JPH06119418A - Stress distribution analysis system - Google Patents

Abstract

PURPOSE:To predict stress and displacement after molding with a metal die and to design the metal die on a computer without repeating an experiment and a test concerning the stress distribution analysis system for analyzing the stress distribution of a shape to be molded by the metal die. CONSTITUTION:This system is provided with a rigidity matrix generation part 7 for generating a rigidity matrix K to be decided by a Young's modulus and a Poisson modulus specific to a designated material for each divided element, load vector generation part 8 for generating a load vector P to be impressed to the surface of an object on designated border conditions, and stress vector calculation part 9 for calculating a stress vector sigma to be stocked at each element corresponding to a displacement vector (u) of each element calculated from these generated load vector P and rigidity matrix K, and the calculated displacement vector (u) and stress vector sigma for each element are outputted.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a stress distribution analysis system for analyzing a stress distribution of a shape to be molded by a mold. In designing a mold for integrally molding materials such as ferrite and ceramics, it is desired to calculate stress distribution in advance using a computer system so that a product can be manufactured with high dimensional accuracy.

[0002]

2. Description of the Related Art Generally, powder molding is performed by filling a mold with a material. At this time, for example, as shown in FIG. 16, when molding is performed with a uniform die, if there is a convex portion such as the portion A, the internal density is not always uniform and the internal stress is increased. It was deformed during sintering in the process, and cracks were generated.

Further, even in the case of forming a trumpet-shaped core for a deflection yoke, there is a shape in which a crack is likely to occur in the outer peripheral portion or the like. In order to avoid these deformations and crevices, conventionally, molds of various shapes have been prepared and experiments have been repeated to empirically design the shape of the molding mold.

[0004]

As described above, since the conventional mold design is performed empirically, it is necessary to repeat the experiment and the trial manufacture until the mold having the optimum shape is decided, and it takes a lot of time. There has been a problem that a lot of expenses are required as well as being required.

The present invention solves these problems.
The purpose is to predict the stress and displacement after molding with a mold, and to realize the design of the mold on a computer without repeating experiments and trial production.

[0006]

[Means for Solving the Problems] Means for solving the problems will be described with reference to FIG. In FIG. 1, the mesh generation function 22 divides the shape of the designated mold into meshes.

The rigidity matrix generator 7 generates a rigidity matrix K for each divided mesh, which represents the degree of deformation resistance determined by the specified Young's modulus and Poisson's ratio peculiar to the material.

The load vector generator 8 generates a load vector P applied to the surface of the object from the specified boundary conditions. The stress vector calculation unit 9 calculates the stress vector σ accumulated in each element from the displacement vector u of each element obtained by solving the generated load vector P and the stiffness matrix K.

[0009]

According to the present invention, as shown in FIG. 1, the mesh generation function 22 divides a specified mold shape into meshes, and the rigidity matrix generation unit 7 divides each mesh into specified mesh materials. A stiffness matrix K that represents the difficulty of deformation determined by the Young's modulus and Poisson's ratio of the object is generated, and the load vector generation unit 8 generates the load vector P applied to the object surface from the specified boundary condition, and the stress vector calculation unit. 9 is a displacement vector u of each element obtained by solving the generated load vector P and the stiffness matrix K.
Then, the stress vector σ accumulated in each element is calculated, and the displacement vector u and the stress vector σ of these calculated elements are calculated.
Is output.

At this time, based on the stress vector σ, the contour lines of the stress distribution connecting the equal points are output. Further, based on the output displacement vector u, the original shape is corrected so as to match the shape to be formed, and if necessary, the original shape is corrected so that the stress distribution is reduced, The element displacement vector u and the stress vector σ are recalculated and output.

Therefore, by predicting and correcting the stress and displacement after molding with the mold, it becomes possible to realize the design of the mold on the computer without repeating the conventional experiment and trial manufacture.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, the construction and operation of an embodiment of the present invention will be described in detail with reference to FIGS.

