A method for calculating the dynamic stiffness of rubber suspension under different preloads

Abstract

The present invention discloses a method for calculating the dynamic stiffness of a rubber suspension under different preloads, comprising: establishing a three-dimensional mathematical model of the rubber suspension, and obtaining a mesh model of the rubber suspension based on the three-dimensional mathematical model of the rubber suspension; importing the mesh model of the rubber suspension into finite element software, completing the finite element preprocessing steps of static analysis and submitting the calculation to obtain the result of the static analysis; grouping the mesh units in the mesh model of the rubber suspension according to the result of the static analysis; assigning different material parameters to mesh units of different groups in the grouped mesh model; completing the finite element preprocessing steps of the dynamic characteristic analysis of the rubber suspension based on the grouped mesh model and submitting the calculation to obtain the analysis result of the dynamic characteristic; extracting the dynamic stiffness of the rubber suspension according to the analysis result of the dynamic characteristic. The present invention effectively reduces the calculation error, improves the calculation accuracy of the dynamic stiffness, and meets the accuracy requirements of the vibration isolation performance of the suspension system under different working conditions.

Description

Technical Field

[0001] The invention relates to the technical field of vibration reduction elements, and in particular to a method for calculating the dynamic stiffness of a rubber suspension under different preloads. Background Art

[0002] As a connector and vibration isolator between the powertrain and the frame of a vehicle, the rubber mount can effectively suppress the vibration and noise caused by the unbalanced excitation of the powertrain, and is widely used in the suspension system of passenger cars. Since electric vehicles have problems such as high-frequency howling during driving, and the noise is partially transmitted to the vehicle through the result path by the motor, a good rubber mount should effectively isolate the noise. At the same time, the power unit motor of the motor vehicle has the characteristics of large torque. When the electric vehicle accelerates at full throttle, the mount is in a fully compressed state, and the mount is under a huge load at this time. In order to improve the vibration isolation rate of the suspension system and effectively improve the driving comfort of the vehicle, the dynamic characteristics of the rubber mount under different preloads and the matching of the suspension system become the key to its design. Therefore, accurately calculating its dynamic characteristics in the early stage of the design of the rubber mount and purposefully designing its dynamic performance under different working conditions are related to the quality of the rubber mount design and will ultimately affect the driving comfort of the vehicle.

[0003] At present, the methods for calculating the dynamic characteristics of rubber suspension under different preloads include: finite element method, which specifically involves establishing a complex finite element model, inputting only a set of viscoelastic constitutive parameters of the rubber material, applying displacement or force excitation at different frequencies, calculating the response of the rubber suspension simulation system, and finally obtaining the dynamic stiffness of the rubber suspension simulation system through data processing. However, the above-mentioned finite element method can only predict the dynamic characteristics of the rubber suspension when there is no preload or the preload is small, and cannot calculate the dynamic characteristics of the rubber suspension under large preload. Shangguan Wenbin and Peng Jie provided a method for predicting the dynamic stiffness of a rubber suspension in the patent application document "A method for predicting the dynamic stiffness of a rubber suspension". This method can only relatively accurately calculate the dynamic stiffness of the rubber suspension under partial preload, and its calculation error is significantly greater than 15% under partial load. Summary of the invention

[0004] The invention provides a method for calculating the dynamic stiffness of a rubber suspension under different preloads, which can effectively solve the problem of large error in dynamic stiffness calculation in the prior art.

[0005] In order to achieve the object of the present invention, the present invention provides a method for calculating the dynamic stiffness of a rubber suspension under different preloads, comprising the following steps:

[0006] S1: establishing a three-dimensional mathematical model of the rubber suspension, and obtaining a mesh model of the rubber suspension based on the three-dimensional mathematical model of the rubber suspension;

[0007] S2: Import the mesh model of the rubber mount into the finite element software, complete the finite element pre-processing steps of the rubber mount static analysis and submit the calculation to obtain the results of the static analysis;

[0008] S3: Group the mesh elements in the mesh model of the rubber suspension according to the results of the static analysis;

[0009] S4: In the grouped grid model, different material parameters are assigned to grid cells in different groups;

[0010] S5: Based on the grouped mesh model, the finite element pre-processing steps of the rubber suspension dynamic characteristics analysis are completed and submitted for calculation to obtain the analysis results of the dynamic characteristics;

[0011] S6: Based on the analysis results of the dynamic characteristics, the dynamic stiffness of the rubber suspension is extracted.

