Method for in-process detection of gear tooth surface waviness

Abstract

The application discloses a kind of gear tooth surface waviness in-machine detection method, high-precision scanning probe is integrated on machine tool, according to the scanning path of tooth profile direction and tooth direction of tooth surface equation planning, and pre-travel error of probe is calibrated;Gear is directly scanned in succession on tooth surface after machining without disassembly, and three-dimensional topography data of tooth surface are obtained;Original data of the measured point collected are restored to real tooth surface state by coordinate inverse rotation transformation, and error compensation is carried out in combination with pre-travel error compensation table;After being compensated, left and right tooth profile measured points are ordered spliced, and after radial truncation, each measured point tooth profile error is calculated based on involute fitting, high-order tooth profile error is extracted after low-order trend item is removed;Finally, high-order error sequence is Fourier transformed, and tooth surface waviness order spectrum is obtained.The application realizes the in-machine detection of tooth surface waviness, improves detection efficiency and precision, and provides technical support for gear closed-loop precision manufacturing.

Description

Technical Field

[0001] This invention belongs to the field of precision manufacturing and measurement technology, specifically a method for in-machine detection of gear tooth surface waviness. By integrating a high-precision scanning probe into a machine tool, the gear tooth surface is scanned in-machine to collect three-dimensional topographic data, and the order spectrum analysis of tooth surface waviness is performed based on the three-dimensional topographic data, thereby realizing in-machine detection and evaluation of gear tooth surface waviness. Background Technology

[0002] Gears, due to their advantages such as smooth transmission, excellent meshing characteristics, and strong load-bearing capacity, are widely used in high-end equipment such as electric drive systems for new energy vehicles, precision robot reducers, and aerospace transmission devices, becoming the core transmission components of these systems. With the continuous improvement of modern industrial requirements for transmission system performance, especially under harsh conditions such as high speed, heavy load, and low noise, the microscopic geometric quality of gear tooth surfaces has an increasingly prominent impact on the service performance of transmission systems.

[0003] Tooth surface waviness, a mid-to-high frequency geometric error existing on the gear surface, is a periodic geometric irregularity between macroscopic shape error and microscopic surface roughness. This error directly threatens the performance and service life of the transmission system. On the one hand, tooth surface waviness is a key excitation source inducing high-frequency noise and vibration in the transmission system. When gears operate at high speeds, the periodic waviness on the tooth surface causes meshing impact, directly leading to a significant deterioration in NVH (Noise, Vibration, Harshness) performance, severely affecting ride comfort and equipment operating quality. On the other hand, waviness causes local stress concentration during tooth meshing, accelerating material failure processes such as contact fatigue and micropitting, thereby shortening the effective service life of the gears. Especially in applications such as electric drive systems for new energy vehicles, the high-speed characteristics of the motor make the order noise problem caused by tooth surface waviness more prominent, becoming a key bottleneck restricting the improvement of NVH performance of the transmission system. Therefore, achieving accurate detection and reliable evaluation of tooth surface waviness is an important technical prerequisite for ensuring the operational stability and long-term reliability of the transmission system.

[0004] Currently, the measurement of tooth surface waviness mainly relies on dedicated offline metrology equipment, such as gear measuring centers (GMCs) or high-precision coordinate measuring machines (CMMs). The typical process involves unloading the machined gear from the machine tool, transporting it to a metrology room with strict environmental control, re-clamping and datum alignment, and then performing scanning measurement. Existing methods can extract tooth profile waviness information based on the measurement results from gear measuring centers, or use measured tooth surface deviation data for waviness analysis. While these offline measurement methods can obtain relatively accurate and reliable measurement results, their inherent drawbacks are significant. First, the disassembly, handling, re-clamping, and environmental adaptation involved in the measurement process not only lead to a lengthy inspection cycle but also result in a significant lag in the obtained measurement data, making real-time monitoring of the machining process impossible and hindering timely feedback of inspection results to the machining stage. Second, the conversion between the machining datum and the measurement datum, as well as the re-clamping and positioning process, inevitably introduces additional measurement errors. These errors may be confused with the machining errors of the gear itself, affecting the accuracy of error tracing. In addition, offline measurement of large gears also faces practical problems such as difficult handling and high inspection costs.

[0005] To overcome the drawbacks of offline measurement, the measurement process is directly integrated into the machining equipment, giving rise to on-machine measurement (OMM). The core value of OMM lies in the fact that after gear machining, measurements can be performed directly on the machining equipment, significantly reducing the adverse effects on measurement efficiency and accuracy caused by secondary clamping, changes in reference standards, and other factors. Simultaneously, it enables timely processing and analysis of measurement data, allowing for adjustments to machining parameters and forming a highly efficient and precise closed-loop manufacturing process of "machining-inspection-analysis-correction."

[0006] However, existing technologies for in-machine gear inspection primarily focus on detecting macroscopic geometric errors such as tooth profile deviation, pitch deviation, and tooth form error, or on compensating for various error sources affecting measurement accuracy. No complete technical solution has yet been disclosed that can truly achieve in-machine detection of tooth surface waviness. In other words, while existing technologies have made progress in the field of in-machine measurement, their measurement targets do not specifically address tooth surface waviness, a specific mid-to-high frequency geometric error. This is mainly because the detection and evaluation of tooth surface waviness has special requirements for the continuity, density, and subsequent signal processing of measurement data, making it difficult to simply adopt trigger-based or low-density scanning measurement schemes used for macroscopic geometric errors. On the other hand, there are already many mature technologies for data processing and analysis of tooth surface waviness. However, existing methods all focus on processing measurement data acquired by offline equipment such as gear measurement centers, without addressing data acquisition and processing in in-machine inspection scenarios.

[0007] In summary, while current technologies have made some progress in both in-machine inspection and tooth surface waviness analysis of gears, a significant technological gap exists between the two: on the one hand, existing in-machine inspection technologies fail to detect and perform order spectrum analysis of tooth surface waviness; on the other hand, existing waviness analysis technologies rely on offline measurement data, making real-time detection and rapid feedback at the machining site impossible. This technological gap makes it difficult to detect and control tooth surface waviness defects in a timely manner during gear manufacturing, becoming one of the key bottlenecks restricting the intelligent development of precision gear manufacturing.

[0008] Therefore, there is an urgent need for a technical solution that can integrate tooth surface waviness measurement into the processing equipment, so that waviness detection and order spectrum analysis can be completed without disassembly after gear processing, thereby providing complete technical support for the closed-loop precision manufacturing of gears of "processing-inspection-analysis-correction". Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide an on-machine inspection method for gear tooth surface waviness. By integrating a scanning probe into a machine tool, on-machine acquisition, error compensation, and order spectrum analysis of three-dimensional tooth surface morphology data are realized, providing technical support for closed-loop precision manufacturing of gears through "machining-inspection-analysis-correction".

[0010] To achieve the above objectives, the present invention provides the following technical solution: A method for in-machine detection of gear tooth surface waviness includes the following steps: Step S1: Plan the scanning path of the probe according to the tooth surface equation. The scanning path includes a scanning path along the tooth profile direction and a scanning path along the tooth direction. Step S2: Calibrate the pre-travel error of the probe in different spatial directions and construct a pre-travel error compensation table. The method is as follows: calculate the actual unit vector for each calibration direction. With the corresponding pre-travel error Combining data entries, all These entries together constitute the pre-trip error compensation table; Step S3: Construct a measurement coordinate system based on the workpiece mounting datum and determine the gear datum origin; Step S4: Integrate a high-precision scanning probe into the machine tool, control the probe to perform on-machine scanning of the gear tooth surface according to the scanning path planned in step S1, collect the three-dimensional topographic data of the tooth surface, and simultaneously collect the corresponding C-axis rotation angle of the machine tool. Step S5: Perform inverse coordinate rotation transformation on the original measurement points of the three-dimensional morphology data of the tooth surface collected in step S4 to restore the coordinate data in the actual tooth surface state; the original measurement points include tooth direction measurement points and tooth profile measurement points. According to the pre-stroke error compensation table constructed in step S2, perform probe pre-stroke error compensation and probe radius compensation on each of the tooth direction measurement points and tooth profile measurement points to obtain the compensated tooth direction measurement points and tooth profile measurement points. Step S6: Based on the tooth profile measuring points, obtain the left tooth profile measuring points and the right tooth profile measuring points of each tooth; connect the left tooth profile measuring points and the right tooth profile measuring points in series according to the tooth surface order and tooth number order of each tooth to form a complete end face tooth profile point sequence. Step S7: The complete end face tooth profile point sequence obtained in step S6 is radially truncated according to the radial evaluation boundary of the effective tooth profile; invalid measurement points in the tooth root transition area and tooth tip trimming area are removed, and the measurement points of the effective involute working segment are retained to obtain the effective tooth profile point sequence on the involute tooth profile. Step S8: Based on the effective tooth profile point sequence truncated in step S7, perform theoretical involute fitting on the left and right tooth profiles of each tooth respectively, and calculate the tooth profile error of each effective tooth profile point in the effective tooth profile point sequence. Step S9: Remove low-order trend terms from the tooth profile errors of each effective tooth profile point obtained in Step S8, extract high-order tooth profile errors and construct a high-order tooth profile error sequence. The high-order tooth profile errors are the data source for subsequent tooth surface waviness analysis. Step S10: Perform Fourier transform on the high-order tooth profile error sequence obtained in step S9 to obtain the order spectrum of tooth profile waviness, and complete the tooth surface waviness analysis based on in-machine detection. In step S7, the radial evaluation boundary of the effective tooth profile is determined by the following formula: Radial starting position: ; Radial termination position: ; in: For the full height of the teeth; The radius of the base circle; The radius of the tooth tip circle; The radius of the tooth root circle; This is the root shrinkage ratio coefficient; The tooth tip shrinkage ratio coefficient; and: ; For each measuring point in the assembled complete end face tooth profile sequence, based on its end face projection coordinates Calculate the polar diameter Only retain the polar radius to satisfy The measuring points.

