Modeling and parameter identification method, system and equipment based on improved Bingham model and medium

Abstract

The invention discloses a modeling and parameter identification method, system and device based on an improved Bingham model and a medium, and the method comprises the steps: introducing a spring model into the Bingham model according to magneto-rheological suspension multi-field coupling simulation and suspension dynamic characteristic test, and obtaining the improved Bingham model; performing parameter identification on the improved Bingham model by using a least square method; and according to the Bingham model after parameter identification, predicting the output damping force of the magnetorheological suspension so as to verify the improved Bingham model. According to the method, the most classical Bingham model with the strongest applicability is improved, main parameters in the improved Bingham model are identified on the basis of a multi-field coupling simulation result, and the capacity of the improved Bingham model for predicting the damping force output by the suspension is evaluated in combination with a finite element simulation result.

Description

Technical Field

[0001] The invention relates to the field of magnetorheological suspension, and in particular to a method, system, equipment and medium for modeling and parameter identification based on an improved Bingham model. Background Art

[0002] An essential feature of magnetorheological suspension is the relationship between the stress and strain of the suspension under different magnetic fields, and this feature can be quantitatively expressed through the magnetorheological suspension mechanical model.

[0003] In the prior art, the Herschel-Bulkley model is used to describe the relationship between the torque and strain rate of the magnetorheological damper. The Herschel-Bulkley model is used to derive the mechanical model of the magnetorheological buffer containing flow inertia. The Rational-Bingham model uses the least squares method to identify the model parameters and verify the model accuracy. The improved dual-viscosity magnetorheological fluid constitutive model can well describe the external performance of the shock absorber. The improved Bouc-Wen model verifies that the improved model has improved fitting accuracy and parameter identification efficiency. The improved Herschel-Bulkley model is applied to the shear magnetorheological damper. The improved Bingham mechanical model verifies that the fitting accuracy of the improved model is greatly improved compared with that before the improvement.

[0004] Existing technologies show that classical mechanical models have certain deficiencies in expressing the rheological properties of magnetorheological fluids. For example, the Bingham model has a simple structure but low fitting accuracy. The Herschel-Bulkley model has improved fitting accuracy, but it is a three-variable model and the calculation is relatively complex. Other typical mechanical models also have similar deficiencies. Although the fitting accuracy of the improved and revised mechanical model has been improved, due to the complex rheological mechanism of the magnetorheological suspension itself, there is currently no unified and accurate mechanical model to describe its performance, which also leads to a more complex modeling method for the parameterized model. Summary of the invention

[0005] In view of the above-mentioned existing technical defects, the present invention improves the most applicable and classic Bingham model, identifies the main parameters in the improved Bingham model based on the multi-field coupling simulation results, and evaluates the ability of the improved Bingham model to predict the suspension output damping force in combination with the finite element simulation results.

[0006] According to one aspect of the present invention, a modeling and parameter identification method based on an improved Bingham model is provided, comprising the following steps:

[0007] According to the multi-field coupling simulation of magnetorheological suspension and the dynamic characteristic test of suspension, the spring model is introduced into the Bingham model to obtain the improved Bingham model.

[0008] The least square method is used to identify the parameters of the improved Bingham model;

[0009] The output damping force of the magnetorheological suspension is predicted based on the Bingham model after parameter identification to verify the improved Bingham model.

[0010] As a further technical solution, the method also includes: before improving the classic Bingham model, performing electromagnetic simulation analysis on the designed suspension structure magnetic circuit, and importing the analysis results into the suspension fluid-solid coupling analysis to obtain magnetorheological suspension multi-field coupling simulation results.

[0011] As a further technical solution, the electromagnetic simulation analysis of the designed magnetic circuit also includes: the electromagnetic simulation is completed in Maxwell software, and the distribution diagram of magnetic lines and magnetic induction intensity is drawn according to the maximum design working current. According to the magnetorheological fluid data, the relationship between the shear yield stress, the viscosity of the magnetorheological fluid and the magnetic induction intensity is determined by polynomial fitting, and the formula is as follows:

[0012] τ=1.09-58.37B+878.68B 2 -987.21B 3

[0013] BZ

[0014] η=η0+0.02-1.14B+17.2B 2 -19.4B 3

[0015] In the formula, τ BZ is the shear yield stress of the magnetorheological fluid, B is the magnetic induction intensity, η is the viscosity of the magnetorheological fluid under different magnetic fields, and η0 is the zero-field viscosity of the magnetorheological fluid.

[0016] As a further technical solution, the magnetorheological suspension mechanical modeling based on the improved Bingham model also includes: simulating the dynamic stiffness of the multi-field coupling simulation model at different frequencies and currents to obtain a force-displacement curve, drawing hysteresis curves under different states by deriving the force-displacement curve, and calculating the dynamic stiffness under different frequencies and currents according to the hysteresis curves under different states.

