A plunger pump slipper pair rapid optimization method based on intrinsic orthogonal decomposition

Abstract

The present application relates to the technical field of hydraulic element friction pair design and digital optimization, and particularly relates to a plunger pump sliding shoe pair rapid optimization method based on intrinsic orthogonal decomposition, which comprises the following steps: constructing a design variable space and generating training samples; calling a high-fidelity elastohydrodynamic lubrication model to solve the oil film pressure field and the actual oil film thickness field of each sample, and forming a sample database; using intrinsic orthogonal decomposition to extract the main variation characteristics of the pressure field and the film thickness field respectively, and obtaining a POD base; establishing a proxy mapping model between the design variables and the POD modal coefficients; for a new design scheme, predicting the POD modal coefficients through the proxy mapping model and combining the POD base to reconstruct the pressure field and the film thickness field; based on the rapid prediction model, carrying out multi-objective optimization search, and performing high-fidelity review and iterative update on the optimal solution set. In the optimization search process, the rapid prediction model is used to replace a large number of repeated high-fidelity simulation calculations, which significantly reduces the calculation cost and improves the optimization efficiency of the axial plunger pump sliding shoe pair.

Description

Technical Field

[0001] This invention relates to the field of hydraulic component friction pair design and digital optimization technology, specifically a rapid optimization method for piston pump slipper pairs based on intrinsic orthogonal decomposition. Background Technology

[0002] Axial piston pumps are core power components in hydraulic systems, widely used in engineering machinery, aerospace, marine equipment, and industrial hydraulic systems. The slipper pair is one of the key friction pairs in an axial piston pump, and its working condition directly affects the pump's volumetric efficiency, mechanical efficiency, wear life, and operational reliability. During operation, a very thin oil film forms between the slipper and the swashplate. The pressure and thickness distribution of this oil film determines the slipper pair's load-bearing capacity, leakage, and frictional power consumption.

[0003] Optimization of existing skate shoe designs typically involves two technical approaches:

[0004] The first type of method determines structural parameters such as sealing strip size and damping orifice size based on empirical formulas and manual calculations. This method is low in cost and fast in calculation, but empirical formulas are usually based on a large number of simplification assumptions, making it difficult to accurately reflect the coupling effect of oil film pressure distribution and elastic deformation, and its adaptability to complex working conditions and local oil film changes is limited.

[0005] The second type involves using high-fidelity elastohydrodynamic lubrication numerical models to perform simulation calculations on each candidate structure. This method can consider the coupling effect of oil film pressure and elastic deformation, and has high calculation accuracy. However, when there are many candidate solutions or when multi-objective optimization is required, the high-fidelity model needs to be called repeatedly, resulting in extremely high calculation costs and long optimization cycles, which seriously restricts the efficiency of optimization design.

[0006] Therefore, there is an urgent need in this field for a rapid design and optimization method for axial piston pump slipper pairs that can significantly shorten the time for optimizing slipper pair structural parameters and evaluating lubrication performance while maintaining high prediction accuracy. Summary of the Invention

[0007] The purpose of this invention is to provide a rapid optimization method for piston pump slipper pairs based on intrinsic orthogonal decomposition, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A rapid optimization method for piston pump slipper pairs based on intrinsic orthogonal decomposition includes the following steps:

[0010] Step 1: Determine the design variables of the skid pair, including structural parameters and operating condition parameters, construct the design variable space, and generate several training samples within the design variable space;

[0011] Step 2: For each training sample, call the high-fidelity elastohydrodynamic lubrication numerical model of the slipper pair that considers pressure-induced elastic deformation, solve the oil film pressure field and the actual oil film thickness field, and calculate the performance index to form a high-fidelity sample database.

[0012] Step 3: Organize the oil film pressure field results of all training samples into a pressure field sample data matrix according to a unified format, and organize the actual oil film thickness field results of all training samples into a film thickness field sample data matrix according to a unified format.

[0013] Step 4: Perform intrinsic orthogonal decomposition on the pressure field sample data matrix and the film thickness field sample data matrix respectively, extract the main variation features of the pressure field and the main variation features of the film thickness field, and obtain the pressure field POD basis and the film thickness field POD basis.

