JP2005149533A - Rolling analysis system and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To eliminate the need for replacing programs, to eliminate the need for inputting the number of analysis dimensions, symmetrical conditions and three-dimensional nodal coordinates and specifying a node number which is brought into contact with a symmetrical surface and a roll for rolling, with high versatility, easy operation and not having to spend a long time for operation, even when the cross-sectional shape of a material as analysis object and the kind of rolling process change. <P>SOLUTION: This rolling analysis system has a wire frame model generating means for generating a wire frame model, based on inputted rolling conditions, a boundary surface setting means for setting a boundary surface on the wire frame model, based on the rolling conditions and a node number calculating means for calculating the node number of a node, which is the node of a three-dimensional division element of the material and is brought into contact with the boundary surface. Initial three-dimensional division and boundary conditions are generated automatically, and a velocity component of the node of the three-dimensional division element of the material to be rolled is calculated by a rigid-plastic finite element method, based on the initial three-dimensional division and the boundary conditions. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a rolling analysis system and a program.

  Conventionally, when a steel material and a non-ferrous metal material are hot-rolled or cold-rolled to produce a plate material, a bar material, a wire material, a pipe material, a deformed material, etc., predict the load, torque, etc. acting on the rolling mill, Rolling analysis that performs computer analysis using the finite element method that divides the material into fine meshes (elements) to predict the plastic flow, stress distribution, shape change, etc. that occur in the material being rolled The system is adopted.

  In the conventional rolling analysis system, generally, a finite element model in which the material to be analyzed is decomposed into minute elements is created, and the elastic deformation of the material is ignored, and the three-dimensional plastic deformation during the rolling process is analyzed. (For example, refer nonpatent literature 1.).

  FIG. 2 is a flowchart in computer analysis using a conventional finite element method.

  First, rolling conditions such as the inlet material outer shape in the rolling direction cross section, the number of divisions in the rolling direction cross section, the analysis target region, the roll shape, the position and rotational angular velocity, the deformation resistance, and the friction coefficient are input (step S1). ). Subsequently, the number of analysis dimensions is input (step S2). If the product produced by rolling is a plate, bar, wire, tube, deformed material, etc., the three-dimensional analysis is performed, so the number of analysis dimensions is 3, but often when the product is a plate Since the two-dimensional analysis is performed, the number of analysis dimensions is two. Since programs used for computer analysis differ for each number of analysis dimensions, when the number of analysis dimensions is different, for example, when the number of analysis dimensions is 2, it is necessary to use another program.

  Next, a symmetry condition is input (step S3). The symmetry condition differs depending on the cross-sectional shape of the material. For example, in the case of a non-symmetrical cross-sectional shape, the symmetry condition is 1/1, and in the case of a left-right symmetric cross-sectional shape, the symmetry condition is 1/2. In the case of a cross-sectional shape that is symmetrical in the vertical and horizontal directions, the symmetry condition is 1/4. Here, since the program used for the computer analysis is different for each symmetry condition, it is necessary to use another program when the symmetry condition is different.

  On the other hand, the three-dimensional coordinates of the nodes in the minute mesh of the material to be rolled are input (step S4). Then, based on the symmetry condition input in step S3 and the three-dimensional node coordinates input in step S4, the node number in contact with the symmetry plane is specified (step S5). Then, the node number which contacts with the roll for rolling is designated (step S6). Thereby, the data input is completed.

  Next, as preprocessing of the input data, registration of local coordinates and boundary conditions of each node is automatically executed according to the program (step S7).

  Subsequently, the calculation is performed according to the program, and the material flow analysis by the finite element method is automatically executed (step S8).

Thus, by performing computer analysis using the finite element method, the material flow as the material to be rolled is analyzed, and the load, torque, etc. acting on the rolling mill are predicted, and the plastic flow and stress generated in the material are predicted. Distribution, shape change, etc. can be predicted.
Published by Japan Iron and Steel Institute, "Text of 169/170 Nishiyama Memorial Technology Course (1998) No. 55"

  However, in the conventional rolling analysis system and program, it is necessary to use a different program when the analysis dimension number is different, and it is also necessary to use a different program even when the symmetry condition is different. In addition, researchers, engineers, and other computer analysts have to input the number of dimensions of analysis, symmetry conditions, and 3D node coordinates, and specify the node numbers that contact the symmetry plane and the roll for rolling. .

