JP6316163B2 - Analysis apparatus and analysis method - Google Patents

Description

  The present invention relates to an analysis apparatus and an analysis method.

  Molecular dynamics method (MD method) and quantum molecular dynamics method (Quantum Molecular) are methods for exploring phenomena in general material science using computers based on classical mechanics and quantum mechanics. Dynamics Method) and simulation based on Renormalized Molecular Dynamics (hereinafter referred to as RMD method), which is an MD method developed to handle a macroscale system, are known.

  Recently, a renormalized molecular dynamics method (hereinafter referred to as RMD method) has been proposed in which the MD method has been developed to handle a macro-scale system (see, for example, Patent Document 1).

JP 2007-199646 A

  In the RMD method, when considering the coupling of the control in the mechanism / elasticity analysis, the calculation time becomes long if the real time of the control is simulated.

  The present invention has been made in view of these problems, and an object thereof is to provide an analysis technique capable of reducing the calculation time of the coupled analysis of the mechanism / elasticity analysis and the control.

  In order to solve the above problems, an analysis apparatus according to an aspect of the present invention is an analysis apparatus that analyzes a particle system by numerically calculating a motion equation of the particle for a particle system including a plurality of particles, A distance between the control force application unit that multiplies the speed command value given from the outside of the particle system by α (α is 1 or more) and applies a control force based on the speed command value multiplied by α to a predetermined particle. Based on the force calculation unit that calculates the force acting on the particle based on the force, the force calculated by the force calculation unit, and the control force if the control force is applied to the particle by the control force applying unit, A particle state calculation unit that calculates at least one of position and velocity.

  It should be noted that any combination of the above-described constituent elements, or those obtained by replacing the constituent elements and expressions of the present invention with each other between apparatuses, methods, systems, computer programs, recording media storing computer programs, and the like are also included in the present invention. It is effective as an embodiment of

  ADVANTAGE OF THE INVENTION According to this invention, the analysis technique which can reduce the calculation time of a mechanism / elasticity analysis and control coupled analysis can be provided.

It is a block diagram which shows the function and structure of the analyzer which concerns on embodiment. It is a data structure figure which shows an example of the particle | grain data holding part of FIG. It is a flowchart which shows an example of a series of processes in the analyzer of FIG. 4A and 4B are graphs showing calculation results using the method according to the present embodiment.

  Hereinafter, the same or equivalent components, members, and processes shown in the drawings are denoted by the same reference numerals, and repeated description is appropriately omitted.

The principle of analysis by the analysis device will be described in the embodiment.
The analysis apparatus according to the embodiment performs a coupled simulation of mechanism / elasticity and control on an actual object such as an injection molding machine. This coupled analysis is difficult with the prior art such as the finite element method, and the currently feasible method is the RMD method. However, in the RMD method, the time increment is on the order of (distance between nearest neighbor particles) / (sound speed), so that it takes a long calculation time to simulate the real time of control. Therefore, in the present embodiment, the object is moved at an actual α times speed. Thereby, the phenomenon is finished earlier than the real time, and the calculation time is shortened.

ここで、ｍは質量、ｖは速度、ｚは位置、ｔは時間、ｖ_ｒは速度指令値、ｚ_ｒは位置指令値、Ｋ_ｄ、Ｋ_ｐは制御パラメータであり、それぞれ速度と位置のゲインである。
本実施の形態では、この式（１）における速度指令値に実際の速度指令値をα（α＞１）倍に変換した値を代入することにより、実際のα倍の速度で物体を運動させる。 Specifically, when a force is applied to a predetermined location of the object in order to move the target object, the force defined by equation (1) (hereinafter referred to as the force) is applied to the equation of motion of the particle corresponding to the predetermined location. Also called “control force”.

Here, m is the mass, v is velocity, z is the position, t is time, _{v r} is the speed command value, _{z r} is the position command _value, K d, _{K p} is a control parameter, gain speed and each position It is.
In the present embodiment, by substituting a value obtained by converting the actual speed command value by α (α> 1) times into the speed command value in the equation (1), the object is moved at an actual α-times speed. .

