Mechanical performance optimization method of leaf spring suspension

Abstract

The present invention relates to the technical field of vehicle chassis system performance optimization, and in particular to a method for optimizing the mechanical properties of a leaf spring suspension, comprising the following steps: S1: establishing a finite element analysis model of a leaf spring suspension based on CAE technology, and verifying the accuracy and effectiveness of the finite element analysis model of the leaf spring suspension. S2: performing simulation analysis under a double full load condition to determine the optimization target. S3: combining the mechanical design theory of the leaf spring suspension, constructing a three-factor three-level test matrix, obtaining significant influencing factors, and determining the optimal parameter range of the significant influencing factors. S4: establishing a Kriging prediction model in combination with the Kriging interpolation algorithm, and using a genetic algorithm for multi-objective optimization to obtain the optimal parameter combination of the three factors. The advantage of the present invention is that a Kriging prediction model of the objective function of the leaf spring suspension is constructed based on the Kriging interpolation algorithm, and a genetic algorithm is used for multi-objective optimization to obtain the optimal structural parameter combination. The mechanical performance of the optimized leaf spring suspension is significantly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle chassis system performance optimization, and in particular to a method for optimizing the mechanical performance of a leaf spring suspension. Background Art

[0002] Leaf spring suspensions consist of leaf springs, shock absorbers, and other components. The combined action of these components absorbs road shock and vibration, effectively mitigating vehicle body vibrations and improving ride smoothness and comfort. Furthermore, their simple structure makes them suitable for prolonged, intensive use, making them widely used on heavy-duty vehicles.

[0003] However, when the leaf spring suspension used in heavy vehicles operates under long-term and complex working conditions, the leaf springs are subjected to cyclic stresses, which can easily lead to failures such as loosening of the U-bolts of the leaf spring suspension, breakage of the leaf springs, and degradation of the leaf spring performance, directly affecting their fatigue life and operational reliability.

[0004] Previous research has often used composite materials to replace traditional leaf springs to achieve lightweight and improved mechanical properties. However, the high cost and complex production process of composite materials pose key technical challenges to leaf spring suspension optimization research. Summary of the Invention

[0005] Based on this, this paper proposes a method for optimizing the mechanical properties of a leaf spring suspension. This method establishes a finite element analysis model for the leaf spring suspension and utilizes orthogonal experimental design to investigate the impact of factors on von Mises stress and mass. A Kriging prediction model is established using the Kriging interpolation algorithm, and a genetic algorithm is employed to perform multi-objective optimization of the leaf spring suspension.

[0006] To achieve the above-mentioned object, the technical solution created by the present invention is implemented as follows: a method for optimizing the mechanical properties of a leaf spring suspension, comprising the following steps:

[0007] S1: Based on CAE technology, a finite element analysis model of the leaf spring suspension is established. By comparing the finite element analysis results with the actual vehicle road test data of the leaf spring suspension, the accuracy and effectiveness of the finite element analysis model of the leaf spring suspension are verified.

[0008] S2: Based on the leaf spring suspension finite element analysis model verified in step S1, perform simulation analysis under double full load conditions to determine the optimization target.

[0009] S3: Based on the optimization goal determined in step S2 and combined with the mechanical design theory of leaf spring suspension, a three-factor three-level test matrix is ​​constructed. The significant influencing factors are obtained through variance analysis, and the optimal parameter range of the significant influencing factors is determined.

[0010] S4: Based on the significant influencing factors obtained in step S3, a Kriging prediction model is established in combination with the Kriging interpolation algorithm, and the Kriging prediction model is optimized by a genetic algorithm to obtain the optimal parameter combination of the three factors.

[0011] Furthermore, step S1 includes the following steps:

[0012] S11: Based on CAE technology, a finite element analysis model of the leaf spring suspension is established to simulate its actual working state. By solving the finite element analysis model of the leaf spring suspension, the mechanical response of stress and deformation is obtained.

[0013] S12: extracting the result data of the finite element analysis in step S1, outputting a simulation load-deformation curve of the leaf spring suspension finite element analysis model, and calculating the simulation stiffness of the leaf spring suspension finite element analysis model based on the simulation load-deformation curve.

[0014] S13: Based on the actual vehicle road test of the leaf spring suspension, the experimental load-displacement curve of the leaf spring suspension is drawn, and the experimental stiffness of the leaf spring suspension is calculated. By comparing the experimental stiffness and simulation stiffness of the leaf spring suspension, the accuracy and effectiveness of the leaf spring suspension finite element analysis model are verified.

[0015] Furthermore, in step S2, the maximum stress value and distribution position of the leaf spring suspension finite element analysis model are determined by simulation analysis of the leaf spring suspension finite element analysis model under double full load conditions, so as to determine the optimization target and optimization parameters.