[0017] As a further technical solution, the suspension dynamic characteristic test also includes: processing and assembling the magnetorheological suspension of the suspension structure and then conducting the test, and when the excitation frequency is fixed, passing a direct current and measuring the suspension dynamic stiffness test data.

[0018] As a further technical solution, the application of the least square method to identify the parameters of the improved Bingham model also includes:

[0019] When the suspension amplitude is X0 and performs simple harmonic motion with a frequency of f, its displacement and velocity are as follows:

[0020] x=X0sin(2πft)

[0021]

[0022] At this time, according to the above formula, the magnetorheological suspension will generate a support reaction force F MR :

[0023]

[0024] In the formula, is the simulation data, (F I ,c ω ,k ω ) are the parameters to be identified. Based on the simulation data, the parameter values ​​of the improved Bingham model can be obtained by solving and analyzing the least squares method.

[0025] Based on the multi-field coupling simulation model, the dynamic characteristics of the suspension are simulated and analyzed under different currents and frequencies, and the changing relationship between the force-displacement and force-velocity of the suspension is determined to provide effective simulation data for parameter identification. The parameter estimator in MATLAB is used to identify the parameters to be identified in the improved Bingham model.

[0026] As a further solution, the prediction of the output damping force of the magnetorheological suspension according to the Bingham model after parameter identification also includes: establishing a mechanical simulation model in Simulink according to the improved Bingham model formula after magnetorheological suspension identification, and performing simulation analysis on the mechanical simulation model under different frequencies and currents. Then, it is compared with the simulation value of the multi-field coupling model and the fitting value of the Bingham model to verify the effectiveness and accuracy of the model.

[0027] According to one aspect of the present specification, a modeling and parameter identification system based on an improved Bingham model is provided, comprising:

[0028] Model building module, based on magnetorheological suspension multi-field coupling simulation and suspension dynamic characteristics test, introduces spring model into Bingham model to obtain improved Bingham model;

[0029] Parameter identification module, which uses the least square method to identify the parameters of the improved Bingham model;

[0030] The result prediction module predicts the output damping force of the magnetorheological suspension according to the Bingham model after parameter identification to verify the improved Bingham model.

[0031] According to one aspect of the present specification, there is provided an electronic device, comprising: at least one processor, at least one memory and a communication interface; wherein the processor, memory and communication interface communicate with each other; the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the described method.

[0032] According to one aspect of the present specification, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions enable the computer to execute the method described above.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) The Bingham mechanical model can simply describe the mechanical properties of the magnetorheological damper, but it is difficult to accurately describe the magnetorheological suspension containing rubber main springs. By improving the Bingham mechanical model and comparing the model fitting effects before and after the improvement based on the multi-field coupling simulation of the suspension, it is found that the improved Bingham model can well describe the mechanical properties of the magnetorheological suspension.

[0035] (2) The parameters of the improved Bingham model were identified by the least squares method. It was found that the controllable damping force of the magnetorheological suspension increases with the increase of current, and the magnetorheological fluid gradually tends to saturation at 1A; the equivalent stiffness increases with the increase of frequency; and the equivalent viscosity damping decreases exponentially with the increase of the applied frequency. This feature is consistent with the performance characteristics shown in the suspension simulation and experiment, which proves the effectiveness of the identification method.

[0036] (3) Compared with other parameter models, the improved Bingham model has the advantages of simple structure, fewer variables, fast parameter identification, and high fitting accuracy. It provides a reference for the performance optimization design, control system construction, and control method research of magnetorheological suspension. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of a flow chart of a modeling and parameter identification method based on an improved Bingham model according to an embodiment of the present invention;

[0038] Figure 2 A schematic diagram of the structure of a modeling and parameter identification system based on an improved Bingham model according to an embodiment of the present invention;