[0012] As an improvement of the above invention solution, the specific steps of S1 obtaining the grid model of the rubber suspension include:

[0013] Use 3D modeling software to establish a 3D mathematical model of the rubber suspension;

[0014] The finite element pre-processing software is used to mesh the three-dimensional mathematical model of the rubber suspension to obtain the mesh model of the rubber suspension.

[0015] As an improvement of the above invention solution, the finite element pre-processing steps of the rubber suspension static analysis in S2 specifically include:

[0016] Import the mesh model of the rubber suspension into the finite element software;

[0017] In the finite element software, the material properties of the unit are assigned, which are the density and hyperelastic parameters of the material. The hyperelastic parameters use the Mooney-Rivlin constitutive model.

[0018] Set the analysis step of the model and select static analysis as the analysis step; set the contact conditions of the model;

[0019] Simulate the interference fit between the rubber mount and the metal outer tube and the process of applying preload to the rubber mount

[0020] Set the preload force and set the constraints of the model;

[0021] Set the cell's grid type;

[0022] Submit the finite element analysis to the server for calculation to obtain the results of the static analysis.

[0023] As an improvement of the above invention solution, the step of grouping units in step (3) specifically includes:

[0024] According to the results of the static analysis of the rubber suspension, the three principal stresses σ1, σ2, σ3 of all unit nodes in the static analysis results are extracted;

[0025] According to the formula of octahedral shear stress and the principal stresses extracted above, calculate the octahedral shear stresses of all unit nodes;

[0026] According to the formula Calculate the octahedral shear strain γ of all unit nodes, where G ∞ is the quasi-static shear modulus;

[0027] Since each unit contains eight unit nodes, based on the shear strain of the unit nodes calculated in the previous steps, the maximum value of the octahedral shear strain of the eight unit nodes is taken as the shear stress value of the unit;

[0028] According to the shear strain value of the unit, all the units of the rubber suspension are divided into arrays. The unit grouping range is determined according to the dynamic characteristics test results of the rubber specimen under different strains.

[0029] In finite element software, elements in the same group are divided into a set according to the grouping of elements.

[0030] As an improvement to the above-mentioned invention solution, the strain value range of the grid division is determined according to the dynamic characteristic test results of the rubber test piece.

[0031] As an improvement of the above invention solution, the step of assigning material parameters in step S4 specifically includes:

[0032] In the grouped mesh model, different material parameters are assigned to the units in different groups. The material parameters include the density, hyperelastic parameters and viscoelastic parameters of the material. The hyperelastic parameters use the Mooney-Rivlin constitutive model, and the viscoelastic parameters use the parameters in the frequency domain. In the finite element software, the viscoelastic parameters are expressed by their real part ωRe(g * ) and the imaginary part ωIm(g * ) indicates that the real part of the viscoelastic parameter ωRe(g * ) and the imaginary part ωIm(g * ) can be expressed as shear storage modulus G s (ω), shear loss modulus G l (ω) and the quasi-static shear modulus G ∞ It means that the calculation formula is:

[0033] ωRe(g * )=G l (ω) / G ∞ ,ωIm(g * )=1-Gs (ω) / G ∞ ;

[0034] According to the formula The shear modulus of the rubber material is calculated based on the dynamic characteristics test of the rubber specimen, where: K d is the experimentally measured dynamic stiffness, is the damping angle measured in the test, 2A is the cross-sectional area of ​​the test piece, and X in is the excitation amplitude, t s is the thickness of the test piece;

[0035] By conducting dynamic characteristic tests on rubber specimens under different tangential pre-strains, the viscoelastic parameters under different strains are identified, and the corresponding viscoelastic parameters are assigned to the corresponding unit groups according to the strain values.

