CN114880904A - Large-scale finite element analysis method for rubber bushing - Google Patents
Large-scale finite element analysis method for rubber bushing Download PDFInfo
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Abstract
The invention belongs to the technical field of rubber bushing manufacturing, and discloses a large-scale finite element analysis method for a rubber bushing. The large-scale finite element analysis method of the rubber bushing uses the simplified rubber bushing model and divides the meshes, obtains model parameters required by simulation calculation by using the design values of the rubber bushing, reduces the number of the meshes required by the simulation calculation, reduces the time required by the simulation calculation and improves the efficiency of the simulation calculation on the premise of not reducing the simulation accuracy.
Description
Technical Field
The invention relates to the technical field of rubber bushing manufacturing, in particular to a large-scale finite element analysis method for a rubber bushing.
Background
The rubber bushing is commonly used for connecting various parts of chassis suspension of the commercial vehicle, and the acting force among the parts is transmitted while the damping effect is achieved, so that the static stiffness (radial stiffness and torsional stiffness) of the rubber bushing directly influences the stress condition among the assembly parts. For large-scale finite element nonlinear calculation (such as a composite air suspension system), finite element modeling and analysis of a rubber bushing directly according to an actual model are impractical, because a metal plate is generally added in rubber for obtaining sufficient radial rigidity of an actual rubber bushing product, the geometric characteristics of a rubber layer and a metal layer are generally small, the structure is complex, if the actual rubber bushing model is directly modeled, the meshing of finite elements is very small, and when the finite element nonlinear calculation method is used for large-scale finite element nonlinear analysis, the calculation consumes a lot of time, and the calculation is easy to calculate and is not convergent.
The analysis method in the prior art adopts different optimization algorithms to identify the constitutive parameters of the rubber, is suitable for the design and analysis of the structure of the rubber bushing, and is not suitable for the field of large-scale finite element nonlinear analysis.
Disclosure of Invention
The invention aims to provide a large-scale finite element analysis method for a rubber bushing, which can improve the efficiency of the large-scale finite element analysis of the rubber bushing and reduce the time required by the finite element analysis on the premise of not reducing the analysis precision.
In order to achieve the purpose, the invention adopts the following technical scheme:
the large-scale finite element analysis method of the rubber bushing comprises the following steps:
s1, determining an objective function of model parameter identification: the objective function being radial stiffness S of the rubber bushing vertical And torsional rigidity S rotational The ratio of (a) to (b) is μ;
s2, determining model identification parameters: the model identification parameters comprise constitutive parameters C of the rubber material 10 And a reinforcement plate thickness h of the rubber bushing;
s3, establishing a rubber bushing simplified model and dividing grids: the rubber bushing simplified model comprises an inner steel ring, a rubber part, a reinforcing plate and an outer steel ring, wherein the inner steel ring is inserted into the rubber part, the outer steel ring is sleeved outside the rubber part, and the reinforcing plate is positioned in the geometric middle of the rubber part and divides the rubber part into two layers;
s4, determining a parameter identification method of the simplified rubber bushing model;
s5, establishing a factor level coding table for identifying model parameters, wherein the factor is the model parameter C to be identified 10 And h, level is C 10 And the value range of h;
s6, outputting a simulation result: inputting design values to obtain model parameters C required for simulation calculation according to the simplified model of the rubber bushing in step S3, the parameter identification method in step S4 and the factor level coding in step S5 10 And h, subsequently simplifying the rubber bushing into a model, model parameters C 10 And h, inputting the simulation software and outputting a simulation result.
Optionally, after step S6, the method further includes the verification step: and S7, comparing the simulation result obtained in the step S6 with a design value, and when the error is not more than a preset value, indicating that the simulation result is accurate.
Optionally, the preset value is 5%.
Optionally, in step S2, a Mooney-Rivlin rubber constitutive material model is adopted, which includes parameter C 10 And parameter C 01 In which C is 10 /C 01 If 4, the model identification parameter includes C 10 And a reinforcement plate thickness h of the rubber bushing.
Optionally, in step S3, the reinforcing plate in step S3 is divided into meshes by using hexahedral cells with a size of 4mm and 8 nodes, and the number of cell layers is 1; the rubber part is divided into grids by adopting hexahedral units with the size of 4mm and 8 nodes, and a HERRMANN unit is adopted, after the rubber part is divided into two layers by a reinforcing plate, the number of unit layers of each layer of rubber part is 2; the outer side steel ring and the inner side steel ring are all divided into grids by adopting hexahedron units with the size of 4mm and 8 nodes, and the number of the unit layers is 1.
