Rolling plastic deformation process calculation method and device based on meshless Galerkin method

Abstract

The embodiment of the invention discloses a rolling plastic deformation process calculation method and device based on a meshless Galerkin method. The method comprises the steps that a model of a rolling plastic deformation area is established; carrying out approximation on the velocity field function of the node by adopting a moving least square method to obtain a shape function; constructing a system discrete equation based on the shape function and the stream function field; based on the system discrete equation, building a total stiffness matrix by using Gaussian integral point information, a speed boundary condition and a friction boundary condition in a solution domain; building a load force matrix by utilizing boundary point information of the friction boundary; obtaining the speed distribution of each node by using the total stiffness matrix and the load force matrix; obtaining a stable velocity field by adopting a direct iteration method based on the velocity distribution; and calculating the rolling plastic deformation process by using the obtained velocity field. According to the method, the efficiency of calculating the rolling plastic deformation process based on the meshless Galerkin method can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation calculation of rolling plastic deformation process, and in particular to a calculation method and device of rolling plastic deformation process based on an elementless Galerkin method. Background Art

[0002] The rolling process is a problem involving multiple nonlinearities and multivariable coupling. At present, the finite element method is often used to simulate the rolling plastic deformation process. However, for rolling problems with large deformation, the finite element software has a large degree of mesh refinement in order to obtain a more accurate solution during the calculation process. In addition, the mesh is prone to distortion during the solution process and needs to be re-meshed. The transfer of new and old mesh data during mesh re-meshing can easily reduce the simulation accuracy, and in severe cases, the calculation will be terminated.

[0003] In the 1970s, the emergence of meshless method effectively solved the mesh distortion and re-division problems encountered by finite element method in solving large deformation problems. This method is based on node approximation, does not require node connection information, avoids cumbersome unit mesh generation, and provides field functions with good continuity and flexible form, so it has great advantages in analyzing large deformation problems.

[0004] Among many meshless methods, the meshless Galerkin method (EFG) has been widely used due to its high accuracy, good stability, and fast convergence speed. The meshless Galerkin method has the characteristics of high calculation accuracy, stable calculation, and no volume locking phenomenon. It is one of the most widely studied and applied methods among meshless methods. However, the meshless Galerkin method requires a large number of numerical integration and matrix inversion operations during the solution process, and the calculation efficiency is low. Summary of the invention

[0005] In order to solve at least one technical problem in the above-mentioned background technology, the present invention proposes a method and device for calculating the rolling plastic deformation process based on the element-free Galerkin method.

[0006] In order to achieve the above object, according to one aspect of the present invention, a method for calculating the rolling plastic deformation process based on the element-free Galerkin method is provided, the method comprising:

[0007] Establishing a model of the rolling plastic deformation zone, and arranging nodes, Gaussian integration points and boundary points in the model;

[0008] The velocity field function of the node is approximated by the moving least square method to obtain the shape function;

[0009] Constructing a system discrete equation based on the shape function and the stream function field, wherein the system discrete equation includes: contribution of node plastic deformation power to the total stiffness matrix, contribution of velocity boundary conditions to the total stiffness matrix, and contribution of friction boundary conditions to the total stiffness matrix;

[0010] Based on the system discrete equation, a total stiffness matrix is ​​constructed using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain;

[0011] The load force matrix is ​​constructed using the boundary point information of the friction boundary;

[0012] Using the total stiffness matrix and the load matrix, the velocity distribution of each node is obtained;

[0013] Based on the velocity distribution, a stable velocity field is obtained by using a direct iteration method;

[0014] The obtained velocity field is used to calculate the rolling plastic deformation process.

[0015] Optionally, the moving least squares method is used to approximate the velocity field function of the node to obtain the shape function, including:

[0016] Construct a weighted discrete sum of squares based on the velocity field function;

[0017] The linear equation is obtained by minimizing the weighted discrete sum of squares;

[0018] Substituting the linear equation into the approximate expression of the field function, we obtain the shape function.

[0019] Optionally, constructing a system discrete equation based on the shape function and the stream function field includes:

[0020] Establish the total energy consumption functional of the rolling process;

[0021] The first-order variation of the total energy consumption functional when taking a stationary value is equal to 0, and a weak function of the total energy consumption functional is obtained, wherein the solution of the boundary value problem is obtained when the total energy consumption functional takes a stationary value, and the first-order variation of the total energy consumption functional is 0 at this time;

[0022] A system discrete equation is constructed according to the shape function, the stream function field and the weak function.

