A Fast Prediction Method for Vibration Response of Gear Transmission System Based on System Division Model Correction

Abstract

The present invention relates to the technical field of vibration response prediction of gear transmission systems, solving the technical problems that the prediction of traditional methods is difficult to meet the timeliness requirements, and the measurement point arrangement is restricted by space and equipment constraints. In particular, it relates to a fast vibration response prediction method for gear transmission systems based on system division model correction. The method includes: dividing the subsystem and establishing a finite element model; correcting the finite element model; establishing a multi-body dynamics model and performing simulations to obtain vibration response data under multiple working conditions; constructing a sample data set, and training and evaluating the vibration response prediction model. The present invention can provide a reliable basis for the condition monitoring of gear transmission systems, effectively evaluate the operating state of the system, provide sufficient preparations for the fault warning and shutdown maintenance of gear transmission systems, thereby providing supplementary data for equipment condition evaluation, avoiding monitoring blind spots, and improving the comprehensiveness and accuracy of monitoring.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration response prediction of gear transmission systems, and particularly to a rapid prediction method for the vibration response of gear transmission systems based on system division model correction. Background Art

[0002] Gear transmission is one of the most important and widely used transmission forms in mechanical transmission, with advantages such as high transmission efficiency, stable transmission ratio, and reliable operation, and is widely used in modern mechanical engineering fields such as aerospace, automobiles, and ships. However, during the operation of gear transmission systems, due to factors such as gear meshing excitation, machining errors, and operating conditions, complex vibration responses will be generated, and important information about the system operating state is contained in these response signals. By analyzing the vibration response, potential faults can be detected in a timely manner and design parameters can be optimized. Therefore, vibration response prediction is of great significance for gear transmission systems.

[0003] With the development of gear transmission systems towards high speed and heavy load, their application scope is continuously expanding, and the requirements for system operating stability and vibration response are also increasing day by day. Under these high-load and high-speed operating conditions, the vibration problems of gear transmission systems are particularly prominent. If the vibration response cannot be accurately predicted, it will not only affect the working reliability of the system, but may also lead to equipment failures and even major safety accidents.

[0004] In the existing vibration response prediction of gear transmission systems, traditional methods based on numerical calculations or simulation models have played an important role. Currently, it mainly includes the finite element method and the dynamic modeling method. The finite element method discretizes a continuous object into a finite number of elements, and determines the dynamic characteristics of the entire system by solving the interaction forces between the elements. By using a parametric programming language and combining the boundary conditions between various components, a finite element equivalent model of the gear transmission system is established to study its dynamic characteristics. The dynamic modeling method mainly describes the vibration response of the system by establishing the dynamic equations of the gears and solving the dynamic equations. For example, the lumped parameter method is a relatively common dynamic modeling method. The lumped parameter method regards the system as a group of concentrated mass points, and the mass points are connected by spring or damping elements, and the dynamic characteristics of the system are described by the connection relationship between the mass points. By using the lumped parameter method to establish the dynamic model of the gear transmission system, comprehensively considering the excitation of gear meshing error and time-varying stiffness, the natural characteristics of the system are solved, and the dynamic models are established for normal gears and faulty gears respectively to study their dynamic characteristics, and the influence of faults such as gear cracks on the vibration response characteristics of the gear transmission system is analyzed.

[0005] In addition, establishing a dynamic model of a gear transmission system using multi-body dynamics simulation software and performing simulation to solve it is also an important method for solving vibration responses. However, such methods rely on the accuracy of system parameters and complex mathematical models. The complexity of model construction and solution makes the prediction process time-consuming, which is difficult to meet the timeliness requirements in engineering application scenarios that require rapid prediction of vibration responses. Therefore, although numerical calculations or simulation models can provide relatively accurate prediction results, their applications are subject to certain timeliness limitations.

[0006] Of course, real-time vibration monitoring of the gear transmission system can also be carried out by installing sensors. However, although the measured data can obtain vibration response signals, in the actual data acquisition process, it often requires a high monitoring cost, and the arrangement of measuring points is often restricted by space and equipment constraints. Especially in the monitoring of rotating machinery, it is difficult to arrange sensors at some key points, resulting in the inability to comprehensively and accurately capture the vibration response characteristics of the system. In addition, the measured data is also easily affected by factors such as the test environment, sensor installation status, and data transmission process, affecting the accuracy and reliability of the test results. Summary of the Invention

[0007] Aiming at the deficiencies of the prior art, the present invention provides a rapid prediction method for the vibration response of a gear transmission system based on system division and model correction, which solves the technical problems that the prediction of traditional methods is difficult to meet the timeliness requirements, and the arrangement of measuring points is restricted by space and equipment constraints.

