Multi-conical friction pair multi-objective optimization method based on mixed agent model

Abstract

The invention relates to a multi-target optimization method for a multi-conical friction pair based on a mixed proxy model, and the method comprises the steps: constructing a three-dimensional transient thermal-flow coupling model of the multi-conical friction pair, and setting a thermal boundary condition for determining the temperature field evolution and friction torque under a clutch engagement working condition; minimizing the peak temperature and the radial temperature difference and maximizing the friction torque as an objective function, performing iteration on the objective function based on the mixed agent model to solve a Pareto optimal solution set, and obtaining an optimal design scheme of the multi-cone friction pair. According to the method, the limitations of single optimization target, insufficient proxy model precision and the like are overcome, an optimization scheme based on the hybrid proxy model is provided, the heat concentration problem of the multi-cone friction pair is effectively relieved, and the torque transmission capacity of the multi-cone friction pair is enhanced.

Description

Technical Field

[0001] This invention relates to the field of clutch design and optimization technology in mechanical transmission systems, and in particular to a multi-objective optimization method for multi-cone friction pairs based on a hybrid surrogate model. Background Technology

[0002] Wet clutches are widely used in transmission systems in vehicles and aviation. The thermal load characteristics of their friction pairs directly affect transmission efficiency and durability. New multi-cone clutches use conical surface contact instead of traditional planar disc contact, significantly increasing the effective contact area and improving torque transmission capability. However, compared to disc structures, the multi-cone structure has more complex convective heat transfer boundary conditions and a more uneven temperature distribution at the friction interface due to variations in the flow of lubricating oil film on the conical surface. Practical studies show that a significant temperature gradient often appears radially along the conical surface, especially forming peak high temperatures at the outer edge of the friction pair. This can cause thermal stress accumulation within the friction plates, potentially leading to clutch failure under harsh operating conditions. Therefore, analyzing the transient temperature distribution of multi-cone friction pairs and optimizing their structural parameters to reduce temperature non-uniformity and improve clutch reliability and lifespan has become an important development direction in this field.

[0003] Currently, thermal analysis of multi-cone friction pairs mainly relies on computational fluid dynamics-finite element method (CFD-FEA) coupled simulations. While these can obtain relatively accurate temperature field and torque data, a single simulation can take several hours to tens of hours, making it difficult to support large-scale parameter optimization. In terms of optimization methods, existing research often focuses on single objectives (such as reducing temperature difference or increasing torque only), lacking a comprehensive multi-objective optimization framework that simultaneously considers thermal uniformity and torque performance. Furthermore, single surrogate models (such as Kriging, RBF, or PRS) are often used to fit the relationship between design variables and response. In complex nonlinear problems, this results in limited prediction accuracy and insufficient generalization ability, affecting the reliability and engineering applicability of the optimization results.

[0004] Existing technical solutions also disclose treating frictional heat generation as an interfacial heat flux density applied to the conical contact area, setting forced convection heat transfer boundaries on the oil groove and exposed surfaces, and applying adiabatic conditions on the symmetry plane. This allows for the acquisition of key results such as the peak temperature at the outer edge of the friction plate, radial temperature difference, and temperature rise rate. While employing a polyhedral mesh with symmetric simplification for single-run three-dimensional transient simulations, this approach also reveals a limitation: "inability to efficiently perform global parameter searches."

[0005] Traditional single surrogate models suffer from large prediction errors in high-dimensional, strongly nonlinear responses, and their effectiveness in multi-objective trade-offs is limited: Kriging models offer good global accuracy but exhibit large fluctuations in local extrema; radial basis function models provide smooth local fitting but are unstable in extrapolation; and polynomial response surfaces are computationally fast but struggle to characterize strong nonlinearities. When using a single surrogate model, errors accumulate or are unevenly distributed, and the Pareto front is prone to producing spurious optimal solutions, requiring repeated interpolation corrections, thus limiting efficiency.

