A robustness optimization method for a commercial vehicle suspension system

Abstract

The present application relates to the technical field of commercial vehicles, and specifically provides a robustness optimization method for a commercial vehicle suspension system, comprising the following steps: establishing a power assembly coordinate system, a power assembly mass matrix and a stiffness matrix, and constructing an expression of system natural frequency and decoupling rate; performing a transmission path analysis, and establishing a mathematical relationship between suspension design parameters and an in-vehicle target point; analyzing the sensitivity of an objective function to variables, and determining design variables and parameter variables; using an interval model to represent design variables, using a probability model to represent parameter variables, and constructing an interval-probability model to describe the uncertainty of suspension system variables; using Monte Carlo random number simulation technology to perform multi-objective robustness optimization; and performing Monte Carlo analysis on the optimization results, and evaluating the robustness of the suspension system. Based on the transmission path analysis method, the response of the suspension system and the in-vehicle target point of interest is linked, and vibration isolation and noise reduction at the vehicle level is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of commercial vehicles, in particular to parameter optimization of damping devices of soft connections such as vehicle suspensions and suspensions based on transmission paths, and specifically provides a robustness optimization method for a commercial vehicle suspension system. BACKGROUND

[0002] With the rapid development of the automobile industry, people gradually change the indicators of power performance and handling stability to ride comfort, and therefore the NVH performance of the vehicle becomes an important indicator. However, for the whole vehicle, the NVH problem is a systematic problem, and factors such as excessive excitation source, excessive excitation source, and serious coupling of vibration path and system components will all affect the NVH performance of the vehicle. Therefore, it is crucial to quickly and effectively determine the cause, which is more conducive to the optimization and improvement work in the later stage.

[0003] Reasonable design of the suspension system can effectively isolate the vibration of the powertrain and the impact caused by the road roughness. At present, there are many studies on the design of the suspension system, but often only a part is studied, such as the dynamic and static characteristics of the suspension, the establishment of the vibration model, the energy decoupling, etc. The decoupling rate and dynamic reaction force cannot ensure the accuracy of the optimization result, and the research on optimizing the suspension parameters based on the requirements of vehicle vibration and noise is relatively less. Due to manufacturing errors, installation errors, and suspension element wear, the suspension system has uncertainty, so the improvement effect often fails to achieve the expected goal of deterministic optimization, and therefore it is necessary to perform robustness optimization based on deterministic optimization. A robustness optimization method for a commercial vehicle suspension system is provided. SUMMARY

[0004] The suspension system has uncertainty due to manufacturing errors, installation errors, and suspension element wear, so the improvement effect often fails to achieve the expected goal of deterministic optimization, and therefore it is necessary to perform robustness optimization based on deterministic optimization. A robustness optimization method for a commercial vehicle suspension system is provided.

[0005] The technical scheme of the present application provides a robustness optimization method for a commercial vehicle suspension system, which includes the following steps:

[0006] Establishing a powertrain coordinate system, a powertrain mass matrix, and a stiffness matrix, and constructing an expression of system natural frequency and decoupling rate;

[0007] Performing transmission path analysis, and establishing a mathematical relationship between suspension design parameters and target points in the vehicle;

[0008] Analyzing the sensitivity of the objective function to the variables, and determining the design variables and parameter variables;

[0009] Using an interval model to represent the design variables, and using a probability model to represent the parameter variables, and constructing an interval-probability model to describe the uncertainty of the suspension system variables;

[0010] The Monte Carlo random number simulation technique is used to perform multi-object robustness optimization.

[0011] Further, the steps of establishing the power assembly coordinate system, the power assembly mass matrix and the stiffness matrix, and constructing the expression of the system natural frequency and the decoupling rate include:

[0012] The power assembly coordinate is established according to the displacement of the power assembly in the X direction, the Y direction and the Z direction and the corresponding rotation angle; wherein the center of mass C is defined as the coordinate origin, the x direction is parallel to the crankshaft center line, the z direction is perpendicular to the cylinder upper end face end cover flange plane, and the y direction is determined by the right-hand rule; the generalized coordinates of the power assembly are represented by q={x y z θ x θ y θ z} T , wherein x, y and z represent the displacement of the power assembly in the X direction, the Y direction and the Z direction, respectively, and θ x , θ y and θ z represent the rotation of the power assembly in the X direction, the Y direction and the Z direction, respectively; and the vibration differential equation of the suspension system is shown in equation (1):

[0013]

[0014] , [C] and [K] represent the mass matrix, the damping matrix and the stiffness matrix, respectively, and F(t) represents the excitation suffered by the power assembly suspension system.