[0008] To solve the above technical problems, the present invention provides the following technical solution: A rapid prediction method for the vibration response of a gear transmission system based on system division and model correction, the method includes the following steps:

[0009] S1. Divide the gear transmission system into different subsystems according to the contact methods and connection relationships between the transmission structures in the gear transmission system, and establish finite element models of each subsystem and the gear transmission system;

[0010] S2. Correct the finite element models of each subsystem and the gear transmission system to obtain the corrected system model parameters;

[0011] S3. Use the multi-body dynamics analysis method to establish a rigid-flexible coupled multi-body dynamics model of the gear transmission system, substitute the system model parameters into the multi-body dynamics model and perform simulation to obtain vibration response data under multiple working conditions;

[0012] S4. Construct a sample data set based on the vibration response data under multiple working conditions, and use the sample data set to train and evaluate a vibration response prediction model based on a BP neural network;

[0013] S5. Take the rotational speed, load, and normalized time ID of the gear transmission system as the inputs of the vibration response prediction model, and the output is the vibration acceleration response value at the corresponding time point, realizing the rapid prediction of vibration signals under different working conditions.

[0014] Further, the subsystem includes a pinion shaft subsystem, a large gear shaft subsystem, a connection system between the housing and the cover, a connection system between the housing and the bearing end cover, a support system between the housing and the input shaft, and a support system between the housing and the output shaft.

[0015] Further, in step S1, the specific process includes the following steps:

[0016] S11. Divide the gear transmission system into different subsystems according to the contact method and connection relationship between them, and use 3D modeling software to establish the geometric models of different subsystems;

[0017] S12. Import the geometric models into the finite element analysis software ANSYS, and perform mesh division on the gear transmission system. Model and simulate the connections and contacts of different components separately to simplify the overall geometric structure. The modeling simulation to simplify the geometric structure includes:

[0018] For the connection between the gear and the gear shaft, simplify it by the thin layer element method;

[0019] For the connections between the housing and the cover, and between the bearing end cover and the housing, use thin layer elements for simulation;

[0020] For the meshing contact modeling between gears, use the Combin14 element in the finite element analysis software ANSYS for simulation;

[0021] For the simulation of the bearing, use the bearing element of the finite element analysis software ANSYS to simulate its radial support and the spring element to simulate its axial support;

[0022] S13. Establish the finite element models of each subsystem and the gear transmission system according to the simplified modeling simulation scheme.

[0023] Further, in step S2, the specific process includes the following steps:

[0024] S21. Conduct modal hammer tests and operational modal analyses on each subsystem and the gear transmission system respectively to obtain their modal parameters including natural frequencies and modal vibration modes;

[0025] S22. Select the correction parameters corresponding to each subsystem and the gear transmission system. In each subsystem, the correction parameters include the elastic modulus of the material, the elastic modulus of the thin layer element, and the support stiffness of the bearing; in the gear transmission system, the correction parameters include the meshing stiffness of the gear and the three-directional support stiffness of the workbench.

[0026] S23. Modify the correction parameters based on the response surface model to obtain more accurate system model parameters.

[0027] Further, in step S21, the specific process includes the following steps:

[0028] S211. Import the finite element model of any subsystem into the finite element analysis software ANSYS, set the initial elastic modulus of the material and the initial elastic modulus of the thin layer element, and solve the modal information of the subsystem;

[0029] S212. Extract a set of nodes from the modal information that can completely reflect its modal vibration mode, use this node combination as the measurement points of the modal test, and construct the required geometric model in LMS Test.lab;

[0030] S213. Adopt the moving force hammer method, paste the sensor on the end face of the geometric model, use the force hammer to excite all the measurement points in turn, strike each measurement point at least 3 times and take the average value to reduce the error;

[0031] S214. After the knocking is completed, process the test results to obtain the modal parameters of the subsystem including the natural frequency and modal vibration mode.

[0032] Further, in step S23, the specific process includes the following steps:

[0033] S231. Construct a response surface model based on the Kriging model;

[0034] S232. Construct the objective function of the response surface model according to the natural frequency measured by the modal knocking test. The expression of the objective function is:

[0035] ;

[0036] In the formula, is the value of the parameter to be corrected, is the lower limit of the value range of the corresponding parameter; is the upper limit of the value range; is the test frequency value; is the response frequency value calculated by the response surface; is the number of parameters to be corrected; is the number of objective functions;

[0037] S233. Based on the objective function, perform iterative optimization through the multi-objective genetic algorithm to seek the combination of input variables that best meets the target results as the system model parameters.

[0038] Further, in step S231, the specific process includes the following steps:

[0039] S2311. Based on any set of input data and the output response establish a Kriging model, the expression of which is:

[0040] ;

[0041] wherein, is a polynomial function; is the coefficient vector corresponding to the polynomial; is a random process, obeying a normal distribution with a mean of zero and a variance of ;

[0042] S2312. Determine the covariance function of the random process , the expression of which is:

[0043] ;

[0044] wherein, is a spatial correlation function, used to describe the correlation between the sampling points and , is a key parameter, used to adjust the correlation between sample points;

[0045] S2313. Use the maximum likelihood estimation method to solve the predicted values of the coefficient vector and the variance , the calculation formula of which is:

[0046] ;

[0047] ;

[0048] wherein, is the number of parameters to be corrected; is the output response data set; is the matrix composed of the polynomial function ;

[0049] S2314. According to the spatial function and the variance to solve the key parameter , the calculation formula of which is:

[0050] ;

[0051] S2315. Determine the correlation vector between the point to be measured and the known sampling points, the expression of which is:

[0052] ;

[0053] S2316. Substitute the relevant vector , key parameters , coefficient vector , spatial function and variance into the Kriging model to obtain a response surface model for correcting the correction parameters, and the expression is:

[0054] ;

[0055] In the formula, is the response prediction value of the point to be measured ; is the matrix composed of the polynomial function .