[0006] Therefore, there is an urgent need for a method that can efficiently and accurately optimize the thermo-mechanical performance of multi-cone friction pairs, so as to improve torque output while reducing peak temperature and radial temperature difference, thereby improving the working reliability and service life of the clutch. Summary of the Invention

[0007] To address the problems existing in the prior art, the purpose of this invention is to provide a multi-objective optimization method for multi-cone friction pairs based on a hybrid surrogate model. Considering the combined influence of friction pair structural parameters on temperature field distribution and friction transmission performance, this invention provides an efficient multi-objective optimization approach to significantly reduce radial temperature non-uniformity at the friction interface (reducing peak temperature and radial temperature difference) and improve the output torque of the friction pair, thereby achieving a synergistic improvement in the thermo-mechanical performance of the clutch. In other words, this invention overcomes the limitations of existing technologies, such as a single optimization objective and insufficient accuracy of the surrogate model, effectively alleviating the heat concentration problem of multi-cone friction pairs and enhancing their torque transmission capability.

[0008] To achieve the above objectives, the present invention provides the following solution: Multi-objective optimization methods for multi-conical friction pairs based on hybrid surrogate models include: A three-dimensional transient thermo-fluid coupling model of a multi-cone friction pair was constructed, and thermal boundary conditions were set to determine the temperature field evolution and friction torque under clutch engagement conditions. With the objective function of minimizing peak temperature and radial temperature difference while maximizing frictional torque, the Pareto optimal solution set is obtained by iteratively solving the objective function based on a hybrid surrogate model, thus obtaining the optimal design scheme for the multi-cone friction pair.

[0009] Optionally, setting the thermal boundary conditions includes: ; in, For the boundary of frictional heat generation, This serves as the forced convection boundary within the oil tank. For planar convection cooling boundary, For the adiabatic boundary, This represents the outward normal vector perpendicular to the i-th boundary surface. Corresponding to each boundary to The normal vector, To take into account the overall surface heat flux density, The initial temperature. Indicates ambient temperature. The thermal conductivity of the material. For temperature field, The convective heat transfer coefficient within the oil tank. is the planar convection heat transfer coefficient.

[0010] Optionally, determining the temperature field evolution and frictional torque under the clutch engagement condition includes: Based on the three-dimensional transient thermal-fluid coupling model of the multi-cone friction pair, the temperature field evolution under the clutch engagement condition is determined, that is, the transient temperature distribution inside the friction plate at any time, and the corresponding friction torque is calculated by combining the contact pressure and the friction coefficient.

[0011] Optionally, the contact pressure includes: ; in, This represents the contact pressure on the friction surfaces. This represents the normal force acting on the cone surface. For the applied axial load, To add external pressure, The contact area under load. It is a cone angle. This represents the total contact surface area.

[0012] Optionally, setting the objective function includes: ; in, To minimize peak temperature, To minimize radial temperature difference, To maximize frictional torque, This is the root height. The tooth surface height, For tooth width, It is the cone angle.

[0013] Optionally, constructing the hybrid agent model includes: Sample points are selected within the design variable space, and the original peak temperature, original radial temperature difference, and original friction torque values ​​are calculated for each sample point. These values ​​are then used to form a training set for fitting and modeling the Kriging model, radial basis function model, and polynomial response surface model, thereby obtaining various surrogate sub-models. The overall accuracy and prediction error of each proxy sub-model are evaluated. The proxy sub-model with the smallest error and the highest accuracy is selected as the reference benchmark model and then weighted and fused to obtain the hybrid proxy model.

[0014] Optionally, weighted fusion of the reference benchmark model includes: ; ; ; in, Let i be the predicted value of the i-th sub-model. This provides an estimate of the prediction variance of the baseline model within this interval. This represents the relative confidence level of the i-th model under the current input. As a weighting factor, The predicted value is the baseline model. Let be the relative credibility of the j-th model. This represents the total number of sub-models.

[0015] Optionally, obtaining the optimal design scheme for the multi-cone friction pair includes: The peak temperature, radial temperature difference, and friction torque of each candidate scheme in the Pareto optimal solution set are weighted, a weighted comprehensive index is calculated, and the set of structural parameters with the highest comprehensive score is determined as the optimal design scheme of the multi-cone friction pair.

[0016] Optionally, calculating the weighted composite index includes: ; ; in, This represents the original value of the i-th scheme for the j-th objective. , Let the minimum and maximum values ​​of the j-th objective be among all alternative solutions. The overall score is based on the three objectives. Let the weight be the weight of the j-th objective. Let be the normalized value of the i-th scheme for the j-th objective.