[0015] Obtain the inertia parameters of the power assembly to generate the mass matrix M of the power assembly;

[0016] The mass matrix [M] needs to obtain the inertia parameters of the power assembly, mainly including the mass of the power assembly, the position of the center of mass of the power assembly, the inertia moment of the power assembly and the inertia product, and the expression is shown in equation (2). The mass of the power assembly and the position of the center of mass are obtained by weighing method and suspension method respectively. The inertia parameters are analyzed by three-line torsion pendulum method. During the three-line torsion pendulum test, the power assembly is placed at the balance position, and the initial angular displacement (less than 5°) is applied to the power assembly by reciprocating torsion around the center axis of the three-line pendulum disc. The angle between each coordinate axis and the center line and the torsional vibration period of the system are measured by a sensor, and the moment of inertia of the power assembly is calculated by a professional instrument.

[0017]

[0018] Obtain the stiffness parameters, installation position parameters and installation angle parameters of the suspension components, and generate the stiffness matrix K of the power assembly according to the obtained parameters;

[0019] The suspension system adopts a multi-point support form, and N suspension elements are required. The design degree, installation position, and installation angle of each suspension element are collectively constituted. The suspension elements are numbered according to the installation position, and the principle of from front to back and from left to right is followed, that is, 1, 2, …, i, …, N, i represents the i th suspension.

[0020] A local coordinate system O i -uvw, k iu represents the design stiffness of the i th suspension on the u-axis of the local coordinate system, k iv represents the design stiffness of the i th suspension on the v-axis of the local coordinate system, k iw represents the design stiffness of the i th suspension on the w-axis of the local coordinate system, k i represents the stiffness parameters of the suspension element i:

[0021]

[0022] x i , y i , z i respectively represent the corresponding axes of the i th suspension in the power assembly coordinate system, and F i represents the installation position parameters of the suspension element i:

[0023]

[0024] x ui represents the angle between the u-axis of the i th suspension local coordinate system and the x-axis of the overall coordinate system, y ui represents the angle between the u-axis of the i th suspension local coordinate system and the y-axis of the overall coordinate system, z ui represents the angle between the u-axis of the i th suspension local coordinate system and the z-axis of the overall coordinate system, x vi represents the angle between the v-axis of the i th suspension local coordinate system and the x-axis of the overall coordinate system, y vi represents the angle between the v-axis of the i th suspension local coordinate system and the y-axis of the overall coordinate system, z vi represents the angle between the v-axis of the i th suspension local coordinate system and the z-axis of the overall coordinate system, x wi represents the angle between the w-axis of the i th suspension local coordinate system and the x-axis of the overall coordinate system, y wi represents the angle between the w-axis of the i th suspension local coordinate system and the y-axis of the overall coordinate system, z wi represents the angle between the w-axis of the i th suspension local coordinate system and the z-axis of the overall coordinate system, E i represents the installation angle parameters of the suspension element i:

[0025]

[0026] In summary, the overall stiffness of the suspension system can be represented as:

[0027]

[0028] Since the main role of suspension element damping is to reduce the resonance peak, the damping can be ignored when solving the system vibration, and the vibration differential equation of the suspension system can be simplified as:

[0029]

[0030] Solving the characteristic matrix M -1 K eigenvalue and eigenvector

[0031]

[0032] Solving the decoupling rate DIP of the suspension system mn :

[0033]

[0034] DIP mn represents the percentage of the total energy occupied by the dominant direction of vibration energy at the mth natural frequency, M(n,j) represents the element in the nth row and jth column of the mass matrix, and respectively represent the nth and jth elements under the ith mode shape.

[0035] Further, complex mechanical systems often have various vibration excitation sources, and these excitations transmit vibration to one or more response points through various paths of system components. Due to the characteristics of system components, vibration may be enhanced or attenuated. The transfer path analysis method is to analyze the system as a "source-path-response" model, and to identify the excitation source and path characteristics of the system by measuring the corresponding vibration data, and to predict the vibration response at the target point. The steps of conducting transfer path analysis and establishing the mathematical relationship between the suspension design parameters and the target point in the vehicle include:

[0036] The suspension system is divided into active end a and passive end p according to the connection relationship. The active end a is connected with the excitation source, and the vibration of the excitation source is transmitted to the passive end p through the damping device and to the target point in the vehicle. The response of the target point is:

[0037]

[0038] where Y(ω) represents the response of the system focus point, [H oThe frequency response function from passive end P to the system focus point, representing the transfer characteristics of the system, whose scale depends on the number of passive end points r and the number of focus points s, such as a four-point suspension system, and the steering wheel in the driver's cabin is selected as the system focus point, and three degrees of freedom are considered for each point, so the scale of the transfer function is 12*3, and there are 36 transfer paths. {F(ω)} represents the input excitation vector, and ω represents the frequency domain;

[0039] The working load is calculated by multiplying the vibration acceleration difference of the active end a and the passive end p by the dynamic stiffness value, and the calculation formula is as follows:

[0040]

[0041] In the formula, F o (ω) represents the size of the i-th path load, K o (ω) represents the dynamic stiffness value of the suspension elastic element, a ao (ω) and a po (ω) represent the vibration acceleration values at the active end and the passive end of the i-th path elastic element, respectively. As can be seen from the theoretical formula, the suspension dynamic stiffness method requires two types of data: the dynamic stiffness data of the suspension elastic element and the vibration acceleration values at the active end and the passive end thereof.