  For this reason, the person who performs the computer analysis replaces the program to be used every time the cross-sectional shape of the material to be analyzed and the type of rolling process are changed, and restarts the computer. In addition, it is necessary to input the three-dimensional node coordinates and to specify the node numbers which come into contact with the symmetry plane and the roll for rolling.

  In general, the rolling process is largely divided into a plate material manufacturing series, a rod wire manufacturing series, a pipe material manufacturing series, and a deformed material manufacturing series. In a rolling mill that actually manufactures products, the series is classified in more detail for each product, a manufacturing line is provided for each product, and the computer analysis is also performed for each product.

  For this reason, when performing computer analysis in line with actual product development, whenever the target product changes, as described above, the program to be used is replaced, the computer is restarted, the analysis dimension number, and the symmetry condition And it is necessary to input the three-dimensional node coordinates and specify the node numbers that come into contact with the symmetry plane and the roll for rolling, so that the computer analysis takes time, and those who perform the computer analysis feel annoying End up.

  The present invention solves the problems of the conventional rolling analysis system and program, and even when the cross-sectional shape of the material to be analyzed and the type of rolling process are changed, it is not necessary to replace the program, and the computer analysis It is not necessary for the person performing the process to input the number of analysis dimensions, symmetry conditions, and 3D node coordinates, or to specify the node numbers that contact the symmetry plane and the roll for rolling. An object of the present invention is to provide a rolling analysis system and a program that are expensive and easy to operate and do not spend a long time.

  Therefore, in the rolling analysis system of the present invention, a wire frame model generating means for generating a wire frame model based on the input rolling conditions, and a boundary surface is set in the wire frame model based on the rolling conditions. And a node number calculation unit for calculating a node number of a node which is a node of the three-dimensional division element of the material and is in contact with the boundary surface. The initial three-dimensional division and the boundary condition are automatically performed. Based on the initial three-dimensional division and boundary conditions, the velocity component of the node of the three-dimensional division element of the material to be rolled is calculated by the rigid plastic finite element method.

  In another rolling analysis system of the present invention, the boundary surface is a surface of a rolling roll and a symmetrical surface.

  In the rolling analysis program of the present invention, a computer for analyzing rolling, a wire frame model generating means for generating a wire frame model based on the input rolling conditions, and the wire frame model based on the rolling conditions A boundary surface setting means for setting a boundary surface on the surface, and a node number calculation means for calculating a node number of a node which is a node of a three-dimensional dividing element of the material and is in contact with the boundary surface. Conditions are automatically generated, and the velocity component of the node of the three-dimensional division element of the material to be rolled is calculated by the rigid plastic finite element method based on the initial three-dimensional division and boundary conditions.

  In another rolling analysis program of the present invention, the boundary surface is a surface of a rolling roll and a symmetrical surface.

  According to the present invention, in the rolling analysis system, a wire frame model generating means for generating a wire frame model based on the input rolling conditions, and a boundary surface is set in the wire frame model based on the rolling conditions. A boundary surface setting means, a node number calculation means for calculating a node number of a node which is a node of the three-dimensional division element of the material and is in contact with the boundary surface, and an initial three-dimensional division and boundary condition are automatically generated, Based on the initial three-dimensional division and boundary conditions, the velocity component of the node of the three-dimensional division element of the material to be rolled is calculated by the rigid plastic finite element method.

  Further, in the rolling analysis program, a computer for analyzing the rolling, a wire frame model generating means for generating a wire frame model based on the input rolling conditions, and the wire frame model based on the rolling conditions. Boundary surface setting means for setting a boundary surface, and node number calculation means for calculating a node number of a node which is a node of a three-dimensional dividing element of the material and is in contact with the boundary surface. Is automatically generated, and the velocity component of the node of the three-dimensional divided element of the material to be rolled is calculated by the rigid plastic finite element method based on the initial three-dimensional division and the boundary condition.

