CN117709152A - Method for predicting meshing stiffness of small-modulus powder metallurgy gear with multiple pores - Google Patents
Method for predicting meshing stiffness of small-modulus powder metallurgy gear with multiple pores Download PDFInfo
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Abstract
The invention discloses a method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores, which belongs to the technical field of gear transmission, and the method comprises the steps of establishing a finite element contact model of the gear with the pores to reveal the change of the meshing stiffness of the gear caused by the porosity; solving by utilizing finite element analysis software, and comparing with a potential energy method to verify the rationality and reliability of the model; introducing a rigidity correction coefficient, providing a rigidity correction potential energy method formula containing pores, and solving the correction coefficient by using a constraint optimization algorithm; and establishing a rigidity correction coefficient prediction model based on a feedforward neural network, and predicting time-varying meshing rigidity within a certain porosity range. The application finds that the meshing stiffness variation and the porosity variation show a certain linear relation, when the porosity is increased by 2%, the root mean square value of the meshing stiffness in the gear meshing period is reduced by 4.8%, and the research result has certain guiding significance on the dynamic analysis of the gear transmission system, noise reduction and life extension.
Description
Technical Field
The invention belongs to the technical field of gear transmission, and particularly relates to a method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores.
Background
The small-modulus powder metallurgy gear is widely applied to the fields of automobile industry, military industry manufacturing industry, electric tools, household appliances, toys and the like due to the advantages of high precision, high strength, low noise, energy conservation, environmental protection and the like. In the process of press forming and sintering, the powder metallurgy gear inevitably forms pores, which account for 6% -14% of the gear matrix. Due to the existence of the pores, the meshing rigidity of the gears can be influenced to a certain extent. Therefore, the correlation rule between the porosity of the small-modulus powder metallurgy gear with the pores and the meshing stiffness of the gear is ascertained, and the method has certain guiding significance for subsequent research on the dynamics characteristics of the small-modulus powder metallurgy gear and suppression of vibration noise of the gear.
The gear can generate important dynamic excitation in the meshing transmission process, the meshing stiffness is not only important internal excitation, but also one of important parameters for modeling gear dynamics, and the working performance and stability of a gear transmission system are both related to the meshing stiffness. Through high-precision time-varying meshing stiffness calculation, researchers can better understand the failure mechanism, dynamic response and inherent characteristics of the gear system. Researchers have done much work on solving the gear engagement stiffness, which is mainly divided into three methods: analytical methods, experimental methods and finite element methods.
The analysis method adopts a relatively complex formula to establish an analysis model of the gear, and potential energy rules based on the Weber-Banaschek method are most widely applied in the numerical analysis method. The analytic method is ideal for model consideration, the solving speed is high, but the limitation is large, and if an actual model is complex, the analytic method can not model and solve.
Along with the continuous updating of the measurement technology and experimental equipment, a learner measures the meshing stiffness of the gear by using an experimental method, and the result is accurate and reliable. Meanwhile, the experimental method can study the influence of different factors on the gear engagement rigidity by changing experimental conditions, which is beneficial to deep understanding of the gear engagement mechanism. However, the experimental method has higher requirements on equipment and conditions, professional experimental equipment and technicians are required to operate, and the cost is higher; moreover, the experimental method can only measure the gear engagement stiffness under specific conditions, can not fully reflect the gear engagement performance, and needs to be comprehensively evaluated by combining other testing methods.
As computer runnability continues to increase, finite element methods based on numerical analysis are increasingly being used to solve for gear mesh stiffness. The finite element method is a numerical calculation-based method, has many advantages compared with the traditional test method, and can simulate the meshing condition of gears under various working conditions. However, the prior art has studied the time-varying meshing stiffness of gears without voids, focusing mainly on the effects of torsional stiffness, root cracking, pitting, tooth profile modification, etc. of the gears on the meshing stiffness of the gears. The rigidity of the gear is weakened by pores generated in the powder metallurgy gear forming process, the influence of the pores on the gear meshing rigidity is rarely researched aiming at the influence factors, and the influence of the pores on the rigidity of the contact, bending, compression, shearing and matrix is difficult to consider simultaneously based on a theoretical calculation formula of a potential energy method.
