Tooth profile parameter optimization design method based on Gaussian regression
By optimizing the gear pump tooth profile parameters using a Gaussian regression model, the problems of high computational cost and low efficiency in traditional design were solved, achieving efficient design and performance improvement for fuel gear pumps.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-24
- Publication Date
- 2026-03-27
AI Technical Summary
In traditional gear pump design, improper tooth profile parameter design leads to nonlinear contact stress concentration, increasing mechanical load. Furthermore, finite element simulation calculation is costly and cannot meet the needs of rapid iterative optimization.
The Gaussian regression method is used to construct the tooth profile parameter optimization design. A Gaussian regression model is built through finite element simulation data to accurately capture the nonlinear mapping relationship between tooth profile parameters and maximum contact stress, thereby reducing computational costs and improving design efficiency.
It significantly reduces the computational cost and cycle of optimizing the gear profile parameters of fuel gear pumps, improves design efficiency, and provides an efficient and reliable optimization path for lightweight design and fatigue life improvement of gear pumps.
Smart Images
Figure CN121744795A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of aero-engine fuel pump, and particularly relates to a gear profile parameter optimization design method based on Gaussian regression. BACKGROUND
[0002] As the core power component of the aero-engine hydraulic system, the performance of the fuel gear pump is highly dependent on the gear profile parameter design. These parameters not only determine the meshing characteristics of the gear, but also directly affect the volumetric efficiency, fatigue life and reliability of the pump under extreme conditions. When the gears mesh, stress concentration under nonlinear contact is the main cause of tooth surface fatigue failure, and improper gear profile parameter design will exacerbate the mechanical load of the gear. Under dynamic load, the nonlinear coupling effect of the gear profile parameters is further amplified, and the traditional empirical formula cannot quantize the influence of the transient contact stress fluctuation, which seriously limits the performance improvement of the gear pump.
[0003] Under this background, the structural strength analysis based on finite element (FEA) simulation has become a key technology to break through the design bottleneck, which can effectively evaluate the fatigue life, structural strength and mechanical response characteristics of the gear under complex conditions. However, in the iterative optimization design process of the gear pump, the gear profile parameters need to be repeatedly modified until the multi-dimensional parameter space is traversed, which significantly increases the simulation calculation cost and period, and consumes a large amount of computing resources. In 2020, Peng Xianlong published "Influence of Installation Error on Load Transmission Performance of Face Gear", which systematically analyzed the influence of installation error on tooth surface contact stress and tooth root bending stress through finite element method. However, the research also exposed the common problem of large amount of simulation data and low calculation efficiency, which is difficult to meet the needs of rapid iterative optimization in engineering practice. SUMMARY
[0004] In order to overcome the above technical problems, the purpose of the present application is to provide a gear profile parameter optimization design method based on Gaussian regression, which selects the key parameter combination that significantly affects the performance, carries out finite element simulation calculation, constructs a Gaussian regression model with simulation data as a training sample set, accurately captures the nonlinear mapping relationship between the gear profile parameters and the maximum contact stress under sparse data conditions, and then obtains the optimal parameter combination. This method can significantly reduce the calculation cost and greatly improve the efficiency of gear profile parameter optimization design.
[0005] The technical scheme adopted by the present application is: A gear profile parameter optimization design method based on Gaussian regression, comprising the following steps: Step 1: Perform gear finite element meshing contact simulation setting, including establishing a gear pair model, establishing a contact pair, meshing and boundary condition setting; Step two: through the gear pump meshing contact simulation setting of step one, solve and monitor force convergence curve in real time, and then analyze the contact stress change of gear dynamic meshing and get the maximum contact stress data set of meshing simulation; Step three: through the gear meshing simulation data set of step two, the data set is used as a training set to build a Gaussian regression model, predict the maximum contact stress data under all tooth profile parameter combinations, and then get the optimal parameter combination and carry out accuracy verification.