  In this case, even if the cross-sectional shape of the material to be analyzed or the type of rolling process changes, the node number that automatically contacts the boundary surface is calculated simply by inputting the rolling conditions, and the local coordinates and boundary of each node are calculated. Since the conditions are registered, there is no need to change the program, and the person who performs the computer analysis inputs the number of analysis dimensions, symmetry conditions and 3D node coordinates, or contacts the symmetry plane and the roll for rolling. There is no need to specify a number. Therefore, it is highly versatile, easy to operate, and does not spend a long time for operation.

  That is, a hot strip (hot rolled thin plate), a cold strip (cold rolled thin plate), a plate (thick plate), a rod (bar), a wire (wire), a pipe (pipe), and a general deformed material are manufactured by rolling. When calculating the load and torque acting on the rolling mill, as well as the plastic flow, stress distribution, and shape change generated in the material being rolled, without changing the program or restarting the computer can do.

  Further, the verification of the rolling accuracy may be performed only for a rolling process capable of performing a rigorous experiment, that is, a hot strip, a cold strip, a plate and a rod, and does not need to be performed for other rolling processes.

  Furthermore, the dimensional accuracy of the product manufactured by rolling is improved, the rolling process is shortened, and the cross-section is easily processed, so that a product having a new shape can be easily manufactured.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a flowchart of initial three-dimensional division and generation under boundary conditions in the embodiment of the present invention, and FIG. 3 is a flowchart of a rolling analysis system in the embodiment of the present invention.

  The rolling analysis system shown in FIG. 3 is a load that acts on a rolling mill when a steel material and a non-ferrous metal material are hot-rolled or cold-rolled to produce a plate material, a bar material, a wire material, a tube material, a deformed material, or the like. , A computer analysis system using a finite element method (FEM) for predicting torque, etc., and predicting plastic flow, stress distribution, shape change, etc. generated in a material to be rolled, Suitable for quantitative calculation of load characteristics. Here, the rolling analysis system is constructed in the computer by installing a rolling analysis program in a computer such as a personal computer, a workstation, or a general-purpose computer provided with a calculation means, a storage means, an input / output means, a communication interface, and the like. System.

  First, a person who performs computer analysis of a rolling process, such as a researcher or an engineer, inputs rolling conditions. Here, the rolling conditions are as follows: (1) Before rolling of the material to be rolled, that is, the outer shape, outer dimensions, etc. of the rolling direction cross section of the material at the entrance of the rolling roll, (2) of the finite element method The number of divisions in the rolling direction cross section of the material, which is the number of element divisions for determining the size of the model to be used in the calculation, (3) analysis target area to be subjected to computer analysis in the material, (4) rolling roll The shape, size, position and rotational angular velocity of (5), (5) deformation resistance of the material, and (6) the coefficient of friction between the material and the roll for rolling.

  When the rolling conditions are input, initial three-dimensional division and boundary conditions are automatically generated.

  First, a wire frame model is automatically generated based on the input rolling conditions. In this case, the plane of symmetry in the wire frame model is set, and the surface shape of the roll for rolling is set.

  FIG. 4 is a diagram illustrating an example of a wire frame model in the embodiment of the present invention, FIG. 5 is a first diagram illustrating an example of setting a symmetry plane in the embodiment of the present invention, and FIG. 6 is a diagram illustrating the implementation of the present invention. FIG. 7 is a second diagram showing an example of setting the symmetry plane in the embodiment of the present invention, and FIG. 8 is a diagram showing an example of setting the symmetry plane in the embodiment of the present invention. FIG.

