A method for constructing a four-degree-of-freedom numerical model of a cab suspension system

Abstract

The present application relates to a kind of cab suspension system four-degree-of-freedom numerical model construction method, comprising the following steps: constructing cab-seat simplified model architecture;Cab free vibration model and cab forced vibration model are constructed;Numerical model is decoupled using modal decoupling method, the transfer function of system is solved;According to random vibration theory, the four-input four-output vibration model of suspension system is obtained;Setting vehicle inertia parameter, stiffness parameter, damping parameter, position parameter, based on above basic parameter, the modal and modal vibration mode of cab suspension system are solved using Matlab code;Spectrum analysis is carried out to the collected Belgium road spectrum to obtain road power spectrum, and road power spectrum is used as the input of random vibration model, and the vertical vibration characteristics of cab and seat are calculated;The optimization design model of suspension system is established by using the joint optimization mode of Isight and Matlab, and the design parameters of cab and seat suspension system are optimized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of cab suspension and relates to a method for constructing a four-degree-of-freedom numerical model of a cab suspension system. BACKGROUND

[0002] With the rapid development of automobile technology, people have higher requirements for vehicle driving comfort. As transport vehicles, commercial vehicles are in a driving state for a long time, so the driving comfort of commercial vehicles is of great concern. The cab suspension system of a commercial vehicle, as a main vibration isolation system of the whole vehicle, directly affects the driving experience. Therefore, scholars at home and abroad have carried out a large number of researches on the cab suspension system. For example, Li Guang et al. carried out researches according to a simplified two-degree-of-freedom suspension model to improve the comfort of the cab. However, for engineering applications, most of them are based on commercial engineering software, which can comprehensively consider the cab suspension system, while the simplified two-degree-of-freedom model cannot consider the influence of the cab roll and the seat on the vibration system.

[0003] Based on this, the application provides a method for constructing a four-degree-of-freedom numerical model of a cab suspension system. SUMMARY

[0004] In view of the defects in the prior art, the application provides a method for constructing a four-degree-of-freedom numerical model of a cab suspension system.

[0005] A method for constructing a four-degree-of-freedom numerical model of a cab suspension system, comprising the following steps:

[0006] S1, constructing a cab-seat simplified model architecture:

[0007] The cab and the seat are simplified as two rigid centers of mass, wherein the suspension system between the cab and the vehicle frame is connected by four air springs and simplified by four mass-damping-spring models; the suspension system between the seat and the cab is connected by seat springs and simplified as a mass-damping-spring model, that is, the cab-seat vibration model mainly consists of four air springs, seat springs, a cab and a seat, wherein the spring model only introduces Z-direction stiffness, so the motion degrees of freedom of the cab are vertical motion displacement Z1, roll angle θ x and pitch angle θ y , and the motion degrees of freedom of the seat are vertical motion displacement Z2.

[0008] S2, constructing a cab free vibration model and a cab forced vibration model;

[0009] S3, decoupling the numerical model by using a modal decoupling method to solve the transfer function of the system;

[0010] S4, obtaining a four-input four-output vibration model of the suspension system according to the random vibration theory.

[0011] S5, set the vehicle inertia parameters, stiffness parameters, damping parameters, position parameters, based on the above basic parameters, using Matlab code to solve the modal and modal shape of the cab suspension system;

[0012] S6, the collected Belgium road spectrum is analyzed to obtain the road power spectrum, and the road power spectrum is used as the input of the random vibration model to calculate the vertical vibration characteristics of the cab and the seat;

[0013] S7, the optimization design model of the suspension system is established by using the joint optimization method of Isight and Matlab, and the design parameters of the cab and seat suspension system are optimized.

[0014] Further, the construction of the cab free vibration model in step S2 includes the following steps:

[0015] Step 1, establish the total kinetic energy equation of the suspension system:

[0016]

[0017] Where T is the total kinetic energy of the system, J x ,J y is the moment of inertia of the cab mass center around the x and y axes, J xy is the section moment of inertia; m1, m2 are the mass of the cab and seat mass centers, Z1, Z2 are the vertical displacement of the cab and seat;

[0018] Step 2, establish the total potential energy equation of the suspension system:

[0019]

[0020] Where U is the total dissipation energy of the system, U i is the damping dissipation energy of the i-th air spring, U2 is the damping dissipation energy of the seat spring, Z1, Z2 are the vertical displacement of the cab and seat, k i is the stiffness of the i-th air spring, k is the stiffness of the seat spring, x i , y i is the coordinate of the upper mounting point of the i-th air spring, x, y is the coordinate of the bottom mounting point of the seat spring;