[0039] Figure 3A schematic diagram of the structure of an electronic device based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0040] Figure 4 An original schematic diagram of a suspension structure based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0041] Figure 5 A magnetic field line distribution diagram based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0042] Figure 6 A magnetic induction intensity distribution diagram based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0043] Figure 7 A schematic diagram of Adina simulation cloud and post-module processing and exporting data based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0044] Figure 8 A schematic diagram of a 5 Hz hysteresis curve based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0045] Fig. 9 A schematic diagram of a dynamic stiffness curve under 1.5A current based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0046] Fig.10 A schematic diagram of a magnetorheological suspension sample based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0047] Fig.11 Schematic diagram of a magnetorheological suspension performance testing system based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0048] Fig.12 A schematic diagram of a dynamic stiffness curve of a suspension test based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0049] Fig.13 A schematic diagram of 1.5A lower dynamic stiffness comparison based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0050] Fig.14 A schematic diagram of a Bingham model based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0051] Fig.15This is a schematic diagram of the relationship between the restoring force, the displacement and the velocity when the frequency is 20 Hz, the amplitude is 0.5 mm and the current is 1.5 A based on the improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0052] Fig.16 This is a schematic diagram of the relationship between the restoring force, displacement and velocity when the frequency is 30 Hz, the amplitude is 0.5 mm and the current is 1 A based on the improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0053] Fig.17 This is a schematic diagram of the relationship between the restoring force, the displacement and the velocity when the frequency is 50 Hz, the amplitude is 0.5 mm and the current is 1.5 A based on the improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0054] Fig.18 A schematic diagram of the relationship between the suspension restoring force, position and speed under different currents based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0055] Fig.19 The relationship between the suspension restoring force, displacement and velocity at different frequencies based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0056] Fig. 20 A schematic diagram of a flat plate laminar flow based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0057] Fig.21 A schematic diagram of an improved Bingham model of a magnetorheological suspension based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0058] Fig. 22 A schematic diagram of a simulation fitting process of parameters to be identified in a parameterized model based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0059] Fig.23 It is a schematic diagram of the fitting results of the controllable damping force of the magnetorheological suspension based on the improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0060] Fig.24 It is a schematic diagram of the equivalent viscosity damping fitting result of the magnetorheological suspension based on the improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0061] Fig.25 A schematic diagram of the equivalent stiffness fitting result of a magnetorheological suspension based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0062] Fig.26 A schematic diagram of a simulation program of an improved Bingham model of a magnetorheological suspension based on improved Bingham model modeling and parameter identification according to an embodiment of the present invention;

[0063] Fig. 27 A schematic diagram of the relationship between the restoring force, displacement and velocity based on modeling and parameter identification of the improved Bingham model according to an embodiment of the present invention, with a frequency of 20 Hz, an amplitude of 0.5 mm and a current of 1.5 A;

[0064] Fig.28 This is a schematic diagram of the relationship between the restoring force, displacement and velocity based on the improved Bingham model modeling and parameter identification with a frequency of 30 Hz, an amplitude of 0.5 mm and a current of 1 A according to an embodiment of the present invention;

[0065] Fig.29 This is a schematic diagram of the relationship between the restoring force, displacement and velocity when the frequency is 50 Hz, the amplitude is 0.5 mm and the current is 1.5 A based on the improved Bingham model modeling and parameter identification according to an embodiment of the present invention. DETAILED DESCRIPTION

[0066] Magnetorheological suspension is a technology that uses the rheological properties of magnetorheological fluid and the superelasticity of rubber to achieve vibration isolation and support. It is often used in automotive powertrain systems. It has the advantages of simple structure, fast response speed, low power consumption, large output damping and continuous adjustment. When applied to automotive powertrain systems, it can achieve vibration isolation effects in a wide frequency range, effectively reduce the vibration and noise of the vehicle under different driving conditions, and improve the riding comfort of drivers and passengers.

[0067] The present invention improves the most applicable and classic Bingham model, identifies the main parameters in the improved Bingham model based on multi-field coupling simulation results, and evaluates the ability of the improved Bingham model to predict the output damping force of the suspension in combination with finite element simulation results.

[0068] The following will clearly and completely describe the technical solutions of various embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0069] This embodiment introduces a modeling and parameter identification method based on the improved Bingham model. The process is as follows: Figure 1 The method shown comprises:

[0070] According to the multi-field coupling simulation of magnetorheological suspension and the test of suspension dynamic characteristics, the spring model is introduced into the Bingham model to obtain the improved Bingham model.

[0071] The least square method is used to identify the parameters of the improved Bingham model;

[0072] The output damping force of the magnetorheological suspension is predicted based on the Bingham model after parameter identification to verify the improved Bingham model.

[0073] Step 1: Verify the magnetorheological mount test and model

[0074] The magnetorheological suspension dynamic characteristics test is aimed at verifying the correctness of the model and the accuracy of the simulation model. The schematic diagram of the designed suspension structure is shown in Figure 4 shown.

[0075] Figure 4 In (a), the parameter data of the magnetic circuit structure are shown in Table 1.

[0076] Table 1 Magnetic circuit structure parameters

[0077]

[0078] Perform electromagnetic simulation analysis on the designed magnetic circuit, and import the analysis results into the suspension fluid-solid coupling analysis, that is, complete the magnetorheological suspension multi-field coupling simulation analysis. First, the electromagnetic simulation is completed in Maxwell software. Taking the maximum design working current I = 1.5A as an example, Figure 5 and Figure 6 The distribution diagrams of magnetic lines of force and magnetic induction intensity are plotted respectively.