[0011] Furthermore, in step S1, the tooth surface equation is a mathematical model of the tooth surface of a standard involute cylindrical helical gear, and the three-dimensional coordinates of any point on the tooth surface are... Represented as:

[0012] in: , and These are the coordinates of any point on the tooth surface along the X, Y, and Z axes. , representing the helical rotation angle, indicating the axial position. end face relative to The angle of rotation of the end face around the gear axis; The base circle helix angle is denoted by , and the helix angle of the helical gear on the cylindrical surface of the base circle is denoted by . For axial coordinates; The radius of the base circle; The initial phase angle of the involute within the end face; Let be the development angle corresponding to a point on the involute.

[0013] Furthermore, in step S1, the scanning path in the tooth profile direction is as follows: within the cross section at the midpoint of the tooth width, the probe moves continuously from the starting point of the base circle along the involute towards the addendum circle. The machine tool C-axis and the machine tool Y-axis establish interpolation linkage, so that the probe moves involute relative to the gear. First, the right tooth surface of the tooth groove is scanned from the starting point corresponding to the base circle radius to the ending point corresponding to the addendum circle. Then, the left tooth surface of the same tooth groove is scanned in the opposite direction of movement. The scanning path in the tooth direction is as follows: on the indexing cylindrical surface, the gear is continuously fed along a spiral line from the upper end face to the lower end face. The probe and the machine tool C-axis are interpolated in linkage. As the probe moves along the machine tool Z-axis, the C-axis rotates synchronously. First, the right tooth surface is continuously scanned from the upper end face to the lower end face, and then the left tooth surface is continuously scanned in reverse from the lower end face to the upper end face.

[0014] Furthermore, in step S2, the method for constructing the pre-travel error compensation table is as follows: S21: Based on the known theoretical radius Using a high-precision standard sphere as the calibration reference, a preset... spatial vector direction The probe is controlled to sequentially trigger measurements on the standard sphere in each direction, and the three-dimensional coordinates of the sphere's center in the machine tool coordinate system are recorded. The set of coordinates of the center of the sphere is obtained:

[0015] S22: Fit the reference sphere using the least squares method from the set of coordinate points of the measured sphere's center to obtain the fitted sphere's center. and fitted radius The objective function is:

[0016] S23: For the first Calculate the pre-travel error in each measurement direction:

[0017] in: To measure the distance from the center of the sphere to the center of the fitted sphere; To measure the radius of the sphere; The theoretical radius of a standard sphere; Indicates the first Measurement directions The corresponding pre-travel error; S24: Combine the actual unit vector of each calibration direction with the corresponding pre-travel error. The entries are combined to form a pre-travel error compensation table; the actual unit vector is represented as:

[0018] in: This indicates the actual approximation direction when the measuring ball contacts the standard ball during the calibration process; This represents the vector pointing from the center of the fitted sphere to the center of the measured sphere; This represents the distance from the center of the measured sphere to the center of the fitted sphere.

[0019] Furthermore, in step S3, the method for constructing a measurement coordinate system based on the workpiece mounting datum is as follows: S31: Without the gear installed, collect several measuring points on the outer cylindrical surface of the machine tool worktable and fit the center of the cross-section. Several measuring points were collected on the upper surface of the workpiece platform, and the average axial coordinate was taken and the radius of the measuring ball was subtracted. The axial height of the upper surface of the workpiece stage is obtained. Obtain the origin of the workpiece stage reference coordinate system. ; S32: Mount the gear on the workpiece stage, collect several measuring points on its outer cylindrical surface and upper end face, and calculate the coordinates of the gear's reference origin using the same method as in step S31. All subsequent tooth surface scanning data are converted to this gear reference coordinate system; among which: , and These represent the X-axis, Y-axis, and Z-axis coordinates of the gear's reference origin, respectively.

[0020] Furthermore, in step S4, a real-time writing strategy for single-tooth surface scanning data is adopted. That is, after the probe collects data for a tooth surface, it immediately writes the sequence number, coordinates and C-axis rotation angle of all measuring points on that tooth surface into a storage file. The data buffer inside the machine tool follows the FIFO rule to ensure that the order of data written into the storage file is strictly consistent with the actual acquisition sequence.

[0021] Furthermore, in step S5, for the tooth-direction scan data, the coordinate data of the tooth-direction measurement points are restored to the coordinate data of the actual tooth surface state through inverse rotation transformation:

[0022] in: The first tooth direction data The coordinate data of each tooth-direction measuring point are around Axis rotation The inverse rotation matrix of the angle; The first tooth direction data Coordinate data of each tooth-direction measuring point; The first tooth direction data The coordinates of each tooth-axis measuring point after inverse rotation transformation; The normal vector at each tooth-axis measurement point is calculated based on the data sequence after inverse rotation transformation, and the actual normal vector is obtained by correction using the theoretical tooth surface normal vector. Based on the pre-stroke error compensation table, the nearest neighbor principle is used to match the calibration direction that is closest to the normal vector of the tooth direction measuring point, thus obtaining the pre-stroke error corresponding to the tooth direction measuring point. Error compensation is then performed to obtain the compensated tooth direction measurement points. :

[0023] in: The coordinates of the tooth-axis measurement point after compensation; To measure the radius of the sphere; For tooth profile scan data, the generating start point is located at the tangent point of the base circle. Then the tooth profile in the preparation state is formed. tooth profile measurement points The coordinates of the end face are:

[0024] in: For the tooth profile in the preparation state for generation tooth profile measurement points coordinate; For the tooth profile in the preparation state for generation tooth profile measurement points coordinate; For the first time to form a line The relative development angles corresponding to each tooth profile measurement point; The radius of the base circle; For tooth profile measurement points Apply a reverse rotation to restore the tooth profile coordinates to the initial state of the gear reference coordinate system, and apply a theoretical rotation angle based on the measured tooth surface. The tooth profile measurement points in the gear reference coordinate system are obtained. The coordinates of the end face are:

[0025] in: For the gear reference coordinate system tooth profile measurement points coordinate; For the gear reference coordinate system tooth profile measurement points Coordinates; after rotation of The coordinates are directly taken from the axial position during measurement. ; The normal vector at each tooth profile measurement point is calculated based on the data sequence after inverse rotation restoration, and the actual normal vector is obtained by directional correction using the theoretical tooth surface normal vector. Based on the pre-stroke error compensation table, the nearest neighbor principle is used to match the calibration direction that is closest to the normal vector of the tooth profile measuring point, thus obtaining the pre-stroke error corresponding to the tooth profile measuring point. Error compensation is then performed to obtain the compensated tooth profile measurement points. :

[0026] in: The coordinates of the tooth profile measurement points after compensation; To measure the radius of the sphere.

[0027] Further, in step S8, the effective tooth profile point sequence is fitted with a theoretical involute curve, and the tooth profile error of each effective tooth profile point is calculated. The method is as follows: For the first tooth in the left or right tooth profile Calculate the polar diameter of each effective tooth profile point in the gear reference coordinate system. and polar angle :

[0028]

[0029] in: and Representing the Coordinates of one effective tooth profile point; Based on the base circle radius Calculate the first tooth in the left or right tooth profile. The median pressure angle of each effective tooth profile point and involute function values :

[0030]

[0031] in: Represents the first tooth in the left or right tooth profile The polar diameter of each effective tooth profile point The radius of the base circle; Since the involutes of the left and right tooth profiles unfold in opposite directions on the end faces, different methods must be used to fit the theoretical involute origin angles; assuming the effective tooth profile point set of the left tooth profile includes... The effective tooth profile point set of the right tooth profile includes [number] points. Points; theoretical involute origin angles of the left and right tooth profiles. and They are fitted as follows:

[0032] in: and These represent the first tooth in the left and right tooth profiles, respectively. The geometric polar angle of each effective tooth profile point relative to the gear center; and These represent the first tooth in the left and right tooth profiles, respectively. The intermediate pressure angle corresponding to each effective tooth profile point; and These represent the first tooth in the left and right tooth profiles, respectively. The involute function value corresponding to each effective tooth profile point; and These represent the number of valid measuring points in the left and right tooth profiles, respectively. For the first in the left or right tooth profile For each effective tooth profile point, calculate the tangent length to the base circle tangent point:

[0033] in: Indicates the first The length of the tangent from each effective tooth profile point to its base circle tangent point; Indicates the first The effective tooth profile point relative to the gear center's extreme diameter; Indicates the base circle radius; The calculation yields the first tooth in the left and right tooth profiles. The base circle unfolded arc length corresponding to each effective tooth profile point:

[0034] in: and These represent the first tooth in the left and right tooth profiles, respectively. The base circle unfolded arc length corresponding to each effective tooth profile point; and These represent the first tooth in the left and right tooth profiles, respectively. The base circle tangent angle corresponding to each effective tooth profile point; and These are the theoretical involute origin angles for the left and right tooth profiles, respectively. Subtracting the tangent length from the developed arc length of the base circle yields the tooth profile error at that measurement point:

[0035] in: and They represent the first and second teeth of the left and right dental profiles, respectively. Tooth profile error at each effective tooth profile point; and They represent the first and second teeth of the left and right dental profiles, respectively. The tangent length from the effective tooth profile point to the base circle tangent point; and They represent the first and second teeth of the left and right dental profiles, respectively. The arc length of the base circle development corresponding to each effective tooth profile point.

