CN117874955A - Gear life fatigue prediction method based on finite element analysis - Google Patents
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Abstract
The invention relates to a gear life fatigue prediction method based on finite element analysis. The method comprises the steps of using ABAQUS and FRANC3D simulation construction samples to respectively analyze single variable data under stress ratio, crack length and crack angle variables; establishing data analysis of the single variable, and verifying the influence of the single variable on the residual cycle life; performing influence analysis on the residual cycle life of the gear engagement model under the single variable combination and the composite factors; constructing a BP neural network structure, and establishing a nonlinear mapping relation between influence factors and contact fatigue life; and inputting data parameters to be predicted into the BP neural network after training is completed, and predicting the residual life. Compared with the prior art, the method has the advantages that the residual contact fatigue life of the gear is predicted from a single variable factor to a multi-variable factor, the operation is simple, the finite element simulation times are reduced by combining a finite element technology and a machine learning algorithm, the residual life is more conveniently and directly predicted, and a novel technical method is provided for intelligent maintenance prediction of the working gear.
Description
Technical Field
The invention relates to the technical field of gear maintenance, in particular to a method for predicting the reliability life of a gear based on finite element analysis and application thereof, which provide basis for optimizing a gear use scheme.
Background
The gear mechanism is a transmission mechanism which is most widely applied to various mechanisms, and is used for transmitting motion and power between any two shafts in space by means of direct contact of tooth profiles of gear teeth, and has the advantages of high transmission efficiency, reliable work, stable transmission ratio and the like. Gears are one of the non-replaceable mechanical parts. It is therefore extremely important to investigate the cause of failure of gears to increase the reliable life of the working system. However, the gear failure modes are various due to the factors of different applications of gear materials, continuous action of cyclic load, complex and variable working conditions and the like, wherein fatigue failure is one of the main failure reasons. Under the working condition of the gear, when the bending stress exceeds the fatigue limit, micro cracks are generated on gear teeth of the gear, and the cracks gradually expand along with the continuous application of working load, so that the gear teeth are broken and the gear fails.
In the existing gear life fatigue prediction research, there are test research methods under different working conditions, nominal stress methods based on S-N curves, gradually developed finite element analysis calculation methods and the like. The test research method has accurate results and strong reliability, but consumes long time period. And meanwhile, due to the complexity of working conditions, such as the influence of the properties of materials, the influence of working loads and the like, difficulties are added to the research. The invention shortens the research time, determines the reliability life prediction under complex working conditions, carries out model construction training under machine learning by simulating a construction sample by means of a digital research method, so as to more conveniently and directly predict the residual life of the gear, reduce the finite element simulation times and provide a new method for intelligently maintaining the gear fatigue life prediction method.
Disclosure of Invention
The invention mainly aims at providing a gear life prediction method based on the defect generation condition in the background of the prior art. The method has the advantages of simple operation, low cost and reduced finite element simulation times.
The invention relates to a gear fatigue life prediction method based on defect generation, which comprises the following steps:
s1, collecting fatigue life data of a gear under the expected fatigue working condition through a finite element analysis software ABAQUS and a crack analysis software FRANC3D simulation structure sample, and determining the crack length of the gear, the angle of the crack based on Z-axis deflection and the stress ratio of the working load as influencing factors of the fatigue life of the gear under the working condition.
S2, taking the influence factors as input parameters of the BP neural network, and taking the fatigue life of the corresponding gear as output parameters. And setting a proper proportion of training samples and test samples in the BP neural network, setting the number of hidden layers according to the determined input parameters and the determined output parameters, and training the BP neural network to obtain a nonlinear mapping relation between influencing factors and fatigue life. And S3, calculating and comparing the precision of the neural network, and resetting the BP neural network related parameters when the precision does not meet the set value, and training again. When the precision can meet the set value, the BP neural network model after completion is obtained, so that the contact fatigue life can be predicted.
S4, inputting parameters of the sample to be predicted into the BP neural network after training is successful, and predicting the service life.