[0079] Depend on Figure 5 It can be seen that the magnetic field lines in the damping channel are distributed evenly, and their direction is perpendicular to the flow direction of the magnetorheological fluid. These characteristics are consistent with the magnetic field line distribution specifications of the magnetorheological suspension. Figure 3 It can be seen that the distribution of magnetic induction intensity in the damping channel is relatively uniform. A certain number of points are uniformly selected in the damping channel, the magnetic induction intensity of the points is summed and the average value B is calculated, and the average value can be used to represent the average magnetic induction intensity in the damping channel. When the maximum working current I = 1.5A, the average magnetic induction intensity B = 0.438T in the damping channel, indicating that the magnetorheological fluid has not reached the saturation magnetic induction intensity of 0.54T, which meets the design requirements. At the corner of the coil slot, the maximum magnetic induction intensity of the entire magnetic circuit is concentrated here, and the average magnetic induction intensity ranges from 1.3 to 1.7T, reaching the saturation state.

[0080] According to the magnetorheological fluid data provided by the enterprise, the relationship between shear yield stress, magnetorheological fluid viscosity and magnetic induction intensity can be determined by polynomial fitting. The formula is as follows:

[0081] τ BZ =1.09-58.37B+878.68B 2 -987.21B 3 (1)

[0082] η=η0+0.02-1.14B+17.2B 2 -19.4B 3 (2)

[0083] In the formula, τ BZ is the shear yield stress of the magnetorheological fluid, B is the magnetic induction intensity, η is the viscosity of the magnetorheological fluid under different magnetic fields, and η0 is the zero-field viscosity of the magnetorheological fluid.

[0084] The magnetic circuit structure in the range of [0-1.5] A was simulated many times. The relationship between the change of magnetorheological fluid parameters can be calculated using the above formula (1) and formula (2), as shown in Table 2.

[0085] Table 2 Variation of magnetorheological fluid parameters

[0086] I(A) 0 0.3 0.6 0.9 1.2 1.5 B(T) 0 0.239 0.312 0.358 0.401 0.436 τ(KPa) 1.09 23.98 38.7 47.93 55.73 61.6 η(pa·s) 0.8 1.265 1.549 1.726 1.874 1.985

[0087] Fluid-structure coupling simulation is performed in Adina software. Taking the simulation of dynamic stiffness of the suspension without current as an example, a preload of 4mm is applied to the suspension, and the dynamic load is an excitation with a frequency of 5Hz and an amplitude of 0.5mm. The force and displacement of the coupling point of the simulation model are extracted, and the dynamic stiffness of the suspension without current can be calculated. The simulation cloud map and data results are shown in the figure. Figure 7 The data was exported and processed, and the hysteresis curve of the suspension was drawn in the Origin software, as shown in Figure 8 shown.

[0088] According to the above method, the above electromagnetic coupling simulation results are brought into the fluid-solid coupling model to obtain a multi-field coupling simulation model of the suspension, and the dynamic stiffness simulation at different frequencies and different currents is performed. The force-displacement curve is derived, and the hysteresis curve under different states can be drawn, and then the dynamic stiffness at different frequencies and different currents can be calculated. The present invention mainly tests the dynamic stiffness of the magnetorheological suspension in the range of 0 to 50 Hz, so the simulation analysis of the dynamic stiffness is only to improve efficiency. Only the dynamic stiffness under full-field current (1.5A) is simulated, and the simulation frequency is 1-50Hz. The dynamic stiffness at each frequency is calculated according to the above method, and the dynamic stiffness of the magnetorheological suspension at a current of 1.5A can be drawn as a function of frequency, such as Fig. 9 shown.

[0089] The designed magnetorheological suspension was processed and assembled before testing. The test sample and the test system were as follows. Fig.10 , 11 In the dynamic stiffness test, a preload of 1000N is applied first, and then a sinusoidal displacement excitation is used as the input signal. The amplitude is set to 0.5mm, the excitation frequency is 1-50Hz, and a test point is taken every 1Hz. When the excitation frequency is fixed, a DC current of 0A, 0.5A, 1A, and 1.5A is passed, and the suspension dynamic stiffness test data is measured, as shown in the figure. Fig.12 shown.

[0090] It can be seen from the figure that the dynamic stiffness of the magnetorheological suspension shows an obvious nonlinear relationship in the measured frequency range. Fig.12 It can be seen that from 1 to 15 Hz, as the frequency increases, the suspension dynamic stiffness increases sharply; after 15 Hz, the dynamic stiffness increases steadily with the increase of frequency. In addition, at the same excitation frequency and amplitude, increasing the current will lead to an increase in the suspension dynamic stiffness.

[0091] The suspension was subjected to multi-field coupling simulation analysis, and the simulation results were compared with the test results. To improve work efficiency, only the results under full field current, i.e., 1.5A current, were compared. Fig.13 As shown in the figure, it can be observed that the overall trend of the simulation results and the test results are consistent, and the test results are slightly larger than the simulation results. At 10Hz, the test result is about 711N / mm, and the simulation result is about 667N / mm, with an error of about 6.6%, which is within a reasonable error range.

