Data driving-physical model fused gear meshing efficiency prediction method and system

Abstract

The invention discloses a data driving-physical model fused gear meshing efficiency prediction method and system, and belongs to the technical field of gear meshing efficiency prediction. The method comprises the following steps: establishing a data driving model for predicting a sliding friction coefficient; constructing a gear pair meshing efficiency model in combination with gear dynamics and kinematics theories; the sliding friction coefficient output by the data driving model is substituted into the gear pair meshing efficiency model, a data driving-physical model fused gear average meshing efficiency prediction model is obtained, and gear meshing efficiency prediction is achieved. Compared with the prior art, the method has the beneficial effects that more than 6000 groups of basic friction test data are learned based on a machine learning algorithm XGBoost, data-driven tooth surface friction coefficient calculation is realized, the obtained friction coefficient is combined with a gear kinematics and dynamics model, and effective prediction of gear meshing power loss and meshing efficiency is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear meshing efficiency prediction, and in particular relates to a data-driven-physical model-fused gear meshing efficiency prediction method and system. Background Art

[0002] Gear transmission is widely used in aerospace, transportation, engineering machinery and other fields due to its high reliability and high transmission efficiency. In the context of the energy crisis, further improvement of the efficiency of gear devices has attracted widespread attention. Excessive power loss will not only reduce the energy economy of the whole machine, but also cause the thermal equilibrium temperature to rise, destroy the normal lubrication system, and cause transmission failure. Meshing power loss is the main form of power loss in heavy-duty gear transmission. Therefore, studying the calculation method of gear meshing power loss and meshing efficiency is crucial to the design of low-energy gear transmission.

[0003] Gear meshing power loss includes sliding and rolling friction losses. Generally, rolling friction loss accounts for a relatively small proportion. Sliding friction loss depends on the tooth surface motion parameters, load parameters and friction coefficient. The meshing efficiency loss of cylindrical gears is summarized as the product of the meshing loss coefficient and the average friction coefficient. The meshing loss coefficient is determined by the geometric characteristics of the gear, such as the number of teeth, helix angle, and overlap. This model is adopted by ISO because it is easy to apply, but rolling friction is ignored, and the load calculation is also relatively rough. A more realistic load distribution can be obtained through gear dynamics modeling. The load distribution model used in the power loss calculation takes into account the flexibility of the gear teeth, and the elastic deformation and load at any point on the tooth surface at each moment can be calculated. The meshing power loss is calculated by considering the coupling effect between gear friction and dynamic characteristics, and the results are in good agreement with the experiment.

[0004] The kinematic and dynamic research of cylindrical gears has been relatively mature, but the calculation model of tooth surface friction coefficient is still imperfect, which directly affects the prediction accuracy of gear meshing efficiency. The reason is that during the gear meshing process, the motion, load, interface temperature, and lubrication degree all continue to undergo complex nonlinear changes, making the theoretical calculation of the tooth surface friction coefficient particularly difficult. Most of the existing tooth surface friction coefficient models are semi-empirical models based on physics, and the calculation accuracy is often limited by the experimental conditions when they were developed. In decades of research, a large amount of basic friction test (double disc, ball disc) data has been accumulated. These data together cover a large range of gear design parameters and operating conditions. In addition, the rise of machine learning technology in recent years has made data-driven tooth surface friction coefficient calculation possible, which has also created conditions for the improvement of gear meshing efficiency models.

[0005] Since most existing gear meshing efficiency prediction methods use a physics-based semi-empirical model to calculate the tooth surface friction coefficient, and the motion, load and lubrication conditions of the tooth surface vary in a complex manner with geometric parameters and working conditions, it is difficult to accurately calculate the friction coefficient from a mechanism perspective. Therefore, the traditional gear friction model has a limited scope of application, which directly affects the prediction accuracy of gear meshing power loss and efficiency, and hinders the optimization of gear transmission devices for efficiency improvement. Summary of the invention

[0006] The purpose of an embodiment of the present invention is to provide a data-driven-physical model fusion gear meshing efficiency prediction method and system, which is based on the machine learning algorithm XGBoost to learn more than 6,000 sets of basic friction test data, realize data-driven tooth surface friction coefficient calculation, and combine the obtained friction coefficient with the gear kinematics and dynamics model to achieve effective prediction of gear meshing power loss and meshing efficiency, thereby solving at least one technical problem involved in the background technology.

