Optimization design method of rubber mount and rubber mount

Abstract

The invention discloses an optimal design method of a rubber suspension and the rubber suspension, and belongs to the technical field of rubber suspensions. The design method comprises the following steps: constructing a response surface model for the rigidity Kv and fatigue life Nf of the rubber mount, calculating polynomial coefficients beta0 and betai by using SPSSAU data analysis software, judging an abnormal value, and detecting whether sample data is available or not; the response surface model is subjected to precision analysis through Latin hypercube sampling, a Kv response curve and an Nf response curve are obtained, the fitting precision of the Kv response curve is not lower than 0.9959, and the fitting precision of the Nf response curve is not lower than 0.9669; matlab software is used, a gametiobj function is used for multi-objective optimization, a plurality of groups of multi-objective optimization non-inferior solution sets are obtained, and simulation verification of an optimization result is carried out. According to the optimization design method, the parameters of the preliminarily designed rubber mount can be optimized, so that the optimized rubber mount is designed, and the performance of the rubber mount meets the use requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of rubber mounts, and more specifically, relates to an optimization design method for rubber mounts based on the Pareto genetic algorithm and a rubber mount. Background Technique

[0002] As an important part of the powertrain mount system, the rubber mount consists of key components such as a rubber main spring, a metal inner core, and a metal outer sleeve. This structure is not only simple and clear, but also has a simple manufacturing process, greatly improving production efficiency. The rubber mount has extremely high cost performance. First of all, compared with hydraulic mounts and other mounts with complex structures, the rubber mount has lower material costs, and due to its simple structure, the processing and assembly processes are also more efficient. This gives the rubber mount an obvious price advantage and can meet the cost control requirements of automobile manufacturers; at the same time, the rubber mount has stable and reliable performance and can meet the usage requirements of the automobile under various working conditions; secondly, the rubber mount has extremely strong adaptability: the rubber material has good elastic and damping properties and can effectively isolate and reduce the vibration and noise generated by the powertrain. Whether it is on urban roads or off-road driving, the rubber mount can maintain good performance and ensure the smoothness and comfort of the vehicle. In addition, the rubber mount also has strong durability and anti-aging ability and can maintain stable performance during long-term use.

[0003] After retrieval, Chinese Patent CN106407573A discloses a multi-objective optimization method for the structural parameters of a hydraulic mount based on Pareto, including the following steps: 1) establishing a multi-objective optimization model for the structural parameters of the hydraulic mount; 2) transforming it into an unconstrained multi-objective optimization problem according to the fuzzy function method; 3) using the Pareto GA genetic algorithm to optimize the multi-step objective optimization problem; 4) using the entropy weight method to determine the objective weights of each optimization target; 5) performing a priority ranking on the Pareto optimal solution set based on the TOPSIS strategy to obtain the best structural scheme. This method can realize the automatic determination of the structural parameters of the hydraulic mount, meet the dynamic requirements of the hydraulic mount of "high stiffness and large damping in the low-frequency domain and low stiffness and small damping in the high-frequency domain", and make up for the deficiencies of the traditional design process of adjusting design parameters by the trial-and-error method.

[0004] However, the method disclosed in the above patent cannot meet the current design and usage requirements of rubber mounts, so it needs to be further improved. Summary of the Invention

[0005] 1. Problems to be Solved

[0006] In view of the technical problems existing in the prior art, the present invention provides an optimization design method and a rubber mount based on the Pareto genetic algorithm, which is an optimization design method for adjusting the parameters of the rubber mount and is beneficial to improving the fatigue life of the rubber mount.

[0007] 2. Technical solutions

[0008] To solve the above problems, the technical solutions adopted by the present invention are as follows:

[0009] The first aspect of the present invention provides an optimization design method for a rubber mount based on the Pareto genetic algorithm, including the steps of:

[0010] Construct a response surface model for the rubber mount stiffness K v and the fatigue life N f Use the SPSSAU data analysis software to calculate the polynomial coefficients β0 and βi, judge the outliers, and detect whether the sample data is available;

[0011] Perform accuracy analysis on the response surface model through Latin hypercube sampling to obtain the Kv response curve and the Nf response curve. The fitting accuracy of the Kv response curve is not less than 0.9959, and the fitting accuracy of the Nf response curve is not less than 0.9669;

[0012] Use the "gamultiobj" function in the Matlab software for multi-objective optimization to obtain several sets of multi-objective optimization non-dominated solution sets, and perform simulation verification on the optimization design results of the rubber mount.