FIG. 1 shows a block diagram of an embodiment of the present invention.
In FIG. 1, analysis condition 1 is a condition such as a material property of a product to be molded by a mold, a boundary condition, and the like, which is specified by a designer.

The mesh generator 2 takes in the outer shape data of the basic shape (or the shape obtained by modifying the dimensions of the basic shape) fetched from the shape database 3 and divides it into specified intervals to generate a mesh. And the input unit 21 and the mesh generation function 22
It is composed of etc.

The input unit 21 takes in the external shape data of the specified shape from the shape database 3.
The mesh generation function 22 divides the outer shape data at specified intervals and generates a mesh. For example, as shown in FIG. 5, which will be described later, the mesh is divided into meshes. After that, various calculations (load vector, displacement vector, stress vector, etc.) are performed for each of the divided mesh units.

The shape database 3 stores the size and shape of the basic shape of various products and shape data for graphical output, and here is composed of a size and shape file 31 and a graphic file 32. Is.

The dimension / shape file 31 is a file in which the dimensions (outer shape) of the basic shape of the product are stored. The graphic file 32 is a file that stores data for graphically displaying the basic shape of the product.

The data generation 4 converts the outer shape data (dimension data) extracted from the shape database 3 into coordinate values so that the stress analysis can be easily performed, and the boundary condition which is the analysis condition 1 with respect to the coordinate values. The load value is added. The converted data for easy analysis is temporarily stored in the solver file 5.

The solver file 5 is for converting the size and shape of the mold into coordinate values so as to facilitate analysis, and adding the boundary conditions and load values to the coordinate values for storage. The solver 6 extracts data from the solver file 5, analyzes the data, outputs the displacement vector u and the stress vector σ as the analysis content output 10, and outputs the stress distribution contour lines as the graphic output 11. That is, it is composed of a stiffness matrix generation unit 7, a load vector generation unit 8, a stress vector calculation unit 9, and the like.

The rigidity matrix generator 7 generates a rigidity matrix K representing the degree of difficulty of deformation, which is determined by the specified Young's modulus and Poisson's ratio of each specified mesh, and will be described later. Figure 7
And a stiffness matrix K is generated as shown in FIG.

The load vector generator 8 generates a load vector P applied to the surface of the object according to the specified boundary condition, and performs a calculation as shown in FIG. 7 described later to generate the load vector P. Is.

The stress vector calculation unit 9 solves the generated load vector P and the stiffness matrix K to obtain the displacement vector u of each element, and calculates the stress vector σ accumulated in each element from the obtained displacement vector u. The stress vector σ is calculated by performing the calculation shown in FIG.
Is calculated.

The analysis content output 10 outputs (displays and prints) the displacement vector u and the stress vector σ analyzed here by the solver 6. The graphic output 11 outputs the analysis result as a graphic, and displays, for example, contour lines of the stress distribution as shown in FIG. 12 described later.

FIG. 2 is a conceptual explanatory view of the present invention. Figure 2
(A) shows an example of the product shape. An example of this is the shape of the final product of a U-shaped core.

FIG. 2 (b) shows how a product as shown by a solid line can be obtained by molding with a die having a dotted line shape and sintering. A deformation amount and a stress which are differences between the two at this time are obtained by calculation, and a die is designed as shown by a solid line in FIG.

In FIG. 2 (c), a solid line mold is designed to mold a product as shown in FIG. 2 (a) based on the deformation amount and stress of FIG. 2 (b). Show the situation. Recalculation using this solid line mold will give the desired product with the dotted line.

As described above, the deformation amount and the stress are calculated on the computer based on the shape of the mold, and the shape of the original mold is corrected so that a desired product can be obtained based on the result. By repeating the steps described above, it becomes possible to design the mold on the computer without repeating the trial manufacture of the mold and the experiment to mold the actual product. At this time, not only the outer shape can be molded with high dimensional accuracy as the final product, but also the shape of the original mold is slightly modified to reduce the internal stress so as to eliminate the high stressed part that causes cracks. To do so. Particularly, in the case of a deflection yoke core shown in FIG. 15 which will be described later, since cracks occur at stress boundaries, the shape is changed so that stress concentration is less likely to occur, and efficient production is performed. As a result of actual experiments, it was found that the design of the mold can reduce the stress concentration and prevent the occurrence of crevices by modifying the basic shape by 1/100 mm to 1/5 mm, so this method is extremely effective. It is a thing.