[0014] Step 5: Project the pressure field of each training sample onto the pressure field POD basis to obtain the pressure field POD modal coefficients; project the actual film thickness field of each training sample onto the film thickness field POD basis to obtain the film thickness field POD modal coefficients.

[0015] Step 6: Establish a first surrogate mapping model between the design variables and the pressure field POD modal coefficients, and a second surrogate mapping model between the design variables and the membrane thickness field POD modal coefficients;

[0016] Step 7: For a new candidate design scheme, input the candidate design variables into the first surrogate mapping model and the second surrogate mapping model respectively to predict the corresponding pressure field POD modal coefficients and film thickness field POD modal coefficients. Combine the pressure field POD basis and film thickness field POD basis to reconstruct the oil film pressure field and actual oil film thickness field of the candidate design scheme.

[0017] Step 8: Based on the rapid prediction results in Step 7, a multi-objective optimization problem is constructed with leakage and frictional power consumption as optimization objectives and minimum oil film thickness and maximum oil film pressure as constraints. The optimal solution set is then searched using a multi-objective optimization algorithm.

[0018] As a further aspect of the present invention: the input variables of the proxy mapping model include structural parameters, operating condition parameters, and spindle rotation angle parameters; the structural parameters include the inner radius of the slipper seal, the outer radius of the slipper seal, the diameter of the damping hole, and the length of the damping hole; the operating condition parameters include the spindle speed and load pressure; and the spindle rotation angle parameters are used to characterize the angular position of the slipper pair within one working cycle.

[0019] As a further aspect of the present invention: in step one, at least one of Latin hypercube sampling, orthogonal experiment, Sobol sequence or adaptive sampling method is used to generate training samples, and the samples cover low speed high pressure, high speed high pressure, low speed low pressure, high speed low pressure, oil suction and discharge switching zone and high risk conditions with thin oil film.

[0020] As a further aspect of the present invention: the high-fidelity elastohydrodynamic lubrication numerical model described in step two obtains the oil film pressure field by solving the Reynolds equation in polar coordinates.

[0021] ,

[0022] In the formula, p is the oil film pressure, h is the oil film thickness, μ is the dynamic viscosity of the oil, r and θ are the polar coordinates in the calculation domain of the slipper pair, and v sr and v sθ These are the radial velocity and the circumferential velocity.

[0023] As a further aspect of the present invention: the actual oil film thickness is determined jointly by the rigid geometric film thickness, the pressure-induced elastic deformation, and the local film thickness variation caused by the surface morphology.

[0024] ,

[0025] Where: h g The rigid body geometric film thickness, δ, is determined by the geometry of the slipper. e δ represents the amount of elastic deformation induced by pressure. s The pressure-induced elastic deformation is calculated using the influence coefficient matrix or half-space elastic theory to represent the local film thickness variation caused by surface morphology.

[0026] As a further aspect of the present invention: the specific method of intrinsic orthogonal decomposition in step four is as follows:

[0027] For pressure field data matrix Perform mean decomposition:

[0028] ,

[0029] in, For the average pressure field, The pressure pulsation field matrix represents the deviation of the pressure field of each sample relative to the average pressure field.

[0030] Singular value decomposition of the pressure pulsation field matrix:

[0031] ,

[0032] In the formula, Let be the left singular vector matrix of the pressure field, and let its column vectors be the POD spatial modes of the pressure field; Here is the singular value matrix of the pressure field; The right singular vector matrix of the pressure field;

[0033] Before selection The first-order pressure field POD mode constitutes the pressure field POD basis:

[0034] ,

[0035] In the formula, Here is the basis matrix of the pressure field POD; For the first First-order pressure field POD mode; The order of the pressure modes to be retained;

[0036] For actual film thickness field data matrix Perform mean decomposition:

[0037] ,

[0038] In the formula, The average field matrix is ​​the film thickness. The film thickness pulsation field matrix represents the deviation of the actual film thickness field of each sample from the average film thickness field.

[0039] Singular value decomposition of the film thickness pulsating field matrix:

[0040] ,

[0041] In the formula, Let be the left singular vector matrix of the film thickness field, and let its column vectors be the POD spatial modes of the film thickness field. Here is the singular value matrix of the film thickness field; Let be the right singular vector matrix of the film thickness field.

