CN114186455B - Method for establishing equivalent model of fixed joint surface based on transverse isotropic virtual material - Google Patents

Method for establishing equivalent model of fixed joint surface based on transverse isotropic virtual material Download PDF

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CN114186455B
CN114186455B CN202111457461.8A CN202111457461A CN114186455B CN 114186455 B CN114186455 B CN 114186455B CN 202111457461 A CN202111457461 A CN 202111457461A CN 114186455 B CN114186455 B CN 114186455B
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国杰
杨亚飞
张新玉
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Abstract

The invention provides a method for establishing a fixed joint surface equivalent model based on a transverse isotropic virtual material, which adopts a transverse isotropic virtual material layer unit to construct the fixed joint surface equivalent model and theoretically deduces a virtual material layer parameter calculation model; carrying out modal test analysis on the combined structure with the joint surface, establishing a parameterized finite element model of the combined structure based on the established equivalent model, and carrying out modal simulation analysis on the parameterized finite element model; and establishing an objective function through the experimental and calculated modal data, optimizing the established objective function by utilizing an optimization algorithm, identifying undetermined parameters, and determining all parameters of the virtual material layer. Compared with the common virtual material method, the method for establishing the equivalent model of the fixed joint surface based on the transverse isotropic virtual material considers different normal and tangential connection characteristics of the joint surface, is more consistent with the actual situation, and can improve the calculation accuracy of dynamic response.

Description

Method for establishing equivalent model of fixed joint surface based on transverse isotropic virtual material
Technical Field
The invention belongs to the technical field of finite element models of fixed joint surfaces, and particularly relates to a method for establishing an equivalent model of a fixed joint surface based on a transverse isotropic virtual material.
Background
A fixed interface is a mechanical interface where the components are held in contact with each other relatively stationary without relative movement. The fixed joint surface plays a role in transmitting force and vibration, and mutual extrusion and slippage with different degrees can be generated under the action of external load, so that the joint surface has the characteristics of rigidity and damping, and the characteristics are important for the dynamic response calculation accuracy of the structure. In a finite element model of a combined structure with a fixed junction surface, an equivalent model is often built by simplifying the connection of the junction surface, wherein a virtual material method is a novel equivalent model building method, and the virtual material refers to a common isotropic virtual material. However, the method does not consider different connection characteristics of the normal direction and the tangential direction of the joint surface, and has a certain influence on the calculation accuracy of the dynamic response of the structure. The establishment of a reasonable equivalent model is an important basic work of the problem of the fixed joint surface, and after the equivalent model is established, the parameters in the equivalent model are required to be determined by adopting a reasonable method, and the parameters are corrected and improved.
Disclosure of Invention
The invention aims to solve the defects of the existing junction surface connection technology and realize a method for establishing an equivalent model of a fixed junction surface based on transverse isotropic virtual materials by accurately modeling and analyzing the fixed junction surface.
A fixed junction equivalent modeling method based on transverse isotropy virtual material comprises the following steps:
step 1: in the finite element model of the structure, a transverse isotropic virtual material layer unit is adopted to replace a fixed joint surface formed by two parts which are contacted with each other, so as to construct a fixed joint surface equivalent model.
The transverse isotropic virtual material layer units have the same properties in the tangential plane of the joint plane and differ from the normal properties, which are different from the isotropic virtual material, taking into account the different connection properties of the joint plane normal and tangential. The transverse isotropy virtual material layer unit is directly and rigidly connected with the two mutually contacted parts.
Step 2: and establishing a virtual material layer parameter calculation model according to constitutive equation of the transverse isotropic material and the fixed junction surface connection parameters.
The parameters of the virtual material layer are 12, and the parameters are respectively the elastic modulus E x ,E y ,E z Shear modulus G yz ,G xz ,G xy Poisson's ratio mu yz ,μ xz ,μ xy Thickness h, density ρ and damping coefficient η. In view of the virtual material layer being a laterally isotropic material, there is E x ＝E y ,G yz ＝G xz ,μ yz ＝μ xz G xy ＝E x /(2+2μ xy )。
Modulus of elasticity E of the virtual Material layer x ,E y ,E z The calculation formula is as follows:
Figure BDA0003388256280000011
Figure BDA0003388256280000021
wherein E is 1 ,E 2 Is the modulus of elasticity, mu, of two mutually contacting parts 1 ,μ 2 Poisson's ratio, sigma, of two mutually contacting parts n ,ε n Is the normal stress and strain, k, of the virtual material layer n Is the normal stiffness per unit area of the bonding surface, and h is the thickness of the virtual material layer.