FIG. 3 shows a flowchart for explaining the operation of the present invention. Here, as a specific example, as shown in FIG.
The following description is based on an example in which the U-shaped core is divided into meshes. In FIG. 3, S1 reads data.
Here, as the data, ・ Outer shape ・ Boundary condition ・ Material characteristic: Young's modulus, Poisson's ratio ・ Load condition is input, and the mesh generation result (for example, as shown in FIG. The result of assigning a node number to) is imported.

Here, the outer shape is, for example, as shown in FIG.
It is read as the shape data shown in. The shape data of FIG. 4A is coordinates (X, Y, Z) corresponding to the node numbers given to the mesh of FIG.

The boundary condition is a boundary condition of mesh nodes. For example, as shown in (b) of FIG. 4, a constraint condition (for example, "constrain all degrees of freedom") and a displacement (corresponding to the node number are associated with each other. For example, the displacement is “0.0”).

The material properties are Young's modulus and Poisson's ratio of the material of the core. For example, as shown in FIG. 4C, Young's modulus "Y" and Poisson's ratio "N". The load condition is a load condition added to the element number of the mesh. For example, as shown in (d) of FIG. 4 and FIG. 6, the pressure value (eg, “3” is associated with the element number (eg, “141”)). 0.00 × E8 ″).

The mesh generation is performed by dividing the outer shape into the intervals (or the number of divisions) designated by the designer, and generating a mesh as shown in FIG. 5, for example. A node number is given to the generated mesh as shown in the figure, and the coordinate value associated with this node number becomes the shape data (outer shape) described above.

By the above S1, the outer shape of the analysis object is divided into meshes, shape data (coordinate values) and boundary conditions (constraint conditions) are added to the node numbers of this mesh, and the mesh element numbers are supported. In addition, load conditions are added, and Young's modulus and Poisson's ratio, which are material properties, are read, and the following calculations are ready.

S2 generates the coefficient K of the stiffness matrix. This produces a coefficient K of the stiffness matrix, as shown on the left side of FIG. The coefficient K of this stiffness matrix is obtained as K _ij (E, NU) as shown in FIG. 8, for example. That is, it is experimentally obtained in advance as a function of E (Young's modulus) and NU (Poisson's ratio).

At S3, a load vector P is generated. As shown in FIG. 7A, the displacement vector u is matrix-operated with the coefficient K of the rigidity matrix generated in S2 to generate the load vector P.

In S4, the simultaneous linear equations Ku = P are solved for u. That is, u = K ⁻¹ P is calculated to obtain the displacement vector u.

In step S5, the stress vector σ is calculated from the displacement vector u. That is, σ = Eu is calculated as shown in FIG. 9A to calculate the stress vector σ.

As described above, data is input in S1 and S
The coefficient K of the stiffness matrix is generated in 2, the load vector P is generated in S3, the displacement vector u is calculated in S4, and the stress vector σ is calculated in S5. Then, the stress vector σ is output as a contour map as shown in FIG.
The displacement vector u (here, u / l) is output as shown in FIG. The designer looks at these analysis results and corrects the original shape so that a desired product (core) can be obtained, or the original shape is reduced so that the stress is reduced, and S1 to S5 are executed again. By repeating the analysis, the optimum mold shape is designed on the computer.

FIG. 4 shows an example of input data of the present invention. FIG. 4A shows an example of shape data. This shape data has coordinates (X, Y, Z) set in association with the node numbers in the mesh division example of FIG.

FIG. 4A-1 shows shape data.
FIG. 4A-2 shows the meaning of each item of the shape data.
The shape data G30 101 0 0 0 shown in the figure includes a rectangular coordinate system, a node number, an X coordinate, and a Y coordinate from the beginning.
Represents the Z coordinate. Here, the node number “101” represents the node number “101” described in the mesh of FIG. 5, and the coordinates (X, Y, Z) of this node number are set.