[0092] Step 2: Analyze the mechanical properties of the magnetorheological mount Bingham model

[0093] Based on the nonlinear characteristics of the ER damper, a mathematical model, the Bingham model, is used to describe its nonlinear behavior. The model has a simple structure and consists of a Coulomb friction element and a viscous damper in parallel, such as Fig.14 As shown. Through experimental data and theoretical analysis, the model can accurately predict the performance of electrorheological dampers in practical engineering applications, providing an important theoretical basis for the design and optimization of dampers. When describing magnetorheological fluid, the model divides it into two states: before yielding and after yielding, and assumes that before yielding, the liquid is a non-flowing non-Newtonian fluid, while after yielding, it exhibits the characteristics of a flowing Newtonian fluid.

[0094] The expression of its output damping force is:

[0095]

[0096] Where F is the output damping force; f y is the Coulomb damping force; is the movement speed of the damper; c0 is the viscous damping coefficient; f0 is the force generated by the compensator, which can be ignored.

[0097] The suspension multi-field coupling simulation results are compared with the Bingham model fitting values ​​to determine the accuracy of the Bingham model in predicting the mechanical properties of the suspension. This paper selects three sets of data with the same simulation conditions for comparative analysis, including simulation data with a frequency of 20 Hz, an amplitude of 0.5 mm, and a current of 1.5 A, simulation data with a frequency of 30 Hz, an amplitude of 0.5 mm, and a current of 1 A, and simulation data with a frequency of 50 Hz, an amplitude of 0.5 mm, and a current of 1.5 A. Comparing and analyzing the simulation values ​​of the multi-field coupling model and the fitting values ​​of the Bingham model, the restoring force-displacement and restoring force-velocity curves are shown in Figure 2. Figure 15-17 shown.

[0098] observe Figure 15-17 It can be seen that the damping force-displacement and damping force-velocity relationship curves of the fitting value of the Bingham model and the simulation value of the multi-field coupling model are quite different. The study found that although Bingham can simulate the mechanical properties of the magnetorheological damper well, it cannot fit the mechanical properties of the magnetorheological suspension containing rubber main springs well. However, the model has the advantages of simplicity, intuitiveness, clear physical meaning and wide application range, making it one of the commonly used rheological models in the engineering field. In view of the problem that the Bingham model is difficult to accurately describe the mechanical properties of the magnetorheological suspension, the present invention improves the traditional Bingham model to obtain a parameter model that can accurately describe the mechanical properties of the magnetorheological suspension.

[0099] Step 3: Analyze the dynamic characteristics of magnetorheological suspension

[0100] First, with fixed frequency and amplitude, the sinusoidal displacement signal with different excitation currents is used as the excitation source, and the current is selected as 0A, 0.5A, 1A, and 1.5A. In order to simulate the working state of the suspension on the whole vehicle, the preload is set to 4mm, the frequency is set to 20Hz, and the amplitude is 0.5mm. The sinusoidal excitation is used as the input excitation source, and the dynamic characteristics simulation analysis is carried out in the simulation software Adina. The restoring force-displacement and restoring force-velocity relationship curves are shown as follows Fig.18 shown.

[0101] By analyzing Fig.18 From the restoring force-displacement and restoring force-velocity relationship curves, it can be seen that the restoring force of the magnetorheological suspension increases with the increase of the loading current. When the current increases from 1A to 1.5A, the trend of the suspension restoring force slows down with the increase of current. This is because the magnetorheological suspension reaches the saturation point of magnetic induction intensity at 1.5A, at which time the suspension restoring force reaches its maximum value.

[0102] Similarly, without changing the current and amplitude, sinusoidal excitation at different frequencies is simulated. This paper mainly focuses on the dynamic characteristics of the magnetorheological suspension under low-frequency excitation. Here, the frequencies are selected as 1Hz, 10Hz, 30Hz, and 50Hz. When the preload is 4mm, the excitation current is 1.5A, and the amplitude is 0.5mm, the restoring force-displacement and restoring force-velocity relationship curves at different frequencies are obtained through simulation calculations. Fig.19 shown.

[0103] By analyzing Fig.19 (a) It can be seen that when the current and amplitude remain unchanged, the suspension restoring force increases accordingly with the increase of frequency. Fig.19 (b) It can be seen that as the frequency increases, the vibration speed of the suspension increases, which causes the exciting force on the suspension to increase. In order to offset the exciting force, the dynamic stiffness of the suspension system also increases.

[0104] Step 4: Establish the improved Bingham model and parameter identification of magnetorheological mount

[0105] During the operation of the magnetorheological suspension, the rubber main spring squeezes the magnetorheological fluid in the cavity, forcing the magnetorheological fluid to flow between the upper and lower chambers. The performance of the suspension is adjusted by changing the loading current to provide various output damping forces. To simplify the suspension model and facilitate calculation, it is assumed that the liquid in the damping channel is in a laminar state, that is, the magnetorheological fluid flows between flat plates. The flow conditions are as follows: Fig. 20 as shown.