[0023] Optionally, the step of calculating the rolling plastic deformation process using the obtained velocity field includes:

[0024] The obtained velocity field is used to obtain the strain rate field and stress field in the rolling zone, and then the rolling process parameters are calculated. The rolling process parameters include rolling force distribution and total rolling force.

[0025] Optionally, the total energy consumption functional of the rolling process includes: the plastic deformation power inside the workpiece, the external force power on the surface of the workpiece, the functional corresponding to the essential boundary imposed by the penalty function method, and the functional corresponding to the friction constraint. The functional corresponding to the friction constraint is calculated using the inverse tangent friction model.

[0026] In order to achieve the above object, according to another aspect of the present invention, a rolling plastic deformation process calculation device based on an element-free Galerkin method is provided, the device comprising:

[0027] A model building unit, used to build a model of the rolling plastic deformation zone and arrange nodes, Gaussian integration points and boundary points in the model;

[0028] A shape function determination unit is used to approximate the velocity field function of the node by using a moving least square method to obtain a shape function;

[0029] A system discrete equation construction unit is used to construct a system discrete equation based on the shape function and the stream function field, wherein the system discrete equation includes: the contribution of the node plastic deformation power to the total stiffness matrix, the contribution of the velocity boundary condition to the total stiffness matrix, and the contribution of the friction boundary condition to the total stiffness matrix;

[0030] A total stiffness matrix building unit is used to build a total stiffness matrix based on the system discrete equations and using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain;

[0031] A load force matrix building unit is used to build a load force matrix using boundary point information of the friction boundary;

[0032] A velocity distribution determination unit, used to obtain the velocity distribution of each node using the total stiffness matrix and the load matrix;

[0033] A velocity field determination unit, configured to obtain a stable velocity field by adopting a direct iteration method based on the velocity distribution;

[0034] The plastic deformation process calculation unit is used to calculate the rolling plastic deformation process using the obtained velocity field.

[0035] Optionally, the shape function determining unit includes:

[0036] A weighted discrete square sum construction module, used for constructing a weighted discrete square sum according to a velocity field function;

[0037] A linear equation determination module, used for obtaining a linear equation according to a minimum value of a weighted discrete square sum;

[0038] The shape function determination module is used to substitute the linear equation into the approximate expression of the field function to obtain the shape function.

[0039] Optionally, the system discrete equation construction unit includes:

[0040] Total energy consumption functional establishment module, used to establish the total energy consumption functional of the rolling process;

[0041] A weak function establishment module is used to make the first-order variation of the total energy consumption functional equal to 0 when taking a stationary value, and obtain a weak function of the total energy consumption functional, wherein the solution of the boundary value problem is obtained when the total energy consumption functional takes a stationary value, and at this time the first-order variation of the total energy consumption functional is 0;

[0042] A discrete equation construction module is used to construct a system discrete equation according to the shape function, the stream function field and the weak function.

[0043] Optionally, the plastic deformation process calculation unit is specifically used to use the obtained velocity field to obtain the strain rate field and stress field in the rolling zone, and then deduce the rolling process parameters, which include: rolling force distribution and total rolling force.

[0044] Optionally, the total energy consumption functional of the rolling process includes: the plastic deformation power inside the workpiece, the external force power on the surface of the workpiece, the functional corresponding to the essential boundary imposed by the penalty function method, and the functional corresponding to the friction constraint. The functional corresponding to the friction constraint is calculated using the inverse tangent friction model.

[0045] In order to achieve the above-mentioned purpose, according to another aspect of the present invention, a computer device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the above-mentioned method for calculating the rolling plastic deformation process based on the gridless Galerkin method are implemented.

[0046] In order to achieve the above-mentioned purpose, according to another aspect of the present invention, a computer-readable storage medium is also provided, on which a computer program / instruction is stored, and when the computer program / instruction is executed by a processor, the steps of the above-mentioned method for calculating the rolling plastic deformation process based on the gridless Galerkin method are implemented.

[0047] In order to achieve the above-mentioned purpose, according to another aspect of the present invention, a computer program product is also provided, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the rolling plastic deformation process based on the gridless Galerkin method.