  FIG. 4 shows a wire frame model of a material in the case where a round bar having a circular rolling direction cross section is manufactured by rolling a material having a flat cross section in the rolling direction. In this case, the rolling direction cross section of the material has a symmetrical shape with respect to the width direction x and the thickness direction y between the entrance and the exit of the roll for rolling. A plane extending in the width direction x and the rolling direction z through the center of the direction cross section and a plane extending in the thickness direction y and the rolling direction z through the center of the rolling direction cross section of the material are symmetrical planes. . The two symmetry planes are orthogonal to each other, and the line of intersection becomes the central axis of the material passing through the center of the cross section in the rolling direction of the material and extending in the rolling direction z. If only one of the four sections divided by the two symmetry planes is to be analyzed, the other three sections are symmetrical with the one section, so that the analysis can be omitted. . Thus, the rolling condition in which only one of the four sections divided by the two planes of symmetry only needs to be analyzed is generally referred to as a 1/4 symmetry condition.

  Therefore, as in the example shown in FIG. 4, it is necessary to perform a three-dimensional analysis, and a material whose cross section in the rolling direction has a symmetrical shape with respect to the width direction x and the thickness direction y. In this case, as shown in FIG. 5, two symmetry planes are set in the wire frame model of the material.

  In the present embodiment, as shown in FIG. 6, a symmetry plane 1 extending in the width direction x and the rolling direction z, and a symmetry plane 2 extending in the width direction y and the rolling direction z and orthogonal to the symmetry plane 1. In addition, a symmetry plane is set by appropriately selecting from the symmetry plane 1 that is inclined at an arbitrary angle with respect to the symmetry plane 1 and the first and extends in the rolling direction z.

  The example shown in FIG. 7 is a case where it is necessary to perform a three-dimensional analysis, and is a symmetry plane in the case of a 1/6 symmetry condition in which a rolling roll sandwiches material from three directions and rolls. In this case, the symmetry plane 3 is set in which the sandwiching angle between the symmetry plane 2 and the symmetry plane 2 is 60 degrees.

  Further, the example shown in FIG. 8 is a case where a two-dimensional analysis is performed as in the case of rolling a wide plate material, and the rolling roll has a vertically symmetric condition in which the material is rolled from above and below. The plane of symmetry in the case. When rolling a wide plate material, in most cases except for the vicinity of the side edge of the plate, it is considered that the material flows only in the axial direction z and the vertical direction y. Therefore, a two-dimensional analysis is usually performed. In this case, the symmetry plane 1 and the two symmetry planes 2 arranged so as to be spaced apart from each other are set.

Subsequently, the surface shape of the rolling roll is set. And the boundary condition in the case of the calculation by the finite element method mentioned later is produced | generated combining the surface and symmetry plane of the set roll for rolling. The method of combining the surface of the rolling roll and the symmetry plane is appropriately set according to the shape of the cross section in the rolling direction of the material. As a typical example, the following (1) There is something like (5).
(1) Three-dimensional analysis and 1/4 symmetry condition: roll + symmetry plane 1 + symmetry plane 2
(2) Three-dimensional analysis and 1/2 symmetry condition (right / left symmetry): roll + roll + symmetric plane 2
(3) 3D analysis with 1/1 symmetry condition (no symmetry): roll + roll (4) 3D analysis with 1 / n symmetry condition (n> 5): roll + symmetry plane 2+ symmetry plane 3
(5) Two-dimensional analysis ignoring deformation in the width direction: roll + symmetry plane 1 + symmetry plane 2+ symmetry plane 2
The generated wire frame data is stored in storage means. In addition, the three-dimensional node coordinates are calculated based on the outer shape, outer dimensions, and the like of the rolling direction cross-section of the material at the input of the rolling roll input.

  Next, based on the three-dimensional node coordinates and the wire frame data, the node number that contacts the symmetry plane is calculated and stored in the storage means. Subsequently, based on the three-dimensional node coordinates, the node number that contacts the roll is calculated and stored in the storage means.

  Then, using vector algebra, the local coordinates and boundary conditions of each node are registered from the vectors for all rolls and symmetry planes.

  FIG. 9 is a diagram showing a roll surface vector in the embodiment of the present invention, Equation (1) is an equation constituting a coordinate transformation matrix, Equation (2) is a stiffness equation, and Equation (3) is a stiffness with boundary conditions introduced. It is an equation.