Disclosure of Invention
The invention discloses a method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores, which comprises the steps of establishing a finite element contact model of the gear with the pores by combining finite element contact analysis, researching the influence rule of the porosity on the meshing stiffness of the powder metallurgy gear, introducing a pore stiffness correction coefficient to correct a potential energy method, solving the correction coefficient by using a constraint optimization algorithm, establishing a neural network-based stiffness correction coefficient prediction model, predicting time-varying meshing stiffness within a certain porosity range, and providing theoretical support for vibration reduction and noise reduction design of the powder metallurgy gear, so that at least one technical problem related in the background technology can be effectively solved.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores comprises the following steps:
step 1, establishing a finite element contact model of a small-modulus powder metallurgy gear with multiple pores;
step 2, solving a finite element contact model, calculating the time-varying meshing stiffness of the gear, comparing with a potential energy method, and verifying the rationality and reliability of the model;
step 3, introducing a rigidity correction coefficient, correcting the gear time-varying meshing rigidity under the potential energy method, establishing a rigidity correction potential energy method formula containing pores, and solving the rigidity correction coefficient by using a constraint optimization algorithm;
and 4, establishing a rigidity correction coefficient prediction model based on a feedforward neural network, and predicting time-varying meshing rigidity within a certain porosity range.
As a preferred improvement of the invention, the small modulus powder metallurgy gear containing multiple pores is prepared from an iron-based powder metallurgy material F-0000-20.
As a preferred improvement of the present invention, the parameters of the finite element contact model are: gear module m=0.5 mm, pressure angle α=20o, pinion number z 1 =17, big gear number z 2 Pinion width b1=1 mm, and bull width b2=1 mm, =31.
As a preferred improvement of the present invention, the establishing of the finite element contact model of the small-modulus powder metallurgy gear containing multiple pores requires setting random irregular pores as uniform defects of regular grid cells, and specifically includes:
splitting the single-tooth model into a plurality of hexahedrons which are beneficial to controlling the grid size, dividing the grids, compiling a script program capable of deleting the finite element units based on secondary development of finite element software, realizing the function of deleting the finite element unit grids according to a preset percentage, simulating the pore structure of the powder metallurgy gear, and then assembling to form the finite element contact model of the powder metallurgy gear considering the pore influence.
As a preferred improvement of the present invention, step 2 specifically comprises the steps of:
respectively setting rigid body reference points on the rotation axes of the pinion and the large gear, establishing coupling constraint between the reference points and the gear tooth inner gear ring, and controlling the movement and stress of the gears by setting boundary conditions on the reference points;
solving by finite element analysis software to obtain an angular displacement value of the gear, and processing the data to obtain a meshing stiffness curve;
and according to the meshing stiffness curve, comparing the meshing stiffness in one meshing period during stable meshing with a potential energy method, and verifying the rationality and reliability of the model.
As a preferred improvement of the present invention, in the third step, the expression of the constraint optimization algorithm is as follows:
wherein,formula k for representing rigidity correction potential energy method h For contact stiffness, k a For compressive stiffness, k b For bending stiffness, k s For shear stiffness, k f For matrix stiffness, k is corrected single tooth mesh stiffness, x h For the contact stiffness correction factor, x a For the compression stiffness correction factor, x b To bend justCoefficient of degree correction, x s For shear stiffness correction factor, x f Lambda is the matrix stiffness correction coefficient i For the matrix rigidity correction coefficient of the existing potential energy method, RMS represents taking a root mean square value, K, of the rigidity value in the meshing period e For the meshing stiffness values obtained by the finite element method, lb represents the lower bound of the solution, ub represents the upper bound of the solution, x 0 Representing the initial value of the solution.
As a preferred improvement of the present invention, step 4 specifically includes:
step 41, a sample set is established, and the rigidity correction coefficient obtained in the step 3 is divided into a training set, a verification set and a test set according to the proportion in a uniform sampling mode;
step 42, model training, namely taking the porosity as input, taking the rigidity correction coefficients under different porosities as training targets, using a least square objective function to combine the conjugate and the steepest descent method to obtain the optimal parameters of the feedforward neural network model, determining the minimum point of the least square objective function, and further establishing a nonlinear mapping relation between the porosity and the rigidity correction coefficients;
and 43, applying the feedforward neural network model obtained through training to different porosities to obtain a correction coefficient value under any porosity in a training range, thereby further obtaining the time-varying meshing stiffness of the small-modulus powder metallurgy gear under any porosity.
