A measurement and calculation method for wear of involute gear based on self-reference datum

Abstract

The application provides a measurement and calculation method based on self-reference reference involute gear wear amount. The method does not need to rely on external reference, effectively reduces the measurement error caused by reference deviation, and finds an accurate and fast calculation method. By changing the basic parameters of the gear, the accurate calculation of different involute gear wear amounts can be realized, and the wear amounts of corresponding involute parts, such as involute splines, can also be accurately calculated. The method provides key technical support for the precision control and data reliability of the gear tooth surface wear amount in the gear wear and gear contact fatigue test, and the process and parameter design of the gear.

Description

Technical Field

[0001] This invention relates to the field of gear tooth profile measurement and calculation technology, and in particular to a method for measuring and calculating the wear of involute gears based on a self-reference datum. Background Technology

[0002] Involute gears, as core components of modern mechanical transmission systems, directly determine the overall level of high-end equipment through their service performance and reliability. Tooth surface wear is one of the most significant gear failure modes, causing not only vibration and noise and reduced transmission accuracy, but also potentially catastrophic equipment malfunctions. Therefore, during gear development, evaluating wear resistance and service life through gear contact fatigue or wear tests is an indispensable step in ensuring product quality. However, existing gear wear measurement technologies suffer from three major drawbacks due to the lack of an inherent reference standard: inaccurate measurement results, unclear physical meaning, and limited engineering value.

[0003] A. Calculating wear usually requires comparing the tooth profile before and after wear. However, in practice, the clamping and positioning of gears before and after a test is almost impossible to be completely identical, with slight alignment errors and angular deviations. Due to the lack of a stable, intrinsic reference standard, the two measurement data are actually in different coordinate systems. Direct comparison will introduce huge systematic errors, leading to distorted wear calculation results, or even rendering them unreliable.

[0004] B. The measurement results cannot accurately reflect the wear depth along the normal direction at the meshing point. Existing general measurement methods can usually only obtain the geometric position change of the tooth profile in the coordinate system, making it difficult to directly convert the measurement data into a normal wear amount with clear physical meaning. This limits the use of measurement data for accurate mechanical analysis and life prediction.

[0005] C. Data obtained from wear tests is highly volatile and unreliable. Engineers cannot make accurate judgments based on this inaccurate data. This significantly reduces the effectiveness of expensive bench tests and hinders the continuous improvement of gear product performance.

[0006] Therefore, it is of great significance to develop a method for measuring and calculating the wear of involute gears based on a self-reference datum. Summary of the Invention

[0007] The purpose of this invention is to provide a method for measuring and calculating the wear of involute gears based on a self-reference datum, in order to solve the problems existing in the prior art.

[0008] The technical solution adopted to achieve the purpose of this invention is as follows: a method for measuring and calculating the wear of involute gears based on a self-reference datum, comprising the following steps:

[0009] 1) Initial measurement of the unworn gear tooth profile to obtain high-precision raw tooth profile data points. The measurement range covers the entire circumference of the gear tooth profile and is scanned at multiple positions along the tooth width.

[0010] 2) Feature point selection. At least 100 feature points are evenly selected from the measured tooth profile data. These feature points cover the critical areas of the gear. These critical areas represent stress concentration and high-risk wear zones on the tooth surface.

[0011] 3) Construct a self-reference datum system. Import the feature point coordinate file into the MATLAB program to reconstruct the gear tooth profile and base circle. Using the center of the base circle as the center and the distance from each feature point to the center as the radius, draw a circle extending to the other side of the tooth profile and calculate the corresponding arc length. Record the arc length and radius data into a TXT file to form a self-reference datum.

[0012] 4) Re-measurement of the worn tooth profile. Rescan the gear tooth profile after friction wear or contact fatigue testing using the same measuring equipment, under the same measurement conditions as in step 1). Reconstruct the worn tooth profile in MATLAB, selecting the same number and radius of feature points as in step 2).

[0013] 5) Arc length difference calculation. Using the center of the same base circle as a reference, calculate the arc length of the worn tooth profile for each feature point according to the corresponding radius. Compare it with the unworn arc length recorded in step 3) to solve for the arc length difference.

[0014] 6) Wear calculation. The actual wear at each characteristic point is derived using theoretical formulas along the normal direction of the gear meshing point.