[0013] According to any implementation scheme of the first aspect of the object of the present invention, the response surface model of the rubber mount stiffness K v and the fatigue life N f is: Kv(N F ) = β 0 + β 1 W + β 2 L + β 3 θ + β 4 D + β 5 r + β 6 W 2 + β 7 L 2 + β 8 θ 2 + β 9 D 2 + β 10 r 2 + β 11 W·L + β 12 W·θ + β 13 W·D + β 14 W·r + β 15 L·θ + β16 L·D + β 17 L·r + β 18 θ·D + β 19 θ·r + β 2 D·r + ε。

[0014] According to any embodiment of the first aspect of the object of the present invention, before performing regression analysis on the data, data cleaning is the primary link; analyzing the outlier data, the purpose is to detect whether there are some sample points whose values deviate significantly from other values, and these points are also called outliers. If outliers are detected, the data needs to be processed or replaced accordingly. Use the "box plot" of SPSSAU software to identify outliers: the data judgment criterion is the range formed by the minimum estimated value and the maximum estimated value calculated for each group of response values. If a certain data exceeds this range, it will be automatically determined as an outlier and represented by a circle in the box plot.

[0015] According to any embodiment of the first aspect of the object of the present invention, for the fitting accuracy analysis of the actual value and the predicted value of the response surface equation, the Latin hypercube sampling method is used to perform random sampling within the parameter ranges of 5 factors and 3 levels, and relevant programming is carried out using the "lhsSamples" function in Matlab R2020a, and a limit setting is made for the randomly selected sample size of not less than 20. For example, except for the r independent variable, the other four independent variables are taken as integers, and r is reserved to two decimal places.

[0016] To detect the accuracy of the response surface model function, according to the coefficient of determination R 2 commonly used in statistics to measure the goodness of fit of the model to the data. The relevant calculation formula is as follows:

[0017]

[0018] where SSres is the sum of squared residuals (the variation not explained by the model); SStot is the total sum of squares (the total variation of the response variable); n is the number of samples; yi is the response value of the i-th sample point, ypi is the predicted value of the i-th sample point; is the mean response of n sample points. The closer R2 is to 1 and greater than 0.9, the better the fitting effect of the response surface curve.

[0019] According to any embodiment of the first aspect of the object of the present invention, use the "gamultiobj" function in Matlab R2020a for multi-objective optimization, with the goal of minimizing the "gamultiobj" objective function component. If the "gamultiobj" objective function takes the maximum value, it is processed by taking the opposite number.

[0020] According to any embodiment of the first aspect of the object of the present invention, in Matlab R2020a, the design variables are set as follows: the optimal individual coefficient is 0.3, the population size is 200, the maximum number of generations for evolution is 300, the stopping generation is 200, and the fitness function deviation is 1e-10. Since the "gaplot" function in Matlab R2020a cannot directly draw the graph of the Pareto Front, the "figure" function is used to plot the optimal solution set.

[0021] According to any embodiment of the first aspect of the object of the present invention, the obtained optimal result set is stored in [x, fval]. "fval" is the objective function value corresponding to x. "fval" forms a curve on the result image. If the solutions are relatively evenly distributed, it indicates that the graph contains most of the optimal solution cases, with global optimality and strong applicability. However, under the condition of Pareto optimality, it is impossible to simultaneously satisfy the two objective functions to be optimal, and one of the objectives will be damaged. Therefore, the optimal solutions obtained need to be selected, that is, the Pareto non-dominated solution set is selected.

[0022] Since the objective functions are mutually contradictory during the optimization process, the obtained Pareto non-dominated solution set needs to be processed, and the weights of the optimization objectives for different variables need to be considered to find the optimal solution. Strive to find K v closest to the target stiffness value of 480 N / mm, where the error in the stiffness value within 15% is compliant, N f Compared with the initial value, the maximum value of the difference is taken for the optimized value, that is, the fatigue life value takes the maximum.