The beneficial effects of the invention are as follows:
1. according to the method, a finite element contact model containing the pore gear is established by combining finite element contact analysis, the influence rule of porosity on the meshing stiffness of the powder metallurgy gear is researched, a pore stiffness correction coefficient is introduced to correct a potential energy method, a constraint optimization algorithm is utilized to solve the correction coefficient, finally, a stiffness correction coefficient prediction model based on a neural network is established, and time-varying meshing stiffness in a certain porosity range can be predicted, so that theoretical support is provided for vibration reduction and noise reduction design of the powder metallurgy gear;
2. the invention discovers that the change of the meshing stiffness of the gear pair and the change of the porosity have a certain linear relation, when the porosity is increased by 2%, the root mean square value of the meshing stiffness in the gear meshing period is reduced by 4.8%, and the research result has a certain guiding significance on the dynamic analysis of a gear transmission system, noise reduction and life extension.
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For a clearer description of the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly introduced below, it being obvious that the drawings in the description below are only some embodiments of the present invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art, wherein:
FIG. 1 is a pictorial view of a powder metallurgy gear provided herein;
FIG. 2 is a schematic diagram of a single tooth model split provided herein;
FIG. 3 is a schematic view of a powder metallurgy gear single tooth finite element contact model provided by the application;
FIG. 4 is a graph of the meshing stiffness of a standard involute spur gear provided herein;
FIG. 5 is a graph of engagement stiffness during an engagement cycle for stable engagement as provided herein;
fig. 6 (a) - (f) are graphs of meshing stiffness at different porosities after substituting the stiffness correction coefficient into the formula of the pore correction potential energy method, wherein the porosity of the graph (a) is 0%, the porosity of the graph (b) is 6%, the porosity of the graph (c) is 8%, the porosity of the graph (d) is 10%, the porosity of the graph (e) is 12%, and the porosity of the graph (f) is 14%.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that all directional indicators (such as up, down, left, right, front, and rear … …) in the embodiments of the present invention are merely used to explain the relative positional relationship, movement, etc. between the components in a particular posture (as shown in the drawings), and if the particular posture is changed, the directional indicator is changed accordingly.
Furthermore, descriptions such as those referred to as "first," "second," and the like, are provided for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implying an order of magnitude of the indicated technical features in the present disclosure. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.
In the present invention, unless specifically stated and limited otherwise, the terms "connected," "affixed," and the like are to be construed broadly, and for example, "affixed" may be a fixed connection, a removable connection, or an integral body; can be mechanically or electrically connected; either directly or indirectly, through intermediaries, or both, may be in communication with each other or in interaction with each other, unless expressly defined otherwise. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
In addition, the technical solutions of the embodiments of the present invention may be combined with each other, but it is necessary to be based on the fact that those skilled in the art can implement the technical solutions, and when the technical solutions are contradictory or cannot be implemented, the combination of the technical solutions should be considered as not existing, and not falling within the scope of protection claimed by the present invention.
The materials used for the powder metallurgy gear are generally formed by mixing materials such as metal, carbon, silicon and the like according to a certain proportion, and the materials are different according to different purposes. The small modulus metal gear is mostly made of iron-based powder metallurgy materials, and the gear processed by the material has good wear resistance and strong compactness, and can be soaked with a certain proportion of lubricating oil by controlling the porosity so as to achieve the function of self lubrication. The application takes the iron-based powder metallurgy material F-0000-20 as a gear raw material, and explores the influence of the porosity on the meshing stiffness.
F-0000-20 is a powder metallurgy material for manufacturing gears with high speed, high strength and high stability, and is widely used because of its excellent mechanical properties, and its material properties are shown in Table 1.
TABLE 1F-0000-20 Material Properties
| Number plate | Young's modulus E (Gpa) | Poisson ratio v | Density ρ (g/mm) 3 ) |
| F-0000-20 | 160 | 0.28 | 7.3 |
Because the small modulus gear is difficult to process, the processing precision is difficult to ensure, and the cost is difficult to control by adopting a traditional experimental method. With the high-speed development of computer and finite element analysis software, the finite element method is widely applied to the design of various fields such as aviation, automobiles, ships, engineering machinery and the like, and the mechanical characteristics of a mechanical structure can be accurately calculated. The basic parameters of the gear pair are shown in table 2, and according to the parameters, a finite element contact model of the gear is established.