[0017] The beneficial effects of this invention are as follows: The method provided by this invention combines transient thermal-fluid simulation, hybrid surrogate modeling, and multi-objective optimization to achieve synergistic optimization of the structural parameters of multi-conical friction pairs, achieving significant results in reducing uneven thermal load and improving transmission performance. Firstly, by using a hybrid surrogate model instead of direct simulation for optimization, the efficiency and accuracy of the optimization solution are greatly improved. Compared with a single model, the hybrid model effectively reduces prediction errors, improves the fitting ability to complex nonlinear problems, and enables the optimization algorithm to more accurately evaluate the performance of candidate designs, thereby enhancing the reliability and convergence speed of the optimization results.

[0018] The optimized design obtained by this invention shows significant improvements in thermo-mechanical performance compared to the original design: the peak temperature of the friction pair during operation is reduced by approximately 6.5%, the radial temperature difference is reduced by approximately 48.9%, while the friction torque is increased by approximately 13.3%. This multi-objective comprehensive improvement is difficult to achieve with existing single-objective optimization, fully demonstrating its effectiveness in improving the thermal uniformity of the friction pair and increasing torque output.

[0019] This invention can significantly alleviate the thermal stress concentration of the clutch disc by reducing the non-uniformity of the temperature field, thereby reducing the risk of thermal warping deformation and thermal fatigue failure; at the same time, the increased torque capacity helps to improve the transmission efficiency of the clutch.

[0020] In summary, this invention provides an efficient and practical technical means for the design and improvement of multi-cone friction pairs, which can significantly improve the working reliability of the clutch and extend its service life. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of the multi-objective optimization method for multi-cone friction pairs based on a hybrid proxy model according to an embodiment of the present invention; Figure 2 This is a schematic diagram of mesh generation and periodic boundary conditions according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the thermal boundary conditions of the multi-cone friction pair clutch according to an embodiment of the present invention; ①-friction heat generation boundary, ②-forced convection boundary in the oil groove, ③-planar convection cooling boundary, ④-insulation (symmetric) boundary; Figure 4 This is a schematic diagram of the loading state of a single contact surface according to an embodiment of the present invention; Figure 5 This is a schematic diagram of clutch optimization parameters according to an embodiment of the present invention; Figure 6 This is a flowchart of the hybrid model according to an embodiment of the present invention; Figure 7 This is a schematic diagram of a multi-objective Pareto solution according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the friction pair of the multi-cone wet clutch according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the clutch oil flow in the disengaged state according to an embodiment of the present invention; Figure 10This is a schematic diagram illustrating the adaptation of the final optimization results of this invention under different engagement speeds. Figure 11 This is a schematic diagram illustrating the comprehensive performance of the optimized multi-cone friction pair under variable load conditions according to an embodiment of the present invention. Figure 12 This is a schematic diagram of the irregular constraint domain sampling process according to an embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] like Figure 1 As shown, this embodiment discloses a multi-objective optimization method for multi-cone friction pairs based on a hybrid surrogate model, including: constructing a three-dimensional transient thermal-fluid coupling model of the multi-cone friction pair and setting thermal boundary conditions to determine the temperature field evolution and friction torque under clutch engagement conditions; taking minimizing peak temperature and radial temperature difference and maximizing friction torque as the objective function, iteratively solving the Pareto optimal solution set based on the hybrid surrogate model to obtain the optimal design scheme of the multi-cone friction pair.

[0026] Specifically, this embodiment discloses a multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model, including: Step 1: Establish a high-fidelity simulation baseline model: First, construct a three-dimensional transient thermal-fluid coupling model of the multi-conical friction pair to reproduce the temperature field evolution and friction torque output under clutch engagement conditions. To improve computational efficiency, it is assumed that frictional heat generation is uniformly distributed in the circumferential direction, the material's thermal properties are isotropic and independent of temperature, and the temperature field is symmetrically distributed with respect to the mid-surface of the friction pair; thus, the complete three-dimensional heat conduction problem can be simplified to a half-section two-dimensional transient thermal analysis.

[0027] like Figure 2-3As shown, the model defines four types of thermal boundary conditions: Frictional heat generation boundary ①—applies a uniform surface heat flux density to the conical contact area to describe the heat converted from frictional work; Forced convection boundary ②—applies a velocity-dependent convective heat transfer coefficient to the grooves between the friction plates and the sidewalls to simulate the heat carried away by the cooling oil; Planar convective cooling boundary ③—applies a convection coefficient calculated by empirical formula to the exposed planes of the steel plates and friction plates to simulate the heat dissipation of the oil by grazing; Adiabatic (symmetric) boundary ④—applies a zero heat flux condition to the symmetric plane of the model, thereby reducing the computational domain.