[0016] Furthermore, step S3 includes the following steps:

[0017] S31: construct objective function;

[0018] S32: Construct stiffness constraint equation based on the stiffness of leaf spring suspension;

[0019] S33: A three-factor, three-level test matrix was constructed using a Box-Behnken experimental design; the three factors included the length, width, and thickness of the leaf spring suspension, and each factor was set at three levels: low, medium, and high.

[0020] S34: Based on a three-factor, three-level test matrix, a parameterized leaf spring suspension 3D model was constructed. Finite element analysis was performed on the leaf spring suspension under various factor configurations. Von Mises stress and mass data were obtained under different factor combinations through finite element analysis. Variances analysis was used to evaluate each factor and identify significant influencing factors.

[0021] S35: Use the response surface method to analyze the response of the objective function to the changes of the significant influencing factors and determine the optimal parameter range of the significant influencing factors.

[0022] Furthermore, the objective function and constraint equations are:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] in, Indicates that the variable is 、 、 The objective function of 、 Represents the weight coefficient of the objective function; 、 The expression and variable are 、 、 Related performance indicators;

[0028] represents the constraint stiffness of the leaf spring suspension; K represents the stiffness of the leaf spring suspension, Indicates the design stiffness of the leaf spring suspension.

[0029] Furthermore, in step S4, the Kriging prediction model takes the length, width, and thickness of the leaf spring suspension as input, and outputs the von Mises stress and mass of the leaf spring suspension through interpolation prediction. The von Mises stress and mass of the leaf spring suspension are used as multi-objective optimization of the genetic algorithm. The predicted value expression of the Kriging prediction model is:

[0030] ;

[0031] Random Item z(x) are all zero, and its spatial covariance function is:

[0032] ;

[0033] in, Represents the predicted value of the Kriging prediction model; represents the jth known regression coefficient; express Correlation coefficient of is the random residual term; k represents the polynomial cardinality the total number of; Represents a random process z(x) covariance of represents the process variance; R represents the correlation function; Represents the correlation function between any two predicted values; represents the correlation coefficient; express The nth component of ; express The nth component of , n represents the nth dimension of the design variable; N represents the total dimension of the design variable.

[0034] Solve the regression coefficient and correlation coefficient based on the experimental data, and calculate the predicted value and mean square error of the unknown point:

[0035] ;

[0036] ;

[0037] in, express The predicted value at represents the estimated value of the regression coefficient; Represents the inverse matrix of the correlation matrix between sample points; y represents the observation response vector, that is, the value of the von Mises stress and mass in the simulation scheme design; p Indicates that it contains components Column vector of ; represents the transpose of the design matrix; express The mean square error at ; represents variance estimation; r represents Correlation vector between sample points; Indicates an unknown point.

[0038] Furthermore, in step S4, the genetic algorithm optimization process includes the following steps:

[0039] S41: Obtain the parameters of the length, width and thickness of the leaf spring suspension through real number encoding;

[0040] S42: Use Latin hypercube sampling to randomly generate the initial population;

[0041] S43: Use the penalty function method to process individuals that do not meet the nonlinear constraints to ensure that all individuals in the population are within the initial population;

[0042] S44: Taking the von Mises stress and mass predicted by the Kriging model as the target, a normalized multi-objective fitness function is constructed, and the normalized multi-objective fitness function is evaluated to select excellent individuals from the parent generation;

[0043] S45: Based on the principle of survival of the fittest, select outstanding individuals and generate the second generation of individuals;

[0044] S46: Perform crossover and mutation on the second generation individuals to generate the third generation individuals;

[0045] S47: Repeat steps S43 to S46 until the maximum number of iterations is reached or convergence occurs.

[0046] Furthermore, the population size is N=100, and the chromosome latitude is , crossover probability , mutation probability , maximum number of iterations .

[0047] Furthermore, the nonlinear constraint in step S43 is a stiffness constraint.

[0048] The invention can achieve the following beneficial effects:

[0049] 1) Through on-road testing of leaf spring suspensions, a comparison of experimental and simulated stiffness revealed a relative error of less than 5%. This result demonstrates the high accuracy and effectiveness of the finite element analysis model for leaf spring suspensions, providing a reliable theoretical basis for optimizing leaf spring suspension design based on simulated and measured data.

[0050] 2) A three-factor three-level test matrix was constructed through Box-Behnken experimental design. The analysis found that the thickness of the leaf spring has the greatest impact on the von Mises stress and mass, while the length has the most significant impact on the mass.