Optionally, in step S4, a multiple nonlinear regression model is used as the parameter identification method for the simplified rubber bushing model, where the expression is:
in the formula, a, b j 、b kj And b jj Is the regression parameter to be solved, x, of the regression model k And x j As a factor variable, C is referred to herein 10 And h; constitutive parameter C of rubber material 10 And the thickness h of the reinforcing plate has a nonlinear relation with the radial stiffness and the torsional stiffness of the rubber bushing respectively to obtain the radial stiffness and the C 10 And h nonlinear regression model, torsional stiffness and C 10 And h, a non-linear regression model.
Alternatively, in step S5, in the factor level coding table, x -1r ≤C 10 ≤x 1r ，x -2r ≤h≤x 2r ，x -1r And x 1r Are respectively C 10 Lower and upper limits of the values, x -2r And x 2r The lower limit and the upper limit of the value h are respectively; the lower limit corresponds to the lower asterisk arm-gamma, and the upper limit corresponds to the upper asterisk arm gamma;
C 10 and zero level values of h are each x 10 And x 20 From
Calculated, where j is 1, 2;
C 10 and h are each a 1 And Δ 2 From
Calculated, j is 1, 2 in the formula.
Optionally, in step S6, the simulation schemes include a rubber bushing radial stiffness simulation scheme and a rubber bushing torsional stiffness simulation scheme.
Optionally, the simulation scheme is provided in plurality.
Optionally, at least two simulation schemes are identical, and the two identical simulation schemes are used for verifying the consistency of the simulation software.
Has the advantages that:
the large-scale finite element analysis method of the rubber bushing firstly determines an objective function identified by model parameters and then determines constitutive parameters C including rubber materials 10 And model identification parameters of the thickness h of the reinforcing plate of the rubber bushing, establishing a rubber bushing simplified model, dividing the grid into grids and a parameter identification method of the rubber bushing simplified model, and establishing a simulation scheme by the parameter identification method of the rubber bushing simplified model and a factor level coding table to obtain model parameters C required by simulation calculation 10 And h, finally obtaining an output simulation result. The large-scale finite element analysis method of the rubber bushing uses the simplified rubber bushing model and divides the meshes, obtains model parameters required by simulation calculation by using the design values of the rubber bushing, reduces the number of the meshes required by the simulation calculation, reduces the time required by the simulation calculation and improves the efficiency of the simulation calculation on the premise of not reducing the simulation accuracy.
Drawings
FIG. 1 is a flow chart of a method for large scale finite element analysis of a rubber bushing according to an embodiment of the present invention;
FIG. 2 is a schematic view of a simplified model of a rubber bushing provided in accordance with an embodiment of the present invention;
FIG. 3 is a schematic view of an outboard steel ring provided in accordance with an embodiment of the present invention;
FIG. 4 is a schematic view of a rubber member provided in accordance with an embodiment of the present invention;
FIG. 5 is a schematic view of a reinforcement panel provided in accordance with an embodiment of the present invention;
fig. 6 is a schematic view of an inner steel ring according to an embodiment of the present invention.
In the figure:
110. a rubber member; 111. mounting grooves; 120. a reinforcing plate; 130. an inner steel ring; 140. and an outer steel ring.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be further noted that, for the convenience of description, only some of the structures related to the present invention are shown in the drawings, not all of the structures.
In the description of the present invention, unless expressly stated or limited otherwise, the terms "connected," "connected," and "fixed" are to be construed broadly, e.g., as meaning permanently connected, removably connected, or integral to one another; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, the first feature "on," "above" and "over" the second feature may include the first feature being directly above and obliquely above the second feature, or simply indicating that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature includes the first feature being directly under and obliquely below the second feature, or simply meaning that the first feature is at a lesser elevation than the second feature.
In the description of the present embodiment, the terms "upper", "lower", "right", etc. are used in an orientation or positional relationship based on that shown in the drawings only for convenience of description and simplicity of operation, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used only for descriptive purposes and are not intended to have a special meaning.