[0006] The step one is specifically: ANSYS Workbench finite element analysis software is used to carry out transient dynamic simulation on the gear meshing process; 1) Establish gear pair model The gear pair model under given geometric parameters is established in UG; 2) Establish contact pair The gear pair model established in UG is imported into ANSYS Workbench, and the transient analysis module is selected for gear meshing simulation analysis; after importing the model, the software automatically identifies the contact pair, sets the meshing surface of the driving gear as the contact surface, and sets the meshing surface of the driven gear as the target surface; 3) Meshing First, the overall gear structure is meshed freely, the overall gear structure is meshed by using the multi-region meshing method, the geometric body is decomposed into mapping region and free region, and the structured mesh is generated for the mapping region, and the unstructured mesh is used for the free region; 4) Set boundary conditions According to the actual working condition of the gear, the rotation pair is added in the inner circle of the driving and driven gears to constrain the degrees of freedom in Ux, Uy, Uz and ROTX, ROTY directions, so that the driving and driven gears rotate around the Z axis respectively. The rotational speed of 8500r / min is applied to the inner circle of the driving gear, and the torque of 80N·m is applied to the inner circle of the driven gear; the rotational speed and torque are applied in two stages, the first stage is applied in the form of slope, and the second stage is applied smoothly.
[0007] The step two is specifically: Further finite element simulation calculation is carried out on the gears with different tooth profile parameter combinations to obtain the maximum contact stress data set; the specific steps are: Select the key positions of the single tooth from the start meshing to the end meshing time period, the key positions are from double tooth meshing to double tooth meshing, from single tooth meshing to single tooth meshing, and from double tooth meshing to double tooth meshing again; The meshing period is mainly divided into double tooth-single tooth-double tooth meshing, the maximum contact stress of the gear in the double tooth meshing area first increases and then decreases, and the maximum contact stress of the gear in the single tooth meshing area also first increases and then decreases.
[0008] Furthermore, the module, number of teeth, tooth width, and pitch circle pressure angle values are divided into three groups. By changing one of the parameters while keeping the others constant, transient meshing simulation of the gear pair is performed to obtain the maximum contact stress on the tooth surface.
[0009] Step three specifically involves: The basic principle of Gaussian regression is as follows: Define a joint Gaussian distribution for any finite number of function values using the mean function and the covariance function: in, This is the mean function, and it is usually set to 0 to simplify calculations; The covariance function describes the similarity between input points, and uses a squared exponential kernel: in, For signal variance, For the first The feature length scale of the dimension, For noise variance, For the Kronecker delta function; Input data is The output is ,in, The pressure angle of the pitch circle. For modulus, Number of teeth For tooth width, For the maximum contact stress, the model is: The joint distribution is: in, for The covariance matrix, yes The covariance vector; For new input Its predicted distribution is a Gaussian distribution: The mean and variance are respectively: Optimize hyperparameters by maximizing the marginal likelihood function. : .
[0010] The specific steps of step three are as follows: A Gaussian regression model was constructed using simulated stress data as training samples, and hyperparameters were optimized in real time. Subsequently, all parameter combinations were generated. The maximum contact stress of all combinations is predicted by constructing a prediction feature, and the optimal parameter combination of the minimum contact stress is searched (considering the mean-standard deviation balance), and the objective function of the optimization is set as: wherein, is the prediction mean, is the prediction variance, is the risk coefficient.
[0011] The beneficial effects of the present application are: The present application provides a tooth profile parameter optimization design method based on Gaussian regression, aiming to reduce the calculation cost and cycle of fuel gear pump tooth profile parameter optimization design. On the basis of carrying out gear finite element meshing contact simulation setting, the maximum contact stress data set under different tooth profile parameter combinations is solved and obtained by simulation, the simulation data is used as a training set to construct a Gaussian regression model, the nonlinear mapping relationship between four tooth profile parameters and the maximum contact stress is accurately predicted, and then the optimal parameter combination is obtained, and its accuracy is verified, and the design efficiency is greatly improved. Through the present application, the multi-dimensional parameter space can be explored more economically, the design and development of the aviation fuel gear pump is accelerated, and an efficient and reliable optimization path is provided for the lightweight design and fatigue life improvement of the aviation fuel gear pump. BRIEF DESCRIPTION OF DRAWINGS
[0012] Figure 1 The flowchart of the present application.
