CN112149286A - Thermodynamic characteristic numerical simulation method and system based on equivalent particle hypothesis - Google Patents
Thermodynamic characteristic numerical simulation method and system based on equivalent particle hypothesis Download PDFInfo
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Abstract
The invention belongs to the technical field related to numerical simulation algorithms, and discloses a thermal characteristic numerical simulation method based on equivalent particle hypothesis, which comprises the following steps: s1, the three-dimensional entity is equivalent to a space geometry composed of a plurality of equivalent particles; s2, establishing a connection relation between adjacent equivalent particles, and acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at the moment t; s3, obtaining the temperature field at the next moment t + dt, updating the thermal balance distance according to the temperature difference between the moment t and the moment t + dt, and obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance, so as to obtain the thermal deformation of the three-dimensional entity in the whole temperature field change process until the temperature field change is finished. A thermal characteristic numerical simulation system based on equivalent particle assumption is also provided. The method is based on the modeling of the balance distance, and does not need to add point constraint or surface constraint without physical facts into the model, so that the precision and the speed of solving are improved.
Description
Technical Field
The invention belongs to the technical field related to numerical simulation algorithms, and particularly relates to a thermal characteristic numerical simulation method and system based on equivalent particle hypothesis.
Background
At present, the thermal stress simulation technology in the casting process is mainly based on numerical simulation methods such as a finite element method, a finite volume method, a finite difference method and the like. The finite difference method is mature when applied to the simulation of a temperature field, but is limited to a certain extent when used for simulating complex parts with irregular geometric shapes; the finite element method can adapt to parts with complex shapes, but the computation process of the finite element method is complex and the computation amount is large.
The theoretical model adopted by the thermal stress simulation in the casting process is a partial differential equation for describing the thermal elastoplasticity mechanics problem, the equation is constructed based on static balance, geometric relation and constitutive equation, and the stress balance of external load and internal stress on the surface of an object, and under the framework of the theoretical model, the thermodynamic process is described as a quasi-static process, namely, the deviation of a system from a balance state in the process is infinitely small, and the balance state is recovered at any time. Based on the situation, current research and commercial software adopts a static implicit algorithm to calculate the thermal stress, the method needs to iteratively solve a static equilibrium equation in each incremental step, and a large linear equation set needs to be solved in each iteration, although the incremental step in the implicit algorithm is much larger than that in the explicit algorithm, the actual calculation process is limited by the nonlinear degree, and the implicit algorithm is not friendly to high-grade nonlinear problems such as contact and friction, needs to be iteratively calculated repeatedly, and can generate solution drift. The casting solidification process involves nonlinearity of material nonlinearity and contact problems, and is a typical nonlinearity problem, and as the structure of the casting is more and more complex, grids for describing the structure of the casting are more and more, and a linear equation set constructed by an implicit algorithm is larger and larger, so that the reason shows that the calculation amount of the implicit algorithm is huge due to the nonlinearity problems and the increase of the number of the grids. Secondly, when describing the thermal deformation process of the object, the equilibrium equation based on the thermo-elastic-plastic theory must constrain the degree of freedom of the solid, for example, the thermal deformation of the object placed on a plane must be solved by adding point or plane constraints without physical facts, which also affects the precision of the solution result.
Therefore, the numerical simulation calculation amount of the thermal stress in the casting process is too large, and the static implicit algorithm is difficult to be applied to the simulation calculation under the nonlinear condition, and the like, so that a new thermal deformation and thermal stress model and a corresponding algorithm in the casting solidification process are urgently needed to be provided.
Disclosure of Invention
In view of the above-mentioned deficiencies in the art or needs for improvement, the present invention provides a method and system for numerical simulation of thermal characteristics based on equivalent particle assumptions. The three-dimensional entity is equivalent into a plurality of equivalent particles, the three-dimensional entity can generate thermal deformation under the action of a temperature field, the geometric balance distance is driven by the thermal balance distance of the equivalent particles subjected to temperature change, the thermal deformation of the three-dimensional entity is realized, the model is not based on stress conservation but based on the balance distance modeling, point constraint or surface constraint without physical facts does not need to be added into the model, and the solving precision is improved.