[0021] Step 3, establish the total dissipation energy equation of the suspension system:

[0022] According to the calculation principle of potential energy, the total dissipation energy of the suspension system is obtained:

[0023]

[0024] Where D is the total dissipation energy of the system, D iD2 is the damping dissipation energy of the seat spring, c i k is the stiffness of the i th air spring, x i , y i is the coordinate of the upper mounting point of the i th air spring, x, y is the coordinate of the bottom mounting point of the seat spring;

[0025] Step 4, the free vibration equation of the system is obtained from the Lagrange equation:

[0026]

[0027] Where the mass matrix [m], the damping matrix [c], the stiffness matrix [k], and the displacement vector {x} are as follows:

[0028]

[0029]

[0030]

[0031] {x}=(Z1 θ x θ y Z2) T (8)。

[0032] Further, the construction of the forced vibration model of the cab in step S2 includes the following steps:

[0033] Step 1, the total kinetic energy equation of the suspension system is established

[0034]

[0035] Where T is the total kinetic energy of the system, J x ,J y is the moment of inertia of the cab mass center around the x and y axes, J xy is the section moment of inertia; m1, m2 are the mass of the cab and seat mass centers, Z1, Z2 are the vertical movement displacements of the cab and seat;

[0036] Step 2, the total potential energy equation of the suspension system is established:

[0037]

[0038] Where U is the total dissipation energy of the system, U i is the damping dissipation energy of the i th air spring, U2 is the damping dissipation energy of the seat spring, Z1, Z2 are the vertical movement displacements of the cab and seat, k i is the stiffness of the i th air spring, k is the stiffness of the seat spring, x i , y iis the coordinate of the upper mounting point of the ith air spring, x, y are the coordinates of the bottom mounting point of the seat spring, ii is the excitation of the lower mounting point of the ith air spring;

[0039] Step 3, the total dissipation energy equation of the suspension system is established:

[0040]

[0041] wherein D is the total dissipation energy of the system, D i is the damping dissipation energy of the ith air spring, D2 is the damping dissipation energy of the seat spring, c i is the stiffness of the ith air spring, x i , y i is the coordinate of the upper mounting point of the ith air spring, x, y are the coordinates of the bottom mounting point of the seat spring, is the excitation of the lower mounting point of the ith air spring;

[0042] Step 4, the forced vibration equation of the system is obtained from the Lagrange equation:

[0043]

[0044] wherein the mass matrix [m], the damping matrix [c], the stiffness matrix [k], the displacement vector {x} are consistent in free vibration, and the excitation vector {f} is as follows:

[0045]

[0046] Convert equation (11) into matrix form:

[0047] {f}=[B]{Z ii} (13)

[0048] wherein [B] is the conversion matrix, {Z ii} is the excitation vector:

[0049]

[0050] {Z ii}={Z 11 Z 22 Z 33 Z 44} T (15)

[0051] Ω in equation (13) is the excitation frequency.

[0052] Further, the step S3 decouples the numerical model by using the modal decoupling method, and the specific steps for solving the transfer function of the system include:

[0053] (1) Using modal decoupling method to decouple forced vibration equation, i.e. equation (11), the decoupled equation is as follows:

[0054]

[0055] Wherein, [M] is the modal mass matrix, [C] is the modal damping matrix, [K] is the modal stiffness matrix, {q(t)} is the generalized coordinate vector, {F(t)} is the excitation vector in the modal coordinate system;

[0056] (2) The mass matrix and stiffness matrix after decoupling are diagonal matrices, and the damping matrix is a non-diagonal matrix. Direct diagonalization of the damping matrix is adopted to completely decouple the dynamic equation, and each degree of freedom equation after decoupling is solved separately,

[0057] q r (t)=H r (Ω)F r (t) (17)

[0058]

[0059] H r (Ω) is the transfer function of the rth degree of freedom in the modal coordinate system;

[0060] (3) Fourier transform is carried out on both sides of the above equation (17):

[0061] q r (Ω)=H r (Ω)F r (Ω) (19);

[0062] (4) Equation (17) to equation (19) is solved for all degrees of freedom, and the converted results are assembled into a matrix as follows:

[0063]

[0064] (5) Equation (20) is converted to the physical coordinate system, so as to obtain the actual dynamic response of the system

[0065]

[0066]

[0067] Wherein, [u] is the modal matrix of the system, i.e. the modal shape matrix.

