CN114781195B - Method for determining incidence relation between stress of glued laminated ball structure and glued layer - Google Patents

Method for determining incidence relation between stress of glued laminated ball structure and glued layer Download PDF

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CN114781195B
CN114781195B CN202210696424.0A CN202210696424A CN114781195B CN 114781195 B CN114781195 B CN 114781195B CN 202210696424 A CN202210696424 A CN 202210696424A CN 114781195 B CN114781195 B CN 114781195B
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闫林统
叶雨农
赵天宇
李嵬
汪志强
戴扬
高香珍
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CETC Information Science Research Institute
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Abstract

The utility model relates to a cementing lamellar ball structural design technical field provides a determining method of cementing lamellar ball structure's stress and cementing layer incidence relation, includes: establishing a cementing layered ball structure model based on the preset material, thickness and outer surface stress of the cementing layered ball structure; determining stress solution of the cementing layered ball structure model under the stress of the outer surface according to an elastic mechanics basic equation and preset boundary conditions, wherein the stress solution contains the progression; verifying the convergence of the stress solution according to different values of the series, and determining the series during convergence as a target series; respectively calculating to obtain stress curves corresponding to the glued joint laminated ball structure models with different materials and thicknesses according to the determined target stress solution corresponding to the target grade; based on each stress curve, a relation table of the stress of the glued joint laminated ball structure model and the glued joint layer material and the thickness is established. The method provides effective guidance for selecting the material and thickness of the cementing layer according to the stress requirement in the practical situation of engineering.

Description

Method for determining incidence relation between stress of glued laminated ball structure and glued layer
Technical Field
The disclosure relates to the technical field of design of glued laminated ball structures, in particular to a method for determining an incidence relation between stress and a glued layer of a glued laminated ball structure.
Background
In the traditional production process of the glued laminated ball structure, because the glued layer is too thin, the shape of the glued layer material can be greatly changed after processing and forming, and after the glued laminated ball structure is formed, because of the sealing property of the spherical structure, the glued layer can be wrapped, so that the stress test of the glued layer becomes difficult, and the reliability of a finished product can not be ensured.
In the design of the glued laminated ball structure, a large number of samples are needed to test by the traditional empirical forward design method, so that more waste is often caused, the accuracy of the result is not high, and the strength of the glued laminated ball structure is not reliable. The cementing lamellar spherical structure can generate larger volume change and stress concentration phenomenon in the using process, and the advanced composite material formed by the cementing lamellar spherical structure can often cause the change of mechanics and volume and even failure and microcrack because of the difference of cementing layers in the process of realizing various advanced functions. Meanwhile, under the conditions of heating, wetting, temperature change or impact and the like, the performance of the cementing material is unstable, and the service life of the cementing material cannot be ensured, so that the strength of the cementing lamellar ball structure is further reduced, and the shell layer is easily peeled off.
Disclosure of Invention
The present disclosure is directed to solve at least one of the problems of the prior art, and provides a method for determining a relationship between a stress of a bonded laminated ball structure and a bonded layer.
In one aspect of the present disclosure, a method for determining a relationship between stress of a bonded laminated ball structure and a bonding layer is provided, including:
establishing a cementing layered ball structure model based on the preset material, thickness and outer surface stress of the cementing layered ball structure;
determining stress solution of the cementing layered ball structure model under the stress of the outer surface according to an elastic mechanics basic equation and preset boundary conditions, wherein the stress solution contains the progression;
verifying the convergence of the stress solution according to different values of the series, and determining the series during convergence as a target series;
respectively calculating stress curves corresponding to the cementing layered ball structure models with different materials and thicknesses according to the determined target stress solution corresponding to the target level;
based on each stress curve, a relation table of the stress of the glued joint layer-shaped ball structure model, the glued joint layer material and the glued joint layer thickness is established.
Optionally, the stress curves corresponding to the cemented lamellar ball structure models of different materials and thicknesses are respectively calculated according to the determined target stress solution corresponding to the target progression, and the method includes:
and respectively keeping the thickness of the adhesive layer unchanged under the conditions that the materials of the inner layer and the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Young modulus of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model.
Optionally, the stress curves corresponding to the cemented lamellar ball structure models of different materials and thicknesses are respectively calculated according to the determined target stress solution corresponding to the target progression, and the method includes:
and respectively keeping the thickness of the adhesive layer unchanged under the conditions that the materials of the inner layer and the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Poisson ratio of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model.
Optionally, the stress curves corresponding to the cemented lamellar ball structure models of different materials and thicknesses are respectively calculated according to the determined target stress solution corresponding to the target progression, and the method includes:
and respectively keeping the material of the glue joint layer unchanged under the conditions that the materials of the inner layer and the outer layer connected by the glue joint layer in the glue joint layered ball structure model are the same and the materials are different, and changing the thickness of the glue joint layer to obtain a stress curve corresponding to the glue joint layered ball structure model.
Alternatively, the outer surface stresses are expressed as radially symmetric equispaced point loads.
Optionally, the elastic mechanics basic equation includes a physical equation, a balance equation and a geometric equation; wherein,
the physical equation is used to express the relationship between stress and strain, and is expressed by the following formula (1):
Figure DEST_PATH_IMAGE001
wherein,ithe numbers of the materials in the glued laminated ball structure model are shown,i=Iwhich represents the material of the inner layer or layers,i=IIthe outer layer material is shown as being,i=gwhich means the material of the glue joint layer,λ i andG i each representing the packing constant of material i and determined by the physical properties of material i itself,
Figure DEST_PATH_IMAGE002
representing material i in a spherical coordinate systemrA positive stress in a direction of the beam,
Figure DEST_PATH_IMAGE003
representing material i in a spherical coordinate systemθThe direction of the positive stress is the direction of the positive stress,
Figure DEST_PATH_IMAGE004
representing material i in a spherical coordinate system
Figure DEST_PATH_IMAGE005
The direction of the positive stress is the direction of the positive stress,
Figure DEST_PATH_IMAGE006
representing material i in a spherical coordinate systemrA positive strain in the direction of the strain,
Figure DEST_PATH_IMAGE007
representing material i in a spherical coordinate systemθA positive strain in the direction of the strain,
Figure DEST_PATH_IMAGE008
representing material i in a spherical coordinate system
Figure 505044DEST_PATH_IMAGE005
A positive strain in the direction of the strain,
Figure DEST_PATH_IMAGE009
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 9843DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure DEST_PATH_IMAGE010
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the direction,
Figure DEST_PATH_IMAGE011
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 839653DEST_PATH_IMAGE005
The shear stress in the direction of the steel wire,
Figure DEST_PATH_IMAGE012
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 746298DEST_PATH_IMAGE005
The shear strain in the direction of the direction,
Figure DEST_PATH_IMAGE013
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear strain in the direction of the direction,
Figure DEST_PATH_IMAGE014
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 370570DEST_PATH_IMAGE005
The direction shear strain is that a spherical coordinate system is established by taking the spherical center of the glue joint layered spherical structure model as an origin, and the glue joint layered spherical structure model sequentially comprises a hollow sphere, an inner layer, a glue joint layer and an outer layer from inside to outside;
the equilibrium equation is expressed as the following formula (2):
Figure DEST_PATH_IMAGE015
（2）
wherein,r、θ、
Figure 628245DEST_PATH_IMAGE005
respectively in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 275127DEST_PATH_IMAGE005
A coordinate component of the direction;
the geometric equation is used to express the relationship between strain and displacement, and is expressed by the following formula (3):
Figure DEST_PATH_IMAGE016
（3）
wherein,
Figure DEST_PATH_IMAGE017
respectively represent the material i in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 226159DEST_PATH_IMAGE005
A displacement component of direction.