To achieve the above object, according to one aspect of the present invention, there is provided a method for numerical simulation of thermal characteristics based on equivalent particle assumption, the method comprising: s1, the three-dimensional entity is equivalent to a space geometry composed of a plurality of equivalent particles; s2, establishing a connection relation between adjacent equivalent particles, and acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at time t, wherein the thermal balance distance is an equivalent distance between two equivalent particles related to temperature, and the geometric balance distance is a steady-state geometric distance between an equivalent particle and an adjacent equivalent particle under the determined temperature; s3, obtaining the temperature field at the next moment t + dt, updating the thermal balance distance according to the temperature difference between the moment t and the moment t + dt, and obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance, so as to obtain the thermal deformation of the three-dimensional entity in the whole temperature field change process until the temperature field change is finished.
Preferably, the updated calculation formula of the thermal equilibrium distance is:
wherein the content of the first and second substances,
the thermal equilibrium distance at time t + dt, i.e. the updated thermal equilibrium distance,
is the thermal equilibrium distance at time T, T1Is equivalent particle P1Temperature change in dt time, T2Is equivalent particle P2Temperature change in dt time, the equivalent point P1And equivalent point P2Two equivalent particles which are connected adjacently.
Preferably, in step S3, obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance specifically includes:
s31, obtaining a thermal balance displacement vector and a geometric displacement vector of the equivalent particle Pi, wherein the thermal balance displacement vector is a vector taking an origin as a starting point and a thermal balance position as an end point, the geometric displacement vector is a vector taking the origin as a starting point and a calculated geometric position as an end point, and the equivalent particle PiA vector connected adjacent to the equivalent point P is 1 … … N;
s32, acquiring a geometric displacement trend vector of the equivalent particle P according to the thermal balance displacement vector and the geometric displacement vector;
s33, acting the geometric displacement trend vector on the equivalent mass point P to obtain the iterative geometric position of the equivalent mass point P;
and S34, repeating the steps S31-S33 until the calculated geometric displacement trend vector is smaller than a preset value, namely obtaining the updated geometric balance position of the equivalent particle P.
Preferably, the geometric displacement trend vector d of the equivalent particle PsThe calculation formula of (2) is as follows:
wherein E is an iteration coefficient, E is less than or equal to 0.25,
for the purpose of the thermal equilibrium displacement vector,
and N is the total number of equivalent points adjacent to the equivalent point P and is the geometric displacement vector.
Preferably, the step S31 further includes determining whether plastic deformation occurs under the thermal equilibrium displacement vector according to a paradigm equivalent stress criterion, if not, performing step S32, and if so, correcting the thermal equilibrium position to obtain a new thermal equilibrium position, wherein a correction coefficient d of the thermal equilibrium positionThe calculation formula of (2) is as follows:
d＝(E1-E2)·d6
wherein d isσIs the equivalent stress strain change value in time dt, E1Is the modulus of elasticity of the three-dimensional entity, E2Is the plastic modulus of the three-dimensional entity;
corrected thermal equilibrium distance between two equivalent particles
The calculation formula of (2) is as follows:
wherein the content of the first and second substances,
the thermal equilibrium distance between the two equivalent particles after the last iteration correction,
the resulting geometric balance distance is calculated for time t.
Preferably, the specific step of equating the three-dimensional entity to a plurality of equivalent particles in step S1 is:
if the three-dimensional entity is a cubic grid, taking the center of each cubic grid as an equivalent mass point;
and if the three-dimensional entity is an irregular grid, taking the vertex of the irregular grid as an equivalent particle.
Preferably, the method is applied in a casting process.
According to another aspect of the present invention, there is provided a thermal behavior numerical simulation system based on equivalent particle assumptions, the system comprising: the system comprises an equivalence module, a data processing module and a data processing module, wherein the equivalence module is used for enabling a three-dimensional entity to be equivalent to a space geometry consisting of a plurality of equivalent particles; the first acquisition module is used for establishing a connection relation between adjacent equivalent particles and acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at time t, wherein the thermal balance distance is characterized by the equivalent distance between the two equivalent particles related to temperature, and the geometric balance distance is characterized by determining the steady-state geometric distance between the equivalent particles and the adjacent equivalent particles; and the second acquisition module is used for acquiring the temperature field at the next moment t + dt, updating the thermal balance distance according to the temperature difference between the moment t and the moment t + dt, and acquiring a corresponding updated geometric balance distance according to the updated thermal balance distance until the temperature field is changed, so as to acquire the thermal deformation of the three-dimensional entity in the whole temperature field change process.