[0048] The beneficial effects of the present invention are:

[0049] The present invention establishes a three-dimensional meshless Galerkin fast solution method for the rolling process on the basis of retaining the basic solution idea and framework of the meshless Galerkin method. The method of the present invention constructs a system discrete equation based on shape function and stream function field. The system discrete equation includes: the contribution of node plastic deformation power to the total stiffness matrix, the contribution of velocity boundary conditions to the total stiffness matrix and the contribution of friction boundary conditions to the total stiffness matrix. Then, based on the system discrete equation, the total stiffness matrix is ​​constructed by utilizing Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain, thereby achieving the reduction of the stiffness matrix and greatly improving the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0051] Figure 1 is a flow chart of a method for calculating a rolling plastic deformation process based on an element-free Galerkin method according to an embodiment of the present invention;

[0052] Figure 2 is a flow chart of establishing a shape function according to an embodiment of the present invention;

[0053] Figure 3 is a flow chart of constructing a system discrete equation according to an embodiment of the present invention;

[0054] Figure 4 It is a schematic diagram of a calculation model of a gridless method node according to an embodiment of the present invention;

[0055] Figure 5 It is a schematic diagram of the calculation process of the gridless method according to an embodiment of the present invention;

[0056] Figure 6 Schematic diagram of the velocity field distribution in the rolling direction of an embodiment of the present invention;

[0057] Figure 7 Schematic diagram of velocity field distribution in the plate thickness direction according to an embodiment of the present invention;

[0058] Figure 8 Schematic diagram of velocity field distribution in the plate width direction according to an embodiment of the present invention;

[0059] Fig. 9 is a schematic diagram of rolling pressure distribution in an embodiment of the present invention;

[0060] Fig.10 It is a schematic diagram of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0062] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0063] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or apparatus.

[0064] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0065] The present invention provides a solution for three-dimensional plastic deformation of a plate and strip in a rolling process based on a meshless Galerkin method, which has high solution accuracy, small amount of calculation process data storage, and high calculation efficiency. Figure 5 It is a schematic diagram of the calculation flow of the gridless method according to an embodiment of the present invention.

[0066] Figure 1 is a flow chart of a method for calculating rolling plastic deformation process based on the element-free Galerkin method according to an embodiment of the present invention, such as Figure 1 As shown, in one embodiment of the present invention, the rolling plastic deformation process calculation method based on the element-free Galerkin method of the present invention includes steps S101 to S108.

[0067] Step S101, establishing a model of the rolling plastic deformation zone, and arranging nodes, Gaussian integration points and boundary points in the model.

[0068] In one embodiment of the present invention, the present invention establishes a quarter model of the deformation zone of the strip according to the symmetry of the plastic deformation of the strip during the rolling process, and then arranges calculation nodes in the quarter model.

[0069] Figure 4 is a schematic diagram of a model established in an embodiment of the present invention, such as Figure 4 As shown, the present invention sets nodes (* points), Gaussian integral points (light points), and boundary points (dark points) in the rolling deformation zone.

[0070] Nodes are the basis of the entire numerical solution and are used to construct shape functions, approximate velocity fields, and construct discrete equations. Gaussian integration points ensure the accuracy of numerical integration, especially in the construction of stiffness matrices and load vectors. Boundary points handle boundary conditions, especially velocity boundary conditions and friction conditions, which directly affect the construction of the load force matrix and the external force input of the system. The arrangement and selection of these points directly affect the accuracy, stability, and convergence of the entire numerical solution. Therefore, when solving plastic deformation problems, it is crucial to arrange these points reasonably to ensure that the final solution is as consistent as possible with the actual physical process.

[0071] Step S102: Approximate the velocity field function of the node using the moving least squares method to obtain a shape function.

[0072] The present invention uses the moving least square method to approximate the node velocity field function.

[0073] For the three-dimensional strain rolling problem, the velocity field v in the rolling zone is described by the stream function, which can be expressed as:

[0074]

[0075] Where u is the stream function of three-dimensional rolling, H 3×2 is the shape function matrix.

[0076] The approximate shape function u of the node flow function is approximated by the moving least squares method h (x):

[0077]

[0078] u=(u x1 u y1 u x2 u y2 … u xn u yn ) (3)

[0079] Φ T (x)=(H 1 H 2 LH n )(3×2n) =p T (x)A -1 (x)B(x) (4)

[0080] In the formula, p T is the basis function of the stream function approximation, which can be taken in three-dimensional conditions:

[0081] Linear basis function: P = [1x yz], m = 4;

[0082] Quadratic basis function: P = [1x yzx 2 xy y 2 yz 2 zx],m=10;

[0083] u is the vector formed by the nodal field function parameters of all nodes in the nodal support domain, which is determined by the arranged Gaussian integration points;

[0084] Φ T (x) is the MLS shape function of the n nodes in the support region corresponding to point x.

[0085] Compared with finite element shape functions, MLS shape functions do not have the property of interpolation, so it is relatively complicated to handle when applying boundary conditions, so Lagrange multiplier method, penalty function method, singular weight function method, etc. are often used. The present invention uses the penalty function method to impose boundary conditions.

