JP2011244623A - Coupled analysis system, analysis system and coupled analysis method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform a high-speed, high-accuracy simulation.SOLUTION: A coupled analysis system 200 comprises a calculation server 204, a first design terminal 206a, a second design terminal 206b and a third design terminal 206c. The calculation server 204, by numerically solving a governing equation, calculates a physical amount. The first design terminal 206a is connected to the calculation server 204 via a network 202, and calculates the control volume of a motor that is the analysis target, with the physical amount calculated by the calculation server 204 as an input. The calculation server 204 calculates the physical amount with the control volume calculated by the first design terminal 206a as an input.

Description

  The present invention relates to a coupled analysis system, an analysis system, and a coupled analysis method.

  In recent years, simulations incorporating magnetic field analysis are often used in the field of design and development of electric devices such as motors as computer computing power increases. When simulation is used, it is possible to evaluate to some extent without actually creating a prototype, so that the speed of design development can be improved.

  For example, Patent Document 1 describes a motor analysis device including an arithmetic processing device that performs magnetic field analysis. The arithmetic processing unit executes a static magnetic field analysis by a finite element method and a torque calculation by Maxwell's stress method according to an external command based on a user operation. Mesh division is performed for static magnetic field analysis by the finite element method. The mesh division is also performed on the core region and the housing region, and also on the outer air layer region.

JP-A-11-146688

  Conventionally, there have been few cases where the magnetic moment method and the control system are coupled and analyzed. As such a coupled system, it is conceivable to couple, for example, MATLAB (registered trademark) provided by MathWorks and general-purpose structural analysis tool ANSYS provided by ANSYS Japan. In this case, it can be considered that the calculation is performed by one computer having high machine power.

  However, when a coupled system is configured by one computer as described above, coupled analysis must be performed by one computer having high machine power. Usually, the higher the machine power, the higher the price of the computer. Therefore, it is often disadvantageous to arrange such expensive computers. Therefore, a small number of coupled analysis computers are shared by many design developers, and the analysis place and the degree of freedom of control design can be restricted.

  Also, ANSYS and MATLAB have a heavy calculation load, and even if one computer with high machine power is used, the simulation time is often not satisfactory.

  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 time required for simulation.

  One embodiment of the present invention relates to a coupled analysis system. This coupled analysis system is connected to an arithmetic unit that calculates a physical quantity by numerically solving a governing equation, and is connected to the arithmetic unit via a network. A control quantity of a predetermined system is input using the physical quantity calculated by the arithmetic unit as an input. And a design device for calculating The arithmetic device calculates a physical quantity using the control amount calculated by the design device as an input.

  According to this aspect, the physical quantity can be calculated by the calculation device, and the control amount can be calculated by the design device.

  Another aspect of the present invention is an analysis system. This analysis system is an analysis system that uses two operations each having an output value of each other as input values, and the two operations are executed in separate devices.

  Yet another embodiment of the present invention is a coupled analysis method. This method includes a step of calculating a physical quantity by numerically solving an equation in a first apparatus, and a physical quantity calculated by the first apparatus in a second apparatus different from the first apparatus. A step of calculating a control amount of a predetermined system; and a step of numerically solving an equation using the control amount calculated by the second device as an input in the first device.

  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

  According to the present invention, the time required for simulation can be shortened.