[0068] Further, the step S4 obtains the four-input four-output vibration model of the suspension system according to the random vibration theory, and specifically includes the following steps:

[0069] (1) The power spectrum response equation of the suspension system is as follows:

[0070] [S yy (Ω)]=[H * (Ω)][S xx (Ω)][H(Ω)] T (23)

[0071] Wherein, [S yy (Ω)] is the system response power spectrum matrix, [H * (Ω)] is the conjugate matrix of the transfer function matrix, [S xx (Ω)] is the excitation power spectrum matrix, and [H(Ω)] is the transfer matrix.

[0072] (2) Since the motions at the four air spring excitation input points are independent of each other, there is no correlation, that is, the mutual power spectrum of the four input excitation sources is zero, and the excitation power spectrum matrix [S xx (Ω)] is as follows:

[0073]

[0074] Further, the step S6 specifically comprises the following steps:

[0075] (1) Spectrum analysis is performed on the test signal, and the spectrum analysis principle is as shown in formulas 25 and 26:

[0076]

[0077] When τ=0:

[0078] In the formula, R x (τ) is the signal correlation function, x(t) is the time domain signal, τ is the time increment, and T is the sampling time period.

[0079] Wiener-Sinchen relationship:

[0080]

[0081]

[0082] In the formula, s x (ω) is the signal power spectrum density function, and ω is the signal angular frequency.

[0083] (2) The displacement excitation signal measured in the experiment is converted into a displacement power spectrum by means of the pwelch function in Matlab.

[0084] Further, the optimization design model of the suspension system in the step S7 is as shown below:

[0085] Six parameters including the stiffness and damping of the four cab air spring suspensions and the stiffness and damping of the seat spring are taken as the optimization variables, and the root mean square value of the total weighted acceleration of the suspension system is taken as the optimization target, wherein the excitation input required by the optimization model is consistent with the excitation in the foregoing:

[0086] The optimization mathematical model of the suspension system can be described as:

[0087]

[0088] The optimization Latin square method in Isight is adopted, wherein each variable factor adopts 50 levels, and a 50X6 experimental design matrix is generated.

[0089] The advantages of the technical scheme are as follows: the technical scheme adopts the principle of dynamics to obtain a dynamic numerical model of a commercial vehicle cab suspension system, adopts a modal decoupling method to perform modal analysis on the dynamic model, and obtains a transfer matrix of the suspension system. According to the principle of a multi-input multi-output random vibration model, a random vibration model of the suspension system is obtained. The entire analysis process is coded by using Matlab, and a road spectrum collected by a road test is analyzed, a road load power spectrum is obtained, and the road load power spectrum is taken as an input boundary of the random vibration model and is used for analyzing the vibration characteristics of the cab. According to the evaluation standard of the national standard, the cab suspension system is optimized and designed, the vertical total weighted acceleration of the cab and the seat is taken as the optimization target, the stiffness and damping of the front suspension, the rear suspension and the seat suspension of the cab are taken as the optimization variables, the optimization Latin square algorithm in Isight is combined with Matlab to perform joint optimization, and the optimal design is obtained, so that the driving comfort of the commercial vehicle is improved. BRIEF DESCRIPTION OF DRAWINGS

[0090] Figure 1 It is a schematic diagram of a cab-seat simplified model;

[0091] Figure 2 It is a schematic diagram of a linear system model;

[0092] Figure 3 It is a displacement excitation time domain signal;

[0093] Figure 4 It is a displacement excitation power spectrum;

[0094] Figure 5 It is a displacement response power spectrum;

[0095] Figure 6 It is an acceleration response power spectrum;

[0096] Figure 7 It is an Isight optimization model;

[0097] Figure 8 It is an air spring stiffness sample diagram;

[0098] Figure 9 Air spring damping sample graph;

[0099] Figure 10 To optimize the front and rear acceleration power spectrum. DETAILED DESCRIPTION

[0100] The construction method of the four-degree-of-freedom numerical model of the cab suspension system will be explained and described in detail below in combination with the drawings of the specification.

[0101] The construction method of the four-degree-of-freedom numerical model of the cab suspension system comprises the following steps:

[0102] S1, construct a cab-seat simplified model architecture:

[0103] S2, construct a cab free vibration model and a cab forced vibration model;

[0104] S3, decouple the numerical model using modal decoupling method, and solve the transfer function of the system;

[0105] S4, according to the random vibration theory, obtain the four-input four-output vibration model of the suspension system;

[0106] S5, set the vehicle inertia parameters, stiffness parameters, damping parameters, and position parameters, and based on the above basic parameters, use Matlab code to solve the modal and modal shape of the cab suspension system;

[0107] S6, perform spectral analysis on the collected Belgian road spectrum to obtain the road power spectrum, and use the road power spectrum as the input of the random vibration model to calculate the vertical vibration characteristics of the cab and the seat;

[0108] S7, use the joint optimization method of Isight and Matlab to establish an optimization design model of the suspension system, and optimize the design parameters of the cab and seat suspension system.