Table 2 gear parameters
| Parameter name | Parameter value | Parameter name | Parameter value |
| Gear modulus m | 0.5mm | Pressure angle alpha | 20° |
| Pinion tooth number z 1 | 17 | Gear tooth number z of large gear 2 | 31 |
| Pinion tooth width B1 | 1mm | Gear width B2 | 1mm |
The application provides a method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores, which comprises the following steps:
and step 1, establishing a finite element contact model of the small-modulus powder metallurgy gear with multiple pores.
In the prior art, a standard involute gear model is generally built according to the following method:
based on the generating method processing principle, numerical calculation software is utilized to generate involute tooth profile and tooth root transition curve of the gear, and three-dimensional modeling software is utilized to obtain a three-dimensional model of the gear. The three-dimensional model is imported into finite element software to divide grids, and the gear teeth belong to irregular bodies, so that the single-tooth model is divided into a plurality of hexahedrons which are beneficial to controlling the grid size in order to improve the grid quality and the calculation accuracy. To reduce the effect of grid distortion on accuracy, the grid cell type selects a linear reduction integration cell C3D8R while grid encrypting the tooth surface contact area. To save computational costs, the meshing logarithm of the gear analysis model needs to be determined. By analyzing the coincidence degree of the spur gears, at most two pairs of gears are simultaneously in a meshed state, so at least three pairs of gears are needed. In order to ensure the stability of various meshing performance parameters from meshing in to meshing out of two pairs of teeth, six pairs of teeth can be adopted for contact calculation, and simultaneously, the tooth width (the gear torque is reduced in equal proportion) is reduced to reduce the number of grids, so that the calculation efficiency is improved.
However, the modeling of the pore-containing powder metallurgy gear has a difficulty in that it does not have a uniform and dense internal structure like a general gear, which is formed by pressing metal powder, and the inside of which has an irregular pore-like structure due to a large number of bubbles, as shown in fig. 1. If such a true pore structure is simulated for modeling, the modeling process is relatively complicated, and even if such an irregular pore model is completed, it becomes extremely difficult to divide the mesh thereof in the later stage, and the probability of distortion of the mesh is greatly increased.
Therefore, the application simplifies the pore structure, namely, random irregular pores are regarded as uniform missing of regular grid cells, and the specific method is as follows:
in order to encrypt the mesh and achieve the uniformity of porosity for each region of the gear, the single tooth model is split into multiple regions, as shown in fig. 2, and mesh division is performed. Based on secondary development of finite element software, a script program capable of deleting finite element units is compiled, the function of deleting the finite element unit grids according to a preset percentage is realized, and the pore structure of the powder metallurgy gear is simulated. By deleting the grids uniformly and individually from the hexahedral model and then assembling, the finite element contact model of the powder metallurgy gear considering the influence of the pores is finally formed, as shown in fig. 3. The pore size of the internal pore of the iron-based powder metallurgy gear is generally below 200 mu m, the pore size of the powder metallurgy material with smaller granularity can be below 10 mu m, the side length of the deleted grid of the model is between 5 and 50 mu m, and the deleted grid is basically close to the real pore size.
And 2, solving a finite element contact model, calculating the time-varying meshing stiffness of the gear, comparing with a potential energy method, and verifying the rationality and reliability of the model. The step 2 specifically includes:
firstly, in order to simulate the fixed-axis rotation of a gear pair, a rigid body reference point coupling constraint model is needed, namely rigid body reference points are respectively arranged on the rotation axes of a pinion and a large gear, coupling constraint is established between the reference points and a gear tooth inner gear ring, and the movement and the stress of the gear are controlled by setting boundary conditions on the reference points; wherein the boundary conditions include applied torque and rotational angle, and the interaction between gears adopts surface-to-surface contact.
Solving by finite element analysis software to obtain angular displacement values of the four meshing period internal gears, and processing the data to obtain a meshing stiffness curve of the standard involute spur gear, as shown in fig. 4;
and thirdly, regarding the obtained meshing stiffness curve, when the meshing is started and the meshing is stopped, the calculated result has larger deviation from the meshing stiffness curve when the intermediate gear is meshed due to unstable boundary conditions.