Optionally, the boundary conditions include a boundary condition of the outer layer, a boundary condition of the inner layer, a boundary condition of a contact surface of the inner layer and the adhesive layer, and a boundary condition of a contact surface of the outer layer and the adhesive layer; wherein,
the boundary condition of the outer layer is represented by the following formula (4):
Figure DEST_PATH_IMAGE018
wherein,
Figure DEST_PATH_IMAGE019
representing the material of the outer layer in a spherical coordinate systemrA positive stress in a direction of the beam,
Figure DEST_PATH_IMAGE020
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction of
Figure 95369DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure DEST_PATH_IMAGE021
the normal direction of the outer layer material in a spherical coordinate system is represented asrDirection and direction ofθThe shear stress in the direction of the direction,θ 0 representing the angle of the range of point load forces to the axis of the point load forces,prepresenting the uniform point load and expressed by the following formula (5),Fthe force of concentration is represented by the force of concentration,Rshowing the outer diameter of the cemented lamellar sphere structural model,
Figure 574760DEST_PATH_IMAGE019
expressed by using Legendre-Fourier series expansion as the following formula (6),nthe number of stages in the stress solution is represented,E n2 is an intermediate variable and is represented by the following formula (7),P n2 representing the legendre series of even powers,P n2-1 legendre series representing odd powers:
Figure DEST_PATH_IMAGE022
Figure DEST_PATH_IMAGE023
Figure DEST_PATH_IMAGE024
the boundary condition of the inner layer is represented by the following formula (8), wherein,
Figure DEST_PATH_IMAGE025
represents the positive stress of the inner layer material in the r direction in a spherical coordinate system,
Figure DEST_PATH_IMAGE026
represents the normal direction of the inner layer material in a spherical coordinate systemrDirection and direction of
Figure 198902DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure DEST_PATH_IMAGE027
the normal direction of the inner layer material in a spherical coordinate system is represented asrDirection and direction ofθThe shear stress in the direction of the direction,p 0 shows the normal stress of the interface between the inner layer and the hollow sphere:
Figure DEST_PATH_IMAGE028
the boundary condition of the contact surface of the inner layer and the adhesive layer is represented by the following formula (9),
Figure DEST_PATH_IMAGE029
showing the normal stress of the cementing layer material in the r direction in the spherical coordinate system,
Figure DEST_PATH_IMAGE030
the normal direction of the material of the cementing layer in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the steel wire,
Figure DEST_PATH_IMAGE031
respectively represents the displacement components of the inner layer material and the cementing layer material in the r direction in a spherical coordinate system,
Figure DEST_PATH_IMAGE032
respectively represents the inner layer material and the cementing layer material in a spherical coordinate systemθDisplacement component of direction:
Figure DEST_PATH_IMAGE033
the boundary condition of the contact surface of the outer layer and the adhesive layer is represented by the following formula (10):
Figure DEST_PATH_IMAGE034
wherein,
Figure DEST_PATH_IMAGE035
respectively represent the outer layer material in a spherical coordinate systemrDirection (b),θA displacement component of direction.
Alternatively, the stress solution of the cemented lamellar sphere structure model under the stress of the outer surface is expressed by the following formula (11) to the following formula (14):
Figure DEST_PATH_IMAGE036
（11）
Figure DEST_PATH_IMAGE037
（12）
Figure DEST_PATH_IMAGE038
（13）
Figure DEST_PATH_IMAGE039
（14）
wherein,A n2 、B n2 、C n2 、D n2 are unknown coefficients and are determined according to the boundary conditions,
Figure DEST_PATH_IMAGE040
Figure DEST_PATH_IMAGE041
are all intermediate variables and are represented by the following formula (15):
Figure DEST_PATH_IMAGE042
（15）。
optionally, after establishing a table of relations between stress of the cemented lamellar sphere structure model and a material and a thickness of the cemented layer based on each stress curve, the method further includes:
and selecting a corresponding cementing layer material and a corresponding cementing layer thickness from the relation table based on the actual stress of the cementing layer-shaped ball structure model to obtain an actual cementing layer corresponding to the actual stress.
In another aspect of the present disclosure, there is provided an apparatus for determining a stress-cement layer correlation of a cement laminated ball structure, including:
the modeling module is used for establishing a cementing layered ball structure model based on the preset material, thickness and external surface stress of the cementing layered ball structure;
the determining module is used for determining the stress solution of the cementing laminated ball structure model under the external surface stress according to the elastic mechanics basic equation and the preset boundary condition, and the stress solution contains the number of stages;
the verification module is used for verifying the convergence of the stress solution according to different values of the series and determining the series during convergence as a target series;
the calculation module is used for respectively calculating stress curves corresponding to the glued joint laminated ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series;
and the establishing module is used for establishing a relation table of the stress of the adhesive layer-shaped ball structure model, the adhesive layer material and the adhesive layer thickness based on each stress curve.
Compared with the prior art, the stress of the glued laminated ball is analyzed by using the glued laminated ball structure model, the whole stress analysis graph corresponding to the glued laminated ball is drawn by changing the material parameters and the thickness of the glued layer, the stress curve of the relation between the stress of the glued laminated ball and the material parameters and the thickness of the glued layer is obtained, the incidence relation between the stress of the glued laminated ball and the material and the thickness of the glued layer is extracted, and the corresponding relation table is obtained, so that the problems of serious sample waste, high test difficulty, low test result precision and the like in the traditional glued laminated ball structure design are solved, effective guidance is provided for selecting the glued laminated material and the thickness according to the stress requirement in the actual engineering situation, and the stability of the glued laminated ball and the service life of the glued layer in the actual engineering situation are improved.
Drawings
One or more embodiments are illustrated by way of example in the accompanying drawings, which correspond to the figures in which like reference numerals refer to similar elements and which are not to scale unless otherwise specified.
Fig. 1 is a flowchart of a method for determining a correlation between stress and a bonding layer of a bonded layered ball structure according to an embodiment of the disclosure;
fig. 2 (a) is a schematic cross-sectional structure view of a cemented layered ball structure model according to another embodiment of the present disclosure;
fig. 2 (b) is a schematic diagram of a spherical coordinate system according to another embodiment of the present disclosure;
FIG. 3 is a stress plot corresponding to stress solutions at different orders provided by another embodiment of the present disclosure;
FIG. 4 is a stress curve diagram corresponding to the change in Young's modulus of the adhesive layer when the inner layer and the outer layer are made of the same material according to another embodiment of the disclosure;
FIG. 5 is a stress plot corresponding to a change in Young's modulus of the adhesive layer for a case where the Young's modulus of the inner layer material is lower than that of the outer layer material provided by another embodiment of the present disclosure;
FIG. 6 is a stress plot corresponding to a change in Young's modulus of the adhesive layer when the Young's modulus of the inner layer material is higher than that of the outer layer material according to another embodiment of the disclosure;
FIG. 7 is a stress plot illustrating the Poisson's ratio change of a cementitious layer for the same materials of the inner and outer layers according to another embodiment of the present disclosure;
FIG. 8 is a stress plot corresponding to a change in Poisson's ratio for an adhesive layer where the Young's modulus of the inner layer material is lower than the Young's modulus of the outer layer material provided by another embodiment of the present disclosure;
FIG. 9 is a stress plot corresponding to a change in Poisson's ratio for an adhesive layer where the Young's modulus of the inner layer material is higher than the Young's modulus of the outer layer material according to another embodiment of the present disclosure;
FIG. 10 is a stress profile corresponding to a change in thickness of an adhesive layer when the inner and outer layers are made of the same material according to another embodiment of the disclosure;
FIG. 11 is a graph of stress versus thickness change for an adhesive layer having a lower Young's modulus for an inner layer material than for an outer layer material, according to another embodiment of the present disclosure;
FIG. 12 is a stress profile corresponding to a change in thickness of an adhesive layer where the Young's modulus of the inner layer material is higher than the Young's modulus of the outer layer material according to another embodiment of the disclosure;
fig. 13 is a schematic structural diagram of an apparatus for determining a relationship between stress and a bonded layer in a bonded layered ball structure according to another embodiment of the present disclosure.