[0023] According to any embodiment of the first aspect of the object of the present invention, in order to verify the credibility of the optimization results, the model is modified in Catia software, and the parameters of the optimized non-dominated solution set are rounded to obtain several optimized models, and the several models are successively used for simulation verification analysis in Abaqus software.

[0024] According to any embodiment of the first aspect of the object of the present invention, during actual processing, in order to reduce stress concentration and increase strength, a fillet of 2 mm is added to the optimized mount model.

[0025] The second aspect of the present invention provides a rubber mount, which is obtained according to the optimized design method of the rubber mount based on the Pareto genetic algorithm described in the first aspect.

[0026] 3. Beneficial effects

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] (1) The optimized design method of rubber mounts based on the Pareto genetic algorithm of the present invention, which is an optimized design method for adjusting the parameters of rubber mounts, is beneficial to improving the fatigue life of rubber mounts. It can optimize the parameters of the preliminarily designed rubber mounts, thereby designing the most optimized rubber mounts to meet the usage requirements.

[0029] (2) In the optimized design method of rubber mounts based on the Pareto genetic algorithm of the present invention, data cleaning is the primary step before performing regression analysis on the data. Analyze the data in the following table to detect whether there are sample points where some values deviate significantly from other values. These points are also called outliers. If outliers are detected, the corresponding data needs to be processed or replaced.

[0030] (3) In the optimized design method of rubber mounts based on the Pareto genetic algorithm of the present invention, in order to reduce stress concentration and increase strength, a fillet of 2 mm is added to the optimized rubber mount. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The technical solutions of the present invention will be further described in detail below in conjunction with the drawings and embodiments. However, it should be noted that these drawings are only designed for explanatory purposes and therefore do not limit the scope of the present invention. In addition, unless otherwise specified, these drawings are only intended to conceptually illustrate the structural configurations described herein and are not necessarily drawn to scale.

[0032] Figure 1 It is a diagram for judging the outlier situation of the response variable of the present invention;

[0033] Figure 2 It is a Latin hypercube sampling distribution diagram of the present invention;

[0034] Figure 3 It is the K v Response curve fitting accuracy test diagram;

[0035] Figure 4 It is the N f Response curve fitting accuracy test diagram;

[0036] Figure 5 It is a Pareto Front diagram of the present invention;

[0037] Figure 6 It is the optimized rubber mount of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0038] The following detailed description of exemplary embodiments of the present invention refers to the accompanying drawings, which form a part of the description, and in which exemplary embodiments in which the present invention can be implemented are shown by way of example. Although these exemplary embodiments are described in sufficient detail to enable those skilled in the art to implement the present invention, it should be understood that other embodiments can be achieved and various changes can be made to the present invention without departing from the spirit and scope of the present invention. The following more detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed present invention, but is merely for illustrative purposes and does not limit the description of the features and characteristics of the present invention, in order to present the best way to implement the present invention and to enable those skilled in the art to implement the present invention. Therefore, the scope of the present invention is defined only by the appended claims.

[0039] The following detailed description of the present invention and exemplary embodiments can be better understood in conjunction with the accompanying drawings, in which the elements and features of the present invention are identified by reference numerals.

[0040] The optimized design method of the rubber mount based on the Pareto genetic algorithm of the present invention includes the steps of: constructing a response surface model for the rubber mount stiffness K v and fatigue life N f using the SPSSAU data analysis software to calculate the polynomial coefficients β0, βi, judge outliers, and detect whether the sample data is available; performing accuracy analysis on the response surface model through Latin hypercube sampling to obtain the K v response curve and the N f response curve, the fitting accuracy of the K v response curve is not less than 0.9959, and the fitting accuracy of the N f response curve is not less than 0.9669; using the "gamultiobj" function in the Matlab software for multi-objective optimization to obtain several groups of multi-objective optimization non-dominated solution sets, and performing simulation verification on the optimized design results of the rubber mount.

[0041] When the stiffness and fatigue life are used as response variables and the respective parameters and the necking amount are used as independent variables, as can be seen from the above experiments, a non-linear relationship is presented. At this time, when using a second-order response surface model, the calculation cost is lower than that of a third-order or higher-order polynomial fitting.