[0028] This coupled model can be used to obtain the transient temperature distribution inside the friction plate at any given time, and combined with the contact pressure ( Figure 4 The output torque is calculated by combining the friction coefficient with the torque output, providing high-fidelity data support for subsequent hybrid surrogate model training and multi-objective optimization. ; in, This represents the outward normal vector perpendicular to the i-th boundary surface. Corresponding to each boundary The normal vector; To take into account the overall surface heat flux density, The initial temperature. Indicates ambient temperature.

[0029] ; in, This represents the contact pressure on the friction surfaces. This represents the normal force acting on the cone surface. For the applied axial load, To add external pressure, The contact area under load. It is a cone angle. This represents the total contact surface area.

[0030] The contact pressure is a prerequisite for the friction torque; that is, the friction torque is first calculated using the contact pressure, and then the friction torque is used as the objective function for subsequent optimization.

[0031] The contact area of ​​the i-th cone surface in a multi-conical friction pair on the friction surface is: ; The total contact area on the n cone surfaces of a multi-conical friction pair is: ; In the formula: The contact pressure of the multi-conical friction pair, For the first The contact area of ​​each conical surface This is the axial clamping force. , The first The outer and inner diameters of the conical surfaces The radius of the cone surface of the multi-cone friction pair is... The number of cone surfaces in a multi-cone friction pair; For the i-th cone surface of a multi-conical friction pair, its tangential friction force is: ; In the formula: For the first Tangential friction on the surface of a cone The contact pressure of the friction surfaces; Calculations show that the first The frictional torque generated on each conical surface is: ; The total frictional torque generated on the conical surface is: ; In the formula, For the first Frictional torque on the contact surface; This represents the total frictional torque.

[0032] Step 2: Determine design variables and optimization objectives: Based on the friction pair structure and thermodynamic analysis, several key structural parameters are selected as optimization design variables. In this invention, four geometric parameters that significantly affect the performance of the friction pair are preferred as design variables: tooth root height, tooth tip height, tooth width, and cone angle. Figure 5 As shown. Simultaneously, the optimization objective function is determined, including three indicators: peak temperature, radial temperature difference, and output friction torque during the friction pair's operation. Peak temperature and radial temperature difference characterize the concentration of the temperature field in the friction pair, while friction torque characterizes the clutch's transmission capacity. The optimization objective is to simultaneously reduce peak temperature and radial temperature difference, and increase friction torque, within the allowable range of design variables.

[0033] The following formula transforms the structural parameter optimization problem of a multi-cone friction pair into a typical three-objective programming model: using four design variables: tooth root height, tooth surface height, tooth width, and cone angle. The independent variable is the peak temperature, which is minimized. Minimize radial temperature difference And maximize frictional torque Furthermore, the design variables are subject to geometric and assembly constraints: , , ,as well as The multi-objective model was then solved using a non-dominated sorting genetic algorithm to obtain the Pareto optimal trade-off between peak temperature, radial temperature difference, and torque performance. Setting the objective function includes: ; in, To minimize peak temperature, To minimize radial temperature difference, To maximize frictional torque, This is the root height. The tooth surface height, For tooth width, It is the cone angle.

[0034] Step 3: Construct a hybrid agent model: Obtain a limited number of sample data within the defined design space for agent model training.

[0035] Specifically, by optimizing Latin hypercube sampling and other methods, a certain number of sample points are selected within the aforementioned 4-dimensional design variable space to calculate the peak temperature, radial temperature difference, and friction torque values ​​for each sample. Using these high-dimensional input-output data as the training set, Kriging, radial basis function (RBF), and polynomial response surface (PRS) models are employed for fitting and modeling, respectively, to obtain three corresponding surrogate sub-models. Subsequently, the prediction errors of each sub-model are evaluated using methods such as cross-validation, and based on this, different weights are assigned to different sub-models. These multiple surrogate models are then integrated to construct a high-precision hybrid surrogate model.