Comparing the meshing stiffness in one meshing period during stable meshing with a potential energy method, as shown in fig. 5, the meshing stiffness curve obtained based on the finite element method is found to be basically coincident with the meshing stiffness curve obtained based on the potential energy method, and the overall error of the root mean square value of the meshing stiffness in one period is 2.65%, so that the rationality and the reliability of the model are verified. When the porosity is 6%, the time-varying meshing stiffness obtained by finite element calculation has larger deviation from a potential energy method, the overall error of the root mean square value of the meshing stiffness in one period is 15.41%, and in order to further study the weakening mechanism of the porosity to the time-varying meshing stiffness of the powder metallurgy gear, the porosity stiffness correction coefficient is introduced to correct the stiffness value under the potential energy method.
And step 3, introducing a rigidity correction coefficient, establishing a rigidity correction potential energy method formula containing pores, and solving the rigidity correction coefficient by using a constraint optimization algorithm.
Based on a finite element contact model, the time-varying meshing stiffness of the gear under a finite element solution can be obtained by solving, a compression stiffness correction coefficient, a bending stiffness correction coefficient, a shearing stiffness correction coefficient, a contact correction coefficient and a matrix stiffness correction coefficient are introduced, the gear time-varying meshing stiffness under a potential energy method is corrected, a potential energy method meshing stiffness solving formula containing pores is provided, and stiffness correction coefficient values under different porosities can be obtained by solving through a constraint optimization algorithm. Specifically, the expression of the constraint optimization algorithm is as follows:
wherein k is h For contact stiffness, k a For compressive stiffness, k b For bending stiffness, k s For shear stiffness, k f For the rigidity of the matrix, a specific calculation formula can be obtained by a potential energy method; x is x h For the contact stiffness correction factor, x a For the compression stiffness correction factor, x b For bending stiffness correction factor, x s For shear stiffness correction factor, x f Lambda is the matrix stiffness correction coefficient i For the matrix rigidity correction coefficient of the existing potential energy method, RMS represents taking a root mean square value, K, of the rigidity value in the meshing period e For the meshing stiffness values obtained by the finite element method, lb represents the lower bound of the solution, ub represents the upper bound of the solution, x 0 Representing an initial value of the solution;
wherein,a formula of a rigidity correction potential energy method is represented, and k is the corrected single tooth meshing rigidity; because the overlap ratio of the standard straight gear is between 1 and 2, a single meshing area and a double meshing area exist, thus the total time-varying meshing rigidity is +.>
The stiffness correction coefficients at 6% to 14% porosity were calculated by the established constraint optimization algorithm, as shown in table 3 below. From Table 3, the contact stiffness correction coefficient x h And shear stiffness correction coefficient x s Insensitive to variations in porosity ζ, whereas the compressive stiffness modifies coefficient x a Bending stiffness correction coefficient x b Matrix stiffness correction coefficient x f Exhibiting a linear relationship to the change in porosity ζ.
TABLE 3 stiffness correction factors at different porosities
| ξ | x h | x a | x b | x f | x s |
| 0％ | 1 | 1 | 1 | 1 | 1 |
| 6％ | 0.9932 | 0.8075 | 0.8006 | 0.8202 | 0.9947 |
| 8％ | 0.9922 | 0.7062 | 0.7005 | 0.7916 | 0.9845 |
| 10％ | 0.9921 | 0.6051 | 0.6004 | 0.7672 | 0.9942 |
| 12％ | 0.9914 | 0.5039 | 0.5002 | 0.7525 | 0.9936 |
| 14％ | 0.9907 | 0.4027 | 0.4002 | 0.7603 | 0.9932 |
In order to verify whether the rigidity correction coefficient obtained by the constraint optimization algorithm meets the expected result, the correction coefficient is brought into a rigidity correction potential energy method formula to obtain a rigidity graph shown in fig. 6. And comparing the obtained mesh stiffness curves with stiffness values obtained by finite element calculation under different porosities, wherein root mean square errors in the mesh period under each porosity are within 3.5%, and the obtained mesh stiffness curves are more consistent with the finite element calculation result.
And 4, establishing a rigidity correction coefficient prediction model based on a feedforward neural network, and predicting time-varying meshing rigidity within a certain porosity range.