[0051] 3) A Kriging prediction model for the leaf spring suspension objective function was constructed based on the Kriging interpolation algorithm. A genetic algorithm was then used for multi-objective optimization to obtain the optimal structural parameter combination. The optimized leaf spring suspension significantly improved its mechanical performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0053] Figure 1 is a flow chart of a method for optimizing the mechanical properties of a leaf spring suspension according to an embodiment of the present invention;

[0054] Figure 2 A finite element analysis model of leaf spring suspension force provided according to an embodiment of the present invention;

[0055] Figure 3 is a comparison diagram of a simulated load-deformation curve and an experimental load-deformation curve of a leaf spring suspension provided according to an embodiment of the present invention;

[0056] Figure 4 is a stress variation diagram of a leaf spring suspension under a double full load condition provided by an embodiment of the present invention;

[0057] Figure 5 is a stress variation diagram of the first leaf spring under a double full load condition provided by an embodiment of the present invention;

[0058] Figure 6 is a stress variation diagram of the second leaf spring under double full load conditions provided by an embodiment of the present invention;

[0059] Figure 7 is a stress variation diagram of the third leaf spring under double full load conditions provided by an embodiment of the present invention;

[0060] Figure 8 is a stress variation diagram of the fourth leaf spring under a double full load condition provided by an embodiment of the present invention;

[0061] Figure 9 is a stress variation diagram of the fifth leaf spring under a double full load condition provided by an embodiment of the present invention;

[0062] Figure 10 is a stress variation diagram of the sixth leaf spring under a double full load condition provided by an embodiment of the present invention;

[0063] Figure 11 is a stress variation diagram of the seventh leaf spring under a double full load condition provided by an embodiment of the present invention;

[0064] Figure 12 is a stress variation diagram of the eighth leaf spring under a double full load condition provided by an embodiment of the present invention;

[0065] Figure 13 3. This is a diagram showing the effect of the length, width and thickness of a leaf spring suspension provided by an embodiment of the present invention on von Mises stress;

[0066] Figure 14 1. This is a diagram showing the effect of the width and thickness of a leaf spring suspension on mass according to an embodiment of the present invention;

[0067] Figure 15 This is a diagram showing the effect of the width and thickness of the leaf spring suspension on the comprehensive performance according to an embodiment of the present invention;

[0068] Figure 16 is a maximum von Mises stress and safety factor variation curve of each leaf spring in the optimized front and rear leaf spring suspension provided by an embodiment of the present invention;

[0069] Figure 17 3. This is a rendering of a seventh-order modal analysis of an optimized front leaf spring suspension according to an embodiment of the present invention;

[0070] Figure 18 3. This is a rendering of an eighth-order modal analysis of an optimized front leaf spring suspension according to an embodiment of the present invention;

[0071] Figure 19 3. This is a rendering of a ninth-order modal analysis of an optimized front leaf spring suspension according to an embodiment of the present invention;

[0072] Figure 20 3. This is a rendering of a tenth-order modal analysis of an optimized front leaf spring suspension according to an embodiment of the present invention;

[0073] Figure 21 3. This is a rendering of an eleventh-order modal analysis of an optimized front leaf spring suspension according to an embodiment of the present invention;

[0074] Figure 22 This is a rendering of a twelfth-order modal analysis of an optimized front leaf spring suspension according to an embodiment of the present invention;

[0075] Figure 23 3. This is a rendering of a seventh-order modal analysis of an optimized leaf spring suspension according to an embodiment of the present invention;

[0076] Figure 24 3. This is a rendering of an eighth-order modal analysis of an optimized leaf spring suspension according to an embodiment of the present invention;

[0077] Figure 25 3. This is a rendering of a ninth-order modal analysis of an optimized leaf spring suspension according to an embodiment of the present invention;

[0078] Figure 26 3. This is a rendering of a tenth-order modal analysis of an optimized leaf spring suspension according to an embodiment of the present invention;

[0079] Figure 27 1 is a diagram showing the effect of performing an eleventh-order modal analysis on the optimized leaf spring suspension provided by an embodiment of the present invention;

[0080] Figure 28 3. This is a diagram showing the effect of a twelfth-order modal analysis of an optimized leaf spring suspension according to an embodiment of the present invention;

[0081] Figure 29 is a flow chart of a genetic algorithm provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0082] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0083] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0084] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0085] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0086] The present invention will be described in detail below with reference to the embodiments.

[0087] like Figures 1 to 29 As shown, an embodiment of the present invention provides a method for optimizing the mechanical properties of a leaf spring suspension, comprising the following steps:

[0088] S1: Based on CAE technology, a finite element analysis model of the leaf spring suspension is established. By comparing the finite element analysis results with the actual vehicle road test data of the leaf spring suspension, the accuracy and effectiveness of the finite element analysis model of the leaf spring suspension are verified. The steps include:

[0089] S11: Based on CAE (Computer-Aided Engineering) technology, a finite element analysis model of the leaf spring suspension was established (e.g. Figure 2 As shown in Figure 3), the actual working state is simulated and the mechanical response of stress and deformation is obtained by solving the finite element analysis model of the leaf spring suspension.