[0042] Before selection Thick-field POD modes constitute the thickness-field POD base:

[0043] ,

[0044] In the formula, The thickness field POD basis matrix; For the first Thick-field POD mode; The modal order of the retained film thickness.

[0045] As a further aspect of the present invention: the first proxy mapping model and the second proxy mapping model respectively adopt any one of the following: Kriging model, Gaussian process regression model, radial basis function model, support vector regression model, neural network model or gradient boosting tree model.

[0046] As a further aspect of the present invention: the method for reconstructing and obtaining the oil film pressure field and the actual oil film thickness field in step seven is as follows:

[0047] ,

[0048] ,

[0049] In the formula, The reconstructed pressure field vector; The average pressure field vector; For pressure field POD base; To predict the pressure modal coefficients, This is the actual film thickness field vector obtained through reconstruction; The average film thickness field vector; For thickness field POD substrate; To predict the film thickness modal coefficients.

[0050] As a further aspect of the present invention: the multi-objective optimization algorithm in step eight adopts NSGA-II, multi-objective particle swarm optimization, or multi-objective Bayesian optimization; the optimal solution set obtained by optimization is verified by calling the high-fidelity elastohydrodynamic lubrication numerical model, and samples with large prediction errors or located at the boundary of the design variable space in the verification results are added to the sample database, and the POD basis and surrogate mapping model are updated.

[0051] Compared with the prior art, the beneficial effects of the present invention are:

[0052] 1. Improve the efficiency of slipper pair optimization design. The POD method is used to extract key patterns from high-fidelity simulation results and establish a rapid prediction model. During the optimization process, the rapid prediction model can replace a large number of repetitive high-fidelity elastohydrolubrication calculations, thereby significantly shortening the evaluation time of candidate design schemes and improving the efficiency of slipper pair structural parameter optimization.

[0053] 2. It can consider the influence of elastic deformation on the film thickness field. This invention uses the actual oil film thickness field after considering elastic deformation as the modeling object, rather than just using the ideal geometric film thickness. Therefore, the film thickness distribution obtained by rapid prediction includes the influence of pressure-induced elastic deformation, which is more consistent with the actual lubrication state of the slipper pair of high-speed, high-pressure axial piston pumps.

[0054] 3. Suitable for multi-objective comprehensive optimization. This invention can simultaneously consider indicators such as leakage and frictional power consumption, avoiding the degradation of other key performance aspects caused by optimizing a single objective.

[0055] 4. It has iterative update capabilities. After performing high-fidelity verification on the optimized recommended design scheme, the verification results can be added to the sample database to update the POD base and surrogate mapping model, thereby gradually improving the model's prediction accuracy. Attached Figure Description

[0056] Figure 1 This is a flowchart of a rapid design and optimization method for axial piston pump slipper pairs based on intrinsic orthogonal decomposition according to the present invention.

[0057] Figure 2 This is a schematic diagram of the slipper sealing strip structure in this invention.

[0058] Figure 3 This is a schematic diagram of the damping hole structure of the slipper in this invention. Detailed Implementation

[0059] The technical solution of this application will be further described in detail below with reference to specific embodiments.

[0060] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0061] like Figure 1 As shown, the present invention provides a rapid optimization method for piston pump slipper pairs based on intrinsic orthogonal decomposition, comprising the following steps:

[0062] Step 1: Determine the design variables of the skid pair, including structural parameters and operating condition parameters, construct the design variable space, and generate several training samples within the design variable space.

[0063] The design variables include, but are not limited to: inner radius r0 of the slipper seal, outer radius R0 of the seal, diameter d0 of the damping hole, length l0 of the damping hole, spindle speed n, and load pressure P. L Within the allowable range of design variables, training sample points are generated using Latin hypercube sampling, orthogonal experiments, Sobol sequences, adaptive sampling, or a combination of the above methods. This ensures that the samples cover low-speed high-pressure, high-speed high-pressure, low-speed low-pressure, high-speed low-pressure, oil suction / discharge switching zones, and high-risk conditions with thin oil films, thereby improving the applicability of the subsequent rapid prediction model.

[0064] Step 2: For each training sample, call the high-fidelity elastohydrodynamic lubrication numerical model of the slipper pair that considers pressure-induced elastic deformation, solve the oil film pressure field (referred to as pressure field) and the actual oil film thickness field (referred to as film thickness field), and calculate the performance index to form a high-fidelity sample database.