となる。
ここで、

である。
速度指令値をα倍したとき、すなわちｖ_ｒをαｖ_ｒに変換したとき、相似な結果を得るには式（２）にαが現われてはならない。これより、変換は以下の通りとなる。

式（３）を満足する場合、計算時間は１／αに短縮され、かつ、各粒子の速度／位置は実際の値と相似になる。 In the present embodiment, the control parameters are also converted so that the phenomenon is similar. That is, the control parameters are also converted so that the speed / position of each particle obtained as a result of the simulation is similar to the actual speed / position (that is, the speed / position when α = 1). When equation (1) is made dimensionless,

It becomes.
here,

It is.
When the speed command value is multiplied by α, that is, when v _r is converted to αv _r , α must not appear in Equation (2) in order to obtain a similar result. From this, the conversion is as follows.

If equation (3) is satisfied, the calculation time is reduced to 1 / α and the velocity / position of each particle is similar to the actual value.

  FIG. 1 is a block diagram illustrating functions and configurations of an analysis apparatus 100 according to an embodiment. Each block shown here can be realized by hardware such as a computer (CPU) (central processing unit) and other elements and mechanical devices, and software can be realized by a computer program or the like. Here, The functional block realized by those cooperation is drawn. Therefore, it is understood by those skilled in the art who have touched this specification that these functional blocks can be realized in various forms by a combination of hardware and software.

  In this embodiment, a case where a particle system is analyzed following the RMD method will be described. However, particle methods such as DEM (Distinct Element Method), SPH (Smoothed Particle Hydrodynamics), and MPS (Moving Particle Semi-implicit) are used. It will be apparent to those skilled in the art who have touched the present specification that the technical idea according to the present embodiment can also be applied when analyzing a particle system in accordance with the MD method that is not performed.

  The analysis device 100 is connected to the input device 102 and the output device 104. The input device 102 may be a keyboard, a mouse, or the like for receiving user input related to processing executed by the analysis device 100. The input device 102 may be configured to receive input from a network such as the Internet or a recording medium such as a CD or a DVD. The output device 104 may be a display device such as a display or a printing device such as a printer.

  The analysis device 100 includes a particle system acquisition unit 110, a command value acquisition unit 112, a numerical value calculation unit 120, a display control unit 140, a particle data holding unit 150, and a command value holding unit 152.

  The particle system acquisition unit 110 is based on input information acquired from the user via the input device 102, and is a particle system consisting of N (N is a natural number) particles defined in a 1, 2, or 3D virtual space. Get the data. The particle system mimics a real object such as an injection molding machine. The particle system is a particle system that has been brought in using the RMD method.

  The particle system acquisition unit 110 arranges N particles in the virtual space based on the input information, and gives a speed to each of the arranged particles. That is, the particle system acquisition unit 110 gives an initial position and an initial velocity to the particle system. The particle system acquisition unit 110 registers the particle ID that identifies the arranged particle, the position of the particle, and the velocity of the particle in the particle data holding unit 150 in association with each other.

  The command value acquisition unit 112 acquires a control command value for controlling the particle system based on input information acquired from the user via the input device 102. In particular, the command value acquisition unit 112 acquires a speed command value and a position command value for each particle to which a control force is applied. In addition, the command value acquisition unit 112 also acquires a double speed command value (that is, a value set in α in Expression (1)) indicating how many times the particle system is moved. The command value acquisition unit 112 holds the acquired control command value and double speed command value in the command value holding unit 152.

  In the following, a case will be described in which all particles of the particle system are set to be the same or equivalent, and the potential energy function is set to have two potentials and have the same shape regardless of the particles. However, it will be apparent to those skilled in the art who have touched this specification that the technical idea according to the present embodiment can be applied to other cases.

The numerical calculation unit 120 numerically calculates a governing equation that governs the motion of each particle in the particle system represented by the data held by the particle data holding unit 150. In particular, the numerical calculation unit 120 repeatedly performs calculations according to the discretized equation of motion of particles.
The numerical value calculation unit 120 includes a force calculation unit 122, a control force applying unit 132, a particle state calculation unit 124, a state update unit 126, and an end condition determination unit 128.

  The control force applying unit 132 refers to the control command value and the double speed command value held by the command value holding unit 152, and applies the control force calculated by the equation (1) to each particle designated by the user. . That is, for each specified particle, a control force according to a deviation between the speed based on the speed command value and the position based on the position command value and the speed and position of the particle held in the particle data holding unit 150 is applied. . The control force applying unit 132 registers the control force to be applied to each specified particle in the particle data holding unit 150.