[0007] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0008] The embodiment of the present invention provides a data-driven-physical model fusion gear meshing efficiency prediction method, comprising the following steps:

[0009] Step S1, establishing a data-driven model for predicting sliding friction coefficient;

[0010] Step S2, combining gear dynamics and kinematics theory to construct a gear pair meshing efficiency model;

[0011] Step S3, substituting the sliding friction coefficient output by the data-driven model into the gear pair meshing efficiency model, obtaining a data-driven-physical model-fused gear average meshing efficiency prediction model, and realizing gear meshing efficiency prediction.

[0012] Optionally, in step S1, a data-driven model for predicting the sliding friction coefficient is established, specifically including:

[0013] Step S11, collecting a friction coefficient data set;

[0014] Step S12, dividing the collected friction coefficient data set into a training set and a test set;

[0015] Step S13, presetting XGBoost hyperparameters, and training a data-driven model based on the machine learning algorithm XGBoost;

[0016] Step S14, optimizing the hyperparameters of the data-driven model by using the GridSearchCV algorithm;

[0017] Step S15, determining whether the root mean square error of the friction coefficient prediction value output by the data-driven model to the measured value is lower than a threshold value, if not, executing step S14; if yes, executing step S16;

[0018] Step S16, retraining the hyperparameter-optimized data-driven model based on the preset XGBoost hyperparameters to obtain the optimal data-driven model.

[0019] Optionally, in step S11, the friction coefficient data set includes 6468 sets of basic friction data of double-disc tests and ball-disc tests.

[0020] Optionally, in step S15, the threshold is 0.0023.

[0021] Optionally, in step S2, the gear pair meshing efficiency model is expressed by the following formula:

[0022] η=1-P loss / P0

[0023] Where, η is the meshing efficiency of the gear pair; P0 is the input power; P loss is the instantaneous meshing power loss of the gear pair.

[0024] Optionally, the gear pair instantaneous meshing power loss P loss It is expressed by the following formula:

[0025] P loss =P s +P r

[0026] Where P s is the instantaneous sliding friction loss of the gear pair; P r is the instantaneous rolling friction loss of the gear pair. Optionally, the instantaneous sliding friction loss of the gear pair P s It is expressed by the following formula:

[0027] P s =μF n V s

[0028] Where μ is the friction coefficient; F n is the normal load at the contact point; V s is the sliding speed;

[0029] The gear pair instantaneous rolling friction loss P r It is expressed by the following formula:

[0030] P r =F r V r

[0031]

[0032] In the formula, F r is the rolling friction; V r is the scroll speed; is the heat reduction coefficient; G, U, W are dimensionless material parameters, motion parameters and load parameters respectively; R is the comprehensive curvature radius of the tooth profile; ζ is the viscosity-pressure coefficient.

[0033] Optionally, in step S3, the sliding friction coefficient output by the data-driven model is substituted into the gear pair meshing efficiency model to obtain a data-driven-physical model-fused gear average meshing efficiency prediction model, which specifically includes:

[0034] Based on the instantaneous meshing power loss P of the gear pair loss =P s +P r =μF n V s +F r V r , introduce the sliding friction coefficient μ predicted by the data-driven model pre , obtain the instantaneous meshing power loss model of data-driven-physical model fusion:

[0035] P loss,ML =μ pre F n V s +F r V r

[0036] Calculate the average meshing power loss during the meshing cycle It is expressed by the following formula:

[0037]

[0038] Where, B1B2 is the meshing line; x is the distance from the meshing point to point B2 on the meshing line;

[0039] Comprehensive gear pair meshing efficiency model, instantaneous meshing power loss model based on data-driven-physical model fusion, and average meshing power loss during the meshing cycle The average meshing efficiency prediction model of gears based on data-driven and physical model fusion is obtained, which is expressed as follows:

[0040]

[0041] The present invention also provides a gear meshing efficiency prediction system that implements the data-driven-physical model fusion method, comprising:

[0042] A data-driven model building module, which is used to build a data-driven model for predicting sliding friction coefficient;

[0043] Gear pair meshing efficiency model building module, which is used to combine gear dynamics and kinematics theory to build a gear pair meshing efficiency model;