Virtual Material layer shear modulus G yz ,G xz The calculation formula is as follows:
Figure BDA0003388256280000022
Figure BDA0003388256280000023
where τ, γ is the normal stress and strain, k, of the virtual material layer τ Is the tangential stiffness per unit area of the joint.
When the joint surface bears the tension and compression load in the tangential plane, the deformation generated in the normal direction is mainly used for filling the gaps among the micro-convex bodies of the joint surface, so that the deformation generated in the normal direction is ignored, and mu exists yz ＝μ xz =0. Similarly, the deformation caused by tangential direction is ignored, so there is mu xy ＝0。
The calculation formula of the thickness h of the virtual material layer is as follows:
h＝h 1 +h 2 (5)
wherein h is 1 ,h 2 Is the thickness of the microscopic microprotrusions on the surfaces of two mutually contacted parts.
The calculation formula of the density rho of the virtual material layer is as follows:
Figure BDA0003388256280000024
wherein m is 1 ,m 2 Is the mass ρ of the micro-convex body on the surface of two mutually contacted parts 1 ,ρ 2 Is the density of microscopic asperities on the surfaces of two mutually contacted parts, V is the volume of the virtual material layer, and A is the contact area of the joint surface.
The calculation formula of the damping coefficient eta of the virtual material layer is as follows:
η＝η 0 (7)
wherein eta 0 Is a damping coefficient constant, and the value of the damping coefficient constant is related to factors such as lubrication conditions of the joint surface, surface roughness and the like.
Step 3: and determining known parameters and undetermined parameters in the virtual material layer according to the fixed junction surface connection parameters.
The known parameters of the virtual material layer are as follows: poisson's ratio μ of two mutually contacting parts 1 ,μ 2 Modulus of elasticity E 1 ,E 2 Surface micro-asperity thickness h 1 ,h 2 Density ρ 1 ,ρ 2 . The value of which is obtained by a material property parameter of the component itself, wherein the thickness is related to the surface roughness. The undetermined parameters of the virtual material layer are as follows: normal stiffness and tangential stiffness k of joint surface per unit area n ,k τ Damping coefficient η.
Step 4: and carrying out modal test analysis on the combined structure with the joint surface to obtain the test natural frequency and damping ratio.
Step 5: establishing a parameterized finite element model of the combined structure based on the fixed junction equivalent model in the step 1, wherein the design variable is a pending parameter k n ,k τ And eta 0 。
Step 6: and (5) carrying out modal simulation analysis based on the parameterized finite element model of the combined structure in the step (5) to obtain the calculated natural frequency and damping ratio.
Step 7: and (3) establishing an objective function based on the test natural frequency and the damping ratio in the step (4) and the calculated natural frequency and the damping ratio in the step (6).
The objective function F is:
Figure BDA0003388256280000031
where m is the order of the mode,
Figure BDA0003388256280000032
is the test natural frequency and damping ratio, +.>
Figure BDA0003388256280000033
Is to calculate the natural frequency and damping ratio.
When the experimental natural frequency and damping ratio are very close to or equal to the calculated natural frequency and damping ratio, it is considered that the virtual material layer can represent the connection characteristics of the real bonding surface.
Step 8: optimizing the objective function F in the step 7 based on an optimization algorithm, and further optimizing the undetermined parameter k n ,k τ And eta 0 And (5) carrying out identification.
The optimization algorithm calculates the value of the objective function by calling the step 5 and the step 6, and simulation integration is realized. The initial range of the optimized design variable is determined according to practical experience, and the optimization termination condition is as follows:
|F i -F i-1 |≤Tol (9)
wherein F is i Is the objective function value of the current iteration step, F i-1 Is the objective function value of the previous iteration step and Tol is the tolerance.
Step 9: based on the optimized recognition result of step 8, all parameters of the virtual material layer can be determined in combination with step 3.
The design variable k obtained in the step 8 is obtained n ,k τ And eta 0 The optimum value is brought into the formulas (2), (3) and (7) to obtain E z ,G yz And η, all parameters of the virtual material layer may be determined in combination with the known parameters of step 3.