[0056] Furthermore, in step S3, the specific process includes the following steps:

[0057] S31. Import the geometric model of the gear transmission system into ADAMS in the STEP neutral format, apply corresponding constraints according to the connection relationship between different components, and perform simulations of gear meshing transmission and simulations of bearings and workbench supports;

[0058] S32. Establish a rigid body dynamics model of the gear transmission system including rigid bodies based on the simulations of gear meshing transmission and simulations of bearings and workbench supports;

[0059] S33. Generate the MNF file of the flexible box body through finite element software, import the MNF file into ADAMS to replace the original rigid body, and create a flexible body through the verification of the centroid position, mass and moment of inertia conditions;

[0060] S34. Couple the degrees of freedom of the rigid body and the flexible body in the form of a bushing force connection between them to obtain a rigid-flexible coupled multi-body dynamics model considering the flexible behavior of the box body components;

[0061] S35. Substitute the corrected system model parameters into the multi-body dynamics model as the corresponding parameter values;

[0062] S36. Build a vibration response test bench and set test conditions, apply rotational speed and load to perform dynamic simulation, and obtain vibration response data under multiple sets of conditions.

[0063] By means of the above technical solutions, the present invention provides a fast prediction method for the vibration response of a gear transmission system based on system division model correction, which has at least the following beneficial effects:

[0064] 1. The present invention can provide a reliable basis for the condition monitoring of the gear transmission system. By comparing the differences between the actual vibration response and the predicted vibration response and formulating appropriate condition determination indicators, the operating state of the system can be effectively evaluated, providing sufficient preparation for the fault warning and shutdown maintenance of the gear transmission system. In addition, it can also help obtain the vibration responses at key positions in the gear transmission system that are difficult to monitor, thereby providing supplementary data for equipment condition assessment, avoiding monitoring blind spots, and improving the comprehensiveness and accuracy of monitoring.

[0065] 2. The present invention comprehensively considers the deviation between the model and the actual structure to improve its accuracy. The gear transmission system is systematically divided, and each subsystem after division can effectively reduce the parameter coupling in the correction process, ensuring the implementation of the subsequent transmission system model correction process, thereby improving the correction accuracy and greatly enhancing the timeliness and accuracy of vibration response prediction.

[0066] 3. The present invention improves the simulation efficiency by constructing a rigid-flexible coupling dynamic model, and can also accurately simulate the interaction of each component of the system, avoiding accuracy loss. At the same time, based on the rigid-flexible coupling multi-body dynamic model of the gear transmission system, the system model parameters obtained by finite element model correction are substituted into the dynamic model to ensure accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The drawings described herein are used to provide a further understanding of the present application, and constitute a part of the present application. The schematic embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings:

[0068] Figure 1 It is a schematic diagram of the subsystem division of the gear transmission system in the present invention;

[0069] Figure 2 It is a flow chart of model correction based on the response surface method in the present invention;

[0070] Figure 3 It is a schematic diagram of the multi-body dynamic model in the present invention;

[0071] Figure 4 It is a comparison diagram of the simulation signal and the filtered test signal in the present invention;

[0072] Figure 5 It is a curve graph of vibration acceleration data under multiple working conditions in the present invention;

[0073] Figure 6 It is a neural network structure diagram of the vibration response prediction model in the present invention;

[0074] Figure 7 It is a fitting effect diagram of the vibration response prediction model on the training set in the present invention;

[0075] Figure 8 This is the fitting effect diagram of the vibration response prediction model in the present invention on the test set;

[0076] Figure 9 This is the comparison diagram of the prediction result and the simulation result in the present invention. Specific embodiments

[0077] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Thereby, the implementation process of how the present application applies technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0078] The accurate prediction of vibration response is of great significance for the optimal design and condition monitoring of gear transmission systems. However, traditional methods based on numerical calculations or simulation models rely on the accuracy of system parameters and complex mathematical models. The complexity of model construction and solution makes the prediction process time-consuming and difficult to meet the timeliness requirements. Moreover, the method of actually measuring vibration response often requires high monitoring costs, and the arrangement of measurement points is often restricted by space and equipment constraints. Especially in the monitoring of rotating machinery, it is difficult to arrange sensors at some key points, resulting in the inability to comprehensively and accurately capture the vibration response characteristics of the system. In addition, the measured data is easily affected by factors such as the test environment, sensor installation status, and data transmission process, affecting the accuracy and reliability of the test results. Therefore, the existing technology still needs to be further developed and improved in vibration response prediction, especially in how to improve the accuracy of vibration response prediction and the rapid prediction of vibration response under multiple working conditions.