[0036] Furthermore, in step S9, using the base circle unfolded arc length as the independent variable and the tooth profile error as the dependent variable, a least-squares fitting is performed using a quadratic polynomial to obtain the low-order trend terms for the left and right tooth profiles:

[0037] in: and These represent the arc lengths of the left and right tooth profiles, respectively. The low-order trend term obtained from the fitting; This represents the arc length of the base circle unfolded corresponding to the tooth profile point; , , Indicates the quadratic fitting coefficient of the left tooth profile; , , Indicates the quadratic fitting coefficient of the right tooth profile; Subtracting the corresponding low-order trend term from the original tooth profile error yields the high-order tooth profile error:

[0038] in: and These represent the original tooth profile errors of the left and right tooth profiles, respectively. and These represent the higher-order errors of the left and right tooth profiles after removing lower-order trend terms, respectively. The higher-order tooth profile error is the data source for subsequent tooth surface waviness analysis.

[0039] Furthermore, in step S10, the method for obtaining the order spectrum of tooth profile waviness is as follows: S101: Perform equal-arc-length resampling on the higher-order tooth profile error sequence to obtain an equally spaced sequence. , ;in: The sequence length; S102: Perform a discrete Fourier transform on the equally spaced sequence:

[0040] in: For the first Complex coefficients of each Fourier component; The imaginary unit; S103: Calculate the single-sided amplitude spectrum:

[0041] in: For the first The amplitude corresponding to each Fourier component; Complex coefficients The model; S104: Convert the spatial frequency of the amplitude spectrum to the ripple order:

[0042] in: For order; The radius of the base circle; Spatial frequency ,and , The interval is the arc length. The horizontal axis of the amplitude spectrum is converted from spatial frequency to order to obtain the order spectrum; where, The order is represented by the horizontal axis of the order spectrum. The magnitude of this order forms the ordinate of the order spectrum.

[0043] The beneficial effects of this invention are as follows: The in-machine detection method for gear tooth surface waviness of the present invention has the following technical effects.

[0044] (1) A technological leap has been achieved from offline to in-machine inspection of tooth surface waviness. The method of this invention extends waviness measurement to the machining site by integrating a high-precision scanning probe into the machine tool and constructing a complete tooth surface scanning, data compensation and waviness order analysis process, filling the gap in existing in-machine inspection technology that cannot detect tooth surface waviness.

[0045] (2) Significantly improves detection efficiency and data feedback timeliness. The method of this invention performs measurement directly on the machine tool after gear processing, without disassembling the workpiece and transferring it to offline metrology equipment. This eliminates the steps of workpiece disassembly, handling, environmental adaptation, secondary clamping, and realignment in traditional offline measurement processes. At the same time, measurement data is acquired, processed, and analyzed in real time, and the detection results can be fed back to the processing stage in a timely manner, effectively avoiding the accumulation of batch processing errors caused by the lag in detection results.

[0046] (3) Improve measurement accuracy and data reliability. The method of this invention performs on-machine inspection of the tooth surface in the original clamping state of the workpiece. The measurement process is based on the machine tool coordinate system and the machining clamping datum, eliminating the need for datum conversion between the machining equipment and the offline measurement equipment. This effectively reduces additional measurement errors introduced by factors such as secondary clamping, positioning deviation, and datum inconsistency. At the same time, the pre-stroke error is obtained by using a standard ball and a compensation table is constructed to correct the measurement data, further improving data accuracy.

[0047] (4) Achieving accurate evaluation and tracing of tooth surface waviness. The method of this invention obtains the tooth surface waviness order spectrum based on Fourier transform by orderly combining the measurement point data of the left and right tooth profiles, radially truncating the effective tooth profile working segment, calculating the tooth profile error based on involute fitting, eliminating low-order trends and extracting high-order errors. This order spectrum can effectively identify the periodic components in the tooth surface error, providing accurate data basis for gear noise, vibration analysis and machining error tracing.

[0048] (5) It facilitates closed-loop control of the gear machining process. The method of this invention enables the machine tool to not only have machining functions, but also the ability to detect and analyze tooth surface waviness. Based on the obtained tooth surface waviness characteristics and order spectrum results, it can be further used to correct machine tool motion parameters, optimize grinding wheel dressing parameters, or adjust grinding process parameters, providing technical support for realizing efficient and precise closed-loop manufacturing of gears through "machining-detection-analysis-correction". Attached Figure Description

[0049] 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 schematic diagram of the in-machine inspection system for machine tools; Figure 2 This is a flowchart of the in-machine detection method for gear tooth surface waviness according to the present invention; Figure 3 This is the coordinate system for involute gears; Figure 4 Preset the orientation and actual image of the standard ball; Figure 5 This is a schematic diagram of the full tooth profile assembly; Figure 6 A schematic diagram of effective tooth profile truncation; Figure 7 For higher-order feature extraction; (a) tooth profile deviation of the left tooth surface; (b) tooth profile deviation of the right tooth surface; (c) higher-order error of the left tooth surface; (d) higher-order error of the right tooth surface; Figure 8 (a) shows the error curves of the left and right tooth profiles; (b) shows the error curve of the right tooth profile; Figure 9 (a) is the order spectrum of the left and right tooth profiles; (b) is the order spectrum of the right tooth profile; (c) is the order spectrum of the left tooth profile.

[0050] Explanation of reference numerals in the attached figures: 0-Bed; 1-C-axis; 2-Helical cylindrical gear; 3-X-axis; 4-Z-axis; 5-A-axis; 6-Y-axis; 7-Probe. Detailed Implementation

[0051] 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.

[0052] To address the problems of long inspection cycles, delayed data feedback, large secondary clamping errors, and difficulty in serving closed-loop control of the machining process that existing gear tooth surface waviness detection methods mainly rely on offline gear measurement centers or coordinate measuring machines, this embodiment aims to provide an in-machine detection method for gear tooth surface waviness.

[0053] like Figure 1 As shown, this embodiment integrates a high-precision scanning probe into the machine tool. After the gear is machined, it can be scanned and measured on-machine using the machine tool's original coordinate system and clamping state to obtain three-dimensional morphological data of the gear tooth surface without disassembling it from the machine tool. Furthermore, based on the collected measurement data, data compensation processing, tooth profile assembly, measurement point truncation, tooth surface error calculation, higher-order error extraction, and Fourier order analysis are performed sequentially to obtain the waviness characteristics of the gear tooth surface and its order spectrum results.

[0054] Compared with existing offline measurement methods, this embodiment can significantly reduce the detection errors introduced by workpiece disassembly, handling, secondary clamping and reference conversion, and improve the measurement efficiency and data feedback timeliness of gear tooth surface waviness. At the same time, it enables gear processing equipment to perform on-machine detection of tooth surface waviness, providing a reliable data foundation and technical support for subsequent processing parameter correction, tool or grinding wheel dressing parameter optimization, and closed-loop precision manufacturing of gears through "processing-inspection-analysis-correction".

[0055] Specifically, such as Figure 2 As shown, the in-machine detection method for gear tooth surface waviness in this embodiment includes the following steps.

[0056] Step S1: Plan the scanning path of the probe based on the tooth surface equation. The scanning path includes a scanning path along the tooth profile direction and a scanning path along the tooth direction.

[0057] To achieve accurate in-machine scanning measurement of gear tooth surfaces, it is first necessary to establish a mathematical model of the gear tooth surface to be measured and plan the spatial scanning path of the probe accordingly. This embodiment takes a standard involute cylindrical helical gear as the object, starting from the end face tooth profile parametric equation, generating a complete tooth surface through helical motion, and then calculating the coordinates and normal vector of any point on the tooth surface; based on this, probe scanning paths along the tooth profile direction and the tooth direction are designed respectively to ensure that the probe can continuously and stably cover the entire tooth surface to be measured.