In the above, the specific steps of S1 are:
the gear meshing model is established through three-dimensional modeling software, a three-tooth model is selected and is guided into ABAQUS software, material property parameters, proper grids, load conditions, interaction and the like which meet working conditions are established, static force analysis of the gear model is carried out, after the whole static force process is obtained, the specific position of stress concentration can be obtained at the tooth root, and the specific position can be used as the generation position of defects.
And (3) importing the static analysis file into a special crack analysis file FRANC3D, and establishing different defect conditions so as to obtain a result which is more applicable to the common conditions, setting crack extension parameters, wherein the parameters are fit with the actual working conditions, and the final crack extension length and the stress intensity factor trend of the cycle life can be determined. And collecting fatigue life under different defect conditions and corresponding working condition parameter data under the condition of completing the simulation construction sample.
To verify the influence of more complex influencing factors on the residual life of gear engagement containing cracks, an experimental method based on control variables is established based on the initial length of the cracks, the load stress ratio and the deflection angle of the cracks based on a Z axis are respectively established as influencing factors, single variable factor analysis is carried out by using Origin data analysis software, the relation between the initial length of the cracks and the fatigue life is respectively verified, a proper function model is established, the trend change of related data is analyzed, and the factor correlation is judged.
In the above, the specific step of S2 is:
after verifying that the initial length of the crack, the load stress ratio and the deflection angle of the crack based on the Z axis are influence factors, constructing a BP neural network prediction model by means of MATLAB software numerical computing environment, taking the factors as characteristic values of the defect-containing model as input parameters of the BP neural network, taking the fatigue life corresponding to the characteristic values as output parameters of the BP neural network, and obtaining a parameter sample of the whole BP neural network, so that the influence analysis on the cycle life under the multivariate factor is carried out, and finally the fatigue life prediction can be carried out.
Setting a BP neural network, firstly setting a proper training set and a proportion of a test set, then setting the hidden layer number of the BP neural network according to input parameters and output parameters, training the BP neural network, and finally judging whether the BP neural network is successfully trained or not by taking the average absolute percentage error (MAPE) of a predicted value and an actual value in the test set as an evaluation index.
The specific steps of S4 are as follows:
repeating the specific process of the step S1 to obtain the simulated residual life of the new sample, taking the stress ratio, the crack length and the crack angle in the sample to be tested as input parameters, and predicting the residual life of the gear meshing model through the trained BP neural network. And performing error analysis with the simulated residual life to judge the feasibility of the method.
The beneficial effects of the invention are as follows:
according to the invention, a training prediction model is constructed by combining a method of simulating a construction sample and a finite element analysis method with machine learning, so that the residual life of the gear can be predicted more conveniently and directly, the finite element simulation times are reduced, and the actual working efficiency is increased; selecting crack length, crack angle and stress ratio as effective factors for influencing the reliability life of the existing micro-gap crack gear, and performing multivariate simulation working condition analysis under the working condition analysis influenced by single variables; the operation is simple, the flow is clear, and the practical engineering application is convenient.
Drawings
The drawings of the present invention are described as follows:
FIG. 1 is a flowchart of an embodiment of a gear life prediction method based on defect occurrence;
FIG. 2 is a graph of crack length versus gear fatigue life;
FIG. 3 is a graph of crack angle versus gear fatigue life;
FIG. 4 is a graph of stress ratio versus gear fatigue life
Detailed Description
The invention is further illustrated by the following specific examples:
as shown in fig. 1, the present embodiment includes the steps of:
s1, under a simulation structure sample, collecting data of initial defects and corresponding residual lives
The method comprises the steps of using SolidWorks three-dimensional modeling software to establish a gear meshing model with relevant parameters, selecting a three-tooth model, introducing the three-tooth model into ABAQUS software, establishing material attribute parameters, grids, load conditions, interaction and the like which meet working conditions, performing static force analysis to obtain an initial gear working condition, analyzing the initial gear working condition to obtain a specific position of stress concentration at a tooth root after a static force process, and taking the specific position as a defect occurrence position.