[0013] Figure 2 The gear meshing contact simulation flowchart.
[0014] Figure 3 The gear pair three-dimensional model.
[0015] Figure 4 The gear contact pair schematic diagram.
[0016] Figure 5 The meshing result.
[0017] Figure 6 The contact stress change cloud picture.
[0018] Figure 7 The Gaussian regression flowchart.
[0019] Figure 8 The actual data and predicted data comparison chart.
[0020] Figure 9 The gear maximum contact stress simulation result under the optimized tooth profile parameters. DETAILED DESCRIPTION
[0021] The technical solutions in the embodiments of the present application will be clearly and completely described with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort belong to the scope of the present application.
[0022] As shown in Figure 1 , for a gear profile parameter optimization design method based on Gaussian regression, the following steps are included: Step one: setting up a finite element meshing contact simulation of gears, including establishing a gear pair model, establishing a contact pair, meshing and boundary condition setting; The specific steps are shown in Figure 2 .
[0023] The highly nonlinear of gear transmission contact problem is mainly manifested in the contact geometric nonlinearity. In the process of gear meshing, the contact position will move along the tooth profile, and the straight gear tooth profile is involute type, which is relatively complex in structure, so the gear meshing process is a nonlinear process. The traditional Hertz contact formula cannot completely solve the nonlinear contact problem of gear meshing, therefore, the ANSYS Workbench finite element analysis software is used to perform transient dynamics simulation on the gear meshing process.
[0024] 1) Establishing a gear pair model A gear pair model under given geometric parameters is established in UG, as shown in Figure 3 . The gear profile parameters are shown in Table 1.
[0025] Table 1 Gear profile parameters
[0026] 2) Establishing a contact pair The gear pair model established in UG is imported into ANSYS Workbench, and the transient analysis module is selected to perform gear meshing simulation analysis. After importing the model, the software automatically identifies the contact pair, sets the meshing surface of the driving gear as the contact surface, and sets the meshing surface of the driven gear as the target surface, as shown in Figure 4 , which is a schematic diagram of gear contact pair.
[0027] 3) Meshing First, the overall gear structure is meshed freely, because the free meshing method has high adaptability to geometric models. The contact surface position is strongly nonlinear, and the meshing of the gear contact surface position is encrypted to improve the calculation accuracy. The overall gear structure is meshed by using a multi-region meshing method, which decomposes the geometric body into a mapping region and a free region, and generates a structured mesh for the mapping region and a non-structured mesh for the free region. The final meshing result is shown in Figure 5shown.
[0028] 4) Set boundary conditions According to the actual working condition of the gear, a rotating pair is added to the inner circle of the driving gear and the driven gear to constrain the degrees of freedom in the Ux, Uy, Uz and ROTX, ROTY directions, so that the driving gear and the driven gear rotate around the Z axis. The rotational speed of 8500 r / min is applied to the inner circle of the driving gear, and the torque of 80 N·m is applied to the inner circle of the driven gear. In order to avoid too large meshing impact when the gear starts to work, the rotational speed and torque are applied in two stages, the first stage is applied in a ramp form, and the second stage is applied smoothly.
[0029] Step two: through step one, the gear pump meshing contact simulation setting is completed, the force convergence curve is solved and monitored in real time, and then the contact stress change of the gear dynamic meshing is obtained and analyzed.
[0030] Further finite element simulation calculation is carried out on the gears with different tooth profile parameter combinations to obtain the maximum contact stress data set. The specific steps are as follows: In order to illustrate the change of the contact stress of the gear when it meshes in and out, the key positions in the time period from the start of the single tooth meshing in to the end of the single tooth meshing out are selected, the key positions are from the double tooth meshing in to the double tooth meshing out, from the single tooth meshing in to the single tooth meshing out, and from the double tooth meshing in to the double tooth meshing out, the contact stress results of the key positions of the gear pair at different simulation times are shown in the following table. Figure 6
[0031] It can be seen that the meshing force of the gear at different positions is also different, the meshing period is mainly divided into double tooth-single tooth-double tooth meshing, the maximum contact stress of the gear in the double tooth meshing area first increases and then decreases, and the maximum contact stress of the gear in the single tooth meshing area also first increases and then decreases. It can be seen from the above figure that the contact stress in the double tooth meshing is smaller than that in the single tooth meshing. The maximum contact stress of the gear pair in the meshing process appears in the single tooth meshing, and the maximum is 1066.3 MPa. Since there is load distribution between the tooth pairs during double tooth meshing, the contact stress is distributed to different tooth pairs, so the contact stress in single tooth meshing is larger than that in double tooth meshing.