[0079] To achieve the rapid prediction of the vibration response of the gear transmission system under different working conditions, please refer to Figures 1-9 , this embodiment proposes a rapid prediction method for the vibration response of a gear transmission system based on system division model correction. This method first divides the subsystems to reduce parameter coupling, corrects material elastic modulus and connection characteristic parameters with the help of finite element model correction technology, and constructs a high-fidelity multi-body dynamics model based on multi-body dynamics analysis technology. Finally, the rapid prediction of the system vibration response under different working conditions is realized through the BP neural network. It is expected to overcome the problems existing in the prior art, improve the timeliness and accuracy of prediction, provide an effective way for the condition monitoring of gear transmission systems, and enhance its engineering application value. This method includes the following steps:

[0080] S1. Divide different subsystems according to the contact methods and connection relationships between the transmission structures in the gear transmission system, and establish finite element models of each subsystem and the gear transmission system. As Figure 1As shown, the divided subsystems include the pinion shaft subsystem, the large gear shaft subsystem, the box body and cover connection system, the box body and bearing end cover connection system, the box body and input shaft support system, and the box body and output shaft support system. The specific process includes the following steps:

[0081] S11. Divide according to the contact method and connection relationship between the gear transmission systems into different subsystems, and use 3D modeling software to establish the geometric models of different subsystems, such as SolidWorks, PROE, UG, etc. At the same time, appropriately simplify the overall geometric structure, ignoring details such as screw connections and chamfers, and complete the assembly process of the overall model.

[0082] S12. Import the geometric model into the finite element analysis software ANSYS, and perform mesh division on the gear transmission system. Model and simulate the connections and contacts of different components separately to simplify the overall geometric structure, and specific and feasible simplified modeling methods are given for the connection parts and contact parts.

[0083] S13. Establish the finite element models of each subsystem and the gear transmission system according to the simplified modeling and simulation scheme. Specifically, for the connection between the gear and the gear shaft, it is simplified by the thin layer element method. The thin layer element method introduces thin layer elements in the connection area and simulates the connection stiffness of the contact part with the elastic modulus of the thin layer element. Its advantage is accurate simulation and can consider nonlinear behaviors such as contact and friction. The connections between the box body and the cover, and between the bearing end cover and the box body are all simulated using thin layer elements. For the meshing contact modeling between gears, the Combin14 element in the finite element analysis software ANSYS is used for simulation. By arranging multiple Combin14 elements along the tooth width direction in the gear contact area, the simulation of gear meshing is realized, reducing the complexity of the model and effectively improving the efficiency of simulation calculation, and avoiding the time cost and parameter errors that may be introduced by traditional nonlinear contact modeling methods. For the simulation of bearings, the bearing elements of the finite element analysis software ANSYS are used to simulate their radial support, and spring elements are used to simulate their axial support. Finally, the finite element models of each subsystem and the entire gear transmission system are established.

[0084] The design of gear transmission systems often requires high precision and high reliability. Its structure is usually composed of multiple interacting subsystems, relying on the coordinated work of different components to achieve complex motion and load transmission. These subsystems of the gear transmission system each undertake different functions, and through the transmission of motion and force with each other, they jointly build the integrity and functionality of the system. By dividing the gear transmission system into multiple subsystems according to the contact method and connection relationship, the interference caused by parameter coupling between subsystems is reduced, ensuring the development of the subsequent transmission system model correction process.

[0085] S2. Modify the finite element models of each subsystem and the gear transmission system to obtain the modified system model parameters. This step is based on the model modification method for system division. For the gear transmission system, it is first divided into multiple subsystems according to connection methods, contact relationships, etc. Subsequently, modal hammer tests and operational modal analysis are respectively carried out on each subsystem and the overall system to obtain their modal parameters, and the response surface method is used to modify parameters such as material elastic modulus, support stiffness, and meshing stiffness to obtain more accurate system model parameters. The specific process includes the following steps:

[0086] S21. Conduct modal hammer tests and operational modal analysis on each subsystem and the gear transmission system respectively to obtain their modal parameters including natural frequencies and modal vibration modes. Among them, for the gear transmission system, obtaining its modal parameters through operational modal analysis can be directly achieved by existing technical means. As a further technological innovation, this embodiment proposes a modal hammer test analysis method to obtain the modal parameters of each subsystem. The specific process includes the following steps:

[0087] S211. Import the finite element model of any subsystem into the finite element analysis software ANSYS, set the initial elastic modulus of the material and the initial elastic modulus of the thin layer element, and solve the modal information of the subsystem;

[0088] S212. Extract a set of nodes from the modal information that can completely reflect its modal vibration mode, use this node combination as the measurement points for the modal test, and construct the required geometric model in LMS Test.lab;

[0089] S213. Adopt the moving force hammer method, paste the sensors on the end face of the geometric model, use the force hammer to sequentially excite all measurement points, strike each measurement point at least 3 times and take the average value to reduce errors;

[0090] S214. After the hammering is completed, process the test results to obtain the modal parameters of the subsystem including natural frequencies and modal vibration modes.

[0091] This embodiment takes the pinion shaft subsystem as an example. Import the finite element model of the pinion and the pinion shaft into ANSYS, conduct modal analysis on the initial finite element model, set the initial elastic modulus of the material and the thin layer element, and solve the modal information of the pinion shaft subsystem. Then extract a set of nodes from the modal information that can completely reflect its modal vibration mode, use this node combination as the measurement points for the modal test, and then construct the required geometric model in LMS Test.lab, construct a simplified geometric structure through the point-line-plane modeling method, and conduct a modal hammer test.