The existing ABAQUS static analysis file is imported into special crack analysis software FRANC3D, the actual condition when defects are found in the actual working process is simulated, the crack length is expanded to 1mm to be used as failure judgment, crack expansion parameters are set, the parameters are attached to the actual working conditions, and the stress intensity factor trend of the final crack expansion length and the cycle life can be determined. And collecting fatigue life under different defect conditions and corresponding working condition parameter data under the condition of completing the simulation construction sample. The invention discloses an experimental method based on control variables, which is characterized in that firstly, under the condition that initial length of cracks, load stress ratio and deflection angle of the cracks based on Z axis are taken as influencing factors, single variable factor analysis is respectively carried out, the relation between the initial length of the cracks, the load stress ratio and the cycle life is respectively verified, and a proper function model is established to judge the relativity.
The method comprises the steps of performing functional relation curve fitting between a single variable and a cycle life through a special data analysis software Origin, firstly inputting data of each variable and the corresponding cycle life in a workbook, and then drawing a relation graph to obtain a relation type showing exponential correlation between the crack length and the residual cycle life, wherein the stress ratio and the cycle life show exponential correlation; and for the crack angle, the left deflection and the right deflection show different related trends, so that the functional relation model is respectively built, and the two deflection are exponentially related.
Functional relationship between the above-mentioned single factor and cycle life:
crack length: 6338840.370 exp (-x/0.443) +4662196.064
Crack angle: 450574.267 exp (-x/26.756) +6587068.294 (left hand side)
2418506.847 x exp (-x/204.990) +9510059.471 (right hand side)
Stress ratio: 206043.734 x exp (8.045 x) +5455764.970 x exp (2.047 x)
The single factors are all exponentially related to the residual cycle life, and the functional relationship model is not completely consistent, but the correlation between each single factor and the residual cycle life is also shown. The relationship between the univariate and fatigue life is plotted as shown in fig. 2, 3 and 4.
The following table 1 is part of the relevant data:
TABLE 1
S2, building and training BP neural network
After verifying that the initial length, the load stress ratio and the deflection angle of the crack based on the Z axis are influence factors, taking the factors as a sample A of input parameters in a working area, normalizing the corresponding cycle life under the condition in the sample A as an output parameter sample B, constructing a BP neural network prediction model by depending on a MATLAB software numerical computing environment, and using the sample A and the sample B for a data set of BP neural network training.
And setting a proper training set and a proportion of a test set, setting the number of hidden layers according to the input parameters and the output parameters, and training the BP neural network. And judging whether the BP neural network is successfully trained or not by taking the average absolute percentage error (MAPE) of the predicted value and the actual value in the test set as an evaluation index. If the data result according to the judgment does not accord with the preferred condition, retraining or modifying the number of the hidden layers.
Table 2 below shows the test set related parameters and MAPE index:
| test set | Angle of crack | Stress ratio | Crack length | Actual life span | MAPE(％) |
| Data set 1 | -40 | 0.3 | 0.38 | 14708030 | 1.874 |
| Data set 2 | -40 | 0.2 | 0.4 | 10758540 | 4.772 |
| Data set 3 | -30 | 0.2 | 0.42 | 9767364 | 8.299 |
| Data set 4 | -10 | 0.3 | 0.44 | 12647680 | 1.027 |
TABLE 2
S3, randomly selecting a plurality of groups of parameters, carrying out S1, taking the stress ratio, the crack length and the crack angle in a sample to be tested as input parameters, wherein the stress ratio range is-0.5-0.5, the crack length is 0.28-0.52 mm, the crack angle (according to deflection, left deflection is regarded as negative angle for simple calculation) is-60 degrees, and carrying out residual life prediction of the gear meshing model by using a trained BP neural network.
And S4, performing error calculation on the simulation life and the predicted life, and verifying the reliability of the whole prediction method as shown in a table 3.
