JP2014067329A - Simulation device, simulation method and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To clarify a mechanism of powder molding causing a large deformation by performing a compression molding on iron powder or iron alloy powder having a particle size distribution and precisely calculate the density distribution, the residual stress distribution and the strain distribution.SOLUTION: After defining a powder model in a DEM method and an SPH method, a pressure is applied to plural powders to perform compression molding; and in the process, a weak coupling is made between the DEM method and the SPH method to calculate the powder density. In an initial stage, when particles achieve complete contact each other, a boundary processing is made by means of a movement least square at the weak coupling between the DEM method and the SPH method to interpolate therebetween. A pressure is applied to plural powders to perform a compression molding, the weak coupling is made between the DEM method and the SPH method until predetermined powder density and the powder density is calculated.

Description

  The present invention relates to a technique for numerical simulation of a processing method in which powder is packed in a mold and compression-molded. In particular, the DEM method and SPH method are weakly coupled, and powder in a compression molding process of a powder having a particle size distribution. The present invention relates to a simulation apparatus, a simulation method, and a program for simulating a phenomenon in which a body is crushed and greatly plastically deforms.

  In recent years, downsizing of electrical equipment and electronic equipment has further progressed, and the demand for downsizing of components used in these equipments is not limited. Against this background, there is an increasing demand for miniaturization and high efficiency of inductors, which are important components used in electrical and electronic devices.

  There are various inductor structures, and a structure in which a magnetic core constituting a closed magnetic circuit is arranged around a coil is often used for the purpose of improving efficiency. The magnetic core used for such an inductor is generally a ferrite magnetic core made of a ferrite sintered body, a laminated magnetic core obtained by laminating plate materials such as amorphous alloy ribbon and high silicon steel, amorphous iron powder, Fe- A powder magnetic core obtained by compression-molding magnetic metal powder such as Si powder, Fe—Cr—Si powder, or Fe—Si—Al powder using a binder is used (for example, see Patent Document 1).

  However, since the above-mentioned compression molding may cause destruction of the molded body during the molding process, the probability that the molded body will be destroyed due to the internal density distribution, residual stress distribution, and residual strain distribution of the molded body. Therefore, there is a need for an analysis technique for obtaining information that is important for knowing where the problem occurs.

JP 2006-294733 A

  Further, there are methods using the finite element method and the DEM method as analysis techniques, but there is a problem that necessary information cannot be obtained by these methods. For example, since the finite element method cannot accurately represent the behavior of the powder, the obtained results often do not match the actual results, and the residual stress distribution and the residual density distribution cannot be obtained by the DEM method.

  Therefore, the present invention has been made in view of the above-described problems, and elucidates the mechanism of powder molding that causes large deformation during compression molding of iron powder or iron alloy powder having a particle size distribution, and its density distribution. An object of the present invention is to provide a simulation apparatus, a simulation method, and a program capable of accurately obtaining a residual stress distribution and a residual strain distribution.

  The present invention proposes the following matters in order to solve the above problems. In addition, in order to make an understanding easy, although the code | symbol corresponding to embodiment of this invention is attached | subjected and demonstrated, it is not limited to this.

  (1) The present invention is a simulation device for simulating powder compression molding, and is a compression molding means for performing compression molding of powder having a particle size distribution (for example, equivalent to the compression molding unit 100 in FIG. 1). A first analysis processing unit (for example, corresponding to the first analysis processing unit 200 in FIG. 1) that executes analysis processing based on the DEM method, and a second analysis that executes analysis processing based on the SPH method Control means for controlling the processing so as to weakly couple the processing means (for example, equivalent to the second analysis processing unit 300 in FIG. 1), the first analysis processing means and the second analysis processing means. (For example, corresponding to the control unit 600 in FIG. 1) is proposed.

  According to the present invention, compression molding of powder having a particle size distribution is weakly coupled with the DEM method and the SPH method, that is, a plurality of phenomena represented by different governing equations are exchanged with each other. However, it is possible to obtain accurate residual stress and residual strain distribution by solving alternately or separately in parallel.

  (2) The present invention relates to the simulation apparatus of (1), wherein in the DEM method, the powder is expressed by a spring-dashpot model, and in the SPH method, the powder is expressed by an elastic-plastic spring force. We have proposed a simulation device characterized by a coupled powder model.