[0036] As an improvement of the above invention solution, the finite element pre-processing steps of the rubber suspension dynamic characteristics analysis in S5 specifically include:

[0037] According to the above steps, a finite element model of rubber suspension unit grouping including material parameters is obtained;

[0038] Set the analysis steps of the model, namely static analysis and harmonic response analysis; set the contact conditions of the model; set the preload force loading; set the constraint conditions of the model; set the grid type of the unit; after the settings are completed, submit the calculation to obtain the analysis results of the dynamic characteristics.

[0039] Compared with the prior art, the method for calculating the dynamic stiffness of the rubber suspension under different preloads provided by the present invention has at least the following beneficial effects:

[0040] 1) Through the finite element method, the dynamic stiffness of the rubber mount can be obtained, and the calculation error of the dynamic stiffness can be reduced, so that the calculation error is stabilized below 15%, which provides a reference for the design of the rubber mount and the design of the vehicle vibration isolation performance, reduces the cost of designing the rubber mount, and effectively reduces the number of tests.

[0041] 2) The dynamic stiffness of the rubber specimen increases first and then decreases with the prestrain, and the variation range is large. The strain of the rubber unit of the rubber suspension under preload is very different. If only one set of viscoelastic parameters is input, the dynamic characteristics of the rubber suspension cannot be fully characterized. The present invention adds the grouping of rubber suspension units on the basis of the original calculation of the dynamic stiffness of the rubber suspension. The results show that the present invention effectively improves the accuracy of the calculation of the dynamic stiffness of the rubber suspension under different preloads by grouping the rubber suspension units and assigning different viscoelastic parameters to different unit groups, so as to meet the accuracy requirements of calculating the vibration isolation performance of the suspension system under different working conditions.

[0042] 3) The cutoff frequency for calculating the dynamic stiffness of the present invention is 1000 Hz, which can meet the calculation requirements of the dynamic characteristics of the electric vehicle suspension. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flow chart of a method for calculating high frequency dynamic stiffness of a rubber suspension under different preloads provided by an embodiment of the present invention;

[0044] Figure 2 It is a schematic diagram of the three-dimensional mathematical model of the rubber suspension;

[0045] Figure 3 is a schematic diagram of the grid model of the rubber suspension;

[0046] Figure 4 It is a schematic diagram of the grouping of rubber suspension units;

[0047] Figure 5 It is a schematic diagram of the dynamic characteristics test results of the rubber specimen under different tangential pre-strains;

[0048] Figure 6 It is a schematic diagram of the identification results of the viscoelastic parameters of rubber materials;

[0049] Figure 7 It is a schematic diagram of the calculation results and test results of the dynamic stiffness of the rubber suspension under different preloads. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0051] See also Figure 1 The present invention provides a method for calculating the dynamic stiffness of a rubber suspension under different preloads, which specifically includes the following steps:

[0052] Step 1: Establish a three-dimensional mathematical model of the rubber suspension, and mesh the three-dimensional mathematical model of the rubber suspension based on finite element pre-processing software to obtain a mesh model of the rubber suspension.

[0053] In some embodiments of the present invention, this step specifically includes:

[0054] Step 1.1: Use 3D modeling software to establish a 3D mathematical model of the rubber suspension. In this embodiment, the 3D modeling software used is UG. The established 3D mathematical model of the rubber suspension is as follows: Figure 2As shown in the figure, 1 is a rubber suspension, 2 is a metal inner tube, and 3 is a metal outer tube.

[0055] Step 1.2: Use finite element pre-processing software to mesh the three-dimensional mathematical model of the rubber suspension to obtain a mesh model of the rubber suspension. The software used in this embodiment is Hypermesh. The mesh model obtained after meshing is as follows: Figure 3 As shown in the figure, hexahedral mesh is used to divide the rubber suspension into meshes to ensure the accuracy of finite element calculation.

[0056] Step 2: Import the mesh model of the rubber suspension into the finite element software, complete the finite element pre-processing steps of the rubber suspension static analysis and submit the calculation to obtain the results of the static analysis.