[0042] Based on the above, formula (10) can be transformed into:

[0043]

[0044] In the formula, [H o (ω)]、a ao (ω)、a po (ω) and ω are known quantities, so the stiffness value can be adjusted to optimize the vibration of the focus points in the vehicle and improve the NVH performance of the vehicle.

[0045] Further, the installation angle, installation position, suspension stiffness and other parameters of the suspension all affect the decoupling rate and the target function. If all of them are taken as design variables, not only the complexity of solving is increased, which is not conducive to finding the optimal solution, but also too many parameter modifications are not conducive to subsequent structural adjustment and increase costs. Therefore, reasonable selection of optimization variables is helpful for subsequent optimization improvement. Through sensitivity analysis, factors with greater influence on the target function are selected as design variables, and variables with less influence are not adjusted. The steps of analyzing the sensitivity of the target function to the variables to determine the design variables and parameter variables include:

[0046] The sensitivity S of the target function to the variable can be expressed as:

[0047]

[0048] Wherein, S(r, t) represents the rth objective function F r derivative of the tth variable X t , L is the number of objective functions, and J is the number of variables.

[0049] S(r, t) is greater than 0, indicating that the objective function F r is positively correlated with the variable X t , and increases with the increase of X t ; S(r, t) is greater than 0, indicating that the objective function F r is negatively correlated with the variable X t , and decreases with the increase of X t . When analyzing the sensitivity, both positive and negative correlations need to be considered. Let:

[0050]

[0051] Through sensitivity analysis, the rth objective function F r , the variables affecting the objective function greater than the first threshold value are screened out, the variables affecting the L objective functions greater than the first threshold value are screened out and integrated as design variables for subsequent optimization, the variables affecting the L objective functions less than the second threshold value are screened out and integrated as parameter variables. Divide them into X B and X S , X B represents a set of variables with greater impact, which is used as a design variable for subsequent optimization, and X S represents a set of variables with smaller impact, which is used as a parameter variable for subsequent optimization.

[0052] Further, the interval model is used to represent the design variable, the probability model is used to represent the parameter variable, and the interval-probability model is used to describe the uncertainty of the suspension system variable before the step of constructing the interval-probability model.

[0053] The design variables screened by sensitivity are subjected to deterministic optimization of the suspension system.

[0054] Specifically, the step of subjecting the design variables screened by sensitivity to deterministic optimization of the suspension system is realized by the following formula:

[0055]

[0056] DIP mn represents the percentage of the total energy occupied by the vibration energy of the mth order natural frequency in the dominant direction, α m represents the weight of the vibration energy of the mth order natural frequency, β c represents the weight of the cth transmission path, X B represents the design variable, and X BLX BU DIP Bounce DIP Roll DIP

[0057] Further, the interval model is used to represent the design variable, and the probability model is used to represent the parameter variable, and the interval-probability model is constructed to describe the uncertainty of the suspension system variable in the step of constructing the model as follows:

[0058]

[0059] X B X BL X BU DIP X The gth probability parameter variable, and μ g and The mean and the upper and lower limits of the gth interval parameter variable X S X SL X SU DIP X

[0060] Further, the traditional optimization design aims to seek the optimal solution of the objective function shown in point 1, when the design variable x is disturbed, the change amplitude of the objective function is large, and point 2 is the robust solution, the change amplitude of the objective function with x disturbance is smaller than the optimal solution, which has good stability and reliability. The core idea of 6Sigma robust design is to reduce the influence of design variable disturbance on the objective function through probability and statistics theory. Sigma can be represented by σ. Its core idea is to define the distribution characteristics of the design variable, generate random sample points near the design variable and substitute them into the objective function, and perform statistical analysis on the objective function to determine its 6Sigma quality level, reliability and other evaluation indexes. Using Monte Carlo random number simulation technology, the steps of multi-objective robust optimization include:

[0061] Calling the MATLAB interface inside the Isight software;

[0062] Calling the written suspension optimization mathematical model, setting input and output variables;

[0063] Drag the Optimization component and add variable value range and objective function, and impose constraint conditions, select the NSGA-II algorithm;

[0064] Drag the 6Sigma optimization component, set the distribution type of the parameter variable and the design variable, and finally solve the robustness of the suspension system by the constructed model.

[0065] Further, the steps of multi-objective robustness optimization using Monte Carlo random number simulation technology include:

[0066] Monte Carlo analysis is performed on the optimization results to evaluate the robustness of the suspension system. The robustness solution is verified by Monte Carlo to test the 6Sigma level.

[0067] From the above technical solutions, the present application has the following advantages: based on the transfer path analysis method, the response of the suspension system and the target point in the vehicle is established, which can achieve the vibration isolation performance of the powertrain suspension system itself, and also realize the vibration isolation and noise reduction of the whole vehicle. The interval probability model is introduced to describe the uncertainty of the parameter variable and the design variable, which can ensure the performance and improve the robustness of the system.