[0042] RSM second-order equation:

[0043]

[0044] In Equation (1-1), Y is the response variable; n is the total number of independent variables; β0, βi are polynomial coefficients, i = 1-21; xi, xj are design variables; ε is the error of the system.

[0045] According to Equation (1-1), establish the rubber mount stiffness K vand fatigue life N f The second - order response surface model is as follows:

[0046] Kv(N F ) = β 0 +β 1 W + β 2 L + β 3 θ + β 4 D + β 5 r + β 6 W 2 +β 7 L 2 +β 8 θ 2 +β 9 D 2 +β 10 r 2 +β 11 W·L + β 12 W·θ + β 13 W·D + β 14 W·r + β 15 L·θ + β 16 L·D + β 17 L·r + β 18 θ·D + β 19 θ·r + β 2 D·r+ε.

[0047] In the formula, βi are coefficients (i = 1, 2, 3, 21), and formula (1 - 2) is a dimensionless calculation formula.

[0048] Writing the above formula (1 - 2) in matrix form, we have:

[0049]

[0050] The multiple linear regression model can be expressed as

[0051] Y = Xβ+ε (1 - 5)

[0052] The unknown coefficient vector β is calculated by the least - squares method. The coefficient vectors β corresponding to Kv and NF are shown in Table 1 - 1. Since there is a high correlation among the variables "L*θ, L*D, L*r, θ*D, θ*r, D*r" among the predictive variables, there is multicollinearity among them, which will lead to unstable results. Therefore, the above 6 variables are excluded.

[0053] Table 1 - 1 Calculation results of the coefficients of the second - order response surface model

[0054]

[0055]

[0056] Before performing regression analysis on the data, data cleaning is the primary step. The handling of outliers is of utmost importance. Analyzing the data in the following table aims to detect sample points where some values deviate significantly from other values. These points are also called outliers. If outliers are detected, the corresponding data needs to be processed or replaced.

[0057]

[0058] Use the "box plot" in SPSSAU software to identify outliers. The data judgment criterion is based on the range formed by the minimum estimated value and the maximum estimated value calculated for each group of response values. If a certain data exceeds this range, it will be automatically determined as an outlier and represented by a circle in the box plot.

[0059] Separate the 27 sets of results of the response variables K v and N f and import them into SPSSAU. Select "box plot" in the "visualization" module. The data processing results are as follows Figure 1 shown in (a) and (b).

[0060] For the fitting accuracy analysis of the actual value and the predicted value (fitted value) of the response surface equation in Equation (1-1), the Latin hypercube sampling method is used to perform random sampling within the parameter ranges of 5 factors and 3 levels. Use the "lhsSamples" function in Matlab R2020a for relevant programming and set restrictions on the randomly selected 20 sample numbers. For example, except for the r independent variable, the other four independent variables are all taken as integers, and r is retained to two decimal places, as follows Figure 2 shown. The 5-dimensional Latin hypercube sampling distribution diagram, and Table 1-2 is the data table of 20 groups after LHS sampling.

[0061] Table 1-2 Latin hypercube sampling data

[0062]

[0063]

[0064] To detect the accuracy of the response surface model function, the coefficient of determination R 2 commonly used in statistics is used to measure how well the model fits the data. Relying on the LHS method, 20 groups of samples are randomly selected; the relevant calculation formula is as follows:

[0065]

[0066] Among them, SSres is the sum of squared residuals (the variation not explained by the model); SStot is the total sum of squares (the total variation of the response variable); n is the number of samples; yi is the response value of the i-th sample point, and ypi is the predicted value of the i-th sample point; is the mean response of n sample points. R 2 Greater than 0.9 and the closer to 1, the better the fitting effect of the response surface curve.

[0067] Let K v response curve and N f response curve be fitted with the LHS sampling points, as Figure 3 and Figure 4 shown. The fitting accuracies R 2 of the two curves are 0.9959 and 0.9669 respectively. The K v response curve is greater than the N f response curve in fitting accuracy because the change range of fatigue life values is large and it is affected by multiple factors.

[0068] Based on the previously established response surface model of the rubber mount, taking the V-direction stiffness K v , and the fatigue life N f of the rubber mount as the objective function, and taking the main spring parameters and the reduced diameter amount r of the rubber mount as the design variables, the multi-objective optimization mathematical model of the rubber mount is established as follows:

[0069] Objective function:

[0070] min F 1 =|K v -480| (1 - 10)

[0071]

[0072] Design variables: W, L, θ, D, r.