[0086] Step S103, constructing a system discrete equation based on the shape function and the stream function field, wherein the system discrete equation includes: contribution of node plastic deformation power to the total stiffness matrix, contribution of velocity boundary conditions to the total stiffness matrix, and contribution of friction boundary conditions to the total stiffness matrix.

[0087] The present invention constructs a system discrete equation based on the constructed shape function and stream function field. The system discrete equation is specifically:

[0088]

[0089] System Discrete Equation K IJ In the equation, the first term is the contribution of the plastic deformation power of the nodes in the solution domain to the total stiffness matrix, the second term is the contribution of the velocity boundary condition to the total stiffness matrix, and the third term is the contribution of the friction boundary condition to the total stiffness matrix.

[0090] The plastic deformation process of metal is a boundary value problem. In order to avoid the difficulty of solving partial differential equations under the rigid-plastic material model, the elementless Galerkin method reduces the boundary value problem of rigid-plastic materials to the extreme value problem of the total energy consumption rate functional with respect to the velocity field.

[0091] Step S104: Based on the system discrete equation, a total stiffness matrix is ​​constructed using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain.

[0092] In the present invention, this step utilizes the Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain to construct a total stiffness matrix K, where K is a sparse positive definite matrix.

[0093] In one embodiment of the present invention, this step constructs the total stiffness matrix K of the system based on the shape function and weight function in the discrete equation by using the Gaussian integral method. The construction of the total stiffness matrix is ​​based on the weak form expression of the system discrete equation obtained in step S103. Through Gaussian integral, each element K in the total stiffness matrix K I,J The total stiffness matrix K will be used together with the load force matrix to solve the distribution of the velocity field as the coefficient matrix of the linear equations.

[0094] Step S105, constructing a load force matrix using the boundary point information of the friction boundary.

[0095] In the present invention, this step constructs the load force matrix F according to the friction boundary conditions and other external force conditions. The load force matrix is ​​the right-hand side term of the discrete equation, which reflects the influence of the external forces and boundary conditions in the system. It depends on the specific conditions of the friction boundary and the external conditions of the system. The load force matrix F is the right-hand side term of the linear equation system KU=F, and will be used together with the total stiffness matrix to solve the velocity distribution of the system.

[0096] Step S106, using the total stiffness matrix and the load matrix, obtain the velocity distribution of each node.

[0097] In the present invention, this step utilizes the total stiffness matrix K and the load force matrix F obtained in the above steps to solve the linear equation group KU=F to obtain the velocity distribution U of the node.

[0098] The velocity distribution obtained in this step is a preliminary result, obtained directly from solving the linear equations. This distribution is based on the approximation of the shape function and the calculation of the discrete physical field quantities. The node velocity distribution U output in this step is the velocity value at the discrete node, specifically the velocity vector at the predefined node position in the grid or meshless method.

[0099] Step S107: obtaining a stable velocity field by using a direct iteration method based on the velocity distribution.

[0100] In the rigid-plastic mechanics problem, due to the nonlinear characteristics, the velocity field is solved multiple times using the direct iteration method until the result converges. The iterative optimization is performed on the basis of the velocity distribution U of the node obtained in step S106. The velocity field is corrected through multiple iterations to ensure the stability and accuracy of the calculation results, and finally a converged and stable velocity field is obtained.

[0101] Since plastic deformation problems are often nonlinear, the velocity distribution directly solved may not be accurate. Therefore, it is necessary to correct the node velocity through iterative optimization until the solution of the entire system converges to a stable result. After iterative optimization, the distribution of the velocity field is not limited to the values ​​of discrete nodes, but can more accurately describe the continuous velocity distribution in the entire deformation domain.

[0102] The node velocity distribution obtained in step S106 is the preliminary solution of the velocity field, and step S107 further improves this solution through iterative optimization to make it more accurate and physically reasonable. Therefore, the final velocity field contains all the information of the node velocity distribution, and on this basis, through iterative correction, the optimization and stability of the entire velocity field are achieved. The final velocity field not only retains the discrete information of the node, but also better describes the velocity distribution in the entire deformation domain through the iterative process.

[0103] Step S108, calculating the rolling plastic deformation process using the obtained velocity field.

[0104] In one embodiment of the present invention, this step specifically utilizes the obtained velocity field to obtain the strain rate field and stress field in the rolling zone, and then deduce the rolling process parameters, which include: rolling force distribution and total rolling force.