Referring to fig. 1, the large-scale finite element analysis method of the rubber bushing includes the steps of:
s1, determining an objective function of model parameter identification: the objective function being radial stiffness S of the rubber bushing vertical And torsional rigidity S rotational The ratio of (a) to (b) is μ;
s2, determining model identification parameters: the model identification parameters comprise constitutive parameters C of the rubber material 10 And a reinforcement plate thickness h of the rubber bushing; optionally, in step S2, a Mooney-Rivlin rubber constitutive material model is adopted, which includes parameter C 10 And parameter C 01 In which C is 10 /C 01 Let C in this example be 4 01 If known, the model identification parameters include C 10 And a rubber bushing reinforcing plate 120 thickness h.
S3, establishing a rubber bushing simplified model and dividing grids: with continuing reference to fig. 2 to fig. 6, the simplified rubber bushing model includes an inner steel ring 130, a rubber member 110, a reinforcing plate 120 and an outer steel ring 140, the inner steel ring 130 is inserted into the rubber member 110, the outer steel ring 140 is sleeved outside the rubber member 110, the reinforcing plate 120 is located at the geometric middle position of the rubber member 110, and divides the rubber member 110 into two layers, as shown in fig. 3, an annular mounting groove 111 is axially formed at the geometric middle position of the rubber member 110, and the reinforcing plate 120 is inserted into the mounting groove 111; specifically, in step S3, the reinforcing plate 120 is divided into meshes by using hexahedral cells with a size of 4mm and 8 nodes, and the number of cell layers is 1; the rubber part 110 is divided into meshes by adopting hexahedral units with the size of 4mm and 8 nodes, the HERRMANN units are adopted, and the HERRMANN units are used for rubber volume incompressible materials, so that volume self-locking can be prevented during simulation, and after the rubber part 110 is divided into two layers by the reinforcing plate 120, the number of unit layers of each layer of the rubber part 110 is 2; the outer steel ring 140 and the inner steel ring 130 are all divided into grids by adopting hexahedron units with the size of 4mm and 8 nodes, and the number of the unit layers is 1.
S4, determining a parameter identification method of the simplified rubber bushing model; in step S4, a multivariate nonlinear regression model is used as a parameter identification method for the simplified model of the rubber bushing, and the expression is as follows:
in the formula, a, b j 、b kj And b jj Is the regression parameter to be solved, x, of the regression model k And x j As a factor variable, C is referred to herein 10 And h; constitutive parameter C of rubber material 10 And the thickness h of the reinforcing plate 120 respectively has nonlinear relation with the radial rigidity and the torsional rigidity of the rubber bushing, and the radial rigidity and the C are respectively obtained 10 And h nonlinear regression model, torsional stiffness and C 10 And h, a non-linear regression model.
S5, establishing a factor level coding table for identifying model parameters, wherein the factor is the model parameter C to be identified 10 And h, level is C 10 And the value range of h; alternatively, in step S5, in the factor level code table, x -1r ≤C 10 ≤x 1r ，x -2r ≤h≤x 2r ，x -1r And x 1r Are respectively C 10 Lower and upper limits of the values, x -2r And x 2r The lower limit and the upper limit of the value h are respectively; the lower limit corresponds to the lower asterisk arm-gamma, and the upper limit corresponds to the upper asterisk arm gamma;
C 10 and zero level values of h are each x 10 And x 20 From
Calculated, where j is 1, 2;
C 10 and h are each a 1 And Δ 2 From
Calculated, j is 1, 2 in the formula.
The factor level coding table in this embodiment is as follows:
s6, outputting a simulation result: inputting design values to obtain model parameters C required for simulation calculation according to the simplified model of the rubber bushing in step S3, the parameter identification method in step S4 and the factor level coding in step S5 10 And h, subsequently simplifying the rubber bushing into a model, model parameters C 10 And h, inputting the simulation software and outputting a simulation result.