Detailed Description
In recent years, the structural problem of the multi-shell sphere has become the most popular research problem in the field because of its powerful function. The electrode material, the photocatalyst, the drug carrier and the super capacitor prepared by the multi-shell hollow sphere have excellent performances. For example, the iridium-carbon electrode layered hollow sphere for catalytic oxygen evolution can be used as an advanced electrode material for lithium storage; novel SnO prepared by utilizing hollow sphere structure 2 The lamellar hollow sphere catalyst has better photocatalytic performance; the layered polymer hollow sphere with independent temperature and PH dual responses can be used for drug delivery; the NiO/ZnO layered hollow sphere prepared by using the nickel oxide and zinc oxide materials can be used for manufacturing a high-performance super capacitor.
However, the multi-shell hollow sphere has large volume change and stress concentration phenomenon in the using process. Evidence shows that in the process of realizing various advanced functions, the advanced composite material prepared by the multi-shell hollow sphere is often changed in mechanics and volume due to different connection modes, even fails or generates microcracks, and the advanced composite material becomes an important bottleneck problem in industrial application of the functional material with the multi-shell hollow sphere structure from a laboratory.
Because the mutual extrusion of the advanced composite material in the actual working process can be similar to the radial point load action, the stress distribution research of the multi-shell hollow sphere under the radial point load action has important research value.
In 1966, Hiramatsu and Oka obtained accurate analytic solutions of isotropic solid spheres under the action of radial point load, and provided a classical basis for point load strength tests. In 1998, Gregory obtains an approximate solution of the thick shell hollow sphere under the action of axially symmetric concentrated force. In 1999, Chau and Wei obtained an accurate analytical solution of a spherical isotropic solid sphere under the action of point load. In 2009, Wei obtained accurate analytical solutions of orthotropic solid spheres under point loading, which can be accurately degraded to the classical solutions of Hiramatsu and Oka, and at the same time, completely coincided with the test results of Frocht and Guernsey under isotropic conditions. In 2015, Wei researches isotropic hollow spheres to obtain an accurate analytic solution of the isotropic hollow spheres under the action of radial point load. In 2019, Yan and Wei also obtain an accurate analytic solution of a two-shell solid sphere under the action of point load by researching the multi-shell hollow sphere. The research lays a solid theoretical foundation for the research of the multi-shell hollow sphere under the action of point load.
However, the above researches relate to the research of the multi-shell solid or hollow sphere under the action of radial load, and the research does not relate to the stress analysis of the connection mode between the layers in the multi-shell sphere.
The traditional connection modes comprise glue joint, welding, mechanical connection and the like. Glue as a connected mode commonly used, compare in other connected modes, glue the lamellar ball and can make the interfacial stress distribution between shell and the glue film even, improve the fatigue resistance and the life of junction by a wide margin, improve the dynamic behavior of component, and simultaneously, whole gluey face can both bear load, total mechanical structure intensity is higher, structure weight is lighter, have better sealed, insulating, thermal-insulated, dampproofing and shock-absorbing function, and, the glued mode can also be connected various same or different materials, simple process, high production efficiency.
However, the lifetime of the glued material is not stable under wet heat, temperature changes or impact, which further reduces the strength of the glued laminated ball structure, resulting in that the outer shell layer is easily peeled off.
To make the objects, technical solutions and advantages of the embodiments of the present disclosure more apparent, the embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. However, it will be appreciated by those of ordinary skill in the art that in various embodiments of the disclosure, numerous technical details are set forth in order to provide a better understanding of the disclosure. However, the technical solution claimed in the present disclosure can be implemented without these technical details and various changes and modifications based on the following embodiments. The following embodiments are divided for convenience of description, and no limitation should be made to specific implementations of the present disclosure, and the embodiments may be mutually incorporated and referred to without contradiction.
One embodiment of the present disclosure relates to a method for determining a relationship between stress and a bonding layer of a bonded laminated ball structure, where a flow of the method is shown in fig. 1, and the method includes:
step 101, establishing a cementing layered ball structure model based on the preset material, thickness and outer surface stress of the cementing layered ball structure.
Specifically, as shown in fig. 2 (a), the bonded layered spherical structural model may sequentially include a hollow sphere, an inner layer, a bonding layer, and an outer layer from inside to outside, where the bonding layer is bonded to the inner layer and the outer layer to connect the inner layer and the outer layer, respectively, so as to obtain a structural model in which the two shell hollow spheres are bonded. The material of the inner layer and the material of the outer layer may be the same or different, and this embodiment is not limited thereto.
Illustratively, the outer surface stresses may be expressed as radially symmetric, uniform point loads. As in fig. 2The outer surface stress can be expressed as a load magnitude ofpThe point loads are radially symmetrically and uniformly distributed.
Compared with the modeling research of the overall structure formed by the glued laminated balls in the prior art, the modeling research of the single glued laminated ball as a unit from a microscopic angle is realized by representing the stress of the outer surface as the radially symmetrical uniformly distributed point loads and approximating the contact points between the glued laminated balls as the point loads, and the detection accuracy of the stress of the glued laminated layer in the glued laminated ball structure is improved.
And 102, determining a stress solution of the cementing layered ball structure model under the stress of the outer surface according to an elastic mechanics basic equation and a preset boundary condition, wherein the stress solution contains a series.
Specifically, on the basis of the glued laminated ball structure model, the stress solution of the glued laminated ball structure model under the external surface stress is obtained by combining an elastic mechanics basic equation and a preset boundary condition, and when the external surface stress is expressed as radially symmetrical uniformly distributed point loads, the stress solution is the stress solution of the glued laminated ball structure model under the action of the point loads.
Illustratively, the elastic mechanics basic equations include physical equations, equilibrium equations, and geometric equations.
The physical equation is used to express the relationship between stress and strain, and can be expressed as the following formula (1):
Figure 917023DEST_PATH_IMAGE001
wherein i represents the number of materials in the cementing laminated ball structure model,i=Iwhich represents the material of the inner layer,i=IIthe material of the outer layer is shown,i=gwhich means the material of the glue joint layer,λ i andG i each represents the lark constant of material i and is determined by the physical properties of material i itself,
Figure 427639DEST_PATH_IMAGE002
represents a material i inIn a spherical coordinate systemrThe direction of the positive stress is the direction of the positive stress,
Figure 269693DEST_PATH_IMAGE003
representing material i in a spherical coordinate systemθThe direction of the positive stress is the direction of the positive stress,
Figure 261307DEST_PATH_IMAGE004
representing material i in a spherical coordinate system
Figure 872417DEST_PATH_IMAGE005
The direction of the positive stress is the direction of the positive stress,
Figure 553934DEST_PATH_IMAGE006
representing material i in a spherical coordinate systemrA positive strain in the direction of the strain,
Figure 414443DEST_PATH_IMAGE007
representing material i in a spherical coordinate systemθA positive strain in the direction of the strain,
Figure 472397DEST_PATH_IMAGE008
representing material i in a spherical coordinate system
Figure 206523DEST_PATH_IMAGE005
A positive strain in the direction of the strain,
Figure 324520DEST_PATH_IMAGE009
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 875587DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 206074DEST_PATH_IMAGE010
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the direction,
Figure 588514DEST_PATH_IMAGE011
the normal direction of the material i in the spherical coordinate system is shown asrDirection and fingerXiang Wei
Figure 815096DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 184285DEST_PATH_IMAGE012
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 318463DEST_PATH_IMAGE005
The shear strain in the direction of the direction,
Figure 758672DEST_PATH_IMAGE013
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear strain in the direction of the direction,
Figure 687314DEST_PATH_IMAGE014
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 275290DEST_PATH_IMAGE005
Directional shear strain.
As shown in fig. 2 (b), the spherical coordinate system is established with the center of the cemented lamellar spherical structure model as the origin. Points in the spherical coordinate system are denoted byr,θ,
Figure 150842DEST_PATH_IMAGE005
) Then, thenrThe direction represents from the origin o to the point: (r,θ,
Figure 256943DEST_PATH_IMAGE005
) In the direction of (a) of (b),θdirection represents from the z-axis to a point: (r,θ,
Figure 622065DEST_PATH_IMAGE005
) In the direction of the radius of the shaft,
Figure 635021DEST_PATH_IMAGE005
direction denotes counterclockwise from the x-axis to a point: (r,θ,
Figure 376581DEST_PATH_IMAGE005
) In the direction of the projection of the xy plane.