[0036] Selecting sample points within the 4D design variable space includes: In structural optimization problems, design variables are typically constrained by various physical constraints such as size and structural stability. Directly performing optimization Latin hypercube sampling (OLHS) within the full variable space can easily lead to a large number of samples falling into infeasible regions, increasing computational costs and reducing the efficiency of surrogate model training. To improve the effective sample acquisition rate and ensure the quality of sample distribution, this invention proposes an optimization Latin hypercube sampling based on irregular constraint domains that combines high-density sampling, constraint determination, perturbation correction, and sample uniformity enhancement, such as... Figure 12 .

[0037] This strategy comprises the following three core phases: Step 1: High-density candidate sample generation. Perform high-density optimized Latin hypercube sampling (OLHS) within the original domain of the design variables to generate a multidimensional candidate sample set.

[0038] To reduce sample redundancy and correlation, a column swapping strategy is used to structurally adjust the sample results, making the distribution of each variable within the sample set more independent and improving the ability of subsequent surrogate models to distinguish the effects of heat response variables.

[0039] ; In the formula, Let Pearson correlation coefficient be the coefficient between the j-th and k-th dimension sample columns. Minimize this coefficient through iterative permutation. This makes the distribution of sample points more orthogonal in all dimensions, improving their spatial resolution and distribution balance.

[0040] Step 2: Constraint Screening and Perturbation Correction. Based on the multiple physical and geometric constraints defined in the optimization problem, the candidate sample set is... Each sample Calculate its maximum constraint violation.

[0041] ; In the formula, Let be the violation quantity of the j-th nonlinear inequality constraint. For constraints satisfying , ... Sample points with a value of 0 are directly retained; for At this point, the following Gaussian perturbation correction mechanism is implemented to improve the efficiency of obtaining feasible samples and reduce the risk of high-quality samples being rejected due to slight out-of-bounds errors.

[0042] ; In the formula, For the perturbation step size, A Gaussian random vector with unit variance. The size limit is 1% of the width of the upper and lower limit interval. This mechanism allows slightly out-of-bounds samples to be pulled back to the feasible region within the control range, effectively improving the retention rate of boundary samples and the structural integrity of the sample set.

[0043] Step 3: Enhanced Sample Uniformity under the Maximum-Minimum Distance Criterion. To enhance the spatial uniformity of the final feasible samples, a subset satisfying the maximum-minimum distance criterion is extracted from the fine-tuned feasible sample set. This criterion not only improves the breadth coverage of thermal response modeling but also avoids fitting bias that may be caused by sample clustering, providing good data support for multi-objective thermal performance optimization.

[0044] This hybrid model combines the advantages of each sub-model, enabling it to more accurately approximate the nonlinear mapping relationship between design variables and optimization objectives. As shown in Table 1, the hybrid surrogate model constructed in this embodiment exhibits a normalized root mean square error (NRMSE) of only about 7.47% on the test set, with a coefficient of determination (R²) exceeding 0.95. The hybrid model shows significantly lower NRMSE, significantly higher R², and effective suppression of NMaxAE on the same sample set, demonstrating higher prediction accuracy compared to any single model, especially showing greater robustness in predicting extreme boundary samples. The comprehensive evaluation of NRMSE and R², along with the local test of NMaxAE, fully reveals the stability and reliability of the surrogate model, providing a reliable foundation for subsequent optimization. Figure 6 As shown.

[0045] Table 1. Accuracy Evaluation Indicators of the Agent Model As shown in Table 1, the hybrid model significantly reduces NRMSE, significantly improves R², and effectively suppresses NMaxAE on the same sample set, especially showing more robust performance in predicting extreme boundary samples.

[0046] The basic form of the hybrid model is: ; ; in, Let represent the prediction value of the i-th sub-agent model for input x. The corresponding weights are set. These can be selected as global fixed values ​​based on model performance, or they can be adaptively adjusted based on the local distribution characteristics of the input samples.

[0047] Leave-one-out cross-validation (LOOCV) is used to evaluate the overall accuracy of multiple base surrogate models. MSE is selected as the error evaluation method for cross-validation. Based on the global performance of each surrogate model, the model with the smallest cross-validation error and the highest overall accuracy is selected as the reference benchmark model and used to score other models, thereby preventing the weaknesses of a single model from being carried into the fusion result.