The invention has the beneficial effects that:
(1) Compared with the common virtual material method, the method for establishing the equivalent model of the fixed joint surface based on the transverse isotropic virtual material considers different normal and tangential connection characteristics of the joint surface, is more consistent with the actual situation, and can improve the calculation accuracy of dynamic response.
(2) The equivalent model parameter determining method is parameterized integrated, can greatly save calculation time and has practical value. The parameter determination only needs to carry out modal analysis, on one hand, a special experimental device is not required to be designed in the modal test, and on the other hand, the modal simulation calculation is faster, so that the method has general convenience.
Drawings
FIG. 1 is a schematic view of a two-part fixed mechanical joint according to the present invention.
Fig. 2 is a schematic flow chart of the equivalent model building and parameter determining method provided by the invention.
Fig. 3 is a schematic diagram of an equivalent model of a virtual material with parameters for landscape isotropy, which is provided by the invention.
The corresponding names of the reference numerals in the figures are:
1. a component 1; 2. fixing the mechanical joint surface; 3. a component 2; 4. the isotropic virtual material layer is viewed transversely.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
In this embodiment, taking a fixed mechanical joint surface formed by two parts as shown in fig. 1 as an example, the present invention is adopted to perform equivalent modeling and parameter determination on the fixed mechanical joint surface, as shown in fig. 2, and specifically implemented according to the following steps:
step 1: in the finite element model of the structure, a transverse isotropic virtual material layer unit is adopted to replace a fixed joint surface formed by two parts which are contacted with each other, so as to construct a fixed joint surface equivalent model.
Step 2: and establishing a virtual material layer parameter calculation model according to constitutive equation of the transverse isotropic material and the fixed junction connection parameters, as shown in figure 3.
The parameters of the virtual material layer are 12, and the parameters are respectively the elastic modulus E x ,E y ,E z Shear modulus G yz ,G xz ,G xy Poisson's ratio mu yz ,μ xz ,μ xy Thickness h, density ρ and damping coefficient η. In view of the virtual material layer being a laterally isotropic material, there is E x ＝E y ,G yz ＝G xz ,μ yz ＝μ xz G xy ＝E x /(2+2μ xy )。
Modulus of elasticity E of the virtual Material layer x ,E y ,E z The calculation formula is as follows:
Figure BDA0003388256280000041
Figure BDA0003388256280000042
wherein E is 1 ,E 2 Is the modulus of elasticity, mu, of two mutually contacting parts 1 ,μ 2 Poisson's ratio, sigma, of two mutually contacting parts n ,ε n Is the normal stress and strain, k, of the virtual material layer n Is the normal stiffness per unit area of the bonding surface, and h is the thickness of the virtual material layer.
Virtual Material layer shear modulus G yz ,G xz ,G xy The calculation formula is as follows:
Figure BDA0003388256280000043
Figure BDA0003388256280000051
where τ, γ is the normal stress and strain, k, of the virtual material layer τ Is the tangential stiffness per unit area of the joint.
When the joint surface bears the tension and compression load in the tangential plane, the deformation generated in the normal direction is mainly used for filling the gaps among the micro-convex bodies of the joint surface, so that the deformation generated in the normal direction is ignored, and mu exists yz ＝μ xz =0. Similarly, the deformation caused by tangential direction is ignored, so there is mu xy ＝0。
The calculation formula of the thickness h of the virtual material layer is as follows:
h＝h 1 +h 2 (14)
wherein h is 1 ,h 2 Is the thickness of the microscopic microprotrusions on the surfaces of two mutually contacted parts.
The calculation formula of the density rho of the virtual material layer is as follows:
Figure BDA0003388256280000052
wherein m is 1 ,m 2 Is the mass ρ of the micro-convex body on the surface of two mutually contacted parts 1 ,ρ 2 Is the density of microscopic asperities on the surfaces of two mutually contacted parts, V is the volume of the virtual material layer, and A is the contact area of the joint surface.
The calculation formula of the damping coefficient eta of the virtual material layer is as follows:
η＝η 0 (16)
wherein eta 0 Is a damping coefficient constant, and the value of the damping coefficient constant is related to factors such as lubrication conditions of the joint surface, surface roughness and the like.
Step 3: and determining known parameters and undetermined parameters in the virtual material layer according to the fixed junction surface connection parameters.