Optionally, in step S6, the simulation schemes include a rubber bushing radial stiffness simulation scheme and a rubber bushing torsional stiffness simulation scheme. Specifically, the simulation schemes are provided in plural, and 10 simulation schemes are shared in the present embodiment. Further, at least two simulation schemes are the same, and the two same simulation schemes are used for verifying the consistency of the simulation software. The simulation scheme including radial stiffness and torsional stiffness in this example is as follows:
| simulation scheme | x 1 (C 10 ) | x 2 (C 01 ) | S vertical /(Kn/mm) | S rotational /(N·m/°) |
| 1 | x 12 ＝x 10 +Δ 1 | x 22 ＝x 20 +Δ 2 | ||
| 2 | x 12 ＝x 10 +Δ 1 | x 22 ＝x 20 -Δ 2 | ||
| 3 | x 12 ＝x 10 -Δ 1 | x 22 ＝x 20 +Δ 2 | ||
| 4 | x 12 ＝x 10 -Δ 1 | x 22 ＝x 20 -Δ 2 | ||
| 5 | x 1r | x 20 | ||
| 6 | x -1r | x 20 | ||
| 7 | x 10 | x 2r | ||
| 8 | x 10 | x -2r | ||
| 9 | x 10 | x 20 | ||
| 10 | x 10 | x 20 |
As a preferred embodiment, after step S6, the method further includes the step of verifying: and S7, comparing the simulation result obtained in the step S6 with a design value, and when the error is not more than a preset value, indicating that the simulation result is accurate. Specifically, the error is S vertical And the error of the simulated value of μ from the design value, the preset value of the error being 5%.
The large-scale finite element analysis method of the rubber bushing firstly determines an objective function identified by model parameters and then determines constitutive parameters C including rubber materials 10 And model identification parameters of the thickness h of the reinforcing plate of the rubber bushing, establishing a rubber bushing simplified model, dividing the grid into grids and a parameter identification method of the rubber bushing simplified model, and establishing a simulation scheme by the parameter identification method of the rubber bushing simplified model and a factor level coding table to obtain model parameters C required by simulation calculation 10 And h, finally obtaining an output simulation result. The large-scale finite element analysis method of the rubber bushing uses the simplified rubber bushing model and divides the meshes, obtains model parameters required by simulation calculation by using the design values of the rubber bushing, reduces the number of the meshes required by the simulation calculation, reduces the time required by the simulation calculation and improves the efficiency of the simulation calculation on the premise of not reducing the simulation accuracy.
In a specific embodiment, the large scale finite element analysis method of the rubber bushing comprises the steps of:
determining an objective function for model parameter identification
Selecting radial rigidity S of rubber bushing vertical And the ratio mu of the radial stiffness to the torsional stiffness as an objective function for parameter identification, in this embodiment, S vertical ＝224KN/mm，μ＝S vertical /S rotational ＝5.5，
Secondly, determining the parameters of model identification
This example uses a Mooney-Rivlin rubber constitutive material model, C 10 And h is the parameter to be identified, where C is assumed 10 /C 01 H is the thickness of the reinforcing plate 120.
Thirdly, establishing a simplified model of the rubber bushing and dividing grids
The simplified rubber bushing model comprises an inner steel ring 130, a rubber part 110, a reinforcing plate 120 and an outer steel ring 140, wherein the inner steel ring 130 is inserted into the rubber part 110, the outer steel ring 140 is sleeved outside the rubber part 110, and the reinforcing plate 120 is positioned in the geometric middle of the rubber part 110 and divides the rubber part 110 into two layers; specifically, in step S3, the reinforcing plate 120 is divided into meshes by using hexahedral cells with a size of 4mm and 8 nodes, and the number of cell layers is 1; the rubber part 110 is subjected to grid division by adopting hexahedral units with the size of 4mm and 8 nodes, HERRMANN units are adopted, the HERRMANN units are used for rubber volume-incompressible materials, the volume self-locking in simulation can be prevented, and after the rubber part 110 is divided into two layers by the reinforcing plate 120, the number of unit layers of each layer of the rubber part 110 is 2; the outer steel ring 140 and the inner steel ring 130 are all divided into grids by adopting hexahedron units with the size of 4mm and 8 nodes, and the number of the unit layers is 1.
Identification method for determining simplified model parameters of rubber bushing
The multivariate nonlinear regression equation of the embodiment is
In the formula, a, b j 、b kj And b jj And obtaining regression parameters to be solved of the regression model. x is the number of k And x j As a factor variable, C is referred to herein 10 And h.
Fifthly, establishing a factor level coding table for model parameter identification
The value ranges of the two design factors are respectively that C is more than or equal to 0.2 10 2, 0.02 h 0.4, the factor level codes are shown in the following table.