Preferably, the updated calculation formula of the thermal equilibrium distance is:
wherein the content of the first and second substances,
the thermal equilibrium distance at time t + dt, i.e. the updated thermal equilibrium distance,
is the thermal equilibrium distance at time T, T1Is equivalent particle P1Temperature change in dt time, T2Is equivalent particle P2Temperature change in dt time, the equivalent point P1And equivalent point P2Two equivalent particles which are connected adjacently.
In general, compared with the prior art, the method and the system for simulating the thermal characteristic value based on the equivalent particles provided by the invention have the following beneficial effects:
1. the model has the advantages that the three-dimensional entity is equivalent to a set consisting of a plurality of equivalent particles, so that the model computation is simplified, the simplification rule is simple, and the realization is easy;
2. the simplified model is not based on stress conservation but on equilibrium distance modeling, and point constraint or surface constraint without physical facts is not required to be added into the model, so that the solving precision is improved;
3. the model is an explicit algorithm and is easy to process nonlinear conditions, particularly the structure of the current casting is more complex, the nonlinear degree of the casting/casting mold contact model is higher and higher, and the nonlinear conditions of material physical property parameters in the casting stress field are met;
4. because the equivalent mass points are adopted, the geometric balance distance is driven by the thermal balance distance of the adjacent mass points, the parallel operation is easy, and compared with a static implicit algorithm, the multi-core parallel operation can be fully utilized to carry out the parallel operation, so that the calculation speed is greatly accelerated.
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FIG. 1 schematically illustrates a step diagram of a method of numerical simulation of thermal characteristics based on an equivalent particle assumption according to an embodiment of the disclosure;
FIG. 2 is a schematic diagram showing the positions of the thermal equilibrium distance and the geometric equilibrium distance of an equivalent particle P and its neighboring equivalent particles at time t according to the embodiment of the present disclosure;
FIG. 3 is a schematic diagram showing the positions of the thermal equilibrium distance and the geometric equilibrium distance of an equivalent particle P and its neighboring equivalent particles at time t + dt according to an embodiment of the present disclosure;
FIG. 4 schematically illustrates a block diagram of a thermal property numerical simulation system based on equivalent particle assumptions, in accordance with an embodiment of the present disclosure;
FIG. 5 schematically illustrates a flow chart of a method of numerical simulation of thermal behavior based on equivalent particle assumptions, according to another embodiment of the present disclosure;
FIG. 6 schematically illustrates a three-dimensional solid structure diagram according to another embodiment of the present disclosure;
fig. 7 is a diagram schematically showing a structure of equivalent particles obtained by discretizing the three-dimensional entity shown in fig. 6.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Example 1
Referring to fig. 1, the present invention provides a method for simulating thermal characteristic values based on the equivalent point assumption, which includes the following steps S1-S2.
And S1, the three-dimensional entity is equivalent to a space geometry composed of a plurality of equivalent particles.
In the disclosed embodiment, a three-dimensional entity is equivalent to a spatial geometry consisting of a set of equivalent particles, each equivalent particle describing information about the entity at the local site, each equivalent particle having an attribute, referred to as the equivalent volume, whose value represents the size of the volume described by the equivalent particle at the local site.
And if the three-dimensional entity is a cubic grid, taking the center of each cubic grid as an equivalent mass point, and taking the volume of each cube as an equivalent volume.
And if the three-dimensional entity is an irregular grid, taking the vertex of the irregular grid as an equivalent particle. Suppose that n number of irregular grids formed by participating in the vertices P are respectively numbered E1，E2，E3……EnWherein E isiContaining a number of vertices of Ni，EiHas a volume of ViThen the equivalent volume corresponding to the equivalent particle P is VpComprises the following steps:
and S2, establishing a connection relation between adjacent equivalent particles, and acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at the time t, wherein the thermal balance distance is characterized by the equivalent distance between the two equivalent particles related to the temperature, and the geometric balance distance is characterized by determining the steady-state geometric distance between the equivalent particle and the adjacent equivalent particle under the temperature.