  The force calculation unit 122 refers to the particle data held by the particle data holding unit 150, and calculates the force acting on the particles based on the distance between the particles for each particle in the particle system. The force calculation unit 122 determines, for the i-th particle (1 ≦ i ≦ N) in the particle system, a particle whose distance from the i-th particle is smaller than a predetermined cutoff distance (hereinafter referred to as a close particle). To do.

  For each neighboring particle, the force calculation unit 122 determines that the neighboring particle is the i-th particle based on the potential energy function between the neighboring particle and the i-th particle and the distance between the neighboring particle and the i-th particle. Calculate the force exerted on. In particular, the force calculator 122 calculates the force from the gradient value of the potential energy function at the distance value between the adjacent particle and the i-th particle. The force calculation unit 122 calculates the force acting on the i-th particle by adding the force exerted by the adjacent particle on the i-th particle for all the adjacent particles.

  The particle state calculation unit 124 refers to the particle system data held in the particle data holding unit 150, and for each particle of the particle system, the force calculated by the force calculation unit 122 to the discrete particle motion equation, When the control force is applied to the particles by the control force applying unit 132, the control force is applied to calculate at least one of the position and velocity of the particles. In the present embodiment, the particle state calculation unit 124 calculates both the position and velocity of the particle.

  The particle state calculation unit 124 is discretized including the force calculated by the force calculation unit 122 and the control force held by the particle data holding unit 150 for the particles to which the control force is given by the control force giving unit 132. The velocity of the particle is calculated from the equation of motion of the particle. For the other particles, the particle state calculation unit 124 calculates the velocity of the particles from the discrete equation of motion of the particles including the force calculated by the force calculation unit 122.

  The particle state calculation unit 124 uses a predetermined minute time step Δt for each particle of the i-th particle system based on a predetermined numerical analysis method such as a jumping method or an Euler method. By substituting the force calculated by the force calculation unit 122 and the control force held by the particle data holding unit 150 into the equation of motion, the velocity of the particles is calculated. For this calculation, the velocity of the particle calculated in the previous cycle of repetition is used. Note that the time increment Δt is constant regardless of the double speed command value.

  The particle state calculation unit 124 calculates the position of the particle based on the calculated particle velocity. The particle state calculation unit 124 calculates, for a particle of the i-th particle system, a relational expression between the position and velocity of the particle discretized using the time step Δt based on a predetermined numerical analysis technique. The particle position is calculated by applying the velocity. For this calculation, the position of the particle calculated in the previous cycle of repetition calculation is used.

  The state update unit 126 updates the state of each particle in each particle system based on the calculation result in the particle state calculation unit 124. The state update unit 126 updates the position and velocity of each particle of each particle system held in the particle data holding unit 150 with the position and velocity calculated by the particle state calculation unit 124.

  The end condition determination unit 128 determines whether or not the repetitive calculation in the numerical value calculation unit 120 should be ended. Termination conditions for ending the repetitive calculation are, for example, that the repetitive calculation has been performed a predetermined number of times, that an end instruction has been received from the outside, or that the particle system has reached a steady state. When the end condition is satisfied, the end condition determination unit 128 ends the repetitive calculation in the numerical value calculation unit 120. When the end condition is not satisfied, the end condition determining unit 128 returns the process to the control force applying unit 132. Then, the control force application unit 132 calculates and applies the control force at the speed and position updated by the state update unit 126.

  The display control unit 140 causes the output device 104 to display the state of the particle system over time and the state at a certain time based on the position and velocity of each particle of each particle system represented by the data held in the particle data holding unit 150. . This display may be performed in the form of a still image or a moving image.

  FIG. 2 is a data structure diagram illustrating an example of the particle data holding unit 150. The particle data holding unit 150 holds the particle ID, the position of the particle, the velocity of the particle, and the control force when the control force is applied to the particle in association with each other.

  In the above-described embodiment, examples of the holding unit are a hard disk and a memory. Based on the description in this specification, each unit is realized by a CPU (not shown), an installed application program module, a system program module, a memory that temporarily stores the contents of data read from the hard disk, and the like. It is understood by those skilled in the art who have touched this specification that they can do this.