[0106] In order to calculate the theoretical damping force of the suspension, the Navier-Stokes equation

[13] is used to analyze the force of the fluid. Due to the incompressibility of magnetorheological fluid, the Navier-Stokes equation can be simplified to:

[0107]

[0108] Where ΔP is the pressure drop in the controllable damping channel, η is the apparent viscosity of the liquid, u represents the velocity in the x direction, and z is the coordinate axis of the magnetic field direction.

[0109] When magnetorheological fluid is subjected to a magnetic field, its shear stress is expressed as:

[0110] τ=τ BZ sgn(dυ / dz)+η0(dυ / dz) (5)

[0111] In the formula, τ BZ is the shear yield stress of the liquid; dv / dz represents the shear rate of the liquid; η0 represents the zero-field viscosity of the magnetorheological fluid.

[0112] Under the action of magnetic field, the apparent viscosity of magnetorheological fluid can be expressed as:

[0113]

[0114] Combination Fig. 20 The flow of magnetorheological fluid in the flat plate, by substituting equations (5) and (6) into the simplified Navier-Stokes equation, can obtain the velocity distribution function relationship of the fluid in the damping channel under the action of the magnetic field:

[0115]

[0116] Wherein, l is the length of the damping channel l=π(2R1+2R2+2R3+R4), and h=H is the height of the damping channel cross section.

[0117] The liquid flow rate Q flowing through the damping channel m for:

[0118]

[0119] Wherein, R is the cross-sectional width of the damping channel, R=R4.

[0120] Combined with the suspension structure parameters, the pressure difference ΔP between the plates can be obtained from the above formula: m for:

[0121]

[0122] When the suspension excitation speed is equal to When the fluid flow rate is the equivalent area of ​​the main spring A p and suspension excitation speed The product of , and the damping force of the damping channel corresponding to the suspended effective magnetic pole is:

[0123]

[0124] In the formula, A P is the equivalent cross-sectional area of ​​the rubber main spring, estimated by structural parameters:

[0125]

[0126] In the formula, D1 and D2 represent the structural dimensions of the main spring and the liquid contact surface. Its structural parameters are D1 = 2r1 = 50mm, D2 = 2r2 = 78.6mm. The equivalent piston area of ​​the rubber main spring can be calculated as A p =3.299×10 3 mm 2 .

[0127] Considering the rubber main spring force, the total restoring force of the magnetorheological suspension can be expressed as:

[0128]

[0129] In the formula, Fη is the viscous damping force, F τ is the Coulomb damping force, F s is the main rubber spring force, k0 and c0 represent the rubber stiffness and damping respectively.

[0130] Through the above analysis, the suspension restoring force formula can be simplified as:

[0131]

[0132]

[0133]

[0134] In the formula, F I The controllable damping force of the suspension is equal to the Coulomb damping force of the suspension; c ω is the equivalent viscous damping of the suspension, which is mainly composed of the damping of the rubber main spring and the viscous damping of the internal magnetorheological fluid; k ω It is the equivalent stiffness of the suspension, which mainly comes from the stiffness generated by the rubber main spring.

[0135] From the above formula, we can find that the restoring force formula of magnetorheological suspension is just based on the mechanical formula derived from the Bingham model, with the elastic force of the rubber main spring added. That is to say, the stiffness k is added to the Bingham model. ω Spring model. When vibration impact occurs, the spring k ω First, the improved Bingham model can be obtained, such as Fig.21 shown.

[0136] The present invention is based on the nonlinear least squares principle and uses the fitting toolbox in MATLAB to perform parameter estimation and identification. The principle formula is as follows:

[0137]

[0138] Where Y d Calculate the value for the model; Y i is the simulation value. Based on the simulation data, the parameter values ​​of the improved Bingham model can be obtained by solving and analyzing the least square method.

[0139] When the suspension amplitude is X0 and performs simple harmonic motion with a frequency of f, its displacement and velocity are as follows:

[0140] x=X0sin(2πft)

[0141]

[0142] At this time, according to formula (13), the magnetorheological suspension will generate a support reaction force F MR :

[0143]

[0144] In the formula, is the simulation data, (F I ,c ω ,k ω ) are the parameters to be identified.

[0145] Therefore, based on the multi-field coupling simulation model, the dynamic characteristics of the suspension are simulated and analyzed under different currents and frequencies, and then the changing relationship between the force-displacement and force-velocity of the suspension is determined, providing effective simulation data for parameter identification.

[0146] According to the simulation results, the present invention selects an amplitude of 0.5 mm, a frequency of 20 Hz, and a current from 0 to 1.5 A, taking a set of data every 0.5 A, for a total of four sets of data. Similarly, the amplitude is fixed at 0.5 mm, the current is 1.5 A, and the simulation data of the frequencies are taken at 1 Hz, 10 Hz, 30 Hz, and 50 Hz. Based on these eight sets of data, according to the principle of least squares, the parameter estimator in MATLAB is used to identify the parameters to be identified in the improved Bingham model. The identification process is as follows: Fig. 22 shown.