[0090] A 3D model of the leaf spring suspension was created in SolidWorks and converted into a finite element model. Displacement constraints were applied to the side surfaces and center section of the leaf spring suspension to simulate the restraining effects of the U-bolts, center bolt, and clamps. Fixed supports were placed on the straight section of the last leaf spring to simulate the support provided by the axle. Working loads were applied to both ends of the first leaf spring to simulate the deformation of the leaf spring suspension under actual operating conditions.

[0091] In this embodiment, the leaf spring suspension includes eight leaf springs, namely a first leaf spring, a second leaf spring, a third leaf spring, a fourth leaf spring, a fifth leaf spring, a sixth leaf spring, a seventh leaf spring, and an eighth leaf spring. The middle end of each leaf spring is a straight section. Each leaf spring has equal width and thickness.

[0092] S12: extracting the result data of the finite element analysis in step S1, outputting a simulation load-deformation curve of the leaf spring suspension finite element analysis model, and calculating the simulation stiffness of the leaf spring suspension finite element analysis model based on the simulation load-deformation curve.

[0093] S13: Based on the actual vehicle road test of the leaf spring suspension, the experimental load-displacement curve of the leaf spring suspension is plotted, and the experimental stiffness of the leaf spring suspension is calculated. By comparing the experimental stiffness and simulation stiffness of the leaf spring suspension, the accuracy and effectiveness of the leaf spring suspension finite element analysis model are verified.

[0094] like Figure 3 As shown in the figure, the black broken line is the simulated load-deformation curve, through which the simulated stiffness of the leaf spring suspension is directly obtained to be 582.28N / mm.

[0095] When conducting a road test of a leaf spring suspension, a laser displacement sensor is installed directly above the axle where the leaf spring suspension is mounted to extract deformation data. An axle load meter is placed under each tire of the vehicle to record the axle load on each axle. During the test, the crane's outrigger height is controlled so that the axle load meter reading decreases linearly from 95% of the initial load to 0 (complete unloading). Based on the displacement load data, an experimental load-deformation curve is plotted, as shown in Figure 1. Figure 3 As shown in the red broken line graph, the experimental stiffness of the leaf spring suspension is directly obtained from this curve, which is 603N / mm.

[0096] Compare the experimental and simulated stiffness to determine whether the simulation results match the experimental results. If so, proceed to the next optimization design step. Otherwise, adjust the finite element analysis until the simulation results match the experimental results. This validates the finite element simulation model.

[0097] Comparing the experimental stiffness with the simulated stiffness, the relative error between the two is 3.6%, which is lower than the allowable threshold of 5%. This shows that the finite element analysis model of the leaf spring suspension has high reliability and accuracy in predicting the actual performance of the leaf spring suspension, and has a high confidence level in predicting the performance.

[0098] S2: Based on the leaf spring suspension finite element analysis model verified in step S1, perform simulation analysis under double full load conditions to determine the optimization target.

[0099] Specifically, double load is applied to both ends of each leaf spring of the leaf spring suspension finite element analysis model to simulate the deformation of the leaf spring suspension under extreme working conditions, and the maximum stress value and distribution position of the leaf spring suspension finite element analysis model are determined to determine the optimization target and optimization parameters. Figures 4 to 12 shown.

[0100] Figure 4 The stress cloud diagram shows the stress under the double full load condition acting on both ends of the leaf spring suspension, with the maximum stress being 1304.7MPa.

[0101] Figure 5 The stress cloud diagram of the first leaf spring under double full load condition shows the maximum stress of 933.91 MPa.

[0102] Figure 6 The stress cloud diagram of the second leaf spring under double full load conditions shows that the maximum stress is 775.58 MPa.

[0103] Figure 7 The stress cloud diagram of the third leaf spring under double full load conditions shows the maximum stress of 778.2 MPa.

[0104] Figure 8 The stress cloud diagram of the fourth leaf spring under double full load conditions shows that the maximum stress is 800.33 MPa.

[0105] Figure 9 The stress cloud diagram of the fifth leaf spring under double full load conditions shows that the maximum stress is 801.93 MPa.

[0106] Figure 10 The stress cloud diagram of the sixth leaf spring under double full load conditions shows that the maximum stress is 866.15 MPa.

[0107] Figure 11 The stress cloud diagram of the seventh leaf spring under double full load conditions shows that the maximum stress is 947.84 MPa.

[0108] Figure 12 The stress cloud diagram of the eighth leaf spring under double full load conditions shows that the maximum stress is 1304.7 MPa.

[0109] It can be seen that the maximum stress of each leaf spring is located at the U-bolt clamping point, and the stress value on the eighth leaf spring is the largest. Therefore, the maximum stress value of the eighth leaf spring is selected as the optimization target. The length, width, and thickness of the eighth leaf spring are selected as optimization parameters.