Neglecting physical effects, the balance equation can be expressed as the following equation (2):
Figure 525802DEST_PATH_IMAGE015
（2）
wherein,r、θ、
Figure 61826DEST_PATH_IMAGE005
respectively in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 361745DEST_PATH_IMAGE005
The coordinate component of the direction.
The geometric equation is used to express the relationship between strain and displacement, and can be expressed as the following equation (3):
Figure 579099DEST_PATH_IMAGE016
（3）
wherein,
Figure 910724DEST_PATH_IMAGE017
respectively represent the material i in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 555332DEST_PATH_IMAGE005
A displacement component of direction.
Exemplary boundary conditions include those of the outer layer, those of the inner layer, those of the interface of the inner layer with the adhesive layer, and those of the interface of the outer layer with the adhesive layer.
The boundary condition of the outer layer, i.e., the boundary condition of the outer surface of the cemented lamellar sphere structure model, can be expressed as the following formula (4):
Figure 74038DEST_PATH_IMAGE018
wherein,
Figure 157400DEST_PATH_IMAGE019
representing the material of the outer layer in a spherical coordinate systemrThe direction of the positive stress is the direction of the positive stress,
Figure 815302DEST_PATH_IMAGE020
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction of
Figure 958707DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 167972DEST_PATH_IMAGE021
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the direction,θ 0 representing the angle of the range of point load forces to the axis of the point load forces,prepresenting the uniform point load and expressed by the following formula (5),Fthe force of concentration is represented by the force of concentration,Rrepresents the outer diameter of the cementing layered ball structure model, namely the distance between the outer surface of the cementing layered ball structure model and the center of the ball,
Figure 789446DEST_PATH_IMAGE019
expressed as the following formula (6) by using Legendre-Fourier series expansion,nthe number of stages in the stress solution is represented,E n2 is an intermediate variable and is represented by the following formula (7),P n2 representing the legendre series of even powers,P n2-1 legendre series representing odd powers:
Figure 564504DEST_PATH_IMAGE022
Figure 613232DEST_PATH_IMAGE023
Figure 109459DEST_PATH_IMAGE024
the boundary condition of the inner layer, i.e., the boundary condition of the contact surface of the inner layer with the hollow ball, may be expressed as the following formula (8), wherein,
Figure 472308DEST_PATH_IMAGE025
represents the positive stress of the inner layer material in the r direction in a spherical coordinate system,
Figure 101872DEST_PATH_IMAGE026
the normal direction of the inner layer material in a spherical coordinate system is represented asrDirection and direction of
Figure 587080DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 302095DEST_PATH_IMAGE027
the normal direction of the inner layer material in a spherical coordinate system is represented asrDirection and direction ofθThe shear stress in the direction of the direction,p 0 shows the normal stress of the interface between the inner layer and the hollow sphere:
Figure 991004DEST_PATH_IMAGE028
the boundary condition of the contact surface of the inner layer with the adhesive layer can be expressed as the following formula (9), wherein,
Figure 6233DEST_PATH_IMAGE029
showing the normal stress of the cementing layer material in the r direction in the spherical coordinate system,
Figure 600026DEST_PATH_IMAGE030
the normal direction of the cementing layer material in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the direction,
Figure 802337DEST_PATH_IMAGE031
respectively represents the displacement components of the inner layer material and the cementing layer material in the r direction in a spherical coordinate system,
Figure 834884DEST_PATH_IMAGE032
respectively showing the material of the inner layer and the material of the cementing layer in a spherical coordinate systemθDisplacement component of direction:
Figure 642303DEST_PATH_IMAGE033
the boundary condition of the interface of the outer layer with the adhesive layer can be expressed as the following formula (10):
Figure 206664DEST_PATH_IMAGE034
wherein,
Figure 161850DEST_PATH_IMAGE035
respectively represent the outer layer material in a spherical coordinate systemrDirection (b),θA displacement component of direction.
Illustratively, general analytical expressions of the stresses at all positions of the bonded layered ball structure model can be obtained by using the above formulas (1) to (3), and a stress solution of the bonded layered ball structure model under the stress of the outer surface is obtained, which is expressed by the following formulas (11) to (14):
Figure 201350DEST_PATH_IMAGE036
（11）
Figure 128855DEST_PATH_IMAGE037
（12）
Figure 861188DEST_PATH_IMAGE038
（13）
Figure 38091DEST_PATH_IMAGE039
（14）
wherein,A n2 、B n2 、C n2 、D n2 are unknown coefficients and are determined from the boundary conditions, i.e. from equations (4) to (10) above. Specifically, the parameters satisfying the boundary conditions in the above expressions (11) to (14), that is, the parameters satisfying the above expressions (4) to (10) except for the unknown coefficients, are used as known coefficients, and the corresponding parameters in the known coefficients are respectively substituted into the above expressions (11) to (14), so that the solution can be obtainedA n2 、B n2 、C n2 、D n2 And further obtain the corresponding stress solution.
Figure 884212DEST_PATH_IMAGE040
Figure 462961DEST_PATH_IMAGE041
Are all intermediate variables and are represented by the following formula (15):
Figure 631774DEST_PATH_IMAGE042
（15）。
and 103, verifying the convergence of the stress solution according to different values of the series, and determining the series during convergence as a target series.
Specifically, when the number of stages in the stress solution is n, since n cannot be infinite in the actual solution process of the stress solution, it is necessary to determine a target number of stages that can converge the stress solution, that is, to determine the value of the number of stages n at which the stress solution converges.
And step 104, respectively calculating to obtain stress curves corresponding to the cementing layered ball structure models with different materials and thicknesses according to the determined target stress solution corresponding to the target grade.
Specifically, the target stress solution corresponding to the target progression can be obtained by replacing the progression in the stress solution with the target progression. Under the target stress solution, the materials and the thicknesses of the inner layer, the adhesive layer and the outer layer in the adhesive layered ball structure model are respectively adjusted, and stress curves corresponding to adhesive layered ball structure models with different materials and thicknesses can be respectively calculated.
Illustratively, step 104 may include:
and respectively keeping the thickness of the adhesive layer unchanged under the conditions that the materials of the inner layer and the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Young modulus of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model.
Specifically, since the young's modulus is a physical quantity describing the deformation resistance of a solid material, the young's modulus of the same material is the same, the young's modulus of different materials is different, and the larger the young's modulus is, the more rigid the material is, the less deformation is likely to occur, therefore, the case that the inner layer and the outer layer are the same in material and different in material can be specifically divided into three types: the young's modulus of the inner layer material is equal to that of the outer layer material, the young's modulus of the inner layer material is lower than that of the outer layer material, and the young's modulus of the inner layer material is higher than that of the outer layer material.
And respectively keeping the thickness of the adhesive layer unchanged under the three conditions, changing the Young modulus of the adhesive layer to obtain stress curves corresponding to the adhesive layered ball structure model, and thus respectively obtaining the influence of the Young modulus change of the adhesive layer on the stress of the adhesive layered ball structure model under the three conditions.
Illustratively, step 104 may include:
and respectively keeping the thickness of the adhesive layer unchanged under the conditions that the materials of the inner layer and the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Poisson ratio of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model.
Specifically, the situations that the materials of the inner layer and the outer layer are the same and the materials are different are also divided into three types: the case where the young's modulus of the inner layer material is equal to that of the outer layer material, the case where the young's modulus of the inner layer material is lower than that of the outer layer material, or the case where the young's modulus of the inner layer material is higher than that of the outer layer material.
And respectively keeping the thickness of the adhesive layer unchanged under the three conditions, changing the Poisson ratio of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model, and thus respectively obtaining the influence of the Poisson ratio change of the adhesive layer on the stress of the adhesive layered ball structure model under the three conditions.