  Based on the spatial coordinate O-xyz component of the unit normal vector n, in-plane tangent vector p, and q of the roll surface as shown in FIG. 9, a coordinate transformation matrix [β] effective for the component of an arbitrary vector a is obtained. The configuration is as shown in Equation (1). The unit normal vector n and the in-plane tangent vectors p and q are orthogonal to each other.

これによって得られた式（３）の中から、前記ロール及び対称面に接している節点について、剛性方程式（２）よりベクトルｎの方向の行・列を縮減して解くことによって、材料の要素についての速度及び静水圧応力の境界条件を満たす解を得ることができる。

From the equation (3) thus obtained, the nodes of the roll and the symmetry plane are solved by reducing the rows and columns in the direction of the vector n from the stiffness equation (2), thereby obtaining the element of the material. A solution that satisfies the boundary conditions of velocity and hydrostatic pressure stress can be obtained.

次に、前記剛性方程式（２）を解析対象領域にあるすべての要素に拡張する際に要求される記憶容量を削減するアルゴリズムについて説明する。

Next, an algorithm for reducing the storage capacity required when expanding the stiffness equation (2) to all elements in the analysis target region will be described.

  FIG. 10 is a diagram showing a method for arranging node numbers in one element in the embodiment of the present invention, FIG. 11 is a diagram showing a method for arranging node numbers in a plurality of elements in the embodiment of the present invention, and FIG. FIG. 13 shows an element number / node number correspondence table in the storage means when the algorithm in the embodiment is not adopted. FIG. 13 shows an element number / node number correspondence table in the storage means when the algorithm in the embodiment of the present invention is adopted. FIG.

  As shown in FIG. 10, each element of the material in the analysis target region is assigned a number to each of the element itself and the node of the element (corresponding to the vertex of the hexahedron). Be placed. Here, in the finite element method, it is considered that pressure acts on the element itself and velocity acts on each node. Since the number of nodes is 8 and the velocity has three components in the x, y, and z directions, one element includes 24 variables for the velocity component and one variable for the pressure, that is, 25 variables. It is.

  Here, when the stiffness equation (2) is applied to one element, the order of storing the variables in the storage means is as follows: node 1, node 2, node 3... Node 6, node 7, node 8, element 1. Become.

  By the way, when there are a plurality of elements, the arrangement method of the node numbers is optimized, and the nodes of the adjacent elements are given so as to share the node numbers. Therefore, the number assigned to the node is smaller than the number obtained by multiplying the number of nodes of one element by the number of elements. For example, in the case of four elements arranged as shown in FIG.

  In this case, the order in which the variables when applying the stiffness equation (2) to the four elements are stored in the storage means as data is considered as in the case of one element, node 1, node 2, node 3,. .. Node 18, node 19, node 20, element 1, element 2, element 3, and element 4.

  Here, when the variables are stored as data in the storage means in a matrix, the data is arranged as an element number / node number correspondence table as shown in FIG. Here, only non-zero data is stored in the storage means, and portions corresponding to zero data are blank. In this case, as can be seen from FIG. 12, the blank area is wide within the storage area assigned as the element number / node number correspondence table, and the storage means is not used effectively.

  Therefore, in the algorithm of the present embodiment, the required storage capacity can be reduced by optimizing the element number / node number correspondence table and reducing the blank area to effectively use the storage means. .

  In this case, the order in which the variables when applying the stiffness equation (2) for the four elements are stored as data in the storage means is the ascending order of the node numbers (the order in which the numbers increase sequentially) for the nodes, For, the element is interrupted after the maximum node number included in the corresponding element. In the case of the four elements shown in FIG. 11, the order in which the variables when applying the stiffness equation (2) are stored as data in the storage means is as follows: node 1, node 2, node 3... Node 11, node 12, Node 13, element 2, node 14, element 3, node 15, node 16, element 4, node 17, node 18, node 19, node 20, and element 1.