Sixthly, establishing a simulation scheme and outputting a simulation model calculation result
And obtaining a simulation analysis scheme table according to the factor level coding table in the last step. A rubber bushing radial rigidity simulation scheme and a rubber bushing torsional rigidity simulation scheme are obtained through a factor level coding table, and 10 simulation schemes (the 9 th group is the same as the 10 th group) are respectively shown in the following table. Respectively establishing 10 simulation schemes C by using a rubber bushing simplified model 10 And h parameter finite element model, the radial stiffness and torsional stiffness results obtained are shown in the following table.
| Simulation scheme | x 1 (C 10 ) | x 2 (C 01 ) | S vertical /(Kn/mm) | S rotational /(N·m/°) |
| 1 | 1.934879 | 0.386252 | 451.3 | 49.5 |
| 2 | 1.934879 | 0.033748 | 251 | 47.9 |
| 3 | 0.265121 | 0.386252 | 67.4 | 6.95 |
| 4 | 0.265121 | 0.033748 | 54.7 | 6.74 |
| 5 | 2 | 0.21 | 416.4 | 50.3 |
| 6 | 0.2 | 0.21 | 48.7 | 5.21 |
| 7 | 1.1 | 0.4 | 269.7 | 28.2 |
| 8 | 1.1 | 0.02 | 145.3 | 27.3 |
| 9 | 1.1 | 0.21 | 246.2 | 27.7 |
| 10 | 1.1 | 0.21 | 246 | 27.5 |
Obtaining the radial stiffness S by using the multiple nonlinear regression data processing knowledge vertical And torsional rigidity S rotational The fitting polynomials of (a) are respectively shown in the following formula.
S vertical ＝-8.55+145.66·C 10 +350.74·h+318.54·C 10 ·h-12.51·C 10 2 -950·h 2
S rotational ＝0.489+24.17·C 10 -2.99·h+2.32·C 10 ·h+0.181·C 10 2 +6.88·h 2
S according to design requirements vertical And μ, can find C 10 And h. S required for design in this embodiment vertical ＝224KN/mm，μ＝S vertical /S rotational When the value is 5.5, C can be obtained from the above two formulas 10 1.65 and h is 0.031, namely the constitutive parameters of the rubber material required by simulation are as follows: c 10 ＝1.65，C 01 1.65/4 is 0.4125, and the thickness h of the reinforcing plate 120 is 0.031.
Seventhly, verifying accuracy
Inputting a finite element model of simulation software according to the parameters and calculating, verifying the rigidity simulation value and the accuracy of the design value of the rubber bushing according to the following table, wherein the error is not more than 5%.
In another specific embodiment, calculation verification is performed by taking the calculation of the roll limit working condition of a composite air suspension assembly system of a certain type of commercial vehicle as an example, a used simulation software platform is an MSC.MARC 2010 version, and a computer performs calculation by adopting 12 threads. The composite air suspension assembly model of the commercial vehicle comprises more parts, is large in grid size, has 2226734 grids in total, and relates to geometric nonlinearity, material nonlinearity and contact nonlinearity calculations, so that the calculations belong to large-scale finite element nonlinearity analysis. The following table shows the simulation results of each part after simplifying the model by using the rubber bushing in the present embodiment.
The comparison result of the calculation efficiency of the simplified rubber bushing model and the real rubber bushing model in the embodiment is shown in the following table, and the result shows that the large-scale finite element analysis method of the rubber bushing in the embodiment can shorten the time required by large-scale finite element nonlinear analysis from 367 hours to 58 hours under the same calculation resources, and the efficiency is improved by at least 80%.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Numerous obvious variations, adaptations and substitutions will occur to those skilled in the art without departing from the scope of the invention. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A large-scale finite element analysis method of a rubber bushing is characterized by comprising the following steps:
s1, determining an objective function of model parameter identification: the objective function is radial rigidity S of the rubber bushing vertical And torsional rigidity S rotational The ratio of (a) to (b) is μ;
s2, determining model identification parameters: the model identification parameters comprise constitutive parameters C of the rubber material 10 And a reinforcement plate (120) thickness h of the rubber bushing;
s3, establishing a rubber bushing simplified model and dividing grids: the simplified rubber bushing model comprises an inner steel ring (130), a rubber piece (110), a reinforcing plate (120) and an outer steel ring (140), wherein the inner steel ring (130) is inserted into the rubber piece (110), the outer steel ring (140) is sleeved outside the rubber piece (110), and the reinforcing plate (120) is positioned in the geometric middle of the rubber piece (110) and divides the rubber piece (110) into two layers;
s4, determining a parameter identification method of the simplified rubber bushing model;
s5, establishing a factor level coding table for identifying model parameters, wherein the factor is the model parameter C to be identified 10 And h, level is C 10 And the value range of h;
s6, outputting a simulation result: establishing a simulation plan according to the simplified rubber bushing model in the step S3, the parameter identification method in the step S4 and the factor level code table in the step S5, inputting design values to obtain model parameters C required for simulation calculation 10 And h, subsequently simplifying the rubber bushing into a model, the model parameters C 10 And h, inputting the simulation software and outputting a simulation result.