[0065] Specifically, for each sample point, a high-fidelity elastohydrodynamic lubrication numerical model for the slipper pair is invoked to solve for the oil film pressure field p(r,θ) and the actual oil film thickness field h(r,θ). The high-fidelity elastohydrodynamic lubrication model refers to a slipper pair lubrication numerical model that considers the oil film pressure distribution, the actual oil film thickness variation, and pressure-induced elastic deformation, and can be solved using the finite difference method or the finite volume method.

[0066] The oil film pressure field can be solved using the Reynolds equation in polar coordinates:

[0067] ,

[0068] In the formula, p is the oil film pressure, h is the oil film thickness, μ is the dynamic viscosity of the oil, r and θ are the polar coordinates in the calculation domain of the slipper pair, and v sr and v sθ These are the radial velocity and the circumferential velocity.

[0069] The thickness of the oil film is composed of the rigid geometric film thickness, pressure-induced elastic deformation, and surface morphology.

[0070] ,

[0071] Where: h g The rigid body geometric film thickness, δ, is determined by the geometry of the slipper. e For pressure-induced elastic deformation, δ s This refers to the local film thickness variation caused by surface morphology.

[0072] Elastic deformation δ e It can be calculated using the influence coefficient matrix or half-space elasticity theory. Its general form can be expressed as:

[0073] ,

[0074] In the formula, δ e (r,θ) represents the elastic deformation; Ω represents the calculation region of the slipper pair oil film; (ξ,ψ) represents the coordinates of the source point within the integration region; p(ξ,ψ) represents the oil film pressure; K(r,θ,ξ,ψ) represents the elastic influence function, indicating the degree of influence of the source point pressure p(ξ,ψ) on the elastic deformation at the target point (r,θ); dξ dψ represents the integral infinitesimal element.

[0075] For each sample point, the high-fidelity lubrication numerical model of the slipper pair is invoked to calculate and save the pressure field, oil film thickness field, and performance indicators, including leakage Q and frictional power consumption W. f Minimum oil film thickness h min Maximum oil film pressure p max This results in a high-fidelity sample database.

[0076] Step 3: Organize the oil film pressure field results of all training samples into a pressure field sample data matrix according to a unified format, and organize the actual oil film thickness field results of all training samples into a film thickness field sample data matrix according to a unified format.

[0077] Specifically, the oil film pressure distribution results calculated from all samples are organized in a unified format to form a pressure field sample data matrix:

[0078] ,

[0079] In the formula, P is the pressure field matrix; p i Let be the pressure field vector under the i-th sample working condition.

[0080] All the actual oil film thickness distribution results calculated from the samples were organized in a unified format to form a film thickness field sample data matrix:

[0081] ,

[0082] In the formula, H is the film thickness field matrix; h i Let be the membrane thickness field vector under the i-th sample working condition.

[0083] Each sample corresponds to a pressure distribution result and a film thickness distribution result. In this way, the pressure field and film thickness field results under different design parameters and different operating conditions can be uniformly saved, providing a data foundation for subsequent POD order reduction processing.

[0084] Step 4: Perform intrinsic orthogonal decomposition on the pressure field sample data matrix and the film thickness field sample data matrix respectively, extract the main variation features of the pressure field and the main variation features of the film thickness field, and obtain the pressure field POD basis and the film thickness field POD basis.

[0085] The role of the Proper Orthogonal Decomposition (POD) method is to extract the main patterns from a large amount of high-fidelity simulation results, using a small number of features to represent the complex pressure and film thickness distributions. This significantly reduces the amount of subsequent computation while preserving the main physical laws. Through this process, the complex pressure and film thickness fields no longer need to be completely recalculated from the high-fidelity model, but can be approximated using a small number of POD features.

[0086] Perform mean decomposition on the pressure field data matrix:

[0087] ,

[0088] in, For the average pressure field, The pressure pulsation field matrix represents the deviation of the pressure field of each sample relative to the average pressure field.

[0089] Singular value decomposition of the pressure pulsation field:

[0090] ,

[0091] In the formula, Let be the left singular vector matrix of the pressure field, and let its column vectors be the POD spatial modes of the pressure field; Here is the singular value matrix of the pressure field; Let be the right singular vector matrix of the pressure field.

