

[0084] During the measurement process, the measurement path covers all teeth of the gear being measured, including the left and right tooth profiles of each tooth, so that the obtained measurement results can completely represent the circumference of the gear being measured. Each measurement point is recorded sequentially according to the actual measurement order to preserve the positional relationship between the measurement points, providing a basis for subsequent measurement data splicing, closed profile reconstruction, and tooth separation.

[0085] When the measuring equipment cannot complete the measurement of one revolution of the gear profile in a single continuous scan, the gear profile is divided into multiple measurement segments, and each segment is scanned and measured sequentially according to a predetermined order. Each measurement segment corresponds to an independent measurement, and the corresponding measurement result is saved as a measurement subset. Each measurement subset is named A, B, C, ... in the order of measurement.

[0086] To facilitate subsequent identification of the connection positions between adjacent measurement segments, an overlapping measurement area is set between adjacent measurement segments. That is, the starting part of the subsequent measurement segment and the ending part of the previous measurement segment cover the same area in the gear profile. The ending part of the last measurement segment and the starting part of the first measurement segment also have an overlapping measurement area, so that the repeated measurement parts at the beginning and end can be eliminated and a complete closed profile of the gear can be formed.

[0087] During measurement, the number of measurement points and the interval between adjacent measurement points are set according to the size and number of teeth of the gear being measured, the sampling capability of the measuring equipment, and the target analysis order. The measurement points should cover the complete gear profile from the tooth root region to the tooth tip region, and ensure that after the tooth root and tooth tip rounding regions are subsequently removed, each tooth's working tooth surface still retains valid measurement points that meet the requirements for normal deviation calculation and waviness order analysis.

[0088] The measuring device is capable of performing coordinate system measurement and outputting coordinate information of the measurement points, including a gear measuring center, a coordinate measuring machine, a white light interferometer, a laser confocal measuring instrument, or a depth-of-field measuring instrument. The measuring device can adopt contact measurement or non-contact measurement methods. This embodiment does not require the measuring device to have the function of generating tooth profile measurement.

[0089] After completing the gear's profile measurement, export the results from the measuring equipment or its software as a data file. The exported data file should at least include the x-coordinate and y-coordinate of each measurement point in the measurement coordinate system, and may also include the measurement point number, measurement sequence, measurement segment name, and other auxiliary identification information.

[0090] The data files are in .DAT, .Mka, .txt, or Excel format. For results obtained from segmented measurements, each measurement segment can be saved as an independent data file, or multiple measurement segments can be saved in different data areas of the same data file. This embodiment only requires that the exported data file contains the coordinate information of the measurement points; it does not require the measuring equipment or software to directly output tooth profile deviation, normal deviation, amplitude curve, or waviness curve.

[0091] After the data is exported, the integrity of each data file is checked to confirm that the data file contains all the measurement segments within one revolution of the gear, that the coordinate data in each measurement segment is continuous and can be read normally, and that there is an overlapping measurement area between adjacent measurement segments and between the first and last measurement segments for subsequent splicing.

[0092] This step obtains the tooth profile measurement results within one revolution of the gear being tested, providing raw data for step S2 to read data files of different formats and uniformly parse the tooth profile measurement results.

[0093] S2: Read and uniformly parse the data file, and uniformly represent the tooth profile measurement results under different formats as a set of tooth profile measurement results. The set of tooth profile measurement results includes several measurement subsets corresponding to segmented measurements.

[0094] The data file exported in step S1 is read, and data files of different formats are parsed to extract the two-dimensional coordinate information of the measurement points in the measurement coordinate system. The tooth profile measurement results of different formats are then uniformly represented as a set of tooth profile measurement results. Specifically, the data file formats include .DAT, .Mka, .txt, Excel files, or other data formats that can record the coordinate information of the measurement points.

[0095] For .DAT and .txt files, data columns are divided according to the spaces, tabs, commas, or other delimiters used in the file, and the x and y coordinates are read according to the pre-set coordinate column positions. For .Mka files, the coordinate data of each measurement segment is read according to the measurement segment name and corresponding data range in the file. For Excel files, the measurement data is read according to the worksheet name, the starting row of data, and the column where the coordinates are located; when different measurement segments are stored in different worksheets, the measurement data in each worksheet is read one by one.

[0096] When reading data, skip file headers, descriptive text, blank lines, and data lines that cannot be converted to numerical values, retaining only valid measurement point coordinates. For data files containing measurement point numbers, measurement order, or measurement segment names, retain the corresponding information; for data files without measurement point numbers, number the measurement points sequentially according to their original arrangement in the data file.

[0097] Since this embodiment uses a segmented approach to measure one revolution of the gear, each measurement forms an independent measurement subset. When reading the data, each measurement subset is saved according to its original measurement segment name. In this embodiment, the measurement subsets are named A, B, C, ... sequentially; when the original data does not have measurement segment names, they are named sequentially according to the reading order.

[0098] Because measuring a gear's revolution using the coordinate system method typically requires multiple segmented measurements, the set of tooth profile measurement results includes several measurement subsets, each corresponding to one measurement or one measurement segment. These measurement subsets can be named sequentially (A, B, C...) according to the naming convention in the measuring equipment or software, or they can be uniformly numbered according to the reading order as the 1st measurement subset, the 2nd measurement subset, ..., the... A subset of measurements.

[0099] In this embodiment, the set of tooth profile measurement results after unified analysis is denoted as:

[0100] in: This is a collection of tooth profile measurement results; For the first A subset of measurements; To measure the total number of subsets; Number the measurement subsets. When measurement subsets are named A, B, C, ..., A, B, C, ... can be respectively assigned to... .

[0101] No. Each measurement subset is represented as:

[0102] in: For the first The first measurement subset One measurement point; and The first The measurement subset of the first The x and y coordinates of each measurement point in the measurement coordinate system; For the first The number of measurement points in each measurement subset; For the first The sequential numbering of measurement points within a measurement subset.

[0103] Through the unified analysis described above, tooth profile measurement results exported from different measuring devices or software can be converted into a unified data structure composed of multiple measurement subsets. This unified data structure retains not only the coordinate information of each measurement point, but also the segmentation relationship between each measurement subset and the order relationship of each measurement point within the corresponding measurement subset, thus providing a data foundation for subsequent segment splicing, removal of duplicate measurements, closed profile reconstruction, and gear parameter identification.

[0104] S3: Preprocess the set of tooth profile measurement results. The preprocessing includes identifying and removing duplicate measurement parts between adjacent measurement subsets and duplicate measurement parts at the beginning and end closing positions, and then splicing the processed measurement subsets in sequence to form a complete closed profile of the gear.

[0105] The set of tooth profile measurement results obtained in step S2 Preprocessing is performed. Specifically, preprocessing includes identifying overlapping areas of adjacent measurement subsets according to the order of measurement subsets, removing duplicate measurements between adjacent measurement subsets, removing duplicate measurements at the beginning and end closing positions, and then stitching the processed measurement subsets together in sequence to form a complete closed profile within one revolution of the gear being measured.

[0106] When measuring a gear's circumference using coordinate system measurement, the gear's contour is typically divided into multiple measurement subsets, and there is often overlap between adjacent subsets. Directly stitching these subsets together sequentially would cause measurement points within the overlapping areas to repeatedly participate in subsequent tooth tip identification, circle fitting, and gear parameter calculations, thus affecting the subsequent analysis results. Therefore, this embodiment trims the overlapping areas based on the geometric positional relationship between the start and end points of adjacent subsets.

[0107] For the A subset of measurements ,when When, take the previous measurement subset. The endpoint in the interval is taken as the end point of the previous measurement subset, and is denoted as:

[0108] in: For the first The endpoint of a measurement subset; For the first The last measurement point in the measurement subset; For the first The number of measurement points in each measurement subset; and The first The x-coordinate and y-coordinate of the endpoint in the measurement coordinate system of each measurement subset.

[0109] Calculate the first Geometric distance from each measurement point in each measurement subset to the end point of the previous measurement subset:

[0110] in: For the first The measurement subset of the first From the measurement point to the... Geometric distance between the endpoints of each measurement subset; and The first The measurement subset of the first The x and y coordinates of each measurement point in the measurement coordinate system; For the first The number of measurement points in a measurement subset.

[0111] In the In each measurement subset, determine the sequence number of the measurement point closest to the end point of the previous measurement subset:

[0112] in: For the first The measurement subset and the first The sequence number of the nearest measurement point to the end point of each measurement subset.

[0113] The closest distance is denoted as:

[0114] in: For the first The measurement subset and the first Minimum geometric distance between subsets of measurements; For the first The measurement subset of the first From the measurement point to the... The geometric distance between the endpoints of each measurement subset.

[0115] Set the overlap judgment tolerance as .when and At that time, the judgment of the first The head of the measurement subset and the first There are overlapping measurement regions at the tail of the measurement subset. In this case, the first subset is removed. In the measurement subset, from the first measurement point to the... The overlapping portion of the measurement points is retained only for the first measurement point. From the first measurement point to the last measurement point, we obtain the trimmed first measurement point. A subset of measurements:

[0116] in: For the first The measurement subset obtained after trimming the measurement subset; For the first The first measurement subset There are 10 measurement points.

[0117] like ,or Then it is considered that the first If there are no overlapping areas in the header of a measurement subset that need to be clipped, the original data of that measurement subset shall be retained.

[0118] For a complete gear rotation measurement, it is also necessary to determine whether there is any overlap between the first and last measurement subsets. The starting point of the first measurement subset is taken as:

[0119] in: This marks the starting point of the first measurement subset; This refers to the first measurement point in the first measurement subset; and These are the x and y coordinates of the first measurement point in the first measurement subset in the measurement coordinate system.

[0120] Calculate the geometric distance from each measurement point in the last measurement subset to the starting point of the first measurement subset:

[0121] in: For the last measurement subset The geometric distance from each measurement point to the starting point of the first measurement subset; This represents the number of measurement points in the last measurement subset after overlapping and cropping of adjacent measurement subsets. and For the last measurement subset The x-coordinate and y-coordinate of each measurement point in the measurement coordinate system.

[0122] Determine the sequence number of the measurement point in the last measurement subset that is closest to the starting point of the first measurement subset. To satisfy:

[0123] in, It is the sequence number of the measurement point in the last measurement subset that is closest to the starting point of the first measurement subset.

[0124] The corresponding minimum distance is denoted as:

[0125] in: This is the minimum geometric distance between the last measurement subset and the starting point of the first measurement subset; For the last measurement subset The geometric distance from each measurement point to the starting point of the first measurement subset.

[0126] when and When the last measurement subset is determined to have an overlapping measurement region with the starting point of the first measurement subset, the measurement subset starting from the first measurement subset is removed. The overlapping portion from the first measurement point to the last measurement point is retained, with only the first to the last measurement point remaining. Using 1 measurement point, we obtain the last measurement subset after closed clipping:

[0127] in, This is the last subset of measurements after removing the closed overlapping region at the tail; For the last measurement subset, the first One measurement point; Tolerance for overlap determination.