[0058] Ignoring the root transition curve and tip trimming, the end face profile of a standard involute cylindrical helical gear consists of a base circle and its two symmetrical involute curves. For example... Figure 3 As shown, the projection point of the gear axis on the end face Establish a Cartesian coordinate system with the origin as the origin, where: The positive axis is vertically upward; The positive axis points horizontally to the right. The base circle radius is... ,point and points These are the starting and ending points of the involute on the left, respectively. and points These are the starting and ending points of the involute on the right side, respectively. and These represent the involute tooth profiles on the left and right sides, respectively. The point is any point on the involute curve on the right. Point is past The point where the involute generating line of a point is tangent to the base circle.

[0059] Taking the right tooth profile as an example, its involute... The parametric equation can be expressed as:

[0060] in: This represents the position vector of a point on the involute curve of the end face; and Represents the x and y coordinates of any point on the involute curve in the end face coordinate system; Represents the base circle radius; The initial phase angle of the involute within the end face depends on the relative position of the tooth groove symmetry line and the coordinate axis; It represents the development angle corresponding to a point on the involute, that is, the angle that the involute rolls along the base circle from the starting point on the base circle; This represents the upper limit of the development angle corresponding to the addendum circle, determined by the addendum circle radius. Decide.

[0061] For helical gears, the involute end face undergoes a helical motion around the gear axis, sweeping to form an involute helical tooth surface. An axial parameter is introduced. (Coordinate along the gear axis, ranging from...) arrive , (where is the tooth width), then the three-dimensional coordinates of any point on the tooth surface are... It can be represented as:

[0062] in: , and These are the coordinates of any point on the tooth surface along the X, Y, and Z axes. , representing the helical rotation angle, indicating the axial position. end face relative to The angle of rotation of the end face around the gear axis; The base circle helix angle is denoted by , and the helix angle of the helical gear on the cylindrical surface of the base circle is denoted by . For axial coordinates, the range of values ​​is: ( , usually take (tooth width) The radius of the base circle; The initial phase angle of the involute within the end face; Let be the development angle corresponding to a point on the involute.

[0063] To facilitate subsequent scan path planning and error compensation, it is necessary to calculate the unit outward normal vector at any point on the tooth surface. According to the theory of surface differential geometry, the normal vector at a point on the tooth surface can be obtained by the cross product of two linearly independent tangent vectors at that point. The two tangent vectors are the tangent vectors along the axial direction ∂... / ∂ and the tangent vector ∂ along the direction of involute expansion / ∂φ.

[0064] First, calculate the partial derivatives to obtain:

[0065]

[0066] in: This is the combined phase angle after introducing spiral motion; The base circle helix angle; For axial coordinates, the range of values ​​is: ( , usually take (tooth width) The radius of the base circle; The initial phase angle of the involute within the end face; Let be the development angle corresponding to a point on the involute.

[0067] The order of taking the cross product of the axial tangent vector and the involute tangent vector is as follows:

[0068] The normal vector is calculated as follows:

[0069] in: This is the combined phase angle after introducing spiral motion; The base circle helix angle; For axial coordinates, the range of values ​​is: ( , usually take (tooth width) The radius of the base circle; The initial phase angle of the involute within the end face; Let be the development angle corresponding to a point on the involute.

[0070] Based on the aforementioned tooth surface mathematical model, the probe scanning path is divided into two mutually orthogonal directions: the tooth profile direction (along the involute development direction) and the tooth direction (along the gear axis). A scanning probe is used on the machine tool. Shaft (workpiece rotation axis) and , , The tooth surface is continuously scanned by the coordinated motion of the linear axes.

[0071] The scan in the tooth profile direction corresponds to the section at the midpoint of the tooth width (take...). Within the tooth groove, the probe moves continuously from the base circle towards the addendum circle along the involute. Specifically, the probe first enters the designated tooth groove radially and positions itself at the midpoint of the tooth width; subsequently, the machine tool... Shaft and machine tool A high-precision interpolation linkage is established between the shaft and the gear, enabling the probe to perform an involute generating motion relative to the gear, i.e., to measure the generated tooth profile. First, the right tooth surface of the tooth space is scanned, starting from the starting point corresponding to the base circle radius and ending at the ending point corresponding to the addendum circle, continuously acquiring the coordinates of the measurement points. After the right tooth surface scanning is completed, the probe and... The shaft is reset to a safe position and scanned on the left tooth surface of the same tooth groove in the same linkage manner, but in the opposite direction.

[0072] The tooth direction corresponds to the direction on the pitch cylinder surface, from the upper end face of the gear ( ) to the lower end face ( Continuous feed along the spiral. The specific execution method is as follows: the probe enters the same tooth groove and is positioned at the pitch circle; the probe and the machine tool... The axis performs high-precision interpolation linkage, moving along the probe along the machine tool. Axial downward movement, The shaft rotates synchronously; for the right tooth surface, from the upper end face ( ) Downward end face ( Continuous scanning is performed; after the right side scan is completed, the probe is reset to the starting position of the tooth pitch circle; for the left tooth surface, scanning is performed from the lower end face ( )Upward end face ( Perform reverse continuous scanning.

[0073] The trajectory planning strategy described above ensures complete tooth surface coverage in both the tooth profile and tooth direction, providing a complete data acquisition foundation for subsequent order spectrum analysis of tooth surface waviness.

[0074] In this embodiment, the parameter of the gear being measured is: number of teeth. Tooth width Tooth tip circle diameter Root circle diameter Base circle diameter Pitch circle diameter Modulus Pressure angle Tooth width Standard sphere radius The radius of the measuring sphere is .

[0075] Based on gear parameters, base circle radius tooth tip circle radius Tooth width The probe scanning path is divided into the tooth profile direction and the tooth direction. The tooth profile direction scanning is performed at the midpoint of the tooth width. At this point, the probe continuously scans from the base circle along the involute towards the addendum circle, and the machine tool... shaft and The shaft linkage realizes the generating motion. First, the right tooth surface is scanned, and after completion, it is reset. Then, the left tooth surface is scanned in the opposite direction of motion.

[0076] The tooth direction scan is at the pitch circle ( ), probe machine tool shaft and Shaft linkage, from the upper end face Downward end face The scanning proceeds continuously along the axial direction. First, the right tooth surface is scanned from top to bottom, and after resetting, the left tooth surface is scanned from bottom to top.

[0077] Step S2: Calibrate the pre-travel error of the probe in different spatial directions and construct a pre-travel error compensation table. The method is as follows: calculate the actual unit vector for each calibration direction. With the corresponding pre-travel error Combining data entries, all These entries together constitute the pre-travel error compensation table.

[0078] During trigger-type scanning measurement, when the probe ball contacts the tooth surface being measured and generates a trigger signal, the center of the probe ball is not exactly located at the theoretical contact point. Instead, due to the hysteresis characteristics of the internal mechanical structure of the probe and the triggering mechanism, the center of the probe ball will cross the contact point by a small distance along the normal direction. This distance is called the pre-travel error (PTE). To achieve high-precision tooth surface measurement, the pre-travel error in each measurement direction must be calibrated, and a compensation table must be established to correct the measurement results in subsequent data processing.

[0079] Specifically, in this embodiment, the steps for constructing the pre-travel error compensation table are as follows.

[0080] S21: Construct the set of coordinate points of the center of the sphere.

[0081] Using a high-precision standard sphere with a known theoretical radius as the calibration reference, let... The theoretical radius of a standard sphere, This is the equivalent radius of the sphere being measured. In this embodiment, .

[0082] Preset spatial vector direction These directions should be distributed as evenly as possible in three-dimensional space, especially covering the normal directions that may appear in subsequent tooth surface measurements. The control probe should sequentially move along each... The direction is triggered for measurement against the standard sphere. The probe moves from a position away from the standard sphere along... The direction approaches the standard ball until the switch is triggered. At this point, the three-dimensional coordinates of the ball's center in the machine tool coordinate system are recorded:

[0083] Finally, the set of coordinates of the center of the sphere can be obtained:

[0084] In this embodiment, The standard ball is calibrated using the 25-point method, such as... Figure 4 As shown, the machine tool controls the probe to approach and trigger the standard sphere in each direction, recording the coordinates of the sphere's center. .

[0085] S22: Construct the objective function to fit the reference sphere.

[0086] To extract the pre-travel error in each direction, a reference sphere must first be fitted from the set of coordinates of the measured sphere's center, thus obtaining the position of the fitted sphere's center and the fitted radius. Let the coordinates of the fitted sphere's center be... The fitting radius is For each measuring point Its distance to the center of the fitted sphere is Based on the least squares method, the objective function is constructed using the criterion of minimizing the sum of squared radial deviations:

[0087] S23: Calculate the pre-travel error.

[0088] For any i Measurement directions Considering the radius of the measuring ball The center of the measuring sphere corresponding to this direction should be located at a radius of [missing information] when there is no pre-travel error. On the sphere. The difference between the actual measured distance and the theoretical distance is the pre-travel error in that direction. for:

[0089] in: To measure the distance from the center of the sphere to the center of the fitted sphere; To measure the radius of the sphere; The theoretical radius of a standard sphere; Indicates the first Measurement directions The corresponding pre-travel error.

[0090] S24: Construct a pre-travel error compensation table.