[0092] Before selection The first-order pressure field POD mode constitutes the pressure field POD basis:

[0093] ,

[0094] In the formula, Here is the basis matrix of the pressure field POD; For the first First-order pressure field POD mode; The order of the pressure modes to be retained.

[0095] Mean decomposition was performed on the actual film thickness field data matrix:

[0096] ,

[0097] In the formula, The average field matrix is ​​the film thickness. The film thickness pulsation field matrix represents the deviation of the actual film thickness field of each sample from the average film thickness field.

[0098] Singular value decomposition of the film thickness pulsating field matrix:

[0099] ,

[0100] In the formula, Let be the left singular vector matrix of the film thickness field, and let its column vectors be the POD spatial modes of the film thickness field. Here is the singular value matrix of the film thickness field; Let be the right singular vector matrix of the film thickness field.

[0101] Before selection Thick-field POD modes constitute the thickness-field POD base:

[0102] ,

[0103] In the formula, The thickness field POD basis matrix; For the first Thick-field POD mode; The modal order of the retained film thickness.

[0104] Step 5: Project the pressure field of each training sample onto the pressure field POD basis to obtain the pressure field POD modal coefficients; project the actual film thickness field of each training sample onto the film thickness field POD basis to obtain the film thickness field POD modal coefficients.

[0105] The POD characteristic coefficients are used to represent the degree of variation of the pressure field and film thickness field relative to the average distribution under different design parameters and operating conditions. These characteristic coefficients allow for the description of originally complex spatial distribution results with less data.

[0106] Projecting the sample pressure field onto the pressure field POD basis yields the pressure field modal coefficients:

[0107] ,

[0108] In the formula, For the first The pressure field POD mode coefficient vector of each sample; This is the average pressure field vector.

[0109] Projecting the sample film thickness field onto the film thickness field POD basis yields the film thickness field modal coefficients:

[0110] ,

[0111] In the formula, For the first The thickness field POD modal coefficient vector of each sample; is the average film thickness field vector.

[0112] Step 6: Establish a first surrogate mapping model between the design variables and the pressure field POD modal coefficients, and a second surrogate mapping model between the design variables and the membrane thickness field POD modal coefficients.

[0113] Specifically, a rapid prediction relationship is established between design variables and the characteristic coefficients of the pressure field (POD). When a new slipper pair design scheme is input, the characteristic coefficients of the pressure field corresponding to that scheme can be quickly predicted. Simultaneously, a rapid prediction relationship is established between design variables and the characteristic coefficients of the film thickness field (POD), used to quickly predict the actual film thickness field characteristic coefficients corresponding to that scheme. The rapid prediction model can employ a Kriging model, a Gaussian process regression model, a radial basis function model, a support vector regression model, a neural network model, a gradient boosting tree model, or a combination of the above models. This rapid prediction model avoids the need for time-consuming high-fidelity elastohydrolubrication calculations for each candidate scheme during the optimization process.

[0114] Establish the mapping relationship between design variables and POD modal coefficients of the pressure field:

[0115] ,

[0116] In the formula, The POD mode coefficients of the predicted pressure field; This is the pressure field proxy mapping model, i.e., the first proxy mapping model.

[0117] Establish a surrogate mapping between design variables and POD modal coefficients in the membrane thickness field:

[0118] ,

[0119] In the formula, The predicted film thickness field POD mode coefficients; This is the film thickness field proxy mapping model, i.e., the second proxy mapping model.

[0120] The surrogate mapping model may be the Kriging model, Gaussian process regression model, radial basis function model, support vector regression model, neural network model, gradient boosting tree model, or a combination of the above models.

[0121] Step 7: For a new candidate design scheme, input the candidate design variables into the first surrogate mapping model and the second surrogate mapping model respectively to predict the corresponding pressure field POD modal coefficients and film thickness field POD modal coefficients. Combine the pressure field POD basis and film thickness field POD basis to reconstruct the oil film pressure field and actual oil film thickness field of the candidate design scheme.

[0122] The actual oil film thickness field already includes the effect of elastic deformation caused by pressure. Therefore, this method can simultaneously and quickly obtain the pressure field and the film thickness field after considering elastic deformation.