[0128] like ,or If the last measurement subset does not have any overlapping areas at the beginning and end that need to be clipped, then it is considered that there are no such overlapping areas at the end of the last measurement subset.

[0129] After completing the overlapping and clipping of adjacent measurement subsets and the first and last closed overlapping and clipping, the measurement subsets are sequentially spliced ​​together according to their order to form a complete closed contour point sequence of the gear, denoted as:

[0130] in: A point array representing the complete closed contour of a gear's revolution; For the first closed contour One measurement point; This represents the total number of measurement points in the closed contour. Number the measurement points sequentially in the closed contour point list.

[0131] Points in a closed contour point array Represented as two-dimensional coordinates in the measurement coordinate system:

[0132] in: and These are the x-coordinate and y-coordinate of the q-th measurement point in the closed contour, respectively, in the measurement coordinate system.

[0133] Through the above preprocessing, multiple segmented measurement subsets obtained by the coordinate system measurement method can be converted into a complete closed profile point series of the gear around a continuous, non-repeating measurement area, thus providing a reliable data foundation for subsequent tooth tip identification, tooth number determination, tooth tip circle and tooth root circle analysis, and gear basic parameter calculation.

[0134] This embodiment is based on the set of tooth profile measurement results obtained in step S2. Following the order of measurement subsets A, B, C, ..., overlapping areas between adjacent measurement subsets are identified sequentially, duplicate measurements are removed, and the processed measurement subsets are sequentially stitched together to form a complete closed profile within one revolution of the measured gear. After data stitching is completed, all measurement subsets are plotted in the same two-dimensional coordinate system, such as... Figure 2 As shown in the diagram. When plotting, different measurement subsets are labeled with different curves, and the corresponding measurement subset names are displayed. Both the x-axis and y-axis use... As a unit.

[0135] S4: Identify the tooth crest and determine the number of teeth based on the closed contour.

[0136] Based on the complete closed profile point list of the gear obtained in step S3 The closed profile is centered using coordinates, and the tooth tip position of each tooth is identified based on the change in the polar diameter after centering, thereby determining the number of teeth z of the gear being measured. The point sequence of the complete closed profile of the gear is as follows:

[0137] in: A point array representing the complete closed contour of a gear's revolution; For the first closed contour One measurement point; and The first The x and y coordinates of each measurement point in the measurement coordinate system; This represents the total number of measurement points in the closed contour. Number the measurement points sequentially in the closed contour point list.

[0138] First, the points of the closed contour are centered. The center coordinates of the closed contour are estimated using the bounding box method, with the midpoint between the maximum and minimum x-coordinates used as the center x-coordinate and the midpoint between the maximum and minimum y-coordinates used as the center y-coordinate.

[0139] in: and These are the center x-coordinate and center y-coordinate estimated from the closed bounding box, respectively. A point array representing the complete closed contour of a gear's revolution; For the first closed contour One measurement point; This represents the total number of measurement points in the closed contour. Sequentially number the measurement points in the closed contour point column; and The first one in the closed contour The x-coordinate and y-coordinate of each measurement point in the measurement coordinate system.

[0140] Convert each measurement point in the closed contour point list to centered coordinates:

[0141] in: and The first The x and y coordinates of each measurement point after centering.

[0142] Calculate the polar radius of each measurement point relative to the center point:

[0143] in: For the first The polar radius of each measurement point relative to the center point.

[0144] To filter for peak values ​​at the tooth tip, the tooth tip radius and tooth root radius are initially estimated based on the polar diameter distribution of the closed profile. The high percentile value of the polar diameter sequence is taken as the initial estimate of the tooth tip radius, and the low percentile value of the polar diameter sequence is taken as the initial estimate of the tooth root radius.

[0145] in: This is a preliminary estimate of the tooth tip radius; This is a preliminary estimate of the tooth root radius; This indicates taking the 99.5 percentile value of the polar radius sequence; This indicates the 0.5 percentile value of the polar diameter sequence. The above preliminary estimate is used to determine the threshold for the tooth tip peak value screening.

[0146] Based on the preliminary estimates of the tooth tip radius and the preliminary estimates of the tooth root radius, determine the minimum protrusion threshold of the tooth tip peak:

[0147] in: The minimum protrusion threshold of the tooth tip peak; This represents the peak prominence coefficient.

[0148] Based on polarity sequence Peak identification will be performed if the local peak condition is met and the peak prominence is not less than [value missing]. The measurement points are determined as candidate tooth tip peak points, forming a set of candidate tooth tip peak points:

[0149] in: This is the set of candidate tooth tip peak points; For the first One candidate tooth tip peak point; These are the measurement points corresponding to the closed contour; For the first The measurement point number of each candidate tooth tip peak point in the closed profile point column; This represents the number of candidate tooth tip peak points.

[0150] Calculate the polar angle corresponding to the peak value of each candidate tooth tip, and then uniformly convert the polar angle to... Within the range:

[0151] in: For the first The polar angle corresponding to the peak point of each candidate tooth tip; and The first The x and y coordinates of the centered peak points of each candidate tooth tip.

[0152] The candidate tooth tip peak points are sorted in ascending order of polar angle to obtain the sorted sequence of candidate tooth tip peak points:

[0153] in: For the sorted number The polar angle corresponding to the peak point of each candidate tooth tip.

[0154] To avoid identifying multiple candidate peak points near the same tooth tip, physical deduplication is performed on the sorted candidate tooth tip peak points. The polar angle interval between adjacent candidate tooth tip peak points is calculated. :

[0155] in: The polar angle interval between adjacent candidate tooth tip peak points.

[0156] For candidate tooth tip peak points that are adjacent at the beginning and end, their polar angle interval is: :

[0157] Set the threshold for the deduplication angle at the tooth tip peak point as follows: When the polar angle interval between adjacent candidate tooth tip peak points is less than or equal to When the corresponding candidate point is considered to be a repeated peak point near the same tooth tip, only one candidate tooth tip peak point is retained; when the polar angle interval between adjacent candidate tooth tip peak points is greater than 100°, the peak point is considered to be a repeated peak point near the same tooth tip. When the corresponding candidate point is considered to be the peak point of the tooth tip of a different tooth.

[0158] After deduplication, the set of effective tooth tip peak points is obtained:

[0159] in: The set of effective tooth tip peak points; For the first One effective tooth tip peak point; This represents the number of effective tooth tip peak points after deduplication.

[0160] The number of effective tooth tip peak points is the number of teeth of the gear being tested.

[0161] in: The number of teeth on the gear being tested; Represents the set of effective tooth tip peak points The number of elements in the middle.

[0162] By following the steps above, the peak point of the tooth tip and the number of teeth can be directly identified from the complete closed profile of the gear obtained by the coordinate system measurement method. This does not require the measuring device to directly output the number of teeth or the position of the tooth tip. The effective tooth tip peak point and the number of teeth are identified. It is used for subsequent analysis and calculation of the addendum circle, dedendum circle, base circle, pitch circle, module, and pressure angle, and can be used to visualize the position of the peak point of the addendum in the closed profile of the gear.

[0163] S5: Based on the closed profile analysis, the addendum circle diameter and the root circle diameter are obtained.

[0164] Based on the centered closed profile point sequence and effective tooth tip peak point set obtained in step S4, the tooth tip circle and tooth root circle of the tested gear are analyzed to obtain the tooth tip circle diameter. and root circle diameter The addendum circle and dedendum circle are used for subsequent calculations of the base circle, pitch circle, module, and pressure angle, as well as for determining the effective working range of the tooth profile.

[0165] As can be seen from step S4, the first point in the closed contour point sequence... The measurement points, after being centered, are represented as follows:

[0166] in: For the first The coordinates of each measurement point after centering; and The first The x and y coordinates of each measurement point after centering; , This represents the total number of measurement points within the closed contour.

[0167] Call the centered coordinates and polar radius of each measurement point obtained in step S4 The polar radii of all measurement points are arranged into a polar radii sequence:

[0168] in: This is the sequence of extreme diameters corresponding to the closed profile of the gear. For the first The polar radius of each measurement point relative to the center point; This represents the total number of measurement points within the closed contour.

[0169] Because the closed profile obtained by the coordinate system measurement method may contain local measurement noise, individual outliers, or boundary fluctuations, directly using the maximum and minimum extreme diameter values ​​as the tooth tip radius and tooth root radius is easily affected by local outliers. Therefore, this embodiment uses the percentile statistical method of extreme diameter sequence to estimate the tooth tip radius and tooth root radius.

[0170] Take the polar sequence The high percentile value is used as the estimate of the tooth tip circle radius:

[0171] in: The radius of the tooth tip circle; Represents the polar radius sequence The 99.5 percentile value.

[0172] Take the polar sequence The lower percentile value is used as an estimate of the root circle radius:

[0173] in: The radius of the tooth root circle; Represents the polar radius sequence The 0.5 percentile value.

[0174] Based on the tooth tip circle radius Calculate the tip circle diameter :

[0175] in: It is the diameter of the tooth tip circle.

[0176] Based on the radius of the tooth root circle Calculate the root circle diameter :

[0177] in: It is the diameter of the tooth root circle.

[0178] The effective tooth tip peak points identified in step S4 are used as auxiliary verification information for tooth tip circle estimation. If the set of effective tooth tip peak points is:

[0179] in: The set of effective tooth tip peak points; For the first One effective tooth tip peak point; The number of teeth on the gear being tested.

[0180] The positions of the effective tooth tip peak points in the closed contour can then be displayed in correspondence with the tooth tip circle to verify whether the tooth tip circle and the position of each tooth tip are consistent. If the effective tooth tip peak points are all distributed near the tooth tip circle, it indicates that the tooth tip circle estimation result matches the tooth tip recognition result.

[0181] Through the above steps, the addendum circle and dedendum circle can be directly obtained from the complete closed profile of the gear obtained by the coordinate system measurement method, without requiring the measuring equipment to directly output the addendum circle diameter or dedendum circle diameter. The obtained addendum circle diameter... and root circle diameter Used for subsequent calculation of gear basic parameters, establishment of theoretical involute curves, and determination of the working tooth surface range of the tooth profile.

[0182] S6: Based on the number of teeth, the addendum circle diameter, the dedendum circle diameter, and the closed profile, calculate the basic parameters of the gear, which include at least the base circle diameter, the pitch circle diameter, the module, and the pressure angle.

[0183] The number of teeth is identified in step S4. And in step S5, the tooth tip circle diameter is obtained. and root circle diameter Based on this, the base circle diameter is further calculated based on the complete closed profile of the gear. Pitch circle diameter Modulus and pressure angle The above parameters are used to subsequently establish the theoretical involute equation and serve as the basis for aligning the working tooth surface measurement data with the theoretical involute and calculating the normal deviation.

[0184] As shown in step S5, the addendum circle radius and the dedendum circle radius are respectively and Then the total height range of the tooth can be expressed as:

[0185] in: This is the radial difference between the addendum circle radius and the dedendum circle radius; The radius of the tooth tip circle; The radius of the tooth root circle is denoted as ...