[0110] S3: Based on the optimization goal determined in step S2 and combined with the mechanical design theory of leaf spring suspension, a three-factor three-level test matrix is ​​constructed. The significant influencing factors are obtained through variance analysis, and the optimal parameter range of the significant influencing factors is determined. The following steps are included:

[0111] S31: Construct the objective function. The formulas of the objective function are:

[0112] ;

[0113] ;

[0114] ;

[0115] in, Indicates that the variable is 、 、 The objective function of 、 Represents the weight coefficient of the objective function; 、 For and variables are 、 、 Related performance indicators.

[0116] In this embodiment, 、 、 They respectively represent the length, width and thickness of the eighth leaf spring. is the von Mises stress, For quality.

[0117] S32: Based on the stiffness of the leaf spring suspension, construct the stiffness constraint equation; the formulas of the constraint equation are:

[0118] ;

[0119] in, is the constraint stiffness of the leaf spring suspension; K represents the stiffness of the leaf spring suspension, Indicates the design stiffness of the leaf spring suspension.

[0120] In this embodiment, is 0.07, It is 540N / mm.

[0121] S33: A three-factor, three-level test matrix was constructed using a Box-Behnken experimental design. The three factors included the length, width, and thickness of the leaf spring suspension, and each factor was set at three levels: low, medium, and high.

[0122] S34: Based on a three-factor, three-level test matrix, a parameterized three-dimensional leaf spring suspension model was constructed. Finite element analysis was performed on the leaf spring suspension under various factor configurations. Von Mises stress and mass data under different factor combinations were obtained through finite element analysis. Variances analysis was used to evaluate each factor and obtain significant influencing factors.

[0123] S35: Use the response surface method to analyze the response of the objective function to the changes of the significant influencing factors and determine the optimal parameter range of the significant influencing factors.

[0124] Using a response surface optimization framework and a Box-Behnken experimental design, a three-factor, three-level test matrix (shown in Table 1) was constructed. This experimental design investigated the nonlinear response characteristics of various influencing factors to the maximum von Mises stress, the variation of the mass function, and the global sensitivity of the overall performance. In this process, a dimensionless weighted comprehensive evaluation index was constructed based on the dimensional consistency principle of von Mises stress and mass to measure the overall performance of the leaf spring suspension.

[0125] First, a pre-defined orthogonal experimental design method was used to generate an intelligent orthogonal experimental plan. Based on this plan, leaf spring suspension models with different parameter configurations were established and finite element simulations were performed on these models to obtain the corresponding simulation data.

[0126] Subsequently, an analysis of variance (ANOVA) was performed on the acquired simulation data using Design-Expert® Software. The results show that when the ANOVA P value is less than 0.01, the influencing factor has a highly significant impact on the objective function. When the P value is less than 0.05, the influencing factor has a relatively significant impact on the objective function (as shown in Table 2). Specifically, the ANOVA results show that thickness has a highly significant effect on von Mises stress, while the interaction between width and thickness has a relatively significant effect on the maximum von Mises stress.

[0127] Table 1 Response surface experiment scheme

[0128]

[0129] Table 2 Variance analysis results of leaf spring performance

[0130]

[0131] Based on the results of variance analysis, a response surface analysis was conducted on the performance of the leaf spring suspension to explore the response of the objective function to the changes of the three factors.

[0132] like Figure 13 As shown in Figure 2, the influence of the three factors on von Mises stress in step S3 is further explained in detail:

[0133] Figure 13 (a) in the figure represents the length-von Mises stress curve. Figure 13 (b) in the figure shows the width-von Mises stress curve. Figure 13 (c) in the figure represents the thickness-von Mises stress curve. Figure 13 (d) shows a three-dimensional plot of the effect of the interaction between width and thickness on the von Mises stress. Figure 13 (e) shows a two-dimensional plot of the effect of the interaction between width and thickness on the von Mises stress.

[0134] in, Figure 13 The black lines in (a), (b), and (c) represent the von Mises stress change curves, and the area surrounded by the red lines represents the 95% confidence interval.

[0135] from Figure 13 As can be seen in the figure, the von Mises stress decreases overall as the width and thickness of the leaf spring suspension increase. This indicates that the maximum von Mises stress on the leaf spring suspension decreases when the width and thickness are set larger. The main reason is that the increase in width and thickness increases the overall size of the system, thereby reducing the von Mises stress. At the same time, the increase in overall size leads to an increase in the mass of the leaf spring suspension.

[0136] When 96 ≤ width ≤ 103 and 10 ≤ thickness ≤ 13, the change in von Mises stress is significant. The results show that in this case, the von Mises stress strongly depends on the thickness and width. Increasing the width and thickness effectively reduces the von Mises stress.