It is a schematic diagram which shows the structure of the coupled analysis system which concerns on embodiment. It is a block diagram which shows the function and structure of the 1st design terminal of FIG. It is a figure which shows the hardware constitutions of the arithmetic server of FIG. It is a figure which shows the memory | storage device of FIG. It is a figure which shows the outline of a structure of a SPM motor. FIG. 4 is an enlarged perspective view of the periphery of one of the stator teeth of the SPM motor of FIG. 3. It is a flowchart which shows the procedure of the analysis of the magnetic field using the calculation server of FIG. FIG. 6A is an enlarged perspective view of the coil, and FIG. 6B is a diagram showing an example in which the coil is divided into local conductors. It is a figure which shows the relationship between a rectangular parallelepiped conductor and a local coordinate. It is a figure which shows the relationship between an arc-shaped columnar conductor and a local coordinate. It is explanatory drawing of the element used for the magnetic field calculation of a magnetic body. It is a figure which shows typically an example of the magnetization curve of a magnetic body (for example, iron). It is a flowchart for demonstrating the magnetic field calculation process which concerns on one Embodiment of this invention. It is a figure which shows the example of the magnetic field calculation by one Embodiment of this invention. It is a figure which shows the example of the magnetic field calculation by one Embodiment of this invention. It is a chart which shows a series of processes in the coupled analysis system of FIG.

  The present invention will be described below based on preferred embodiments with reference to the drawings. The same code | symbol may be attached | subjected to the same or equivalent component, member, and process which are shown by each drawing. Moreover, the description which overlaps suitably is abbreviate | omitted.

The coupled analysis system according to the embodiment is preferably used in a case where a physical quantity calculation and a control quantity calculation are coupled and analyzed. The physical quantity is, for example, a magnetic field or electric field which is an electromagnetic quantity, a temperature which is a thermodynamic quantity, a force vector, a velocity vector or a position vector which is a dynamic quantity, or any combination thereof. The control amount is, for example, the direction and magnitude of the current flowing through the coil or the potential of the conductor.
In the coupled analysis system according to the embodiment, the calculation of the physical quantity and the calculation of the control amount are performed by separate apparatuses, and the calculation result of one apparatus is used as the input of the calculation of the other apparatus. Thereby, it is possible to reduce the time required for the simulation by distributing the calculation load.

  Below, the case where the coupled analysis system which concerns on embodiment is utilized for the design of a motor is demonstrated. Further, the case where the physical quantity is a force vector caused by the calculated magnetic field, a velocity vector caused by the force vector, and a position vector caused by the velocity vector will be described. A case where the control amount is a current density vector of a current flowing through the motor coil will be described.

FIG. 1 is a schematic diagram illustrating a configuration of a coupled analysis system 200 according to an embodiment. The coupled analysis system 200 includes a network 202, a calculation server 204, a first design terminal 206a, a second design terminal 206b, and a third design terminal 206c.
The first design terminal 206a, the second design terminal 206b, and the third design terminal 206c are each connected to the calculation server 204 via the network 202, and communicate with the calculation server 204 according to a communication protocol such as a TCP / IP protocol. The network 202 is, for example, a LAN (Local Area Network) or the Internet.

  The calculation server 204 calculates a magnetic field, a force vector caused by the magnetic field, a velocity vector caused by the force vector, and a position vector caused by the velocity vector in response to a request from each design terminal, Provide to design terminals. At that time, the calculation server 204 calculates the magnetic field, the force vector, and the position vector by numerically solving the governing equation with the calculation result in the design terminal as an input. Details of the arithmetic server 204 will be described later.

Hereinafter, a case where a coupled analysis is performed using the first design terminal 206a and the calculation server 204 will be described. In this case, the first design terminal 206 a and the calculation server 204 alternately perform simulation while transmitting and receiving packets through the network 202.
It should be understood by those skilled in the art who have touched the present specification that the same explanation as described below holds true when the second design terminal 206b or the third design terminal 206c and the calculation server 204 are used.

  FIG. 2 is a block diagram showing the function and configuration of the first design terminal 206a. 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.

The first design terminal 206a calculates the current density vector of the current flowing through the coil of the motor to be analyzed using the calculation result in the calculation server 204 as an input.
The first design terminal 206a includes a communication unit 208, a control calculation unit 210, a data holding unit 212, a history holding unit 214, and a resume unit 220. The data holding unit 212 includes a data file 218 and, in some cases, a flag file 216. The history holding unit 214 accumulates history related to computations in the coupled analysis system 200.