[0068] In addition, the design principle of the present application is reliable, the structure is simple, and it has very wide application prospect.

[0069] Therefore, compared with the prior art, the present application has outstanding substantial characteristics and significant progress, and the beneficial effects of its implementation are also obvious. BRIEF DESCRIPTION OF DRAWINGS

[0070] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiment or prior art description will be briefly introduced as follows, and obviously, other drawings can also be obtained by those skilled in the art without creative labor.

[0071] Figure 1 The structural diagram of the present application.

[0072] Figure 2 The simplified schematic diagram of the TPA model of the present application.

[0073] Figure 3 The TPA transmission scale schematic diagram of the present application.

[0074] Figure 4 The robustness optimization principle diagram of the present application.

[0075] Figure 5 The robustness optimization flowchart schematic diagram of the present application. DETAILED DESCRIPTION

[0076] In order to make the technical solutions in the present application better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work should fall within the protection scope of the present application.

[0077] As shown in Figure 1 , the embodiment of the present application provides a robustness optimization method of a commercial vehicle suspension system, comprising the following steps:

[0078] Step (1): establishing a powertrain coordinate system, a powertrain mass matrix and a stiffness matrix, and constructing an expression of system natural frequency and decoupling rate;

[0079] Step (2): performing a transfer path analysis, and establishing a mathematical relationship between suspension design parameters and an in-vehicle target point;

[0080] Step (3): analyzing the sensitivity of the objective function to the variables, and determining the design variables and the parameter variables;

[0081] Step (4): using an interval model to represent the design variables, using a probability model to represent the parameter variables, and constructing an interval-probability model to describe the uncertainty of the suspension system variables;

[0082] Step (5): using Monte Carlo random number simulation technology to perform multi-objective robustness optimization;

[0083] Step (6): performing Monte Carlo analysis on the optimization results, and evaluating the robustness of the suspension system.

[0084] In some embodiments, the step of establishing a powertrain coordinate system, a powertrain mass matrix and a stiffness matrix, and constructing an expression of system natural frequency and decoupling rate comprises:

[0085] S11: establishing a powertrain coordinate according to the displacement of the powertrain X, Y and Z directions and the corresponding rotation angles; wherein the center of mass C is defined as the coordinate origin, the x direction is parallel to the crankshaft center line, the z direction is perpendicular to the cylinder upper end face end cover flange plane, and the y direction is determined by the right-hand rule; the generalized coordinates of the powertrain are represented by q = {x y z θ x θ y θ z} T , wherein x, y and z represent the displacement of the powertrain X, Y and Z directions, respectively, and θ x , θ y , θz , respectively represent the rotation of the power assembly in the X, Y and Z directions, and the vibration differential equation of the suspension system is shown in equation (1):

[0086]

[0087] wherein [M], [C], [K] represent the mass matrix, the damping matrix and the stiffness matrix, respectively, and F(t) represents the excitation received by the power assembly suspension system.

[0088] Obtain the inertia parameters of the power assembly to generate the mass matrix M of the power assembly;

[0089] The mass matrix [M] needs to obtain the inertia parameters of the power assembly, mainly including the mass of the power assembly, the position of the mass center of the power assembly, the inertia moment of the power assembly and the inertia product, and the expression is shown in equation (2). The mass of the power assembly and the position of the mass center are obtained by weighing method and suspension method, respectively. The inertia parameters are analyzed by three-wire torsion pendulum method. During the three-wire torsion pendulum test, the power assembly is placed at the balance position, and the initial angular displacement (less than 5°) is applied to the power assembly by reciprocating torsion around the central axis of the three-wire pendulum disc. The angle between each coordinate axis and the center line and the torsional vibration period of the system are measured by a sensor, and the moment of inertia of the power assembly is calculated by a professional instrument.

[0090]

[0091] Obtain the stiffness parameters, installation position parameters and installation angle parameters of the suspension elements, and generate the stiffness matrix K of the power assembly according to the obtained parameters;

[0092] The suspension system adopts a multi-point support form, and N suspension elements are required. The design degree, installation position and installation angle of each suspension element jointly constitute a suspension element, and the suspension elements are numbered and processed according to the installation position, following the principle of from front to back and from left to right, i.e. 1, 2, …, i, …, N, i represents the i-th suspension.