[0092] For experimental modal analysis, the moving force hammer method is adopted. The sensors are pasted on the end face of the gear shaft. The force hammer sequentially excites all measurement points, and each measurement point is struck 3 times and the average value is taken to reduce errors. After the striking is completed, the experimental results are processed to obtain the experimental modal parameters such as the natural frequency and modal vibration mode of the pinion shaft subsystem. According to the Modal Assurance Criteria (MAC), the mode matching between the experimental vibration mode and the simulation vibration mode is carried out, and it is represented by the MAC value to indicate the correlation between the two modal vibration modes. The calculation method is as follows:

[0093] ; (1)

[0094] In the formula, is the element in the th row and the th column of the matrix; is the th order vibration mode of the experiment; is the th order vibration mode of the simulation; represents the transpose.

[0095] S22. Select the correction parameters corresponding to each subsystem and the gear transmission system. In each subsystem, its correction parameters include the elastic modulus of the material, the elastic modulus of the thin layer element, and the support stiffness of the bearing; in the gear transmission system, its correction parameters include the meshing stiffness of the gear and the three-direction support stiffness of the workbench.

[0096] Next, the finite element model of the pinion shaft subsystem is corrected. Considering the sensitivity of each modal parameter to each order of natural frequency, the elastic modulus E1 of the pinion, the elastic modulus E2 of the thin layer element, and the elastic modulus E3 of the pinion shaft are selected as the correction parameters. The Kriging response surface model is selected to correct the finite element model of the pinion shaft subsystem. The Kriging response surface is an interpolation method based on spatial statistics, and its core idea is to estimate the response surface by considering the correlation between spatial positions and samples. The Kriging response surface not only interpolates through the existing experimental data, but also can provide error estimation, so it has significant advantages in optimization and simulation.

[0097] S23. Based on the response surface model, the correction parameters are corrected to obtain more accurate system model parameters. The specific process includes the following steps:

[0098] S231. Construct a response surface model based on the Kriging model. The specific process includes the following steps:

[0099] S2311. Based on any set of input data and output response Establish a Kriging model, and the expression is:

[0100] ; (2)

[0101] In the formula, is a polynomial function; is the coefficient vector corresponding to the polynomial; is a stochastic process, following a normal distribution with a mean of zero and a variance of ;

[0102] S2312. Determine the covariance function of the stochastic process , and the expression is:

[0103] ; (3)

[0104] In the formula, is the spatial correlation function, used to describe the correlation between the sampling points and , is a key parameter, used to adjust the correlation between sample points;

[0105] S2313. Use the maximum likelihood estimation method to solve the predicted values of the coefficient vector and the variance . Since the general form of the spatial correlation function is as follows:

[0106] ; (4)

[0107] In the formula, is the number of variables; and are the -th and -th components of the sample points and

[0108] ; (5)

[0109] According to the maximum likelihood estimation method, it can be obtained that:

[0110] ; (6)

[0111] ; (7)

[0112] In the formula, is the number of parameters to be corrected; is the output response data set; is the matrix composed of the polynomial function , is a correlation matrix, i.e., a spatial function, and its specific expression is as follows:

[0113] ; (8)

[0114] ; (9)

[0115] It can be seen from equations (5), (6) and (7) that , and all depend on the key parameter . Based on the maximum likelihood estimation theory, the value can be obtained.

[0116] S2314. According to the spatial function and variance to solve the key parameter , the calculation formula is:

[0117] ; (10)

[0118] S2315. Determine the correlation vector between the point to be measured and the known sampling points, and the expression is:

[0119] ; (11)

[0120] S2316. Substitute the correlation vector , the key parameter , the coefficient vector , the spatial function and variance into the Kriging model to obtain a response surface model for correcting the correction parameters, and the expression is:

[0121] ; (12)

[0122] In the formula, is the response prediction value of the point to be measured ; is the matrix composed of the polynomial function .

[0123] S232. Construct the objective function of the response surface model according to the natural frequencies measured by the modal hammer test, and the expression of the objective function is:

[0124] ; (13)

[0125] In the formula, is the value of the parameter to be corrected, is the lower limit of the value range of the corresponding parameter; is the upper limit of the value range; is the test frequency value; is the response frequency value calculated by the response surface; is the number of parameters to be corrected; is the number of objective functions.

[0126] S233. Based on the objective function, iterative optimization is carried out through the multi-objective genetic algorithm to seek the input variable combination that best meets the target result as the system model parameters. During the optimization process, the iterative convergence criterion is set such that the error of the objective function meets a certain accuracy requirement, that is, the correction is completed when the set error range is reached.

[0127] This embodiment greatly improves the timeliness and accuracy of vibration response prediction. The proposed model correction comprehensively considers the deviation between the model and the actual structure to improve its accuracy. The gear transmission system is systematically divided, and each subsystem after division can effectively reduce the parameter coupling during the correction process, thereby improving the correction accuracy. At the same time, based on the strong non-linear fitting ability of the neural network, a vibration response prediction model based on the BP neural network is constructed to achieve the rapid prediction of vibration responses under different working conditions.