[0091] In order to quickly match the error value according to the actual contact direction in subsequent tooth surface measurements, the pre-stroke error needs to be included. It is stored in association with its corresponding actual contact direction. The actual contact direction is defined as a unit vector from the center of the fitted sphere to the center of the measured sphere, i.e.:

[0092] in: This indicates the actual approximation direction when the measuring ball contacts the standard ball during the calibration process (which is also the direction corresponding to the pre-stroke error). This represents the vector pointing from the center of the fitted sphere to the center of the measured sphere; This represents the distance from the center of the measured sphere to the center of the fitted sphere.

[0093] The actual unit vector in each calibration direction With the corresponding pre-travel error The data is compiled into entries to form a pre-stroke error compensation table, and some of the pre-stroke error compensation table data is shown in Table 1. During subsequent tooth surface measurement data compensation processing, for any measured point on the tooth surface, the corresponding pre-stroke error can be matched in the compensation table based on the actual contact normal vector of that point using the nearest neighbor principle, thereby achieving compensation for the probe's pre-stroke error.

[0094] Table 1 Pre-stroke Error Table

[0095] Step S3: Construct a measurement coordinate system based on the workpiece mounting datum and determine the gear datum origin.

[0096] To unify the reference system for tooth surface measurement data, a measurement coordinate system based on the gear's own installation datum needs to be established within the machine tool coordinate system. In this embodiment, the workpiece stage datum origin is first determined by sampling the outer cylindrical surface and end face of the machine tool workpiece stage; then, after installing the gear, sampling is repeated to obtain the gear datum origin. All subsequent measurement points are converted to this gear datum coordinate system.

[0097] Specifically, in this embodiment, the method steps for constructing a measurement coordinate system based on the workpiece mounting reference are as follows.

[0098] S31: Obtain the origin of the workpiece stage reference coordinate system.

[0099] When the gear is not installed, the outer cylindrical surface of the workpiece stage is sampled. Each measuring point Data collection from the end face Each measuring point The radius of the measuring sphere is In this embodiment, , , Using the coordinates of the measuring points on the outer cylindrical surface The center of the fitted cross section is the coordinate. The radius of the fitted circle is The standard equation of the cross-section circle can be obtained as follows:

[0100] Expanding and rearranging it into linear form, we get:

[0101] in: Then, by least squares, we obtain... .

[0102] At the same time, the coordinates of the end face measuring points Take the mean and subtract the radius The axial height of the upper surface of the workpiece stage is obtained. :

[0103] Thus, the origin of the workpiece stage reference coordinate system is obtained. .

[0104] S32: Obtain the coordinates of the gear reference origin.

[0105] The gear is mounted on the workpiece stage, and its outer cylindrical surface is sampled. Each measuring point Collect samples from its upper surface. Each measuring point Following the same steps as above, the coordinates of the gear's reference origin can be obtained as follows:

[0106] in: , and These represent the X-axis, Y-axis, and Z-axis coordinates of the gear's reference origin, respectively. The reference origin of the gear serves as the unified measurement benchmark for subsequent tooth surface scanning and data processing, thereby eliminating installation eccentricity and tilting errors and ensuring the consistency of measurement data. All subsequent tooth surface scanning data is converted to the gear reference coordinate system. In this embodiment, , .

[0107] Step S4: In-machine acquisition of tooth surface scanning data. A high-precision scanning probe is integrated into the machine tool. The probe is controlled to perform in-machine scanning of the gear tooth surface according to the scanning path planned in step S1, acquiring three-dimensional topographic data of the tooth surface, and simultaneously acquiring the corresponding C-axis rotation angle of the machine tool.

[0108] During the scanning process, the probe continuously scans the gear tooth surface along a preset tooth profile or tooth direction trajectory, simultaneously acquiring three-dimensional coordinate data of the tooth surface in the measurement coordinate system and the corresponding machine tool data. The rotation angle of the axis (workpiece rotation axis) is recorded and temporarily stored in the machine tool's built-in data storage unit. Specifically, it is assumed that a single continuous scan will collect a total of [number] data. There are [number] measurement points, numbered sequentially according to the acquisition time sequence. For the first For each measurement point, record its coordinate vector in the measurement coordinate system. And the timing bed triggered at that point Real-time rotation angle of the axis The data from all measurement points are organized sequentially into the following ordered dataset:

[0109] in, For the first The original coordinates of each measuring point in the gear reference coordinate system; When collecting data at this point, the machine bed The rotation angle of the axis relative to the zero position of the machine tool; the integer in parentheses is the measurement point number, which is convenient for subsequent data verification.

[0110] In actual high-density scanning conditions, the number of measurement points for scanning the entire tooth surface is large. If all scanning data is temporarily stored in the machine tool's internal data buffer, it is very easy to exceed its rated storage capacity, leading to buffer overflow and data loss. To completely avoid this problem, this embodiment adopts a real-time writing strategy for single-tooth-surface scanning data. That is, after the probe collects data for each tooth surface, it immediately writes all the sequence numbers, coordinates, and... The axis rotation angle is written to a storage file instead of accumulating large amounts of data in the machine tool's internal data buffer. Simultaneously, the machine tool's internal data buffer strictly adheres to the FIFO (First In First Out) rule, meaning that data written first is output to the storage file first, ensuring that the data order written to the file strictly matches the actual acquisition sequence and avoiding data misalignment or out-of-order processing. This real-time writing strategy guarantees the integrity of the measurement data while also meeting the continuity requirements of subsequent steps for large-scale tooth surface point cloud data.

[0111] Step S5: Restore tooth surface data and compensate for errors. Perform inverse coordinate rotation transformation on the original measuring points of the three-dimensional morphology data of the tooth surface collected in Step S4 to restore the coordinate data in the actual tooth surface state; the original measuring points include tooth direction measuring points and tooth profile measuring points. According to the pre-stroke error compensation table constructed in Step S2, perform probe pre-stroke error compensation and measuring ball radius compensation on the coordinates of each tooth direction measuring point and tooth profile measuring point to obtain the compensated tooth direction measuring points and tooth profile measuring points.

[0112] After acquiring the tooth surface scanning data, coordinate transformation and error compensation are required for the original measurement points to restore the true coordinates of the tooth surface contact points. In this step, all measurement data have been converted to the gear reference coordinate system established in step S3. Therefore, subsequent transformations only correct for machine tool C-axis rotation and probe errors, without the need for further coordinate system translation or rotation. The following restoration and compensation strategies are adopted for the different acquisition methods of tooth direction scanning data and tooth profile scanning data.

[0113] (1) Tooth direction scan data.

[0114] During tooth-axis scanning, the probe feeds along the gear axis (machine tool Z-axis) while the machine tool C-axis rotates simultaneously. Therefore, the coordinates of the tooth-axis measurement points include coordinate offsets caused by the rotation of the machine tool C-axis. To restore the true tooth surface coordinates, an inverse rotation transformation needs to be applied to the coordinates of each tooth-axis measurement point to eliminate the influence of the machine tool C-axis rotation angle.

[0115] For tooth-axis scan data, the coordinate data of the tooth-axis measurement points are restored to the coordinate data of the actual tooth surface state through inverse rotation transformation. Let the first... The coordinates of each tooth-axis measuring point are: When collecting data at this tooth direction measuring point, the rotation angle of the C-axis of the machine tool relative to the zero position of the machine tool is: Then the coordinates of the restored tooth direction measurement point Calculate using the following formula:

[0116] in: The first tooth direction data The coordinate data of each tooth-direction measuring point are around Axis rotation The inverse rotation matrix of the angle; The first tooth direction data Coordinate data of each tooth-direction measuring point; The first tooth direction data The coordinates of each tooth-axis measuring point are obtained through an inverse rotation transformation. This transformation restores all tooth-axis measuring points to their true tooth surface state, eliminating coordinate offsets caused by the machine tool's C-axis linkage.

[0117] Based on the data sequence after inverse rotation, the normal vector at each tooth-axis measuring point is calculated sequentially. To further improve accuracy, the theoretical tooth surface normal vector is used for correction, thus obtaining the actual normal vector. Subsequently, based on the pre-stroke error compensation table established in the second step, the nearest neighbor principle is used to match the calibration direction that is closest to the normal vector of the tooth direction measuring point, thus obtaining the pre-stroke error corresponding to the tooth direction measuring point. Combined with the sphere radius Error compensation is performed on the restored tooth direction measurement points to obtain the compensated tooth direction measurement points. :

[0118] in: The coordinates of the tooth-axis measurement point after compensation; The radius of the measuring ball is determined. This compensation eliminates the effects of radius error and pre-stroke error.

[0119] (2) Tooth profile scan data.

[0120] During tooth profile scanning, the machine tool Shafts and machine tools The axis performs the involute tooth profile generating measurement motion, assuming the generating line in the tooth profile scan data is the first... The ordinate of each tooth profile measuring point is The base circle radius is and satisfy The starting point of the formation is located at the tangent point of the base circle. Then the tooth profile in the preparation state is formed. tooth profile measurement points The coordinates of the end face are:

[0121] in: For the tooth profile in the preparation state for generation tooth profile measurement points coordinate; For the tooth profile in the preparation state for generation tooth profile measurement points coordinate; For the first time to form a line The relative development angles corresponding to each tooth profile measuring point; Let be the radius of the base circle.