[0147] According to the improved Bingham model proposed in the present invention, after parameter identification, the identification results are shown in Tables 3 and 4.

[0148] Table 3 Parameter identification results at the same frequency, amplitude and different currents

[0149] 0A 0.5A 1A 1.5A FI(N) 8.866 78.068 126.96 140.97 kω(N / mm) 353.7 353.33 353.54 353.43 cω(Ns / mm) 2.893 2.943 2.624 2.563

[0150] Table 4 Parameter identification results at the same current, amplitude and different frequencies

[0151] 1Hz 10Hz 30Hz 50Hz FI(N) 120.44 119.93 122.35 121.6 kω(N / mm) 236.36 320.23 385.82 436.49 cω(Ns / mm) 32.7 4.164 1.455 1.023

[0152] At the same time, through parameter identification, Figure 23-25 The curves respectively represent the relationship between the controllable damping force, equivalent viscosity damping and equivalent stiffness of the magnetorheological suspension and the loading current and the excitation frequency.

[0153] From Table 3 and Fig.23 It can be seen that under the same frequency and amplitude, as the current increases, the controllable damping force also increases accordingly. When the current is 1-1.5A, the controllable damping increases slowly, indicating that the magnetorheological fluid gradually tends to saturation; when the current is 0-1.5A, the controllable damping force varies in the range of 8.87-140.97N, indicating that the controllable range of the suspension damping force is large.

[0154] From Table 4 and Fig.24It can be seen that under the same current and amplitude, the equivalent viscosity damping decreases rapidly with the increase of frequency, which is consistent with the damping decrease trend in the previous suspension performance test, indicating that the fitting result is relatively reasonable.

[0155] Observe Table 4 and Fig.25 It can be seen that under the same current and amplitude, as the frequency increases, the equivalent stiffness also increases accordingly, and there is a strong correlation between the two.

[0156] The controllable damping force and equivalent stiffness are fitted with binomial according to current I and frequency ω. Since the equivalent viscosity damping decreases in a power function as the frequency increases, the relationship between the equivalent viscosity damping and the frequency is fitted with a power function, and the following relationship can be obtained:

[0157] F I =-34.269I 2 +128.48I+3.1469

[0158] k=-0.068ω 2 +7.323ω+237.74

[0159] ω

[0160] c ω =33.01ω -0.886 (17)

[0161] Substituting the relationship between the dynamic characteristic parameters of the magnetorheological suspension and the external load current and frequency in equation (17) into the improved Bingham model equation (16), the nonlinear parameter model of the output damping force of the magnetorheological suspension can be obtained:

[0162]

[0163] Step 5: Simulation and verification of the improved Bingham model

[0164] According to the improved Bingham model formula after magnetorheological suspension identification, a mechanical simulation model is established in Simulink, such as Fig.26 To verify the correctness of the improved Bingham model in predicting the dynamic characteristics of magnetorheological suspension, the mechanical simulation model was simulated and analyzed at different frequencies and currents. It was then compared with the simulation values ​​of the multi-field coupling model and the fitting values ​​of the Bingham model to verify the effectiveness and accuracy of the model.

[0165] Compare the simulation results to verify the accuracy and effectiveness of the prediction results of the improved Bingham model. Figure 15-17The same simulation conditions are compared. The simulation values ​​of the multi-field coupling model, the fitting values ​​of the Bingham model and the improved Bingham model are analyzed, and their restoring force-displacement and restoring force-velocity curves are shown in Figure 2. Figure 27-29 shown.

[0166] from Figure 27-29 It can be seen that the damping force-displacement and damping force-velocity relationship curves of the improved Bingham model fitting value are consistent with the suspension multi-field coupling model simulation value data curve, and the fitting accuracy is greatly improved compared with the Bingham model fitting value. This shows that the improved Bingham model of the present invention can accurately and effectively describe the dynamic characteristics of the magnetorheological suspension.

[0167] Based on the same inventive concept as the embodiment, this embodiment introduces a modeling and parameter identification system based on an improved Bingham model, such as Figure 2 As shown, the system comprises:

[0168] The model building module improves the classic Bingham model by adding a spring model to the Bingham model based on the magnetorheological suspension multi-field coupling simulation and suspension dynamic characteristics test;

[0169] Parameter identification module, which uses the least square method to identify the parameters of the improved Bingham model;

[0170] The result verification module verifies the prediction results of the improved Bingham model according to the improved Bingham model formula after magnetorheological suspension identification.

[0171] The method of the embodiment of the present invention is implemented by relying on electronic devices, so it is necessary to introduce the relevant electronic devices. Based on this purpose, the embodiment of the present invention provides an electronic device, such as Figure 3 As shown, the electronic device includes: at least one processor, a communication interface, at least one memory, and a communication bus, wherein at least one processor, the communication interface, and at least one memory communicate with each other through the communication bus. At least one processor calls the logic instructions in at least one memory to execute all or part of the steps of the method provided by the aforementioned various method embodiments.