[0032] Further, the modulus, the number of teeth, the tooth width and the pressure angle of the pitch circle are divided into three groups, one parameter is changed and the other parameters remain unchanged, the transient meshing simulation of the gear pair is carried out, the maximum contact stress of the tooth surface is obtained, and the simulation calculation result data is shown in Table 2.
[0033] Table 2 Maximum contact stress under different tooth profile parameters
[0034] Step three: the gear meshing simulation data set is obtained by step two, a Gaussian regression model is constructed by taking the sparse data set as a training set, the maximum contact stress data under all tooth profile parameter combinations is predicted, and then the optimal parameter combination is obtained. Finally, finite element simulation is carried out on the optimized parameter combination, the error between the predicted maximum contact stress and the simulation value is compared, and the accuracy of the model is verified.
[0035] The basic principle of the Gaussian regression is as follows: Gaussian process (GP) is a non-parametric probability model used to describe the distribution in the function space. Its core is to define the joint Gaussian distribution of any finite function values through the mean function and the covariance function (kernel function): Wherein, is the mean function, which is usually set to 0 to simplify the calculation; is the covariance function used to describe the similarity between input points, and the square exponential kernel is adopted: Wherein, is the signal variance, is the characteristic length scale of the dimension, is the noise variance, is the Kronecker delta function.
[0036] In the present application, the input data is , and the output is , wherein, is the pressure angle of the pitch circle, is the modulus, is the number of teeth, is the tooth width, is the maximum contact stress, and the model is: The joint distribution is: Wherein, is the covariance matrix of , and is the covariance vector of .
[0037] For a new input , the prediction distribution is a Gaussian distribution: Wherein, the mean and variance are: The hyperparameters are optimized by maximizing the marginal likelihood function: : The specific steps of step three are as follows Figure 7
[0038] The independent data in Table 2 are 9 groups. The simulation stress data are used as training samples to construct a Gaussian regression model, and the hyperparameters are optimized in real time. Then all parameter combinations (P) are generated, the prediction features are constructed, and the maximum contact stress of all combinations is predicted, and the optimal parameter combination of the minimum contact stress (considering the mean-standard deviation balance) is found. The objective function of optimization is set as: wherein, is the predicted mean, is the predicted variance, is the risk coefficient.
[0039] The comparison between the actual training sample data and the predicted data obtained by applying the Gaussian process regression is shown in Figure 8 It can be seen that the model prediction value is highly consistent with the finite element simulation data, indicating that the fitting accuracy of the model is high. Finally, the optimized gear tooth profile parameters are shown in Table 3. The predicted maximum contact stress under the parameter combination is 795.1194 MPa.
[0040] Table 3 Optimized tooth profile parameters Finite element simulation analysis is carried out on the gear pair under the tooth profile parameter combination, and the maximum contact stress obtained is shown in Figure 9 The value is 789.47 MPa. The difference between the predicted maximum contact stress and the simulation value is about 5.65 MPa, and the relative error is 0.72%, indicating that the accuracy of the regression model is high.
Claims
1. A tooth profile parameter optimization design method based on Gaussian regression, characterized in that, Includes the following steps; Step 1: Set up the gear meshing contact simulation using finite element methods, including creating the gear pair model, creating contact pairs, meshing, and setting boundary conditions; Step 2: Using the gear pump meshing contact simulation settings from Step 1, solve and monitor the force convergence curve in real time, then analyze the contact stress changes during dynamic gear meshing and obtain the maximum contact stress dataset from the meshing simulation. Step 3: Using the gear meshing simulation dataset from Step 2, construct a Gaussian regression model as the training set to predict the maximum contact stress data under all tooth profile parameter combinations, thereby obtaining the optimal parameter combination and verifying its accuracy.