[0057] In some embodiments of the present invention, the finite element pre-processing steps of the rubber suspension static analysis are completed and submitted for calculation to obtain the results of the static analysis, which specifically include:

[0058] Step 2.1: Assign material properties to the unit section. In the material properties, the density of the material is measured by a densitometer; the hyperelastic constitutive model of the material is selected as the Mooney-Rivlin constitutive model, where the constitutive parameter C 10 ,C 01 The value of is obtained through uniaxial tensile test, plane tensile test and equibiaxial tensile test of rubber specimens.

[0059] Step 2.2: Analysis step of static analysis Select the static analysis step and set contact constraints at possible contact locations.

[0060] Step 2.3: Simulate the interference fit between the rubber mount and the metal outer tube and the process of applying preload to the rubber mount. A certain Z-direction preload is applied to the elastic center point of the rubber mount, and the elastic center point is coupled with the inner wall of the rubber.

[0061] Step 2.4: Apply a preload analysis step to constrain the six degrees of freedom of the metal outer tube.

[0062] Step 2.5: Set the mesh type of the rubber suspension, and the mesh type in this embodiment is C3D8H. After the setting is completed, submit the finite element analysis to the server for calculation to obtain the result of the static analysis.

[0063] In some embodiments of the present invention, the mesh model of the rubber suspension is imported into finite element pre-processing software ABAQUS.

[0064] Step 3: According to the results of static analysis, the mesh units of the mesh model of the rubber suspension are divided into arrays. The unit grouping range is determined by the dynamic characteristics test results of the rubber specimen under different pre-strains. A single group of viscoelastic parameters cannot fully characterize the dynamic characteristics of the rubber suspension. By grouping, the dynamic characteristics of the rubber suspension can be fully characterized in the future to improve the calculation accuracy.

[0065] In some embodiments of the present invention, the specific steps of grouping include:

[0066] Step 3.1: According to the results of the static analysis of the rubber suspension, extract the three principal stresses σ1, σ2, σ3 of all unit nodes in the static analysis results;

[0067] Step 3.2: According to the formula of octahedral shear stress And the principal stresses σ1, σ2, σ3 extracted above, calculate the octahedral shear stress of all unit nodes;

[0068] Step 3.3: According to the formula Calculate the octahedral shear strain γ, G, of all element nodes ∞ is the quasi-static shear modulus;

[0069] Step 3.4: Since each unit contains eight unit nodes, based on the shear strain of the unit nodes calculated in the previous steps, the maximum value of the octahedral shear strain of the eight unit nodes is taken as the shear strain value of the unit;

[0070] Step 3.5: According to the shear strain value of the grid unit, all the grid units of the rubber suspension are divided into arrays. The grouping of this embodiment is as follows: Figure 4 As shown, in this embodiment, the numerical ranges of different groups are determined according to the dynamic characteristic test results of the rubber test piece. Finally, in the finite element software, according to the grouping of the units, the grid units of the same group are divided into a set.

[0071] Step 4: In the grouped mesh model, assign different material parameters to mesh units in different groups.

[0072] In some embodiments of the present invention, the material parameters include density, hyperelastic parameters and viscoelastic parameters of the material. The hyperelastic parameters use the Mooney-Rivlin constitutive model, and its parameters are the same as those in static analysis. The viscoelastic parameters use parameters in the frequency domain.

[0073] In some embodiments of the present invention, the viscoelastic parameters are determined as follows:

[0074] (1) The real part of the viscoelastic parameter ωRe(g * ) and the imaginary part ωIm(g *) can be expressed as shear storage modulus G s (ω), shear loss modulus G l (ω) and the quasi-static shear modulus G ∞ It means that the calculation formula is:

[0075] ωRe(g * )=G l (ω) / G ∞ ,ωIm(g * )=1-G s (ω) / G ∞ ;

[0076] (2) The viscoelastic parameters of rubber materials are identified through dynamic characteristics experiments of rubber shear specimens. The formula is: The quasi-static shear modulus of the rubber material is calculated based on the dynamic characteristics test of the rubber specimen, where: K d is the dynamic stiffness measured in the test, is the damping angle measured in the experiment, 2A is the cross-sectional area of ​​the test piece, t s is the thickness of the test piece, X in is the excitation amplitude of the test bench, and ω is the circular frequency.