[0128] S3. Use the multi-body dynamics analysis method to establish a rigid-flexible coupling multi-body dynamics model of the gear transmission system, substitute the system model parameters into the multi-body dynamics model, and perform simulations to obtain vibration response data under multiple working conditions.

[0129] Since the finite element method is difficult to balance simulation accuracy and simulation efficiency in dynamic analysis, reducing the number of meshes and simplifying the modeling can improve the solution efficiency, but it will cause the system degrees of freedom to deviate too much from the actual situation, resulting in an untrustworthy solution result. And directly using non-linear contact and other methods for modeling and simulation will lead to an excessive time cost for solving, and the solution efficiency is difficult to meet the requirements of engineering applications. Therefore, the multi-body dynamics analysis technology is used to realize the dynamic simulation of the gear transmission system. By constructing a rigid-flexible coupling multi-body dynamics model, the simulation efficiency is improved, and at the same time, the interaction between the components of the system can be accurately simulated, avoiding accuracy loss. At the same time, based on the rigid-flexible coupling multi-body dynamics model of the gear transmission system, the system model parameters corrected from the finite element model are substituted into the multi-body dynamics model to ensure the accuracy of the model. The specific process includes the following steps:

[0130] S31. Import the geometric model of the gear transmission system into ADAMS in the STEP neutral format, apply corresponding constraints according to the connection relationships between different components, and conduct simulations of gear meshing transmission and simulations of bearings and workbench supports. Among them, the collision function method is used to simulate gear meshing transmission. The collision function method calculates the contact force between components based on the IMPACT function. The gear meshing contact force is converted into two parts: the elastic force caused by mutual penetration during tooth meshing and the damping force caused by the relative velocity. The specific calculation method is as follows:

[0131] ; (14)

[0132] In the formula, is the contact stiffness coefficient; is the contact penetration; is the maximum allowable penetration depth; is the maximum contact damping when reaching the maximum penetration depth; is the non - linear spring force index.

[0133] In ADAMS The function is defined as follows:

[0134] ; (15)

[0135] In the formula, is the independent variable, .

[0136] For the simulations of bearings and workbench supports, they can be realized through the bushing force tool. The bushing force model is a commonly used simplified modeling method for simulating the supporting force and damping effect of bearings on rotors or shafts. This model equivalent the complex dynamic behavior of bearings to a linear spring - damping system, mainly describing the stiffness and damping characteristics of bearings in the radial and axial directions. The values of gear meshing stiffness, bearing stiffness, and workbench support stiffness are substituted with the results of model correction.

[0137] S32. Establish a rigid - body dynamics model of the gear transmission system including rigid bodies based on the simulations of gear meshing transmission and bearings and workbench supports. At the same time, to achieve a more accurate simulation of the vibration response of the gear transmission system, construct a rigid - flexible coupled multi - body dynamics model considering the flexible behavior of the box - body components.

[0138] S33. Generate the MNF file of the flexible box through finite - element software, import the MNF file into ADAMS to replace the original rigid body, and realize the creation of the flexible body through the verification of the centroid position, mass, and moment of inertia conditions;

[0139] S34. After the flexible body is created, it is necessary to couple the degrees of freedom of the rigid body and the flexible body in the form of a bushing force connection between them to obtain a rigid-flexible coupled multi-body dynamics model considering the flexible behavior of the box body components. For example, apply a bushing force between the rigid region of the bolt hole of the flexible box body and the ground, and set the stiffness value of the bushing force to the corrected three-way support stiffness value, so as to achieve the rigid-flexible coupling of the multi-body dynamics model, as Figure 3 shown.

[0140] S35. Substitute the corrected system model parameters into the multi-body dynamics model as the corresponding parameter values;

[0141] S36. Build a vibration response test bench and set the test conditions, apply rotational speed and load to conduct dynamic simulation, and obtain vibration response data under multiple sets of conditions. Specifically, on the constructed multi-body dynamics model, set the test conditions, apply rotational speed and load to conduct dynamic simulation, and build a test bench to verify the accuracy of the multi-body dynamics model.

[0142] In this embodiment, multi-body dynamics analysis technology is used to realize the dynamic simulation of the gear transmission system. By constructing a rigid-flexible coupled dynamics model, the simulation efficiency is improved, and at the same time, the interaction of each component of the system can be accurately simulated, avoiding accuracy loss. At the same time, based on the rigid-flexible coupled multi-body dynamics model of the gear transmission system, the system model parameters corrected from the finite element model are substituted into the dynamics model to ensure accuracy.

[0143] S4. Construct a sample data set based on the vibration response data under multiple sets of conditions, and use the sample data set to train and evaluate the vibration response prediction model based on the BP neural network. In this embodiment, 20 sets of vibration response data are obtained by sampling according to the optimal Latin hypercube sampling method, the original data is obtained through dynamic simulation, and data resampling and other processes are carried out to construct a sample data set, as Figure 4 and Figure 5 shown.