The known parameters of the virtual material layer are as follows: poisson's ratio μ of two mutually contacting parts 1 ,μ 2 Modulus of elasticity E 1 ,E 2 Surface micro-asperity thickness h 1 ,h 2 Density ρ 1 ,ρ 2 . The value of which is obtained by a material property parameter of the component itself, wherein the thickness is related to the surface roughness. The undetermined parameters of the virtual material layer are as follows: normal stiffness and tangential stiffness k of joint surface per unit area n ,k τ Damping coefficient η.
Step 4: and carrying out modal test analysis on the combined structure with the joint surface to obtain the test natural frequency and damping ratio.
Step 5: establishing a parameterized finite element model of the combined structure based on the fixed junction equivalent model in the step 1, wherein the design variable is a pending parameter k n ,k τ And eta 0 。
Step 6: and (5) carrying out modal simulation analysis based on the parameterized finite element model of the combined structure in the step (5) to obtain the calculated natural frequency and damping ratio.
Step 7: and (3) establishing an objective function based on the test natural frequency and the damping ratio in the step (4) and the calculated natural frequency and the damping ratio in the step (6).
The objective function F is:
Figure BDA0003388256280000061
where m is the order of the mode,
Figure BDA0003388256280000062
is the test natural frequency and damping ratio, +.>
Figure BDA0003388256280000063
Is to calculate the natural frequency and damping ratio.
When the experimental natural frequency and damping ratio are very close to or equal to the calculated natural frequency and damping ratio, it is considered that the virtual material layer can represent the connection characteristics of the real bonding surface.
Step 8: optimizing the objective function F in the step 7 based on an optimization algorithm, and further optimizing the undetermined parameter k n ,k τ And eta 0 And (5) carrying out identification.
The optimization algorithm calculates the value of the objective function by calling the step 5 and the step 6, and simulation integration is realized. The initial range of the optimized design variable is determined according to practical experience, and the optimization termination condition is as follows:
|F i -F i-1 |≤Tol (18)
wherein F is i Is the objective function value of the current iteration step, F i-1 Is the last oneThe objective function value of the iteration step, tol is the tolerance.
Step 9: based on the optimized recognition result of step 8, all parameters of the virtual material layer can be determined in combination with step 3.
The design variable k obtained in the step 8 is obtained n ,k τ And eta 0 The optimum value is brought into the formulas (11), (3) and (7) to obtain E z ,G yz And η, in combination with the known parameters of step 3, determine all parameters of the layer of virtual material.
In this embodiment, taking a fixed mechanical joint surface formed by two parts as an example, a parameterized finite element model of a combined structure is built based on a transverse isotropic virtual material equivalent model, an objective function is built through experimental and calculated modal data, and undetermined parameters in the equivalent model are determined by means of an optimization algorithm.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. The method for establishing the equivalent model of the fixed joint surface based on the transverse isotropic virtual material is characterized by comprising the following steps of:
step 1: in the finite element model of the structure, a transverse isotropy virtual material layer unit is adopted to replace a fixed joint surface formed by two parts which are contacted with each other, so as to construct an equivalent model of the fixed joint surface;
the transverse isotropic virtual material layer units have the same performance in the tangential plane of the joint surface and are different from the normal performance, which is different from the isotropic virtual material, and the transverse isotropic virtual material layer units consider different connection characteristics of the normal direction and the tangential direction of the joint surface; the transverse isotropic virtual material layer unit is directly and rigidly connected with the two mutually contacted parts;
step 2: establishing a virtual material layer parameter calculation model according to constitutive equation of transverse isotropic material and fixed junction surface connection parameters;
the parameters of the virtual material layer are 12, and the parameters are respectively the elastic modulus E x ,E y ,E z Shear modulus G yz ,G xz ,G xy Poisson's ratio mu yz ,μ xz ,μ xy Thickness h, density ρ and damping coefficient η; in view of the virtual material layer being a laterally isotropic material, there is E x ＝E y ,G yz ＝G xz ,μ yz ＝μ xz G xy ＝E x /(2+2μ xy )；
Modulus of elasticity E of the virtual Material layer x ,E y ,E z The calculation formula is as follows:
Figure FDA0004125354470000011
Figure FDA0004125354470000012