[0186] To avoid the influence of the tooth tip rounding region and tooth root transition region on the base circle estimation, the initial tooth profile region used for base circle estimation is first determined based on the total tooth height range. A radial safety factor is set to... Then the lower boundary radius and upper boundary radius of the initial tooth profile region are respectively:

[0187] in: The radius of the lower boundary of the initial tooth profile region; The radius of the upper boundary of the initial tooth profile region; This is the radial safety factor.

[0188] Call the centered coordinates obtained in step S4 , and polar diameter Perform difference or gradient operations on the closed contour point sequence to obtain the first... Local tangential change at each measurement point:

[0189] in: and They represent the first The changes in the abscissa and ordinate at each measurement point along the sequence of measurement points. This represents the gradient operation along the sequence of measurement points.

[0190] Calculate the modulus of the local tangential change:

[0191] in, For the first The local tangential change modulus at each measurement point.

[0192] Based on the local tangential change and the location of the measurement point, calculate the estimated local normal value for each measurement point:

[0193] in: For the first The estimated local normal value corresponding to each measurement point. This value is used to estimate the base circle radius from the geometric changes in the working area of ​​the tooth profile.

[0194] Based on the initial tooth profile region, determine the set of measurement points involved in the statistical estimation of the base circle:

[0195] in: This is the set of measurement point indices that participate in the statistical estimation of the base circle.

[0196] For sets The median of the local normal estimates at each measurement point within the circle is used to obtain the base circle radius estimate.

[0197] in, The radius of the base circle; This indicates that the median is used. Using the median can reduce the impact of local outliers, tooth tip rounding areas, and tooth root transition areas on the base circle estimation.

[0198] Based on the base circle radius Calculate the base circle diameter :

[0199] in: The base circle diameter is denoted by .

[0200] Order No. The position vectors of the measurement points are: The local normal reference vector is Then the angle between the two satisfy:

[0201] in: This is the angle between the position vector and the local normal reference vector. When there exists a measurement point such that... When the angle is close to 90°, the polar diameter corresponding to the measurement point can be used as an auxiliary estimate of the base circle radius. When no measurement point meets the conditions, it indicates that the base circle may be located below the effective area of ​​the measured tooth profile. In this case, the base circle radius obtained by statistically analyzing the local normal is used. As the final base circle radius.

[0202] To establish an effective working section, the effective lower boundary of the tooth profile can be further modified based on the base circle radius. The modified effective lower boundary radius is:

[0203] in: The corrected effective lower boundary radius; This represents the safety margin above the base circle.

[0204] The corrected effective tooth profile region is represented as follows:

[0205] in: This is the set of measurement point numbers corresponding to the corrected effective tooth profile region.

[0206] After obtaining the base circle radius Then, the tooth profile measurement points are converted from geometric polar angles to base circle development angles. First, the first... Geometric polar angles of each measurement point:

[0207] in: For the first The geometric polar angle of each measurement point.

[0208] Determine the tooth surface orientation based on the change in polar diameter, and define the orientation discrimination quantity:

[0209] in: For the first The direction discrimination of each measurement point is used to distinguish the rising and falling sides of the tooth profile.

[0210] Calculate the pressure angle auxiliary value corresponding to the q-th measurement point:

[0211] in: For the first The pressure angle auxiliary quantity corresponding to each measurement point.

[0212] Define the involute function as:

[0213] in: For the first The involute function values ​​corresponding to each measurement point.

[0214] Then the first The base circle expansion angle corresponding to each measurement point is:

[0215] in: For the first The base circle development angle corresponding to each measurement point.

[0216] Determine the tooth pitch angle based on the number of teeth z:

[0217] in: The pitch angle between adjacent teeth.

[0218] The polar angle corresponding to the first effective tooth tip peak point is taken as the reference angle, denoted as . For those located in the effective tooth profile region The measurement points within the tooth are assigned to their corresponding teeth based on the difference between their geometric polar angle and the reference angle. The relative angles corresponding to the measurement points are:

[0219] in: For the first The normalized angle difference between each measurement point and the reference angle.

[0220] No. The tooth number corresponding to each measurement point is:

[0221] in: Let q be the tooth number to which the q-th measurement point belongs.

[0222] Therefore, based on the effective tooth profile area Combined with direction discrimination quantity Tooth number The effective measurement point set for the left and right tooth surfaces is obtained. For the first... For each tooth, the set of effective measurement points on its tooth surface is defined as:

[0223] in: and The first The set of effective measurement points for the right and left tooth surfaces of each tooth; This indicates that the point is located within the corrected effective tooth profile region; This indicates that the point belongs to the th One tooth; This indicates that the point is located on the right tooth surface. This indicates that the point is located on the left tooth surface.

[0224] For the Each tooth, according to and The base circle development angle at the internal measurement point is used to calculate the average development angle of the right and left tooth faces on the base circle. To avoid angle jumps at the 0° and 360° junction, the average development angle is calculated using the complex mean method.

[0225]

[0226] in: and The first The average development angle of the base circle of the right and left tooth surfaces of each tooth; and Sets , The number of measurement points in the data; Indicates taking the complex argument; It is the imaginary unit.

[0227] Based on the number of teeth Determine the number of virtual teeth :

[0228] For the For each tooth, select the right tooth surface and the span. The corresponding left tooth surface after the first tooth forms a set of virtual common normal measurement pairs. The tooth numbering after the second tooth is:

[0229] in: In order to be with the first The right tooth surface of each tooth forms a virtual common normal measurement pair with the tooth number of the left tooth surface.

[0230] when and If both exist, calculate the corresponding base circle span:

[0231] in: For the first The virtual common normal is used to measure the span of the development angle on the base circle.

[0232] From the base circle radius Calculate the first Group virtual common normal length:

[0233] in: For the first Group virtual common normal length.

[0234] For all valid pairs of virtual common normal measurements, calculate the average value of the virtual common normal:

[0235] in: The average value of the virtual common normal; To effectively measure the number of virtual common normals.

[0236] Calculate the equivalent base circle tooth thickness angle based on the average value of the virtual common normal:

[0237] in: It is the equivalent base circle tooth thickness angle.

[0238] Calculate the target involute function value based on the equivalent base circle tooth thickness angle:

[0239] in: This is the target involute function value used to solve for the pressure angle.

[0240] The pressure angle is obtained by solving the following formula. :

[0241] in: This is the pressure angle. Pressure angle The above equations are solved using radians, and the output can be converted to degrees.

[0242] After obtaining the base circle diameter Number of teeth z and pressure angle Then, calculate the modulus. :

[0243] in: Modulus; z is the base circle diameter; z is the number of teeth; This is the pressure angle.

[0244] According to the modulus Calculate the pitch circle diameter using the number of teeth z. :

[0245] in: It is the pitch circle diameter.

[0246] Specifically, such as Figure 3 As shown, in this embodiment, through the above steps, the number of teeth can be automatically calculated from the complete closed profile of the gear obtained by the coordinate system measurement method. Tooth tip circle diameter Root circle diameter Base circle diameter Pitch circle diameter Modulus and pressure angle The above parameters are used for subsequent left and right tooth profile splitting, working tooth surface truncation, establishment of the theoretical involute equation, and alignment of working tooth surface measurement data with the theoretical involute.

[0247] S7: Based on the closed profile and the polar angle of each effective tooth tip peak point, the closed profile is divided into the left tooth profile data and the right tooth profile data of each tooth.

[0248] Based on the effective tooth tip peak points and their polar angles obtained after identification and deduplication in step S4, the tooth pitch angle obtained in step S6 is called. and the geometric polar angle of each measurement point in the closed profile According to the angular position of each measurement point relative to the corresponding tooth tip peak point, the complete closed profile of the gear formed in step S3 is split into tooth by tooth, and further divided into left tooth profile data and right tooth profile data for each tooth.

[0249] The first The polar angle of the effective tooth tip peak point is denoted as ,in, For the first closed contour The measurement point is calculated relative to the measurement point . Relative polar angle of each effective tooth tip peak point:

[0250] in: For the first The measurement point relative to the first The relative polar angle of each effective tooth tip peak point. Through the above angle transformation, the relative polar angle is limited to the range of [-π, π) to eliminate the angle jump that occurs when crossing the 0 and 2π positions.

[0251] The measurement points whose relative polar angles satisfy the following conditions are divided into the first... Measurement points corresponding to each tooth:

[0252] That is, the first Centered on the effective tooth tip peak point, the measurement points within each half-tooth pitch angle range before and after it are assigned to the _th_ effective tooth tip peak point. Each tooth. This embodiment does not set extreme diameter limitations for the measurement points to preserve the complete gear profile from the tooth root region to the tooth tip region.

[0253] In the Among the measurement points corresponding to each tooth, the left tooth profile measurement points and the right tooth profile measurement points are divided according to the sign of the relative polar angle. When When, the corresponding measurement points are divided into the first... The measurement point of the left tooth profile of each tooth; when When, the corresponding measurement points are divided into the first... The measurement point of the right tooth profile of each tooth.

[0254] According to the order of increasing relative polar angle, the first... The measurement points of the left and right tooth profiles of each tooth are sorted. The sorted points are then... The measurement points on the left tooth profile of each tooth are numbered sequentially as follows:

[0255] in: The number of measurement points in the left profile of the i-th tooth.

[0256] Therefore, we obtain the first... Complete left tooth profile data for each tooth:

[0257] in: For the first Complete left tooth profile data for each tooth; and The first The left profile of the first tooth The centered x-coordinate and centered y-coordinate of each measurement point.

[0258] The sorted number The measurement points on the right tooth profile of each tooth are numbered sequentially as follows:

[0259] in: For the first The number of measurement points in the right profile of each tooth.

[0260] Therefore, we obtain the first... Complete right tooth profile data for each tooth:

[0261] in: For the first Complete right tooth profile data for each tooth; and The first The right profile of the first tooth The centered x-coordinate and centered y-coordinate of each measurement point. These are determined according to tooth numbering, from tooth 1 to tooth 2. The above processing is performed on each tooth sequentially to obtain complete left and right tooth profile data for all teeth, as follows: Figure 4 As shown.

[0262] S8: Based on the tooth tip circle radius, tooth root circle radius, base circle radius and total tooth height, radially truncate the left and right tooth profile data of each tooth to extract the working tooth surface data.

[0263] Based on the result obtained in step S7 Complete left tooth profile data and complete right tooth profile data The tooth tip circle radius obtained from the aforementioned steps is called. Root radius Base circle radius and full tooth height The left and right tooth profiles of each tooth are radially truncated, and the root rounding area and the tip rounding area are removed, while the involute working tooth surface is retained.

[0264] Let the safety margin factor of the tooth root be The safety margin factor at the tooth tip is Based on the root circle radius, base circle radius, addendum circle radius, and total tooth height, determine the lower and upper boundary radii for evaluation of the working tooth surface:

[0265] in: The lower boundary radius for evaluating the working tooth surface; The upper boundary radius for evaluating the working tooth surface; This is the safety margin coefficient for the tooth root; This is the safety margin factor at the tooth tip. In this embodiment, , .