[0048] The global prediction error (MSE) of each sub-model was evaluated using leave-one-out cross-validation. LOOCV The model with the smallest error is selected as the baseline model. Using the predictions of this baseline model as a reference, weighted fusion is performed in the following form, without considering local optima: ; in, This represents the true response value of the i-th sample. This indicates the proxy model constructed without including the i-th sample. The predicted value.

[0049] The prediction results within each model are extracted separately, and the locally optimal sub-model is selected based on the MSE evaluation results of the current region and then weighted and fused in the following manner.

[0050] ; ; in, Let i be the predicted value of the i-th sub-model. This provides an estimate of the prediction variance of the baseline model within this interval. This represents the relative confidence level of the i-th model under the current input. This is the weighting factor.

[0051] Step 4: Perform multi-objective optimization: Based on the above hybrid surrogate model, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II algorithm) is used to perform multi-objective optimization on the multi-cone friction pair structure. NSGA-II is a commonly used multi-objective optimization genetic algorithm that completes a global search of the design space through population evolution iteration. Using this algorithm to optimize the surrogate model, Pareto optimal solution sets that satisfy different objective trade-offs can be obtained simultaneously. In this invention, peak temperature, radial temperature difference, and friction torque are used as optimization objectives input into the NSGA-II algorithm. Through genetic evolution, a Pareto front solution set covering these three performance parameters is obtained, such as... Figure 7 As shown in the figure, this solution set describes possible trade-offs between thermal and mechanical properties for the structural parameters of the multi-cone friction pair, providing a candidate basis for selecting the optimal design.

[0052] Step 5: Selecting the optimal compromise solution: For the obtained Pareto optimal solution set, a compromise optimal design that balances various objectives can be selected using methods such as weighted decision-making, based on specific needs. In this embodiment, considering the need to reduce the risk of thermal deformation, temperature-related objectives are assigned higher weights. Specifically, peak temperature and radial temperature difference are weighted at 0.4, and friction torque is weighted at 0.2. Then, a weighted comprehensive index is calculated for each solution in the Pareto solution set, and the set of structural parameters with the highest comprehensive score is selected as the optimal solution. Through this preference weighting, it is ensured that the finally selected design significantly reduces the temperature gradient while also achieving a certain torque increase.

[0053] ; In the formula, This represents the original value of the i-th scheme for the j-th objective. , Let be the minimum and maximum values ​​of the j-th objective among all alternatives.

[0054] Then, weights are assigned to each objective based on the decision-maker's assessment of its importance, and a comprehensive score for the three objectives is constructed: ; Pick The smallest solution is the compromise solution that is "weighted optimal". Since the weighted sum method is only used on the fully dominant Pareto solution set after screening, it will not miss solutions due to the non-convex shape of the frontier. At the same time, it can quickly analyze and verify the robustness of the selected solution under the preference scenario by using different weights.

[0055] Step 6: Verify the optimization effect: Finally, substitute the selected optimal design scheme into the three-dimensional thermal-fluid coupling model for finite element simulation verification, and compare the performance differences before and after optimization to confirm the effectiveness of the invention. If conditions permit, the optimization effect can also be further verified through prototype testing, demonstrating that the optimization method has good engineering applicability.

[0056] This invention combines three-dimensional transient thermo-fluid coupling simulation, a hybrid surrogate model, and the NSGA-II multi-objective genetic algorithm to form a complete structural parameter optimization technology scheme, which can be used to simultaneously optimize the temperature field distribution and torque transmission performance of friction pairs. A hybrid surrogate model integrating multiple modeling techniques such as Kriging, RBF, and PRS is constructed. By assigning weights to the prediction errors of each individual model and fusing them, this hybrid model significantly improves the prediction accuracy of complex nonlinear mapping relationships (test error NRMSE approximately 7.5%, R²>0.95), ensuring the efficiency and reliability of evaluation calculations during the optimization process, and achieving a coordinated improvement in the thermo-mechanical performance of the friction pairs. Compared with the original design, the optimized friction pair shows a reduction of approximately 6% in peak temperature, a reduction of nearly 50% in radial temperature difference, and an increase of approximately 13% in friction torque, effectively alleviating the thermal instability problem caused by uneven temperature field in the friction pair and improving the reliability and service life of the clutch.

