Arc tooth full parameter measurement method under error driving

Abstract

The present application relates to the technical field of measurement, in particular to a kind of full parameter measurement method of arc end tooth under error driving, to solve the problem that traditional projection method cannot obtain correct addendum position, three-coordinate scanning needs to rely on standard division circle parameter, it is difficult to accurately measure when there is no original processing parameter, the present application is directly measured and the key parameters are preliminarily calibrated by optical projection method, the number of gear teeth is determined by three-coordinate scanning, and the preliminary value of full parameter is calculated, the theoretical tooth profile model is constructed by inputting preliminary parameter into gear measuring center, the actual topological map is obtained by scanning actual tooth surface, and the key parameters such as pitch diameter are adjusted iteratively according to error mode after comparison, until the error is up to standard, three-dimensional model is constructed based on correction parameter and compared with workpiece to verify.The method does not need original processing parameter, and the accuracy and applicability of arc end tooth parameter measurement are improved.

Description

Technical Field

[0001] This invention relates to the field of measurement technology, and more specifically, to a method for measuring the full parameters of circular arc end teeth under error-driven conditions. Background Technology

[0002] Measurement is a crucial technology. Circular arc end teeth are a special structural form of end gear discs, and their machining is achieved by grinding the tooth blank using a pre-designed "forming grinding wheel." Currently, gauges are all self-designed. Without obtaining the original machining parameters, quality control is impossible. Therefore, the accuracy of measuring the tooth profile dimensions of standard circular arc end teeth is particularly important. However, methods for measuring the parameters of circular arc end teeth are limited, and the accuracy of the results needs further investigation. Existing methods have many limitations: projection methods cannot project the section at the pitch circle, only perform preliminary calibration, and cannot obtain the correct tooth tip height position. Furthermore, the three-coordinate scanning method requires the standard pitch circle parameters first, which is impossible without them. To address the aforementioned technical limitations... To address this issue, we propose an error-driven method for measuring the full parameters of circular arc end teeth. Summary of the Invention

[0003] The purpose of this invention is to provide a method for measuring all parameters of circular arc end teeth under error-driven conditions, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, one of the objectives of this invention is to provide a method for measuring the full parameters of a circular arc end tooth under error-driven conditions, comprising the following steps: S1. For workpieces with circular arc end teeth, the number of teeth, gear outer diameter, inner diameter, tooth tip height, tooth root height, and pressure angle parameters are initially calibrated by direct measurement and optical projection. Based on the calibrated tooth tip height, the number of teeth spanned by the grinding wheel is determined by three-coordinate scanning. Then, the preliminary parameters of pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and tip clearance are obtained by calculation. S2. Input the preliminary parameters into the gear measurement center to construct the theoretical tooth profile model of the arc end tooth. Use the gear measurement center to scan the actual tooth surface of the workpiece to obtain the actual topology map. Compare the actual topology map with the theoretical topology map generated based on the theoretical tooth profile model. Adjust the key parameters in the theoretical tooth profile model in reverse according to the error pattern generated by the comparison. Iterate the scanning, comparison and parameter adjustment process until the error between the actual topology map and the theoretical topology map is within the preset range. Output the corrected arc end tooth parameters. The key parameters include at least the pitch circle diameter and the number of teeth spanned by the grinding wheel. S3. Based on the corrected arc end tooth parameters, simulate the machining scenario in 3D modeling software, draw a 3D model of the arc end tooth, and compare the dimensions of the 3D model with the arc end tooth workpiece to verify the accuracy of the corrected parameters.

[0005] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention does not rely on the original machining parameters of the arc-shaped end teeth. It accurately calibrates basic parameters such as the number of teeth, tooth tip height, and pressure angle through direct measurement and optical projection. Combined with three-coordinate scanning, it determines the number of teeth spanned by the grinding wheel and calculates the core preliminary parameters. This effectively overcomes the limitation of traditional methods that rely on standard pitch circle parameters. Based on a gear measurement center, a theoretical tooth profile model is constructed. By comparing actual tooth surface scanning with topological diagrams, key parameters such as the pitch circle diameter and the number of teeth spanned by the grinding wheel are iteratively adjusted in reverse according to the error mode until the error meets the standard. This improves the accuracy of tooth profile parameter measurement and avoids the problem of inaccurate tooth tip height positioning in traditional projection methods. Based on the corrected parameters, a three-dimensional model is constructed and compared with the measured data of the workpiece for verification, further ensuring the reliability of the parameters and improving the applicability and accuracy of full parameter measurement of arc-shaped end teeth. This provides reliable technical support for tooth profile quality control in scenarios without original machining parameters. Attached Figure Description

[0006] Figure 1 Refer to the flowchart of this invention; Figure 2 This is a diagram of the tooth-shaped structure; Figure 3 This is a diagram showing the relationship between end gear machining and the grinding wheel. Detailed Implementation

[0007] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0008] Please see Figure 1 As shown, this embodiment provides a method for measuring all parameters of a circular arc end tooth under error-driven conditions, including the following steps: S1. For workpieces with circular arc end teeth, the number of teeth, gear outer diameter, inner diameter, tooth tip height, tooth root height, and pressure angle parameters are initially calibrated by direct measurement and optical projection. Based on the calibrated tooth tip height, the number of teeth spanned by the grinding wheel is determined by three-coordinate scanning. Then, the preliminary parameters of pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and tip clearance are obtained by calculation. S2. Input the preliminary parameters into the gear measurement center to construct the theoretical tooth profile model of the arc end tooth. Use the gear measurement center to scan the actual tooth surface of the workpiece to obtain the actual topology map. Compare the actual topology map with the theoretical topology map generated based on the theoretical tooth profile model. Adjust the key parameters in the theoretical tooth profile model in reverse according to the error pattern generated by the comparison. Iterate the scanning, comparison and parameter adjustment process until the error between the actual topology map and the theoretical topology map is within the preset range. Output the corrected arc end tooth parameters. The key parameters include at least the pitch circle diameter and the number of teeth spanned by the grinding wheel. S3. Based on the corrected arc-shaped end tooth parameters, simulate the machining scenario in 3D modeling software, draw a 3D model of the arc-shaped end tooth, and compare the dimensions of the 3D model with the arc-shaped end tooth workpiece to verify the accuracy of the corrected parameters.

[0009] In S1, the optical projection method specifically involves placing the arc-shaped end tooth workpiece on the worktable of an optical projector. The number of teeth, tooth tip height, tooth root height, and pressure angle are identified and calibrated through the projected contour image. When determining the number of teeth spanned by the grinding wheel through a three-coordinate scanning, the three-coordinate measuring machine is operated to obtain the actual spatial coordinate data of the tooth groove at the height of the pitch circle of the arc-shaped end tooth workpiece. Based on the forming principle of the arc-shaped end tooth, the symmetry, curvature change law of the tooth surface on both sides of the tooth groove and the geometric characteristics of the bottom of the tooth groove are analyzed. The relative meshing relationship between the grinding wheel node position corresponding to the tooth groove and the workpiece is deduced. Based on the relative meshing relationship, the number of teeth that the grinding wheel can grind simultaneously in one feed under ideal processing conditions is determined. This number of teeth is the number of teeth spanned by the grinding wheel. Preliminary parameters such as pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and tip clearance are obtained by calculation. Specifically, the calculation is based on the calibrated number of teeth, gear outer diameter, inner diameter, tooth tip height, tooth root height, pressure angle, and number of teeth spanned by the grinding wheel, and is calculated using gear geometry principles.