[0123] Specifically, for new candidate design variables The pressure field and membrane thickness field modal coefficients are predicted using a surrogate mapping model, and the pressure field is reconstructed.

[0124] ,

[0125] In the formula, The reconstructed pressure field vector; The average pressure field vector; For pressure field POD base; To predict the pressure modal coefficients.

[0126] Reconstructing the actual film thickness field:

[0127] ,

[0128] In the formula, This is the actual film thickness field vector obtained through reconstruction; The average film thickness field vector; For thickness field POD substrate; To predict the film thickness modal coefficients.

[0129] Step 8: Based on the rapid prediction results in Step 7, a multi-objective optimization problem is constructed with leakage and frictional power consumption as optimization objectives and minimum oil film thickness and maximum oil film pressure as constraints. The optimal solution set is then searched using a multi-objective optimization algorithm.

[0130] The optimization algorithm can employ NSGA-II, multi-objective particle swarm optimization, multi-objective Bayesian optimization, or a combination of these algorithms. During the optimization process, the numerous candidate design schemes generated by the algorithm are primarily evaluated using the POD fast prediction model, without requiring the invocation of a high-fidelity elastohydrolubrication model for each candidate scheme. This significantly improves the computational efficiency of multi-objective optimization of the slipper pair.

[0131] Using leakage and frictional power consumption as optimization objectives or constraints, and minimum oil film thickness and maximum oil film pressure as constraints, a multi-objective optimization problem is constructed:

[0132] ,

[0133] In the formula, Q(x) represents the leakage amount, and W f (x) represents the frictional power consumption, h min (x) represents the minimum oil film thickness, h safe The minimum permissible safe oil film thickness; p max (x) represents the maximum oil film pressure, p allow x is the maximum allowable oil film pressure, and x is the design variable.

[0134] The optimal solution set obtained through optimization is then applied using a high-fidelity elastohydrolubrication numerical model. The non-dominated optimal solution set refers to a set of candidate solutions that are not simultaneously and comprehensively superior to other solutions among multiple objectives; in engineering terms, it can be understood as a set of compromise recommendations regarding leakage and frictional power consumption. After verification, samples with large errors or located at the design space boundary are added to the sample library, and the POD basis and fast prediction model are updated, forming an iterative improvement mechanism.

[0135] The present invention will be further described below through specific embodiments.

[0136] Example

[0137] like Figure 2 and Figure 3As shown, the inner radius r0 of the slipper seal, the outer radius R0 of the seal, the diameter d0 of the damping hole, the length l0 of the damping hole, the spindle speed n, and the load pressure P are selected. L As the main design variables, their specific value ranges are shown in Table 1.

[0138] Table 1. Range of Design Variables

[0139]

[0140] Within the aforementioned design variable space, 200 training samples were generated using Latin hypercube sampling. For each training sample, 361 angular positions were taken at 1° intervals along the principal axis rotation angle from 0° to 360°, and high-fidelity simulations were performed for each angular position of each training sample.

[0141] The oil film pressure field p(r,θ), actual oil film thickness field h(r,θ), leakage Q, and frictional power consumption W were obtained at 361 angular positions. f Minimum oil film thickness h min and maximum oil film pressure p max The actual oil film thickness field is determined by the rigid geometric film thickness, pressure-induced elastic deformation, and surface morphology.

[0142] The pressure field at each angular position is flattened into a column vector according to the same node order to form the pressure field matrix P; the actual film thickness field at each angular position is flattened into a column vector according to the same node order to form the film thickness field matrix H. Then, mean decomposition and singular value decomposition are performed on P and H respectively, and the pressure field POD mode and film thickness field POD mode are selected according to the principle that the cumulative energy contribution rate is greater than 99.9%.

[0143] The pressure field and film thickness field of each training sample are projected onto the corresponding POD basis to obtain the POD modal coefficients for the pressure field and the POD modal coefficients for the film thickness field. Let x = [r0, R0, d0, l0, n, P...]. L Using [value] as input and POD modal coefficients as output, pressure field proxy mapping models and film thickness field proxy mapping models are established respectively. In this embodiment, the Kriging model is used as the proxy mapping model.