[0015] Furthermore, in step 1), a precision tooth profile measuring instrument is used to measure the gear tooth profile.

[0016] Furthermore, the key areas of the gear include the pitch circle, the transition position between double-tooth meshing and single-tooth meshing, the gear tooth tip, and the tooth root.

[0017] Furthermore, in step 6), the formula calculation is implemented in MATLAB, and the wear amount at each point is output to a TXT file.

[0018] Furthermore, the formula for calculating the wear depth at any feature point is as follows:

[0019]

[0020] In the formula, Δh i Let Δs be the normal wear depth at the i-th feature point. i Before and after wear, with the base circle center as the center and the feature point radius r as the radius, the image shows the image before and after wear. i Draw a circle, and the angle difference between the corresponding two sides of the tooth profile is expressed in radians. b Let be the base circle radius of the gear.

[0021] Furthermore, following step 6), there is a step of using wear data for design verification. Design flaws are identified and corrected through a data-driven approach.

[0022] Furthermore, the wear distribution is displayed through visual charts to accurately locate localized wear anomalies. Based on the wear distribution data, weak points in the tooth surface design are identified. These weak points include the root transition fillet, tooth tip edge, pitch circle region, and high-wear areas at the single / double tooth meshing transition position.

[0023] Furthermore, after step 6), there is a step of using wear as an evaluation index for process iteration to guide the adjustment of actual production processes.

[0024] Furthermore, by comparing the wear distribution of different process samples, the process parameter combination corresponding to the minimum wear is selected.

[0025] Furthermore, based on the correlation between tooth surface roughness and wear, the machining process is adjusted to reduce the risk of abnormal wear caused by process defects.

[0026] The technical advantages of this invention are undeniable: it provides a method for measuring and calculating the wear of involute gears based on a self-referenced datum, eliminating the need for an external datum, effectively reducing measurement errors caused by datum deviations, and providing an accurate and rapid calculation method. Furthermore, by changing the basic parameters of the gear, it can accurately calculate the wear of different involute gears, and similarly, it can accurately calculate the wear of corresponding involute components. This provides crucial technical support for the accuracy control and data reliability of gear tooth surface wear in gear wear and gear contact fatigue tests. Attached Figure Description

[0027] Figure 1 This is a flowchart of the overall operation process;

[0028] Figure 2 This is a schematic diagram of wear on the tooth profile end face;

[0029] Figure 3 A 3D model of a planetary gear reducer and a schematic diagram of its gear transmission mechanism;

[0030] Figure 4 A precision tooth profile inspection instrument is used to examine the profile of the sun gear before and after wear.

[0031] Figure 5 Wear distribution diagram of planetary gear reducer gear wear experiment. Detailed Implementation

[0032] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0033] Example 1:

[0034] This embodiment aims to solve the technical problem of measurement and calculation errors in gear wear before and after wear caused by the difficulty in determining the reference datum in gear contact fatigue tests and wear tests. This embodiment provides a method for measuring and calculating the wear of involute gears based on a self-reference datum, including the following steps:

[0035] 1) Initial measurement of the unworn gear tooth profile to obtain high-precision raw tooth profile data points. The measurement range covers the entire circumference of the gear tooth profile and is scanned at multiple positions along the tooth width.

[0036] 2) Feature point selection. At least 100 feature points are evenly selected from the measured tooth profile data. These feature points cover the critical areas of the gear. These critical areas represent stress concentration and high-risk wear zones on the tooth surface.

[0037] 3) Construct a self-reference datum system. Import the feature point coordinate file into the MATLAB program to reconstruct the gear tooth profile and base circle. Using the center of the base circle as the center and the distance from each feature point to the center as the radius, draw a circle extending to the other side of the tooth profile and calculate the corresponding arc length. Record the arc length and radius data into a TXT file to form a self-reference datum.

[0038] 4) Re-measurement of the worn tooth profile. Rescan the gear tooth profile after friction wear or contact fatigue testing using the same measuring equipment, under the same measurement conditions as in step 1). Reconstruct the worn tooth profile in MATLAB, selecting the same number and radius of feature points as in step 2).

[0039] 5) Arc length difference calculation. Using the center of the same base circle as a reference, calculate the arc length of the worn tooth profile for each feature point according to the corresponding radius. Compare it with the unworn arc length recorded in step 3) to solve for the arc length difference.