  According to this invention, in the DEM method, the powder is expressed by a spring-dashpot model, and in the SPH method, the powder is expressed by a powder model in which a plurality of particles are coupled by an elastic-plastic spring force. A simulation of compression molding can be executed in a powder model composed of multiple particles.

  (3) The present invention relates to the simulation apparatus of (1) or (2), in which the control means establishes a boundary condition from a discontinuous body to a continuous body when the initial particles are in complete contact with each other. The simulation apparatus characterized by determining is proposed.

  According to the present invention, when the initial particles are in complete contact with each other, it is determined that the boundary condition from the discontinuous body to the continuous body is established. The body can be subjected to a simulation of the entire compression molding by performing an analysis by the SPH method.

  (4) In the simulation apparatus of (1) to (3), the present invention is an interpolation means for executing boundary processing at the time of weak coupling between the DEM method and the SPH method by moving least square approximation (for example, FIG. A simulation apparatus characterized by having an interpolation unit 400).

  According to the present invention, the boundary processing at the time of weak coupling between the DEM method and the SPH method is executed by moving least square approximation, and the density is changed by large compression and the portion is close to a continuum. The interpolation error of the physical quantity at the boundary due to the difference in the particle distribution in the powder portion where compression is not yet applied can be corrected.

  (5) The present invention proposes a simulation apparatus characterized in that, for the simulation apparatuses of (1) to (4), the powder compression molding simulation is applied to an inductor having a magnetic core integrated structure. .

  According to the present invention, compression molding of powder having a particle size distribution is weakly coupled with the DEM method and the SPH method, that is, a plurality of phenomena represented by different governing equations are exchanged with each other. However, since it is possible to obtain accurate residual stress and residual strain distribution by solving alternately or separately in parallel, it is particularly preferable to use for simulation of compression molding of an inductor having a magnetic core integrated structure. .

  (6) The present invention is a simulation method in a simulation apparatus for simulating powder compression molding, and the first step of defining a powder model in the DEM method and the SPH method (for example, in step S100 in FIG. 10) And a second step of calculating the powder density by applying a pressure to a plurality of powders to perform compression molding, and weakly coupling the DEM method and the SPH method in the process (for example, 10), and when the initial particles are in complete contact with each other, the boundary processing at the time of weak coupling between the DEM method and the SPH method is executed by the moving least square approximation to perform interpolation. Step 3 (e.g., equivalent to step S300 in FIG. 10), pressure is applied to a plurality of powders, compression molding is performed, and the previous powder density is reached until a predetermined powder density is reached. Proposed a simulation method characterized by comprising a fourth step (for example, equivalent to step S400 in FIG. 10) of executing a powder density calculation by weakly coupling the DEM method and the SPH method. doing.

  According to the present invention, compression molding of powder having a particle size distribution is weakly coupled with the DEM method and the SPH method, that is, a plurality of phenomena represented by different governing equations are exchanged with each other. However, it is possible to obtain accurate residual stress and residual strain distribution by solving alternately or separately in parallel.

  (7) The present invention is a program for causing a computer to execute a simulation method in a simulation apparatus for simulating powder compression molding, and a first step of defining a powder model in the DEM method and the SPH method ( For example, this corresponds to step S100 in FIG. 10) and pressure is applied to a plurality of powders to perform compression molding, and in the process, the DEM method and the SPH method are weakly coupled to calculate the powder density. When the second step (for example, corresponding to step S200 in FIG. 10) and the initial particles are in complete contact with each other, the boundary processing at the time of weak coupling between the DEM method and the SPH method is performed as a moving least square. A third step (for example, corresponding to step S300 in FIG. 10) executed by approximation and interpolated, and pressure is applied to a plurality of powders to perform compression molding And a fourth step (for example, corresponding to step S400 in FIG. 10) of executing the calculation of the powder density by weakly coupling the DEM method and the SPH method until a predetermined powder density is reached. , A program for causing a computer to execute is proposed.

  According to the present invention, compression molding of powder having a particle size distribution is weakly coupled with the DEM method and the SPH method, that is, a plurality of phenomena represented by different governing equations are exchanged with each other. However, it is possible to obtain accurate residual stress and residual strain distribution by solving alternately or separately in parallel.