The equivalent particles of "adjacent" have a connection relationship, and the concept of "adjacent" depends on the definition of the connection mode. For an equivalent point P, different connection modes define different sets of adjacent equivalent points, and an equivalent point pair having a connection relationship has two properties: thermal equilibrium distance LhAnd aggregate average distance LgWherein, the thermal equilibrium distance is used for characterizing and only considering the thermal expansion or cold contraction effect between two equivalent particles caused by temperature change; the geometric balance distance is characterized in that under the temperature distribution determined at a certain moment, the equivalent particle P is under the joint action of all the adjacent equivalent particlesThe position of each equivalent particle at the steady-state distance is the steady-state position. In the cooling process, the temperature changes to cause the transmission of the thermal equilibrium distance to change, the thermal equilibrium distance changes to enable the geometric equilibrium distance in the steady state to change into the unstable state again, and finally the geometric equilibrium distance reaches the stable state again through iterative calculation to obtain a new geometric equilibrium distance and a new steady-state position. Firstly, acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at the moment t, and further carrying out change analysis when the temperature field changes at the next moment.
S3, obtaining the temperature field at the next moment t + dt, updating the thermal balance distance according to the temperature difference between the moment t and the moment t + dt, and obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance, so as to obtain the thermal deformation of the three-dimensional entity in the whole temperature field change process until the temperature field change is finished.
Regarding the calculation of the thermal equilibrium distance, we make the following assumptions: for equivalent dots P1 and P2, the thermal equilibrium distance is L at a certain time, after dt time interval, the temperature at P1 changes by T1 degrees celsius, the temperature at P2 decreases by T2 degrees celsius, and the new updated thermal equilibrium distance is calculated as:
wherein the content of the first and second substances,
the thermal equilibrium distance at time t + dt, i.e. the updated thermal equilibrium distance,
is the thermal equilibrium distance at time T, T1Is equivalent particle P1Temperature change in dt time, T2Is equivalent particle P2Temperature change in dt time, the equivalent point P1And equivalent point P2Two equivalent particles connected adjacently are provided, alpha is (T)1+T2) And/2 the thermal expansion coefficient of the material at the temperature.
In step S3, obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance specifically includes:
s31, obtaining a thermal balance displacement vector and a geometric displacement vector of the equivalent particle Pi, wherein the thermal balance displacement vector is a vector taking an origin as a starting point and a thermal balance position as an end point, the geometric displacement vector is a vector taking the origin as a starting point and a calculated geometric position as an end point, and the equivalent particle PiA vector connected adjacent to the equivalent point P is 1 … … N;
regarding the calculation of the geometric equilibrium distance, a short time interval dt is considered, the time is changed from t to t + dt, and the thermal equilibrium distance and the geometric equilibrium distance of an equivalent dot P and its neighboring dots at the time t are shown in fig. 2, where P1, P2, P3 and P4 are the neighboring equivalent dots of the equivalent dot P. The black node position is a geometric equilibrium position of each equivalent particle at the time t, namely a steady-state position, each triangle position corresponds to a thermal equilibrium position of an adjacent equivalent node, the distance from each triangle position to the equivalent node P is a thermal equilibrium distance, the triangle nodes do not exist in the simulation process, and the thermal equilibrium distances are only expressed in order to display, and the equivalent particles P are subjected to the sum effect of the adjacent equivalent particles under the current condition to reach the steady state without displacement tendency.