[0040] 6) Wear Calculation. The actual wear amount at each feature point is derived using theoretical formulas along the normal direction of the gear meshing point. The formula calculation is implemented in MATLAB, and the wear amount at each point is output to a TXT file. The formula for calculating the wear depth at any feature point is as follows:

[0041]

[0042] In the formula, Δh i Let Δs be the normal wear depth at the i-th feature point. iBefore and after wear, with the base circle center as the center and the feature point radius r as the radius, the image shows the image before and after wear. i Draw a circle, and the angle difference between the corresponding two sides of the tooth profile is expressed in radians. b Let be the base circle radius of the gear.

[0043] This embodiment provides a method for measuring and calculating the wear of involute gears based on a self-referenced datum. It eliminates the need for an external reference, effectively reducing measurement errors caused by datum deviations. Furthermore, it provides an accurate and rapid calculation method. By changing the basic parameters of the gear, it can accurately calculate the wear of different involute gears, and similarly, it can accurately calculate the wear of corresponding involute components. This provides key technical support for the accuracy control and data reliability of gear tooth surface wear in gear wear and gear contact fatigue tests.

[0044] Example 2:

[0045] The main content of this embodiment is the same as that of embodiment 1, except that a precision tooth profile comprehensive testing instrument is used to measure the gear tooth profile.

[0046] Example 3:

[0047] The main content of this embodiment is the same as that of embodiment 1 or 2. The key areas of the gear include the pitch circle, the transition position between double-tooth meshing and single-tooth meshing, the gear tooth tip and tooth root.

[0048] Example 4:

[0049] This embodiment provides a method for measuring and calculating the wear of involute gears based on a self-reference datum, according to... Figure 1 The measurement process shown includes the following steps:

[0050] 1) Before conducting gear friction and wear or gear contact fatigue tests, a precision tooth profile measuring instrument or other professional gear tooth profile measuring equipment such as a gear measuring center, laser scanner, or cylindrical gear measuring instrument can be used to measure the unworn gear tooth profile.

[0051] 2) In the measured unworn gear tooth profile, take one hundred sampling points evenly, or increase the number of sampling points according to the measurement accuracy requirements. These selected feature points should be calculated by precise formulas and should include some special positions of the gear, such as the single-tooth / double-tooth switching area, the gear node, the gear meshing and disengagement areas. If there is an interference area when the gears mesh, the interference area should be included.

[0052] 3) Using the center of the base circle of the gear as the center, draw a circle with the distance from the feature point to the center as the radius until the other side of the gear, obtain the corresponding arc length, and record and save the radius from each feature point to the center of the base circle, thereby constructing a self-reference datum system.

[0053] 4) After the gear has completed the wear test, measure its tooth profile data again, and take the same number and radius of feature points as in step 2). Draw an involute with the same shape as the unworn tooth profile through these feature points.

[0054] 5) Using the center of the same gear base circle as a reference, calculate the corresponding arc length of the worn tooth profile according to the corresponding radius, and solve for the arc length difference with the arc length corresponding to the feature point of the unworn gear tooth profile.

[0055] 6) The wear of the gear is along the normal direction of the gear meshing point. The wear of each characteristic point is calculated by deriving the theoretical formula and implementing it in MATLAB.

[0056] Figure 2 This is a schematic diagram of the tooth profile end face. The following parameters are defined: circle ED1D is the base circle, r... b Let B1 be the radius of the base circle, AD be the arc length of the original involute, and A1D1 be the involute profile curve constructed through point B1. r b1 Let r be the distance from B to the center O of the base circle. b2 Let B1 be the distance from the center O of the base circle, and let arc FB be... Therefore, r b1 Let FB1 be the radius of the arc centered at the base circle O, extending from one side of the involute tooth profile to the other side of the unworn involute tooth profile. It is the wear of the gears that causes the gears to wear down. b1 Let DD1 be the radius of the arc centered at the base circle O, extending from one side of the involute tooth profile to the worn involute tooth profile on the other side. Arc BB1 is , arc ED is Arc ED1 is BE is the tangent to the base circle, with the point of tangency at E. The derivation process is as follows.