[0266] Specifically, assess the lower boundary radius. Take the radius of the tooth root circle With base circle radius The larger value in the range is used as a base, and a root safety margin is added to exclude the root transition region and the region below the base circle that is unsuitable for involute evaluation; the upper boundary radius is evaluated. From the tooth tip circle radius The result is obtained by subtracting the tooth tip safety margin, and is used to exclude the tooth tip rounding area.

[0267] For the Left tooth profile data The section is truncated based on the polar radius of each measurement point. The extreme diameters of the left tooth profile measurement points are:

[0268] in: For the first The left profile of the first tooth The polar diameter of each measurement point; and The first The left profile of the first tooth The centered x-coordinate and centered y-coordinate of each measurement point.

[0269] The left tooth profile measurement point, whose polar diameter lies between the lower and upper boundary radii of the evaluation, is retained as the left tooth profile working surface measurement point, thus obtaining the first... Left tooth profile working surface data for each tooth:

[0270] in: For the first Data on the working tooth surface of the left tooth profile of each tooth.

[0271] For the Right tooth profile data The section is truncated based on the polar radius of each measurement point. The extreme diameters of the right tooth profile measurement points are:

[0272] in, For the first The right profile of the first tooth The polar diameter of each measurement point; and The first The right profile of the first tooth The centered x-coordinate and centered y-coordinate of each measurement point.

[0273] The measurement point of the right tooth profile, whose polar diameter lies between the lower and upper boundary radii of the evaluation, is retained as the measurement point of the working tooth surface of the right tooth profile, thus obtaining the first... Working tooth surface data of the right profile of each tooth:

[0274] in: For the first Data of the working tooth surface of the right tooth profile of each tooth.

[0275] Repeat the above truncation process for all teeth to obtain the data sets of the working tooth surfaces of the left and right tooth profiles:

[0276] in: The set of working tooth surface data for the left tooth profile of all teeth; This is the set of working tooth surface data for the right tooth profile of all teeth.

[0277] Through the above steps, the influence of the root transition region, the region below the base circle, and the tip rounding region on subsequent analysis was eliminated. Working tooth surface data from the left and right tooth profiles of each tooth, which can be used for theoretical involute alignment, normal deviation calculation, and higher-order feature extraction, were retained. Figure 5 As shown.

[0278] S9: Establish the theoretical involute curve based on the basic parameters, align the working tooth surface measurement data with the theoretical involute curve, and determine the starting angle of the theoretical involute curve of the left and right tooth profiles of each tooth.

[0279] Based on the base circle radius obtained in step S6 And the working tooth surface evaluation lower boundary radius obtained in step S8 1. Evaluate the upper boundary radius Left tooth profile working tooth surface data set and right tooth profile working tooth surface data set The theoretical involute curves corresponding to the left and right tooth profiles of each tooth are established respectively, and the starting angle of the theoretical involute curves is determined based on the measurement data of the working tooth surface, so that the theoretical involute curves are aligned with the corresponding measurement data of the working tooth surface.

[0280] For any radius on the theoretical involute Its value range is:

[0281] in: Let be the radius of any point on the theoretical involute line relative to the center of the gear; The lower boundary radius for evaluating the working tooth surface; The upper boundary radius for evaluating the working tooth surface.

[0282] From the base circle radius and radius Calculate the pressure angle auxiliary value corresponding to this point:

[0283] in: For the radius on the theoretical involute The corresponding pressure angle auxiliary value.

[0284] The involute function is:

[0285] in: radius The corresponding involute function value at that location.

[0286] For the Left tooth profile working surface data of each tooth Calculate the polar radius and polar angle of each measurement point relative to the center of the gear. The polar radius of each measurement point is:

[0287] No. The polar angles of the measurement points are:

[0288] The polar angles are made continuous along the arrangement of the measurement points on the left tooth profile to avoid polar angle crossing. and The value may suddenly change.

[0289] According to the Calculate the pressure angle auxiliary quantity corresponding to the extreme diameter of each measurement point:

[0290] The corresponding involute function value is:

[0291] The left tooth profile is unfolded in a clockwise direction. Based on the polar angle and involute function values ​​at each measuring point on the working tooth surface of the left tooth profile, the first... The starting angle of the theoretical involute of the left tooth profile of each tooth:

[0292] in: For the first The theoretical involute starting angle corresponding to the left tooth profile of each tooth; For the first The number of measurement points in the working tooth surface data of the left tooth profile of each tooth; For the first The first tooth on the left working tooth surface Polar angles at each measurement point; For the first The first tooth on the left working tooth surface The pressure angle auxiliary quantity corresponding to each measurement point; For the first The first tooth on the left working tooth surface The involute function values ​​corresponding to each measurement point.

[0293] According to the left tooth profile theory, the involute starting angle Establish the theoretical involute polar angle equation for the left profile of the i-th tooth:

[0294] in, For the first The theoretical involute of the left tooth profile of a single tooth is at a radius... The polar angle at that location.

[0295] Therefore, we obtain the first... The coordinate equation of the theoretical involute of the left tooth profile of each tooth:

[0296] in: and The theoretical involute of the left tooth profile of the i-th tooth is at the radius... The x-coordinate and y-coordinate of the location.

[0297] For the Working tooth surface data of the right tooth profile of each tooth Calculate the polar radius and polar angle of each measurement point relative to the center of the gear. The polar radius of each measurement point is:

[0298] No. The polar angles of the measurement points are:

[0299] The polar angles are made continuous along the arrangement of the measurement points on the right tooth profile to avoid polar angle crossing. and The value may suddenly change.

[0300] According to the Calculate the pressure angle auxiliary quantity corresponding to the extreme diameter of each measurement point:

[0301] The corresponding involute function value is:

[0302] Based on the counterclockwise development relationship of the right tooth profile, the theoretical involute starting angle of the right tooth profile is determined:

[0303] in: For the first The theoretical involute starting angle corresponding to the right tooth profile of each tooth; For the first The number of measurement points in the working tooth surface data of the right tooth profile of each tooth; For the first The right tooth profile working surface of the first tooth Polar angles at each measurement point; For the first The right tooth profile working surface of the first tooth The pressure angle auxiliary quantity corresponding to each measurement point; For the first The right tooth profile working surface of the first tooth The involute function values ​​corresponding to each measurement point.

[0304] According to the right tooth profile theory, the involute starting angle , establish the first The theoretical involute polar angle equation for the right profile of a tooth:

[0305] in: For the first The theoretical involute of the right tooth profile of a single tooth has a radius of... The polar angle at that location.

[0306] Therefore, we obtain the first... The coordinate equation of the theoretical involute of the right tooth profile of each tooth:

[0307] in: and The theoretical involute of the right tooth profile of the i-th tooth is at the radius... The x-coordinate and y-coordinate of the location.

[0308] By matching the polar angle information of the measurement data of the left and right tooth profiles of each tooth with the involute function relationship of the corresponding theoretical involute, the theoretical involute is arranged along the gear circumference to the actual position of the corresponding working tooth surface, thereby completing the alignment of the working tooth surface measurement data with the theoretical involute. Figure 6 As shown. During the alignment process, the base circle radius... The coordinates of the measurement points on the working tooth surface remain unchanged. They are not translated, rotated, scaled, or deformed. The circumferential position of the theoretical involute and the measurement data of the working tooth surface are matched only by determining the starting angle of the theoretical involute.

[0309] The starting angles of the theoretical involutes of the left and right tooth profiles of each tooth, as well as the aligned theoretical involutes, are used in the next step to calculate the normal deviation of the working tooth surface measurement data relative to the theoretical involute.

[0310] S10: Calculate the normal deviation of the working tooth surface measurement point relative to the theoretical involute based on the starting angle of the theoretical involute.

[0311] Based on the theoretical involute starting angles of the left and right tooth profiles of each tooth obtained in step S9, and the working tooth surface measurement data obtained in step S8, the normal deviation of the working tooth surface measurement points relative to the theoretical involute is calculated. This normal deviation is calculated from the measurement data obtained by the coordinate system measurement method, and directly outputs the tooth profile deviation, normal deviation, or waviness curve without relying on the measuring equipment.

[0312] For the The first tooth on the left working tooth surface of the tooth profile At each measurement point, the polar radius obtained in step S9 is used. Polar angle Pressure angle auxiliary amount and the theoretical involute starting angle of the left tooth profile The left tooth profile is unfolded clockwise, and the polar angle of the base circle tangent point corresponding to its measurement point is:

[0313] in: For the first The left profile of the first tooth Polar angle of the base circle tangent point corresponding to each measurement point on the working tooth surface.

[0314] Based on the involute initiation angle and the polar angle of the base circle tangent point in the left tooth profile theory, calculate the arc length of the base circle development corresponding to this measurement point:

[0315] in: For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; Let be the radius of the base circle.

[0316] Calculate the tangent length from the measurement point to the point of tangency on the base circle:

[0317] in: For the first The left profile of the first tooth The tangent length from the measurement point on the working tooth surface to the corresponding tangent point on the base circle.

[0318] The difference between the tangent length and the developed arc length of the base circle is taken as the normal deviation of the measurement point relative to the theoretical involute, and the units are changed from... Convert to :

[0319] in: For the first The left profile of the first tooth Normal deviation of each measuring point on the working tooth surface, in units of .

[0320] For the The first tooth on the right tooth profile working surface of the tooth At each measurement point, the polar radius obtained in step S9 is used. Polar angle Pressure angle auxiliary amount and the starting angle of the involute in the right tooth profile theory The right tooth profile is unfolded counterclockwise, and the polar angle of the base circle tangent point corresponding to its measurement point is:

[0321] in: For the first The right profile of the first tooth Polar angle of the base circle tangent point corresponding to each measurement point on the working tooth surface.

[0322] Calculate the arc length of the base circle development corresponding to the measurement point based on the polar angle of the base circle tangent point of the right tooth profile and the theoretical involute starting angle:

[0323] in: For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface.

[0324] Calculate the tangent length from the measurement point to the point of tangency on the base circle:

[0325] in: For the first The right profile of the first tooth The tangent length from the measurement point on the working tooth surface to the corresponding tangent point on the base circle.

[0326] The difference between the tangent length and the developed arc length of the base circle is taken as the normal deviation of the measurement point relative to the theoretical involute, and the units are changed from... Convert to :

[0327] in: For the first The right profile of the first tooth Normal deviation of each measuring point on the working tooth surface, in units of .

[0328] To facilitate subsequent low-order feature fitting and high-order feature extraction, the normal deviation of each tooth surface is sorted in ascending order according to the base circle unfolded arc length. For the ... The left tooth profiles of each tooth are sorted to obtain the left tooth profile deviation data:

[0329] in, For the first A set of deviation data for the left profile of each tooth; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The left profile of the first tooth Normal deviation of each working tooth surface measurement point; data within the set according to... Arranged from smallest to largest.

[0330] For the The right tooth profiles of each tooth are sorted to obtain the right tooth profile deviation data:

[0331] in, Let be the set of deviation data for the right profile of the i-th tooth; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The right profile of the first tooth Normal deviation of each working tooth surface measurement point. Data within the set according to... Arranged from smallest to largest.