[0010] In S2, preliminary parameters are input into the gear measurement center to construct the theoretical tooth profile model of the circular arc end teeth, specifically including: The preliminary parameters, including pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and clearance, along with the calibrated number of teeth and pressure angle, are input into the control software of the gear measurement center. Based on the input parameters and the preset mathematical equation of the arc end tooth profile, the control software generates an idealized three-dimensional tooth surface model corresponding to the preliminary parameters. This idealized three-dimensional tooth surface model is the theoretical tooth profile model.

[0011] The actual tooth surface of the workpiece is scanned using a gear measuring center to obtain an actual topology map. Specifically, the probe of the gear measuring center is operated to perform contact or non-contact scanning measurements on the actual tooth surface of the arc-end tooth workpiece according to a preset measurement path and sampling density. The measurement path covers multiple tooth grooves and tooth surfaces of the arc-end tooth workpiece. During the scanning process, the gear measuring center records the spatial coordinate data of the contact points between the probe and the workpiece tooth surface in real time. After the scanning is completed, the control software performs coordinate transformation and surface fitting processing on all the collected spatial coordinate data points to generate a three-dimensional point cloud map that reflects the true tooth surface shape and position of the arc-end tooth workpiece. This three-dimensional point cloud map is the actual topology map.

[0012] The actual topology diagram is compared with the theoretical topology diagram generated based on the theoretical tooth profile model. Specifically: The control software aligns the actual topology map with the theoretical tooth profile model in the same coordinate system. After alignment, the control software calculates the spatial deviation distance between each data point in the actual topology map and the corresponding theoretical point in the theoretical tooth profile model. The control software then visually overlays the calculated spatial deviation distance onto the theoretical topology map using color mapping to generate a deviation distribution map. The deviation distribution map shows the specific deviation direction and magnitude of the actual tooth surface relative to the theoretical tooth surface in each region, thus completing the comparison.

[0013] Based on the error patterns generated by the comparison, the key parameters in the theoretical tooth profile model are adjusted in reverse, specifically including: Based on the error pattern presented by the deviation distribution diagram, if the deviation distribution diagram shows that the deviation between the actual tooth surface and the theoretical tooth surface is within the preset error threshold range, and if the distribution diagram shows a situation where the left side is lower than the right side or vice versa, then it is determined that there is a deviation in the pitch circle diameter parameter. If the deviation distribution diagram shows that the deviation between the actual tooth surface and the theoretical tooth surface exceeds the preset error threshold, it is determined that there is a deviation in the grinding wheel span tooth number parameter. Based on the above analysis results of the error mode, the control software automatically adjusts the corresponding pitch circle diameter parameter value and grinding wheel span tooth number parameter value in the theoretical tooth profile model according to the preset adjustment rules, so as to reduce the deviation between the actual topology diagram and the theoretical topology diagram.

[0014] It iteratively executes the scanning, comparison, and parameter adjustment process, specifically including: After the key parameters are adjusted, the control software uses the adjusted pitch circle diameter and grinding wheel tooth span parameter values ​​to reconstruct the updated theoretical tooth profile model and generate an updated theoretical topology map. The control software repeats the scanning process to obtain a new actual topology map and repeats the comparison process, comparing the new actual topology map with the updated theoretical topology map to generate a new deviation distribution map. The process of analyzing error patterns and adjusting key parameters in reverse is repeated to form an iterative optimization loop.

[0015] Once the error between the actual topology diagram and the theoretical topology diagram is within a preset range, the corrected arc end tooth parameters are output, specifically including: In each iteration, the control software calculates the statistical value of the spatial deviation distance of all data points in the new deviation distribution map. The control software compares the calculated statistical value with the preset error allowable threshold. When the statistical value is less than or equal to the preset error allowable threshold, it is determined that the error between the actual topology map and the theoretical topology map of the current iteration has reached an acceptable level, and the iteration cycle terminates. At this time, the control software outputs the pitch circle diameter and grinding wheel tooth span parameter values ​​in the current iteration, along with other unadjusted preliminary parameters, as the final corrected arc end tooth parameters.

[0016] Based on the corrected arc-shaped end tooth parameters, the machining scenario is simulated in 3D modeling software to draw a 3D model of the arc-shaped end tooth, specifically including: The corrected parameters of the arc-shaped end teeth, including the corrected pitch circle diameter, number of teeth across the grinding wheel, number of teeth, pressure angle, addendum, dedendum, tooth width, cross-tooth angle, grinding wheel node radius, offset distance, and clearance, are input into a separate 3D computer-aided design software. Based on the input corrected parameters, the 3D computer-aided design software calls its built-in gear modeling toolkit to reconstruct a theoretical 3D digital model of the arc-shaped end teeth that perfectly matches the corrected parameters.

[0017] The 3D model was compared with the dimensions of the arc-shaped end tooth workpiece to verify the accuracy of the corrected parameters. Specifically, this included: The theoretical three-dimensional digital model of the arc-shaped end tooth is imported into the three-dimensional inspection software. At the same time, a coordinate measuring machine is used to measure the key dimensions and tooth profile of the arc-shaped end tooth workpiece to obtain the actual three-dimensional measurement data of the arc-shaped end tooth workpiece. The 3D inspection software registers and aligns the theoretical 3D digital model of the arc-shaped end tooth with the actual 3D measurement data of the arc-shaped end tooth workpiece in a unified coordinate system. After alignment, the 3D inspection software automatically calculates and reports the differences in key dimensions between the theoretical 3D digital model of the arc-shaped end tooth and the actual measurement data of the arc-shaped end tooth workpiece. If the difference shown in the report is within the acceptable engineering tolerance range, the accuracy of the corrected parameters output is verified; otherwise, the measurement process needs to be reviewed again.

[0018] Further explanation is needed regarding the process: The workpiece with the arc-shaped end teeth is placed on the worktable of the optical projector. Precise clamping and alignment are performed, ensuring the workpiece is stably positioned on the projector's precision worktable. The workpiece's position is adjusted using the fine-tuning knobs on the worktable, ensuring its central axis is coaxial with the projector's optical axis. Simultaneously, the workpiece is leveled using the worktable's leveling device, and then secured with a special fixture to prevent measurement deviations caused by workpiece shifting during projection. This ensures the workpiece's tooth profile is accurately imaged on the projection screen. The number of teeth, addendum, dedendum, and pressure angle are identified and calibrated using the projected profile image. The projector's light source brightness, focal length, and magnification are then adjusted until... A clear, distortion-free projection image of the arc-shaped end tooth profile is obtained on the projection screen. Then, using the projector's built-in digital measuring scale and intelligent profile recognition function, the number of tooth profiles in the projection image is counted one by one. The average value of multiple counts is then calibrated as the number of teeth on the workpiece. The vertical distance from the tooth tip to the tooth root in the projection image is measured and converted into the actual size using the projector's magnification. This distance is measured multiple times for different tooth profiles and the average value is calibrated as the tooth tip height and tooth root height, respectively. The tilt angle of the tooth profile in the projection image is captured by the projector's angle measurement module. Combined with the tooth profile design principle of the arc-shaped end tooth, the pressure angle of the workpiece is calculated and calibrated. All calibration results are recorded in the measurement data file.

