A method for quantitatively sampling full geometric information of a gear tooth surface and application thereof

Abstract

The present application belongs to the technical field of large-size gear measurement, and particularly relates to a large gear tooth surface full-geometric information quantitative sampling method and application thereof. Under the constraint of measurement uncertainty set in different characteristic regions of a large gear tooth surface, an optimal critical value of sample size of each different characteristic is determined with the minimum total detection cost as the target, the total detection cost including total measurement cost and detection error cost, and the sample size being the total sampling point number covering the full tooth surface. The optimal critical value of sample size of a single tooth surface of a large gear or the optimal critical value of sample size of all tooth surfaces of the entire gear is determined, and the tooth surface of a gear standard is sampled according to the optimal critical value of sample size, and the full-geometric information of the tooth surface is fitted according to the sampling data to calibrate the measuring instrument. The present application can well balance the sampling accuracy and sampling cost, avoid blindly increasing the sampling points for pursuing the sampling accuracy, and greatly reduce the total cost consumption generated in the large-size tooth surface profile sampling process.

Description

Technical Field

[0001] This invention belongs to the field of large-size gear measurement technology, specifically relating to a quantitative sampling method for the full geometric information of a large gear tooth surface and its application. Background Technology

[0002] In important fields such as metallurgy, mining, shipbuilding, hoisting, wind power generation, national defense, and aerospace, large, complex, and critical components, represented by large gears, are the core and foundation of major equipment. Their processing and manufacturing quality directly determines the performance, level, and lifespan of major equipment.

[0003] To measure the geometric features of large gears, sampling is required. Currently, sampling is generally performed only on a single arc at the center of the tooth surface. However, sampling points on a single arc are insufficient to fully and accurately represent the tooth surface features, especially for large gears (diameter over 500mm). Therefore, the inventors have proposed a method for sampling the entire tooth surface to obtain the full geometric information of the large gear tooth surface. The full geometric information of the tooth surface refers to the geometric relationship information composed of all the sampling data of the tooth surface, including the helical lines and involutes on the tooth surface, as well as the helical surfaces and involute surfaces corresponding to the helical lines and involutes.

[0004] The difficulty in tooth surface sampling lies in the fact that the relationship between the sample size, sample distribution and measurement accuracy for large tooth surfaces with multiple features cannot be quantitatively characterized and standardized. This results in inconsistent measurement strategies for large gears and non-optimal measurement costs, making it difficult to accurately measure the full geometric information of large gears. Summary of the Invention

[0005] The purpose of this invention is to solve the problems existing in the prior art and provide a method for quantitative sampling of the full geometric information of a large gear tooth surface.

[0006] This invention is achieved through the following technical solution: a quantitative sampling method for the full geometric information of a large gear tooth surface, comprising the following steps: under the constraint of measurement uncertainty set for different feature regions of the large gear tooth surface, with the goal of minimizing the total detection cost, determining the optimal critical value of the sample size for each different feature, wherein the total detection cost includes the total cost of measurement actions and the cost of detection errors, and the sample size is the total number of sampling points covering the entire tooth surface.

[0007] Furthermore, the total cost of the measurement action is calculated using the following formula: C M =c m t m In the formula, C M t represents the total cost of the measurement action. m c represents the number of measurements taken by the instrument used. m This indicates the cost of a single measurement operation using the instrument.

[0008] Furthermore, the cost of a single measurement includes the energy and labor costs of the instruments used.

[0009] Furthermore, when performing contact measurements via instrument probes, the formula for calculating the total cost of the measurement action is as follows:

[0010]

[0011] In the formula, C M c represents the total cost of the measurement action. m t represents the cost of a single measurement action. m Indicates the number of measurements; N is the number of tooth surfaces of the large gear, w ai The n represents the weight of the motion cost for measuring the i-th tooth surface. ai This indicates the number of measurements performed on the i-th tooth surface.

[0012] Furthermore, when scanning and measuring using laser, the formula for calculating the total cost of the measurement action is as follows:

[0013]

[0014] In the formula, C M c represents the total cost of the measurement action. m t represents the cost of a single scan operation. m Indicates the number of scans; N is the number of tooth surfaces of the large gear, I j c represents the number of key features contained in the j-th tooth surface. ai w represents the cost per scan of the i-th key feature. ai The n represents the action cost weight for scanning the i-th key feature. ai This represents the number of scans for the i-th key feature.