[0332] Repeat the above calculation for all teeth to obtain the left tooth profile deviation data set and the right tooth profile deviation data set:

[0333]

[0334] in, This is the set of left tooth profile deviation data for all teeth; This is the set of right profile deviation data for all teeth.

[0335] like Figure 7 As shown, Figure 7 (a) represents the set of left profile deviation data for all teeth. , Figure 7 (b) represents the set of right profile deviation data for all teeth. . Figure 7 (a) and Figure 7 In (b), the x-coordinates are all the arc lengths of the base circle. The unit is The vertical axis represents tooth profile deviation, in units of Each curve represents the change in tooth profile deviation at the corresponding base circle unfolded arc length position for different teeth. Through the above steps, the working tooth surface measurement data obtained by the coordinate system measurement method can be converted into tooth profile deviation data with the base circle unfolded arc length as the independent variable and the normal deviation as the dependent variable, providing a foundation for subsequent low-order feature fitting, high-order feature extraction, and gear waviness order spectrum analysis.

[0336] S11: Perform a low-order fitting on the normal deviation to obtain a low-order feature that slowly changes along the arc length of the base circle.

[0337] Based on the set of left tooth profile deviation data for each tooth obtained in step S10 And right tooth profile deviation data set Arc length unfolded from base circle For independent variable and normal deviation Using the left and right tooth profiles of each tooth as the dependent variable, a quadratic polynomial least squares fitting is performed to obtain the low-order features of the corresponding tooth surface.

[0338] For the The low-order features of the left tooth profile of each tooth are represented as follows:

[0339] in, For the first The arc length of the left tooth profile of each tooth when unfolded on the base circle Low-order features at the location; , and The first The coefficients of the quadratic term, the coefficients of the linear term, and the constant term of the quadratic polynomial of the left tooth profile of each tooth.

[0340] Determined using the least squares method , and This minimizes the sum of squared residuals between the quadratic polynomial fitted value and the left tooth profile normal deviation obtained in step S10, i.e.:

[0341] in: For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point; For the first The left profile of the first tooth Normal deviation corresponding to each measurement point; For the first The number of effective measurement points on the working tooth surface of the left tooth profile of each tooth.

[0342] Substituting the fitted coefficients into the quadratic polynomial, we obtain the... The low-order feature expression of the left tooth profile corresponding to each measurement point:

[0343] in, For the first The left profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point.

[0344] Therefore, the first The low-order feature data of the left profile of each tooth are represented as follows:

[0345] in, For the first Low-order feature data of the left profile of each tooth.

[0346] For the The low-order features of the right tooth profile of each tooth are represented as follows:

[0347] in: For the first The arc length of the right tooth profile of each tooth when unfolded on the base circle Low-order features at the location; , and The first The quadratic coefficients, linear coefficients, and constant term of the quadratic polynomial of the right tooth profile of each tooth.

[0348] Determined using the least squares method , and This minimizes the sum of squared residuals between the quadratic polynomial fitted value and the right tooth profile normal deviation obtained in step S10, i.e.:

[0349] in: For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point; For the first The right profile of the first tooth Normal deviation corresponding to each measurement point; For the first The number of effective measurement points on the working tooth surface of the right tooth profile of each tooth.

[0350] Substituting the fitted coefficients into the quadratic polynomial, we obtain the... Low-order eigenvalues ​​of the right tooth profile corresponding to each measurement point:

[0351] in: For the first The right profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point.

[0352] Therefore, the first The low-order feature data of the right tooth profile of each tooth are represented as follows:

[0353] in: For the first Low-order feature data of the right profile of each tooth.

[0354] The above fitting was performed on all teeth to obtain the low-order feature data sets for the left and right tooth profiles:

[0355]

[0356] in: This is the set of low-order feature data of the left tooth profile for all teeth; This is the set of low-order feature data of the right tooth profile for all teeth.

[0357] Quadratic polynomial fitting is used to characterize the low-order components of the normal deviation that change slowly along the base circle unfolded arc length, including overall tooth profile tilting, bending, and other macroscopic trends. This embodiment does not change the base circle unfolded arc length and normal deviation corresponding to each measurement point; it obtains low-order features only based on the relationship between the normal deviation and the base circle unfolded arc length.

[0358] Through the above steps, the low-order features of the left and right tooth profiles of each tooth are obtained, which provides the basis for step S12 to remove low-order features from the normal deviation and extract high-order features.

[0359] S12: Remove the low-order features from the normal deviation to obtain the high-order features.

[0360] Based on the normal deviations of the left and right tooth profiles of each tooth obtained in step S10, and the corresponding low-order features obtained in step S11, the normal deviations are subtracted from the low-order features at the base circle unfolded arc length positions corresponding to each measurement point to obtain the high-order features of the left and right tooth profiles of each tooth.

[0361] For the The first tooth in the left profile of the tooth The higher-order eigenvalues ​​of the measurement points are expressed as follows:

[0362] in: For the first The first tooth in the left profile of the tooth Higher-order eigenvalues ​​of each measurement point; For the first The left profile of the first tooth Normal deviation of each working tooth surface measurement point; For the first The left profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point.

[0363] Therefore, the first The high-order feature data of the left profile of each tooth are represented as follows:

[0364] in: For the first High-order feature data of the left profile of each tooth; For the first The left profile of the first tooth The base circle unfolded arc length at each measurement point; For the first The number of effective measurement points on the working tooth surface of the left tooth profile of each tooth.

[0365] For the The first tooth in the right profile of the tooth The higher-order eigenvalues ​​of the measurement points are expressed as follows:

[0366] in, For the first The first tooth in the right profile of the tooth Higher-order eigenvalues ​​of each measurement point; For the first The right profile of the first tooth Normal deviation of each working tooth surface measurement point; For the first The right profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point.

[0367] Therefore, the first The high-order feature data of the right profile of each tooth are represented as follows:

[0368] in: For the first High-order feature data of the right tooth profile of each tooth; For the first The right profile of the first tooth The base circle unfolded arc length at each measurement point; For the first The number of effective measurement points on the working tooth surface of the right tooth profile of each tooth.

[0369] The above processing was performed on all teeth to obtain the high-order feature data sets of the left and right tooth profiles:

[0370]

[0371] in: This is the set of high-order feature data of the left tooth profile for all teeth; This is the set of high-order feature data of the right tooth profile for all teeth.

[0372] like Figure 8 As shown, Figure 8 (a) shows the fitting result between the left tooth profile deviation and the corresponding low-order feature, where the solid line represents the left tooth profile deviation data and the dashed line represents the low-order feature of the left tooth surface obtained by fitting a quadratic polynomial. This low-order feature is used to characterize the arc length of the left tooth profile deviation as a function of the base circle. Slowly changing trend components include overall tooth profile tilting, bending, and other macroscopic changing trends. Figure 8(b) shows the fitting result between the right tooth profile deviation and the corresponding low-order feature, where the solid line represents the right tooth profile deviation data and the dashed line represents the low-order feature of the right tooth surface obtained by fitting a quadratic polynomial. This low-order feature is used to characterize the arc length unfolded along the base circle in the right tooth profile deviation. The trend component with a slow change in direction reflects the macroscopic changes in the overall tooth profile morphology of the right tooth surface. Figure 8 (c) represents the higher-order features of the left tooth surface, which are the remaining deviation components obtained after removing the lower-order features from the left tooth surface profile deviation data. These higher-order features retain the positional relationship of the base circle unfolded arc length in the original profile deviation data; that is, each higher-order feature value still corresponds to its specific position on the left tooth surface and working tooth surface of its corresponding tooth. It is mainly used to reflect the periodic higher-order geometric features in the left tooth surface. Figure 8 (d) represents the higher-order features of the right tooth surface, which are the remaining deviation components obtained after removing the lower-order features of the right tooth surface from the right tooth surface profile deviation data. These higher-order features also retain the positional relationship of the base circle unfolded arc length, ensuring that each higher-order feature value corresponds to a specific measurement position on the right tooth surface. They are primarily used to reflect the periodic higher-order geometric features of the right tooth surface. Figure 8 (a) to Figure 8 In (d), the x-coordinates are all the arc lengths of the base circle unfolded. The unit is The vertical axis represents the corresponding tooth profile deviation, low-order feature, or high-order feature, in units of... By extracting low-order and high-order features from the left and right tooth surfaces respectively, the influence of low-frequency trends such as overall tooth profile tilting and bending on subsequent gear waviness order spectrum analysis can be reduced, ensuring that the retained data mainly reflects the periodic high-order geometric features in the tooth profile.

[0373] Through the above steps, the distribution of high-order features of the left and right tooth profiles along the working tooth surface of each tooth can be obtained, and the correspondence between the high-order features and the tooth number, tooth surface side and base circle unfolded arc length position can be preserved. This provides a data basis for subsequently mapping the high-order features to the gear's circumference angle domain, calculating its influence on gear vibration and locating problem tooth surfaces.

[0374] S13: Map the higher-order features to the gear's one-turn angle domain, and calculate the influence of each higher-order feature on the gear vibration to obtain the higher-order feature vibration influence signal in the gear's one-turn angle domain.

[0375] like Figure 9 As shown, based on the tooth sequence, tooth pitch angle, left or right tooth surface side, and the position of each measurement point on the working tooth surface, the high-order features obtained in step S12 are mapped to the gear's circumference angle domain, forming a high-order feature angle domain distribution within the gear's circumference range. Figure 9(a) represents the error angle domain diagram of the left tooth surface, which is used to show the distribution of the higher-order features of the left tooth surface as the circumferential angle changes within one revolution of the gear. Figure 9 In (a), the circumferential angular coordinates represent the angular position of the measuring point on the circumference of the gear, with an angle range of 0° to 360°; the radial scale represents the error or higher-order characteristic amplitude at the corresponding position on the left tooth face, in units of [missing information]. The curves in the figure reflect the variation of the left tooth surface error at different circumferential angle positions, thus providing a direct representation of the periodic higher-order geometric features of the left tooth surface along the entire circumference. Figure 9 (b) represents the error angle domain diagram of the right tooth surface, which is used to show the distribution of the higher-order features of the right tooth surface as the circumferential angle changes within one revolution of the gear. Figure 9 In (b), the circumferential angular coordinates also represent the angular position of the measuring point on the circumference of the gear, with an angle range of 0° to 360°; the radial scale represents the error or higher-order characteristic amplitude at the corresponding position on the right tooth face, in units of... The curves in the figure reflect the variation of the right tooth surface error at different circumferential angle positions, thus characterizing the periodic higher-order geometric features of the right tooth surface along the entire circumference. By establishing error angle domain diagrams for the left and right tooth surfaces respectively, the higher-order features originally represented by the arc length of the base circle can be converted into distribution results represented by the gear circumferential angles, providing an angle domain data foundation for subsequent gear waviness order spectrum analysis.