[0137] like Figure 14 As shown, the rule of exploring the influence of the three factors on quality in step S3 is further explained in detail:

[0138] Figure 14 (a) in the figure represents the width-mass curve. Figure 14 (b) in the figure shows the thickness-mass curve. Figure 14 (c) shows a three-dimensional diagram of the interaction effect of width and thickness on quality. Figure 14 (d) in the figure shows the two-dimensional diagram of the interaction between width and thickness on quality. Figure 14 In (a) and (b), the black lines represent the mass change curves, and the areas surrounded by red lines represent the 95% confidence bands.

[0139] from Figure 14 As can be seen from the figure, the mass changes steadily with increasing width, while the mass increases rapidly with increasing thickness.

[0140] When the thickness is 10 mm or less and 13 mm or less, the mass of the leaf spring suspension reaches a minimum value, indicating that the length and width have little effect on the mass, while the thickness has a more significant effect on the mass.

[0141] like Figure 15 As shown, the influence of the three factors on the comprehensive performance in step S3 is further explained in detail:

[0142] Figure 15 (a) in the figure represents the width-comprehensive performance curve. Figure 15 (b) in the figure shows the width-comprehensive performance curve. Figure 15 (c) shows a three-dimensional graph showing the effect of the interaction between width and thickness on the comprehensive performance. Figure 15 (d) in the figure shows the two-dimensional graph of the effect of the interaction between width and thickness on the comprehensive performance. Figure 15 The black lines in (a) and (b) represent the comprehensive performance change curves, and the area surrounded by the red lines represents the 95% confidence band.

[0143] from Figure 15 As can be seen from the figure, with the increase of width, the comprehensive performance first increases and then decreases. This is because with the increase of width, the influence of mass on the comprehensive performance gradually increases from a dominant position and then gradually weakens.

[0144] As the thickness increases, the overall performance decreases. This is because the increase in thickness can significantly increase the section moment of inertia, thereby reducing stress, while the mass increases slightly.

[0145] When 96<width<103 and 10<thickness<11, the response surface is relatively steep because when they increase, the increment brought by the increase in mass is significantly greater than the decrease in the stress due to uniform distribution.

[0146] S4: Based on the significant influencing factors obtained in step S3, a Kriging prediction model is established in combination with the Kriging interpolation algorithm, and the Kriging prediction model is optimized by a genetic algorithm to obtain the optimal parameter combination of the three factors.

[0147] Specifically, the Kriging prediction model takes the length, width, and thickness of the leaf spring suspension as input and outputs the von Mises stress and mass of the leaf spring suspension through interpolation prediction. The von Mises stress and mass of the leaf spring suspension are used as multi-objective optimizations using a genetic algorithm. The predicted value expression of the Kriging prediction model is:

[0148] ;

[0149] ;

[0150] in, represents the predicted value of the prediction model; represents the jth known regression coefficient; express Correlation coefficient of is the random residual term; k represents the polynomial basis function In this embodiment, k is 10.

[0151] Random residual term z(x) The mean of is zero, and its spatial covariance function is:

[0152] ;

[0153] in, Represents a random process covariance of represents the process variance; R represents the correlation function; Represents the correlation function between any two predicted values; represents the jth sample point; represents the correlation parameter in the nth direction; express The nth component of ; express The nth component of , n represents the nth dimension of the design variable; N represents the total dimension of the design variable. In this embodiment, N is 3.

[0154] Solving regression coefficients based on experimental data β and correlation coefficient , calculate the predicted value at the unknown point as:

[0155] ;

[0156] ;

[0157] in, express The predicted value at represents the estimated value of the regression coefficient; Represents the inverse matrix of the correlation matrix between sample points; y represents the observation response vector, that is, the value of the von Mises stress and mass in the simulation scheme design; p Indicates that it contains components Column vector of ; represents the transpose of the design matrix; express The transpose of the correlation vector between the sample points; express and The correlation function between Indicates an unknown point; represents the response value for each predicted value.

[0158] At the unknown point At , the predicted mean square error using the Kriging prediction model is:

[0159] ;

[0160] in, express The mean square error at ; represents variance estimation; r represents Correlation vector between and sample points.

[0161] Furthermore, the genetic algorithm optimization process includes the following steps:

[0162] S41: The parameters of the length, width and thickness of the leaf spring suspension are encoded by real numbers to obtain an individual.

[0163] Specifically, the parameters of the length, width and thickness of the leaf spring suspension are represented as chromosome individuals in the genetic space through real number encoding. Each chromosome individual is composed of multiple genes, and the value of the gene corresponds to the actual physical value of the optimization variable.

[0164] S42: Use Latin hypercube sampling to randomly generate the initial population.

[0165] Specifically, Latin hypercube sampling is used to randomly generate an initial population in the feasible region as the initial solution to the problem to be optimized.

[0166] The population size is N=100, and the chromosome latitude is , crossover probability , mutation probability , maximum number of iterations The larger the population size, the less likely the genetic algorithm is to fall into a local optimal solution.