[0093] A local coordinate system O i -uvw, k iu represents the design stiffness of the i-th suspension in the local coordinate system u-axis, k iv represents the design stiffness of the i-th suspension in the local coordinate system v-axis, k iw represents the design stiffness of the i-th suspension in the local coordinate system w-axis, k i represents the stiffness parameters of the suspension element i:

[0094]

[0095] x i , y i , z irespectively represent the coordinate of the i-th suspension element on the corresponding axis of the powertrain coordinate system, and F i represents the installation position parameter of the i-th suspension element:

[0096]

[0097] x ui represents the angle between the u-axis of the i-th suspension local coordinate system and the x-axis of the global coordinate system, y ui represents the angle between the u-axis of the i-th suspension local coordinate system and the y-axis of the global coordinate system, z ui represents the angle between the u-axis of the i-th suspension local coordinate system and the z-axis of the global coordinate system, x vi represents the angle between the v-axis of the i-th suspension local coordinate system and the x-axis of the global coordinate system, y vi represents the angle between the v-axis of the i-th suspension local coordinate system and the y-axis of the global coordinate system, z vi represents the angle between the v-axis of the i-th suspension local coordinate system and the z-axis of the global coordinate system, x wi represents the angle between the w-axis of the i-th suspension local coordinate system and the x-axis of the global coordinate system, y wi represents the angle between the w-axis of the i-th suspension local coordinate system and the y-axis of the global coordinate system, z wi represents the angle between the w-axis of the i-th suspension local coordinate system and the z-axis of the global coordinate system, E i represents the installation angle parameter of the i-th suspension element:

[0098]

[0099] In summary, the overall stiffness of the suspension system can be represented as:

[0100]

[0101] Since the main function of the suspension element damping is to reduce the resonance peak, the damping can be ignored when solving and analyzing the system vibration, and the vibration differential equation of the suspension system can be simplified as:

[0102]

[0103] S14: Solve the characteristic matrix M -1 K and the eigenvector

[0104]

[0105] S15: Solve the decoupling rate DIP of the suspension system mn :

[0106]

[0107] DIP mn represents the percentage of the total energy occupied by the dominant direction of vibration energy of the mth order natural frequency, M(n,j) represents the element in the nth row and the jth column of the mass matrix, and respectively represent the n th and j th elements under the i th mode shape.

[0108] In some embodiments, a complex mechanical system often has various vibration excitation sources, which transmit vibrations to one or more response points through paths such as sub-components of the system. Due to the characteristics of the sub-components of the system, the vibrations may be enhanced or attenuated. The transfer path analysis (TPA) method regards the system as a "source-path-response" model, and identifies the excitation source and path characteristics of the system by measuring the corresponding vibration data, and predicts the vibration response at the target point. As shown in Figure 2 、 3 The steps of performing the transfer path analysis and establishing the mathematical relationship between the suspension design parameters and the target point in the vehicle include:

[0109] S21: The suspension system is divided into an active end a and a passive end p according to the connection relationship. The active end a is connected to the excitation source. The vibration of the excitation source is transmitted to the passive end p through the damping device and to the target point in the vehicle. The response of the target point is:

[0110]

[0111] where Y(ω) represents the response of the system focus point, [H o (ω)] is the frequency response function from the passive end p to the system focus point, which represents the transfer characteristics of the system, and its size depends on the number r of passive end points and the number s of focus points, such as a four-point suspension system, and the steering wheel in the vehicle is selected as the system focus point. Each point considers three degrees of freedom, so the size of the transfer function is 12*3, and there are 36 transfer paths.{F(ω)} represents the input excitation vector, and ω represents the frequency domain;

[0112] S22: The vibration acceleration difference of the passive end p is multiplied by the dynamic stiffness value of the working load through the active end a. The calculation formula is as follows:

[0113]

[0114] In the formula, F o (ω) represents the i th path load size, K o (ω) represents the dynamic stiffness value of the elastic element such as the suspension, a ao (ω) and a po(ω) represents the vibration acceleration values ​​at the active and passive ends of the elastic element in the i-th path, respectively. As can be seen from this theoretical formula, the mount dynamic stiffness method requires two types of data: the dynamic stiffness data of the elastic element such as the mount and the vibration acceleration values ​​at its active and passive ends.

[0115] In summary, formula (10) can be transformed into:

[0116]

[0117] In the formula, [H o (ω)]、a ao (ω), a po Since (ω) and ω are both known quantities, the stiffness value can be adjusted to optimize the vibration conditions at the focus points in the vehicle and improve the NVH performance of the entire vehicle.

[0118] In some embodiments, parameters such as the installation angle, installation position, and suspension stiffness of the suspension all affect the objective function such as the decoupling rate. If all of them are used as design variables, it will not only increase the complexity of the solution, which is not conducive to finding the optimal solution, but also excessive parameter modifications will be detrimental to subsequent structural adjustments and increase costs. Therefore, a reasonable selection of optimization variables will help with subsequent optimization improvements. Through sensitivity analysis, factors that have a greater impact on the objective function are screened and used as design variables, and variables with less impact are used as design variables without adjustment. The steps of analyzing the sensitivity of the objective function to the variables and determining the design variables and parameter variables include:

[0119] The sensitivity S of the objective function to the variable can be expressed as:

[0120] The sensitivity S of the objective function to the variable can be expressed as:

[0121]

[0122] Among them, S(r,t) represents the rth objective function F r For the t-th variable X t The derivative of , L is the number of objective functions, and J is the number of variables.

[0123] When S(r,t) is greater than 0, it means that the objective function F r With variable X t Positively correlated, with X t When S(r,t) is greater than 0, it means that the objective function F r With variable X t Negatively correlated with X t When analyzing sensitivity, both positive and negative correlations need to be taken into account.