[0019] When determining the number of teeth spanned by a three-coordinate measuring machine (CCM) scan, the CCM is operated to precisely scan the tooth profile arc of each tooth along the height of the pitch circle of the arc-shaped end tooth workpiece, obtaining the actual spatial coordinate point set of each tooth surface. Subsequently, the control software performs circle fitting processing on the tooth profile point set of each tooth obtained by scanning based on the least squares method, calculates and outputs the coordinates of the fitted center of each tooth profile arc, and then calculates the spatial distance between the two fitted center points. If the distance is less than the preset center coincidence judgment threshold, it is determined that the centers of the tooth profile arcs of the two teeth coincide in the machining coordinate system, as shown in the attached figure. Figure 3As shown, based on the generating principle of arc-shaped teeth, the coincidence of the centers of the arc-shaped tooth profiles indicates that the two teeth are simultaneously ground by the grinding wheel at the same node position. Based on this simultaneous grinding determination, the number of tooth pairs satisfying the center coincidence condition in a single feed is counted along the circumference of the gear disc. This determines the number of teeth that the grinding wheel can grind simultaneously in one feed, which is the number of teeth the grinding wheel can span. Preliminary parameters such as pitch circle diameter, tooth width, span angle, grinding wheel node radius, offset distance, and clearance are obtained through calculation. Specific parameters are based on the calibrated number of teeth, gear outer diameter, and inner diameter. The pitch circle diameter, addendum, dedendum, pressure angle, and number of teeth spanned by the grinding wheel are calculated using gear geometry principles. All calibrated and calculated basic parameters are entered into professional gear parameter calculation software. The software, relying on the gear geometry principles specific to arc-end teeth, calculates each derived parameter: the pitch circle diameter is calculated by combining the number of teeth and the module derived from the addendum and pressure angle; the tooth width is obtained by directly measuring the tooth thickness of the workpiece using a coordinate measuring machine; and the tooth span angle is determined based on the number of teeth spanned by the grinding wheel and the number of teeth spanned by the arc-end teeth. The calculation formula is as follows: In the formula The cross-tooth angle is defined as Nx, the number of teeth the grinding wheel crosses, and Z is the number of teeth at the arc end. The specific value of the cross-tooth angle is calculated based on these values. The grinding wheel node radius is derived based on the geometric relationship between the pitch circle diameter and the pressure angle. The offset distance and clearance are calculated by combining the tooth tip height, tooth root height, and the number of teeth the grinding wheel crosses. All calculation results retain the appropriate number of precision bits, forming a complete preliminary parameter set, which provides complete data support for the subsequent construction of the theoretical tooth profile model.

[0020] After completing the calibration, estimation, and calculation of all preliminary parameters for the arc-shaped end tooth workpiece, these parameters will be immediately used to construct the theoretical tooth profile model, providing an idealized reference model for subsequent comparison between the actual tooth surface and the theoretical tooth surface. The specific implementation method is as follows: The preliminary parameters, including pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and clearance, along with the calibrated number of teeth and pressure angle, are input into the control software of the gear measurement center. The dedicated control software for the arc end teeth of the gear measurement center is opened, and the parameter input interface for model construction is entered. This interface is divided into dedicated input fields according to parameter type. The operator will accurately enter various parameters from the preliminary parameter set according to the field requirements, while checking the parameter values, units, and accuracy to avoid input errors. After the input is completed, the parameter file is saved to the local database of the control software to ensure that the parameters can be retrieved and modified at any time. Based on the input parameters and the preset mathematical equation for the arc-shaped end tooth profile, the control software generates an idealized three-dimensional tooth surface model corresponding to the initial parameters. This idealized three-dimensional tooth surface model is the theoretical tooth profile model. The control software has a built-in dedicated mathematical equation for the arc-shaped end tooth design. This equation integrates the core geometric features of the arc-shaped end tooth, such as the tooth profile curvature, tooth direction distribution, and tooth surface spatial position. The software automatically reads all the input initial parameters, accurately substitutes them into the preset mathematical equation for the tooth profile, and calculates the theoretical three-dimensional coordinates of the tooth surface point by point through a numerical solution algorithm. Then, a three-dimensional modeling algorithm is used to smoothly stitch these discrete theoretical coordinate points together and reconstruct the surface to form an idealized three-dimensional tooth surface model without machining errors, assembly deviations, or contour distortion. This model perfectly matches the input initial parameters and is the theoretical tooth profile model used for subsequent comparison. After constructing the theoretical tooth profile model of the arc-shaped end teeth, it is necessary to obtain the topological features of the actual tooth surface of the workpiece. To do this, a gear measurement center is used to accurately scan the actual tooth surface of the workpiece. Through a series of data processing steps, an actual topological map that can truly reflect the actual tooth surface state is generated. The specific implementation method is as follows: The actual tooth surface of a workpiece is scanned using a gear measurement center to obtain an actual topological map. Specifically, the probe of the gear measurement center is operated to perform contact or non-contact scanning measurements on the actual tooth surface of the workpiece with arc-shaped end teeth according to a preset measurement path and sampling density. Based on the machining accuracy, tooth profile size, and surface roughness of the workpiece with arc-shaped end teeth, a suitable measuring probe is selected. For workpieces with high tooth surface accuracy and small tooth profile size, a small-diameter ruby ​​contact probe is used; for workpieces with easily scratched tooth surfaces and low roughness, a laser non-contact probe is used. Subsequently, the selected probe is calibrated for accuracy and system error compensation is performed to eliminate measurement deviations caused by the probe itself and the motion mechanism. Then, the control software of the gear measurement center automatically plans the scanning path based on the tooth surface geometry of the theoretical tooth profile model. Simultaneously, a differentiated sampling density is set according to the tooth surface curvature variation. Sampling points are increased in key areas of the tooth surface with large curvature variations, while the sampling density is appropriately reduced in areas with gentle curvature, balancing measurement accuracy and efficiency. Finally, the operator starts the gear measurement center, controlling the motion axis to drive the probe to complete the contact or non-contact scanning measurement on the actual tooth surface of the workpiece according to the preset path. The measurement path covers multiple tooth grooves and tooth surfaces of the arc-shaped end tooth workpiece. When planning the scanning path, the control software does not only cover a single tooth groove and tooth surface, but selects 3-6 tooth grooves and corresponding tooth surfaces evenly distributed on the circumference of the workpiece according to the circumferential distribution characteristics of the workpiece. This ensures that the scanning path can completely cover the representative tooth surface area of ​​the workpiece, avoiding the influence of local errors of a single tooth surface on the judgment of the overall tooth surface condition of the workpiece. During the scanning process, the probe will move strictly according to the planned path, with no missed scans or offsets, ensuring the comprehensiveness of the scanning data. During the scanning process, the gear measurement center records the spatial coordinate data of the contact point between the probe and the workpiece tooth surface in real time. During the scanning process, the high-precision grating ruler and displacement sensor of the gear measurement center will capture the changes in the spatial position of the probe in real time. For contact scanning, it will accurately record the X, Y, and Z three-dimensional spatial coordinates of each point where the probe actually contacts the tooth surface. For non-contact laser scanning, it will record the three-dimensional spatial coordinates of each reflection point on the tooth surface by analyzing the laser reflection signal. All coordinate data are stored in real time according to the scanning sequence, with timestamps and probe position markers. The data accuracy is retained to the micrometer level, forming a complete dataset of actual tooth surface spatial coordinates. After scanning, the control software performs coordinate transformation and surface fitting on all the collected spatial coordinate data points. The control software preprocesses the collected coordinate data to remove abnormal and noise points caused by probe vibration and tooth surface impurities. Then, it transforms the preprocessed coordinate data from the probe coordinate system to the workpiece coordinate system to ensure complete consistency with the coordinate system of the theoretical tooth profile model, eliminating coordinate system deviations caused by clamping and probe movement. Then, a non-uniform rational B-spline surface fitting algorithm is used to fit the discrete spatial coordinate data points according to the geometric characteristics of the tooth surface of the arc end tooth, fitting the discrete points into a continuous and smooth three-dimensional surface to restore the true contour shape of the actual tooth surface to the greatest extent.A 3D point cloud map reflecting the actual tooth surface shape and position of the arc-end tooth workpiece is generated. This 3D point cloud map is the actual topology map. The control software converts the fitted 3D surface into high-density 3D point cloud data. The point cloud density matches the preset sampling density, which can clearly present the overall shape, spatial position, and local details such as concavity, convexity, and contour deviation of the actual tooth surface. At the same time, the software adds the workpiece coordinate system scale, orientation mark, and tooth surface area label to the 3D point cloud map. The generated 3D point cloud map is the actual topology map, which can realistically and accurately reflect the actual tooth surface state of the arc-end tooth workpiece, providing reliable actual data basis for subsequent comparison with the theoretical topology map.