[0167] S43: The penalty function method is used to process individuals that do not meet the nonlinear constraints to ensure that all individuals in the population are within the initial population.

[0168] Specifically, the constraints of each chromosome in the population are verified, and the penalty function method is used to deal with chromosomes that do not meet the nonlinear constraints to ensure that all chromosomes in the population are located in the feasible solution space. In this embodiment, the nonlinear constraints are stiffness constraints.

[0169] S44: Taking the von Mises stress and mass predicted by the Kriging model as the target, a normalized target fitness function is constructed, and the normalized multi-objective fitness function is evaluated to select excellent individuals from the parent generation.

[0170] Specifically, a normalized multi-objective fitness function is constructed, targeting the von Mises stress and quality of the Kriging prediction model, to generate Pareto-front candidate solutions in the objective space. An elite retention strategy is employed to extract Pareto-optimal solutions from the population. The fitness of the stored chromosome individuals is used as a parameter to evaluate the objective fitness function. This function is used to select the best chromosome individuals from the parent generation.

[0171] S45: Based on the principle of survival of the fittest, select outstanding individuals and generate the second generation of individuals.

[0172] S46: Perform crossover and mutation on the second generation individuals to generate the third generation individuals.

[0173] S47: Repeat steps S43 to S46 until the maximum number of iterations is reached or convergence occurs.

[0174] like Figure 16 As shown, Figure 16 (a) shows the curves of leaf spring suspension number and stress value before and after genetic algorithm optimization. Figure 16 Figure (a) shows that the stress values ​​in the first, third, fourth, fifth, sixth, and eighth leaf springs after optimization decreased by 1.6%-6.4% compared to the pre-optimization values. The stress values ​​in the second and seventh leaf springs increased by 1.3%-11.8%. Furthermore, the increased stress values ​​in these two leaf springs are all within the safe stress range. The maximum stress difference between the seventh and eighth leaf springs decreased sharply from 356.8 MPa in the initial design to 160.9 MPa.

[0175] Figure 16 (b) shows the curves of the number of leaf spring suspension and safety factor before and after genetic algorithm optimization. Figure 16 It can be seen from (b) that the safety factors of each leaf spring after optimization are greater than 1.2.

[0176] like Figures 17 to 28 As shown in the figure, modal analysis is performed on the leaf spring suspension before and after optimization, and the analysis results are further explained in detail:

[0177] Figure 17Represents the seventh-order modal analysis of the optimized front leaf spring suspension. Figure 18 Represents the eighth-order modal analysis of the optimized front leaf spring suspension. Figure 19 Represents the ninth-order modal analysis of the optimized front leaf spring suspension.

[0178] Figure 20 Represents the tenth-order modal analysis of the optimized front leaf spring suspension. Figure 21 Represents the eleventh-order modal analysis of the optimized front leaf spring suspension. Figure 22 Represents the twelfth-order modal analysis of the optimized front leaf spring suspension.

[0179] Figure 23 Represents the seventh mode of the optimized leaf spring suspension. Figure 24 Represents the eighth mode of the optimized leaf spring suspension. Figure 25 Represents the ninth mode of the optimized leaf spring suspension. Figure 26 Represents the tenth mode of the optimized leaf spring suspension. Figure 27 Represents the eleventh mode of the optimized leaf spring suspension. Figure 28 Represents the twelfth mode of the optimized leaf spring suspension.

[0180] from Figures 17 to 28 It can be seen that the low-order vibration frequency decreases, the high-order vibration frequency increases, and the maximum deformation value decreases to a certain extent. The optimized system reduces local vibration and enhances the safety of the leaf spring suspension.