[0172] In addition, when the logic instructions in the above-mentioned at least one memory are implemented in the form of a software functional unit and sold or used as an independent product, they are stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or partly in other words, the part that contributes to the prior art or part of the technical solution is embodied in the form of a software product, and the computer software product is stored in a storage medium, including several instructions for enabling a computer device (a personal computer, a server, or a network device) to perform all or part of the steps of the method described in each method embodiment of the present invention. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a disk or an optical disk, and various media for storing program codes.

[0173] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.

Claims

1. Based on the improved Bingham model modeling and parameter identification method, it is characterized by: The following steps are involved: According to the multi-field coupling simulation of magnetorheological suspension and the test of suspension dynamic characteristics, the spring model is introduced into the Bingham model to obtain the improved Bingham model. The least square method is used to identify the parameters of the improved Bingham model; The output damping force of the magnetorheological suspension is predicted based on the Bingham model after parameter identification to verify the improved Bingham model.

2. The modeling and parameter identification method based on the improved Bingham model according to claim 1 is characterized in that: The method also includes: before improving the classic Bingham model, performing electromagnetic simulation analysis on the designed suspension structure magnetic circuit, and importing the analysis results into the suspension fluid-solid coupling analysis to obtain the magnetorheological suspension multi-field coupling simulation results.

3. The modeling and parameter identification method based on the improved Bingham model according to claim 2 is characterized in that: The electromagnetic simulation analysis of the designed suspension structure magnetic circuit also includes: drawing a distribution diagram of magnetic lines of force and magnetic induction intensity according to the maximum designed working current, and determining the relationship between shear yield stress, magnetorheological fluid viscosity and magnetic induction intensity by polynomial fitting in combination with magnetorheological fluid data, the formula is as follows: t BZ =1.09-58.37B+878.68B 2 -987.21B 3 η=η0+0.02-1.14B+17.2B 2 -19.4B 3 In the formula, τ BZ is the shear yield stress of the magnetorheological fluid, B is the magnetic induction intensity, η is the viscosity of the magnetorheological fluid under different magnetic fields, and η0 is the zero-field viscosity of the magnetorheological fluid.

4. The modeling and parameter identification method based on the improved Bingham model according to claim 2 is characterized in that: The magnetorheological suspension mechanical modeling based on the improved Bingham model also includes: simulating the dynamic stiffness of the multi-field coupling simulation model at different frequencies and different currents to obtain a force-displacement curve, drawing a hysteresis curve under different states by deriving the force-displacement curve, and calculating the dynamic stiffness under different frequencies and different currents according to the hysteresis curves under different states.

5. The modeling and parameter identification method based on the improved Bingham model according to claim 2 is characterized in that: The suspension dynamic characteristic test also includes: testing the magnetorheological suspension after processing and assembling it according to the designed suspension structure, passing a direct current and measuring the suspension dynamic stiffness test data when the excitation frequency is fixed.

6. The modeling and parameter identification method based on the improved Bingham model according to claim 1, characterized in that: The method of using the least square method to identify the parameters of the improved Bingham model also includes: When the suspension amplitude is X0 and performs simple harmonic motion with a frequency of f, its displacement and velocity are as follows: x=X0sin(2πft) According to the above formula, the reaction force F of the magnetorheological suspension is MR : In the formula, is the simulation data, (F I ,c ω ,k ω ) is the parameter to be identified; Based on the simulation data, the parameter values ​​of the improved Bingham model are obtained by solving and analyzing the problem through the least squares method.

7. The modeling and parameter identification method based on the improved Bingham model according to claim 1 is characterized in that: The prediction of the output damping force of the magnetorheological suspension according to the Bingham model after parameter identification also includes: establishing a mechanical simulation model in Simulink according to the improved Bingham model formula after the magnetorheological suspension is identified, performing simulation analysis on the mechanical simulation model under different frequencies and currents, and then comparing it with the simulation value of the multi-field coupling model and the fitting value of the Bingham model to obtain a verification result.

8. Modeling and parameter identification system based on improved Bingham model, including: Model building module, based on magnetorheological suspension multi-field coupling simulation and suspension dynamic characteristics test, introduces spring model into Bingham model to obtain improved Bingham model; Parameter identification module, which uses the least square method to identify the parameters of the improved Bingham model; The result verification module predicts the output damping force of the magnetorheological suspension according to the Bingham model after parameter identification to verify the improved Bingham model.

9. An electronic device, characterized in that: include: At least one processor, at least one memory and a communication interface; wherein the processor, memory and communication interface communicate with each other; the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the method described in any one of claims 1 to 7.

10. A non-transitory computer readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores computer instructions, which cause the computer to execute the method of any one of claims 1 to 7.

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