FIG. 4B shows an example of boundary conditions (constraint conditions). FIG. 4B-1 shows boundary conditions (constraint conditions). FIG. 4B-2 shows the meaning of each term of the boundary condition (constraint condition). Boundary condition 101 (1) AL 0.0 in the figure represents a node number from the beginning, an increment of the node number, all degrees of freedom are constrained, and a displacement is 0.0. If this description is displayed in an easy-to-understand manner, a small circle will appear at the position of node number “101” in FIG.
All the degrees of freedom are constrained and the displacement is set to 0.0, so that (representing constraint conditions) is added.

FIG. 4C shows an example of material characteristics. Here, E Y → Young's modulus NU N → Poisson's ratio. This means that the Young's modulus of the core material is Y and the Poisson's ratio is N. Actually, Y and N have numerical values corresponding to the core material.

FIG. 4D shows an example of load conditions. Figure 4
(D-1) indicates the load condition. (D-2) in FIG.
Indicates the meaning of each term of the load condition. The load condition 141 (1) 3.00 * E8 in the figure represents the element number from the beginning, the increment of the element number, and the pressure value. If this description is displayed in an easy-to-understand manner, ▽ (representing load) "3.00 * E" will be displayed at the position of element number "141" in FIG.
8 "is added.

FIG. 5 shows an example of mesh division according to the present invention.
Here, when the shape of the U-shaped core is given by H1, H2, V1, and V2, the U-shaped core is automatically divided into meshes as illustrated. A node number is assigned to each node of this divided mesh from 101 as shown in the figure.

FIG. 6 shows an example of restraint / load according to the present invention. This is done by assigning an element number to the mesh of FIG. 5, assigning a constraint condition to the position of small circle corresponding to the element number (see (b) of FIG. 4), and assigning a load condition to the position of ▽. (Fig. 4
(See (d)).

FIG. 7 shows an example stiffness matrix / load vector of the present invention. FIG. 7A shows that the result of matrix calculation of the coefficient K of the stiffness matrix and the displacement vector u is the load vector P. The coefficient K of this stiffness matrix
Is calculated by the formula of FIG. 8 described later.

FIG. 7B is a vector representation of the matrix representation of FIG. 7A. FIG. 7C shows
The meaning of each symbol in (a) of FIG. 7 is described.

K _ij : A stiffness matrix, which represents how hard an object is to deform, and which is determined by the Young's modulus and Poisson's ratio peculiar to each substance (see FIG. 8). P _i : a load vector, which represents the pressure applied to the surface of the object.

U _i : displacement vector, which represents the amount of displacement of the object with respect to the load. FIG. 8 shows an example stiffness matrix of the present invention. FIG. 8A shows the relationship between the input, the mesh generation, and the solver 6.

Generates a mesh with H ₁ , H ₂ , V ₁ and V ₂ as inputs (see FIG. 5). The mesh intervals at this time are l ₁ to l _n .・ P, NU, E are input, and solver 6 uses K _ij (E, N
U), ie, the coefficient _{Kij of the} stiffness matrix as a function of E (Young's modulus) and NU (Poisson's ratio).

FIG. 8B shows an example of calculating the value of K.
Here, K = E / (2 * (1 + NU)) is calculated.

FIG. 8C shows a specific example of K. Here, for example, K = 2.6 * 10 ¹⁰ /(2*(1+0.25))=1.
It has a value of 04 * 10 ¹⁰ .

FIG. 8D shows the meaning of symbols. Here, P: load vector, NU: Poisson's ratio, E: Young's modulus, u: displacement vector, σ: stress vector, and K: stiffness matrix.

FIG. 9 shows an example of the stress vector of the present invention.
FIG. 9A shows how to obtain the stress vector. Here, as shown in the figure, the stress vector σ is obtained by the matrix operation represented by the description of σ = E · u / l = Eε.