[0021] After generating the actual topological map of the arc-shaped end tooth workpiece using a gear measurement center and constructing the corresponding theoretical tooth profile model, the control software performs high-precision spatial alignment of the two in the same coordinate system to accurately compare the deviation characteristics of the actual tooth surface and the theoretical tooth surface. This is the core prerequisite for subsequent deviation calculation. Only by achieving comprehensive and accurate alignment can the authenticity and effectiveness of the deviation calculation at each data point be guaranteed. After alignment, the software calculates the spatial deviation distance point by point and visualizes the deviation characteristics through color mapping, generating a distribution map that intuitively reflects the tooth surface deviation. This completes a comprehensive comparison between the actual topological map and the theoretical topological map. The specific implementation method is as follows: The control software aligns the actual topology diagram and the theoretical tooth profile model in the same coordinate system, progressively eliminating subtle spatial deviations caused by workpiece clamping, scanning errors, and model construction to achieve high-precision alignment. The software retrieves the point cloud data of the actual topology diagram, converted to the workpiece coordinate system, and the data of the theoretical tooth profile model. First, it performs coarse alignment of the datum features, using the inner and outer datum surfaces of the arc-shaped end tooth and the central positioning hole as the core global datum. From the point cloud data of the actual topology diagram, a contour extraction algorithm accurately identifies and extracts the 3D contour coordinate sets of these datum features. Simultaneously, it retrieves the standard contour coordinate sets of the corresponding datum features from the theoretical tooth profile model. The two sets of coordinate sets are then matched using rigid body transformation. By calculating and eliminating translational deviations in the X, Y, and Z axes, as well as rotational deviations around these axes, the core datum features of the actual topology diagram and the theoretical tooth profile model completely overlap, completing the coarse alignment. This step quickly eliminates significant spatial deviations between the two, laying the foundation for subsequent fine alignment. Building upon the initial coarse alignment, the software performs fine alignment of key tooth profile features. For core tooth surface feature points such as the apex of the arc-shaped end tooth, the lowest point of the arc-shaped root tooth, and the midpoint of the working section of the tooth profile, it extracts the precise 3D coordinates of these discrete feature points from the actual topology map. Simultaneously, it locates and retrieves the standard coordinates of the corresponding feature points in the theoretical tooth profile model, matching the actual and theoretical feature points one by one. The least squares method is used to calculate the average positional deviation of all matched feature points. Based on the average deviation, a slight rigid body transformation is performed on the actual topology map for adjustment. This process is iterated until the average deviation of the feature points drops below the preset fine-tuning threshold, completing the fine alignment. This step enables the core tooth profile features of both to achieve precise alignment, avoiding local tooth profile offsets caused by only benchmark alignment. To achieve omnidirectional fit of the continuous tooth surface, the software performs a final global surface iterative registration fine-tuning. An improved iterative nearest-point algorithm is used to globally register the full point cloud data of the actual topology map with the continuous surface of the theoretical tooth profile model. Point by point, the software searches for the spatial nearest point on the theoretical surface for each data point in the actual point cloud, calculating the root mean square (RMS) deviation of the global registration. If this value does not reach the preset optimal alignment threshold, the spatial position of the actual topology map is adjusted slightly based on the deviation value, and the nearest-point search and deviation calculation are repeated. This process iterates until the RMS deviation of the global registration reaches the optimal threshold. This completes the high-precision spatial alignment of the actual topology map and the theoretical tooth profile model in the same coordinate system, ensuring that every data point in the actual point cloud accurately matches its corresponding position on the theoretical tooth profile model. After alignment, the control software calculates the spatial deviation distance between each data point in the actual topology map and the corresponding theoretical point on the theoretical tooth profile model. The software performs a valid point screening on the point cloud data of the actual topology map, and removes isolated abnormal points caused by scanning jitter and tooth surface impurities through neighborhood point density analysis, retaining only valid data points that can truly reflect the tooth surface state, thus avoiding abnormal points from interfering with the accuracy of deviation calculation.For each selected valid actual data point, the software will use the normal projection matching method to accurately locate the unique corresponding theoretical point on the continuous surface of the theoretical tooth profile model based on its three-dimensional coordinates in the unified workpiece coordinate system. That is, starting from the actual data point, a projection line is drawn along the tooth surface normal at its location. The intersection of the projection line and the theoretical tooth profile model surface is the corresponding theoretical point of the actual point. This matching method can ensure that the spatial correspondence between the actual point and the theoretical point fits the geometric features of the tooth surface and avoids the correspondence deviation caused by simple coordinate projection. After identifying the one-to-one correspondence between actual and theoretical points, the software calculates the coordinate difference between the actual data point and the corresponding theoretical point along the X, Y, and Z axes, based on the distance calculation logic between the two points in three-dimensional space. Then, through spatial distance synthesis logic, it obtains the straight-line distance between the points. This distance represents the spatial deviation distance of the actual data point relative to the theoretical tooth profile model. Simultaneously, the software records the spatial direction of this deviation, precisely marking whether the actual data point is radially inside / outside, axially positive / negative, or protruding / recessed in the tooth surface normal direction of the corresponding theoretical point, ensuring that each deviation value carries a clear directional attribute. Following this logic, the software sequentially locates the corresponding theoretical point and calculates the spatial deviation distance and direction for all valid data points in the actual topology map. This ultimately forms a complete point cloud deviation dataset that binds the three-dimensional coordinates of each data point, the coordinates of the corresponding theoretical point, the spatial deviation distance, and the deviation direction, providing accurate numerical data for subsequent deviation visualization. The control software visualizes the calculated spatial deviation distance by overlaying it onto the theoretical topology map using color mapping, generating a deviation distribution map. The software pre-sets a set of gradient color mapping rules that match the deviation distance and direction. These rules are differentiated according to the deviation characteristics. Cool colors represent negative deviations of the actual point relative to the theoretical point, such as when the actual point is recessed into the theoretical surface, and the larger the negative deviation value, the higher the color saturation. Warm colors represent positive deviations of the actual point relative to the theoretical point, such as when the actual point is convex into the theoretical surface, and the larger the positive deviation value, the higher the color brightness. Neutral green represents areas with no deviation or deviation values ​​within a preset small threshold range. At the same time, a color-deviation value comparison scale is set on the side of the visualization interface, marking the specific deviation distance range corresponding to different colors, so that the colors and deviation values ​​form a precise one-to-one correspondence. The software matches the deviation distance of each data point in the point cloud deviation dataset with the corresponding color according to the color mapping rule, and then accurately overlays the color onto the spatial position of the corresponding theoretical point in the theoretical topology map. For continuous tooth surface areas, the software performs smooth interpolation processing on the matched colors of each data point to make the color transition between adjacent areas natural and avoid color block breaks. At the same time, it preserves the color boundaries of key areas such as tooth tip, tooth root, and tooth profile working segment to ensure the recognizability of deviation features. Finally, the theoretical topology map overlaid with color mapping is used to generate a complete deviation distribution map.The deviation distribution map displays the specific direction and magnitude of the deviation between the actual tooth surface and the theoretical tooth surface in various regions. After comparison, the generated deviation distribution map completely recreates the overall tooth profile structure of the arc-shaped end tooth. Simultaneously, the color distribution visually presents the degree of deviation in each region of the tooth surface. Operators can use the software's interactive functions to zoom in, select regions, and query points on the deviation distribution map. Clicking on any location in the distribution map allows real-time viewing of the specific deviation distance, deviation direction, and the corresponding 3D coordinates of the actual and theoretical points. This allows for understanding the overall deviation distribution trend of the tooth surface—for example, whether there is a positive deviation in the tooth tip region, a negative deviation in the tooth root region, or localized periodic deviations in the working section of the tooth profile—as well as precisely viewing the subtle deviation characteristics of individual locations. This deviation distribution map transforms the originally abstract point cloud deviation data into intuitive visual graphics, clearly and comprehensively displaying all deviation information between the actual and theoretical tooth surfaces. This completes a comprehensive comparison between the actual and theoretical topology maps, providing accurate and visualized core error data for subsequent reverse adjustment of key parameters of the theoretical tooth profile model based on error patterns.