After dt times, the thermal equilibrium position changes due to changes in the temperature field, resulting in a change in the thermal equilibrium distance of each equivalent particle. At the time t + dt, the thermal equilibrium positions of the adjacent equivalent points are changed from the triangle nodes to the quadrilateral nodes, as shown in fig. 3, the steady-state condition of the equivalent point P is broken, and to obtain the geometric equilibrium position of the equivalent point P, calculation needs to be performed according to the thermal equilibrium position and the geometric position of the equivalent point Pi adjacent to the equivalent point P, and the thermal equilibrium displacement vector of the equivalent point Pi is obtained
And geometric displacement vector
Calculating what displacement change is obtained through thermal displacement change in a reverse mode, judging whether plastic deformation occurs under the thermal equilibrium displacement vector according to a paradigm equivalent stress criterion, if not, executing the step S32, if so, correcting the thermal equilibrium position to obtain a new thermal equilibrium position, wherein the correction coefficient d of the thermal equilibrium positionThe calculation formula of (2) is as follows:
d＝(E1-E2)·dσ
wherein d isσIs the equivalent stress strain change value in time dt, E1Is the modulus of elasticity of the three-dimensional entity, E2Is the plastic modulus of the three-dimensional entity;
corrected thermal equilibrium distance between two equivalent particles
The calculation formula of (2) is as follows:
wherein the content of the first and second substances,
the thermal equilibrium distance between the equivalent particles for the last iteration of the corrected quantity,
the resulting geometric balance distance is calculated for time t.
And S32, acquiring the geometric displacement trend vector of the equivalent particle P according to the thermal balance displacement vector and the geometric displacement vector.
Geometric displacement trend vector dsThe calculation formula of (2) is as follows:
wherein the content of the first and second substances,
for the purpose of the thermal equilibrium displacement vector,
for the geometric displacement vector, N is the total number of equivalent particles adjacent to the equivalent particles P, E is an iteration coefficient, and theoretically, the size of E is between 0 and 1, but the applicant finds that iteration divergence is easy to occur when E is greater than 0.25 through calculation, so that E is greater than or equal to 0 and less than or equal to 0.25, and in the embodiment of the present disclosure, E is preferably equal to 0.2.
And S33, applying the geometric displacement trend vector to the equivalent particle P to obtain the iterative geometric position of the equivalent particle P.
Geometric displacement trend vector dsActing on the equivalent particle P to obtain a new position, updating the geometric equilibrium position for the position, and substituting the new value into the above formula again to obtain d of the next rounds。
And S34, repeating the steps S31-S33 until the calculated geometric displacement trend vector is smaller than a preset value, namely obtaining the updated geometric balance position of the equivalent particle P.
Repeating the steps S31-S33, and iteratively calculating until the geometric displacement trend vector dsSmall enough that the equivalent point is considered to have reached a new geometric equilibrium position at the current temperature conditions. And when the new geometric equilibrium position is reached, importing the files of the previous temperature field, updating the thermal equilibrium distance, and repeating the steps S1-S3 until all the files of the temperature field are processed.
The above method is particularly suitable for casting processes with constantly changing temperatures.
In another aspect, the present disclosure further provides a thermal behavior numerical simulation system based on equivalent particle assumption, as shown in fig. 4, the system 400 includes:
an equivalence module 410 for equating a three-dimensional entity to a spatial geometry consisting of a plurality of equivalent particles;
a first obtaining module 420, configured to establish a connection relationship between adjacent equivalent particles, and obtain a thermal balance distance, a geometric balance distance, and a temperature field in the connection relationship at time t, where the thermal balance distance is an equivalent distance between two equivalent particles related to temperature, and the geometric balance distance is a steady-state geometric distance between an equivalent particle and its adjacent equivalent particle at a certain temperature;
the second obtaining module 430 is configured to obtain a temperature field at a next time t + dt, update the thermal equilibrium distance according to a temperature difference between the time t and the time t + dt, and obtain a corresponding updated geometric equilibrium distance according to the updated thermal equilibrium distance, in this way, until a temperature field changes, so as to obtain a thermal deformation of the three-dimensional entity in the whole temperature field change process.
The updated calculation formula of the heat balance distance is as follows:
wherein the content of the first and second substances,
the thermal equilibrium distance at time t + dt, i.e. the updated thermal equilibrium distance,
is the thermal equilibrium distance at time T, T1Is equivalent particle P1Temperature change in dt time, T2Is equivalent particle P2Temperature change in dt time, the equivalent point P1And equivalent point P2Two equivalent particles which are connected adjacently.