[0044] The gear meshing efficiency prediction module is used to substitute the sliding friction coefficient output by the data-driven model into the gear pair meshing efficiency model to obtain the gear average meshing efficiency prediction model that integrates the data-driven and physical models, thereby realizing the gear meshing efficiency prediction.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] In view of the shortcomings of existing gear meshing efficiency prediction methods, which mostly use physics-based semi-empirical models to calculate the tooth surface friction coefficient, limited application scope and low overall accuracy, a gear meshing efficiency prediction method integrating data-driven and physical model is proposed. More than 6000 sets of basic friction test data are used for XGBoost machine learning to obtain a friction coefficient data-driven model with friction pair speed, stress, roughness and lubricant viscosity as input features; the time-varying friction coefficient output by the data-driven model is substituted into the gear meshing power loss physical model, and the integral median is calculated within the meshing cycle to realize the prediction of gear meshing efficiency under a larger operating range and multiple lubrication conditions. It makes up for the shortcomings of the existing model, takes into account the influence of gear motion parameters, load parameters, roughness and lubrication conditions, and effectively improves the scope of application and prediction accuracy of the gear meshing efficiency model. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0048] Figure 1 A flow chart of a data-driven-physical model-fused gear meshing efficiency prediction method provided by the present invention;

[0049] Figure 2 A flow chart for establishing a data-driven model provided by the present invention;

[0050] Figure 3 A comparison chart of the predicted value and the measured value of the friction coefficient provided by the present invention;

[0051] Figure 4 A diagram showing the movement regularity of the meshing point of the involute tooth profile provided by the present invention;

[0052] Figure 5A structural block diagram of a data-driven-physical model-fused gear meshing efficiency prediction system provided by the present invention;

[0053] Figure 6 This is a diagram of meshing efficiency prediction results for different models provided by the present invention. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] See also Figure 1 As shown, the present invention provides a data-driven-physical model fusion gear meshing efficiency prediction method, comprising the following steps:

[0056] Step S1, establishing a data-driven model for predicting sliding friction coefficient;

[0057] Step S2, combining gear dynamics and kinematics theory to construct a gear pair meshing efficiency model;

[0058] Step S3, substituting the sliding friction coefficient output by the data-driven model into the gear pair meshing efficiency model, obtaining a data-driven-physical model-fused gear average meshing efficiency prediction model, and realizing gear meshing efficiency prediction.

[0059] Recombination Figure 2 As shown, in step S1, a data-driven model for predicting the sliding friction coefficient is established, specifically including:

[0060] Step S11, collecting a friction coefficient data set, where the friction coefficient data set includes 6468 sets of basic friction data of double-disc test and ball-disc test;

[0061] Step S12, dividing the collected friction coefficient data set into a training set and a test set;

[0062] Step S13, presetting XGBoost hyperparameters, and training a data-driven model based on the machine learning algorithm XGBoost, so that a data-driven model with friction pair velocity, stress, roughness, and lubricant viscosity as input features can be obtained;

[0063] Step S14, optimizing the hyperparameters of the data-driven model by using the GridSearchCV (grid search optimization) algorithm;

[0064] Step S15, determining whether the root mean square error (RMSE) of the friction coefficient prediction value output by the data-driven model to the measured value is lower than a threshold value, if not, executing step S14; if yes, executing step S16;

[0065] In this specific embodiment, the threshold is 0.0023, and the comparison between the predicted value and the measured value of the friction coefficient is Figure 3 shown.

[0066] Step S16, retraining the hyperparameter-optimized data-driven model based on the preset XGBoost hyperparameters to obtain the optimal data-driven model.

[0067] In step S2, the gear pair meshing efficiency model is expressed by the following formula:

[0068] η=1-P loss / P0

[0069] Where, η is the meshing efficiency of the gear pair; P0 is the input power; P loss is the instantaneous meshing power loss of the gear pair.

[0070] Furthermore, the instantaneous meshing power loss of the gear pair P loss It is expressed by the following formula:

[0071] P loss =P s +P r

[0072] Where P s is the instantaneous sliding friction loss of the gear pair; P r is the instantaneous rolling friction loss of the gear pair.

[0073] The instantaneous sliding friction loss P of the gear pair s It is expressed by the following formula:

[0074] P s =μF n V s

[0075] Where μ is the friction coefficient; F n is the normal load at the contact point; V s is the sliding speed;

[0076] The gear pair instantaneous rolling friction loss P r It is expressed by the following formula:

[0077] P r =F r V r

[0078]

[0079] In the formula, F r is the rolling friction; V r is the scroll speed; is the heat reduction coefficient; G, U, W are dimensionless material parameters, motion parameters and load parameters respectively; R is the comprehensive curvature radius of the tooth profile; ζ is the viscosity-pressure coefficient.