[0015] Furthermore, the formula for calculating the detection error cost is as follows:

[0016]

[0017] In the formula, C E Indicates the cost of detection error; This represents the probability distribution of the cost of Type A errors, where Type A errors are false positives. EA The cost incurred by the error of discarding data due to measurement; This represents the probability distribution of the cost of Type B errors, where Type B errors are nano-pseudo-errors, c. EB The cost incurred due to measurement-induced false positives; N is the number of tooth surfaces of the large gear.

[0018] Furthermore, the probability distributions of the Type A error cost and the Type B error cost are as follows:

[0019]

[0020]

[0021] In the formula, the characteristic surface S of the measured tooth surface i The tolerance range is LSL i To USL i e i S is the characteristic surface of the tooth surface being measured. i The true value of geometric measurement error, Γ i For its actual measured value, U i This indicates that the instrument measures the characteristic surface S of the tooth surface being measured. i The measurement uncertainty is N, where N is the number of tooth surfaces of the large gear.

[0022] Furthermore, the formula for calculating the total detection cost is as follows: C I =C M +C E

[0023] In the formula, C I C represents the total testing cost. M C represents the total cost of the measurement action. E This represents the cost of detection errors.

[0024] Furthermore, the sample size is the product of the number of sampling lines and the number of sampling points per line.

[0025] The present invention also provides an application of the quantitative sampling method for the full geometric information of the tooth surface of a large gear as described in any one of claims 1 to 9, which is used to determine the optimal critical value of the sample size of a single tooth surface of a large gear or the optimal critical value of the sample size of all tooth surfaces of the entire gear, and to sample the tooth surface of the gear standard according to the optimal critical value of the sample size, and to fit the full geometric information of the tooth surface according to the sampled data to calibrate the measuring instrument.

[0026] Compared with the prior art, the beneficial effects of the present invention include:

[0027] This invention can effectively balance sampling accuracy and sampling cost, avoiding the blind increase of sampling points in pursuit of sampling accuracy, and greatly reducing the total cost of sampling large-size tooth surface contours. Attached Figure Description

[0028] Figure 1 For large tooth surface samples and accuracy theoretical models;

[0029] Figure 2 The rejection region for the upper and lower limits of the tolerance of multiple features on a single large tooth surface;

[0030] Figure 3This is a schematic diagram of the sampling path for the tooth surface.

[0031] Figure 4 This is a test analysis chart showing the measurement accuracy of a single scribe line in an involute template and the size of the sample size. Detailed Implementation

[0032] A quantitative sampling method for full geometric information of a large gear tooth surface includes the following steps: under the constraint of measurement uncertainty set for different feature regions of the large gear tooth surface, with the goal of minimizing the total detection cost, the optimal critical value of the sample size for each different feature is determined. The total detection cost includes the total cost of measurement actions and the cost of detection errors. The sample size is the total number of sampling points covering the entire tooth surface.

[0033] The present invention will now be described in further detail with reference to the accompanying drawings.

[0034] 1) Establish a total testing cost model

[0035] A mechanism model for the relationship between measurement accuracy, sample distribution, and sample size, with the goal of minimizing detection cost, is referenced. Figure 1 As shown.

[0036] Measurement cost function: Taking into account the performance of measuring instruments for large tooth surfaces, measurement strategies, and the tolerance range of the measured tooth surface, the total inspection cost C is... I Divided into total cost of measurement actions C M And detection error cost C E .

[0037] like Figure 1 As shown, optimizing the total detection cost first requires determining the measurement cost, and then determining the relationship between the instrument's measurement uncertainty and the sample size of the measurement data. By quantifying the cost of a single instrument operation and considering the tooth surface measurement strategy, a measurement cost C for the full information sample size of a single tooth surface is established. M With the number of measurements t m Mathematical model for measuring motion cost c m As shown in equation (1). Based on the comprehensive characteristics of the large gear tooth surface, a total measurement cost function can be established.

[0038] C M =c m t m (1)

[0039] In the formula, C M t represents the total cost of the measurement action. m c represents the number of measurements taken by the instrument used. m This indicates the cost of a single measurement operation performed by the instrument used. The cost of a single measurement operation includes the energy and labor costs incurred by the instrument.

[0040] When contact measurement is performed using an instrument probe, the total cost of the measurement action is calculated using the following formula:

[0041]

[0042] In the formula, C M c represents the total cost of the measurement action. m t represents the cost of a single measurement action. m Indicates the number of measurements; N is the number of tooth surfaces of the large gear, w ai The n represents the action cost weight when measuring the i-th tooth surface (considering the unique characteristics of each tooth surface). ai This indicates the number of measurements performed on the i-th tooth surface.