While the constraint optimization algorithm can solve the rigidity correction coefficient under each porosity, the solving process is extremely dependent on finite element calculation data, and the efficiency is low. Therefore, the method and the device perform data fitting and prediction on the meshing stiffness correction coefficient of the powder metallurgy gear by constructing a two-layer feedforward neural network model.
The feedforward neural network is a neural network structure which is easy to construct and consists of an input layer, a hidden layer and an output layer. The output of each neuron is connected only to the neurons of the upper layer, without feedback connection. The feedforward neural network can adapt to nonlinear relations, complex data can be fitted, and the hidden layer provides a nonlinear conversion mechanism, so that the network can learn complex characteristics and modes.
The step 4 specifically includes:
step 41, establishing a sample set;
and (3) dividing the rigidity correction coefficient obtained in the step (3) into a training set, a verification set and a test set according to the proportion in a uniform sampling mode.
Step 42, model training;
taking the porosity as input, taking the rigidity correction coefficients under different porosities as training targets, namely 'learning labels', using a least square objective function to combine conjugation and a steepest descent method, constructing a group of conjugation directions by utilizing gradients at known points, searching along the directions to obtain optimal parameters of a feedforward neural network model, thereby determining minimum points of the objective function, and further establishing a nonlinear mapping relation between the porosity and the rigidity correction coefficients.
Step 43, model application;
and applying the feedforward neural network model obtained through training to different porosities to obtain a correction coefficient value under any porosity in a training range, thereby further obtaining the time-varying meshing stiffness of the small-modulus powder metallurgy gear under any porosity.
And (3) respectively calculating correction coefficients under 50 groups of different porosities between 6% and 14% by using a constraint optimization algorithm, taking 70% of data as a training set, 15% of data as a test set and 15% of data as a verification set, importing the data into numerical calculation software, and performing a large number of tests on main parameters such as the number of hidden layers, the number of neurons, the number of iterations and the like when constructing a rigidity correction coefficient prediction model based on a feedforward neural network. And finally selecting two layers of feedforward neural network training model parameters which are used for 2 hidden layers, 10 neurons and iterated 200 times by comparing the calculation efficiency with the correlation coefficient of the prediction result. The training process correlation coefficients for each set of stiffness correction coefficients are shown in table 4 below.
Table 4 training correlation coefficients
| Correlation coefficient | ρ xh | ρ xa | ρ xb | ρ xf | ρ xs |
| Training set | 0.9938 | 0.9982 | 0.9875 | 0.9924 | 0.9973 |
| Test set | 0.9932 | 0.9928 | 0.9844 | 0.9946 | 0.9989 |
| Verification set | 0.9928 | 0.9974 | 0.9968 | 0.9937 | 0.9926 |
| Total data | 0.9891 | 0.9954 | 0.9924 | 0.9838 | 0.9894 |
By comparing the correlation coefficients of the 5 groups of stiffness correction coefficients in the training process, the following conclusion can be drawn: the training model based on the two layers of feedforward neural networks is very accurate in prediction of the rigidity coefficient, and each group of correlation coefficients are close to 1, so that the training result of the model is good. Thus, a neural network model was successfully trained that can predict correction coefficient values at arbitrary porosities over a range of 6% to 14% porosity.
The beneficial effects of the invention are as follows:
1. according to the method, a finite element contact model containing the pore gear is established by combining finite element contact analysis, the influence rule of porosity on the meshing stiffness of the powder metallurgy gear is researched, a pore stiffness correction coefficient is introduced to correct a potential energy method, a constraint optimization algorithm is utilized to solve the correction coefficient, finally, a stiffness correction coefficient prediction model based on a neural network is established, and time-varying meshing stiffness in a certain porosity range can be predicted, so that theoretical support is provided for vibration reduction and noise reduction design of the powder metallurgy gear;
2. the invention discovers that the change of the meshing stiffness of the gear pair and the change of the porosity have a certain linear relation, when the porosity is increased by 2%, the root mean square value of the meshing stiffness in the gear meshing period is reduced by 4.8%, and the research result has a certain guiding significance on the dynamic analysis of a gear transmission system, noise reduction and life extension.
The embodiments of the present application have been described above with reference to the accompanying drawings, but the present application is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those of ordinary skill in the art without departing from the spirit of the present application and the scope of the claims, which are also within the protection of the present application.