[0057] like Figure 4 , 8 As shown in Figure 9, the method of the present invention will be specifically described using a multi-cone wet clutch friction pair as an example. This clutch friction pair consists of upper and lower annular steel plates and a middle friction plate. Multiple concentrically distributed conical friction rings (tooth-shaped structures) are machined on the friction plate, evenly arranged in the radial direction. Each conical friction ring independently bears a portion of the normal load during engagement and contributes to the overall output torque through combined action. Compared to traditional multi-plate clutches, under the same axial clamping force, this multi-cone structure effectively increases the pressure-bearing capacity per unit area and the total contact area, thereby achieving a higher torque density output within a limited axial space. This friction pair achieves engagement and disengagement through hydraulic control, and its working cycle includes stages such as engagement, locking, disengagement, and idling. When entering the engagement stage, the axial pressure applied by the piston presses the conical surface of the middle friction plate tightly against the conical surfaces of the upper and lower steel plates. During this process, only a small amount of lubricating oil passes through the friction pair interface; most of the oil flows around the outside of the clutch assembly, carrying away heat through the top and bottom surfaces of the steel plates and the inner and outer edges of the clutch. Since the amount of oil passing through the interface is extremely limited, most of the frictional heat of the friction pair must be dissipated through the local thin oil film and solid material conduction at the interface. Therefore, under continuous slippage friction, heat is more likely to accumulate in the outer edge region of the friction plate, and the temperature is significantly higher than that of the inner side, forming a significant temperature gradient along the radial direction. This also confirms the heat concentration phenomenon mentioned in the background art.

[0058] like Figure 10As shown, to systematically evaluate the generalization ability and engineering applicability of the optimized model under different operating conditions, the thermal performance of the clutch over a wide speed range was further monitored based on the geometric configuration obtained from single-point optimization at 800 r / min. The main analysis range was selected as 400 r / min to 2000 r / min, and five typical operating points of 400, 800, 1200, 1600, and 2000 r / min were set at equal intervals to compare the differences between the original model and the optimized model in terms of maximum temperature, radial temperature difference, and transmitted torque.

[0059] The optimized model exhibits superior overall performance across the entire speed range: Since the optimized model is designed based on a single-point operating condition, the performance improvement is most significant at this speed point. Compared with the original model, the peak temperature decreases by approximately 11.7%, and the maximum temperature difference decreases by 29.28%, fully demonstrating the targeted optimization effect of this invention for this operating condition. At other speeds, the optimized model maintains good adaptability: the peak temperature decreases by an average of 11.61% in the range of 400–2000 r / min, and the maximum temperature difference decreases by an average of approximately 17.25%. Especially in the high-speed region, the optimized model can still effectively suppress temperature rise and thermal gradient, indicating that the obtained configuration has strong thermal robustness.

[0060] The optimization design based on a single-point operating condition not only achieves optimal performance at that point, but also demonstrates good adaptability and robustness over a wide speed range, verifying the effectiveness and promotional value of the proposed hybrid proxy model and multi-objective optimization framework in engineering practice.

[0061] like Figure 11 As shown, to further evaluate the comprehensive performance and engineering applicability of the optimized multi-cone friction pair under variable load conditions, a comparative analysis was conducted under different loading pressure conditions. Loading pressure, as a key operating parameter directly affecting the clutch contact state, frictional heat generation, and interface temperature distribution, significantly impacts the thermo-mechanical performance of the system.

[0062] This invention selects five loading pressure levels of 0.05MPa, 0.10MPa, 0.15MPa, 0.20MPa and 0.25MPa at a fixed rotation speed of 800 r / min, and conducts a systematic comparison of the thermal-fluid-structure interaction response of the model before and after optimization. The optimized model shows an overall performance improvement under all pressure levels.

[0063] The optimization effect is most significant at a design pressure of 0.10 MPa: the radial temperature difference is reduced by 29.28%, the peak temperature decreases by 9.82%, and the transmitted torque is increased by 33%. It is worth noting that the frictional torque mainly depends on the geometric configuration. Therefore, under the fixed geometry optimized in this invention, it maintains a relatively stable gain trend under various pressures.

[0064] At lower pressures, the optimized model still significantly improves temperature uniformity, and the peak temperature decreases by approximately 3.65%, indicating that the optimized design can effectively alleviate local overheating under low load conditions. In the higher pressure range, although the overall temperature rise increases with increasing load, the increase is significantly suppressed in the optimized model compared to the original model, demonstrating good thermal management robustness and load-bearing adaptability.