  A communication unit 208 is connected to the network 202, receives a packet sent from the calculation server 204, and transmits the packet to the calculation server 204. The communication unit 208 confirms the received packet using a known error correction technique, and confirms whether or not there is data skipping during the coupling calculation.

  The communication unit 208 extracts a command for coupled analysis and a position vector, a force vector, and a velocity vector, which are calculation results in the calculation server 204, from the received packet. The communication unit 208 accesses the data file 218 of the data holding unit 212 and registers the extracted position vector, force vector, and velocity vector.

  When accessing the data file 218, the communication unit 208 generates an empty flag file 216 in the data holding unit 212. The communication unit 208 deletes the flag file 216 from the data holding unit 212 when the data registration to the data file 218 is completed and the access to the data file 218 is completed.

  Before the communication unit 208 registers the extracted position vector, force vector, and velocity vector in the data file 218, the communication unit 208 sets a predetermined convergence criterion in consideration of the convergence of the control calculation in the control calculation unit 210. It is determined whether or not it is satisfied. If it is determined that the convergence criterion is not satisfied, the communication unit 208 discards data that does not satisfy the convergence criterion or replaces the data with another data that satisfies the convergence criterion.

  The convergence criterion is, for example, an upper limit value, a lower limit value, or both of the magnitudes of the position vector, the force vector, and the velocity vector. Alternatively, the convergence criterion may be the number of decimal places in the data. These upper limit value, lower limit value, and number of digits are set so that the convergence calculation in the control calculation unit 210 converges.

  The communication unit 208 registers the history of communication with the calculation server 204 and the extracted data in the history holding unit 214.

  The control calculation unit 210 calculates the current density vector of the current to be passed through the coil of the analysis target motor by inputting the position vector, force vector, and velocity vector registered in the data file 218 for feedback control of the analysis target motor. To do. Except for the following three points, the control calculation unit 210 is realized using a known design tool such as MATLAB and Simulink (registered trademark) provided by MathWorks, for example.

1. The control calculation unit 210 accesses the data file 218 of the data holding unit 212, and acquires a position vector, a force vector, and a velocity vector as inputs from the data file 218. At this time, the control calculation unit 210 does not access the data file 218 when the flag file 216 exists in the data holding unit 212. In other words, while the flag file 216 exists in the data holding unit 212, access to the data file 218 by the control calculation unit 210 is restricted.
2. The control calculation unit 210 registers the calculation result in the history holding unit 214.
3. The control calculation unit 210 passes the calculation result to the communication unit 208. The communication unit 208 transmits the received communication result and the coupled analysis command to the arithmetic server 204 in the form of a packet.

  When the calculation in the first design terminal 206a is stopped, the resume unit 220 automatically restarts the calculation from the middle with reference to the history holding unit 214. When the calculation is resumed, the resume unit 220 registers the condition when the calculation is stopped in the history holding unit 214.

  With reference to FIG. 3, the hardware configuration of the arithmetic server 204 will be described.

  It should be noted that the hardware configuration in FIG. 3 is an example, and is not limited to this.

  As shown in FIG. 3, the calculation server 204 is connected to the control unit 3, the storage device 5, the media input / output unit 6, the input unit 7, the display unit 9, the printer port 11, the communication unit 201, and the like via the bus 13. ing.

  The communication unit 201 is connected to the network 202, receives a packet sent from the first design terminal 206a, and transmits the packet to the first design terminal 206a. The communication unit 201 extracts a command for coupled analysis and a current density vector as a calculation result in the first design terminal 206a from the received packet.

  The control unit 3 includes a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like, and is connected via the bus 13 according to a program stored in the storage device 5 as a storage unit. Each of the devices is driven and controlled.

  As shown in FIG. 4, the storage device 5 stores a control program 15 for driving and controlling each component of the arithmetic server 204 and a magnetic field analysis program 17 for carrying out the present invention.