Illustratively, step 104 may include:
and respectively keeping the material of the glue joint layer unchanged under the conditions that the materials of the inner layer and the outer layer connected by the glue joint layer in the glue joint layered ball structure model are the same and the materials are different, and changing the thickness of the glue joint layer to obtain a stress curve corresponding to the glue joint layered ball structure model.
Specifically, the same material and different material of the inner layer and the outer layer are divided into three types: the young's modulus of the inner layer material is equal to that of the outer layer material, the young's modulus of the inner layer material is lower than that of the outer layer material, and the young's modulus of the inner layer material is higher than that of the outer layer material.
And respectively keeping the material of the glue joint layer unchanged under the three conditions, changing the thickness of the glue joint layer to obtain a stress curve corresponding to the glue joint layered ball structure model, and thus respectively obtaining the influence of the thickness change of the glue joint layer on the stress of the glue joint layered ball structure model under the three conditions.
And 105, establishing a relation table of the stress of the adhesive layer-shaped ball structure model, the adhesive layer material and the adhesive layer thickness based on each stress curve.
For example, in this step, a relationship table between the stress of the bonded layered ball structure model and the thickness of the bonded layer material and the thickness of the bonded layer may be established according to the influence of the young's modulus change, the poisson's ratio change, and the thickness change of the bonded layer on the stress of the bonded layered ball structure model under different conditions, that is, according to each stress curve corresponding to the bonded layered ball structure model under different conditions. The relation table may include a corresponding relation between the stress of the glue joint layered ball structure model and the young's modulus of the glue joint layer material and the thickness of the glue joint layer under the condition that the inner layer and the outer layer are made of the same material or different materials, so as to obtain the correlation between the stress of the glue joint layered ball structure and the glue joint layer.
Compared with the prior art, the stress of the glued laminated ball is analyzed by using the glued laminated ball structure model, the whole stress analysis graph corresponding to the glued laminated ball is drawn by changing the material parameters and the thickness of the glued layer, the stress curve of the relation between the stress of the glued laminated ball and the material parameters and the thickness of the glued layer is obtained, the incidence relation between the stress of the glued laminated ball and the material and the thickness of the glued layer is extracted, and the corresponding relation table is obtained, so that the problems of serious sample waste, high test difficulty, low test result precision and the like in the traditional glued laminated ball structure design are solved, effective guidance is provided for selecting the glued layer material and the thickness according to the stress requirement in the actual engineering situation, and the stability of the glued laminated ball and the service life of the glued layer in the actual engineering situation are improved.
Illustratively, after step 105, the method further comprises:
and selecting a corresponding cementing layer material and a corresponding cementing layer thickness from the relation table based on the actual stress of the cementing layer-shaped ball structure model to obtain an actual cementing layer corresponding to the actual stress.
Specifically, the relation table records the corresponding relation between the stress of the glued laminated ball structure model and the thickness of the glued layer material and the glued layer thickness, so that under the condition that the actual stress of the glued laminated ball structure model is determined, the corresponding glued layer material and the thickness of the glued layer can be selected according to the relation table, and the actual glued layer corresponding to the actual stress is obtained, so that the inverted design, the accurate design and the optimized design of the glued laminated ball structure are realized, and the glued laminated ball which is more solid and reliable can be produced and prepared in the engineering practice.
In order to enable those skilled in the art to better understand the above embodiments, a specific example is described below.
A method for determining the incidence relation between the stress of a glued laminated ball structure and a glued layer comprises the following steps:
the method comprises the following steps: modeling is performed for a cemented layered ball structure.
As shown in FIG. 2 (a), the material of the inner layer of the glued layered ball is referred to asⅠThe material of the outer layer is denotedⅡMaterials for the adhesive layer are denotedgThe internal diameter of the hollow ball is marked asR 0 The radius of the contact surface of the inner layer and the adhesive layer is recorded asR 1 The radius of the contact surface of the outer layer and the adhesive layer is recorded asR 2 The radius of the outer surface of the cemented layer is given asRThe external surface stress is expressed as a radially symmetrical uniform point load and the magnitude of the load is recorded aspAnd obtaining a structural model of the two shell hollow spheres in glue joint, namely a glue joint layered sphere structural model.
As shown in fig. 2 (b), a spherical coordinate system is established with the center of the glue laminated ball structure model as the origin. Points in the spherical coordinate system are denoted byr,θ,
Figure 30394DEST_PATH_IMAGE005
)，r、θ、
Figure 677276DEST_PATH_IMAGE005
Respectively represent the point in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 113461DEST_PATH_IMAGE005
The coordinate component of the direction is,rthe direction represents from the origin o to a point: (r,θ,
Figure 453176DEST_PATH_IMAGE005
) In the direction of (a) of (b),θdirection represents from the z-axis to a point: (r,θ,
Figure 339092DEST_PATH_IMAGE005
) In the direction of the radius of the shaft,
Figure 992928DEST_PATH_IMAGE005
direction means from the x-axis in a counter-clockwise direction toPoint (A)r,θ,
Figure 280689DEST_PATH_IMAGE005
) In the direction of the projection of the xy plane.
Step two: on the basis of the cementing laminated ball structure model, determining the stress solution of the cementing laminated ball structure model under the external surface stress by combining an elastic mechanics basic equation and a preset boundary condition, wherein the stress solution contains the order n.
The elastic mechanics basic equations include physical equations, equilibrium equations, and geometric equations. The physical equation shows the relationship between stress and strain, and can be expressed as the following formula (1):
Figure 791305DEST_PATH_IMAGE001
wherein,ithe numbers of the materials in the glued laminated ball structure model are shown,i=Iwhich represents the material of the inner layer,i=IIthe material of the outer layer is shown,i=gwhich means the material of the glue joint layer,λ i andG i each representing the packing constant of material i and determined by the physical properties of material i itself,
Figure 444745DEST_PATH_IMAGE002
representing material i in a spherical coordinate systemrThe direction of the positive stress is the direction of the positive stress,
Figure 636692DEST_PATH_IMAGE003
representing material i in a spherical coordinate systemθThe direction of the positive stress is the direction of the positive stress,
Figure 778961DEST_PATH_IMAGE004
representing material i in a spherical coordinate system
Figure 726057DEST_PATH_IMAGE005
The direction of the positive stress is the direction of the positive stress,
Figure 789828DEST_PATH_IMAGE006
represents a material i inIn a spherical coordinate systemrA positive strain in the direction of the beam,
Figure 316624DEST_PATH_IMAGE007
representing material i in a spherical coordinate systemθA positive strain in the direction of the strain,
Figure 378646DEST_PATH_IMAGE008
representing material i in a spherical coordinate system
Figure 231064DEST_PATH_IMAGE005
A positive strain in the direction of the strain,
Figure 516552DEST_PATH_IMAGE009
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 378197DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 495058DEST_PATH_IMAGE010
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the steel wire,
Figure 255728DEST_PATH_IMAGE011
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 90829DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 225007DEST_PATH_IMAGE012
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 196374DEST_PATH_IMAGE005
The shear strain in the direction of the direction,
Figure 390595DEST_PATH_IMAGE013
the normal direction of the material i in the spherical coordinate system is shown asrDirectionIs directed toθThe shear strain in the direction of the direction,
Figure 650675DEST_PATH_IMAGE014
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 591474DEST_PATH_IMAGE005
Directional shear strain.