2. The tooth profile parameter optimization design method based on Gaussian regression according to claim 1, characterized in that, Step one specifically involves: Transient dynamics simulation of the gear meshing process was performed using ANSYS Workbench finite element analysis software. 1) Establish a gear pair model Create a gear pair model in UG with given geometric parameters; 2) Establish contact pairs Import the gear pair model created in UG into ANSYS Workbench, and select the transient analysis module to perform gear meshing simulation analysis; after importing the model, the software automatically identifies the contact pair, sets the meshing surface of the driving gear as the contact surface, and sets the meshing surface of the driven gear as the target surface; 3) Grid generation First, the overall gear structure is divided into free meshes. A multi-region meshing method is used to decompose the geometry into a mapped region and a free region. A structured mesh is generated for the mapped region, and an unstructured mesh is used for the free region. 4) Set boundary conditions Based on the actual working conditions of the gears, a revolute joint is added to the inner rings of the driving and driven gears to constrain the degrees of freedom in the UX, UY, UZ and ROTX, ROTY directions, allowing the driving and driven gears to rotate around the Z-axis respectively. A rotational speed of 8500 r / min is applied to the inner ring of the driving gear, and a torque of 80 N·m is applied to the inner ring of the driven gear. Apply the speed and torque in two stages: the first stage is applied in a ramp manner, and the second stage is applied smoothly.
3. The tooth profile parameter optimization design method based on Gaussian regression according to claim 1, characterized in that, Step two specifically involves: Finite element simulation calculations were performed on gears with different combinations of tooth profile parameters to obtain the maximum contact stress dataset; the specific steps are as follows: Select the key positions within the time period from the start of engagement to the end of engagement of a single tooth. The key positions are from the engagement of two teeth to the engagement of two teeth, from the engagement of a single tooth to the engagement of a single tooth, and then from the engagement of two teeth to the engagement of two teeth. The meshing cycle is mainly divided into double-tooth-single-double-tooth meshing. In the double-tooth meshing area, the maximum contact stress of the gear first increases and then decreases. In the single-tooth meshing area, the maximum contact stress of the gear also first increases and then decreases.
4. The tooth profile parameter optimization design method based on Gaussian regression according to claim 3, characterized in that, The module, number of teeth, tooth width, and pitch circle pressure angle are divided into three groups. By changing one parameter while keeping the others constant, transient meshing simulation of the gear pair is performed to obtain the maximum contact stress on the tooth surface.
5. The tooth profile parameter optimization design method based on Gaussian regression according to claim 1, characterized in that, Step three specifically involves: The basic principle of Gaussian regression is as follows: Define a joint Gaussian distribution for any finite number of function values using the mean function and the covariance function: in, This is the mean function, and it is usually set to 0 to simplify calculations; The covariance function describes the similarity between input points, and uses a squared exponential kernel: in, For signal variance, For the first The feature length scale of the dimension, For noise variance, For the Kronecker delta function; Input data is The output is ,in, The pressure angle of the pitch circle. For modulus, Number of teeth For tooth width, For the maximum contact stress, the model is: The joint distribution is: in, for The covariance matrix, yes The covariance vector; For new input Its predicted distribution is a Gaussian distribution: The mean and variance are respectively: Optimize hyperparameters by maximizing the marginal likelihood function. : 。 6. The tooth profile parameter optimization design method based on Gaussian regression according to claim 1, characterized in that, The specific steps of step three are as follows: Simulated stress data is used as training samples to construct a Gaussian regression model, and hyperparameters are optimized in real time. Then, all parameter combinations are generated, predictive features are constructed, and the maximum contact stress of all combinations is predicted. Finally, the optimal parameter combination for minimizing contact stress is sought. The objective function for optimization is set as follows: in, To predict the mean, To predict variance, This represents the risk coefficient.