[0109] In this embodiment, the cab is simplified as a rigid body, and the influence of the deformation of the vehicle frame is introduced through the test of the vibration excitation at the connection between the air spring and the vehicle frame.

[0110] (1) Construct a cab-seat simplified model architecture

[0111] In this embodiment, the projection point of the cab mass center on the cab floor is taken as the coordinate origin, the cab is simplified as a rigid body, and the seat is simplified as a mass point. The suspension system between the cab and the vehicle frame is connected by four air springs, which is simplified by four pairs of spring and damping models. The suspension system between the seat and the cab is simplified as a pair of spring and damping model. The excitation input point of the model is the connection position between the bottom of the four air springs and the vehicle frame, and the simplified four-degree-of-freedom model is as followsFigure 1 As shown in Figure 1 , a is the distance from the front suspension to the coordinate origin, b is the distance from the rear suspension to the coordinate origin, c is the left-right distance of the front suspension, d is the left-right distance of the rear suspension, x and y are the distances from the seat spring bottom mounting point to the coordinate origin, k1 and c1 are the front suspension stiffness and damping, k2 and c2 are the rear suspension stiffness and damping, k3 and c3 are the seat spring stiffness and damping, m1 and m2 are the mass of the cab and seat center of mass, Z1 and Z2 are the vertical movement displacements of the cab and seat, Z 11 , Z 22 , Z j3 , Z 44 is the system excitation input.

[0112] The cab and seat are simplified as two rigid centers of mass, wherein the suspension system between the cab and the frame is connected by four air springs, which is simplified by a four mass-damping spring model; the suspension system between the seat and the cab is connected by a seat spring, which is simplified as a mass-damping spring model, that is, the cab and seat vibration model mainly consists of four air springs, a seat spring, a cab and a seat, wherein the spring model only introduces Z-direction stiffness, so the movement degrees of freedom of the cab are vertical movement displacement Z1, roll angle θ x , pitch angle θ y , and the movement degrees of freedom of the seat are vertical movement displacement Z2.

[0113] According to the four-degree-of-freedom model architecture in Figure 1 , the following derivation of the dynamics equation of the vibration model is expanded.

[0114] (2) Construction of the free vibration model of the cab

[0115] Step 1, establish the total kinetic energy equation of the suspension system:

[0116]

[0117] Wherein, T is the total kinetic energy of the system, J x ,J y is the moment of inertia of the cab center of mass around the x and y axes, J xy is the section moment of inertia; m1 and m2 are the mass of the cab and seat center of mass, Z1 and Z2 are the vertical movement displacements of the cab and seat;

[0118] Step 2, establish the total potential energy equation of the suspension system:

[0119]

[0120] Wherein, U is the total dissipation energy of the system, U iLet U1 be the damping dissipation energy of the i-th air spring, U2 be the damping dissipation energy of the seat spring, Z1 and Z2 be the vertical displacements of the cab and seat, and k be the vertical displacements of the cab and seat. i Let x be the stiffness of the i-th air spring, k be the stiffness of the seat spring, and x be the stiffness of the i-th air spring. i y i Let x and y be the coordinates of the upper mounting point of the i-th air spring, and let x and y be the coordinates of the bottom mounting point of the seat spring.

[0121] Step 3: Establish the total energy dissipation equation for the suspension system:

[0122] By analogy with the calculation principle of potential energy, the total energy dissipated by the suspension system is obtained:

[0123]

[0124] Where D is the total energy dissipated by the system, D i Let D1 be the damping dissipation energy of the i-th air spring, D2 be the damping dissipation energy of the seat spring, and c be the damping dissipation energy of the seat spring. i Let x be the stiffness of the i-th air spring. i y i Let x and y be the coordinates of the upper mounting point of the i-th air spring, and let x and y be the coordinates of the bottom mounting point of the seat spring.

[0125] Step 4: Obtain the free vibration equation of the system from the Lagrange equation:

[0126]

[0127] The mass matrix [m], damping matrix [c], stiffness matrix [k], and displacement vector {x} are as follows:

[0128]

[0129]

[0130]

[0131] {x}=(Z1 θ x θ y Z2) T (8).