[0077] In some embodiments of the present invention, the viscoelastic parameters of the dynamic characteristics test of the rubber test piece under different tangential pre-strains are tested, the viscoelastic parameters under different strains are identified, and the corresponding viscoelastic parameters are assigned to the corresponding unit groups according to the strain values. In this embodiment, the tangential pre-strains of the rubber test piece in the test are no pre-strain, 16.5%, 32.2%, 46.4%, 58.8%, and 69.5%, respectively.

[0078] In some embodiments of the present invention, the dynamic characteristics test results of the rubber test pieces under different tangential pre-strains are as follows: Figure 5 As shown in the figure, it can be seen that the dynamic stiffness of the rubber specimen under different pre-strains is quite different. The identification results of the viscoelastic parameters of the rubber material are shown in Figure 6 shown.

[0079] Step 5: Based on the grouped mesh model, complete the finite element pre-processing steps for the dynamic characteristics analysis of the rubber suspension and submit the calculation to obtain the analysis results of the dynamic characteristics.

[0080] In some embodiments of the present invention, the analysis step of the finite element pre-processing of the dynamic characteristics analysis includes static analysis and harmonic response analysis, and the frequency range of the harmonic response analysis step is set to 50 to 1000 Hz, and the frequency increases in a linear form.

[0081] Specifically, step 5 includes the following sub-steps:

[0082] Step 5.1: Set the contact conditions and preload. In the static analysis step, apply the corresponding preload in the Z direction to the elastic center of the rubber suspension, and the elastic center is coupled with the inner wall of the rubber. In the harmonic response analysis step, apply displacement load or acceleration load to the elastic center of the rubber suspension.

[0083] Step 5.2: Set constraints. In both the static analysis step and the harmonic response analysis step, the six degrees of freedom of the metal outer tube are constrained.

[0084] Step 5.3: Set the mesh type of the rubber mount to C3D8H.

[0085] Step 5.4: After the settings are completed, submit the finite element analysis to the server for calculation to obtain the analysis results of the dynamic characteristics.

[0086] Step 6: Based on the analysis results of the dynamic characteristics, extract the dynamic stiffness of the rubber suspension.

[0087] In some embodiments of the present invention, the dynamic characteristics calculation results and test results when the preload of the rubber suspension is in the Z direction are as follows: Figure 7 As shown in the figure, the calculation results of the dynamic stiffness of the rubber mount are basically consistent with the test results. Within the frequency range, the calculation error of the dynamic stiffness of the rubber mount under different preloads is less than 15%, which effectively reduces the calculation error of the dynamic stiffness of the rubber mount under different preloads.

[0088] The finite element software may be Hypermesh and ABAQUS, or other finite element software, such as ANSYS, ANSA, Nastran, etc. The pre-strain is not limited to the examples in the embodiments of the present invention, but may also be other pre-strain ranges. The research object is not limited to rubber suspension, but may also be rubber isolators, rubber sealing rings, etc.

[0089] It should be noted that what is described above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications are considered to be within the scope of protection of the present invention.