[0073] The constraint conditions are set as:

[0074] s.t.

[0075] 13mm ≤ W ≤ 17mm (1 - 12)

[0076] 38mm ≤ L ≤ 44mm (1 - 13)

[0077] 68° ≤ θ ≤ 90° (1 - 14)

[0078] 0mm ≤ D ≤ 4mm (1 - 15)

[0079] 0.1mm ≤ r ≤ 0.2mm (1 - 16)

[0080] In Equation (1 - 10), K vMeet the desired characteristic, K v The target design value of v is 480 N / mm; the F2 value in Equation (1-11) is the calculated maximum response value, specifically 659032. The purpose of this equation is to maximize the fatigue life value to improve the usage efficiency of the rubber mount; Equations (1-12) to (1-16) are the respective value ranges of the rubber mount parameters; Equation (1-16) is the range of the necking-down amount.

[0081] Use the "gamultiobj" function in Matlab for multi-objective optimization, aiming to minimize the components of the objective function. If the objective function takes a maximum value, process it with the opposite number. Set the design variables: the optimal individual coefficient is 0.3, the population size is 200, the maximum number of generations for evolution is 300, the stopping generation is 200, and the fitness function deviation is 1e-10. In Matlab, the "gaplot" function cannot directly draw the graph of the Pareto Front, so use "figure" to plot the optimal solution set.

[0082] In addition, the obtained optimal result set is stored in [x, fval]. "fval" is the objective function value corresponding to x. "fval" forms a curve on the result image. If the solutions are relatively evenly distributed, it indicates that the graph contains most of the optimal solution cases, with good global optimality and strong applicability. However, under the condition of Pareto optimality, it is impossible to simultaneously satisfy the two objective functions to be optimal, and one of the objectives will be damaged. Therefore, the optimal solutions obtained need to be selected, that is, select the Pareto non-dominated solution set; Table 1-3 is the non-dominated solution set of the multi-objective optimization by the NSGA-II genetic algorithm.

[0083] The Pareto optimal solution set is as Figure 5 shown. The two coordinate axes respectively correspond to 2 objective functions. Since the objective functions are contradictory to each other during the optimization process, the obtained solution set needs to be processed. The weights of different variables for the optimization objectives need to be considered to find the optimal solution. In order to obtain K v closest to the target stiffness value of 480 N / mm, where the error in the stiffness value within 15% is in line with the requirements, N f Compared with the initial value, the maximum value of the difference is taken for the optimized value, that is, the fatigue life value is taken as the maximum. Table 1-3 is the table of the non-dominated solution set of the multi-objective optimization by the NSGA-II genetic algorithm. A total of 10 groups of optimal candidate points are generated in the table.

[0084] Table 1-3 Table of the non-dominated solution set of the multi-objective optimization by the NSGA-II genetic algorithm

[0085]

[0086] To verify the credibility of the optimization results, the obtained optimized parameters were rounded, and the model was modified in Catia software. After rounding the parameters respectively, 10 optimized parameter models were obtained. The 10 parameter models were successively used for simulation analysis in Abaqus software. As shown in Table 1-4, the simulation calculation results of the 10 parameter models were obtained, and the differences between the ten groups of models and the target stiffness value were compared respectively.

[0087] Table 1-4 Comparison between the optimized parameter models and the target stiffness

[0088]

[0089] Considering the precision requirements and processing difficulties in actual processing, the parameter values in Table 1-3 were rounded. The comparison table of the rubber mount dimensions before and after optimization is shown in Table 1-5.

[0090] Table 1-5 Comparison before and after dimension optimization

[0091]

[0092] Considering the differences in the comprehensive stiffness value and fatigue life value, the 4th group of candidate points was selected as the optimal design point. The difference between it and the target stiffness value was -1.08%, the magnitude was 474.81 N / mm, and the fatigue life was 1,429,402 times, meeting the safety use requirements of the rubber mount. To reduce stress concentration and increase strength, a fillet of 2 mm was added to the optimized rubber mount, and the optimized rubber mount is as Figure 6 shown.