[0132] (2) Forced vibration model of the cab

[0133] Step 1: Construction of the kinetic energy equation for the forced vibration model

[0134] Due to the introduction of external excitation, the motion of the cab and seat relative to the coordinate origin is absolute motion, and the motion of the lower mounting point of the air spring is related to the excitation source Z. 11 Z 22 Z 33 Z44 In this case, the motion is a coupled motion, however the restoring force of the spring and damper depends on the relative motion and relative velocity of the upper and lower mounting points of the air spring, so the elastic potential energy and the damping dissipation energy of the system are different from the free vibration case.

[0135] Step 2, establish the total potential energy equation of the suspension system:

[0136]

[0137] Where, U is the total dissipation energy of the system, U ii is the damping dissipation energy of the i-th air spring, U2 is the damping dissipation energy of the seat spring, Z1, Z2 is the vertical motion displacement of the cab and the seat, k ii is the stiffness of the i-th air spring, k is the stiffness of the seat spring, x 11 , y 22 is the coordinate of the upper mounting point of the i-th air spring, x, y is the coordinate of the bottom mounting point of the seat spring, 33 is the excitation of the lower mounting point of the i-th air spring;

[0138] Step 3, establish the total dissipation energy equation of the suspension system:

[0139]

[0140] Where, D is the total dissipation energy of the system, D 44 is the damping dissipation energy of the i-th air spring, D2 is the damping dissipation energy of the seat spring, c T is the stiffness of the i-th air spring, x r , y r is the coordinate of the upper mounting point of the i-th air spring, x, y is the coordinate of the bottom mounting point of the seat spring, r is the excitation of the lower mounting point of the i-th air spring;

[0141] Step 4, the forced vibration equation of the system is obtained from the Lagrange equation:

[0142]

[0143] Where, the mass matrix [m], the damping matrix [c], the stiffness matrix [k], the displacement vector {x} are consistent with the free vibration, and the excitation vector {f} is as follows:

[0144]

[0145] Convert equation (11) to matrix form:

[0146] {f}=[B]{Z r} (13)

[0147] where [B] is the transformation matrix, {Z ii} is the excitation vector:

[0148]

[0149] {Z ii} = {Z 11 Z 22 Z 33 Z 44} T (15)

[0150] Ω in equation (13) is the excitation frequency.

[0151] (3) Solution of the vibration system transfer matrix

[0152] Step 1, since the dynamic equation (11) is obtained based on the physical coordinate system, there is a coupling relationship between the degrees of freedom, in order to facilitate the solution of the dynamic equation, the modal decoupling method is used to decouple equation (11), and the decoupled equation is as follows:

[0153]

[0154] where [M] is the modal mass matrix, [C] is the modal damping matrix, [K] is the modal stiffness matrix, {q(t)} is the generalized coordinate vector, and {F(t)} is the excitation vector in the modal coordinate system;

[0155] Step 2, the mass matrix and the stiffness matrix after decoupling are diagonal matrices, and the damping matrix is a non-diagonal matrix, in order to facilitate the solution, the direct diagonalization of the damping matrix is adopted, so that the dynamic equation is completely decoupled, and each degree of freedom equation after decoupling is solved separately.

[0156] q r (t) = H r (Ω)F r (t) (17)

[0157]

[0158] H r (Ω) is the transfer function of the rth degree of freedom in the modal coordinate system;

[0159] Step 3, Fourier transform is performed on both sides of the above equation (17):

[0160] q r (Ω) = H r (Ω)F r (Ω) (19);

[0161] Step 4, the equation (17) to equation (19) is solved to all degrees of freedom, the conversion of the results assembled into a matrix as follows:

[0162]

[0163] Step 5, equation (20) is converted to the physical coordinate system, thus obtaining the actual dynamic response of the system

[0164] (22)

[0166] Where, [u] is the modal matrix of the system, namely the modal shape matrix;

[0167]

[0168] (4) cab random vibration model

[0169] In this embodiment, referring to the multi-input multi-output model in the random vibration theory, a linear system with m inputs and n outputs is as shown in Figure 2 i (Ω) is the input power spectrum, H ji (Ω) is the transfer function of the system, y j (Ω) is the response power spectrum of the system.