[0022] After the control software generates a deviation distribution map that accurately shows the deviation characteristics between the actual tooth surface and the theoretical tooth surface, it immediately performs a systematic analysis of the overall error pattern presented in the map. Based on the tooth profile geometry forming principle of the arc-shaped end tooth, it accurately locates the key parameters with deviations in the theoretical tooth profile model. The core focus is on the deviation judgment of the two parameters that play a decisive role in the tooth profile shaping: the pitch circle diameter and the number of teeth across the grinding wheel. Then, based on the judgment results, the parameter values ​​are automatically adjusted according to preset rules. Subsequently, through iterative execution of scanning, comparison, and parameter adjustment processes, the deviation between the actual tooth surface and the theoretical tooth surface is continuously reduced until the deviation reaches the preset acceptable range. Finally, the corrected full parameters of the arc-shaped end tooth are output. The specific implementation method is as follows: The control software performs a full-domain scan and feature extraction of the overall error characteristics and local deviation patterns of the deviation distribution map. Combining this with the tooth profile machining and geometric design principles of the arc-shaped end tooth, it conducts targeted analysis of the error patterns to determine the deviation type of key parameters. If the deviation distribution map shows a systematic radial offset of the actual tooth profile contour, either overall or in a localized area, relative to the theoretical tooth surface, the software extracts radial deviation data for the working section, tip area, and root area of ​​the tooth profile using a contour extraction algorithm. When the deviations in each area exhibit a consistent inward or outward bias along the workpiece radius, and the trend of the deviation values ​​remains synchronous without significant periodic fluctuations, it is determined that there is a deviation in the pitch circle diameter parameter. This is because the pitch circle diameter, as the core geometric parameter of the arc-shaped end tooth, directly determines the radial distribution range of the tooth surface; its deviation directly leads to a systematic radial offset of the entire tooth surface. If the deviation distribution diagram shows periodic fluctuations in the tooth groove depth or tooth tip height deviation, the software extracts the number of cycles, amplitude, and range of these fluctuations. It then performs correlation verification with the tooth pitch cycle corresponding to the number of teeth spanned by the grinding wheel. When the fluctuation cycle and the number of tooth pitches covered by the number of teeth spanned by the grinding wheel form a precise match, and the start and end positions of the fluctuation coincide with the processing area of ​​the number of teeth spanned by the grinding wheel, it is determined that there is a deviation in the grinding wheel's number of teeth span parameter. This is because the number of teeth spanned by the grinding wheel directly determines the meshing position between the grinding wheel and the workpiece during processing. Deviations in this parameter will cause periodic processing errors related to the number of teeth spanned in the tooth groove depth and tooth tip height during processing. After determining the deviation of key parameters, the control software retrieves built-in preset adjustment rules. Based on the analysis results of the error mode and the actual deviation, it automatically and precisely adjusts the corresponding pitch circle diameter parameter value and the grinding wheel's number of teeth span parameter value in the theoretical tooth profile model. The adjustment rules fully incorporate the geometric conversion relationship of the arc-shaped end teeth, avoiding unfounded blind adjustments, and minimizing the deviation between the actual and theoretical topology diagrams. For adjusting the pitch circle diameter, the software calculates the average radial offset value of all valid data points in the tooth profile working section. This value is the core adjustment basis. Then, based on the geometric conversion relationship between the number of teeth at the arc end and the radial deviation, the average radial offset value is converted into the specific adjustment amount of the pitch circle diameter. If the actual tooth surface is radially outward, the pitch circle diameter parameter is reduced according to the converted value. If it is radially inward, the pitch circle diameter parameter is increased according to the converted value. At the same time, the software sets a reasonable step size limit for the adjustment amount. The single adjustment amount does not exceed the preset maximum step size to prevent the deviation from increasing in the opposite direction due to excessive single adjustment. For adjusting the number of teeth spanned by the grinding wheel, the software calculates the deviation between the actual fluctuation period and the ideal period corresponding to the theoretical number of teeth spanned by the grinding wheel, based on the periodic fluctuation characteristics of the tooth groove depth and tooth tip height deviation. Then, combined with the actual angle of the adjacent tooth tips of the workpiece, the deviation is converted into a fine adjustment amount for the number of teeth spanned by the grinding wheel. The number of teeth spanned by the grinding wheel is finely adjusted in integer order according to the fine adjustment amount to ensure that the adjusted number of teeth spanned by the grinding wheel matches the tooth pitch distribution of the workpiece. After adjustment, the software records the new parameter values ​​and the adjustment amount in real time, forming a parameter adjustment log.After the initial parameter adjustments for the pitch circle diameter and the number of teeth spanned by the grinding wheel are completed, the control software immediately initiates an iterative optimization loop, continuously executing the scanning, comparison, and parameter adjustment process until the deviation between the actual tooth surface and the theoretical tooth surface reaches the preset range. The software integrates the adjusted pitch circle diameter and number of teeth spanned by the grinding wheel with other preliminary parameters that have not deviated, substitutes them into the preset mathematical equation for the arc-end tooth profile, reconstructs an updated theoretical tooth profile model, and generates a corresponding updated theoretical topology map based on this model, ensuring that the new theoretical topology map is completely matched with the adjusted parameters. Subsequently, the software controls the gear measurement center to repeatedly scan and measure the actual tooth surface of the arc-end tooth workpiece, maintaining the same measurement path, sampling density, probe type, and coordinate system settings as the initial scan, to obtain a new actual topology map, ensuring the comparability of the scan data before and after and eliminating deviation interference caused by changes in measurement parameters. Next, the software will use the previous spatial alignment strategy to align the new actual topology map with the updated theoretical topology map in the same coordinate system with high precision. Then, it will calculate the spatial deviation distance point by point to generate a new deviation distribution map. Subsequently, it will repeatedly perform error pattern analysis to determine whether there are still deviations in key parameters. If so, it will continue to fine-tune the relevant parameters according to preset rules. Each iteration will make the theoretical tooth profile model more closely match the actual tooth surface characteristics of the workpiece. In each iteration cycle, the control software will perform full data analysis on the newly generated deviation distribution map and calculate a multi-dimensional statistical measure of the spatial deviation distance of all valid data points. The calculation of this statistical measure is the core innovation. It is not a single numerical judgment, but a comprehensive statistical judgment that integrates the mean deviation, root mean square deviation, and maximum deviation value, which can comprehensively reflect the overall deviation level between the actual tooth surface and the theoretical tooth surface. The software extracts the spatial deviation distances of all valid data points in the deviation distribution map, calculates the mean deviation (arithmetic mean of deviation distances for all valid data points), reflecting the overall average deviation level; then it calculates the root mean square deviation (RMS), which involves squaring the deviation distance of each data point, taking the arithmetic mean of all squares, and then taking the square root, reflecting the dispersion and overall fluctuation of the deviation; simultaneously, it extracts the maximum deviation value among all data point deviation distances, reflecting the local maximum deviation characteristics of the tooth surface. The software then compares the calculated mean deviation, RMS deviation, and maximum deviation value with preset error tolerance thresholds. These thresholds are set based on the machining accuracy requirements of the arc-shaped end teeth and engineering standards. Only when all three statistics are less than or equal to their corresponding preset error tolerance thresholds does the software determine that the error between the actual topology and the theoretical topology of the current iteration has reached an acceptable engineering level, at which point the iterative optimization loop terminates immediately. If any statistic exceeds its corresponding threshold, the software continues with the next iteration until all statistics meet the threshold.After the iteration cycle terminates, the control software integrates the corrected pitch circle diameter and grinding wheel tooth span parameter values ​​from the current iteration with other unadjusted preliminary parameters to form a complete set of arc end tooth parameters. This parameter set is then output as the final corrected arc end tooth parameters. Simultaneously, the software binds and stores all corrected parameters, parameter adjustments from each iteration, final deviation statistics, and deviation distribution charts to form a complete measurement data archive. This provides comprehensive data for subsequent arc end tooth machining, inspection, and quality analysis.