[0057] EB and EC1 are generating lines. According to the definition of an involute, the following properties are easily obtained.

[0058] (1)

[0059] (2)

[0060] Geometric relations can be obtained

[0061] (3)

[0062] (4)

[0063] (5)

[0064] (6)

[0065] Since the gear wear direction is normal to the gear meshing point, and BE and C'E are tangents to the base circle, we can obtain:

[0066] (7)

[0067] (8)

[0068] because We can obtain the following equation:

[0069] (9)

[0070] From the given information, we can obtain

[0071] (10)

[0072] From the arc length formula, we can obtain

[0073] (11)

[0074] By combining equations (6), (7), (9), and (10), we can obtain...

[0075] (12)

[0076] By replacing B with any feature point and B1 with any feature point corresponding to the wear condition, the wear depth of any feature point can be calculated. .

[0077] Example 5:

[0078] The main content of this example is the same as any one of Examples 1 to 4. The example includes a three-dimensional model of the planetary gear reducer and a schematic diagram of the gear transmission mechanism, obtained through a planetary gear train wear test. Figure 3 As shown. A precision tooth profile inspection instrument was used to inspect the profile of the sun gear before and after wear, as shown. Figure 4 As shown in Table 1, the specific parameters of the gear pair are as follows. This example uses a gear wear test and measures the tooth profile of the experimental gear using a precision tooth profile comprehensive testing instrument. It combines this with a method for measuring and calculating the wear of involute gears based on a self-reference datum, and demonstrates the superiority and accuracy of the method by calculating the actual wear on the tooth surface using a self-developed MATLAB program. The specific steps include:

[0079] Table 1 Basic parameters of gear pairs

[0080]

[0081] 1) Before conducting gear friction and wear or gear contact fatigue tests, a precision tooth profile measuring instrument can be used with appropriate fixtures to measure the unworn sun gear tooth profile to avoid misalignment, angular deviation and other related errors during gear measurement;

[0082] 2) Move the measuring probe to the root of a tooth of the sun gear, and then start scanning measurement until the complete tooth profile of the sun gear is measured. Move the Z coordinate to three positions along the tooth width of 8mm, 13mm, and 18mm in the unworn sun gear tooth profile, and take 100 sampling points evenly on the tooth profile. These feature points should include some special positions of the sun gear, such as the single and double tooth switching area between the sun gear and the planet gear, the node of the sun gear, the meshing area of ​​the sun gear and the meshing area of ​​the gear. If there is an interference area when the sun gear and the planet gear mesh, the interference area should be included.

[0083] 3) Extract the txt file containing the coordinates of the feature points of the measured tooth profile from the precision tooth profile comprehensive inspection instrument. Reconstruct the sun gear tooth profile and the sun gear base circle in the MATLAB program. In the program, draw a circle with the center of the sun gear base circle as the center and the distance from the feature point to the center as the radius until the other side of the sun gear tooth profile, and obtain the corresponding arc length. Record the arc length and the radius from each feature point to the center of the base circle in the txt file to construct a self-reference datum system.

[0084] 4) After the planetary gear train has completed the wear test, measure its tooth profile data again, reconstruct the tooth profile of the sun gear after wear in MATLAB, and use the program to take the same number and the same radius of feature points as in step 2).

[0085] 5) In MATLAB, using the center of the same gear base circle as a reference, calculate the corresponding arc length of the worn tooth profile according to the corresponding radius, and compare it with the arc length corresponding to the feature point of the unworn gear tooth profile to solve for the arc length difference.

[0086] 6) The wear amount of the gear is along the normal direction of the gear meshing point. In MATLAB, the wear amount of each characteristic point is calculated using formula (12) and saved to a txt file. The wear distribution diagram of the planetary gear reducer gear wear experiment is shown below. Figure 5 As shown.

[0087] Furthermore, by changing the basic parameters of the gear, it is possible to accurately calculate the wear amount of different involute gears. Similarly, it is also possible to accurately calculate the wear amount of corresponding involute components, such as involute splines.