[0105] It can be seen that the present invention, while retaining the basic solution idea and framework of the meshless Galerkin method, establishes a three-dimensional meshless Galerkin fast solution method for the rolling process. The method of the present invention constructs a system discrete equation based on shape function and stream function field. The system discrete equation includes: the contribution of node plastic deformation power to the total stiffness matrix, the contribution of velocity boundary conditions to the total stiffness matrix, and the contribution of friction boundary conditions to the total stiffness matrix. Then, based on the system discrete equation, the total stiffness matrix is ​​constructed using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain, thereby achieving order reduction of the stiffness matrix and greatly improving the calculation efficiency.

[0106] like Figure 2 As shown, in one embodiment of the present invention, the above step S102 uses the moving least squares method to approximate the velocity field function of the node to obtain the shape function, including steps S201 to S203.

[0107] Step S201, constructing a weighted discrete square sum according to the velocity field function.

[0108] In the solution domain, it is assumed that the field value of the stream function u at n nodes is known, that is, u i =u(x i ), is the field function of the ith field node, then within the solution domain, the approximate form of the constructed field function is as shown in the above formula (2).

[0109] In the solution domain, the weighted discrete sum of squares can be constructed based on the field function:

[0110]

[0111] In the formula, ω i (x) is the weight function of the node.

[0112] Step S202: obtaining a linear equation according to the minimum value of the weighted discrete square sum.

[0113] The present invention can obtain the linear equation a(x)=A according to the minimum value of the weighted discrete square sum -1 (x)B(x)u, where:

[0114]

[0115]

[0116] Step S203: Substitute the linear equation into the approximate expression of the field function to obtain the shape function.

[0117] The present invention substitutes the linear equation a(x) into the approximate expression of the field function, and obtains the above formula (2) u h =Φ T (x)u, that is, the approximate value function of the velocity of any point in the deformation zone in the neighborhood of the calculation point:

[0118]

[0119] like Figure 3 As shown, in one embodiment of the present invention, the above step S103 of constructing a system discrete equation based on the shape function and the stream function field includes steps S301 to S303.

[0120] Step S301, establishing a total energy consumption functional for the rolling process.

[0121] In one embodiment of the present invention, the total energy consumption functional of the rolling process includes: the plastic deformation power inside the workpiece, the external force power on the surface of the workpiece, the functional corresponding to the essential boundary applied by the penalty function method, and the functional corresponding to the friction constraint. The functional corresponding to the friction constraint is calculated using the inverse tangent friction model.

[0122] The plastic deformation process of metal is a boundary value problem. In order to avoid the difficulty of solving partial differential equations under the rigid-plastic material model, the elementless Galerkin method reduces the boundary value problem of rigid-plastic materials to the extreme value problem of the total energy consumption rate functional with respect to the velocity field.

[0123] The original total energy consumption functional of the rolling process is:

[0124]

[0125] In the formula, is the equivalent stress;

[0126] is the equivalent strain rate, and is the strain rate component;

[0127] For surface S t Upper given surface force;

[0128] u t For surface S t Upper given speed;

[0129] The first term on the right side of the original total energy consumption functional formula (9) is the plastic deformation power inside the workpiece, and the second term is the external force power on the workpiece surface.

[0130] According to formula (1), the strain rate vector can be expressed as:

[0131]

[0132] Equivalent strain rate Can be transformed into:

[0133]

[0134] The D matrix form is:

[0135]

[0136] The volumetric strain rate is:

[0137]

[0138] The penalty function is used to impose essential boundary conditions on the total energy consumption functional without adding unnecessary variables. The resulting stiffness matrix is ​​positive definite and has a fast calculation speed, but its accuracy is lower than that of Lagrangian. In addition, if the penalty factor is not properly selected, it will cause an ill-conditioned equation.

[0139] When selecting the initial velocity field, since the meshless Galerkin method uses the moving least squares approximation, it does not satisfy the Kronecker Delta condition, that is, it does not pass the node parameter value. The penalty function method is used to impose the essential boundary. The functional corresponding to the penalty function method for imposing the essential boundary is:

[0140]

[0141] Where α u is the essential boundary penalty factor.

[0142] In view of the treatment of volume incompressibility conditions, when the stream function is used to set the velocity field, the expression of volume strain rate is:

[0143]

[0144] It can be seen from the above formula that when the velocity field is set using the stream function, the volume strain rate is zero, that is, the material deformation automatically satisfies the volume incompressibility condition.

[0145] Since there is friction in the metal rolling process and friction has a huge impact on metal flow, it is necessary to select a reasonable friction model to truly reflect the friction between the workpiece and the roller. Since the rolling zone includes the front sliding zone and the rear sliding zone, there is a friction step problem at the neutral point. Therefore, the inverse tangent friction model is selected, that is, the friction force is the inverse tangent function of the relative sliding velocity, as shown in formula (16).