[0080] In step S3, the sliding friction coefficient output by the data-driven model is substituted into the gear pair meshing efficiency model to obtain a gear average meshing efficiency prediction model fused with the data-driven and physical models, which specifically includes:

[0081] Based on the instantaneous meshing power loss P of the gear pair loss =P s +P r =μF n V s +F r V r , introduce the sliding friction coefficient μ predicted by the data-driven model pre , obtain the instantaneous meshing power loss model of data-driven-physical model fusion:

[0082] P loss,ML =μ pre F n V s +F r V r

[0083] The meshing power loss changes periodically with the rotation of the gear. To calculate the average meshing efficiency of the gear, it is necessary to obtain the average meshing power loss within the meshing cycle. Figure 4 is the movement law of the meshing point of the involute tooth profile, the subscripts 1 and 2 represent the driving wheel and the driven wheel respectively, O is the rotation center, and r a is the radius of the tooth tip circle, r b is the base circle radius, B1B2 is the meshing line. The meshing period of the cylindrical gear end face tooth profile is the meshing point moving along the meshing line by one base circle pitch p. b = |B2A| = |CB1|. When meshing tooth pair 1 moves from point B2 to point C, meshing tooth pair 2 simultaneously moves from point A to point B1 and generates power loss. Therefore, the average meshing power loss during the meshing cycle is Calculated by the following formula:

[0084]

[0085] Where, B1B2 is the meshing line; x is the distance from the meshing point to point B2 on the meshing line;

[0086] Comprehensive gear pair meshing efficiency model, instantaneous meshing power loss model based on data-driven-physical model fusion, and average meshing power loss during the meshing cycle The average meshing efficiency prediction model of gears based on data-driven and physical model fusion is obtained, which is expressed as follows:

[0087]

[0088] See also Figure 5 As shown, the present invention also provides a gear meshing efficiency prediction system that implements the data-driven-physical model fusion method described above, including a data-driven model establishment module 1, a gear pair meshing efficiency model construction module 2 and a gear meshing efficiency prediction module 3.

[0089] The data-driven model building module 1 is used to build a data-driven model for predicting the sliding friction coefficient.

[0090] The gear pair meshing efficiency model construction module 2 is used to construct a gear pair meshing efficiency model by combining gear dynamics and kinematics theory.

[0091] The gear meshing efficiency prediction module 3 is used to substitute the sliding friction coefficient output by the data-driven model into the gear pair meshing efficiency model to obtain a gear average meshing efficiency prediction model integrating the data-driven and physical models, thereby realizing the gear meshing efficiency prediction.

[0092] The data-driven-physical model fusion gear meshing efficiency prediction method provided by the present invention is described in detail below with reference to specific embodiment 1.

[0093] Example 1

[0094] According to the design parameters in Table 1, this method is used to calculate the time-varying friction coefficient of a cylindrical spur gear at a pinion speed of 2175rpm and a pinion torque of 94-535N·m. The comprehensive roughness of the tooth surface is 1.17μm. The gear elastic modulus is 207GPa and the Poisson's ratio is 0.25. Eastman2380 oil spray lubrication is used, and the oil pool temperature is 90±3℃ during stable operation. The gear transmission efficiency test is carried out according to the above parameter conditions.

[0095] Table 1 Design parameters of cylindrical spur gears

[0096] parameter unit Numeric Center distance mm 91.5 Working tooth width mm 20 Number of pinion teeth \ 16 Number of teeth on large gear \ 24 Pinion gear modification coefficient \ 0.8532 Gear modification coefficient \ -0.5 Normal modulus mm 4.5 Pressure Angle ° 20

[0097] Comparison of meshing efficiency prediction results based on fusion model and experimental results Figure 6As shown. The dotted line represents the test results, and the solid line is the predicted result. It can be seen from the test value curve that within the test range, the gear meshing efficiency increases with the increase of torque and tends to a certain peak value. The data-driven-physical fusion model effectively restores this change law. Affected by the discreteness of the training data, the prediction results fluctuate in a small range. The maximum error between the predicted value and the test value is 0.206%, and the average error is 0.048%, which has good consistency.