Neglecting physical effects, the balance equation is expressed as the following formula (2):
Figure 682927DEST_PATH_IMAGE015
（2）
wherein,rthe value range of (1) is 0 toR. When in userThe value of (a) is within a range of 0 toR 0 In time (in time of), (r,θ,
Figure 782470DEST_PATH_IMAGE005
) Representing points within the hollow sphere. When in userIs taken asR 0 At the time point (r,θ,
Figure 857742DEST_PATH_IMAGE005
) Indicating the points in the interface of the inner layer with the hollow spheres. When in userIs taken from the value ofR 0 ~R 1 In time (in time of), (r,θ,
Figure 536985DEST_PATH_IMAGE005
) Representing dots in the inner layer. When in userIs taken asR 1 At the time point (r,θ,
Figure 482944DEST_PATH_IMAGE005
) Indicating a point in the interface of the inner layer with the adhesive layer. When in userIs taken from the value ofR 1 ~R 2 In time (in time of), (r,θ,
Figure 744599DEST_PATH_IMAGE005
) Indicating a point in the glue layer. When in userIs taken asR 2 Time, point (a)r,θ,
Figure 776009DEST_PATH_IMAGE005
) Indicating a point in the interface of the outer layer with the adhesive layer. When in userIs taken from the value ofR 2 ~RIn time (in time of), (r,θ,
Figure 55681DEST_PATH_IMAGE005
) Representing points in the outer layer. When in userIs taken asRAt the time point (r,θ,
Figure 856147DEST_PATH_IMAGE005
) Representing points in the outer surface of the cemented lamellar sphere structure model.
The geometric equation represents the relationship between strain and displacement, and is expressed by the following formula (3):
Figure 828651DEST_PATH_IMAGE016
（3）
wherein,
Figure 553549DEST_PATH_IMAGE017
respectively represent the material i in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 371332DEST_PATH_IMAGE005
A displacement component of direction.
The boundary conditions comprise the boundary conditions of the outer layer, the boundary conditions of the inner layer, the boundary conditions of the contact surface of the inner layer and the cementing layer and the boundary conditions of the contact surface of the outer layer and the cementing layer.
The boundary condition of the outer layer is represented by the following formula (4):
Figure 291884DEST_PATH_IMAGE018
wherein,
Figure 169710DEST_PATH_IMAGE019
representing the material of the outer layer in a spherical coordinate systemrThe direction of the positive stress is the direction of the positive stress,
Figure 910133DEST_PATH_IMAGE020
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction of
Figure 797186DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 575174DEST_PATH_IMAGE021
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the steel wire,θ 0 representing the angle of the range of point load forces to the axis of the point load forces,prepresenting the uniform point load and expressed by the following formula (5),Fthe force of concentration is represented by the force of concentration,
Figure 623901DEST_PATH_IMAGE019
expressed by using Legendre-Fourier series expansion as the following formula (6),E n2 is an intermediate variable and is represented by the following formula (7),P n2 representing the legendre series of even powers,P n2-1 legendre series representing odd powers:
Figure 586041DEST_PATH_IMAGE022
Figure 745627DEST_PATH_IMAGE023
Figure 578454DEST_PATH_IMAGE024
the boundary condition of the inner layer, i.e., the boundary condition of the interface between the hollow sphere and the inner layer, is represented by the following formula (8),
Figure 798082DEST_PATH_IMAGE025
represents the positive stress of the inner layer material in the r direction in a spherical coordinate system,
Figure 516027DEST_PATH_IMAGE026
the normal direction of the inner layer material in a spherical coordinate system is represented asrDirection and direction of
Figure 744883DEST_PATH_IMAGE005
The shear stress in the direction of the steel wire,
Figure 494533DEST_PATH_IMAGE027
the normal direction of the inner layer material in a spherical coordinate system is represented asrDirection and direction ofθThe shear stress in the direction of the direction,p 0 shows the normal stress of the interface between the inner layer and the hollow sphere:
Figure 885064DEST_PATH_IMAGE028
the boundary condition of the contact surface of the inner layer and the adhesive layer is represented by the following formula (9),
Figure 556216DEST_PATH_IMAGE029
represents the normal stress of the cementing layer material in the r direction in a spherical coordinate system,
Figure 72253DEST_PATH_IMAGE030
the normal direction of the cementing layer material in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the direction,
Figure 676410DEST_PATH_IMAGE031
respectively represents the displacement components of the inner layer material and the cementing layer material in the r direction in a spherical coordinate system,
Figure 237841DEST_PATH_IMAGE032
respectively showing the material of the inner layer and the material of the cementing layer in a spherical coordinate systemθDisplacement component of direction:
Figure 130711DEST_PATH_IMAGE033
the boundary condition of the interface of the outer layer with the adhesive layer can be expressed as the following formula (10):
Figure 701370DEST_PATH_IMAGE034
wherein,
Figure 425612DEST_PATH_IMAGE035
respectively represent the outer layer material in a spherical coordinate systemrDirection (b),θA displacement component of direction.
By using the above formulas (1) to (3), a general analytical expression of the stress at each position of the bonded layered ball structure model can be obtained, and a stress solution of the bonded layered ball structure model under the stress of the outer surface is obtained, which is expressed by the following formulas (11) to (14):
Figure 160874DEST_PATH_IMAGE036
（11）
Figure 541040DEST_PATH_IMAGE037
（12）
Figure 649810DEST_PATH_IMAGE038
（13）
Figure 228559DEST_PATH_IMAGE039
（14）
wherein,A n2 、B n2 、C n2 、D n2 for the unknown coefficients and in dependence on the boundary conditions, i.e. parameters of the above equations (11) to (14) other than the unknown coefficients which satisfy the boundary conditions, i.e. which satisfy the above equations (4) to (10), are knownThe coefficients are then substituted into the above equations (11) to (14) to obtain the corresponding parametersA n2 、B n2 、C n2 、D n2 。
Figure 335055DEST_PATH_IMAGE040
Figure 798922DEST_PATH_IMAGE041
Are all intermediate variables and are represented by the following formula (15):
Figure 242542DEST_PATH_IMAGE042
（15）。
step three: and verifying the convergence of the stress solution according to different values of the series n, and determining the series n during convergence as a target series. For the number of stages n in the stress solution, since n cannot be infinite in the actual solving process, a target number of stages that can converge the stress solution, that is, a value of the number of stages n at the time of convergence of the stress solution, needs to be determined. In the verification process, stress solutions when n is a value of 5, 10, 20, 30 or more than 30 can be respectively calculated to obtain corresponding stress curves. As shown in fig. 3, the predetermined reference stress is
Figure DEST_PATH_IMAGE043
、rA positive stress in a direction of
Figure 100002_DEST_PATH_IMAGE044
、θA positive stress in a direction of
Figure DEST_PATH_IMAGE045
In this case, the larger n is, the higher the fitting degree of the stress curve is, and the more the stress solution is converged. As proved by verification, when n is larger than or equal to 30, the fitting degree of the stress curve is high, and the stress solution is converged, so that n is larger than or equal to 30 can be determined as a target series, and the stress solution when n is larger than or equal to 30 can be determined as a target stress solution.
Step four: according to the target stress solution, under the condition that the materials of the inner layer and the outer layer are the same and the materials are different, the thickness of the adhesive layer is kept unchanged, the Young modulus of the adhesive layer is changed, and a corresponding stress curve is obtained. By usingE g Which represents the young's modulus of the adhesive bond layer,E I representing the young's modulus of the inner layer material, this step specifically comprises:
under the condition that the materials of the inner layer and the outer layer are the same, the thickness of the adhesive layer is kept unchanged, the Young modulus of the adhesive layer is changed, and a stress curve corresponding to the target stress solution is obtained, as shown in FIG. 4.
Under the condition that the Young's modulus of the inner layer material is lower than that of the outer layer material, the thickness of the adhesive layer is kept unchanged, the Young's modulus of the adhesive layer is changed, and a stress curve corresponding to target stress solution is obtained, as shown in FIG. 5.
Under the condition that the Young's modulus of the inner layer material is higher than that of the outer layer material, the Young's modulus of the adhesive layer is changed while the thickness of the adhesive layer is kept unchanged, so that a stress curve corresponding to the target stress solution is obtained, as shown in FIG. 6.
Step five: according to the target stress solution, under the condition that the materials of the inner layer and the outer layer are the same and the materials are different, the thickness of the adhesive layer is kept unchanged, the Poisson ratio of the adhesive layer is changed, and a corresponding stress curve is obtained. By usingv g Showing the Poisson's ratio of the adhesive layer, the method specifically comprises the following steps:
under the condition that the materials of the inner layer and the outer layer are the same, the thickness of the cementing layer is kept unchanged, the Poisson ratio of the cementing layer is changed, and a stress curve corresponding to the target stress solution is obtained, as shown in FIG. 7.