  When the algorithm according to the present embodiment is employed, as shown in FIG. 13, a blank may be generated in the vicinity of the opposite two corners of the rectangular storage area assigned as the element number / node number correspondence table. I understand. Therefore, when many combinations of the four elements are combined, the storage area in the entire storage means is compressed and assigned as a whole by allocating blank portions of the rectangular storage area to other combinations. Storage capacity can be reduced.

  As described above, the algorithm of the present embodiment optimizes the arrangement of the node numbers and stores them in the storage means in the order of the data numbers for the nodes, and interrupts the data for the elements next to the maximum node numbers included in the elements. The element number / node number correspondence table is optimized so that not only can the memory resources of the computer be saved, but also the storage capacity necessary for the calculation can be reduced, so that the calculation speed can be improved. Can do.

  As described above, when the initial three-dimensional division and the creation of the boundary condition are completed, the calculation and storage of the boundary condition are subsequently executed.

  First, based on the data already stored in the storage means, the presence or absence of contact between each node of the material and the roll is automatically determined. Then, the contact angle, the normal direction, and the peripheral speed vector of the roll are calculated and stored in the storage means for all the nodes in the area in contact with the roll.

  Subsequently, based on all data calculated and stored as described above, the velocity distribution of the material is calculated as the velocity component of each node by the Lagrange multiplier method rigid-plastic finite element method. The Lagrangian multiplier rigid plastic finite element method creates a finite element model in which the material to be analyzed is decomposed into minute elements, ignores elastic deformation of the material, and performs three-dimensional plasticity during rolling. A method for analyzing deformation, and a program for executing computer analysis is also known. In this embodiment, since the material velocity distribution is calculated as the velocity component of each node using the known program, the details of the calculation by the Lagrange multiplier method rigid-plastic finite element method are described. Omitted.

  Next, based on the velocity distribution calculated by the Lagrange multiplier method rigid plastic finite element method, the material flow is tracked and calculated, the contact position between the material and the roll is corrected, and the amount of interference and separation between the material and the roll. To correct the required amount.

  Finally, it is determined whether the three-dimensional deformation shape and the stress state of the material are in a steady state, that is, in a state where there is no time change, that is, whether the calculation result has converged. If it is determined that there is no time change, the calculation result stored in the storage means is output to an external file or the like as the result of rolling analysis, assuming that the calculation result has converged.

  On the other hand, if it is determined that there is no time change, assuming that it has not converged, calculation and storage of boundary conditions resumes execution, calculation by Lagrange multiplier method rigid plastic finite element method, and Repeat calculations to track material flow.

Next, a flowchart will be described. First, the flowchart of the rolling analysis system shown in FIG. 3 will be described.
Step S11 The person who performs the computer analysis of the rolling process, as rolling conditions, (1) the outer shape of the rolling direction cross section of the material at the entrance of the rolling roll, (2) the number of divisions in the rolling direction cross section of the material, ( 3) Analysis target area to be subjected to computer analysis, (4) Shape, dimensions, position and rotational angular velocity of rolling roll, (5) Deformation resistance of material, and (6) Between material and rolling roll Enter the coefficient of friction.
Step S12: An initial three-dimensional division and boundary conditions are generated. Details of step S12 are shown in FIG.
Step S13 The boundary condition is calculated and stored. In this case, (1) the presence or absence of contact between each node of the material and the roll is automatically determined. Is calculated and stored in the storage means.
Step S14 The material velocity distribution is calculated as the velocity component of each node by the Lagrange multiplier method rigid plastic finite element method.
Step S15: The material is automatically corrected for the three-dimensional element division. In this case, (1) the material flow line is corrected, (2) the contact position between the material and the roll is corrected, and (3) the amount of interference between the material and the roll and the separation amount are calculated and corrected.
Step S16: It is determined whether the calculation result has converged. If converged, the process proceeds to step S17, and if not converged, the process returns to step S13.
Step S17: Output the result.

Next, the initial three-dimensional division and boundary condition generation flowchart shown in FIG. 1 will be described.
Step S21: A wire frame model is generated.
Step S22: A symmetry plane and a roll surface are set as boundary conditions.
Step S23: The node number that contacts the symmetry plane is calculated.
Step S24: Calculate the node number in contact with the roll.
Step S25: Register local coordinates and boundary conditions of each node using vector algebra.
Step S26: The node numbers are optimally arranged, and the element number-node number correspondence table is optimized.