[0146]

[0147] In formula (16), Δu f is the tangential relative sliding velocity between the workpiece and the roller on the friction surface. In the three-dimensional case, {Δu f}=[Δu τ1 Δu τ2 ] T Δu τ1 and Δu τ2 are the relative tangential velocity components of the workpiece and the roller in the first and second main directions of the friction surface, respectively;

[0148] u 0 It is a small positive number, usually 10 times the roller speed. -4 -10 -5 times;

[0149] Δu f | is the relative sliding velocity norm, satisfying

[0150] When the inverse tangent friction model is used to calculate the friction force, the total energy consumption rate functional corresponding to the friction constraint is:

[0151]

[0152] S f is the friction boundary.

[0153] Combining equations (9), (14) and (17), the total energy consumption functional of the rolling process adopted by the present invention is obtained:

[0154]

[0155] Step S302, making the first-order variation of the total energy consumption functional when taking a stationary value equal to 0, obtaining a weak function of the total energy consumption functional, wherein the solution of the boundary value problem is obtained when the total energy consumption functional takes a stationary value, and the first-order variation of the total energy consumption functional is 0 at this time.

[0156] The total energy consumption functional of the rolling process of the present invention obtains the solution of the boundary value problem when the stationary value is taken, and the first-order variation of the functional is 0. The first-order variation of formula (18) is calculated to obtain:

[0157]

[0158] Step S303: constructing a system discrete equation according to the shape function, the stream function field and the weak function.

[0159] The present invention substitutes the shape function of equation (2) and the stream function field of equation (8) into the weak function of equation (19), and according to KU=F, the discrete equations (5) and (6) of the system can be obtained.

[0160] in, is a 2×6 submatrix, B J is a 6×2 submatrix, is a 2×3 submatrix, Φ J is a 3×2 submatrix, so K is calculated IJ is a 2n×2n square matrix, F I It is a 2n×1 square matrix, where n is the total number of nodes in the plastic deformation zone. Compared with the conventional meshless method, it reduces the matrix order and improves the computational efficiency.

[0161] In one embodiment of the present invention, the present invention calculates the three-dimensional plastic deformation of the plate strip based on the working conditions in the following Table 1:

[0162]

[0163] Table 1

[0164] The calculation results are as follows Figure 6 , Figure 7 , Figure 8 and Fig. 9 shown.

[0165] Figure 6 is the calculated velocity field distribution in the rolling direction, Figure 7 is the calculated velocity field distribution in the thickness direction of the plate, Figure 8 is the calculated velocity field distribution in the plate width direction, Fig. 9 is the calculated rolling pressure distribution.

[0166] It can be seen from the above embodiments that the present invention, while retaining the basic solution idea and framework of the meshfree Galerkin method, utilizes boundary conditions and known conditions to limit the degrees of freedom of certain discrete nodes to reduce the number of unknowns, and establishes a three-dimensional meshfree Galerkin fast solution method for the plate and strip rolling process. This method successfully reduces the order of the stiffness matrix from 3N×3N to 2N×2N, thereby achieving the order reduction of the stiffness matrix and greatly improving the calculation efficiency.

[0167] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0168] Based on the same inventive concept, an embodiment of the present invention also provides a rolling plastic deformation process calculation device based on the gridless Galerkin method, which can be used to implement the rolling plastic deformation process calculation method based on the gridless Galerkin method described in the above embodiment, as described in the following embodiment. Since the principle of solving the problem by the rolling plastic deformation process calculation device based on the gridless Galerkin method is similar to the rolling plastic deformation process calculation method based on the gridless Galerkin method, the embodiment of the rolling plastic deformation process calculation device based on the gridless Galerkin method can refer to the embodiment of the rolling plastic deformation process calculation method based on the gridless Galerkin method, and the repeated parts will not be repeated. As used below, the term "unit" or "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiment is preferably implemented in software, the implementation of hardware, or a combination of software and hardware, is also possible and conceived.

[0169] In one embodiment of the present invention, the rolling plastic deformation process calculation device based on the element-free Galerkin method of the present invention comprises:

[0170] A model building unit, used to build a model of the rolling plastic deformation zone and arrange nodes, Gaussian integration points and boundary points in the model;

[0171] A shape function determination unit is used to approximate the velocity field function of the node by using a moving least square method to obtain a shape function;

[0172] A system discrete equation construction unit is used to construct a system discrete equation based on the shape function and the stream function field, wherein the system discrete equation includes: the contribution of the node plastic deformation power to the total stiffness matrix, the contribution of the velocity boundary condition to the total stiffness matrix, and the contribution of the friction boundary condition to the total stiffness matrix;

[0173] A total stiffness matrix building unit is used to build a total stiffness matrix based on the system discrete equations and using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain;

[0174] A load force matrix building unit is used to build a load force matrix using boundary point information of the friction boundary;

[0175] A velocity distribution determination unit, used to obtain the velocity distribution of each node using the total stiffness matrix and the load matrix;

[0176] A velocity field determination unit, configured to obtain a stable velocity field by adopting a direct iteration method based on the velocity distribution;

[0177] The plastic deformation process calculation unit is used to calculate the rolling plastic deformation process using the obtained velocity field.