Claims (7)
1. The method for predicting the meshing stiffness of the small-modulus powder metallurgy gear with multiple pores is characterized by comprising the following steps of:
step 1, establishing a small-modulus powder metallurgy gear finite element contact model containing multiple pores;
step 2, solving a finite element contact model, calculating the time-varying meshing stiffness of the gear, comparing with a potential energy method, and verifying the rationality and reliability of the model;
step 3, introducing a rigidity correction coefficient, correcting the gear time-varying meshing rigidity under the potential energy method, establishing a rigidity correction potential energy method formula containing pores, and solving the rigidity correction coefficient by using a constraint optimization algorithm;
and 4, establishing a rigidity correction coefficient prediction model based on a feedforward neural network, and predicting time-varying meshing rigidity within a certain porosity range.
2. The method for predicting the meshing stiffness of a small-modulus powder metallurgy gear with multiple pores according to claim 1, wherein the small-modulus powder metallurgy gear with multiple pores is prepared from an iron-based powder metallurgy material F-0000-20.
3. The method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores according to claim 1 or 2, wherein the parameters of the finite element contact model are as follows: gear module m=0.5 mm, pressure angle α=20°, pinion number z 1 =17, big gear number z 2 Pinion width b1=1 mm, and bull width b2=1 mm, =31.
4. The method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores according to claim 3, wherein the establishing a finite element contact model of the small-modulus powder metallurgy gear with multiple pores requires setting random irregular pores as uniform defects of regular grid cells, and specifically comprises the following steps:
splitting the single-tooth model into a plurality of hexahedrons which are beneficial to controlling the grid size, dividing the grids, compiling a script program capable of deleting the finite element units based on secondary development of finite element software, realizing the function of deleting the finite element unit grids according to a preset percentage, simulating the pore structure of the powder metallurgy gear, and then assembling to form the finite element contact model of the powder metallurgy gear considering the pore influence.
5. The method for predicting the meshing stiffness of a small-modulus powder metallurgy gear with multiple pores according to claim 1, wherein the step 2 specifically comprises the following steps:
respectively setting rigid body reference points on the rotation axes of the pinion and the large gear, establishing coupling constraint between the reference points and the gear tooth inner gear ring, and controlling the movement and stress of the gears by setting boundary conditions on the reference points;
solving by finite element analysis software to obtain an angular displacement value of the gear, and processing the data to obtain a meshing stiffness curve;
and according to the meshing stiffness curve, comparing the meshing stiffness in one meshing period during stable meshing with a potential energy method, and verifying the rationality and reliability of the model.
6. The method for predicting meshing stiffness of a small-modulus powder metallurgy gear with multiple pores according to claim 1, wherein in the step 3, the expression of the constraint optimization algorithm is as follows:
wherein,formula k for representing rigidity correction potential energy method h For contact stiffness, k a For compressive stiffness, k b For bending stiffness, k s For shear stiffness, k f For matrix stiffness, k is corrected single tooth mesh stiffness, x h For the contact stiffness correction factor, x a For the compression stiffness correction factor, x b For bending stiffness correction factor, x s For shear stiffness correction factor, x f Lambda is the matrix stiffness correction coefficient i For the matrix rigidity correction coefficient of the existing potential energy method, RMS represents taking a root mean square value, K, of the rigidity value in the meshing period e For the meshing stiffness values obtained by the finite element method, lb represents the lower bound of the solution, ub represents the upper bound of the solution, x 0 Representing the initial value of the solution.
7. The method for predicting the meshing stiffness of a small-modulus powder metallurgy gear with multiple pores according to claim 6, wherein the step 4 specifically comprises:
step 41, a sample set is established, and the rigidity correction coefficient obtained in the step 3 is divided into a training set, a verification set and a test set according to the proportion in a uniform sampling mode;
step 42, model training, namely taking the porosity as input, taking the rigidity correction coefficients under different porosities as training targets, using a least square objective function to combine the conjugate and the steepest descent method to obtain the optimal parameters of the feedforward neural network model, determining the minimum point of the least square objective function, and further establishing a nonlinear mapping relation between the porosity and the rigidity correction coefficients;
and 43, applying the feedforward neural network model obtained through training to different porosities to obtain a correction coefficient value under any porosity in a training range, thereby further obtaining the time-varying meshing stiffness of the small-modulus powder metallurgy gear under any porosity.
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