  As described above, in the present embodiment, the rolling roll as the boundary surface and the symmetry surface are set based on the wire frame model to calculate the node number in contact with the boundary surface, and each node is calculated using the vector algebra. The initial three-dimensional division and the generation of the boundary condition are automatically performed by registering the local coordinates and the boundary condition, and optimally arranging the node numbers and optimizing the element number-node number correspondence table.

  Therefore, even when the cross-sectional shape of the material to be analyzed and the type of rolling process change, the node number that automatically contacts the boundary surface is calculated simply by inputting the rolling conditions, and the local coordinates and boundary conditions of each node are calculated. Therefore, it is not necessary to replace the program, and the person who performs the computer analysis inputs the number of analysis dimensions, symmetry conditions and 3D node coordinates, or the node number that contacts the symmetry plane and the roll for rolling. There is no need to specify. Therefore, it is highly versatile, easy to operate, and does not spend a long time for operation.

  In addition, since the node numbers are optimally arranged and the element number-node number correspondence table is optimized, not only the memory resources of the computer can be saved, but also the storage capacity necessary for the calculation can be reduced, so that the calculation Speed can be improved.

  In addition, this invention is not limited to the said embodiment, It can change variously based on the meaning of this invention, and does not exclude them from the scope of the present invention.

It is a flowchart of the production | generation in the initial three-dimensional division | segmentation and boundary condition in embodiment of this invention. It is a flowchart in the computer analysis using the conventional finite element method. It is a flowchart of the rolling analysis system in embodiment of this invention. It is a figure which shows an example of the wire frame model in embodiment of this invention. It is a 1st figure which shows the example of a setting of the symmetry plane in embodiment of this invention. It is a figure which shows the kind of symmetry plane in embodiment of this invention. It is a 2nd figure which shows the example of a setting of the symmetry plane in embodiment of this invention. It is a 3rd figure which shows the example of a setting of the symmetry plane in embodiment of this invention. It is a figure which shows the vector of the roll surface in embodiment of this invention. It is a figure which shows the arrangement | positioning method of the node number in 1 element in embodiment of this invention. It is a figure which shows the arrangement | positioning method of the node number in the some element in embodiment of this invention. It is a figure which shows the element number in the memory | storage means in case the algorithm in embodiment of this invention is not employ | adopted, and a node number correspondence table. It is a figure which shows the element number and node number correspondence table in a memory | storage means in the case of employ | adopting the algorithm in embodiment of this invention.

Claims (4)

(A) a wire frame model generating means for generating a wire frame model based on the input rolling conditions;
(B) a boundary surface setting means for setting a boundary surface in the wire frame model based on the rolling conditions;
(C) node number calculation means for calculating a node number of a node which is a node of the three-dimensional division element of the material and is in contact with the boundary surface;
(D) Automatically generating the initial three-dimensional division and boundary condition, and the velocity component of the node of the three-dimensional division element of the material to be rolled by the rigid plastic finite element method based on the initial three-dimensional division and boundary condition A rolling analysis system characterized by calculating The rolling analysis system according to claim 1, wherein the boundary surface is a surface of a rolling roll and a symmetrical surface. (A) a computer to analyze the rolling;
(B) a wire frame model generating means for generating a wire frame model based on the input rolling conditions;
(C) a boundary surface setting means for setting a boundary surface in the wire frame model based on the rolling conditions; and
(D) function as a node number calculating means for calculating a node number of a node which is a node of the three-dimensional division element of the material and is in contact with the boundary surface;
(E) Automatically generating initial three-dimensional division and boundary conditions, and velocity components of nodes of the three-dimensional division elements of the material to be rolled by the rigid plastic finite element method based on the initial three-dimensional division and boundary conditions Rolling analysis program that calculates The rolling analysis program according to claim 3, wherein the boundary surface is a surface of a rolling roll and a symmetrical surface.

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