[0124]

[0125] By sensitivity analysis, the rth objective function F r , screening variables affecting the objective function greater than the first threshold, integrating the screened variables affecting the L objective functions greater than the first threshold as design variables for subsequent optimization, screening variables affecting the objective function less than the second threshold, and integrating the screened variables affecting the L objective functions less than the second threshold as parameter variables. Divide them into X B and X S , X B represents a set of variables with greater impact as design variables for subsequent optimization, and X S represents a set of variables with smaller impact as parameter variables for subsequent optimization.

[0126] In some embodiments, the step of constructing an interval-probability model to describe the uncertainty of the suspension system variables includes:

[0127] By sensitivity screening of design variables, the suspension system is subjected to deterministic optimization.

[0128] Specifically, the step of subjecting the suspension system to deterministic optimization by sensitivity screening of design variables is implemented by the following formula:

[0129]

[0130] DIP mn represents the percentage of the total energy occupied by the dominant direction of vibration energy of the mth order natural frequency, α m represents the weight of the vibration energy of the mth order natural frequency, β c represents the weight of the cth transmission path, X B represents the design variable, X BL represents the lower limit of the design variable, X BU represents the upper limit of the design variable, DIP Bounce represents the decoupling rate of the suspension vertical, DIP Roll represents the decoupling rate of the suspension lateral.

[0131] In some embodiments, the step of constructing an interval-probability model to describe the uncertainty of the suspension system variables includes constructing the model as follows:

[0132]

[0133] wherein, X B represents the design variable, X BL represents the lower limit of the design variable, X BUupper limit of the design variable, lower limit of the design variable, and d design variables. the gth probability parameter variable, and μg and σg represent the mean and variance of the gth probability parameter variable, μ g and μg and σg represent the mean and variance of the gth probability parameter variable, μ upper and lower limits of the mean of the gth interval parameter variable upper and lower limits of the mean of the gth interval parameter variable S X represents a parameter variable, SL X represents a lower limit of a parameter variable, SU X represents an upper limit of a parameter variable, and e design variables. lower limit of the design variable, and e design variables.

[0134] In some embodiments, conventional optimization design aims to seek an optimal solution of the objective function shown in point 1, and when the design variable x is disturbed, the objective function changes greatly, and point 2 is a robust solution, and the change amplitude of the objective function with x disturbance is smaller than that of the optimal solution, and has better stability and reliability. 6Sigma robust design mainly reduces the influence of design variable disturbance on the objective function through probability and statistics theory. Sigma can be represented by σ. The core idea is to define the distribution characteristics of the design variable, generate random sample points near the design variable and substitute them into the objective function, and statistically analyze the objective function to determine its 6Sigma quality level, reliability and other evaluation indexes. As shown in Figure 4 , 5 The steps of multi-objective robust optimization include:

[0135] calling the MATLAB interface in the Isight software;

[0136] calling the written suspended optimization mathematical model, setting input and output variables;

[0137] dragging the Optimization component and adding variable value range and objective function, and imposing constraint conditions, and selecting the NSGA-II algorithm;

[0138] dragging the 6Sigma optimization component, setting the distribution type of the parameter variable and the design variable, and finally solving the robustness of the suspended system by the constructed model;

[0139] Monte Carlo verification is performed on the robustness solving result to test its 6Sigma level.

[0140] For example, a commercial vehicle equipped with a six-cylinder diesel engine is used as the target vehicle model. The engine adopts a front-mounted, front-wheel drive layout, and the powertrain is supported by a four-point suspension system consisting of front left, front right, rear left, and rear right suspensions. The moment of inertia of the powertrain is obtained by three-wire torsion pendulum testing, and the mass is obtained by weighing. [M] is obtained. For the suspension parameters, the installation position and installation angle of the suspension are obtained from the three-dimensional installation diagram of the suspension bracket, and F is obtained. i and E i The matrix and suspension stiffness parameters are provided by the parts supplier. If they are not available, they can be tested with professional dynamic stiffness testing equipment to obtain G i The overall stiffness K of the suspension is solved by equation (6).

[0141] The vibration differential equation of the suspension system can be simplified to Equation (7);

[0142] Solve the characteristic matrix M -1 The eigenvalues ​​of K With the eigenvector As shown in formula (8);

[0143] Solve to get the decoupling rate DIP of the suspension system mn , the mathematical relationship between each parameter and the suspension decoupling rate is established as shown in formula (9).

[0144] This analysis primarily focuses on the "powertrain-suspension-cabin" system, treating the powertrain as the sole excitation source and the steering wheel within the cab as the focal point. Ignoring the rotational degrees of freedom at each point, the X, Y, and Z directions of the suspension and focal point are analyzed. This allows for the development of a 12-input, 3-output vehicle vibration TPA analysis model and the acquisition of test data.