[0144] This embodiment provides the pressure field average, film thickness field average, pressure field POD basis, film thickness field POD basis, pressure field proxy mapping model, and film thickness field proxy mapping model. After inputting new design variables and spindle rotation angle parameters, the POD modal coefficients at the corresponding angle position can be quickly predicted, and the oil film pressure field and actual oil film thickness field can be further reconstructed without needing to re-call the complete high-fidelity elastohydrodynamic lubrication model for each candidate scheme.

[0145] With the design variables x=[r0,R0,d0,l0] taken as optimization variables, the spindle speed n and the load pressure P L are input as a given working condition or working condition group. The optimization objectives are to simultaneously reduce the leakage Q(x) and the friction power consumption W f (x), and the constraint conditions are h min (x)≥1.0μm, p max (x)≤35MPa, while satisfying r0<R0 and structural processing constraints.

[0146] NSGA-II is adopted as the multi-objective optimization algorithm, with a population size of 60, an iteration number of 80, a crossover probability of 0.9, and a mutation probability of 1 / 4. During the optimization process, the pressure field, film thickness field, leakage, friction power consumption, minimum oil film thickness and maximum oil film pressure of each individual are obtained through the POD rapid prediction model established in the embodiments, instead of calling the high-fidelity elastohydrodynamic lubrication model for each individual.

[0147] After optimization is completed, a set of non-dominated optimal candidate schemes is obtained. Five recommended schemes are selected according to the comprehensive trade-off principle of leakage, friction power consumption and minimum oil film thickness, and the high-fidelity elastohydrodynamic lubrication model is called for rechecking the recommended schemes. If the prediction error of leakage or friction power consumption of a recommended scheme is greater than 10%, or the scheme is located near the boundary of the design variable space, the scheme and its high-fidelity rechecking result are supplemented to the sample library, and the POD basis and the surrogate mapping model are updated again.

[0148] In a practicable example, compared with calling the high-fidelity elastohydrodynamic lubrication model one by one, the present invention uses the POD rapid prediction model to evaluate a large number of candidate schemes, which can reduce the main calculation time in the multi-objective optimization process from the order of hundreds to thousands of hours to the order of several hours. Performing high-fidelity rechecking on a small number of recommended schemes can significantly improve optimization efficiency while ensuring evaluation accuracy.

[0149] The above are only the preferred embodiments of the present invention. It should be noted that for those skilled in the art, several modifications and improvements can be made without departing from the inventive concept of the present invention, and these should also be regarded as the protection scope of the present invention, and none of these will affect the effect of the implementation of the present invention and the practicability of the patent.

Claims

1. A rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition, characterized in that, Includes the following steps: Step 1: Determine the design variables of the skid pair, including structural parameters and operating condition parameters, construct the design variable space, and generate several training samples within the design variable space; Step 2: For each training sample, call the high-fidelity elastohydrodynamic lubrication numerical model of the slipper pair that considers pressure-induced elastic deformation, solve the oil film pressure field and the actual oil film thickness field, and calculate the performance index to form a high-fidelity sample database. Step 3: Organize the oil film pressure field results of all training samples into a pressure field sample data matrix according to a unified format, and organize the actual oil film thickness field results of all training samples into a film thickness field sample data matrix according to a unified format. Step 4: Perform intrinsic orthogonal decomposition on the pressure field sample data matrix and the film thickness field sample data matrix respectively, extract the main variation features of the pressure field and the main variation features of the film thickness field, and obtain the pressure field POD basis and the film thickness field POD basis. Step 5: Project the pressure field of each training sample onto the pressure field POD basis to obtain the pressure field POD modal coefficients; project the actual film thickness field of each training sample onto the film thickness field POD basis to obtain the film thickness field POD modal coefficients. Step 6: Establish a first surrogate mapping model between the design variables and the pressure field POD modal coefficients, and a second surrogate mapping model between the design variables and the membrane thickness field POD modal coefficients; Step 7: For a new candidate design scheme, input the candidate design variables into the first surrogate mapping model and the second surrogate mapping model respectively to predict the corresponding pressure field POD modal coefficients and film thickness field POD modal coefficients. Combine the pressure field POD basis and film thickness field POD basis to reconstruct the oil film pressure field and actual oil film thickness field of the candidate design scheme. Step 8: Based on the rapid prediction results in Step 7, a multi-objective optimization problem is constructed with leakage and frictional power consumption as optimization objectives and minimum oil film thickness and maximum oil film pressure as constraints. The optimal solution set is then searched using a multi-objective optimization algorithm.

2. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The input variables of the proxy mapping model include structural parameters, operating condition parameters, and spindle rotation angle parameters. The structural parameters include the inner radius of the slipper seal, the outer radius of the slipper seal, the diameter of the damping hole, and the length of the damping hole. The operating condition parameters include the spindle speed and load pressure. The spindle rotation angle parameters are used to characterize the angular position of the slipper pair within one working cycle.

3. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, In step one, at least one of the following methods is used to generate training samples: Latin hypercube sampling, orthogonal experiment, Sobol sequence or adaptive sampling. The samples cover low-speed high pressure, high-speed high pressure, low-speed low pressure, high-speed low pressure, oil suction and discharge switching zone and high-risk working conditions with thin oil film.

4. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The high-fidelity elastohydrodynamic lubrication numerical model described in step two obtains the oil film pressure field by solving the Reynolds equation in polar coordinates: ， In the formula, p is the oil film pressure, h is the oil film thickness, μ is the dynamic viscosity of the oil, r and θ are the polar coordinates in the calculation domain of the slipper pair, and v sr and v sθ These are the radial velocity and the circumferential velocity.

5. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The actual oil film thickness is determined by the rigid geometric film thickness, pressure-induced elastic deformation, and local film thickness variations caused by surface morphology. ， Where: h g The rigid body geometric film thickness, δ, is determined by the geometry of the slipper. e δ represents the amount of elastic deformation induced by pressure. s The pressure-induced elastic deformation is calculated using the influence coefficient matrix or half-space elastic theory to represent the local film thickness variation caused by surface morphology.

6. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The specific method of intrinsic orthogonal decomposition described in step four is as follows: For pressure field data matrix Perform mean decomposition: ， in, For the average pressure field, The pressure pulsation field matrix represents the deviation of the pressure field of each sample relative to the average pressure field. Singular value decomposition of the pressure pulsation field matrix: ， In the formula, Let be the left singular vector matrix of the pressure field, and let its column vectors be the POD spatial modes of the pressure field; Here is the singular value matrix of the pressure field; The right singular vector matrix of the pressure field; Before selection The first-order pressure field POD mode constitutes the pressure field POD basis: ， In the formula, Here is the basis matrix of the pressure field POD; For the first First-order pressure field POD mode; The order of the pressure modes to be retained; For actual film thickness field data matrix Perform mean decomposition: ， In the formula, The average field matrix is ​​the film thickness. The film thickness pulsation field matrix represents the deviation of the actual film thickness field of each sample from the average film thickness field. Singular value decomposition of the film thickness pulsating field matrix: ， In the formula, Let be the left singular vector matrix of the film thickness field, and let its column vectors be the POD spatial modes of the film thickness field. Here is the singular value matrix of the film thickness field; Let be the right singular vector matrix of the membrane thickness field. Before selection Thick-field POD modes constitute the thickness-field POD base: ， In the formula, The thickness field POD basis matrix; For the first Thick-field POD mode; The modal order of the retained film thickness.

7. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The first surrogate mapping model and the second surrogate mapping model each adopt any one of the following: Kriging model, Gaussian process regression model, radial basis function model, support vector regression model, neural network model, or gradient boosting tree model.

8. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The method for reconstructing the oil film pressure field and the actual oil film thickness field in step seven is as follows: ， ， In the formula, The reconstructed pressure field vector; The average pressure field vector; For pressure field POD base; To predict the pressure modal coefficients, This is the actual film thickness field vector obtained through reconstruction; The average film thickness field vector; For thickness field POD substrate; To predict the modal coefficients of film thickness.

9. The rapid optimization method for plunger pump slipper pairs based on intrinsic orthogonal decomposition according to claim 1, characterized in that, The multi-objective optimization algorithm described in step eight uses NSGA-II, multi-objective particle swarm optimization, or multi-objective Bayesian optimization. The optimal solution set obtained by optimization is verified by calling a high-fidelity elastohydrodynamic lubrication numerical model. Samples with large prediction errors or located at the boundary of the design variable space in the verification results are added to the sample database, and the POD basis and surrogate mapping model are updated.

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