[0170] Step 1, according to the correlation and spectral analysis related theory, the power spectrum response equation of the system is as follows:

[0171] [S yy (Ω)]=[H * (Ω)][S xx (Ω)][H(Ω)] T (23)

[0172] Where, [S yy (Ω)] is the system response power spectrum matrix, [H * (Ω)] is the conjugate matrix of the transfer function matrix, [S xx (Ω)] is the excitation power spectrum matrix, and [H(Ω)] is the transfer matrix;

[0173] Step 2, since the motions at the input points of the four air springs are independent of each other, there is no correlation, that is, the cross power spectrum of the four input excitation sources is zero, and the excitation power spectrum matrix [S xx (Ω)] is as follows

[0174]

[0175] For the above mathematical model, Matlab is used for coding. ​

[0176] (5) Set the basic parameters of the suspension system

[0177] Taking a certain model of commercial vehicle as the analysis object, the inertial parameters, stiffness parameters, damping parameters, and position parameters of this model are shown in Table 1.

[0178] Table 1 Model Input Parameters

[0179] Table 1 Model input parameters

[0180] Parameter name Value cabin mass m1 (kg) 1056 Cab rotational inertia J x (kg·m 2 )]]> 2050 Cab rotational inertia J y (kg·m 2 )]]> 1875 Seat mass m2 (kg) 65.5 Front suspension stiffness k1 (N / mm) 55 rear suspension stiffness k2 (N / mm) 42.5 Seat spring stiffness k3 (N / mm) 21.887 front suspension damping c1 (n / (mm / s)) 8.4 rear suspension damping c2 (N / (mm / s)) 4 seat spring damping c3 (N / (mm / s)) 1.385 Front suspension to origin distance a (mm) 862.5 Front suspension to origin distance b (mm) 1032.5 Front suspension left-right spacing c (mm) 1430 Front suspension left-right spacing d (mm) 1350 Seat spring mounting point coordinates x, y (mm) (310.086，433.49)

[0181] Taking a certain model of commercial vehicle as the analysis object, the inertial parameters, stiffness parameters, damping parameters, and position parameters of this model are shown in Table 1.

[0182] Based on the above basic parameters, the modes and mode shapes of the cab suspension system were solved using Matlab code, as shown in the table.

[0183] Table 2 Mode Shapes of Suspension System

[0184]

[0185] (6) Road spectrum excitation analysis

[0186] The test track used Belgian road surfaces as the test road. Vibration excitation was obtained at four connection points between the chassis and the cab suspension through testing. The experimental displacement data are as follows: Figure 3 As shown.

[0187] As a typical random signal, road surface excitation is usually converted into a frequency domain power spectrum to facilitate the study of the dynamic characteristics of the cab under random road surface excitation signals. Therefore, spectral analysis of the test signal is required. The principle of spectral analysis is shown in Equations 25 and 26. First, correlation analysis is performed on the time-domain signal to obtain the correlation function. Then, the power spectral density function of the signal can be obtained by performing a Fourier transform on the correlation function.

[0188]

[0189] When τ = 0:

[0190] In the formula, R x (τ) is the signal correlation function, x(t) is the time domain signal, τ is the time increment, and T is the sampling time period.

[0191] Wiener-Shinchin relationship:

[0192]

[0193]

[0194] In the formula, s x (ω) is the signal power spectral density function, and ω is the signal angular frequency;

[0195] The experimentally measured displacement excitation signal was converted into a displacement power spectrum using the pwelch function in Matlab, such as... Figure 4 As shown.

[0196] (7) Analysis of cab vibration results

[0197] Using Matlab code and taking the road power spectrum as input, the vibration response of the cab suspension system was calculated. The vertical displacement vibration responses of the cab and seat are shown below. Figure 5 As shown, the acceleration-velocity vibration response is as follows: Figure 6 As shown.

[0198] Refer to Appendix A of GB / T 4970-200 Test Method for Ride Comfort of Automobiles for calculation of total weighted acceleration. The root mean square value calculation method, using Matlab. Figure 6 The total weighted acceleration of the suspension system was calculated to be 1.4047 m / s² using weighted average calculations of the data. According to the subjective human perception in Appendix A, when the root mean square value of the weighted acceleration is less than 1 m / s², the human body can barely accept it. Therefore, the original suspension system design cannot meet the requirements for vehicle ride comfort design.

[0199] (8) Suspension system optimization design

[0200] Since the cab suspension uses air springs, according to the manufacturer's design requirements, the suspension parameters are symmetrical left and right. Simultaneously, the impact of these parameters on cab ride comfort is fully considered. Six parameters—the stiffness and damping of the four cab air spring suspensions, and the stiffness and damping of the seat springs—are used as optimization variables. The root mean square value of the total weighted acceleration of the suspension system is used as the optimization objective. The excitation input required for the optimization model remains consistent with the excitation described earlier. The mathematical model for the suspension system optimization can be described as follows:

[0201]

[0202] To fully consider the impact of the six variable factors on the optimization objective and reduce the number of experimental designs, the Latin square optimization method in Isight is adopted, where each variable factor has 50 levels, generating a 50x6 experimental design matrix. The optimization model is as follows: Figure 7 As shown.