[0023] The core parameters of the end gear include: number of teeth (Z), gear outer diameter (Do), inner diameter (Di), pitch circle diameter (Dm), tooth width (B), total tooth height (ht), number of teeth spanned by the grinding wheel (Nx), and span angle (…). ), grinding wheel node radius (Rgw), offset distance (S), tooth tip height (ha), tooth root height (hb), tooth tip chamfer height (Cf), tooth tip chamfer angle ( ), tooth root fillet (R), clearance (c), and pressure angle ( After the control software completes iterative optimization and outputs the corrected full parameters of the arc-shaped end teeth, in order to further verify the actual accuracy and engineering adaptability of these parameters, a precise reconstruction of the theoretical three-dimensional digital model will be completed using independent three-dimensional computer-aided design software. This will be combined with actual workpiece measurement data from a coordinate measuring machine and professional comparative analysis using three-dimensional inspection software to achieve the final engineering verification of the corrected parameters. If the verification passes, the parameters are confirmed to be valid; otherwise, the entire measurement process needs to be reviewed and revised. The specific implementation method is as follows: After obtaining the corrected full parameters of the arc end teeth, the corrected pitch circle diameter Dm, grinding wheel tooth span number Nx, number of teeth z, and pressure angle are calculated. Tooth tip height ha, tooth root height hB, tooth width B, tooth span angle All parameters, including grinding wheel node radius Rgw, offset distance S, and clearance c, are categorized by geometric feature type and entered into a separate 3D computer-aided design software. This software requires a professional gear modeling toolkit. During the data entry process, select the arc end tooth modeling template in the software's dedicated gear modeling module, and then enter the basic tooth profile parameters, grinding process parameters, and geometric feature parameters sequentially according to the template's parameter fields. Simultaneously, the software automatically performs format verification and process rationality checks on the entered parameters. For example, it verifies the matching between the pitch circle diameter and the number of teeth using the module calculation formula m=Dm / z, and verifies the rationality of the clearance parameter using the process relationship between tooth tip height and tooth root height c=hB-ha. If parameter conflicts occur, it will immediately remind the user and re-verify and correct the parameters to ensure the completeness and accuracy of the entered parameters. The 3D computer-aided design software, based on the input corrected parameters, calls its built-in gear modeling toolkit to reconstruct a 3D digital model of the theoretical circular arc end tooth that perfectly matches the corrected parameters. After calling the toolkit, the software calculates the core tooth profile curve of the circular arc end tooth based on the corrected parameters, and constructs the basic equation of the tooth profile using the polar coordinate method. ,in Polar radius, Using the polar angle as an example, this equation, combined with core parameters such as the corrected pitch circle diameter and pressure angle, accurately calculates the contour coordinates of the tooth tip arc, tooth root arc, and tooth profile working section. Then, through the software's surface modeling function, the tooth profile curve is stretched along the tooth width direction, with the stretching length matching the corrected tooth width B. Simultaneously, the tooth surface is fitted with process features by combining grinding parameters such as the number of teeth spanned by the grinding wheel Nx and the grinding wheel node radius Rgw. Finally, a theoretical arc end tooth three-dimensional digital model that corresponds completely one-to-one with the corrected parameters and is error-free is generated. After modeling is completed, the model is geometrically verified to ensure that features such as tooth profile, tooth pitch, and tooth span angle are completely consistent with the corrected parameters. After reconstructing the theoretical circular arc end tooth 3D digital model, the model will be exported in a common inspection format and imported into professional 3D inspection software. Simultaneously, a high-precision coordinate measuring machine (CMM) will be used to accurately measure the key dimensions and tooth profile of the circular arc end tooth workpiece, obtaining actual 3D measurement data. Before using the CMM, the circular arc end tooth workpiece will be clamped on the precision table of the CMM. Using the workpiece's inner circle reference surface and end face positioning hole as the core reference, a measurement coordinate system O-XYZ consistent with the 3D inspection software will be established, with the inner hole center as the origin, the workpiece reference end face as the XY plane, and the workpiece axis as the Z-axis. After completing the coordinate system calibration and probe radius compensation, key measurement features are selected according to the engineering inspection requirements of the arc-shaped end teeth, including the addendum circle, root circle, pitch circle fitting surface, tooth profile working section of each tooth groove, and tooth width end face. An equal curvature sampling strategy is adopted for the tooth profile, with denser sampling points in the addendum and root regions where curvature changes are large, and a reasonable reduction in sampling density in the tooth profile working section with gentle curvature. For key dimensions such as pitch circle diameter, addendum height, and root height, no fewer than 6 measurement points are evenly selected on the circumference of the workpiece. After the coordinate measuring machine completes the scan according to the planned measurement path, it automatically calculates the measured values ​​of each key dimension, such as the measured value of the addendum height. ,in The average Z-axis coordinate of the fitting center of the tooth tip circle. The average Z-axis coordinate of the tooth root circle fitting center; the measured value of the pitch circle diameter. ,in and Let be the planar coordinates of the i-th measurement point on the pitch circle fitting surface, and n be the number of pitch circle measurement points. Finally, the three-dimensional coordinates of all measurement points are integrated with the measured values ​​of key dimensions to form the actual three-dimensional measurement data of the arc-end tooth workpiece. This data is then imported into the three-dimensional inspection software in the same format to form a comparison dataset with the theoretical three-dimensional digital model. The three-dimensional inspection software registers and aligns the theoretical arc-end tooth three-dimensional digital model with the actual three-dimensional measurement data of the arc-end tooth workpiece in a unified coordinate system. First, coarse registration is completed based on datum features, extracting the geometric features of the inner circle datum and end face datum from the theoretical model and measured data. Rigid body transformation is used to eliminate significant translational and rotational deviations in the coordinate system, making the datum features of the theoretical model and measured data initially coincide. Then, an improved Iterative Closest Point (ICP) algorithm is used to complete high-precision fine registration, aiming to minimize the spatial deviation between the theoretical point cloud and the measured point cloud. By iteratively adjusting the pitch circle diameter and the number of teeth spanned by the grinding wheel in the theoretical tooth profile model, the theoretical tooth surface gradually approaches the actual tooth surface, thereby reducing the deviation. Its core objective function is: in, Let i be the three-dimensional coordinates of the i-th point in the measured point cloud. In theoretical point clouds and The three-dimensional coordinates of the nearest matching point. The effective number of point clouds participating in registration. It is a 3×3 orthogonal rotation matrix. The translation vector is 3×1. The software initializes R0 as the identity matrix and T0 as the zero vector, and searches for corresponding point pairs between the measured and theoretical point clouds point by point. The objective function is then solved using singular value decomposition (SVDm). Minimal rotation matrix With translation vector Then perform rigid body transformation on the measured point cloud. The root mean square (RMS) deviation between the transformed point cloud and the theoretical point cloud is recalculated. If the deviation does not reach the preset registration threshold, the process of finding corresponding points and solving rigid body transformations is repeated until the RMS deviation is less than the threshold. At this point, the high-precision registration and alignment of the theoretical arc-end tooth 3D digital model and the actual 3D measurement data in a unified coordinate system is completed, ensuring that each measured point can accurately match the corresponding position in the theoretical model. After the registration and alignment are completed, the 3D inspection software automatically calculates and reports the differences in key dimensions between the theoretical arc-end tooth 3D digital model and the measured data of the arc-end tooth workpiece. The software automatically extracts the theoretical values ​​of the key dimensions corresponding to the correction parameters from the registered theoretical model. Extract the corresponding key dimension measured values ​​from the measured data. Then, calculate the absolute and relative errors of each critical dimension separately. The calculation formula is as follows: ; The software automatically generates a test report containing the theoretical, measured, absolute, and relative errors of all key dimensions. It also visually annotates the location and amount of deviation for each dimension within the software interface. Subsequently, it displays the absolute errors of each key dimension. Each parameter is compared with the preset acceptable engineering tolerance range, which is determined based on the machining accuracy level of the arc-shaped end teeth and the engineering usage requirements. If the absolute error of all key dimensions in the inspection report is within the corresponding acceptable engineering tolerance range, the accuracy of the output corrected parameters is directly verified. This set of parameters can serve as the final valid basis for the machining, inspection, and rework of the arc-shaped end teeth workpiece. If the absolute error of any key dimension exceeds the acceptable engineering tolerance range, the corrected parameters are deemed not to have passed verification. At this point, it is necessary to re-examine the entire measurement process, including the optical projection calibration and three-coordinate scanning process in stage S1, and the theoretical tooth profile model construction, scanning comparison, and parameter iteration adjustment process in stage S2. Problems such as clamping deviation, scanning error, and algorithm iteration deviation are checked one by one. After the problem is located and resolved, the parameter calibration, iteration, and verification work is carried out again until the difference in key dimensions meets the engineering tolerance requirements.