  According to the present invention, there is an effect that deformation of powder, change in density distribution, and change in strain distribution are required in a process in which the powder is crushed while being largely deformed. In addition, there is an effect that it is possible to know the conditions for obtaining an accurate molded product that is difficult to break from the result obtained by the simulation. Furthermore, we can provide unprecedented new analysis methods for each field that requires powder molding simulation, solve technical problems in each field, and create new product creation opportunities. There is an effect.

It is a figure which shows the structure of the simulation apparatus which concerns on embodiment of this invention. It is a figure which shows the simulation model which concerns on embodiment of this invention. It is a figure which shows the simulation model by the DEM method which concerns on embodiment of this invention. It is a figure which shows the process of the compression molding which concerns on embodiment of this invention. It is a figure which shows the simulation model by SPH method which concerns on embodiment of this invention. It is a figure which shows the simulation model which concerns on embodiment of this invention. It is a figure which shows the simulation model which concerns on embodiment of this invention. It is a figure which shows the simulation model which concerns on embodiment of this invention. It is a figure which shows the transition process from the discrete model which concerns on embodiment of this invention to a continuum model. It is a figure which shows the process of the simulation apparatus which concerns on embodiment of this invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
Note that the constituent elements in the present embodiment can be appropriately replaced with existing constituent elements and the like, and various variations including combinations with other existing constituent elements are possible. Therefore, the description of the present embodiment does not limit the contents of the invention described in the claims.

<Embodiment>
Hereinafter, embodiments of the present invention will be described with reference to FIGS. 1 to 9.

<Configuration of simulation device>
The configuration of the simulation apparatus according to the present embodiment will be described with reference to FIG.
As shown in FIG. 1, the simulation apparatus according to the present embodiment includes a compression molding unit 100, a first analysis processing unit 200, a second analysis processing unit 300, an interpolation unit 400, a display unit 500, It is comprised from the control part 600. FIG.

  The compression molding unit 100 executes compression molding of powder having a particle size distribution. The first analysis processing unit 200 executes analysis processing based on the DEM method. The second analysis processing unit 300 executes analysis processing based on the SPH method. The interpolation unit 400 executes boundary processing at the time of weak coupling between the DEM method and the SPH method by moving least square approximation. The display unit 500 displays a simulation process and a simulation result on a display device such as a display.

  The control unit 600 includes a compression molding unit 100, a first analysis processing unit 200, a second analysis processing unit 300, an interpolation unit 400, and a display unit 500 according to a control program stored in advance in a ROM (Read Only Memory) or the like. Control the behavior. According to the present embodiment, in particular, the process is controlled so that the first analysis processing unit 200 and the second analysis processing unit 300 are weakly coupled.

<Outline of model definition and simulation>
In the present invention, in order to simulate large deformation and plastic behavior of powder particles, simulation is performed assuming that one powder is composed of a plurality of particles as shown in FIG.

  That is, one powder is modeled using many basic particles. All basic particles are spherical particles of the same size. The basic particles and the basic particles are joined together by springs to form an overall shape. FIG. 2 shows a basic particle and one powder (hereinafter referred to as a powder particle) prepared by combining a plurality of basic particles. The combination of basic particles is free, and powder particles having any shape can be modeled. The spring connecting the basic particles and the basic particles undergoes elasto-plastic deformation. A large number of powder models are combined and placed in a mold. The arrangement of the powder particles is set so that the powder particles are in light contact with each other.

  The compression analysis of the powder particles is performed using DEM theory. The basic particles used in the present invention correspond to the DEM particles in the DEM theory. In the DEM theory, the motion of a particle is obtained over time by obtaining the motion equation of the DEM particle. In the present invention, a new motion equation in which a spring force for connecting DEM particles (basic particles) to the motion equation is introduced is solved.

FIG. 3 shows a conceptual diagram of DEM particles (basic particles). Further, the motion of this element is expressed by Equation 1 which is a motion equation representing the following translational motion and rotational motion, as mass m _i and moment of inertia I _i .

  Here, F is an external force acting on the element, M is a moment acting on the element, C is a damping constant, μ is a displacement vector of the element, D is a rotational displacement of the element (scalar in the case of two dimensions, 3 In the case of dimensions, it is a vector), and the displacement vector μ and the rotational displacement φ are obtained by numerically integrating Equation 1 with a time history.