  The magnetic field analysis program 17 includes input information 21 that is information having analysis conditions, and an arithmetic program 19 that calculates a magnetic field based on the input information 21 and the motion equation of the magnetic field and calculates a dynamic equation of motion. .

  The media input / output unit 6 is a device for inputting / outputting information to / from a medium such as a floppy (registered trademark) disk, CD, or DVD.

  The input unit 7 is an input device such as a keyboard and a mouse, and the display unit 9 is a display device such as a display.

  A printer 12 as an output device is connected to the printer port 11.

  Next, the procedure of magnetic field analysis using the calculation server 204 will be described with reference to FIGS.

  Here, a case where an SPM motor 31 (Surface Permanent Magnet Motor), which is a kind of permanent magnet motor, is employed as the motor to be analyzed will be described.

  First, an outline of the configuration of the SPM motor 31 will be described with reference to FIGS. 5 and 6.

  As shown in FIG. 5, the SPM motor 31 has a rotor 33 that is a rotor (moving element) and a stator 35 that is a stator.

  The rotor 33 has a cylindrical rotor core 37 that is a magnetic body such as iron, and a permanent magnet 39 is provided on the surface of the rotor core 37.

  A rod-shaped rotor shaft 41 is provided at the axial center of the rotor core 37.

  The stator 35 includes a tooth-like stator teeth 43 that is a magnetic body, a core back 44 that is a cylindrical magnetic body provided outside the stator teeth 43, and a cylindrical frame 46 that is provided outside the core back 44. Has been.

  As shown in FIGS. 5 and 6, a coil 45 that is a conductor such as metal is wound around the stator teeth 43.

  In the actual SPM motor 31, the coil 45 is wound around the stator teeth 43 with the number of turns according to the specifications to form a bundle, but in this embodiment, as illustrated in FIGS. 5 and 6. The coil bundle is handled as one conductor without modeling each coil.

  In the SPM motor 31 having such a structure, the rotor 33 and the stator 35 are magnetized by the magnetic field of the permanent magnet 39 and the magnetic field generated by passing a current through the coil 45. The SPM motor 31 is driven by the deviation of the magnetic energy of the magnetic material.

  Therefore, in order to perform the magnetic field analysis of the SPM motor 31, it is necessary to calculate the magnetic field vector that the coil 45 and the permanent magnet 39 form on the magnetic body constituting the rotor 33 and the stator 35, and to analyze the magnetization phenomenon of these magnetic bodies. is there.

  Next, the analysis procedure will be described with reference to FIGS.

  In the following procedure, the SPM motor 31 is divided into a plurality of elements to form an aggregate of particles for each element, and is handled as a rigid model. However, the present invention is not limited to this, and particles are used. Instead, it may be handled as a rigid model for each element.

  In the following procedure, the magnetic material indicates the magnetic material constituting the rotor 33 and the stator 35 and the permanent magnet 39, and these are distinguished by a function representing a magnetization curve.

When a coupled analysis is newly started, the communication unit 201 of the calculation server 204 acquires a setting file for coupled analysis from the first design terminal 206a. This setting file includes a three-dimensional structure (shape, coordinate points), a mass density, a function representing a magnetization curve of a magnetic material, and a current density vector of a conductor as analysis conditions of the SPM motor 31 to be analyzed.
The control unit 3 of the arithmetic server 204 activates the magnetic field analysis program 17 and stores the contents of the acquired setting file as the input information 21 of the storage device 5.

  These physical quantities may be read from a recording medium such as a CD-ROM via the media input / output unit 6, for example.

  The information of the three-dimensional structure of the SPM motor 31 is data such as CAD.

  Further, when the physical quantity is stored in advance as the input information 21, the above step is not necessary.

  The current density vector is necessary when calculating the magnetic field vector formed by the coil 45.

  Furthermore, a function representing the magnetization curve of the magnetic material is required when calculating the magnetization vector (bold) M.