[0178] In one embodiment of the present invention, the shape function determining unit includes:

[0179] A weighted discrete square sum construction module, used for constructing a weighted discrete square sum according to a velocity field function;

[0180] A linear equation determination module, used for obtaining a linear equation according to a minimum value of a weighted discrete square sum;

[0181] The shape function determination module is used to substitute the linear equation into the approximate expression of the field function to obtain the shape function.

[0182] In one embodiment of the present invention, the system discrete equation construction unit includes:

[0183] Total energy consumption functional establishment module, used to establish the total energy consumption functional of the rolling process;

[0184] A weak function establishment module is used to make the first-order variation of the total energy consumption functional equal to 0 when taking a stationary value, and obtain a weak function of the total energy consumption functional, wherein the solution of the boundary value problem is obtained when the total energy consumption functional takes a stationary value, and at this time the first-order variation of the total energy consumption functional is 0;

[0185] A discrete equation construction module is used to construct a system discrete equation according to the shape function, the stream function field and the weak function.

[0186] In one embodiment of the present invention, the plastic deformation process calculation unit is specifically used to use the obtained velocity field to obtain the strain rate field and stress field in the rolling zone, and then deduce the rolling process parameters, which include: rolling force distribution and total rolling force.

[0187] In order to achieve the above object, according to another aspect of the present application, a computer device is also provided. Fig.10 As shown, the computer device includes a memory, a processor, a communication interface and a communication bus. A computer program that can be executed on the processor is stored in the memory. When the processor executes the computer program, the steps in the above-mentioned embodiment method are implemented.

[0188] The processor may be a central processing unit (CPU). The processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or a combination of the above chips.

[0189] The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer executable programs and units, such as the corresponding program units in the above method embodiments of the present invention. The processor executes various functional applications of the processor and works data processing by running the non-transitory software programs, instructions and modules stored in the memory, that is, implementing the method in the above method embodiments.

[0190] The memory may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function; the data storage area may store data created by the processor, etc. In addition, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0191] The one or more units are stored in the memory, and when executed by the processor, the method in the above embodiment is performed.

[0192] The specific details of the above-mentioned computer device can be understood by referring to the corresponding related descriptions and effects in the above-mentioned embodiments, and will not be repeated here.

[0193] In order to achieve the above purpose, according to another aspect of the present application, a computer-readable storage medium is also provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed in a computer processor, the steps in the rolling plastic deformation process calculation method based on the meshless Galerkin method are implemented. Those skilled in the art can understand that the implementation of all or part of the processes in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the storage medium can be a disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory (Flash Memory), a hard disk (Hard Disk Drive, abbreviated as: HDD) or a solid-state drive (SSD), etc.; the storage medium can also include a combination of the above-mentioned types of memory.

[0194] In order to achieve the above-mentioned purpose, according to another aspect of the present application, a computer program product is also provided, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the rolling plastic deformation process based on the gridless Galerkin method.

[0195] Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

[0196] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating rolling plastic deformation process based on the element-free Galerkin method, characterized in that: include: Establishing a model of the rolling plastic deformation zone, and arranging nodes, Gaussian integration points and boundary points in the model; The velocity field function of the node is approximated by the moving least square method to obtain the shape function; Constructing a system discrete equation based on the shape function and the stream function field, wherein the system discrete equation includes: contribution of node plastic deformation power to the total stiffness matrix, contribution of velocity boundary conditions to the total stiffness matrix, and contribution of friction boundary conditions to the total stiffness matrix; Based on the system discrete equation, a total stiffness matrix is ​​constructed using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain; The load force matrix is ​​constructed using the boundary point information of the friction boundary; Using the total stiffness matrix and the load matrix, the velocity distribution of each node is obtained; Based on the velocity distribution, a stable velocity field is obtained by using a direct iteration method; The obtained velocity field is used to calculate the rolling plastic deformation process.