[0043] When scanning and measuring using laser, the total cost of the measurement action is calculated using the following formula:

[0044]

[0045] In the formula, C M c represents the total cost of the measurement action. m t represents the cost of a single scan operation. m Indicates the number of scans; N is the number of tooth surfaces of the large gear, I j c represents the number of key features contained in each tooth surface. a w represents the cost per scan of this key feature. a This represents the action cost weight when scanning this feature, n. ai This indicates the number of scans for the key feature. Key features include various areas to be measured, such as the tooth root, tooth tip, involute, and helix.

[0046] Detection error cost: such as Figure 2 As shown, considering the characteristic surface S of the tooth surface being measured. i The tolerance range is LSL i To USL i The detection error cost is divided into type A (false positive error) and type B (false negative error), with probability distributions as shown in equations (4) and (5), where e i For surface S i The true value of geometric measurement error, Γ i Its actual measured value.

[0047]

[0048]

[0049] The instrument was used to measure the surface S i Measurement uncertainty U iTo constrain the objects, determine the probability of occurrence of type A and type B errors, and introduce the costs of false positive and false negative events to establish a detection cost function model, as shown in equation (6).

[0050]

[0051] In the formula, C E Indicates the cost of detection error; This represents the probability distribution of the cost of Type A errors, where Type A errors are false positives. EA The cost of errors caused by measurement errors (errors where a product that was originally qualified is mistakenly judged as unqualified due to inaccurate measurement). This represents the probability distribution of the cost of Type B errors, where Type B errors are nano-pseudo-errors, c. EB The cost of measurement errors (incorrect measurement results in products that are not actually qualified being mistakenly judged as qualified); N is the number of tooth surfaces of the large gear.

[0052] (ii) Quantitative characterization of sample size and solution method for saturation critical value of large tooth surface features

[0053] Quantitative model of sample size for large tooth surface features: such as Figure 3 As shown, for the three-dimensional curved surface of the large tooth surface, the starting and ending points of the tooth profile, tooth direction sampling interval, and curve features are determined. The action cost of the contact detection system is decomposed, the scanning path strategy is planned, and the total detection cost function model is established using equation (6). For the large tooth surface features, with the set measurement uncertainty as a constraint, the total detection cost function is simulated and optimized in a virtual digital environment to determine the relationship mechanism between the tooth profile, tooth direction sampling interval, and the number of measurements of the detection system, and then to determine the existence law of the saturation region of sample size under the equivalent measurement uncertainty condition.

[0054] Solving for the saturation critical value: For large tooth surface features with known measurement uncertainty U i Under constraints, a stochastic gradient descent method is employed to find the global minimum total detection cost through neural network optimization, thereby obtaining the critical region approaching the global minimum and solving for the quantitative value n of the sample size for each feature. ai and tooth profile, tooth direction sampling intervals Δl1, Δl2 ( Figure 3 In a virtual measurement environment, the full information measurement process of a large gear is simulated to verify the feasibility and stability of the method, establish the optimal measurement strategy for a standard template of a large gear, and standardize its application in the transfer of measurement values.

[0055] refer to Figure 3As shown, when performing contact measurements via the instrument probe, to simplify calculations and operations, the tooth profile sampling interval Δl2 is set to the instrument's usual sampling interval, which determines the number of single-line sampling points. The number of measurements n for the i-th tooth surface is determined by the optimized solution. ai The sample size of the i-th tooth surface can be obtained. The sample size is the product of the number of sampling lines and the number of sampling points per line. Then the number of sampling lines can be obtained, and the size of the tooth direction sampling interval Δl1 can be determined based on the number of sampling lines.

[0056] The sample size is the product of the number of sampling lines and the number of sampling points per line. When performing contact measurements via an instrument probe, the optimal solution for n... ai (Number of measurements for the i-th tooth surface).

[0057] When scanning measurements are performed using lasers, the optimized solution for n... ai This indicates the number of scans for the key feature. The number of scans is equal to the number of sampling lines. The size of the tooth sampling interval Δl1 can be determined based on the number of sampling lines.

[0058] III) Practical Applications

[0059] An application of a large gear tooth surface sampling method is used to determine the optimal critical value of the sample size of a single tooth surface of a large gear or the optimal critical value of the sample size of all tooth surfaces of the entire gear, and to sample the tooth surface of a gear standard according to the optimal critical value of the sample size. Based on the sampling data, the full geometric information of the tooth surface is fitted to calibrate the measuring instrument, including but not limited to coordinate measuring machines, gear measuring centers and other instruments and equipment.