[0088] Example 6:

[0089] This example is essentially the same as any one of Examples 1-4, except that after step 6), it also includes a step of using wear data for design verification. Design defects are identified and corrected through a data-driven approach. Wear distribution is displayed through visual charts to accurately locate localized wear anomalies. Based on the wear distribution data, weak points in the tooth surface design are identified. These weak points include the root transition fillet, tooth tip edge, pitch circle region, and high-wear areas in the single / double tooth meshing transition position. Simultaneously, the rationality of gear design parameters (such as module, pressure angle, and face width coefficient) can be quantitatively verified. If the wear corresponding to a certain parameter exceeds a preset threshold, the design scheme can be directly corrected in reverse to improve the gear's wear resistance and service life.

[0090] Example 7:

[0091] This example is essentially the same as any one of Examples 1-4, except that after step 6), it also includes a step of using wear amount as a process iteration evaluation index to guide the adjustment of the actual production process. By comparing the wear amount distribution of different process samples, the process parameter combination corresponding to the minimum wear amount is selected. In actual production, the optimal process parameters are screened based on the wear amount differences corresponding to different heat treatment processes (such as carburizing and quenching, tempering). Based on the correlation between tooth surface machining accuracy (such as roughness) and wear amount, the machining process is optimized to reduce the risk of abnormal wear caused by process defects.

Claims

1. A method for measuring and calculating the wear of involute gears based on a self-reference datum, characterized in that, Includes the following steps: 1) Initial measurement of the unworn gear tooth profile to obtain high-precision original tooth profile data points; the measurement range covers the entire circumference of the gear tooth profile and is scanned at multiple positions along the tooth width; 2) Feature point selection: Select at least 100 feature points evenly from the measured tooth profile data; The feature points cover the critical areas of the gear; these critical areas represent stress concentration and high-risk wear zones on the gear tooth surface. 3) Construct a self-reference datum system; import the feature point coordinate file into the MATLAB program to reconstruct the gear tooth profile and base circle; draw a circle with the center of the base circle as the center and the distance from each feature point to the center as the radius, extending to the other side of the tooth profile, and calculate the corresponding arc length; record the arc length and radius data in a TXT file to form a self-reference datum. 4) Re-measurement of the tooth profile after wear; Rescan the gear tooth profile after friction wear or contact fatigue test using the same measuring equipment, with the measurement conditions consistent with step 1); reconstruct the worn tooth profile in MATLAB, and select the same number and radius of feature points as in step 2); 5) Calculation of arc length difference: Using the center of the same base circle as a reference, calculate the arc length of the tooth profile after wear for each feature point according to the corresponding radius; compare it with the unworn arc length recorded in step 3) to solve for the arc length difference. 6) Wear calculation: The actual wear of each characteristic point is derived by using theoretical formulas along the normal direction of the gear meshing point.

2. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 1, characterized in that: In step 1), a precision tooth profile measuring instrument is used to measure the gear tooth profile.

3. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 1, characterized in that: The key areas of the gear include the pitch circle, the transition position between double-tooth meshing and single-tooth meshing, the gear tooth tip, and the tooth root.

4. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 1, characterized in that: In step 6), the formula calculation is performed in MATLAB, and the wear amount at each point is output to a TXT file.

5. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 1, characterized in that, The formula for calculating the wear depth at any feature point is as follows: In the formula, Δh i Δs represents the normal wear depth at the i-th feature point. i Before and after wear, with the base circle center as the center and the feature point radius r as the radius, the image shows the image before and after wear. i Draw a circle, and the angular difference between the corresponding two tooth profiles, in radians; r b Let be the base circle radius of the gear.

6. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 1, characterized in that: Following step 6), there is also a step of using wear data for design verification; identifying and correcting design defects through a data-driven approach.

7. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 6, characterized in that: Wear distribution is displayed through visual charts to accurately locate local wear anomalies; based on wear distribution data, weak points in tooth surface design are identified; these weak points include the tooth root transition fillet, tooth tip edge, pitch circle region, and high-wear areas in the single / double tooth meshing transition position.

8. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 1, characterized in that: After step 6), there is also a step of using wear as an evaluation index for process iteration to guide the adjustment of actual production processes.

9. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 8, characterized in that: By comparing the wear distribution of different process samples, the process parameter combination corresponding to the minimum wear is selected.

10. The method for measuring and calculating the wear of involute gears based on a self-reference datum as described in claim 8, characterized in that: Based on the correlation between tooth surface roughness and wear, the machining process can be adjusted to reduce the risk of abnormal wear caused by process defects.

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