The operation of the analysis apparatus 100 configured as above will be described.
FIG. 3 is a flowchart illustrating an example of a series of processes in the analysis apparatus 100. The particle system acquisition unit 110 acquires a particle system that has been transferred in accordance with the RMD method (S202). The command value acquisition unit 112 acquires a control command value and a double speed command value for controlling the particle system (S204). The control force applying unit 132 applies a control force based on the control command value and the double speed command value to predetermined particles (S206). The force calculator 122 calculates the force acting on the particles from the distance between the particles (S208). The particle state calculation unit 124 calculates the velocity and position of the particle from the particle motion equation (S210). Here, a control force is introduced into the equation of motion of a predetermined particle. The state updating unit 126 updates the position and speed of the particles held in the particle data holding unit 150 with the calculated position and speed (S212). The end condition determination unit 128 determines whether or not the end condition is satisfied (S214). If the end condition is not satisfied (N in S214), the process returns to S206. If the end condition is satisfied (Y in S214), the process ends.

  According to analysis apparatus 100 according to the present embodiment, the particle system moves at a speed that is α times the actual speed (that is, the speed command value). Therefore, the calculation time for the simulation can be shortened to the actual 1 / α. In addition, since the control parameters are converted so that the phenomenon is similar, the velocity / position of each particle is similar to the actual value.

  The inventor performed verification using the analysis apparatus 100 according to the present embodiment. Specifically, a control force based on the speed command value and the position command value was applied to a predetermined position of the movable type of the injection molding machine, and the movement was simulated. 4A and 4B are graphs showing calculation results using the method according to the present embodiment. FIG. 4A shows the speed command value and the calculated speed. FIG. 4B shows the position command value and the position of the calculation result. 4A is a speed command value, graph 304 is a calculation result when α = 1, graph 306 is a calculation result when α = 2, graph 308 is a calculation result when α = 5, graph Reference numeral 310 denotes a calculation result when α = 10. The graph 312 in FIG. 4B shows the speed command value, and the graph 314 shows the calculation result when α = 1 to 10. 4A and 4B, when α = 1, that is, when calculated in real time, when α = 2, 5, and 10, that is, when the phenomenon is finished earlier than real time. Similar results are obtained.

  The configuration and operation of the analysis apparatus 100 according to the embodiment has been described above. This embodiment is an exemplification, and it is understood by those skilled in the art that various modifications can be made to each component and combination of processes, and such modifications are within the scope of the present invention.

  In the embodiment, the case where both the position and the speed of the particle are calculated in the numerical value calculation unit 120 has been described. For example, there is a numerical analysis method such as the Verlet method in which the particle position is directly calculated from the force acting on the particle when calculating the particle position, and the velocity of the particle does not have to be calculated explicitly. The technical idea according to the present embodiment may be applied to such a method.

  DESCRIPTION OF SYMBOLS 100 Analysis apparatus, 102 Input apparatus, 104 Output apparatus, 110 Particle system acquisition part, 120 Numerical calculation part, 122 Force calculation part, 124 Particle state calculation part, 126 State update part, 128 End condition determination part, 132 Control power provision part 140 display control unit, 150 particle data holding unit, 152 command value holding unit.

Claims (3)

An analysis device for analyzing a particle system by numerically calculating a motion equation of a particle system including a plurality of particles,
A control force applying unit for multiplying a speed command value given from the outside of the particle system by α (α> 1) and applying a control force based on the speed command value multiplied by α to a predetermined particle;
A force calculator that calculates the force acting on the particles based on the distance between the particles;
Particle state for calculating at least one of the position and velocity of the particles based on the force calculated by the force calculation unit and the control force when the control force is applied to the particles by the control force applying unit An arithmetic unit,
Analysis characterized in that control parameters for deriving control force are converted so that the particle system phenomenon when the speed command value is multiplied by α and the particle system phenomenon when it is not so are similar apparatus. an acquisition unit for acquiring a value to be set to α,
The analysis apparatus according to claim 1 , wherein the control force applying unit sets the value acquired by the acquiring unit as α and multiplies the speed command value by α. An analysis method for analyzing a particle system by numerically calculating the equation of motion of a particle system including a plurality of particles,
Multiplying a speed command value given from the outside of the particle system by α (α> 1), and applying a control force based on the speed command value multiplied by α to a predetermined particle;
Calculating the force acting on the particles based on the distance between the particles;
And the calculated force, seen including its control force if the control force is applied to the particles, a step of computing at least one of the position and velocity of the particles based on the,
Analysis characterized in that control parameters for deriving control force are converted so that the particle system phenomenon when the speed command value is multiplied by α and the particle system phenomenon when it is not so are similar Method.

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