[0145] The LMS Test.Lab vibration and noise test and analysis system was used, consisting of a data acquisition front-end, a triaxial accelerometer, and a force hammer. The data acquisition front-end was required to have a sampling frequency of at least 10 kHz and a dynamic range of at least 80 dB. The equipment accuracy must meet IEC 651 standards or be within ±0.7 dB. The triaxial accelerometer required high precision and a relatively flat frequency response curve in the 2-3 kHz range.

[0146] A three-axis acceleration sensor is arranged at the passive end and active end of each suspension. The vehicle is operated under the working condition with problems. The time domain vibration data of each suspension passive end and active end are measured by the three-axis acceleration sensor, and the frequency domain data is processed to obtain a po (ω) and a ao (ω), the load data transferred to the passive end of the suspension is calculated using Equation (11).

[0147] The time-domain vibration data of the passive end of the suspension and the target point in the cab are measured by applying excitation to the passive end of the suspension through a hammer, and frequency-domain analysis is performed on the Test.Lab vibration noise test analysis system to obtain the frequency response function [H o (ω)] from the passive end of the suspension to the steering wheel of the cab, with three degrees of freedom considered for each point, and the size of [H o (ω)] is 12*3, i.e., the size of the transfer path is 12 inputs and 3 outputs.

[0148] The frequency-domain response at the steering wheel is solved from the load data F o (ω) and the frequency response function [H o (ω)], and compared with the frequency-domain processing of the actually measured time-domain vibration data of the steering wheel to verify the correctness of the transfer path model.

[0149]

[0150] where Y(ω) represents the response of the point of interest of the system, [H o (ω)] is the frequency response function from the passive end P to the steering wheel, and represents the transfer characteristic of the system.

[0151] The installation angle, installation position, and design stiffness of the suspension are taken as optimization variables, where the installation angle of the suspension has 3*3*4=36 variables, the installation position of the suspension has 3*4=12 variables, and the design stiffness of the suspension has 3*4=12 variables, for a total of 60 variables. The decoupling rate of the suspension and the vibration at the steering wheel of the cab are taken as objective functions.

[0152] If all are taken as design variables, not only does it increase the complexity of solving, which is not conducive to finding the optimal solution, but too many parameter modifications are not conducive to subsequent structural adjustment and increase costs. Therefore, reasonable selection of optimization variables is helpful for subsequent optimization improvement. Through sensitivity analysis, factors that have a greater impact on the objective function are selected as design variables, and factors that have a smaller impact are not adjusted as design variables.

[0153] The sensitivity S of the objective function to the variable can be expressed as formula (13);

[0154] The design variables selected through sensitivity are subjected to deterministic optimization of the suspension system, as shown in formula (15);

[0155] By using an interval model to represent the design variables and a probability model to represent the parameter variables, an interval-probability model is constructed to describe the uncertainty of the variables of the suspension system, as shown in formula (16);

[0156] For the design variables X B±5% is used to describe the interval variation range, and the distribution type of the design variable and the parameter variable is regarded as a normal distribution with a standard deviation of 0.03.

[0157] The mean and variance of the objective function under different design parameter combinations are obtained by using Monte Carlo random number simulation technology, and the multi-objective robustness optimization based on the non-dominated sorting genetic algorithm is carried out. Monte Carlo analysis is performed on the optimization results to evaluate the robustness of the suspension system, and the robustness optimization model is solved. The main steps include the following:

[0158] Through the MATLAB interface in the Isight software;

[0159] Call the written suspension optimization mathematical model, set the input and output variables;

[0160] Drag the Optimization component and add variable value range and objective function, and impose constraint conditions, and select the NSGA-II algorithm;

[0161] Drag the 6Sigma optimization component, set the distribution type of the parameter variable and the design variable, and finally solve the robustness of the suspension system by the built model;

[0162] Monte Carlo verification is performed on the robustness solution to test the 6Sigma level.