[0093] Through a large number of tests, it is concluded that the rubber mount produced by the present invention has at least a 0.1% improvement in fatigue life and saves at least tens of millions of yuan in cost compared with that before optimization.

[0094] The above schematically describes the present invention and its implementation manners. This description is not restrictive. What is shown in the drawings is only one of the implementation manners of the present invention, and the actual structure is not limited thereto. Therefore, if those of ordinary skill in the art are inspired by it and design similar structural manners and embodiments without creative work without departing from the spirit of the present invention, they shall fall within the protection scope of the present invention.

Claims

1. A Pareto genetic algorithm-based rubber suspension optimization design method, characterized in that: Includes steps: The rubber suspension stiffness K v and fatigue life N f Construct a response surface model, use SPSSAU data analysis software to calculate the polynomial coefficients β0, βi, where i = 1-21, judge the outliers, and test whether the sample data is usable; The accuracy of the response surface model was analyzed by Latin hypercube sampling, and K v Response Curve and N f Response curve, K v The fitting accuracy of the response curve is not less than 0.9959, N f The fitting accuracy of the response curve is not less than 0.9669; The "gamultiobj" function of Matlab software is used to perform multi-objective optimization, and several sets of multi-objective optimization non-inferior solution sets are obtained. Simulation is then performed to verify the optimization design results of the rubber suspension.

2. The Pareto genetic algorithm-based rubber mount optimization design method according to claim 1, characterized in that: The rubber mount stiffness K v and fatigue life N f have a response surface model as follows: Kv(N F ) = β0 + β1W + β2L + β3θ + β4D + β5r + β6W 2 + β7L 2 + β8θ 2 + β9D 2 + β 10 r 2 + β 11 W·L + β 12 W·θ + β 13 W·D + β 14 W·r + β 15 L·θ + β 16 L·D + β 17 L·r + β 18 θ·D + β 19 θ·r + β2D·r + ε.

3. The Pareto genetic algorithm-based rubber mount optimization design method according to claim 2, characterized in that: Use the "Box Plot" of SPSSAUAU software to identify outliers: the data judgment standard is based on the range formed by the minimum and maximum estimated values ​​in each group of calculated response values. If a data exceeds this range, it will be automatically determined as an outlier and represented by a circle in the box plot.

4. The Pareto genetic algorithm-based rubber mount optimization design method according to claim 3, characterized in that: The fitting accuracy analysis of the response surface equation between the actual value and the predicted value uses the Latin hypercube sampling method to perform random sampling within the range of each parameter of 5 factors and 3 levels. The "lhsSamples" function is used for programming in Matlab R2020a, and a limit is set on the number of randomly selected samples of no less than 20. For example, except for the r independent variable, the other four independent variables are all integers, and r retains two decimal places.

5. The Pareto genetic algorithm-based rubber mount optimization design method according to claim 1, characterized in that: In Matlab R2020a, the "gamultiobj" function is used for multi-objective optimization, with the goal of minimizing the components of the "gamultiobj" objective function. If the "gamultiobj" objective function takes a maximum value, the opposite value is used for processing.

6. The Pareto genetic algorithm-based rubber mount optimization design method according to claim 5, characterized in that: In Matlab R2020a, the design variables are set as follows: the optimal individual coefficient is 0.3, the population size is 200, the maximum evolutionary generation is 300, the stop generation is 200, and the fitness function deviation is 1e-10; use "figure" to plot the optimal solution set.

7. The Pareto genetic algorithm-based rubber mount optimization design method according to claim 6, characterized in that: The optimal solution set is stored in [x,fval], where "fval" is the objective function value corresponding to x. When the two objective functions cannot be simultaneously optimal under the Pareto optimal condition, the optimal solution is selected, that is, the Pareto non-inferior solution set is selected.

8. The Pareto genetic algorithm-based optimization design method for rubber suspension according to claim 7, characterized in that: The model was modified in Catia software, and the parameters of the optimized non-inferior solution set were rounded to obtain several optimized models. Several models were simulated, verified and analyzed in turn using Abaqus software.

9. A rubber suspension, characterized in that: The optimization design method of the rubber suspension based on the Pareto genetic algorithm according to any one of claims 1 to 8 is obtained.

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