[0024] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for measuring all parameters of a circular arc end tooth under error-driven conditions, characterized in that: Includes the following steps: S1. For workpieces with circular arc end teeth, the number of teeth, gear outer diameter, inner diameter, tooth tip height, tooth root height, and pressure angle parameters are initially calibrated by direct measurement and optical projection. Based on the calibrated tooth tip height, the number of teeth spanned by the grinding wheel is determined by three-coordinate scanning. Then, the preliminary parameters of pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and tip clearance are obtained by calculation. S2. Input the preliminary parameters into the gear measurement center to construct the theoretical tooth profile model of the arc end tooth. Use the gear measurement center to scan the actual tooth surface of the workpiece to obtain the actual topology map. Compare the actual topology map with the theoretical topology map generated based on the theoretical tooth profile model. Adjust the key parameters in the theoretical tooth profile model in reverse according to the error pattern generated by the comparison. Iterate the scanning, comparison and parameter adjustment process until the error between the actual topology map and the theoretical topology map is within the preset range. Output the corrected arc end tooth parameters. The key parameters include at least the pitch circle diameter and the number of teeth spanned by the grinding wheel. S3. Based on the corrected arc end tooth parameters, simulate the machining scenario in 3D modeling software, draw a 3D model of the arc end tooth, and compare the dimensions of the 3D model with the arc end tooth workpiece to verify the accuracy of the corrected parameters.

2. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 1, characterized in that: In S1, the optical projection method specifically involves placing the arc-shaped end tooth workpiece on the worktable of an optical projector. The number of teeth, addendum, dedendum, and pressure angle are identified and calibrated using the projected contour image. Based on the calibrated addendum and pressure angle, and while determining the number of teeth spanned by the grinding wheel through a three-coordinate measuring machine (CCM), the CCM scans the arc profile of each tooth along the pitch line of the arc-shaped end tooth workpiece to obtain the actual spatial coordinate data of each tooth surface. Based on the coordinate point set obtained from the scan… The tooth profile arc of each tooth is fitted with a circle, and the coordinates of the fitted center of each tooth profile arc are calculated. By comparing the fitted center positions of the tooth profile arcs of each tooth, if the two fitted centers coincide within the preset tolerance range, it is determined that the two teeth are two teeth that are simultaneously ground by the grinding wheel during processing. The coincidence of the centers of the two tooth profile arcs indicates the simultaneous meshing position of the grinding wheel node. Based on the simultaneous grinding determination result, the number of teeth that can be covered by a single feed is counted along the circumference of the tooth disk. This number of teeth is the number of teeth that the grinding wheel spans. The preliminary parameters, such as pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and tip clearance, are obtained through calculation. Specifically, they are calculated based on the calibrated number of teeth, gear outer diameter, inner diameter, tooth tip height, tooth root height, pressure angle, and the number of teeth spanned by the grinding wheel, using the principles of gear geometry.

3. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 2, characterized in that: In S2, the step of inputting preliminary parameters into the gear measurement center to construct the theoretical tooth profile model of the arc-shaped end tooth specifically includes: The preliminary parameters, including pitch circle diameter, tooth width, tooth span angle, grinding wheel node radius, offset distance, and clearance, along with the calibrated number of teeth and pressure angle, are input into the control software of the gear measurement center. Based on the input parameters and a preset mathematical equation for the arc end tooth profile, the control software generates an idealized three-dimensional tooth surface model corresponding to the preliminary parameters. This idealized three-dimensional tooth surface model is the theoretical tooth profile model.

4. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 3, characterized in that: The method of using the gear measurement center to scan the actual tooth surface of the workpiece to obtain the actual topology map involves operating the probe of the gear measurement center to perform contact or non-contact scanning measurements on the actual tooth surface of the arc-end tooth workpiece according to a preset measurement path and sampling density. The measurement path covers multiple tooth grooves and tooth surfaces of the arc-end tooth workpiece. During the scanning process, the gear measurement center records the spatial coordinate data of the contact point between the probe and the workpiece tooth surface in real time. After the scanning is completed, the control software performs coordinate transformation and surface fitting processing on all the collected spatial coordinate data points to generate a three-dimensional point cloud map that reflects the true tooth surface shape and position of the arc-end tooth workpiece. This three-dimensional point cloud map is the actual topology map.

5. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 4, characterized in that: The actual topology diagram is compared with the theoretical topology diagram generated based on the theoretical tooth profile model, specifically: The control software aligns the actual topology map and the theoretical tooth profile model in the same coordinate system. After alignment, the control software calculates the spatial deviation distance between each data point in the actual topology map and the corresponding theoretical point in the theoretical tooth profile model. The control software then visually overlays the calculated spatial deviation distance onto the theoretical topology map using color mapping to generate a deviation distribution map. The deviation distribution map shows the specific deviation direction and magnitude of the actual tooth surface relative to the theoretical tooth surface in each region, thus completing the comparison.

6. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 5, characterized in that: Based on the error patterns generated by the comparison, the key parameters in the theoretical tooth profile model are adjusted in reverse, specifically including: Based on the error pattern presented by the deviation distribution diagram, if the deviation distribution diagram shows that the deviation between the actual tooth surface and the theoretical tooth surface is within the preset error threshold range, and if the distribution diagram shows a situation where the left side is lower than the right side or vice versa, then it is determined that there is a deviation in the pitch circle diameter parameter. If the deviation distribution diagram shows that the deviation between the actual tooth surface and the theoretical tooth surface exceeds the preset error threshold, it is determined that there is a deviation in the grinding wheel span tooth number parameter. Based on the above analysis results of the error mode, the control software automatically adjusts the corresponding pitch circle diameter parameter value and grinding wheel span tooth number parameter value in the theoretical tooth profile model according to the preset adjustment rules, so as to reduce the deviation between the actual topology diagram and the theoretical topology diagram.

7. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 6, characterized in that: The iterative process of scanning, comparing, and adjusting parameters specifically includes: After the key parameters are adjusted, the control software uses the adjusted pitch circle diameter and grinding wheel tooth span parameter values ​​to reconstruct the updated theoretical tooth profile model and generate an updated theoretical topology diagram. The control software repeats the scanning process to obtain a new actual topology diagram and repeats the comparison process, comparing the new actual topology diagram with the updated theoretical topology diagram to generate a new deviation distribution diagram. The process of analyzing error patterns and adjusting key parameters in reverse is repeated to form an iterative optimization loop.

8. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 7, characterized in that: The process continues until the error between the actual topology and the theoretical topology is within a preset range, then outputting the corrected arc end tooth parameters, specifically including: In each iteration, the control software calculates the statistical value of the spatial deviation distance of all data points in the new deviation distribution map. The control software compares the calculated statistical value with a preset error allowable threshold. When the statistical value is less than or equal to the preset error allowable threshold, it is determined that the error between the actual topology map and the theoretical topology map of the current iteration has reached an acceptable level, and the iteration cycle terminates. At this time, the control software outputs the pitch circle diameter and grinding wheel tooth span parameter values ​​in the current iteration, along with other unadjusted preliminary parameters, as the final corrected arc end tooth parameters.

9. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 7, characterized in that: The step of simulating the machining scenario in 3D modeling software based on the corrected arc-shaped end tooth parameters and drawing a 3D model of the arc-shaped end tooth specifically includes: The corrected arc end tooth parameters, including the corrected pitch circle diameter, number of teeth across the grinding wheel, number of teeth, pressure angle, addendum, dedendum, tooth width, cross-tooth angle, grinding wheel node radius, offset distance, and clearance, are input into independent three-dimensional computer-aided design software. Based on the input corrected parameters, the three-dimensional computer-aided design software calls its built-in gear modeling toolkit to reconstruct a theoretical arc end tooth three-dimensional digital model that perfectly matches the corrected parameters.

10. The method for measuring all parameters of a circular arc end tooth under error-driven conditions according to claim 9, characterized in that: The step of comparing the dimensions of the three-dimensional model with those of the arc-shaped end tooth workpiece to verify the accuracy of the corrected parameters specifically includes: The theoretical arc-shaped end tooth three-dimensional digital model is imported into the three-dimensional detection software. At the same time, a coordinate measuring machine is used to measure the key dimensions and tooth shape of the arc-shaped end tooth workpiece to obtain the actual three-dimensional measurement data of the arc-shaped end tooth workpiece. The 3D inspection software registers and aligns the theoretical arc-shaped end tooth 3D digital model with the actual 3D measurement data of the arc-shaped end tooth workpiece in a unified coordinate system. After alignment, the 3D inspection software automatically calculates and reports the differences in key dimensions between the theoretical arc-shaped end tooth 3D digital model and the actual measurement data of the arc-shaped end tooth workpiece. If the differences shown in the report are within the acceptable engineering tolerance range, the accuracy of the output corrected parameters is verified; otherwise, the measurement process needs to be reviewed again.

Images