[0060] When the number of tooth surfaces N of the large gear is set to 1, it can be used to determine the optimal critical value of the sample size of a single tooth surface of the large gear.

[0061] refer to Figure 4 As shown, the test results of a 200mm diameter involute template using a gear measuring center indicate that the measurement accuracy of the engraved lines on the involute template decreases with increasing sample size until it stabilizes. Therefore, this project continues to conduct in-depth research on the relationship between the overall measurement accuracy of the large gear surface and the sample size, and provides a quantitative and standardized expression of the measurement process, thereby achieving the overall transfer of the large gear's measurement value. The method is objective and reasonable.

[0062] The above technical solutions are merely specific embodiments of the present invention. For those skilled in the art, based on the principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the technical solutions described in the above specific embodiments of the present invention. Therefore, the foregoing descriptions are only preferred and not restrictive.

Claims

1. A method for quantitative sampling of the full geometric information of a large gear tooth surface, characterized in that, Includes the following steps: Under the constraint of measurement uncertainty set for different feature areas of the large gear tooth surface, with the goal of minimizing the total detection cost, the optimal critical value of the sample size for each different feature is determined. The total detection cost includes the total cost of measurement actions and the cost of detection errors. The sample size is the total number of sampling points covering the entire tooth surface. The formula for calculating the cost of the detection error is as follows: In the formula, Indicates the cost of detection error; Let represent the probability distribution of the cost of Type A errors, where Type A errors are false positives. The cost incurred due to errors in measurement that result in false negatives; This represents the probability distribution of the cost of Type B errors, which are nano-spurious errors. The cost incurred by measurement-induced pseudo-errors; This refers to the number of tooth surfaces on the large gear. The probability distributions of the Type A error cost and the Type B error cost are as follows: In the formula, the characteristic surface of the tooth surface being measured is... The tolerance range is LSL i to USL i , e i The characteristic surface of the tooth surface being measured The true value of geometric measurement error, Γ i Its actual measured value, This indicates that the instrument measures the characteristic surface of the tooth surface being measured. Measurement uncertainty, This refers to the number of tooth surfaces on the large gear.

2. The method for quantitative sampling of full geometric information of the tooth surface of a large gear according to claim 1, characterized in that, The total cost of the measurement action is calculated using the following formula: In the formula, This represents the total cost of the measurement action. This indicates the number of measurements taken by the instrument used. This indicates the cost of a single measurement operation using the instrument.

3. The method for quantitative sampling of full geometric information of the tooth surface of a large gear according to claim 2, characterized in that, The cost of a single measurement includes the energy cost and labor cost of the instruments used.

4. The method for quantitative sampling of the full geometric information of the tooth surface of a large gear according to claim 2, characterized in that, When contact measurement is performed using an instrument probe, the total cost of the measurement action is calculated using the following formula: In the formula, This represents the total cost of the measurement action. This represents the cost of a single measurement action. Indicates the number of measurements; This refers to the number of tooth surfaces on the large gear. Indicates the measurement of the first i Weight of the motion cost of each tooth surface Indicates the first i The number of measurements performed on each tooth surface.

5. The method for quantitative sampling of the full geometric information of the tooth surface of a large gear according to claim 2, characterized in that, When scanning and measuring using laser, the total cost of the measurement action is calculated using the following formula: In the formula, This represents the total cost of the measurement action. Indicates the cost of a single scan operation. Indicates the number of scans; This refers to the number of tooth surfaces on the large gear. Indicates the first The number of key features contained in each tooth surface Indicates the scan of the first The single-transaction cost of each key feature Indicates the scan of the first Action cost weights for key features Indicates the first Number of scans for each key feature.

6. The method for quantitative sampling of the full geometric information of the tooth surface of a large gear according to claim 5, characterized in that, The formula for calculating the total testing cost is as follows: In the formula, This represents the total testing cost. This represents the total cost of the measurement action. This represents the cost of detection errors.

7. The method for quantitative sampling of the full geometric information of the tooth surface of a large gear according to claim 1, characterized in that, The sample size is the product of the number of sampling lines and the number of sampling points per line.

8. An application of a quantitative sampling method for the full geometric information of a large gear tooth surface as described in any one of claims 1 to 7, characterized in that, The optimal critical value for the sample size of a single tooth surface of a large gear or the optimal critical value for the sample size of all tooth surfaces of the entire gear is used to determine the optimal critical value for the sample size. The tooth surfaces of the gear standard are sampled according to the optimal critical value for the sample size, and the full geometric information of the tooth surface is fitted according to the sampled data to calibrate the measuring instrument.

Images