Under the condition that the Young's modulus of the inner layer material is lower than that of the outer layer material, the thickness of the adhesive layer is kept unchanged, the Poisson ratio of the adhesive layer is changed, and a stress curve corresponding to a target stress solution is obtained, as shown in FIG. 8.
Under the condition that the Young modulus of the inner layer material is higher than that of the outer layer material, the thickness of the adhesive layer is kept unchanged, the Poisson ratio of the adhesive layer is changed, and a stress curve corresponding to a target stress solution is obtained, as shown in FIG. 9.
Step six: according to the target stress solution, under the condition that the materials of the inner layer and the outer layer are the same and different, the material of the adhesive layer is kept unchanged, the thickness of the adhesive layer is changed, and a corresponding stress curve is obtained. By usingR g Which represents the thickness of the glue joint layer,R I indicating the thickness of the inner layer material, the steps specifically include:
under the condition that the materials of the inner layer and the outer layer are the same, the material of the adhesive layer is kept unchanged, the thickness of the adhesive layer is changed, and a stress curve corresponding to the target stress solution is obtained, as shown in fig. 10.
Under the condition that the young modulus of the inner layer material is lower than that of the outer layer material, the material of the adhesive layer is kept unchanged, the thickness of the adhesive layer is changed, and a stress curve corresponding to the target stress solution is obtained, as shown in fig. 11.
Under the condition that the Young modulus of the inner layer material is higher than that of the outer layer material, the material of the adhesive layer is kept unchanged, the thickness of the adhesive layer is changed, and a stress curve corresponding to the target stress solution is obtained, as shown in FIG. 12.
Step seven: based on each stress curve, a relation table of the stress of the cementing layer-shaped ball structure model, the cementing layer material and the cementing layer thickness is established. The relationship table may be as shown in table 1 below. Wherein, the maximum tensile stress of the adhesive surface refers to the normal stress of the contact surface of the outer layer and the adhesive surface, and the tensile stress of the inner surface refers to the normal stress of the contact surface of the inner layer and the hollow ball. The relation table can provide guidance for the design of the glued laminated ball structure and the selection of the gluing material in the actual engineering situation. For example, the corresponding material and thickness of the adhesive layer can be selected from the relation table according to the actual engineering stress intensity index to obtain the actual material and thickness of the adhesive layer corresponding to the actual engineering stress intensity index, so as to produce and prepare the adhesive layered ball under the actual engineering stress intensity index.
TABLE 1 Association between stress and adhesive layer of adhesive layered ball structure
Figure DEST_PATH_IMAGE046
Another embodiment of the present disclosure relates to an apparatus for determining a stress-adhesive layer correlation of an adhesive laminated ball structure, as shown in fig. 13, including:
the modeling module 1301 is used for establishing a cementing layered ball structure model based on the preset material, thickness and external surface stress of the cementing layered ball structure;
a determining module 1302, configured to determine a stress solution of the cemented layered ball structure model under the external surface stress according to a basic equation of elasticity and a preset boundary condition, where the stress solution includes a number of stages;
the verification module 1303 is used for verifying the convergence of the stress solution according to different values of the series and determining the series during convergence as a target series;
a calculating module 1304, configured to respectively calculate stress curves corresponding to the bonded layered ball structure models of different materials and thicknesses according to the determined target stress solutions corresponding to the target levels;
the establishing module 1305 is configured to establish a relation table between the stress of the bonded layered ball structure model and the thickness of the bonded layer material and the bonded layer thickness based on each stress curve.
The concrete implementation method of the apparatus for determining the incidence relation between the stress of the glued joint laminated ball structure and the glued joint layer provided by the embodiment of the present disclosure can be referred to as the method for determining the incidence relation between the stress of the glued joint laminated ball structure and the glued joint layer provided by the embodiment of the present disclosure, and details thereof are not repeated here.
Compared with the prior art, the stress of the glued laminated ball is analyzed by using the glued laminated ball structure model, the whole stress analysis graph corresponding to the glued laminated ball is drawn by changing the material parameters and the thickness of the glued layer, the stress curve of the relation between the stress of the glued laminated ball and the material parameters and the thickness of the glued layer is obtained, the incidence relation between the stress of the glued laminated ball and the material and the thickness of the glued layer is extracted, and the corresponding relation table is obtained, so that the problems of serious sample waste, high test difficulty, low test result precision and the like in the traditional glued laminated ball structure design are solved, effective guidance is provided for selecting the glued layer material and the thickness according to the stress requirement in the actual engineering situation, and the stability of the glued laminated ball and the service life of the glued layer in the actual engineering situation are improved.
It will be understood by those of ordinary skill in the art that the foregoing embodiments are specific embodiments for practicing the present disclosure, and that various changes in form and details may be made therein without departing from the spirit and scope of the present disclosure in practice.

Claims (6)

1. A method for determining the correlation between the stress of a glued laminated ball structure and a glued layer is characterized by comprising the following steps:
establishing a cementing layered ball structure model based on the preset material, thickness and outer surface stress of the cementing layered ball structure;
determining a stress solution of the cementing layered ball structure model under the external surface stress according to an elastic mechanics basic equation and a preset boundary condition, wherein the stress solution contains a series;
verifying the convergence of the stress solution according to different values of the series, and determining the series during convergence as a target series;
respectively calculating stress curves corresponding to the cementing layered ball structure models with different materials and thicknesses according to the determined target stress solution corresponding to the target level;
establishing a relation table of the stress of the cementing layer-shaped ball structure model, the cementing layer material and the cementing layer thickness based on each stress curve;
the outer surface stress is expressed as radially symmetrical uniform point load;
and respectively calculating stress curves corresponding to the cementing layered ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series, wherein the stress curves comprise: respectively keeping the thickness of the adhesive layer unchanged under the condition that the materials of the inner layer and the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Young modulus of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model;
or, respectively calculating to obtain stress curves corresponding to the cemented lamellar ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series, including: respectively keeping the thickness of the adhesive layer unchanged under the condition that the materials of an inner layer and an outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Poisson ratio of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model;
or, respectively calculating to obtain stress curves corresponding to the cemented lamellar ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series, including: and respectively keeping the material of the adhesive layer unchanged under the conditions that the material of the inner layer and the material of the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the thickness of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model.