Example 2
In the embodiment of the disclosure, as shown in fig. 5, for a three-dimensional entity, a space geometry of an equivalent particle combination is first constructed based on technologies such as finite difference grids, and then an initial thermal balance distance and an initial geometric balance distance are obtained by initializing a thermal balance distance and a geometric balance distance for the equivalent space geometry; then, reading the temperature field file at the current moment, wherein the thermal balance distance and the geometric mean distance at the current moment are the initialized thermal balance distance and the geometric balance distance, so that calculation is not needed, if the moment is not the initial moment, the thermal balance distance and the geometric balance distance need to be updated according to the temperature difference between the moment and the previous moment, in the embodiment of the disclosure, because the thermal balance distance and the geometric balance distance at the current moment are known, the judgment of whether the temperature field file at the next moment exists is directly carried out, if so, the temperature field file at the next moment is read, the thermal balance distance is updated according to the temperature difference between adjacent moments, then whether the geometric balance distance reaches a stable state is judged, if not, iterative calculation is continued, if the geometric balance state is reached, the iterative calculation at the next moment is carried out, until the entire temperature field is traversed.
Fig. 6 schematically illustrates a three-dimensional entity in an embodiment of the disclosure, the geometry of which is as follows: the profile has a length of 200mm, a width of 100mm and a height of 30mm, and the through-hole is located at the geometric center and has a diameter of 50 mm. As shown in fig. 7, first discretizing the three-dimensional model to obtain a set of equivalent particles with a discretization size of 2mm, and establishing a connection relationship between spatially adjacent equivalent particles according to a geometric relationship, in the embodiment of the present disclosure, each equivalent particle is connected with 26 surrounding adjacent equivalent particles. Then, the model is subjected to temperature field calculation, assuming that the length direction is an X axis, the width direction is a Y axis and the height direction is a Z axis, constant temperature boundary conditions are added on two surfaces parallel to an XZ plane, the lower surface is 20 ℃, the upper surface is 100 ℃, other surfaces are in contact with surrounding wrapping objects, and the thermophysical parameters of a three-dimensional entity, a wrapping object material and air are as shown in the following table 1.
TABLE 1
The temperature field simulation step length is 0.01s, and the temperature field data is stored every 1 s. And sequentially loading each temperature field data, performing iterative solution by adopting the algorithm, considering convergence when the data change of the current iteration and the later iteration is less than 10e-4, and performing the next temperature field calculation until all the temperature field calculations are completed.
In summary, the present application performs numerical simulation on the thermal characteristics of a three-dimensional entity based on the assumption of equivalent particles, and can make up for the defect that additional constraints must be added in thermal analysis under the current free boundary condition by using a surface variable temperature field, particularly suitable for the thermal deformation behavior of a material in the casting process. According to the method, the three-dimensional entity is simplified into a plurality of equivalent particles, the simplified model is not based on stress conservation but on equilibrium distance modeling, point constraint or surface constraint without physical facts is not required to be added into the model, the solving precision is improved, parallel computing is facilitated, and the computing speed is greatly improved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method for numerical simulation of thermal behavior based on an equivalent particle assumption, the method comprising:
s1, the three-dimensional entity is equivalent to a space geometry composed of a plurality of equivalent particles;
s2, establishing a connection relation between adjacent equivalent particles, and acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at time t, wherein the thermal balance distance is an equivalent distance between two equivalent particles related to temperature, and the geometric balance distance is a steady-state geometric distance between an equivalent particle and an adjacent equivalent particle under the determined temperature;
s3, obtaining the temperature field at the next moment t + dt, updating the thermal balance distance according to the temperature difference between the moment t and the moment t + dt, and obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance, so as to obtain the thermal deformation of the three-dimensional entity in the whole temperature field change process after the temperature field change is finished.
2. The numerical simulation method of claim 1, wherein the updated thermal equilibrium distance is calculated by the formula:
wherein the content of the first and second substances,
the thermal equilibrium distance at time t + dt, i.e. the updated thermal equilibrium distance,
is the thermal equilibrium distance at time T, T1Is equivalent particle P1Temperature change in dt time, T2Is equivalent particle P2Temperature change in dt time, the equivalent point P1And equivalent point P2Two equivalent particles connected adjacently are provided, alpha is (T)1+T2) And/2 the thermal expansion coefficient of the material at the temperature.