[0181] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the mechanical properties of a leaf spring suspension, characterized in that: The following steps are involved: S1: Based on CAE technology, a finite element analysis model of the leaf spring suspension is established. The accuracy and effectiveness of the finite element analysis model of the leaf spring suspension are verified by comparing the finite element analysis results with the actual vehicle road test data of the leaf spring suspension. S2: Based on the leaf spring suspension finite element analysis model verified in step S1, perform simulation analysis under double full load conditions to determine the optimization target; S3: Based on the optimization goal determined in step S2 and combined with the mechanical design theory of leaf spring suspension, a three-factor three-level test matrix is ​​constructed, and significant influencing factors are obtained through variance analysis, and the optimal parameter range of the significant influencing factors is determined; Step S3 includes the following steps: S31: construct objective function; S32: constructing a stiffness constraint equation according to the stiffness of the leaf spring suspension; S33: A three-factor, three-level test matrix was constructed using a Box-Behnken experimental design; the three factors included the length, width, and thickness of the leaf spring suspension, and each factor was set at three levels: low, medium, and high; S34: Based on a three-factor, three-level test matrix, a parameterized leaf spring suspension 3D model was constructed. Finite element analysis was performed on the leaf spring suspension under various factor configurations. Von Mises stress and mass data were obtained under different factor combinations through finite element analysis. Variances analysis was used to evaluate each factor and identify significant influencing factors. S35: Analyzing the response of the objective function to the change of the significant influencing factor using the response surface method, and determining the optimal parameter range of the significant influencing factor; The objective function and the constraint equation are respectively: ； ； ； ； in, Indicates that the variable is 、 、 The objective function of 、 Represents the weight coefficient of the objective function; 、 The expression and variable are 、 、 Related performance indicators; among them, 、 、 Respectively represent the length, width and thickness of the eighth leaf spring; is the von Mises stress, For quality; represents the constraint stiffness of the leaf spring suspension; K represents the stiffness of the leaf spring suspension, represents the design stiffness of the leaf spring suspension; S4: Based on the significant influencing factors obtained in step S3, a Kriging prediction model is established in combination with a Kriging interpolation algorithm, and a genetic algorithm is used to perform multi-objective optimization on the Kriging prediction model to obtain an optimal parameter combination of the three factors; The Kriging prediction model takes the length, width, and thickness of the leaf spring suspension as input and outputs the von Mises stress and mass of the leaf spring suspension through interpolation prediction. The von Mises stress and mass of the leaf spring suspension are used as multi-objective optimization of the genetic algorithm. The predicted value expression of the Kriging prediction model is: ； Random residual term z(x) The mean of is zero, and its spatial covariance function is: ； in, Represents the predicted value of the Kriging prediction model; represents the jth known regression coefficient; express Correlation coefficient of is the random residual term; k represents the polynomial basis function the total number of; Represents a random process z(x) covariance of represents the process variance; R represents the correlation function; Represents the correlation function between any two predicted values; represents the correlation coefficient; express The nth component of ; express The nth component of , n represents the kth dimension of the design variable; N represents the total dimension of the design variable; Solve the regression coefficient and correlation coefficient based on the experimental data, and calculate the predicted value and mean square error of the unknown point: ； ； in, express The predicted value at represents the estimated value of the regression coefficient; Represents the inverse matrix of the correlation matrix between sample points; y represents the observation response vector, that is, the value of the von Mises stress and mass in the simulation scheme design; p Indicates that it contains components Column vector of ; represents the transpose of the design matrix; express The mean square error at ; represents variance estimation; r represents Correlation vector between sample points; Indicates an unknown point.

2. The leaf spring suspension mechanical performance optimization method according to claim 1, characterized in that: Step S1 includes the following steps: S11: Based on CAE technology, a finite element analysis model of the leaf spring suspension is established to simulate its actual working state. By solving the finite element analysis model of the leaf spring suspension, the mechanical response of stress and deformation is obtained; S12: extracting the result data of the finite element analysis in step S1, outputting a simulated load-deformation curve of the leaf spring suspension finite element analysis model, and calculating a simulated stiffness of the leaf spring suspension finite element analysis model based on the simulated load-deformation curve; S13: Based on the actual vehicle road test of the leaf spring suspension, the experimental load-displacement curve of the leaf spring suspension is drawn, and the experimental stiffness of the leaf spring suspension is calculated. By comparing the experimental stiffness and the simulated stiffness of the leaf spring suspension, the accuracy and effectiveness of the finite element analysis model of the leaf spring suspension are verified.

3. The leaf spring suspension mechanical performance optimization method according to claim 1, characterized in that: In step S2, the maximum stress value and distribution position of the leaf spring suspension finite element analysis model are determined by simulation analysis of the leaf spring suspension finite element analysis model under a double full load condition, thereby determining the optimization target and optimization parameters.

4. The leaf spring suspension mechanical performance optimization method according to claim 1, characterized in that: In step S4, the genetic algorithm optimization process includes the following steps: S41: Obtain individual parameters of the length, width and thickness of the leaf spring suspension by real number encoding; S42: Use Latin hypercube sampling to randomly generate the initial population; S43: Processing individuals that do not satisfy the nonlinear constraints by a penalty function method to ensure that all individuals in the population are within the initial population; S44: Taking the von Mises stress and mass predicted by the Kriging model as the target, a normalized multi-objective fitness function is constructed, and the normalized multi-objective fitness function is evaluated to select excellent individuals from the parent generation; S45: Based on the principle of survival of the fittest, select outstanding individuals and generate the second generation of individuals; S46: Perform crossover and mutation on the second generation individuals to generate the third generation individuals; S47: Repeat steps S43 to S46 until the maximum number of iterations is reached or convergence occurs.

5. The leaf spring suspension mechanical performance optimization method according to claim 4, characterized in that: The population size is N=100, and the chromosome latitude is , crossover probability , mutation probability , maximum number of iterations .

6. The leaf spring suspension mechanical performance optimization method according to claim 4, characterized in that: The nonlinear constraint in step S43 is a stiffness constraint.

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