wherein E is 1 ,E 2 Is the modulus of elasticity, mu, of two mutually contacting parts 1 ,μ 2 Poisson's ratio, sigma, of two mutually contacting parts n ,ε n Is the normal stress and strain, k, of the virtual material layer n The normal stiffness of the unit area of the bonding surface is h, and the thickness of the virtual material layer is h;
virtual Material layer shear modulus G yz ,G xz The calculation formula is as follows:
Figure FDA0004125354470000013
Figure FDA0004125354470000014
where τ, γ is the normal stress and strain, k, of the virtual material layer τ Tangential stiffness per unit area of the joint surface;
when the joint surface bears the tensile and compressive load in the tangential plane, the deformation generated in the normal direction is used for filling the gaps among the microscopic micro-convex bodies of the joint surface, so that the deformation generated in the normal direction is ignored, and mu exists yz ＝μ xz =0; similarly, the deformation caused by tangential direction is ignored, so there is mu xy ＝0；
The calculation formula of the thickness h of the virtual material layer is as follows:
h＝h 1 +h 2 (5)
wherein h is 1 ,h 2 Is the thickness of the microcosmic microprotrusions on the surfaces of the two mutually contacted parts;
the calculation formula of the density rho of the virtual material layer is as follows:
Figure FDA0004125354470000021
wherein m is 1 ,m 2 Is the mass ρ of the micro-convex body on the surface of two mutually contacted parts 1 ,ρ 2 Is the density of microscopic micro-convexities on the surfaces of two mutually contacted parts, V is the volume of the virtual material layer, and A is the contact area of the joint surface;
the calculation formula of the damping coefficient eta of the virtual material layer is as follows:
η＝η 0 (7)
wherein eta 0 Is a damping coefficient constant, the value of which is related to the lubrication condition of the joint surface and the surface roughness factor;
step 3: determining known parameters and undetermined parameters in the virtual material layer according to the fixed junction surface connection parameters;
the known parameters of the virtual material layer are as follows: poisson's ratio μ of two mutually contacting parts 1 ,μ 2 Modulus of elasticity E 1 ,E 2 Surface micro-asperity thickness h 1 ,h 2 Density ρ 1 ,ρ 2 The method comprises the steps of carrying out a first treatment on the surface of the The value of which is obtained by a material property parameter of the component itself, wherein the thickness is related to the surface roughness; the undetermined parameters of the virtual material layer are: normal stiffness and tangential stiffness k of joint surface per unit area n ,k τ Damping coefficient eta; because it is related to the lubrication conditions of the joint surface, the surface roughness factor;
step 4: carrying out modal test analysis on the combined structure with the joint surface to obtain a test natural frequency and a damping ratio;
step 5: establishing a parameterized finite element model of the combined structure based on the fixed junction equivalent model in the step 1, wherein the design variable is a pending parameter k n ,k τ And eta 0 ；
Step 6: performing modal simulation analysis based on the parameterized finite element model of the combined structure in the step 5 to obtain a calculated natural frequency and damping ratio;
step 7: establishing an objective function based on the test natural frequency and the damping ratio in the step 4 and the calculated natural frequency and the damping ratio in the step 6;
the objective function F is:
Figure FDA0004125354470000031
where m is the order of the mode, f i e ,
Figure FDA0004125354470000032
Is the test natural frequency and damping ratio, f i c ,/>
Figure FDA0004125354470000033
The natural frequency and the damping ratio are calculated;
when the test natural frequency and the damping ratio are equal to the calculated natural frequency and the damping ratio, the virtual material layer is considered to be capable of representing the connection characteristic of the real joint surface;
step 8: optimizing the objective function F in the step 7 based on an optimization algorithm, and further optimizing the undetermined parameter k n ,k τ And eta 0 Identifying;
the optimization algorithm calculates the value of the objective function by calling the step 5 and the step 6, so that the integration of simulation is realized; the initial range of the optimized design variable is determined according to practical experience, and the optimization termination condition is as follows:
|F i -F i-1 |≤Tol (9)
wherein F is i Is the objective function value of the current iteration step, F i-1 Is the objective function value of the previous iteration step, and Tol is the tolerance;
step 9: based on the optimized recognition result of the step 8, all parameters of the virtual material layer can be determined in combination with the step 3;
the design variable k obtained in the step 8 is obtained n ,k τ And eta 0 The optimum value is brought into the formulas (2), (3) and (7) to obtain E z ,G yz And η, in combination with the known parameters of step 3, determine all parameters of the layer of virtual material.
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