[0376] In this embodiment, the number of sampling points per tooth is only 42, which greatly reduces the requirements for measurement data and significantly improves the gear inspection speed. Based on this, the influence of each higher-order feature on gear vibration is calculated, obtaining the higher-order feature vibration influence signal over the gear's angular domain. The higher-order feature vibration influence signal retains the correspondence between each influence quantity and the tooth number, left or right tooth profile, and the position of the working tooth surface.

[0377] S14: Perform Fourier analysis on the high-order characteristic vibration influence signal to obtain the gear waviness order spectrum, and identify the principal order, ghost order and their amplitudes from it.

[0378] Based on the vibration influence signal of higher-order features in the gear's angular domain obtained in step S13, Fourier analysis is performed on it to decompose the angular domain signal into harmonic components corresponding to different gear orders, thus obtaining the gear waviness order spectrum. The order spectrum is used to characterize the distribution of the influence of higher-order features on gear vibration at different gear orders.

[0379] Suppose that the high-order characteristic vibration influence signal of the gear in the angular domain is represented by equal-angle resampling as follows:

[0380] in: For the first The higher-order characteristic vibration influence values ​​corresponding to each angle sampling position; For the first Each angle sampling position; This represents the number of resampling points within the angular domain of one revolution of the gear.

[0381] Discrete Fourier transform of the high-order characteristic vibration influence signal in the angle domain:

[0382] in: For the first Complex coefficients of each Fourier component; The Fourier component index; It is the imaginary unit.

[0383] Since the angular domain signal being analyzed covers one revolution of the gear, therefore, the first The gear order corresponding to each Fourier component is:

[0384] in: For the first The gear order corresponding to each Fourier component indicates the number of times that component changes periodically within one revolution of the gear.

[0385] For a one-sided order spectrum with non-zero frequencies, its corresponding amplitude can be expressed as:

[0386] in: Gear order The corresponding amplitude; Fourier coefficients The mold. Derived from gear order. and their corresponding amplitude The gear waviness order spectrum is formed as follows:

[0387] in: This is the gear waviness order spectrum. The horizontal axis of the order spectrum represents the gear order, and the vertical axis represents the amplitude of the corresponding order.

[0388] Based on the amplitude and distribution of each order in the order spectrum, the principal and ghost orders of gear waviness are identified. For a gear with z teeth, the orders corresponding to the number of teeth and its integer multiples are expressed as:

[0389] in: The value is a positive integer. Orders with significant amplitudes near the number of teeth and integer multiples thereof are identified as principal orders; orders other than principal orders that have amplitudes reaching a preset threshold and have a significant impact on vibration anomalies are identified as ghost orders, and the principal order, principal order amplitude, ghost order, and ghost order amplitude are output respectively.

[0390] like Figure 10 As shown, the high-order characteristic vibration influence signal in the gear's circumference angle domain is converted into a tooth profile waviness order spectrum. Based on the amplitude and distribution position of each order in the order spectrum, the principal order, ghost order, and their corresponding amplitudes of the gear waviness are identified. Figure 10 In the figure, the horizontal axis represents the order, and the vertical axis represents the order magnitude, with units of 1. Each bar represents the amplitude of tooth profile waviness at the corresponding order. Figure 10 (a) represents the right tooth profile order spectrum, which characterizes the amplitude distribution of higher-order features of the right tooth surface at different orders. For a number of teeth... The order corresponding to the number of teeth and its integer multiples of the gear under test is expressed as follows: ,in It is a positive integer. Figure 10 In (a), the magnitudes of the corresponding orders are marked at the 26th, 52nd, 78th, 104th, 130th, 156th, and 182nd orders, which are approximately 0.11. 0.27 0.12 0.14 0.04 0.02 and 0.03 By analyzing the order spectrum of the right tooth profile, the amplitude distribution of the right tooth surface waviness at the principal order and other significant orders can be obtained. Figure 10 (b) represents the left tooth profile order spectrum, which is used to characterize the amplitude distribution of higher-order features of the left tooth surface at different orders. Figure 10 In (b), the magnitudes of the corresponding orders are marked at the 26th, 52nd, 78th, 104th, 130th, 156th, and 182nd orders, which are approximately 0.33. 0.07 0.10 0.11 0.11 0.05 and 0.04 By using the left tooth profile order spectrum, the amplitude distribution of the waviness of the left tooth surface at the principal order and other significant orders can be obtained. By establishing the right and left tooth profile order spectra respectively, the higher-order geometric features of the left and right tooth surfaces can be converted into amplitude distribution results in the order domain. Specifically, orders with significant amplitudes near the number of teeth and their integer multiples can be used to identify the principal order, while orders outside the principal order that reach a preset threshold and have a significant impact on vibration anomalies can be used to identify ghost orders, thus outputting the principal order, principal order amplitude, ghost order, and ghost order amplitude respectively.

[0391] S15: Based on the correspondence between the higher-order characteristic vibration influence signal and the tooth number, tooth surface side and working tooth surface position, locate the problematic tooth surface that causes abnormal waviness.

[0392] Based on the vibration influence signals of the gear's higher-order characteristics in the circumference domain of the left and right tooth surfaces obtained in step S13, and the gear waviness order spectra of the left and right tooth surfaces obtained in step S14, the distribution and order characteristics of higher-order features on different tooth surface sides are visualized and analyzed.

[0393] During the analysis, the distribution of the principal order, ghost order and their amplitude in the order spectrum is combined to observe whether there are obvious periodic excitations, broadband excitations or anomalous order components. The order positions, amplitudes and overall distribution differences of the corresponding order spectra of the left and right tooth surfaces are compared to determine whether the waviness anomaly mainly originates from the left or right tooth surface.

[0394] By further combining the vibration influence signal of higher-order features in the gear's one-turn angle domain, the changes in local higher-order features within the corresponding angle range of different teeth are observed. Since step S13 retains the correspondence between higher-order features and tooth number, tooth surface side, and working tooth surface position when forming the gear's one-turn angle domain signal, the corresponding tooth and its tooth surface can be traced back to the angle position where abnormal higher-order features appear.

[0395] Based on the above analysis, auxiliary positioning results for the problematic tooth surface are output. These auxiliary positioning results include at least the tooth number of the suspected problematic tooth and the abnormal tooth surface, which can be either the left or right tooth surface.

[0396] This embodiment of the gear waviness order spectrum extraction method based on coordinate system measurement has the following advantages compared with the prior art: (1) Break the dependence of gear waviness analysis on specific measuring equipment.

[0397] This invention employs a coordinate system measurement method to obtain the tooth profile measurement results for one revolution of a gear. It does not require the measuring equipment to have the capability to measure generated tooth profiles, nor does it require the measuring equipment to directly output tooth profile deviation, normal deviation, amplitude curve, or waviness curve. As long as the measuring equipment can obtain the coordinate information of the gear's one-way profile, its measurement results can be used for subsequent analysis. Therefore, it is compatible with various measuring equipment such as gear measuring centers, coordinate measuring machines, white light interferometers, laser confocal measuring instruments, and ultra-depth-of-field measuring instruments, improving the equipment versatility for gear waviness order analysis.

[0398] (2) It can extract the tooth profile normal deviation from the coordinate information.

[0399] This invention establishes a theoretical involute curve based on the identified and calculated gear foundation parameters, and determines the theoretical involute starting angles for the left and right tooth profiles of each tooth, aligning the measured working tooth surface with the theoretical involute curve. Subsequently, based on the geometric relationship between the base circle tangent point, the base circle unfolded arc length, and the tangent length, the normal deviation of the measured working tooth surface relative to the theoretical involute curve is calculated. Thus, even when the measuring equipment only outputs the coordinates of the measurement points, normal deviation data for waviness analysis can still be obtained.

[0400] (3) Reduce reliance on measurement software.

[0401] This invention can read and uniformly parse data files in various formats such as .DAT, .Mka, .txt, and Excel, and convert measurement results output by different measuring devices or software into a unified data structure composed of multiple measurement subsets. Therefore, this invention does not rely on deviation curves or waviness analysis functions provided by specific measuring software, and can improve compatibility between different measuring devices, software, and data formats.

[0402] (4) It can independently identify and calculate the basic parameters of the gear from the measurement results.

[0403] This invention can identify the tooth tip position and determine the number of teeth z based on the complete closed profile of a gear. It further analyzes and obtains the addendum circle and dedendum circle, and calculates the base circle, pitch circle, module, and pressure angle based on the local geometric relationships of the measurement points, the base circle development angle, and the length of the virtual common normal. Therefore, this invention does not require complete theoretical gear parameters to be provided at the input end, expanding the applicability of this method to gears with unknown or incomplete parameter information.

[0404] (5) It can locate the problematic tooth surface that causes abnormal vibration.

[0405] This invention, when constructing the vibration influence signal of higher-order characteristics in the gear's angular domain, retains the correspondence between higher-order characteristics and tooth number, left or right tooth profile, and specific position of the working tooth surface. Therefore, when a major or ghost order with abnormal amplitude appears in the order spectrum, the problematic tooth surface causing the vibration abnormality can be located based on the influence of different teeth, different tooth surfaces, and different positions on the abnormal order, and the corresponding tooth number, tooth surface flank, and abnormal position information can be output. This result is beneficial for targeted re-inspection, quality judgment, and anomaly analysis of the tested gear, and can provide a basis for subsequent gear machining adjustments and machining quality improvements.

[0406] (6) It can improve measurement efficiency with fewer sampling points.

[0407] This invention does not require the use of high-density measurement points to reconstruct the gear waviness signal. In a specific embodiment, only about 50 effective sampling points are needed for each working tooth surface to complete the calculation of normal deviation, extraction of higher-order features, analysis of gear waviness order spectrum, and location of problematic tooth surfaces. Compared with the existing commercial waviness analysis method using 480 measurement points, under the same or similar inspection task conditions, this invention can effectively reduce the amount of measurement data and measurement time, which is beneficial for batch gear inspection and rapid quality evaluation.

[0408] (7) Wide range of applications.

[0409] This invention can be applied to spur gears or helical gears, and can analyze the left tooth profile, right tooth profile, or both tooth profiles separately. It is also compatible with different measuring devices and different data file formats. Through a complete processing procedure from coordinate system measurement results to gear waviness order spectrum and problem tooth surface positioning results, this invention can provide a unified data analysis method for gear noise analysis, gear inspection and evaluation, quality traceability, and gear machining guidance.