  The powder particles are gradually compressed by DEM compression calculation. In this compression process, the powder particles are gradually greatly deformed. This is shown in FIG. In the conventional method, since calculation was performed using only basic particles, the deformation of the powder could not be obtained. In this method, it is possible to obtain a state in which a powder having an arbitrary shape undergoes a large deformation under pressure from surrounding powder.

  Obtain the relative density distribution of the powder inside the mold. The relative density distribution calculation determines the density of the basic particles. Relative density is also measured as the ratio of the volume of an object that occupies a fixed volume. A relative density of 1 indicates that the volume is entirely occupied by a substance, and 0 indicates an empty state in which no substance exists.

  The relative density increases as compression proceeds. The powder particles are in close contact with the surrounding powder particles, and the mutual movement is integrated. Further, when the relative density exceeds a certain value, the powders coalesce and thereafter perform an integrated movement. If the integration of the powders progresses over a wide range, the DEM theory, which has so far required the movement of individual powders, cannot be applied.

  When the powder particles are integrated, it can be regarded as a state close to one continuous solid (continuum). To express the motion of this continuum, the DEM theory cannot be used and the SPH theory is used. The SPH theory is a method of solving a field called continuum mechanics, which is used when dealing with deformation of a single metal. Using the SPH theory, the distribution of stress and strain in a state where the powder becomes a very strong molded product is obtained. Stress distribution and strain distribution cannot be obtained by DEM theory, but must be based on the SPH method.

  FIG. 5 shows a basic conceptual diagram of SPH particles. As shown in FIG. 5, in the SPH method, a powder can be expressed by a powder model in which a plurality of particles are coupled by an elastic-plastic spring force. With this model, powder having an arbitrary shape can be expressed as shown in FIG. Therefore, small powder and large powder are modeled. Moreover, as shown in FIG. 7, when particles are arranged and modeled along a surface arc shape, the initial shape can be expressed. Analysis that leads to final molding is possible while maintaining this initial shape.

  The SPH method is a kind of interpolation method for discretely obtaining a spatial first or second derivative (Laplacian) of a function f (x) using a weighting function W based on the concept of an influence radius. The physical quantity of other particles inside the circle called the influence radius shown in FIG. 8 is expressed by Equation 2 for the spatial first derivative using the first derivative of the weight function.

  For partial differentiation of 2, the interpolated values are obtained discretely based on Equation 3.

  Further, in the range of the elastic analysis, the elastic motion of the particles using only the first-order partial differential equation is expressed by Equation 4 according to Newton's equation of motion.

  Here, a is acceleration, ρ is density, and σ is Cauchy stress tensor. Applying equation (5) to equation (6) makes it possible to calculate the acceleration of particle I.

  Here, m is the mass, I is the particle at the center position for which the interpolation value is obtained, and J is the other particle inside the influence radius.

  Equation 6 shows that the force exerted by the particle i on the particle j is equal to the force exerted by the particle j on the particle i, and that the law of conservation of momentum holds between the particles i and j. From this acceleration value, the particle velocity and further the particle displacement are incrementally obtained from the Crank-Nicolson difference formula relating to the time history, which is normally used in the explicit method. Further, the stress value of the particle can be obtained using a stress-strain matrix in FEM analysis based on the obtained displacement increment.

  In this simulation, particle motion is performed by a discrete model (DEM). When the particles are densely packed and begin to show a substantially continuous behavior, physical evaluation (stress / strain) of the particle group is performed by SPH theory. Therefore, a criterion for determining the transition from a discontinuous body to a continuous body must be provided. In this simulation, the particle density is determined using the concept of the influence radius of SPH. That is, as shown in FIG. 9, when the initial spherical particles achieve complete contact, it is considered that they are continuous (determination of boundary conditions).

  In addition, there is a difference in the particle distribution between the portion (SPH) in which the density has changed due to large compression and the state is close to a continuum (SPH), and the powder portion (DEM) that has not yet been compressed. For this reason, an error is likely to occur in the physical quantity interpolation at the boundary between the two. In order to correct this, processing using a moving least square approximation is performed at the boundary between the two. In order to obtain the interpolation function by this method, the physical quantity of the interpolation point inside the influence radius is described as in Expression 7.