2. The method of claim 1, wherein the elastic mechanics base equations include a physical equation, an equilibrium equation, and a geometric equation; wherein,
the physical equation is used to express the relationship between stress and strain, and is expressed by the following formula (1):
Figure 735069DEST_PATH_IMAGE001
（1）
wherein,ithe numbers of the materials in the glued laminated ball structure model are shown,i=Iwhich represents the material of the inner layer,i=IIthe outer layer material is shown as being,i=gwhich means the material of the glue joint layer,λ i andG i each representing the packing constant of material i and determined by the physical properties of material i itself,
Figure 842702DEST_PATH_IMAGE002
representing material i in a spherical coordinate systemrPositive of directionThe stress is applied to the surface of the steel sheet,
Figure 50961DEST_PATH_IMAGE003
representing material i in a spherical coordinate systemθThe direction of the positive stress is the direction of the positive stress,
Figure 193229DEST_PATH_IMAGE004
representing material i in a spherical coordinate system
Figure 828741DEST_PATH_IMAGE005
The direction of the positive stress is the direction of the positive stress,
Figure 174403DEST_PATH_IMAGE006
representing material i in a spherical coordinate systemrA positive strain in the direction of the strain,
Figure 435620DEST_PATH_IMAGE007
representing material i in a spherical coordinate systemθA positive strain in the direction of the strain,
Figure 917548DEST_PATH_IMAGE008
representing material i in a spherical coordinate system
Figure 238808DEST_PATH_IMAGE005
A positive strain in the direction of the strain,
Figure 806186DEST_PATH_IMAGE009
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 605515DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 207529DEST_PATH_IMAGE010
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the steel wire,
Figure 699690DEST_PATH_IMAGE011
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 754365DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 357385DEST_PATH_IMAGE012
the normal direction of the material i in the spherical coordinate system is shown asθDirection and direction of
Figure 813905DEST_PATH_IMAGE005
The shear strain in the direction of the direction,
Figure 227700DEST_PATH_IMAGE013
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction ofθThe shear strain in the direction of the direction,
Figure 18938DEST_PATH_IMAGE014
the normal direction of the material i in the spherical coordinate system is shown asrDirection and direction of
Figure 176381DEST_PATH_IMAGE005
The spherical coordinate system is established by taking the spherical center of the glued laminated spherical structure model as an origin, and the glued laminated spherical structure model sequentially comprises a hollow sphere, an inner layer, a glued layer and an outer layer from inside to outside;
the equilibrium equation is expressed as the following formula (2):
Figure 736676DEST_PATH_IMAGE015
（2）
wherein,r、θ、
Figure 321372DEST_PATH_IMAGE005
respectively in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 334327DEST_PATH_IMAGE005
A coordinate component of the direction;
the geometric equation is used to express the relationship between strain and displacement, and is expressed by the following formula (3):
Figure 295461DEST_PATH_IMAGE016
（3）
wherein,
Figure 710262DEST_PATH_IMAGE017
respectively represent the material i in a spherical coordinate systemrDirection (b),θDirection (b),
Figure 465860DEST_PATH_IMAGE005
A displacement component of direction.
3. The method of claim 2, wherein the boundary conditions comprise a boundary condition of the outer layer, a boundary condition of the inner layer, a boundary condition of the interface of the inner layer with the adhesive layer, a boundary condition of the interface of the outer layer with the adhesive layer; wherein,
the boundary condition of the outer layer is represented by the following formula (4):
Figure 966111DEST_PATH_IMAGE018
（4）
wherein,
Figure 188059DEST_PATH_IMAGE019
representing the material of the outer layer in a spherical coordinate systemrThe direction of the positive stress is the direction of the positive stress,
Figure 988524DEST_PATH_IMAGE020
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction of
Figure 915023DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 918882DEST_PATH_IMAGE021
the normal direction of the outer layer material in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the direction,θ 0 representing the angle of the range of point load forces to the axis of the point load forces,prepresents the uniform point load and is expressed by the following formula (5),Fthe force of concentration is represented by the force of concentration,Rrepresents the outer diameter of the cemented lamellar sphere structure model,
Figure 205507DEST_PATH_IMAGE019
expressed as the following formula (6) by using Legendre-Fourier series expansion,nrepresenting the number of stages in the stress solution,E n2 is an intermediate variable and is represented by the following formula (7),P n2 representing the legendre series of even powers,P n2-1 legendre series representing odd powers:
Figure 345633DEST_PATH_IMAGE022
（5）
Figure 692300DEST_PATH_IMAGE023
（6）
Figure 183456DEST_PATH_IMAGE024
（7）
the boundary condition of the inner layer is represented by the following formula (8), wherein,
Figure 273772DEST_PATH_IMAGE025
represents the positive stress of the inner layer material in the r direction in a spherical coordinate system,
Figure 268403DEST_PATH_IMAGE026
the normal direction of the inner layer material in a spherical coordinate system is represented asrDirection and direction of
Figure 520393DEST_PATH_IMAGE005
The shear stress in the direction of the direction,
Figure 498845DEST_PATH_IMAGE027
represents the normal direction of the inner layer material in a spherical coordinate systemrDirection and direction ofθThe shear stress in the direction of the steel wire,p 0 shows the normal stress of the interface of the inner layer and the hollow sphere:
Figure 127272DEST_PATH_IMAGE028
（8）
the boundary condition of the contact surface of the inner layer and the adhesive layer is expressed as the following formula (9),
Figure 241990DEST_PATH_IMAGE029
showing the normal stress of the cementing layer material in the r direction in the spherical coordinate system,
Figure 664881DEST_PATH_IMAGE030
the normal direction of the material of the cementing layer in a spherical coordinate system is shown asrDirection and direction ofθThe shear stress in the direction of the steel wire,
Figure 865049DEST_PATH_IMAGE031
respectively represents the displacement components of the inner layer material and the cementing layer material in the r direction in a spherical coordinate system,
Figure 297168DEST_PATH_IMAGE032
respectively showing the material of the inner layer and the material of the cementing layer in a spherical coordinate systemθDisplacement component of direction:
Figure 266392DEST_PATH_IMAGE033
（9）
the boundary condition of the contact surface of the outer layer and the adhesive layer is represented by the following formula (10):
Figure 876496DEST_PATH_IMAGE034
（10）
wherein,
Figure 547648DEST_PATH_IMAGE035
respectively represent the outer layer material in a spherical coordinate systemrDirection (b),θA displacement component of direction.
4. The method of claim 3, wherein the cemented lamellar sphere structure model has a stress solution under the outer surface stress represented by the following equations (11) to (14):
Figure 799769DEST_PATH_IMAGE036
（11）
Figure 872768DEST_PATH_IMAGE037
（12）
Figure 919352DEST_PATH_IMAGE038
（13）
Figure 77801DEST_PATH_IMAGE039
（14）
wherein,
Figure 602454DEST_PATH_IMAGE040
for unknown coefficients and determined from the boundary conditions,
Figure 529959DEST_PATH_IMAGE041
Figure 747445DEST_PATH_IMAGE042
are all intermediate variables and are represented by the following formula (15):
Figure DEST_PATH_IMAGE044
（15）。
5. the method of claim 1, wherein after the step of building a table of relationships between the stress of the cemented lamellar ball structure model and the materials and the thickness of the cemented layer based on each stress curve, the method further comprises:
and selecting a corresponding cementing layer material and a corresponding cementing layer thickness from the relation table based on the actual stress of the cementing layer-shaped spherical structure model to obtain an actual cementing layer corresponding to the actual stress.
6. An apparatus for determining a relationship between stress of a bonded laminated ball structure and a bonding layer, the apparatus comprising:
the modeling module is used for establishing a cementing layered ball structure model based on the preset material, thickness and external surface stress of the cementing layered ball structure;
the determining module is used for determining a stress solution of the cementing layered ball structure model under the external surface stress according to an elastic mechanics basic equation and a preset boundary condition, wherein the stress solution contains a series;
the verification module is used for verifying the convergence of the stress solution according to different values of the series and determining the series during convergence as a target series;
the calculation module is used for respectively calculating stress curves corresponding to the glued joint laminated ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series;
the building module is used for building a relation table of the stress of the cementing layer-shaped ball structure model, the cementing layer material and the cementing layer thickness based on each stress curve;
the outer surface stress is expressed as radially symmetrical uniform point load;
and respectively calculating stress curves corresponding to the cementing layered ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series, wherein the stress curves comprise: respectively keeping the thickness of the adhesive layer unchanged under the conditions that the materials of an inner layer and an outer layer connected by the adhesive layer in the adhesive layer-shaped ball structure model are the same and the materials are different, and changing the Young modulus of the adhesive layer to obtain a stress curve corresponding to the adhesive layer-shaped ball structure model;
or, respectively calculating to obtain stress curves corresponding to the cemented lamellar ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series, including: respectively keeping the thickness of the adhesive layer unchanged under the condition that the materials of an inner layer and an outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the Poisson ratio of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model;
or, respectively calculating to obtain stress curves corresponding to the glued joint laminated ball structure models with different materials and thicknesses according to the determined target stress solutions corresponding to the target series, wherein the stress curves comprise: and respectively keeping the material of the adhesive layer unchanged under the conditions that the material of the inner layer and the material of the outer layer connected by the adhesive layer in the adhesive layered ball structure model are the same and the materials are different, and changing the thickness of the adhesive layer to obtain a stress curve corresponding to the adhesive layered ball structure model.
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