[0410] Note: In this invention, the coordinate system measurement method is a non-generating tooth profile measurement method. For details on generating and non-generating methods, please refer to the tooth profile measurement methods in the national standard GB-Z 18620.1-2025. Figure 11 As shown, tooth profile measurement methods include generating tooth profile measurement method and coordinate system tooth profile measurement method. Figure 11 (a) indicates a gear generating profile measurement method. In this method, the linkage between the rotary axis and the linear axis of the measuring device causes the probe to form a generating measurement trajectory corresponding to the theoretical involute relative to the tooth surface of the gear being measured, and tooth profile measurement data is collected along this trajectory. This method can be used to obtain deviation information of the gear tooth profile relative to the theoretical involute. Figure 11(b) represents the coordinate system tooth profile measurement method, also known as the non-generating tooth profile measurement method. In this method, the measuring equipment determines the position of the measuring points based on the workpiece coordinate system, and scans or samples the tooth surface being measured along a predetermined measurement path using a probe to obtain the coordinates of each measuring point on the working tooth surface. Unlike the generating tooth profile measurement method, the coordinate system tooth profile measurement method does not rely on directly forming a theoretical involute trajectory through the linkage of the rotary axis and the linear axis, but rather obtains the tooth profile measurement results based on the positional relationship of the measuring points in the coordinate system. In this invention, the coordinate system measurement method is the non-generating tooth profile measurement method. After obtaining the coordinate measurement data of the left or right tooth profile using the coordinate system tooth profile measurement method, the measurement results can be further converted into tooth profile deviation data with the base circle unfolded arc length as the independent variable and the normal deviation as the dependent variable, thereby providing a data foundation for subsequent low-order feature extraction, high-order feature extraction, and gear waviness order spectrum analysis.

[0411] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for extracting gear waviness order spectrum based on coordinate system measurement method, characterized in that: Includes the following steps: S1: Use the coordinate system measurement method to obtain the tooth profile measurement results of the gear under test for one revolution, and export them as a data file containing the coordinate information of the measurement points; S2: Read and uniformly parse the data file, and uniformly represent the tooth profile measurement results under different formats as a tooth profile measurement result set, the tooth profile measurement result set including several measurement subsets corresponding to segmented measurements; S3: Preprocess the set of tooth profile measurement results. The preprocessing includes identifying and removing duplicate measurement parts between adjacent measurement subsets and duplicate measurement parts at the beginning and end closing positions. Then, the processed measurement subsets are spliced ​​together in sequence to form a complete closed profile of the gear. S4: Identify the tooth tip and determine the number of teeth based on the closed contour; S5: Based on the closed profile analysis, the addendum circle diameter and the root circle diameter are obtained; S6: Based on the number of teeth, the addendum circle diameter, the dedendum circle diameter, and the closed profile, calculate the basic parameters of the gear, which include at least the base circle diameter, the pitch circle diameter, the module, and the pressure angle. S7: Based on the closed profile and the polar angle of each effective tooth tip peak point, the closed profile is divided into the left tooth profile data and the right tooth profile data of each tooth; S8: Based on the tooth tip circle radius, tooth root circle radius, base circle radius and total tooth height, radially truncate the left and right tooth profile data of each tooth to extract the working tooth surface data; S9: Establish the theoretical involute based on the basic parameters, align the working tooth surface measurement data with the theoretical involute, and determine the starting angle of the theoretical involute of the left and right tooth profiles of each tooth; S10: Calculate the normal deviation of the working tooth surface measurement point relative to the theoretical involute based on the starting angle of the theoretical involute; S11: Perform a low-order fitting on the normal deviation to obtain a low-order feature that slowly changes along the arc length of the base circle. S12: Remove the low-order features from the normal deviation to obtain the high-order features; S13: Map the higher-order features to the gear one-turn angle domain, and calculate the influence of each higher-order feature on gear vibration to obtain the vibration influence signal of higher-order features in the gear one-turn angle domain; S14: Perform Fourier analysis on the high-order characteristic vibration influence signal to obtain the gear waviness order spectrum, and identify the principal order, ghost order and their amplitudes from it; S15: Based on the correspondence between the higher-order characteristic vibration influence signal and the tooth number, tooth surface side and working tooth surface position, locate the problematic tooth surface that causes abnormal waviness.

2. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S3, for the first measurement subset , when , the end point in the previous measurement subset is taken as the end point of the previous measurement subset, denoted as: wherein: is an end point of the th measurement subset; is the last measurement point in the th measurement subset; is the number of measurement points in the th measurement subset; and are the horizontal and vertical coordinates of the end point in the measurement coordinate system in the th measurement subset, respectively. calculating the geometric distance of each measurement point in the set of measurements to the end point; in: For the first The measurement subset of the first The measurement point to the first Geometric distance between the endpoints of each measurement subset; and The first The measurement subset of the first The x and y coordinates of each measurement point in the measurement coordinate system; For the first The number of measurement points in each measurement subset; Determine the first The sequence number of the measurement point closest to the end point in the measurement subset: in: For the first The measurement subset and the first The sequence number of the nearest measurement point to the end point of each measurement subset; Let the minimum distance be: in: For the first The measurement subset and the first Minimum geometric distance between subsets of measurements; For the first The measurement subset of the first The measurement point to the first Geometric distance between the endpoints of each measurement subset; Setting overlap judgment tolerance :when and When an overlapping region is determined, the first one is removed. In the measurement subset, from the first measurement point to the... The overlapping portion of the measurement points is retained. From the first measurement point to the last measurement point, we obtain the trimmed first measurement point. A subset of measurements: in: For the first The measurement subset obtained after trimming the measurement subset; For the first The first measurement subset There are 10 measurement points.

3. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S3, the method for removing repeated measurements at the beginning and end of the closed position is as follows: Take the starting point of the first measurement subset: in: This marks the starting point of the first measurement subset; This refers to the first measurement point in the first measurement subset; and Let x and y be the x and y coordinates of the first measurement point in the first measurement subset in the measurement coordinate system. Calculate the geometric distance from each measurement point in the last measurement subset to the starting point of the first measurement subset: in: For the last measurement subset The geometric distance from each measurement point to the starting point of the first measurement subset; This represents the number of measurement points in the last measurement subset after overlapping and cropping of adjacent measurement subsets. and For the last measurement subset The x and y coordinates of each measurement point in the measurement coordinate system; Determine the index of the measurement point in the last measurement subset that is closest to the starting point of the first measurement subset: Let the minimum distance be: in: This is the minimum geometric distance between the last measurement subset and the starting point of the first measurement subset; For the last measurement subset The geometric distance from each measurement point to the starting point of the first measurement subset; when and When an overlapping region is determined, the last measurement subset is removed from the first measurement. The overlapping portion from the first measurement point to the last measurement point is retained, and the overlap from the first measurement point to the last measurement point is also retained. Using 1 measurement point, we obtain the last measurement subset after closed clipping: in: This is the last subset of measurements after removing the closed overlapping region at the tail; For the last measurement subset, the first One measurement point; Tolerance for overlap determination.

4. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S4, the method for identifying tooth tips and determining the number of teeth based on closed contours is as follows: For closed contour point array Coordinate centering is performed, and the center coordinates are estimated using the bounding box method. : in: and These are the center x-coordinate and center y-coordinate estimated from the closed bounding box, respectively. A point array representing the complete closed contour of a gear's revolution; For the first closed contour One measurement point; This represents the total number of measurement points in the closed contour. Sequentially number the measurement points in the closed contour point column; and The first one in the closed contour The x and y coordinates of each measurement point in the measurement coordinate system; Convert each measurement point in the closed contour point list to centered coordinates: in: and The first The x and y coordinates of each measurement point after centering; Calculate the polar radius of each measurement point relative to the center point: in: For the first The polar radius of each measurement point relative to the center point; The high percentile value of the extreme diameter sequence is taken as the preliminary estimate of the tooth tip radius, and the low percentile value of the extreme diameter sequence is taken as the preliminary estimate of the tooth root radius. in: This is a preliminary estimate of the tooth tip radius; This is a preliminary estimate of the tooth root radius; This indicates taking the 99.5 percentile value of the polar radius sequence; This indicates taking the 0.5 percentile value of the polar radius sequence; Determine the minimum protrusion threshold for the peak tooth tip: in: The minimum protrusion threshold of the tooth tip peak; Peak prominence coefficient; Based on polarity sequence Peak identification will be performed if the local peak condition is met and the peak prominence is not less than [value missing]. The measurement points are determined as candidate tooth tip peak points, forming a set of candidate tooth tip peak points: in: This is the set of candidate tooth tip peak points; For the first One candidate tooth tip peak point; These are the measurement points corresponding to the closed contour; For the first The measurement point number of each candidate tooth tip peak point in the closed profile point column; The number of candidate tooth tip peak points; Calculate the polar angle corresponding to the peak point of each candidate tooth tip: in: For the first The polar angle corresponding to the peak point of each candidate tooth tip; and The first The x and y coordinates of the centered peak points of each candidate tooth tip; Sort by polar angle from smallest to largest: in: For the sorted number The polar angle corresponding to the peak point of each candidate tooth tip; Calculate the polar angle interval between adjacent candidate tooth tip peak points : in: The polar angle interval between adjacent candidate tooth tip peak points; For candidate tooth tip peak points that are adjacent at the beginning and end, their polar angle interval is: : Set deduplication angle threshold When the polar angle interval is less than or equal to If one is selected, retain one; otherwise, retain the peak points at the apex of different teeth. After deduplication, the set of valid peak points at the apex of teeth is obtained. in: The set of effective tooth tip peak points; For the first One effective tooth tip peak point; This represents the number of effective tooth tip peak points after deduplication. The number of effective tooth tip peak points is the number of teeth of the gear being tested. in: The number of teeth on the gear being tested; Represents the set of effective tooth tip peak points The number of elements in the middle.

5. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S5, the method for analyzing and obtaining the addendum circle diameter and dedendum circle diameter is as follows: The polar radii of all measurement points are arranged into a polar radii sequence: in: This is the sequence of extreme diameters corresponding to the closed profile of the gear. For the first The polar radius of each measurement point relative to the center point; This represents the total number of measurement points in the closed contour. Take the high percentile value of the polar diameter sequence as the estimated value of the tooth tip circle radius: in: The radius of the tooth tip circle; Represents the polar radius sequence The 99.5 percentile value; Take the lower percentile value as the estimated value of the tooth root circle radius: in: The radius of the tooth root circle; Represents the polar radius sequence The 0.5 percentile value; Calculate the tip circle diameter Root circle diameter .

6. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S6, the method for calculating the basic parameters of the gear is as follows: Calculate the total height of the teeth Set the radial safety factor Determine the lower boundary radius of the initial tooth profile region. and upper boundary radius ;in: and These are the addendum circle radius and the dedendum circle radius, respectively. Gradient calculations are performed on the closed contour point sequence to obtain the local tangential variation. , Calculate the modulus of the local tangential change. ;in: and They represent the first The changes in the abscissa and ordinate at each measurement point along the sequence of measurement points; This represents the gradient operation along the sequence of measurement points; and The first The x and y coordinates of each measurement point after centering; For the first Local tangential change modulus at each measurement point; Calculate the estimated local normal value for each measurement point. ;in: For the first Local normal estimates corresponding to each measurement point; Determine the set of measurement points to participate in the statistical estimation of the base circle. The base circle radius is obtained by taking the median of the local normal estimates for each point within the set. and base circle diameter ;in: For the first The polar radius of each measurement point relative to the center point; This represents the total number of measurement points in the closed contour. This indicates taking the median; Correct the effective lower boundary radius based on the base circle radius. ,in: The effective tooth profile region is obtained by considering the safety margin above the base circle. ;in: This represents the safety margin above the base circle; This is the set of measurement point numbers corresponding to the corrected effective tooth profile region. Calculate the geometric polar angle of the measurement point Direction discrimination quantity Pressure angle auxiliary amount Involute function value Base circle development angle ;in: For the first Geometric polar angles of each measurement point; For the first The direction discrimination of each measurement point is used to distinguish the rising and falling sides of the tooth profile; For the first The pressure angle auxiliary quantity corresponding to each measurement point; The radius of the base circle; For the first The involute function values ​​corresponding to each measurement point; For the first The base circle unfolding angle corresponding to each measurement point; Determine the tooth pitch angle based on the number of teeth z. Polar angle of the first effective tooth tip peak point For reference, the measurement points are assigned to the corresponding teeth to obtain the effective measurement point set for the left and right tooth surfaces; The average development angle of the base circle of the left and right tooth surfaces of each tooth is calculated using the complex mean method, and the pressure angle is solved based on the virtual common normal method. ,make ,in: The target involute function value is calculated from the equivalent base circle tooth thickness angle. Calculate the modulus Pitch circle diameter ;in: Modulus; z is the base circle diameter; z is the number of teeth; The pressure angle; It is the pitch circle diameter.

7. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S7, the method for splitting the closed contour into left tooth profile data and right tooth profile data is as follows: The first The polar angle of the effective tooth tip peak point is denoted as For the first closed contour Calculate the relative polar angle of each measurement point. ;in: , The number of teeth on the gear being tested; For the first The measurement point relative to the first The relative polar angle of each effective tooth tip peak point; For the first Geometric polar angles of each measurement point; Will satisfy The measurement points were assigned to the first One tooth; when When the left tooth profile measurement point is marked, The measurement points for the right tooth profile were marked, and the data for the left tooth profile were obtained by sorting them according to their relative polar angles. and right tooth profile data .

8. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S8, the method for extracting the working tooth surface data is as follows: Setting the root safety margin factor and tooth tip safety margin factor Determine the lower boundary radius of the evaluation for the working tooth surface. And assess the upper boundary radius ;in: The radius of the tooth tip circle; The radius of the base circle; The radius of the tooth root circle; Full tooth height; For left tooth profile data Calculate the polar diameter at each measurement point. , retain satisfaction The measurement points are used as the working tooth surface data of the left tooth profile. ; For right tooth profile data Calculate the polar diameter at each measurement point. , retain satisfaction The measurement points are used as the working tooth surface data of the right tooth profile. .

9. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S9, the method for establishing the theoretical involute and performing alignment is as follows: For the working tooth surface data of the left tooth profile Calculate the theoretical involute starting angle of the left tooth profile: in: For the first The theoretical involute starting angle corresponding to the left tooth profile of each tooth; For the first The number of measurement points in the working tooth surface data of the left tooth profile of each tooth; For the first The first tooth on the left working tooth surface Polar angles at each measurement point; For the first The first tooth on the left working tooth surface The pressure angle auxiliary quantity corresponding to each measurement point; For the first The first tooth on the left working tooth surface The involute function values ​​corresponding to each measurement point; Establish the involute polar angle equation for the left tooth profile theory: in: For the first The theoretical involute of the left tooth profile of a single tooth is at a radius... The polar angle at that location; For the radius on the theoretical involute The corresponding pressure angle auxiliary value; The radius of the base circle; Let be the radius of any point on the theoretical involute line relative to the center of the gear; The coordinate equation of the left involute is obtained from the theoretical involute of the tooth profile: in: and The first The theoretical involute of the left tooth profile of a single tooth is at a radius... The x and y coordinates of the location; Data for the working tooth surface of the right tooth profile Calculate the theoretical involute starting angle of the right tooth profile: in: For the first The theoretical involute starting angle corresponding to the right tooth profile of each tooth; For the first The number of measurement points in the working tooth surface data of the right tooth profile of each tooth; For the first The right tooth profile working surface of the first tooth Polar angles at each measurement point; For the first The right tooth profile working surface of the first tooth The pressure angle auxiliary quantity corresponding to each measurement point; For the first The right tooth profile working surface of the first tooth The involute function values ​​corresponding to each measurement point; Establish the involute polar angle equation for the right tooth profile theory: in: For the first The theoretical involute of the right tooth profile of a single tooth is at a radius... The polar angle at that location; Get the first The coordinate equation of the theoretical involute of the right tooth profile of each tooth: in: and The first The theoretical involute of the right tooth profile of a single tooth is at a radius... The x-coordinate and y-coordinate of the location.

10. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S10, the method for calculating the normal deviation is as follows: For the first tooth surface of the left tooth profile working tooth surface Calculate the polar angle of the base circle tangent point at each measurement point. Base circle unfolded arc length Tangent length and normal deviation ;in: For the first The left profile of the first tooth Polar angle of the base circle tangent point corresponding to each measurement point on the working tooth surface; For the first The first tooth on the left working tooth surface Polar angles at each measurement point; For the first The first tooth on the left working tooth surface The pressure angle auxiliary quantity corresponding to each measurement point; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; The radius of the base circle; For the first The left profile of the first tooth The tangent length from each measurement point on the working tooth surface to the corresponding tangent point on the base circle; For the first The left profile of the first tooth Extreme diameter of each measuring point on the working tooth surface; For the first The left profile of the first tooth Normal deviation of each measuring point on the working tooth surface, in units of ; For the first tooth surface of the right tooth profile working tooth surface Calculate the polar angle of the base circle tangent point at each measurement point. Base circle unfolded arc length Tangent length and normal deviation ;in: For the first The right profile of the first tooth Polar angle of the base circle tangent point corresponding to each measurement point on the working tooth surface; For the first The right tooth profile working surface of the first tooth Polar angles at each measurement point; For the first The right tooth profile working surface of the first tooth The pressure angle auxiliary quantity corresponding to each measurement point; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The right profile of the first tooth The tangent length from each measurement point on the working tooth surface to the corresponding tangent point on the base circle; For the first The right profile of the first tooth Extreme diameter of each measuring point on the working tooth surface; For the first The right profile of the first tooth Normal deviation of each measuring point on the working tooth surface, in units of ; The first The normal deviations of each tooth surface are sorted in ascending order of the base circle unfolded arc length to obtain the first tooth. Data set of deviations in the left profile of each tooth and the Data set of deviations in the right profile of each tooth ; Repeat the above calculation for all teeth to obtain the left tooth profile deviation data set. And right tooth profile deviation data set .

11. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S11, the method for performing low-order fitting on the normal deviation is as follows: For the The left profile of each tooth, with low-order features represented as follows: in: For the first The arc length of the left tooth profile of each tooth when unfolded on the base circle Low-order features at the location; , and The first The coefficients of the quadratic term, the coefficients of the linear term, and the constant term of the quadratic polynomial of the left tooth profile of each tooth are determined by the least squares method. Get the first Low-order eigenvalues ​​of the left tooth profile corresponding to each measurement point: in: For the first The left profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point; Get the first The low-order feature data of the left tooth profile of each tooth are represented as follows: in: For the first Low-order feature data of the left profile of each tooth; For the first The number of effective measurement points on the working tooth surface of the left tooth profile of each tooth; For the The low-order features of the right tooth profile of each tooth are represented as follows: in: For the first The arc length of the right tooth profile of each tooth when unfolded on the base circle Low-order features at the location; , and The first The coefficients of the quadratic term, the coefficients of the linear term, and the constant term of the quadratic polynomial of the right tooth profile of each tooth are determined by the least squares method. Get the first Low-order eigenvalues ​​of the right tooth profile corresponding to each measurement point: in: For the first The right profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; Get the first The low-order feature data of the right tooth profile of each tooth are represented as follows: in: For the first Low-order feature data of the right tooth profile of each tooth; For the first The number of effective measurement points on the working tooth surface of the right tooth profile of each tooth; The above fitting was performed on all teeth to obtain the set of low-order feature data of the left tooth profile. and the set of low-order features of the right tooth profile .

12. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S12, the method for obtaining higher-order features is as follows: For the The first tooth in the left profile of the tooth For each measurement point, the higher-order eigenvalues ​​are represented as: in: For the first The left profile of the first tooth Higher-order eigenvalues ​​of each measurement point; For the first The left profile of the first tooth Normal deviation of each working tooth surface measurement point; For the first The left profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; No. The high-order feature data of the left profile of each tooth are represented as follows: in: For the first High-order feature data of the left profile of each tooth; For the first The left profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The number of effective measurement points on the working tooth surface of the left tooth profile of each tooth; For the The first tooth in the right profile of the tooth For each measurement point, the higher-order eigenvalues ​​are represented as: in: For the first The right profile of the first tooth Higher-order eigenvalues ​​of each measurement point; For the first The right profile of the first tooth Normal deviation of each working tooth surface measurement point; For the first The right profile of the first tooth The low-order eigenvalues ​​corresponding to each measurement point; No. The high-order feature data of the right profile of each tooth are represented as follows: in: For the first High-order feature data of the right tooth profile of each tooth; For the first The right profile of the first tooth The base circle unfolded arc length corresponding to each measurement point on the working tooth surface; For the first The number of effective measurement points on the working tooth surface of the right tooth profile of each tooth; The above processing was performed on all teeth to obtain the high-order feature data sets of the left and right tooth profiles: in: This is the set of high-order feature data of the left tooth profile for all teeth; This is the set of high-order feature data of the right tooth profile for all teeth; The number of teeth on the gear being tested.

13. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S14, the method for obtaining the gear waviness order spectrum is as follows: The vibration influence signal of the high-order characteristic feature in the gear's angular domain after equal-angle resampling is represented as follows: in: For the first The higher-order characteristic vibration influence values ​​corresponding to each angle sampling position; For the first Each angle sampling position; This represents the number of resampling points within the angle domain of one revolution of the gear. Discrete Fourier transform of the high-order characteristic vibration influence signal in the angle domain: in: For the first Complex coefficients of each Fourier component; The Fourier component index; The imaginary unit; No. The gear order corresponding to each Fourier component Amplitude ,Depend on Constructing the gear waviness order spectrum : For the number of teeth is For the gear under test, the order corresponding to the number of teeth and its integer multiples is determined. Orders with significant amplitudes in the vicinity are identified as principal orders, and orders whose amplitudes reach a preset threshold outside of principal orders are identified as ghost orders; where: It is a positive integer.

14. The method for extracting the gear waviness order spectrum based on coordinate system measurement according to claim 1, characterized in that: In step S15, the method for locating the problematic tooth surface causing abnormal waviness is as follows: Combining the amplitude anomalies of the principal and ghost orders in the order spectrum, and the correspondence between the high-order characteristic vibration influence signal retained in step S13 and the tooth number, tooth surface side and working tooth surface position, observe the local high-order characteristic changes in the corresponding angle range of different teeth, trace back to the corresponding tooth and its tooth surface according to the angle position of the abnormal high-order characteristics, and output the tooth number of the suspected problem tooth and the abnormal tooth surface as the left tooth surface or the right tooth surface.

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