Table 3 below shows the results of the partial validation set:
| data to be predicted | Crack length | Angle of crack | Stress ratio | Actual data | Error (%) |
| Data set 1 | 0.36 | 40 | 0.2 | 10255180 | 0.85 |
| Data set 2 | 0.42 | 20 | 0.3 | 12878910 | 3.39 |
Table 3.
Claims (4)
1. A gear fatigue life prediction method based on finite element analysis is characterized by comprising the following steps:
s1, collecting fatigue life data of a gear under the fatigue working condition of an expected gear through a finite element analysis software ABAQUS and a crack analysis software FRANC3D simulation structure sample, and determining the crack length of the gear, the angle of the crack based on Z-axis deflection and the stress ratio of the working load as influencing factors of the fatigue life of the gear under the working condition;
s2, taking the influence factors as input parameters of the BP neural network, and taking the fatigue life of the corresponding gear as output parameters: setting a proper proportion of training samples and test samples in the BP neural network, setting the number of hidden layers according to the determined input parameters and the determined output parameters, and training the BP neural network to obtain a nonlinear mapping relation between influencing factors and fatigue life;
s3, calculating and comparing the precision of the neural network, and resetting the BP neural network related parameters when the precision does not meet the set value, and training again; when the precision can meet the set value, a BP neural network model after completion is obtained, so that the contact fatigue life can be predicted;
s4, inputting parameters of the sample to be predicted into the BP neural network after training is successful, and predicting the service life.
2. The gear fatigue life prediction method based on the defect generation situation according to claim 1, wherein the specific method of S1 is as follows:
establishing a gear meshing model through three-dimensional modeling software, selecting a three-tooth model, introducing the three-tooth model into ABAQUS software, establishing material attribute parameters, proper grids, load conditions, interaction and the like which meet working conditions, performing static force analysis on the gear model, obtaining a specific position of stress concentration after the whole static force process, and taking the specific position as a generation position of a defect at a tooth root;
leading the static analysis file into a special crack analysis file FRANC3D, establishing different defect conditions so as to obtain a result which is more applicable to common conditions, setting crack extension parameters, and enabling the parameters to be attached to actual working conditions, wherein the stress intensity factor trend of the final crack extension length and the cycle life can be determined; collecting fatigue life under different defect conditions and corresponding working condition parameter data under the condition of completing a simulation construction sample;
to verify the influence of more complex influencing factors on the residual life of gear engagement containing cracks, an experimental method based on control variables is established based on the initial length of the cracks, the load stress ratio and the deflection angle of the cracks based on a Z axis are respectively established as influencing factors, single variable factor analysis is carried out by using Origin data analysis software, the relation between the initial length of the cracks and the fatigue life is respectively verified, a proper function model is established, the trend change of related data is analyzed, and the factor correlation is judged.
3. The gear fatigue life prediction method based on the defect generation situation according to claim 1, wherein the specific method of S2 is as follows:
after verifying that the initial length of the crack, the load stress ratio and the deflection angle of the crack based on the Z axis are influence factors, constructing a BP neural network prediction model by means of MATLAB software numerical computing environment, taking the factors as characteristic values of the defect-containing model, taking the characteristic values as input parameters of the BP neural network, taking the fatigue life corresponding to the characteristic values as output parameters of the BP neural network, and obtaining a parameter sample of the whole BP neural network, so that the influence analysis on the cycle life under the multivariate factor is carried out, and finally, the fatigue life can be predicted;
setting a BP neural network, and performing proper proportion setting of a training set and a testing set; setting the number of hidden layers of the BP neural network according to the input parameters and the output parameters, and training the BP neural network; and measuring whether the BP neural network is successfully trained by taking the average absolute percentage error (MAPE) of the predicted value and the actual value in the test set as an evaluation index.
4. The gear fatigue life prediction method based on the defect generation situation according to claim 1, wherein the specific method of S4 is as follows:
repeating the specific process of the step S1 to obtain the simulated residual life of the new sample, taking the stress ratio, the crack length and the crack angle in the sample to be tested as input parameters, and predicting the residual life of the gear meshing model through the BP neural network after training; and performing error analysis with the simulation life to judge the feasibility of the method.
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