FIG. 9B is a vector representation of the matrix representation of FIG. 9A. FIG. 9C shows
The meaning of each symbol in (a) and (b) of FIG. 9 is described.

Σ: a stress vector, which is a stress accumulated in each element. E: Young's modulus. U: displacement vector, which is the displacement amount when a load is applied to each element.

L: element length, which is the length before the load of each element is applied. FIG. 10 shows an example of the displacement vector of the present invention. here,
The displacement vector u is calculated by u = K ⁻¹ P and is the displacement vector at the position of each node number. l, l ₁ , l ₂ ... l _n represent the length before applying a load to each object element. Here, it is found that the larger the value of the displacement vector u, the larger the displacement at the position of the node number.

FIG. 11 shows a graphic output flow chart of the present invention. This is a procedure for graphically outputting a contour map for the stress vector obtained as shown in FIGS. 9 and 10 (obtained in S4 and S5 of FIG. 3).

In FIG. 11, S11 takes in coordinate values and stress values (stress vector σ). In step S12, the maximum value and the minimum value are identified, and n is equally divided. For example, in the case of FIG. 12, the maximum value MAX = −608.7 and the minimum value MIN = −880.0 are divided into six equal parts here.

In step S13, each area divided into n equal parts is calculated. For example, as described in the lower right of FIG.
Calculation of each equally divided region is performed. In step S14, an iso surface divided into n equal parts is drawn. For example, as described in the upper right of FIG. 12, when a -653.9 isosurface is drawn, for example, the values "-650", "-680", and "-64" in the vicinity are drawn.
Based on "0" and "-670", the isosurface of -653.9 is obtained and these isosurfaces are connected.
Draw a contour map as shown in 2.

As described above, it becomes possible to take in the coordinate values and stress values of the mesh and draw a contour map of the stress distribution as shown in FIG. FIG. 12 shows an example of stress distribution (contour map) of the present invention. This is a drawing of the stress distribution (contour map) for the U-shaped core described above. Here, MAX and MIN of stress values are divided into 6 equal parts,
A contour map is drawn. As can be seen from this contour diagram, the stress in the part marked MAX is the largest, and
The stress in the portion marked with N is the smallest.

Next, another shape data example of the present invention will be described with reference to FIGS. 13 to 15. This is a drawing of the deflection yoke core by obtaining the stress vector and the like.

FIG. 13 shows another shape data example of the present invention. FIG. 13A shows shape data. Here, R3 101 (20) 25.00 (10) 0 in the upper part represents the cylindrical coordinates, node number, increment, radius, angle Θ, increment, and height from the beginning.

FIG. 13B shows a sectional view of the shape represented by the shape data shown in FIG. Here, the numbers represent the node numbers. Θ represents an angle. h1, h10,
hn represents height.

As described above, the position of the shape of the deflection yoke core is specified by the radius, the angle Θ and the height in association with the node number. FIG. 14 shows another input data example of the present invention. 14 is another example of input data of the deflection yoke core expressed by the shape data of FIG. 13.

FIG. 14A shows Young's modulus and Poisson's ratio. This is the Young's modulus and Poisson's ratio, which are material characteristics, and is E Y → Young's modulus NU N → Poisson's ratio. Actually, Y and N have numerical values corresponding to the core material.

FIG. 14B shows the boundary condition (constraint condition).
Here is an example: Boundary condition 371 (1) AL 0.0 in the upper part of the figure represents a node number from the beginning, an increment of the node number, all degrees of freedom are constrained, and the displacement is 0.0. If this description is displayed in an easy-to-understand manner, all degrees of freedom will be constrained and displacement will be zero, as indicated by a small circle (representing a constraint condition) added to the position of the node number “101” in FIG. .0.

FIG. 14C shows the load condition. Load condition 101 (1) 3.00 * E8 in the upper part of the figure represents the element number from the beginning, the increment of the element number, and the pressure value. If this description is displayed in an easy-to-understand manner, (d) in FIG.
Load "3.00 * E8" perpendicular to the arrowed surface marked P
Is added.