[0144] In this embodiment, a vibration response prediction model based on the BP neural network is established to complete the network structure design as Figure 6 shown. The activation function is selected as the ReLU function, the loss function is the mean squared error (MSE) function, and the optimization algorithm is selected as the Adam algorithm. Before neural network training, the Z-score standardization method is selected to convert the original data into a standard normal distribution with a mean of 0 and a standard deviation of 1, so as to ensure the balanced contribution of each feature to model training. Then the vibration response prediction model is trained, and MSE, MAE, RMSE, R 2 are used as evaluation indicators to evaluate the model training results on the training set and the test set respectively, asFigure 7 and Figure 8 as shown. The normalization formula is:

[0145] ; (16)

[0146] In the formula, is the data before normalization, is the sample mean, is the sample standard deviation, is the data after normalization.

[0147] In this embodiment, the training set is the rotational speed range of 800 r / min to 2000 r / min and the load torque range of 2 to 18 Nm, and 20 groups of sample numbers are selected. The distribution of the 20 groups of working condition parameters obtained by using the optimal Latin hypercube sampling is relatively uniform in the sample space. Therefore, the constructed data set can better represent the entire sample space. During the training process, the data set contains a total of 4000 pieces of data, and the data set division ratio is 80% training set and 20% test set. The initial learning rate is 0.001, and the number of training times is 500. The structure of the neural network is an input layer, two hidden layers and an output layer. The number of nodes in the input layer of the neural network is 3, the number of nodes in both hidden layers is 128, and the number of nodes in the output layer is 1. Select a group of working conditions outside the training set to verify the training effect of the model. The rotational speed is 1300 r / min and the load torque is 7.5 N·m. It is found that the MSE between the prediction result and the simulation result is 0.255, the RMSE is 0.505, and the MAE is 0.383. The prediction error is small, indicating that the prediction model can predict the vibration response signal of the gear transmission system more accurately.

[0148] Based on the vibration response prediction model construction method of the BP neural network in this embodiment, it is proposed to construct a high-fidelity multi-body dynamics model of the gear transmission system by modifying the system model parameters, and perform simulations to obtain vibration response data under multiple working conditions. Finally, a vibration response prediction model of the gear transmission system is constructed in combination with the BP neural network to realize the rapid prediction of the vibration response under different working condition parameters.

[0149] S5. Take the rotational speed, load and normalized time ID of the gear transmission system as the input of the vibration response prediction model, and the output is the vibration acceleration response value at the corresponding time point, so as to realize the rapid prediction of the vibration signal under different working conditions.

[0150] The input of the vibration response prediction model is the rotational speed, load and normalized time ID, and the output is the vibration acceleration response value at the corresponding time point. Select a group of data outside the training set and the test set for verification. The prediction curve obtained by the vibration response prediction model is in good agreement with the dynamic simulation result. As Figure 9As shown, the present invention has been applied and verified on a first-stage gear transmission system. The results of the application and verification show that, when comparing the prediction results obtained by using the proposed method with the dynamic simulation results, the prediction curve and the simulation curve are highly coincident, being relatively close at the extreme values of the vibration acceleration signal, and at the same time, the corresponding curve change trends are basically the same at different time points. This indicates that the constructed vibration response prediction model can achieve rapid prediction of vibration signals under different working conditions.

[0151] Those of ordinary skill in the art can understand that all or part of the steps in implementing the methods of the above embodiments can be completed by instructing relevant hardware through a program. Therefore, this application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer-usable program code.