2. The method for calculating rolling plastic deformation process based on the element-free Galerkin method according to claim 1, characterized in that: The moving least square method is used to approximate the velocity field function of the node to obtain the shape function, including: Construct a weighted discrete sum of squares based on the velocity field function; The linear equation is obtained by minimizing the weighted discrete sum of squares; Substituting the linear equation into the approximate expression of the field function, we obtain the shape function.

3. The method for calculating rolling plastic deformation process based on the element-free Galerkin method according to claim 1, characterized in that: The system discrete equations are constructed based on the shape function and the stream function field, including: Establish the total energy consumption functional of the rolling process; The first-order variation of the total energy consumption functional when taking a stationary value is equal to 0, and a weak function of the total energy consumption functional is obtained, wherein the solution of the boundary value problem is obtained when the total energy consumption functional takes a stationary value, and the first-order variation of the total energy consumption functional is 0 at this time; A system discrete equation is constructed according to the shape function, the stream function field and the weak function.

4. The method for calculating rolling plastic deformation process based on the element-free Galerkin method according to claim 1, characterized in that: The method of calculating the rolling plastic deformation process using the obtained velocity field includes: The obtained velocity field is used to obtain the strain rate field and stress field in the rolling zone, and then the rolling process parameters are calculated. The rolling process parameters include rolling force distribution and total rolling force.

5. The method for calculating rolling plastic deformation process based on the element-free Galerkin method according to claim 1, characterized in that: The total energy consumption functional of the rolling process includes: the plastic deformation power inside the workpiece, the external force power on the workpiece surface, the functional corresponding to the essential boundary imposed by the penalty function method, and the functional corresponding to the friction constraint. The functional corresponding to the friction constraint is calculated using the inverse tangent friction model.

6. A rolling plastic deformation process calculation device based on the element-free Galerkin method, characterized in that: include: A model building unit, used to build a model of the rolling plastic deformation zone and arrange nodes, Gaussian integration points and boundary points in the model; A shape function determination unit is used to approximate the velocity field function of the node by using a moving least square method to obtain a shape function; A system discrete equation construction unit is used to construct a system discrete equation based on the shape function and the stream function field, wherein the system discrete equation includes: the contribution of the node plastic deformation power to the total stiffness matrix, the contribution of the velocity boundary condition to the total stiffness matrix, and the contribution of the friction boundary condition to the total stiffness matrix; A total stiffness matrix building unit is used to build a total stiffness matrix based on the system discrete equations and using Gaussian integral point information, velocity boundary conditions and friction boundary conditions in the solution domain; A load force matrix building unit is used to build a load force matrix using boundary point information of the friction boundary; A velocity distribution determination unit, used to obtain the velocity distribution of each node using the total stiffness matrix and the load matrix; A velocity field determination unit, configured to obtain a stable velocity field by adopting a direct iteration method based on the velocity distribution; The plastic deformation process calculation unit is used to calculate the rolling plastic deformation process using the obtained velocity field.

7. The rolling plastic deformation process calculation device based on the element-free Galerkin method according to claim 6, characterized in that: The shape function determining unit comprises: A weighted discrete square sum construction module, used for constructing a weighted discrete square sum according to a velocity field function; A linear equation determination module, used for obtaining a linear equation according to a minimum value of a weighted discrete square sum; The shape function determination module is used to substitute the linear equation into the approximate expression of the field function to obtain the shape function.

8. The rolling plastic deformation process calculation device based on the element-free Galerkin method according to claim 6, characterized in that: The system discrete equation building unit comprises: Total energy consumption functional establishment module, used to establish the total energy consumption functional of the rolling process; A weak function establishment module is used to make the first-order variation of the total energy consumption functional equal to 0 when taking a stationary value, and obtain a weak function of the total energy consumption functional, wherein the solution of the boundary value problem is obtained when the total energy consumption functional takes a stationary value, and at this time the first-order variation of the total energy consumption functional is 0; A discrete equation construction module is used to construct a system discrete equation according to the shape function, the stream function field and the weak function.

9. The rolling plastic deformation process calculation device based on the element-free Galerkin method according to claim 6, characterized in that: The plastic deformation process calculation unit is specifically used to obtain the strain rate field and stress field in the rolling zone using the obtained velocity field, and then deduce the rolling process parameters, which include: rolling force distribution and total rolling force.

10. The rolling plastic deformation process calculation device based on the element-free Galerkin method according to claim 6, characterized in that: The total energy consumption functional of the rolling process includes: the plastic deformation power inside the workpiece, the external force power on the workpiece surface, the functional corresponding to the essential boundary imposed by the penalty function method, and the functional corresponding to the friction constraint. The functional corresponding to the friction constraint is calculated using the inverse tangent friction model.

11. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

12. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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