However, h ^j corresponds to the smoothing length in the SPH method, and the influence radius of the contact is kh. W is a weighting function, a polynomial basis vector is a moment matrix expressed by Equation 8, and p is an MLS shape function. A cubic spline function (k = 2) is often used as the function w (x, h) used for the MLS approximation. Further, assuming that Equation 9 is further used as a two-dimensional polynomial basis vector, a differential value in the _xi direction based on the MLS approximation is described as Equation 10. Interpolation at the boundary between SPH and DEM is performed based on this differential equation to increase the interpolation accuracy.

<Processing of simulation device>
The process of the simulation apparatus according to this embodiment will be described with reference to FIG.

  First, a powder model in the DEM method and the SPH method is defined (step S100), pressure is applied to a plurality of powders to perform compression molding, and in the process, the DEM method and the SPH method are weakly coupled. Thus, the powder density is calculated (step S200). Then, when the initial particles are in complete contact with each other, the boundary processing at the time of weak coupling between the DEM method and the SPH method is performed by interpolation by moving least square approximation (step S300), and a plurality of powders Pressure is applied, compression molding is performed, and the powder density is calculated by weakly coupling the DEM method and the SPH method until a predetermined powder density is reached (step S400).

  As described above, according to the present embodiment, compression molding of powder having a particle size distribution is weakly coupled with the DEM method and the SPH method, that is, a plurality of phenomena expressed by separate governing equations. By exchanging information related to each other and solving in parallel or separately, accurate residual stress and residual strain distribution can be obtained.

  The simulation apparatus of the present invention can be realized by recording the processing of the simulation apparatus on a recording medium readable by the computer system, causing the simulation apparatus to read and execute the program recorded on the recording medium. The computer system here includes an OS and hardware such as peripheral devices.

  Further, the “computer system” includes a homepage providing environment (or display environment) if a WWW (World Wide Web) system is used. The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.

  The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, what is called a difference file (difference program) may be sufficient.

  The embodiments of the present invention have been described in detail with reference to the drawings. However, the specific configuration is not limited to the embodiments, and includes designs and the like that do not depart from the gist of the present invention.

DESCRIPTION OF SYMBOLS 100; Compression molding part 200; 1st analysis process part 300; 2nd analysis process part 400; Interpolation part 500; Display part 600;

Claims (7)

A simulation device for simulating powder compression molding,
Compression molding means for performing compression molding of powder having a particle size distribution;
First analysis processing means for executing analysis processing based on the DEM method;
Second analysis processing means for executing analysis processing based on the SPH method;
Control means for controlling processing so as to weakly couple the first analysis processing means and the second analysis processing means;
A simulation apparatus comprising:   The powder is represented by a spring-dashpot model in the DEM method, and the powder is represented by a powder model in which a plurality of particles are coupled by an elastic-plastic spring force in the SPH method. 1. The simulation apparatus according to 1.   3. The simulation apparatus according to claim 1, wherein the control unit determines that a boundary condition from a discontinuous body to a continuous body is satisfied when initial particles completely contact each other. .   The simulation apparatus according to any one of claims 1 to 3, further comprising interpolation means for executing boundary processing at the time of weak coupling between the DEM method and the SPH method by moving least square approximation.   5. The simulation apparatus according to claim 1, wherein the powder compression molding simulation is applied to an inductor having a magnetic core integrated structure. A simulation method in a simulation device for simulating powder compression molding,
A first step of defining a powder model in the DEM and SPH methods;
A second step of calculating a powder density by applying pressure to a plurality of powders to perform compression molding and weakly coupling the DEM method and the SPH method in the process;
A third step of interpolating by executing a boundary process at the time of weak coupling between the DEM method and the SPH method by moving least square approximation when initial particles are in complete contact;
Fourth step of applying a pressure to a plurality of powders, performing compression molding, and weakly coupling the DEM method and the SPH method until a predetermined powder density is reached, and calculating the powder density When,
A simulation method characterized by comprising: A program for causing a computer to execute a simulation method in a simulation apparatus for simulating powder compression molding,
A first step of defining a powder model in the DEM and SPH methods;
A second step of calculating a powder density by applying pressure to a plurality of powders to perform compression molding and weakly coupling the DEM method and the SPH method in the process;
A third step of interpolating by executing a boundary process at the time of weak coupling between the DEM method and the SPH method by moving least square approximation when initial particles are in complete contact;
Fourth step of applying a pressure to a plurality of powders, performing compression molding, and weakly coupling the DEM method and the SPH method until a predetermined powder density is reached, and calculating the powder density When,
A program that causes a computer to execute.