[0065] The above analysis shows that the optimized configuration obtained by this invention based on the hybrid surrogate model and the NSGA-II algorithm not only exhibits optimal performance under the target pressure, but also demonstrates stable performance improvement and good operating condition extrapolation capability over a wider pressure range. This proves that the optimized design improves the overall thermo-mechanical robustness of the friction pair system, providing a reliable basis for its engineering application in variable load transmission systems.

[0066] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model, characterized in that, include: A three-dimensional transient thermo-fluid coupling model of a multi-cone friction pair was constructed, and thermal boundary conditions were set to determine the temperature field evolution and friction torque under clutch engagement conditions. With the objective function of minimizing peak temperature and radial temperature difference while maximizing frictional torque, the Pareto optimal solution set is obtained by iteratively solving the objective function based on a hybrid surrogate model, thus obtaining the optimal design scheme for the multi-cone friction pair.

2. The multi-objective optimization method for multi-cone friction pairs based on a hybrid surrogate model according to claim 1, characterized in that, Setting the thermal boundary conditions includes: ； in, For the boundary of frictional heat generation, This serves as the forced convection boundary within the oil tank. For planar convection cooling boundary, For the adiabatic boundary, This represents the outward normal vector perpendicular to the i-th boundary surface. Corresponding to each boundary to The normal vector, To take into account the overall surface heat flux density, The initial temperature, Indicates ambient temperature. The thermal conductivity of the material. For the temperature field, The convective heat transfer coefficient within the oil tank. is the planar convection heat transfer coefficient.

3. The multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model according to claim 1, characterized in that, Determining the temperature field evolution and frictional torque under the clutch engagement condition includes: Based on the three-dimensional transient thermal-fluid coupling model of the multi-cone friction pair, the temperature field evolution under the clutch engagement condition is determined, that is, the transient temperature distribution inside the friction plate at any time, and the corresponding friction torque is calculated by combining the contact pressure and the friction coefficient.

4. The multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model according to claim 3, characterized in that, The contact pressure includes: ； in, This represents the contact pressure on the friction surfaces. This represents the normal force acting on the cone surface. For the applied axial load, To add external pressure, The contact area under load. It is a cone angle. This represents the total contact surface area.

5. The multi-objective optimization method for multi-cone friction pairs based on a hybrid surrogate model according to claim 1, characterized in that, Setting the objective function includes: ； in, To minimize peak temperature, To minimize radial temperature difference, To maximize frictional torque, This is the root height. The tooth surface height, For tooth width, It is the cone angle.

6. The multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model according to claim 1, characterized in that, Constructing the hybrid agent model includes: Sample points are selected within the design variable space, and the original peak temperature, original radial temperature difference, and original friction torque values ​​are calculated for each sample point. These values ​​are then used to form a training set for fitting and modeling the Kriging model, radial basis function model, and polynomial response surface model, thereby obtaining various surrogate sub-models. The overall accuracy and prediction error of each proxy sub-model are evaluated. The proxy sub-model with the smallest error and the highest accuracy is selected as the reference benchmark model and then weighted and fused to obtain the hybrid proxy model.

7. The multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model according to claim 6, characterized in that, The weighted fusion of the reference benchmark model includes: ； ； ； in, Let i be the predicted value of the i-th sub-model. This provides an estimate of the prediction variance of the baseline model within this interval. This represents the relative confidence level of the i-th model under the current input. As a weighting factor, The predicted value is the baseline model. Let be the relative credibility of the j-th model. This represents the total number of sub-models.

8. The multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model according to claim 1, characterized in that, Obtaining the optimal design scheme for the multi-cone friction pair includes: The peak temperature, radial temperature difference, and friction torque of each candidate scheme in the Pareto optimal solution set are weighted, a weighted comprehensive index is calculated, and the set of structural parameters with the highest comprehensive score is determined as the optimal design scheme of the multi-cone friction pair.

9. The multi-objective optimization method for multi-conical friction pairs based on a hybrid surrogate model according to claim 8, characterized in that, The calculation of the weighted composite index includes: ； ； in, This represents the original value of the i-th scheme for the j-th objective. , Let the minimum and maximum values ​​of the j-th objective be among all alternative solutions. The overall score is based on the three objectives. Let the weight be the weight of the j-th objective. Let be the normalized value of the i-th scheme for the j-th objective.

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