[0122] For tooth profile measurement points Apply a reverse rotation to restore the tooth profile coordinates to the initial state of the gear reference coordinate system, and apply a theoretical rotation angle based on the measured tooth surface. (For the right tooth surface, the theoretical rotation angle is positive; for the left tooth surface, the theoretical rotation angle is negative), thus restoring the tooth profile measurement points in the gear reference coordinate system. The coordinates of the end face are:

[0123] in: For the gear reference coordinate system tooth profile measurement points coordinate; For the gear reference coordinate system tooth profile measurement points Coordinates; after rotation of The coordinates are directly taken from the axial position during measurement. .

[0124] The normal vector at each tooth profile measuring point is calculated based on the data sequence after inverse rotation restoration. To further improve accuracy, the direction is corrected using the theoretical tooth surface normal vector to obtain the actual normal vector. Subsequently, based on the pre-stroke error compensation table established in step S2, the nearest neighbor principle is used to match the actual normal vector of the tooth profile measuring point. The closest calibration direction is used to obtain the pre-travel error corresponding to the tooth profile measuring point. Error compensation is then performed to obtain the compensated tooth profile measurement points. :

[0125] in: The coordinates of the tooth profile measurement points after compensation; To measure the radius of the sphere.

[0126] Through the above transformations and compensations, the effects of radius error and pre-stroke error are eliminated from the tooth profile scanning data.

[0127] Step S6: Orderly combine the left and right tooth profile measurement point data. Based on the tooth profile measurement points obtained in Step S5, the left and right tooth profile measurement points of each tooth are obtained. The left and right tooth profile measurement points are then connected and combined end to end according to the tooth surface order and tooth number order of each tooth to form a complete end face tooth profile point sequence.

[0128] Specifically, in completing step S5, the tooth profile measuring points... After solving the problem, a set of three-dimensional coordinate points has been obtained for the left and right tooth profiles of each tooth, i.e., the left and right tooth profile measurement points for each tooth. To facilitate subsequent unified truncation and error extraction, the left and right tooth profile measurement points of all teeth need to be concatenated and combined end-to-end according to the tooth surface order and tooth number order to form a complete end face tooth profile point sequence. Let the number of teeth of the gear being measured be... For the first One tooth The point set of its left tooth profile measurement points is denoted as The point set of its right tooth profile measurement points is denoted as ,in This represents the point number within the tooth profile. Following a left-to-right order, the left and right tooth profile measurement points of each tooth are sequentially connected in series. Then, the point sets of each tooth are joined end-to-end according to tooth number order to obtain the complete end-face tooth profile point sequence after assembly.

[0129] in: Indicates the first The point set of the left tooth profile measurement points of each tooth; Indicates the first The point set of the right tooth profile measurement points of each tooth. For example... Figure 5 As shown, the left and right profiles of all 26 teeth were effectively spliced ​​together, providing a data foundation for subsequent single-tooth error extraction and Fourier order spectrum calculation.

[0130] The above-mentioned assembly method preserves the original measurement order of each tooth and the relative positional relationship of the left and right tooth surfaces, forming a unified data organization form, which provides technical support for subsequent tooth profile truncation and high-order error extraction.

[0131] Step S7: Radial truncation of the effective tooth profile working segment. The complete end face tooth profile point sequence obtained by assembling in Step S6 is radially truncated according to the radial evaluation boundary of the effective tooth profile; invalid measuring points on non-working tooth surfaces such as the tooth root transition area and tooth tip trimming area are removed, and the measuring points of the effective involute working segment are retained to obtain the effective tooth profile point sequence on the involute tooth profile.

[0132] According to the definition of the tooth profile direction scanning path in step S1, the probe starts from the base circle radius. Start scanning, up to the tooth tip circle radius The sequence ends here, therefore the original complete end face tooth profile point sequence after assembly is complete. It covers the complete involute segment from the base circle to the addendum circle. In actual waviness evaluation, it is usually necessary to remove invalid measurement points on non-working tooth surfaces such as the root transition area and the addendum trimming area in order to retain the pure involute working segment. Assume the geometric parameters of the gear being measured include the addendum circle radius. Root circle radius and base circle radius Define the root shrinkage ratio coefficient. and tooth tip shrinkage ratio coefficient In this embodiment, the root shrinkage ratio is taken as... The tooth tip shrinkage ratio is taken as Tooth tip circle diameter Root circle diameter Base circle diameter The radial evaluation boundary of the effective tooth profile is determined by the following formula: Radial starting position (tooth root side):

[0133] Radial termination position (tooth tip side):

[0134] in: For full tooth height. When hour, That is, retain the starting point of the base circle; when hour, That is, the position of the tooth tip circle is retained.

[0135] For the assembled complete end face tooth profile sequence For each measuring point, firstly, based on its end face projection coordinates... Calculate the polar diameter Only retain the polar radius to satisfy The measuring points are selected, and the remaining points falling in the tooth root transition zone or tooth tip trimming zone are eliminated. After truncation, the effective tooth profile point sequence on the involute tooth profile is obtained. The sequence retains the original The order of all valid tooth profile points. (By...) Figure 6 As shown, the truncated tooth profile data is mainly located within the involute working region. Invalid measurement points on these non-working tooth surfaces are effectively eliminated, providing reliable and valid tooth surface data for subsequent tooth profile error extraction and Fourier order spectrum analysis. The above truncation operation eliminates interfering data outside the involute working region, providing a clean data foundation for subsequent extraction of higher-order waviness errors.

[0136] Step S8: Calculation of tooth profile error based on involute fitting. Based on the effective tooth profile point sequence truncated in Step S7. Theoretical involute fitting is performed on the left and right tooth profiles of each tooth respectively, and the tooth profile error of each effective tooth profile point in the effective tooth profile point sequence is calculated.

[0137] In this embodiment, the effective tooth profile point sequence is fitted with a theoretical involute curve, and the tooth profile error of each effective tooth profile point is calculated. The method is as follows.

[0138] For the first tooth in the left or right tooth profile Calculate the polar diameter of each effective tooth profile point in the gear reference coordinate system. and polar angle :

[0139]

[0140] in: and Representing the Coordinates of one effective tooth profile point; Based on the base circle radius Calculate the first tooth in the left or right tooth profile. The median pressure angle of each effective tooth profile point and involute function values :

[0141]

[0142] in: Represents the first tooth in the left or right tooth profile The polar diameter of each effective tooth profile point Let be the radius of the base circle.

[0143] Specifically, based on the base circle radius For the first tooth in the left tooth profile There are 1 effective tooth profile point, whose polar radius in the gear reference coordinate system is 1 / 2 * 1 / 3 ... The polar angle is Based on the base circle radius The midpoint of the pressure angle at that point Involute function value .

[0144] Similarly, for the first tooth in the right tooth profile... There are 1,000 effective tooth profile points:

[0145] in: and Represents the right tooth profile Coordinates of one effective tooth profile point; Represents the right tooth profile The extreme diameter of each effective tooth profile point; Represents the right tooth profile The polar angle of each effective tooth profile point; Represents the right tooth profile The intermediate value of the pressure angle at each effective tooth profile point; Represents the right tooth profile The involute function value corresponding to each effective tooth profile point.

[0146] Since the involutes of the left and right tooth profiles unfold in opposite directions on the end faces, different methods are needed to fit the theoretical involute origin angle. Let the effective tooth profile point set of the left tooth profile include... The effective tooth profile point set of the right tooth profile includes [number] points. Points. Theoretical involute origin angles of the left and right tooth profiles. and Fit them respectively according to the following formulas:

[0147] in: and These represent the first tooth in the left and right tooth profiles, respectively. The geometric polar angle of each effective tooth profile point relative to the gear center; and These represent the first tooth in the left and right tooth profiles, respectively. The intermediate pressure angle corresponding to each effective tooth profile point; and These represent the first tooth in the left and right tooth profiles, respectively. The involute function value corresponding to each effective tooth profile point; and These represent the number of valid measuring points in the left and right tooth profiles, respectively.

[0148] For the first in the left or right tooth profile For each effective tooth profile point, calculate the tangent length to the base circle tangent point:

[0149] in: Indicates the first The length of the tangent from each effective tooth profile point to its base circle tangent point; Indicates the first The effective tooth profile point relative to the gear center's extreme diameter; Indicates the radius of the base circle.

[0150] Calculate the base circle tangent angle based on the left and right tooth profiles respectively, i.e.:

[0151] in: and These represent the first tooth in the left and right tooth profiles, respectively. The base circle tangent angle corresponding to each effective tooth profile point.

[0152] This leads to the determination of the first tooth profile in the left and right tooth profiles. The base circle development arc length corresponding to each effective tooth profile point is, i.e.:

[0153] in: and These represent the first tooth in the left and right tooth profiles, respectively. The base circle unfolded arc length corresponding to each effective tooth profile point; and These represent the first tooth in the left and right tooth profiles, respectively. The base circle tangent angle corresponding to each effective tooth profile point; and These are the theoretical involute origin angles for the left and right tooth profiles, respectively.