Claims

1. A method for calculating the dynamic stiffness of a rubber suspension under different preloads, characterized in that: The following steps are involved: S1: establishing a three-dimensional mathematical model of the rubber suspension, and obtaining a mesh model of the rubber suspension based on the three-dimensional mathematical model of the rubber suspension; S2: Import the mesh model of the rubber mount into the finite element software, complete the finite element pre-processing steps of the rubber mount static analysis and submit the calculation to obtain the results of the static analysis; S3: Group the mesh elements in the mesh model of the rubber suspension according to the results of the static analysis; S4: In the grouped grid model, different material parameters are assigned to grid cells in different groups; S5: Based on the grouped mesh model, the finite element pre-processing steps of the rubber suspension dynamic characteristics analysis are completed and submitted for calculation to obtain the analysis results of the dynamic characteristics; S6: Extract the dynamic stiffness of the rubber suspension based on the analysis results of the dynamic characteristics; The finite element pre-processing steps of the rubber suspension static analysis are completed in S2 and the calculation is submitted to obtain the results of the static analysis, which specifically include: Assign material properties to the element cross-section; Select static analysis step and set corresponding contact conditions; Simulate the interference fit between the rubber mount and the metal outer tube and the process of applying preload to the rubber mount; Apply a preload analysis step to constrain the six degrees of freedom of the metal outer tube; Set the mesh type for the rubber suspension; Submit the finite element analysis to the server for calculation to obtain the results of the static analysis; Wherein, the S3 specifically includes: According to the results of the static analysis of the rubber suspension, the three principal stresses of all unit nodes in the static analysis results are extracted. ; According to the formula of octahedral shear stress And the three principal stresses , calculate the octahedral shear stress of all unit nodes; According to the formula Calculate the octahedral shear strains at all element nodes , where is the quasi-static shear modulus; Calculate the shear stress of the unit node. Since each mesh unit contains eight unit nodes, take the maximum value of the octahedral shear strain of the eight unit nodes as the shear strain value of the mesh unit. All mesh cells of the rubber suspension are divided into arrays according to the shear strain values ​​of the mesh cells; In finite element software, mesh cells in the same group are divided into a set according to the grouping of mesh cells.

2. The method for calculating the dynamic stiffness of the rubber mount under different preloads according to claim 1, characterized in that: S1 The specific steps of obtaining the grid model of the rubber suspension include: Use 3D modeling software to establish a 3D mathematical model of the rubber suspension; The finite element pre-processing software is used to mesh the three-dimensional mathematical model of the rubber suspension to obtain the mesh model of the rubber suspension.

3. The method for calculating the dynamic stiffness of the rubber mount under different preloads according to claim 1, characterized in that: The rubber suspension is replaced by a rubber isolator or a rubber sealing ring.

4. The method for calculating the dynamic stiffness of the rubber mount under different preloads according to claim 1, characterized in that: The strain value range of the mesh division is determined according to the dynamic characteristics test results of the rubber specimen.

5. The method for calculating the dynamic stiffness of the rubber mount under different preloads according to claim 1, characterized in that: The material parameters described in S4 include the density, hyperelastic parameters and viscoelastic parameters of the material. The hyperelastic parameters use the Mooney-Rivlin constitutive model, and the viscoelastic parameters use parameters in the frequency domain.

6. The method for calculating the dynamic stiffness of the rubber mount under different preloads according to claim 5, characterized in that: Real part of viscoelastic parameter With the imaginary part Shear storage modulus , shear loss modulus and the quasi-static shear modulus It means that the calculation formula is: ； By conducting dynamic characteristic tests on rubber specimens under different tangential pre-strains, the viscoelastic parameters under different strains are identified, and the corresponding viscoelastic parameters are assigned to the corresponding unit groups according to the strain values.

7. The method for calculating the dynamic stiffness of the rubber mount under different preloads according to claim 6, characterized in that: The viscoelastic parameters are given by the formula And the dynamic characteristics test data of the rubber specimen are identified, where is the experimentally measured dynamic stiffness, s is the experimentally measured damping angle, is the cross-sectional area of ​​the specimen, is the excitation amplitude, is the thickness of the rubber specimen.

8. The method for calculating the dynamic stiffness of a rubber mount under different preloads according to any one of claims 1 to 7, characterized in that: The finite element pre-processing steps of the dynamic characteristics analysis described in S5 include static analysis and harmonic response analysis, specifically: Set contact conditions and preload force loading. In the static analysis step, apply corresponding preloads to the elastic center of the rubber suspension. The elastic center is coupled with the inner wall of the rubber. In the harmonic response analysis step, apply displacement load or acceleration load to the elastic center of the rubber suspension. Set constraint conditions. Set the mesh type for the rubber suspension; After the setting is completed, the finite element pre-processing of the dynamic characteristic analysis is submitted to the server for calculation to obtain the analysis results of the dynamic characteristics.

Images