[0152] The above embodiments have introduced the present invention in detail. Specific examples are used herein to elaborate on the principle and implementation of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A rapid prediction method for the vibration response of a gear transmission system based on the correction of a system division model, characterized in that, The method includes the following steps: S1. Divide according to the contact mode and connection relationship between the transmission structures in the gear transmission system into different subsystems, and establish finite element models of each subsystem and the gear transmission system; S2. Modify the finite element models of each subsystem and the gear transmission system to obtain the modified system model parameters. The specific process includes the following steps: S21. Conduct modal hammer tests and operational modal analyses on each subsystem and the gear transmission system respectively to obtain their modal parameters including natural frequencies and modal vibration modes; S22. Select the correction parameters corresponding to each subsystem and the gear transmission system. In each subsystem, its correction parameters include the elastic modulus of the material, the elastic modulus of the thin layer element, and the support stiffness of the bearing; in the gear transmission system, its correction parameters include the meshing stiffness of the gear and the three-direction support stiffness of the workbench; S23. Modify the correction parameters based on the response surface model to obtain more accurate system model parameters. The specific process includes the following steps: S231. Construct a response surface model based on the Kriging model, and the expression is: ； Wherein, is the point to be measured 's response prediction value; is a matrix composed of polynomial functions ; is the correlation vector; is the key parameter; is the coefficient vector; is the spatial function; is the output response data set; represents transpose; In step S231, the specific process includes the following steps: S2311. Based on any set of input data and output response establish a Kriging model, the expression of which is: ； In the formula, is a polynomial function; is the coefficient vector corresponding to the polynomial; is a random process, following a normal distribution with a mean of zero and a variance of ; S2312. Determine the covariance function of the stochastic process as follows The expression is ； In the formula, is a spatial correlation function used to describe the correlation between sampling points and ; is a key parameter used to adjust the correlation between sample points; S2313. Solve the coefficient vector using the maximum likelihood estimation method and variance predicted value of , , and the calculation formula is: ； wherein, is the number of parameters to be corrected; is the output response data set; is a polynomial function constituting a matrix; S2314. Solve for the key parameters according to the spatial function with variance The calculation formula is as follows: ​ ； S2315. Determine the correlation vector between the point to be measured and the known sampling point , and the expression is: ； S2316. Substitute the relevant vector , the key parameter , the coefficient vector , the spatial function and the variance into the Kriging model to obtain a response surface model for correcting the correction parameter; S232. Construct the objective function of the response surface model according to the natural frequencies measured by the modal hammer test. The expression of the objective function is: ； wherein, is the parameter value to be corrected, is the lower limit of the value range of the corresponding parameter; is the upper limit of the value range; is the test frequency value; is the response frequency value calculated by the response surface; is the number of parameters to be corrected; is the number of objective functions; S233. Perform iterative optimization through the multi-objective genetic algorithm based on the objective function to seek the input variable combination that best meets the target result as the system model parameters; S3. Establish a rigid-flexible coupling multi-body dynamics model of the gear transmission system by using the multi-body dynamics analysis method, substitute the system model parameters into the multi-body dynamics model and conduct simulations to obtain vibration response data under multiple working conditions; S4. Construct a sample data set based on the vibration response data under multiple working conditions, and use the sample data set to train and evaluate the vibration response prediction model based on the BP neural network; S5. Take the rotational speed, load, and normalized time ID of the gear transmission system as the inputs of the vibration response prediction model, and the output is the vibration acceleration response value at the corresponding time point, realizing the rapid prediction of vibration signals under different working conditions.

2. The rapid prediction method for the vibration response of the gear transmission system according to claim 1, characterized in that The subsystems include the pinion shaft subsystem, the big gear shaft subsystem, the connection system between the box body and the box cover, the connection system between the box body and the bearing end cover, the support system of the box body and the input shaft, and the support system of the box body and the output shaft.

3. The rapid prediction method for the vibration response of the gear transmission system according to claim 1, characterized in that, In step S1, the specific process includes the following steps: S11. Divide according to the contact mode and connection relationship between the gear transmission systems into different subsystems, and use 3D modeling software to establish the geometric models of different subsystems; S12. Import the geometric model into the finite element analysis software ANSYS, and conduct mesh division on the gear transmission system. Model and simulate the connection and contact of different components separately to simplify the overall geometric structure. Conducting modeling and simulation to simplify the overall geometric structure includes: For the connection between the gear and the gear shaft, simplify it by the thin layer element method; For the connection between the box body and the box cover and the connection between the bearing end cover and the box body, both are simulated by thin layer elements; For the meshing contact modeling between gears, the Combin14 element in the finite element analysis software ANSYS is used for simulation; For the simulation of bearings, the bearing element of the finite element analysis software ANSYS is used to simulate its radial support, and the spring element is used to simulate its axial support; S13. Establish the finite element models of each subsystem and the gear transmission system according to the simplified modeling and simulation scheme.

4. The rapid prediction method for the vibration response of the gear transmission system according to claim 1, characterized in that In step S21, the specific process includes the following steps: S211. Import the finite element model of any subsystem into the finite element analysis software ANSYS, set the initial elastic modulus of the material and the initial elastic modulus of the thin layer element, and solve the modal information of the subsystem; S212. Extract a set of nodes from the modal information that can completely reflect its modal vibration mode, use this node combination as the measurement points for the modal test, and construct the required geometric model in LMS Test.lab; S213. Adopt the moving force hammer method, paste the sensor on the end face of the geometric model, use the force hammer to excite all the measurement points in turn, strike each measurement point at least 3 times and take the average value to reduce the error; S214. After the percussion is completed, process the test results to obtain the modal parameters of the subsystem including the natural frequency and modal vibration mode.

5. The rapid prediction method for the vibration response of the gear transmission system according to claim 1, wherein In step S3, the specific process includes the following steps: S31. Import the geometric model of the gear transmission system into ADAMS in the STEP neutral format, apply the corresponding constraints according to the connection relationship between different components, and conduct the simulation of gear meshing transmission and the simulation of bearing and workbench support; S32. Establish the rigid body dynamics model of the gear transmission system including rigid bodies according to the simulation of gear meshing transmission and the simulation of bearing and workbench support; S33. Generate the MNF file of the flexible box by the finite element software, import the MNF file into ADAMS to replace the original rigid body, and realize the creation of the flexible body through the verification of the centroid position, mass and moment of inertia conditions; S34. Couple the degrees of freedom of the rigid body and the flexible body in the connection mode of the bushing force to obtain the rigid-flexible coupling multi-body dynamics model considering the flexible behavior of the box components; S35. Substitute the corrected system model parameters into the multi-body dynamics model as the corresponding parameter values; S36. Build a vibration response test bench and set the test conditions, apply the rotational speed and load to conduct the dynamic simulation, and obtain the vibration response data under multiple working conditions.

Images