2. The method of finite element analysis of a rubber bushing according to claim 1, further comprising a verification step after the step S6:
and S7, comparing the simulation result obtained in the step S6 with the design value, and when the error is not more than a preset value, indicating that the simulation result is accurate.
3. The large scale finite element analysis method of a rubber bushing of claim 2, wherein the preset value is 5%.
4. The method of finite element analysis for rubber bushings according to claim 1, characterized in that in step S2, a Mooney-Rivlin rubber constitutive material model is used, which includes parameter C 10 And parameter C 01 In which C is 10 /C 01 If 4, the model identification parameter includes C 10 And a reinforcement plate thickness h of the rubber bushing.
5. The large scale finite element analysis method of a rubber bushing according to claim 1, wherein in the step S3, the reinforcing plate (120) is meshed with 8-node hexahedral cells with a size of 4mm in the step S3, and the number of cell layers is 1; the rubber part (110) is subjected to grid division by adopting hexahedral units with the size of 4mm and 8 nodes, HERRMANN units are adopted, and after the rubber part (110) is divided into two layers by the reinforcing plate (120), the number of unit layers of each layer of the rubber part (110) is 2; the outer side steel ring (140) and the inner side steel ring (130) are all divided into grids by adopting hexahedron units with the size of 4mm and 8 nodes, and the number of unit layers is 1.
6. The method of finite element analysis for rubber bushings according to claim 1, characterized in that in step S4, a multivariate nonlinear regression model is used as the parameter identification method of the simplified rubber bushing model, and the expression is:
in the formula, a, b j 、b kj And b jj Is the regression parameter to be solved, x, of the regression model k And x j As a factor variable, C is referred to herein 10 And h;
constitutive parameter C of rubber material 10 And the thickness h of the reinforcing plate (120) has nonlinear relations with the radial stiffness and the torsional stiffness of the rubber bushing respectively, and the radial stiffness and the C are obtained respectively 10 And h, the torsional stiffness and C 10 And h, a non-linear regression model.
7. The method of finite element analysis of rubber bushing in large scale according to claim 1, wherein in step S5, the factor level code table contains x -1r ≤C 10 ≤x 1r ，x -2r ≤h≤x 2r ，x -1r And x 1r Are respectively C 10 Lower and upper limits of the values, x -2r And x 2r The lower limit and the upper limit of the value h are respectively; the lower limit corresponds to the lower asterisk arm-gamma, and the upper limit corresponds to the upper asterisk arm gamma;
C 10 and zero level values of h are each x 10 And x 20 From
Calculated, where j is 1, 2;
C 10 and h are each a 1 And Δ 2 From
Calculated, j is 1, 2 in the formula.
8. The method of finite element analysis of a rubber bushing according to claim 1, wherein in the step S6, the simulation schemes include a rubber bushing radial stiffness simulation scheme and a rubber bushing torsional stiffness simulation scheme.
9. The large scale finite element analysis method of a rubber bushing according to claim 8, wherein the simulation scheme is provided in plurality.
10. The method of finite element analysis of a rubber bushing of claim 9, wherein at least two of the simulation scenarios are identical, and wherein the two identical simulation scenarios are used to verify the consistency of the simulation software.
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|---|---|---|---|---|
| CN117454722A (en) * | 2023-12-22 | 2024-01-26 | 西南石油大学 | Screw drilling tool bushing design method based on rubber swelling |
| CN117454722B (en) * | 2023-12-22 | 2024-03-01 | 西南石油大学 | Screw drilling tool bushing design method based on rubber swelling |
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