  Next, the control unit 3 of the arithmetic server 204 determines that the magnetic material is N particles (polyhedral element having a center of gravity of the position vector of the particle (cubic element in this embodiment) from the three-dimensional structure information included in the input information 21. ), And the position vector of the particle is calculated and stored in the storage device 5.

  Here, N is an arbitrary integer, and the number N of particles and the position vector are calculated based on the three-dimensional structure of the input information 21 and the shape of the polyhedral element stored in the storage device 5 in advance.

  The above is the details of step 101 in FIG.

When the coupled analysis has already started, the communication unit 201 of the calculation server 204 acquires the current density vector calculated in the first design terminal 206 a and stores it as the input information 21 of the storage device 5.
The above is the details of step 117 in FIG.

  Next, the control unit 3 determines that the conductor (coil 45 shown in FIG. 8A) is a local conductor (rectangular conductors 45a, 45b) as shown in FIG. And arc-shaped columnar conductors 45c and 45d), and a coefficient for calculating a magnetic field vector formed by each conductor is calculated and stored in the storage device 5.

  First, the case where the local conductor is a rectangular parallelepiped conductor 45a will be described.

  In addition, since it is the same as that of the case where a local conductor is the rectangular parallelepiped conductor 45a when a local conductor is the rectangular parallelepiped conductor 45b, description is abbreviate | omitted.

When the local conductor is a rectangular parallelepiped conductor 45a, the control unit 3 applies a local coordinate system (x _s , y _s , z _s ) as shown in FIG.

What this in the local coordinate system to the center of gravity of the local conductor (rectangular conductor 45a) and the origin _{O s,} dimensions of rectangular conductor 45a is having a length of _{x s} direction 2a, _{y s} direction 2b, _{z s} directions 2c And

And shall particles is located at the origin O _s.

  The control unit 3 has a three-dimensional structure of conductors stored in the storage device 5 as input information 21 from step 101, a current density vector stored in the storage device 5 as input information 21 from step 101 or step 117, and , And a, b, c, which are the dimensions of the local conductor (cuboid conductor 45a), and the particle position vector are calculated and stored in the storage device 5.

  Next, a case where the local conductor is an arc-shaped columnar conductor 45c will be described.

  Note that the case where the local conductor is the arc-shaped columnar conductor 45d is the same as the case where the local conductor is the arc-shaped columnar conductor 45c, and a description thereof will be omitted.

When the local conductor is the arc-shaped columnar conductor 45c, the control unit 3 applies the local coordinate system (x _c , y _c , z _c ) as shown in FIG.

Origin O _c are present on an arc of the central axis, and that the arcuate columnar conductor 45c are symmetrical with respect to the height direction of the arcuate columnar conductor 45c (z _c direction in FIG. 10) in this local coordinate system Shall exist.

_{Moreover, x c, y c, z} c _, when viewed in x c -y _c plane, + _{x c-axis} as a base point, and so the arc of the arcuate columnar conductor 45c is + when viewed from the _{z c-axis} counterclockwise decide.

The average value of the inner diameter and the outer diameter of the arcuate columnar conductor 45c and _{R c, 2r} the thickness in the radial direction a, the _{z c} direction height and 2z _b.

Current as a base point a + x _c-axis, + when viewed from the z _c the angle a θ of the counter-clockwise direction, current is assumed to flow in a uniform current density j in this direction.

It is assumed that the particles are located at (R _c , θ / 2, 0) in the cylindrical coordinate system.

The control unit 3 has a three-dimensional structure of conductors stored in the storage device 5 as input information 21 from step 101, a current density vector stored in the storage device 5 as input information 21 from step 101 or step 117, and , R _a , z _b , θ, R _c and particle position vectors, which are dimensions of the local conductor (arc-shaped columnar conductor 45 _c ), are calculated and stored in the storage device 5.