[0203] Since Latin hypercube sampling (LHS) was proposed in 1979, it has been an important method in the field of "space-filling" design and is currently widely used. Latin hypercube sampling is a random matrix formed by arranging each factor vertically according to the number of levels, wherein the levels in the same vertical column have no repeated factors. Due to the instability of random sampling, LHS has been improved, and centering LHS, symmetrical LHS, column orthogonal LHS, and optimized LHS have appeared. The optimized Latin hypercube sampling method uses an initial solution with good orthogonality, and considers the orthogonality and uniformity of the Latin hypercube matrix. The initial solution is constructed, and the Latin hypercube matrix is also optimized.

[0204] The sample points of the suspension system are generated by using the optimized Latin hypercube sampling method, and the following figure only shows the sample point number of the air spring stiffness and damping distribution of the cab, Figure 8 for the air spring stiffness sample distribution, Figure 9 for the air spring damping sample distribution.

[0205] Optimization result analysis

[0206] After 50 tests, the scheme with the smallest target result is selected as the optimal design scheme, and the design parameters and weighted acceleration root mean square values before and after optimization are shown in Table 3, and the acceleration power spectral density of the cab and seat before and after optimization is compared as shown in Figure 10 .

[0207] Table 3 results before and after optimization

[0208]

[0209] After optimization, the total weighted acceleration root mean square value of the suspension system is 0.58 m / s^2, which is slightly acceptable compared with the original design scheme, so the optimization scheme meets the vehicle ride comfort index.

[0210] Conclusion: Firstly, based on the theories of free vibration, forced vibration, modal decoupling and random vibration in vibration mechanics, the vibration analysis model of the cab suspension system is established; the road test test excitation is used as the model input boundary, and after analysis and verification, the original design scheme cannot meet the requirements of vehicle ride comfort. Therefore, according to the design requirements, the optimization design model of the suspension system is established, and through the optimization of the Latin hypercube sampling algorithm, the suspension system is optimized for multiple rounds, which greatly improves the ride comfort of the suspension system.

Claims

1. A method for constructing a four-degree-of-freedom numerical model of a cab suspension system, characterized by comprising the following steps: S1, constructing a cab-seat simplified model architecture; S2, constructing a cab free vibration model and a cab forced vibration model; S3, decoupling the numerical model using a modal decoupling method to solve the transfer function of the system; S4, obtaining a four-input four-output vibration model of the suspension system according to the random vibration theory; S5, setting the vehicle inertia parameters, stiffness parameters, damping parameters, and position parameters, and based on the above parameters, using Matlab code to solve the modal and modal shape of the cab suspension system; S6, performing spectral analysis on the collected Belgian road spectrum to obtain the road power spectrum, taking the road power spectrum as the input of the random vibration model, and calculating the vertical vibration characteristics of the cab and seat; S7, using the Isight and Matlab joint optimization method to establish an optimization design model of the suspension system, and optimizing the design parameters of the cab and seat suspension system. θ The specific operation of the step S1 is as follows: the cab and the seat are simplified as two rigid centers of mass, wherein the suspension system between the cab and the frame is connected by four air springs, and is simplified by using four mass-damping spring models; the suspension system between the seat and the cab is connected by seat springs, and is simplified as one mass-damping spring model, that is, the vibration model of the cab and the seat is composed of four parts of the four air springs, the seat springs, the cab and the seat, wherein the spring model only introduces the Z-direction stiffness, so the motion freedom degree of the cab is the vertical motion displacement Z1, the roll angle θ x , the pitch angle The construction of the cab free vibration model in step S2 comprises the following steps: y , and the motion freedom degree of the seat is the vertical motion displacement Z2. Step 1, establishing the total kinetic energy equation of the suspension system: Step 2, establishing the total potential energy equation of the suspension system: ； wherein T is the total kinetic energy of the system, J x , J y Ixxand Iyyare the rotational inertia of the cab mass center around the x and y axes, J xy Izzis the section moment of inertia; m 1 , m 2 m is the mass of the cab and seat mass center, Z 1 , Z 2 is the vertical motion displacement of the cab and seat. Step 3, establishing the total dissipation energy equation of the suspension system: ； wherein, U is the total dissipated energy of the system, U i is the dissipated energy of the i-th air spring, U2 is the dissipated energy of the seat spring, Z 1 , Z 2 is the vertical displacement of the cab and seat, k i is the stiffness of the i-th air spring, k is the stiffness of the seat spring, x i , y i is the coordinate of the upper mounting point of the i-th air spring, x, y is the coordinate of the bottom mounting point of the seat spring; Analogous to the calculation principle of potential energy, the total dissipation energy of the suspension system is obtained: Step 4, obtaining the free vibration equation of the system from the Lagrange equation: ； where D is the total dissipated energy of the system, D i is the dissipated energy of the i-th air spring, D 2 is the dissipated energy of the seat spring, c i is the stiffness of the i-th air spring, x i , y i is the coordinate of the upper mounting point of the i-th air spring, x, y is the coordinate of the bottom mounting point of the seat spring; The construction of the cab forced vibration model in step S2 comprises the following steps: ； wherein the mass matrix [m], the damping matrix [c], the stiffness matrix [k], and the displacement vector {x} are as follows: ; ； ； 。 2. The method of claim 1, wherein: Step 1, establishing the total kinetic energy equation of the suspension system; Step 2, establishing the total potential energy equation of the suspension system; Step 3, establishing the total dissipation energy equation of the suspension system; Step 4, obtaining the forced vibration equation of the system from the Lagrange equation: Convert equation (10) to matrix form: ； Among them, the mass matrix [m], the damping matrix [c], and the stiffness matrix [m] are... k The displacement vector {x} is consistent with that in free vibration, and the excitation vector { f }as follows: ； In equation (12), Ω is the excitation frequency. ； where, B ] is a transformation matrix, Z ii is an excitation vector: ； ； The step S3 utilizes the modal decoupling method to decouple the numerical model to solve the transfer function of the system, which specifically comprises the following steps:

3. The method of claim 2, wherein: (1) Decoupling the forced vibration equation, i.e. equation (9), using the modal decoupling method, and the decoupled equation is as follows: Where [M] is the modal mass matrix, [c] is the modal damping matrix, [K] is the modal stiffness matrix, {q(t)} is the generalized coordinate vector, and {F(t)} is the excitation vector in the modal coordinate system; ； (2) The mass matrix and stiffness matrix after decoupling are diagonal matrices, and the damping matrix is a non-diagonal matrix. Direct diagonalization of the damping matrix is adopted to completely decouple the dynamic equation, and each degree of freedom equation after decoupling is solved separately, (3) Fourier transform both sides of the above equation (15): ； ； H r (Ω) is the transfer function of the rth degree of freedom in the modal coordinate system; (4) Solve equation (15) to equation (17) for all degrees of freedom, and assemble the converted results into a matrix as follows: ; (5) Convert equation (18) to the physical coordinate system to obtain the actual dynamic response of the system ; Where [u] is the modal matrix of the system, i.e. the modal shape matrix. ; ; The step S4 according to the random vibration theory to obtain the four-input four-output vibration model of the suspension system specifically comprises the following steps:

4. The method of claim 1, wherein: (1) Constructing the power spectrum response equation of the suspension system as follows: ​ ; where [S yy (Ω)] is the system response power spectral matrix, [H*(Ω)] is the conjugate matrix of the transfer function matrix, [S xx (Ω)] is the excitation power spectral matrix, and [H(Ω)] is the transfer matrix. (2) Since the motions at the four air spring excitation input points are independent of each other, there is no correlation, i.e., the cross power spectrum of the four input excitations is zero, the excitation power spectrum matrix [S xx (Ω)] is as follows: 。 5. The method of claim 1, wherein: The step S6 specifically includes the following operations: (1) performing spectral analysis on the test signal, and the spectral analysis principle is shown in formulas 23 and 24: ; wherein R x (τ) is a signal correlation function, τ is a time domain signal, t is a time increment, T is a sampling time period; Wiener-Sinai relation: ; wherein S x (ω) is the signal power spectral density function, ω is the signal angular frequency; (2) converting the displacement excitation signal measured in the experiment into a displacement power spectrum by means of a pwelch function in Matlab.

6. The method according to claim 1, characterized in that: The optimization design model of the suspension system in the step S7 is as follows: Taking the stiffness and damping of the air spring suspension of the four cabs and the stiffness and damping of the seat spring as 6 optimization variables, and taking the total weighted acceleration root mean square value of the suspension system as the optimization target, wherein the excitation input required by the optimization model is consistent with the excitation in the foregoing, the optimization mathematical model of the suspension system can be described as: ； The method of optimization Latin square in Isight is adopted, wherein each variable factor adopts 50 levels, and a 50X6 experimental design matrix is generated.

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