3. The numerical simulation method according to claim 2, wherein in step S3, obtaining the corresponding updated geometric balance distance according to the updated thermal balance distance specifically includes:
s31, obtaining equivalent particle PiThe thermal equilibrium displacement vector and the geometric displacement vector of (2), wherein the thermal equilibrium displacement vector is a vector with an origin as a starting point and a thermal equilibrium position as an end point, the geometric displacement vector is a vector with the origin as a starting point and a calculated geometric position as an end point, and the equivalent particle PiIs the vector connected adjacent to the equivalent point P, i is 1 … … N, N is the vector connected to the equivalent point PThe total number of equivalent particles connected to the adjacent particles P;
s32, acquiring a geometric displacement trend vector of the equivalent particle P according to the thermal balance displacement vector and the geometric displacement vector;
s33, acting the geometric displacement trend vector on the equivalent mass point P to obtain the iterative geometric position of the equivalent mass point P;
s34, repeating the steps S31-S33 until the calculated geometric displacement trend vector is smaller than a preset value, and obtaining the updated geometric balance position of the equivalent particle P.
4. A numerical simulation method according to claim 3, wherein the geometric displacement trend vector d of the equivalent particle P issThe calculation formula of (2) is as follows:
wherein E is an iteration coefficient, E is more than or equal to 0 and less than or equal to 1,
for the purpose of the thermal equilibrium displacement vector,
is the geometric displacement vector.
5. The numerical simulation method of claim 1, wherein E is 0. ltoreq. E.ltoreq.0.25.
6. The numerical simulation method of claim 1, wherein the step S31 further comprises determining whether plastic deformation occurs under the thermal equilibrium displacement vector according to a norm equivalent stress criterion, if no plastic deformation occurs, performing the step S32, and if plastic deformation occurs, correcting the thermal equilibrium position to obtain a new thermal equilibrium position, wherein the correction coefficient d of the thermal equilibrium positionThe calculation formula of (2) is as follows:
d＝(E1-E2)·dσ
wherein d isσIs the equivalent stress strain change value in time dt, E1Is the modulus of elasticity of the three-dimensional entity, E2Is the plastic modulus of the three-dimensional entity;
corrected thermal equilibrium distance between two equivalent particles
The calculation formula of (2) is as follows:
wherein the content of the first and second substances,
the thermal equilibrium distance between the two equivalent particles after the last iteration correction,
the resulting geometric balance distance is calculated for time t.
7. The numerical simulation method of claim 1, wherein the step of equating the three-dimensional entity to a plurality of equivalent particles in step S1 comprises the steps of:
if the three-dimensional entity is a cubic grid, taking the center of each cubic grid as an equivalent mass point;
and if the three-dimensional entity is an irregular grid, taking the vertex of the irregular grid as an equivalent particle.
8. A numerical simulation method according to claim 1, characterized in that the method is applied in a casting process.
9. A thermal performance numerical simulation system based on equivalent particle assumptions, the system comprising:
the system comprises an equivalence module, a data processing module and a data processing module, wherein the equivalence module is used for enabling a three-dimensional entity to be equivalent to a space geometry consisting of a plurality of equivalent particles;
the first acquisition module is used for establishing a connection relation between adjacent equivalent particles and acquiring a thermal balance distance, a geometric balance distance and a temperature field in the connection relation at time t, wherein the thermal balance distance is characterized by the equivalent distance between the two equivalent particles related to temperature, and the geometric balance distance is characterized by determining the steady-state geometric distance between the equivalent particles and the adjacent equivalent particles;
and the second acquisition module is used for acquiring the temperature field at the next moment t + dt, updating the thermal balance distance according to the temperature difference between the moment t and the moment t + dt, and acquiring a corresponding updated geometric balance distance according to the updated thermal balance distance until the temperature field is changed, so as to acquire the thermal deformation of the three-dimensional entity in the whole temperature field change process.
10. The numerical simulation system of claim 9, wherein the updated calculation formula of the thermal equilibrium distance is:
wherein the content of the first and second substances,
the thermal equilibrium distance at time t + dt, i.e. the updated thermal equilibrium distance,
is the thermal equilibrium distance at time T, T1Is equal toEffect point P1Temperature change in dt time, T2Is equivalent particle P2Temperature change in dt time, the equivalent point P1And equivalent point P2Two equivalent particles which are connected adjacently.
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