FIG. 14D shows a sectional view. The numbers in the figure represent element numbers. The arrow P indicates the surface to which the load is applied. FIG. 15 is a graphic output example (stress) of the present invention.
Indicates. This is based on the input data (shape data, Young's modulus, Poisson's ratio, boundary conditions,
The stress vector is obtained according to the flow chart of FIG. 3 described above based on the load conditions), and the contour map of the stress distribution is obtained and drawn according to the flow chart of FIG.

[0070]

As described above, according to the present invention,
Since the specified shape is divided into meshes, the displacement vector u and the stress vector σ are calculated and output for each of these elements, and the contour line portion of the stress distribution is drawn It is possible to graphically display the predicted values of stress and displacement when molding with a mold. As a result, the designer looks at the prediction result, corrects the shape of the original mold so that it will have the desired shape of the final product, re-calculates it, and predicts it repeatedly to accurately obtain the product with the desired shape. It becomes possible to generate. In addition, the contour diagram of the stress distribution is displayed graphically, and the parts with high possibility of high stress cracks are slightly modified by reducing the original shape to prevent cracks from occurring. It is possible to design a die that has been made. As described above, by predicting and correcting the stress after molding by the mold, it becomes possible to realize the design of the mold on the computer without repeating the conventional experiment and trial production.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an embodiment of the present invention.

FIG. 2 is a conceptual explanatory diagram of the present invention.

FIG. 3 is a flowchart for explaining the operation of the present invention.

FIG. 4 is an example of input data of the present invention.

FIG. 5 is an example of mesh division according to the present invention.

FIG. 6 is an example of restraint / load of the present invention. .

FIG. 7 is an example stiffness matrix / load vector of the present invention.

FIG. 8 is an example stiffness matrix of the present invention.

FIG. 9 is an example of a stress vector of the present invention.

FIG. 10 is an example of a displacement vector of the present invention.

FIG. 11 is a graphic output flowchart of the present invention.

FIG. 12 is an example of stress distribution (contour map) of the present invention.

FIG. 13 is another example of shape data of the present invention.

FIG. 14 is another example of input data of the present invention.

FIG. 15 is a graphic output example (stress) of the present invention.

FIG. 16 is an explanatory diagram of a conventional technique.

[Explanation of symbols] 1: Analysis condition 2: Mesh generator 21: Input unit 22: Mesh generation function 3: Geometry database 31: Dimension shape file 32: Graphic file 4: Data generation 5: Solver file 6: Solver 7: Rigidity Matrix generator 8: Load vector generator 9: Stress vector calculator 10: Analysis content output 11: Graphic output

Front page continuation (72) Inventor Takeo Maeda 5-36-11 Shimbashi, Minato-ku, Tokyo Inside Fuji Electric Chemical Co., Ltd.

Claims (3)

[Claims] 1. A stress distribution analysis system for analyzing a stress distribution of a shape to be formed by a die, and a mesh generation function (22) for dividing the shape of a designated die into meshes, and each of these divided pieces. With respect to the mesh, a rigidity matrix generation unit (7) that generates a rigidity matrix K that represents the difficulty of deformation determined by the specified Young's modulus and Poisson's ratio of the material, and the load applied to the object surface by the specified boundary conditions. A load vector generation unit (8) that generates a vector P, and a stress vector that calculates a stress vector σ that accumulates in each element from the generated load vector P and the displacement vector u of each element obtained by solving from the stiffness matrix K A calculation unit (9) and configured to output the displacement vector u and the stress vector σ of the calculated element. Stress distribution analysis system, characterized in that. 2. The stress distribution analysis system according to claim 1, wherein the stress distribution analysis system is configured to output contour lines of stress distribution connecting the same points based on the stress vector σ. 3. Referring to the output displacement vector u,
Recalculate the displacement vector u and stress vector σ of the element corresponding to the modification of the original shape so as to match the shape to be molded and the modification of the original shape so that the above stress distribution becomes smaller if necessary. The stress distribution analysis system according to claim 1 or 2, wherein the stress distribution analysis system is configured to output the data.