[0154] Subsequently, the tangent length from the effective tooth profile point to the base circle tangent point is subtracted from the corresponding base circle unfolded arc length to obtain the tooth profile error at that effective tooth profile point:

[0155] in, and They represent the first and second teeth of the left and right dental profiles, respectively. Tooth profile error at each effective tooth profile point; and They represent the first and second teeth of the left and right dental profiles, respectively. The tangent length from the effective tooth profile point to the base circle tangent point; and They represent the first and second teeth of the left and right dental profiles, respectively. The arc length of the base circle development corresponding to each effective tooth profile point.

[0156] Step S9: Extract and remove high-order errors that have eliminated low-order trends. From the tooth profile errors of each effective tooth profile point obtained in Step S8, low-order trend terms are removed, and high-order tooth profile errors are extracted to obtain a high-order tooth profile error sequence. These high-order tooth profile errors serve as the data source for subsequent tooth surface waviness analysis, such as... Figure 7 As shown.

[0157] After calculating the original tooth profile error, low-order trend terms need to be removed to obtain the high-order waviness error. Using the base circle unfolded arc length as the independent variable and the tooth profile deviation as the dependent variable, a least-squares fitting with a quadratic polynomial is performed to obtain the low-order trends of the left and right tooth profiles:

[0158] in: and These represent the arc lengths of the left and right tooth profiles, respectively. The low-order trend term obtained from the fitting; This represents the arc length of the base circle unfolded corresponding to the tooth profile point; , , Indicates the quadratic fitting coefficient of the left tooth profile; , , This represents the quadratic fitting coefficient of the right tooth profile.

[0159] Subsequently, the corresponding low-order trend term is subtracted from the original tooth profile error to obtain the high-order tooth profile error:

[0160] in: and These represent the original tooth profile errors of the left and right tooth profiles, respectively. and These represent the higher-order errors of the left and right tooth profiles after removing lower-order trend terms, respectively. These higher-order errors primarily retain the local fluctuation components of the tooth profile errors and can be used as input data for subsequent Fourier order spectral analysis.

[0161] Based on the tooth sequence, tooth pitch angle, left or right tooth profile flank, and the position of each effective tooth profile point on the working tooth surface, the obtained high-order features are mapped onto the gear's angular domain around its circumference, forming a distribution of high-order feature angular domains within the gear's circumference. For example... Figure 8 As shown.

[0162] Step S10: Order spectrum analysis based on Fourier transform. Perform Fourier transform on the high-order tooth profile error sequence obtained in step S9 to obtain the order spectrum of tooth profile waviness, thus completing the tooth surface waviness analysis based on in-machine inspection.

[0163] In this embodiment, the method for obtaining the order spectrum of tooth profile waviness is as follows.

[0164] S101: Perform equal-arc-length resampling on the higher-order tooth profile error sequence to obtain an equally spaced sequence. , ;in: The sequence length is given.

[0165] S102: Perform a discrete Fourier transform on the equally spaced sequence:

[0166] in: For the first Complex coefficients of each Fourier component; The imaginary unit; S103: Calculate the single-sided amplitude spectrum:

[0167] in: For the first The amplitude corresponding to each Fourier component; Complex coefficients The model; S104: Convert the spatial frequency of the amplitude spectrum to the ripple order:

[0168] in: For order; The radius of the base circle; Spatial frequency ,and , The interval is the arc length.

[0169] The horizontal axis of the amplitude spectrum is converted from spatial frequency to order to obtain the order. The order is represented by the horizontal axis of the order spectrum. The magnitude of this order forms the ordinate of the order spectrum, such as... Figure 9 As shown.

[0170] By identifying the amplitude corresponding to each order in the order spectrum, the main fluctuation components and energy distribution of gear tooth surface waviness can be determined, thereby assessing the vibration characteristics and noise level that may be induced during gear meshing. Based on the order spectrum analysis results, it can be quantitatively determined whether the waviness meets the design requirements and provide data for the correction of subsequent machining parameters. The above analysis process provides fundamental support for the closed-loop precision manufacturing of gears, encompassing "machining-inspection-analysis-correction".

[0171] 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 in-machine detection of gear tooth surface waviness, characterized in that: Includes the following steps: Step S1: Plan the scanning path of the probe according to the tooth surface equation. The scanning path includes a scanning path along the tooth profile direction and a scanning path along the tooth direction. Step S2: Calibrate the pre-travel error of the probe in different spatial directions and construct a pre-travel error compensation table. The method is as follows: calculate the actual unit vector for each calibration direction. With the corresponding pre-travel error Combining data entries, all These entries together constitute the pre-trip error compensation table; Step S3: Construct a measurement coordinate system based on the workpiece mounting datum and determine the gear datum origin; Step S4: Integrate a high-precision scanning probe into the machine tool, control the probe to perform on-machine scanning of the gear tooth surface according to the scanning path planned in step S1, collect the three-dimensional topographic data of the tooth surface, and simultaneously collect the corresponding C-axis rotation angle of the machine tool. Step S5: Perform inverse coordinate rotation transformation on the original measurement points of the three-dimensional morphology data of the tooth surface collected in step S4 to restore the coordinate data in the actual tooth surface state; the original measurement points include tooth direction measurement points and tooth profile measurement points. According to the pre-stroke error compensation table constructed in step S2, perform probe pre-stroke error compensation and probe radius compensation on each of the tooth direction measurement points and tooth profile measurement points to obtain the compensated tooth direction measurement points and tooth profile measurement points. Step S6: Based on the tooth profile measuring points, obtain the left tooth profile measuring points and the right tooth profile measuring points of each tooth; connect the left tooth profile measuring points and the right tooth profile measuring points in series according to the tooth surface order and tooth number order of each tooth to form a complete end face tooth profile point sequence. Step S7: The complete end face tooth profile point sequence obtained by step S6 is radially truncated according to the radial evaluation boundary of the effective tooth profile; invalid measurement points in the tooth root transition area and tooth tip trimming area are removed, and the measurement points of the effective involute working segment are retained to obtain the effective tooth profile point sequence on the involute tooth profile. Step S8: Based on the effective tooth profile point sequence truncated in step S7, perform theoretical involute fitting on the left and right tooth profiles of each tooth respectively, and calculate the tooth profile error of each effective tooth profile point in the effective tooth profile point sequence. Step S9: Remove low-order trend terms from the tooth profile errors of each effective tooth profile point obtained in Step S8, extract high-order tooth profile errors and construct a high-order tooth profile error sequence. The high-order tooth profile errors are the data source for subsequent tooth surface waviness analysis. Step S10: Perform Fourier transform on the high-order tooth profile error sequence obtained in step S9 to obtain the order spectrum of tooth profile waviness, and complete the tooth surface waviness analysis based on in-machine detection. In step S7, the radial evaluation boundary of the effective tooth profile is determined by the following formula: Radial starting position: ; Radial termination position: ; in: For the full height of the teeth; The radius of the base circle; The radius of the tooth tip circle; The radius of the tooth root circle; This is the root shrinkage ratio coefficient; This is the tooth tip shrinkage ratio coefficient; and: ; For each measuring point in the assembled complete end face tooth profile sequence, based on its end face projection coordinates Calculate the polar diameter Only retain the polar radius to satisfy The measuring points.

2. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S1, the tooth surface equation is the mathematical model of the tooth surface of a standard involute cylindrical helical gear, and the three-dimensional coordinates of any point on the tooth surface are... Represented as: in: , and These are the coordinates of any point on the tooth surface along the X, Y, and Z axes. , representing the helical rotation angle, indicating the axial position. end face relative to The angle of rotation of the end face around the gear axis; The base circle helix angle is denoted by , and the helix angle of the helical gear on the cylindrical surface of the base circle is denoted by . For axial coordinates; The radius of the base circle; The initial phase angle of the involute within the end face; Let be the development angle corresponding to a point on the involute.

3. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S1, the scanning path in the tooth profile direction is as follows: within the cross section at the midpoint of the tooth width, the probe moves continuously from the starting point of the base circle along the involute towards the addendum circle. The machine tool C-axis and the machine tool Y-axis establish interpolation linkage, so that the probe moves involute relative to the gear. First, the right tooth surface of the tooth groove is scanned from the starting point corresponding to the base circle radius to the ending point corresponding to the addendum circle. Then, the left tooth surface of the same tooth groove is scanned in the opposite direction of movement. The scanning path in the tooth direction is as follows: on the indexing cylindrical surface, the gear is continuously fed along a spiral line from the upper end face to the lower end face. The probe and the machine tool C-axis are interpolated in linkage. As the probe moves along the machine tool Z-axis, the C-axis rotates synchronously. First, the right tooth surface is continuously scanned from the upper end face to the lower end face, and then the left tooth surface is continuously scanned in reverse from the lower end face to the upper end face.

4. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S2, the method for constructing the pre-travel error compensation table is as follows: S21: Based on the known theoretical radius Using a high-precision standard sphere as the calibration reference, a preset... spatial vector direction The probe is controlled to sequentially trigger measurements on the standard sphere in each direction, and the three-dimensional coordinates of the sphere's center in the machine tool coordinate system are recorded. The set of coordinates of the center of the sphere is obtained: S22: Fit the reference sphere using the least squares method from the set of coordinate points of the measured sphere's center to obtain the fitted sphere's center. and fitted radius The objective function is: S23: For the first Calculate the pre-travel error in each measurement direction: in: To measure the distance from the center of the sphere to the center of the fitted sphere; To measure the radius of the sphere; The theoretical radius of a standard sphere; Indicates the first Measurement directions The corresponding pre-travel error; S24: Combine the actual unit vector of each calibration direction with the corresponding pre-travel error. The entries are combined to form a pre-travel error compensation table; the actual unit vector is represented as: in: This indicates the actual approximation direction when the measuring ball contacts the standard ball during the calibration process; This represents the vector pointing from the center of the fitted sphere to the center of the measured sphere; This represents the distance from the center of the measured sphere to the center of the fitted sphere.

5. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S3, the method for constructing a measurement coordinate system based on the workpiece mounting datum is as follows: S31: Without the gear installed, collect several measuring points on the outer cylindrical surface of the machine tool worktable and fit the center of the cross-section. Several measuring points were collected on the upper surface of the workpiece platform, and the average axial coordinate was taken and the radius of the measuring ball was subtracted. The axial height of the upper surface of the workpiece stage is obtained. Obtain the origin of the workpiece stage reference coordinate system. ; S32: Mount the gear on the workpiece stage, collect several measuring points on its outer cylindrical surface and upper end face, and calculate the coordinates of the gear's reference origin using the same method as in step S31. All subsequent tooth surface scanning data are converted to this gear reference coordinate system; among which: , and These represent the X-axis, Y-axis, and Z-axis coordinates of the gear's reference origin, respectively.

6. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S4, a real-time writing strategy for single tooth surface scanning data is adopted. That is, after the probe collects data for a tooth surface, it immediately writes the sequence number, coordinates and C-axis rotation angle of all measuring points on that tooth surface into the storage file. The data buffer inside the machine tool follows the FIFO rule to ensure that the order of data written into the storage file is strictly consistent with the actual acquisition sequence.

7. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S5, for the tooth-direction scan data, the coordinate data of the tooth-direction measurement points are restored to the coordinate data of the actual tooth surface state through inverse rotation transformation: in: The first tooth direction data The coordinate data of each tooth-direction measuring point are around Axis rotation The inverse rotation matrix of the angle; The first tooth direction data Coordinate data of each tooth-direction measuring point; The first tooth direction data The coordinates of each tooth-axis measuring point after inverse rotation transformation; The normal vector at each tooth-axis measurement point is calculated based on the data sequence after inverse rotation transformation, and the actual normal vector is obtained by correction using the theoretical tooth surface normal vector. Based on the pre-stroke error compensation table, the nearest neighbor principle is used to match the calibration direction that is closest to the normal vector of the tooth direction measuring point, thus obtaining the pre-stroke error corresponding to the tooth direction measuring point. Error compensation is then performed to obtain the compensated tooth direction measurement points. : in: The coordinates of the tooth-axis measurement point after compensation; To measure the radius of the sphere; For tooth profile scan data, the generating start point is located at the tangent point of the base circle. Then the tooth profile in the preparation state is formed. tooth profile measurement points The coordinates of the end face are: in: For the tooth profile in the preparation state for generation tooth profile measurement points coordinate; For the tooth profile in the preparation state for generation tooth profile measurement points coordinate; For the first time to form a line The relative development angles corresponding to each tooth profile measuring point; The radius of the base circle; For tooth profile measurement points Apply a reverse rotation to restore the tooth profile coordinates to the initial state of the gear reference coordinate system, and apply a theoretical rotation angle based on the measured tooth surface. The tooth profile measurement points in the gear reference coordinate system are obtained. The coordinates of the end face are: in: For the gear reference coordinate system tooth profile measurement points coordinate; For the gear reference coordinate system tooth profile measurement points Coordinates; after rotation of The coordinates are directly taken from the axial position during measurement. ; The normal vector at each tooth profile measurement point is calculated based on the data sequence after inverse rotation restoration, and the actual normal vector is obtained by directional correction using the theoretical tooth surface normal vector. Based on the pre-stroke error compensation table, the nearest neighbor principle is used to match the actual normal vector of the tooth profile measuring point. The closest calibration direction is used to obtain the pre-travel error corresponding to the tooth profile measuring point. Error compensation is then performed to obtain the compensated tooth profile measurement points. : in: The coordinates of the tooth profile measurement points after compensation; To measure the radius of the sphere.

8. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S8, the effective tooth profile point sequence is fitted with a theoretical involute curve, and the tooth profile error of each effective tooth profile point is calculated. The method is as follows: For the first tooth in the left or right tooth profile Calculate the polar diameter of each effective tooth profile point in the gear reference coordinate system. and polar angle : in: and Representing the Coordinates of the effective tooth profile points; Based on the base circle radius Calculate the first tooth in the left or right tooth profile. The median pressure angle of each effective tooth profile point and involute function values : in: Represents the first tooth in the left or right tooth profile The polar diameter of each effective tooth profile point The radius of the base circle; Since the involutes of the left and right tooth profiles unfold in opposite directions on the end faces, different methods must be used to fit the theoretical involute origin angles; assuming the effective tooth profile point set of the left tooth profile includes... The effective tooth profile point set of the right tooth profile includes [number] points. Points; theoretical involute origin angles of the left and right tooth profiles. and They are fitted as follows: in: and These represent the first tooth in the left and right tooth profiles, respectively. The geometric polar angle of each effective tooth profile point relative to the gear center; and These represent the first tooth in the left and right tooth profiles, respectively. The intermediate pressure angle corresponding to each effective tooth profile point; and These represent the first tooth in the left and right tooth profiles, respectively. The involute function value corresponding to each effective tooth profile point; and These represent the number of valid measuring points in the left and right tooth profiles, respectively. For the first in the left or right tooth profile For each effective tooth profile point, calculate the tangent length to the base circle tangent point: in: Indicates the first The length of the tangent from each effective tooth profile point to its base circle tangent point; Indicates the first The effective tooth profile point relative to the gear center's extreme diameter; Indicates the base circle radius; The calculation yields the first tooth in the left and right tooth profiles. The base circle unfolded arc length corresponding to each effective tooth profile point: in: and These represent the first tooth in the left and right tooth profiles, respectively. The base circle unfolded arc length corresponding to each effective tooth profile point; and These represent the first tooth in the left and right tooth profiles, respectively. The base circle tangent angle corresponding to each effective tooth profile point; and These are the theoretical involute origin angles for the left and right tooth profiles, respectively. Subtracting the tangent length from the base circle unfolded arc length yields the tooth profile error at the corresponding effective tooth profile point: in: and They represent the first and second teeth of the left and right dental profiles, respectively. Tooth profile error at each effective tooth profile point; and They represent the first and second teeth of the left and right dental profiles, respectively. The tangent length from the effective tooth profile point to the base circle tangent point; and They represent the first and second teeth of the left and right dental profiles, respectively. The arc length of the base circle development corresponding to each effective tooth profile point.

9. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S9, using the base circle unfolded arc length as the independent variable and the tooth profile error as the dependent variable, a least-squares fitting is performed using a quadratic polynomial to obtain the low-order trend terms for the left and right tooth profiles: in: and These represent the arc lengths of the left and right tooth profiles, respectively. The low-order trend term obtained from the fitting; This represents the arc length of the base circle unfolded corresponding to the tooth profile point; , , Indicates the quadratic fitting coefficient of the left tooth profile; , , Indicates the quadratic fitting coefficient of the right tooth profile; Subtracting the corresponding low-order trend term from the original tooth profile error yields the high-order tooth profile error: in: and These represent the original tooth profile errors of the left and right tooth profiles, respectively. and These represent the higher-order errors of the left and right tooth profiles after removing lower-order trend terms, respectively. The higher-order tooth profile error is the data source for subsequent tooth surface waviness analysis.

10. The method for in-machine detection of gear tooth surface waviness according to claim 1, characterized in that: In step S10, the method for obtaining the order spectrum of tooth profile waviness is as follows: S101: Perform equal-arc-length resampling on the higher-order tooth profile error sequence to obtain an equally spaced sequence. , ;in: The sequence length; S102: Perform a discrete Fourier transform on the equally spaced sequence: in: For the first Complex coefficients of each Fourier component; The imaginary unit; S103: Calculate the single-sided amplitude spectrum: in: For the first The amplitude corresponding to each Fourier component; Complex coefficients The model; S104: Convert the spatial frequency of the amplitude spectrum to the ripple order: in: For order; The radius of the base circle; Spatial frequency ,and , The interval is the arc length. The horizontal axis of the amplitude spectrum is converted from spatial frequency to order to obtain the order spectrum; where, The order is represented by the horizontal axis of the order spectrum. The magnitude of this order forms the ordinate of the order spectrum.

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