[0098] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0099] In addition, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0100] The embodiments of the present invention are described above, but the present invention is not limited to the above-mentioned specific implementation modes. The above-mentioned specific implementation modes are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A data-driven-physical model fusion gear meshing efficiency prediction method, characterized in that: The steps include: Step S1, establishing a data-driven model for predicting sliding friction coefficient; Step S2, combining gear dynamics and kinematics theory to construct a gear pair meshing efficiency model; Step S3, substituting the sliding friction coefficient output by the data-driven model into the gear pair meshing efficiency model, obtaining a data-driven-physical model-fused gear average meshing efficiency prediction model, and realizing gear meshing efficiency prediction.

2. The method according to claim 1, characterized in that In step S1, a data-driven model for predicting the sliding friction coefficient is established, specifically including: Step S11, collecting a friction coefficient data set; Step S12, dividing the collected friction coefficient data set into a training set and a test set; Step S13, presetting XGBoost hyperparameters, and training a data-driven model based on the machine learning algorithm XGBoost; Step S14, optimizing the hyperparameters of the data-driven model by using the GridSearchCV algorithm; Step S15, determining whether the root mean square error of the friction coefficient prediction value output by the data-driven model to the measured value is lower than a threshold value, if not, executing step S14; if yes, executing step S16; Step S16, retraining the hyperparameter-optimized data-driven model based on the preset XGBoost hyperparameters to obtain the optimal data-driven model.

3. The method according to claim 2, characterized in that In step S11, the friction coefficient data set includes 6468 sets of basic friction data of double-disc test and ball-disc test.

4. The method according to claim 2, characterized in that: In step S15, the threshold is 0.0023.

5. The method according to claim 1, characterized in that In step S2, the gear pair meshing efficiency model is expressed by the following formula: n=1-P loss / P0 Where, η is the meshing efficiency of the gear pair; P0 is the input power; P loss is the instantaneous meshing power loss of the gear pair.

6. The method according to claim 5, characterized in that The gear pair instantaneous meshing power loss P loss It is expressed by the following formula: P loss =P s +P r Where P s is the instantaneous sliding friction loss of the gear pair; P r is the instantaneous rolling friction loss of the gear pair.

7. The method according to claim 6, characterized in that The instantaneous sliding friction loss P of the gear pair s It is expressed by the following formula: P s =μF n V s Where μ is the friction coefficient; F n is the normal load at the contact point; V s is the sliding speed; The gear pair instantaneous rolling friction loss P r It is expressed by the following formula: P r =F r V r In the formula, F r is the rolling friction; V r is the scroll speed; is the heat reduction coefficient; G, U, W are dimensionless material parameters, motion parameters and load parameters respectively; R is the comprehensive curvature radius of the tooth profile; ζ is the viscosity-pressure coefficient.

8. The method according to claim 7, characterized in that In step S3, the sliding friction coefficient output by the data-driven model is substituted into the gear pair meshing efficiency model to obtain a gear average meshing efficiency prediction model fused with the data-driven and physical models, which specifically includes: Based on the instantaneous meshing power loss P of the gear pair loss =P s +P r =μF n V s +F r V r , introduce the sliding friction coefficient μ predicted by the data-driven model pre , obtain the instantaneous meshing power loss model of data-driven-physical model fusion: P loss,ML =μ pre F n 5 s +F r 5 r Calculate the average meshing power loss during the meshing cycle It is expressed by the following formula: Where, B1B2 is the meshing line; x is the distance from the meshing point to point B2 on the meshing line; Comprehensive gear pair meshing efficiency model, instantaneous meshing power loss model based on data-driven-physical model fusion, and average meshing power loss during the meshing cycle The average meshing efficiency prediction model of gears based on data-driven and physical model fusion is obtained, which is expressed as follows:

9. A gear meshing efficiency prediction system that implements the data-driven-physical model fusion method of any one of claims 1 to 8, characterized in that: include: A data-driven model building module, which is used to build a data-driven model for predicting sliding friction coefficient; Gear pair meshing efficiency model building module, which is used to combine gear dynamics and kinematics theory to build a gear pair meshing efficiency model; The gear meshing efficiency prediction module is used to substitute the sliding friction coefficient output by the data-driven model into the gear pair meshing efficiency model to obtain the gear average meshing efficiency prediction model that integrates the data-driven and physical models, thereby realizing the gear meshing efficiency prediction.

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