[0163] Although the present application has been described in detail with reference to the preferred embodiments, the present application is not limited thereto. Various equivalent modifications or replacements can be made to the embodiments of the present application by those skilled in the art without departing from the spirit and essence of the present application, and these modifications or replacements shall be within the scope of the present application. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or replacements, which shall be within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A method of robustness optimization of a commercial vehicle suspension system, characterized in that, Comprise the following steps: Establish power assembly coordinate system, power assembly mass matrix, stiffness matrix, construct the expression of system natural frequency and decoupling rate; Perform transfer path analysis, and establish mathematical relationship between suspension design parameters and in-vehicle target points; Specifically comprising: Divide the suspension system into active end a and passive end p according to the connection relationship, the active end a is connected with the excitation source, the vibration of the excitation source is transmitted to the passive end p through the damping device, and is transmitted to the in-vehicle target point, and the response of the target point is: wherein, a response of the target point, a frequency response function of the passive end P to the target point is a known quantity, denotes an input excitation vector, denotes the frequency domain; The working load is transmitted through the active end a, and the vibration acceleration difference of the passive end p is multiplied by the dynamic stiffness value to solve, and the calculation formula is as follows: wherein, represents the i-th path load size, represents the dynamic stiffness value of the suspension, and represent the known vibration acceleration values at the primary and secondary ends of the i-th path suspension, respectively, and the stiffness value is adjusted to optimize the vibration at the target point in the vehicle. Analyze the sensitivity of the objective function to the variable to determine the design variable and the parameter variable; An interval model is used to represent the design variable, a probability model is used to represent the parameter variable, and an interval-probability model is constructed to describe the uncertainty of the suspension system variable; Use Monte Carlo random number simulation technology to perform multi-objective robustness optimization; In the step of constructing an interval-probability model to describe the uncertainty of the suspension system variable by using an interval model to represent the design variable and a probability model to represent the parameter variable, the model is constructed as follows: wherein, denotes a design variable, denotes a lower limit of a design variable, denotes an upper limit of a design variable, denotes a lower limit of a design variable, and d denotes the number of design variables, a gth probability parameter variable, and denote a mean and a variance of a gth probability parameter variable, and denote a mean and a variance of a gth interval parameter variable, denote an upper limit and a lower limit of a mean of a gth interval parameter variable, denote an upper limit and a lower limit of a mean of a gth interval parameter variable, denotes a parameter variable, denotes a lower limit of a parameter variable, denotes an upper limit of a parameter variable, and e denotes the number of design variables, denotes a lower limit of a parameter variable, and e denotes the number of design variables.

2. The robustness optimization method of a commercial vehicle suspension system according to claim 1, characterized in that, The steps of establishing power assembly coordinate system, power assembly mass matrix, stiffness matrix, and constructing the expression of system natural frequency and decoupling rate include: Establish the power assembly coordinate according to the displacement of the power assembly X, Y and Z directions and the corresponding rotation angle; wherein the center of mass C is defined as the coordinate origin, the x direction is parallel to the crankshaft center line, the z direction is perpendicular to the flange plane of the cylinder upper end cover, and the y direction is determined by the right hand rule; Obtain the inertia parameters of the power assembly to generate the power assembly mass matrix M; Obtain the stiffness parameters, installation position parameters and installation angle parameters of the suspension components, and generate the power assembly stiffness matrix K according to the obtained parameters; The eigenvalues of the characteristic matrix are found and the eigenvectors : Solving for the decoupling rate of the suspended system : represents the percentage of the total energy occupied by the dominant direction of vibration energy of the natural frequency of the represents the element in the mass matrix at the row and the column, and respectively represent the th element and the th element under the th mode shape.

3. The robustness optimization method of a commercial vehicle suspension system according to claim 2, characterized in that, The steps of analyzing the sensitivity of the objective function to the variable to determine the design variable and the parameter variable include: rth objective function derivative of the tth variable sensitivity of the objective function to the variable ; Wherein, L is the number of objective functions, and J is the number of variables; Through sensitivity analysis, select the variables that have greater than the first threshold value on the target function, integrate the selected variables that have greater than the first threshold value on the L target functions as design variables, and select the variables that have less than the second threshold value on the target function, integrate the selected variables that have less than the second threshold value on the L target functions as parameter variables.

4. The robustness optimization method of a commercial vehicle suspension system according to claim 3, characterized in that, The steps before constructing an interval-probability model to describe the uncertainty of the suspension system variable by using an interval model to represent the design variable and a probability model to represent the parameter variable include: Through the sensitivity selected design variable, the suspension system is subjected to deterministic optimization.

5. The robustness optimization method of a commercial vehicle suspension system according to claim 4, characterized in that, The step of performing deterministic optimization on the suspension system through the sensitivity selected design variable is realized by the following formula: represents the direction in which the vibration energy of the cth natural frequency is dominant, represents the percentage of the total energy occupied by the vibration energy of the cth natural frequency, represents the weight of the cth represents a design variable, represents a lower limit of the design variable, represents an upper limit of the design variable, represents the decoupling rate of the suspension vertical, represents the decoupling rate of the suspension lateral.

6. The robustness optimization method of a commercial vehicle suspension system of claim 5, characterized by, The steps of using Monte Carlo random number simulation technology to perform multi-objective robustness optimization include: Call the MATLAB interface in the Isight software; Call the written suspension optimization mathematical model, set the input and output variables; Drag the Optimization component and add variable value range and target function, and apply constraint conditions, select NSGA-II algorithm; Drag 6Sigma optimization component, set the parameter variable and the distribution type of design variable, and finally solve the robustness of the suspension system by the built model.

7. The robustness optimization method of a commercial vehicle suspension system of claim 6, characterized by, The steps of multi-objective robustness optimization using Monte Carlo random number simulation technology include: Monte Carlo analysis is performed on the optimization results to evaluate the robustness of the suspension system.

8. The robustness optimization method of a commercial vehicle suspension system of claim 7, characterized by, The Monte Carlo analysis on the optimization results to evaluate the robustness of the suspension system specifically includes: Monte Carlo verification is performed on the robustness solution to test its 6Sigma level.

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