  Next, the control unit 3 of the calculation server 204 calculates the position vector of the N particles constituting the magnetic body calculated up to this step and stored in the storage device 5, and the polyhedron stored in the storage device 5 in advance. The coefficient of the equation of motion of the magnetic field of the particles constituting the magnetic material is calculated according to the shape of the element and stored in the storage device 5.

  When the divided polyhedron elements (cubic elements in this embodiment) are displayed two-dimensionally, the shape shown in FIG. 11 is obtained.

Here, r _{g is} the particle position vector (bold), q is the midpoint of the element boundary surface of the polyhedral element centered on the particle position vector, and p is the midpoint between the particle position vector and q point. Define points.

  The control unit 3 reads the position vector of the particles (polyhedral elements having a center of gravity (cubic elements in this embodiment)) constituting the magnetic body calculated in step 101 and stored in the storage device 5.

  If the particle position vector is updated and stored in the storage device 5 in step 114, the control unit 3 reads the value.

  From the particle position vector and the shape of the polyhedron element stored in the storage device 5 in advance, the control unit 3 calculates the points p and q in the polyhedron element whose center of gravity is the position vector of all particles constituting the magnetic body. The position vector and the normal vector (bold) n to the element boundary surface are calculated and stored in the storage device 5.

  Next, the control unit 3 includes a polyhedral element having the boundary area ΔS of the polyhedral element having the particle constituting the magnetic body as its center of gravity and the vertex of the boundary surface of the polyhedral element having the center of gravity as the particle position vector and the particle position as the vertex The volume ΔV is calculated and stored in the storage device 5.

  Next, the control unit 3 of the arithmetic server 204 uses the dimensions of the coil stored in the storage device 5 and the current density vector stored in the storage device 5 to integrate the Bio-Savart law. Based on the analytical solution, the energized coil 45 calculates the magnetic field vector formed on the particles constituting the magnetic material and stores it in the storage device 5.

  Here, when it is assumed that an arbitrary position vector is the point P where the stator teeth 43 as the magnetic body in FIG. 6 is present, a procedure for calculating the magnetic field vector that the energized coil 45 creates on the position vector of the point P is calculated. Will be described as an example.

  First, the case where the local conductor is a rectangular parallelepiped conductor 45a will be described.

  In addition, since it is the same as that of the case where a local conductor is the rectangular parallelepiped conductor 45a when a local conductor is the rectangular parallelepiped conductor 45b, description is abbreviate | omitted.

When the local conductor is a rectangular parallelepiped conductor 45a, the local coordinate system (x _s , y _s , z _s ) is applied as shown in FIG.

Next, the position vector of the point P is converted into the local coordinate system (x _s , y _s , z _s ).

  Magnetic field vectors created at the point P by the energized rectangular parallelepiped conductor are described by the following equations (1) to (3).

Here, _{(bold) r ps} is the position vector of the point P in the local coordinate system _{(x s, y s, z} s), x ps, y ps, z ps is _{x s, y s, z s} Direction value.
π is the circumference ratio.

H _xs , H _ys , and H _zs are each component of the magnetic field vector in the local coordinate system (x _s , y _s , z _s ).
j is the current density.

X _i , y _j , and z _k represent the upper and lower limits of integration in the x _s , y _s , and z _s directions, and the relationship shown in Expression (4) is established.

  Here, a, b, and c are dimensions of a rectangular parallelepiped conductor.

  Next, a case where the local conductor is an arc-shaped columnar conductor 45c will be described.

  Note that the case where the local conductor is the arc-shaped columnar conductor 45d is the same as the case where the local conductor is the arc-shaped columnar conductor 45c, and a description thereof will be omitted.

When the local conductor is the arc-shaped columnar conductor 45c, the local coordinate system (x _c , y _c , z _c ) is applied as shown in FIG.

The position vector of the P point after being converted to the local coordinate system (x _c , y _c , z _c ) is expressed by the cylindrical coordinate system (bold) r _pc = (R _pc , φ _pc , Z _pc ).

  A magnetic field vector formed at the point P by the energized circular columnar conductor 45c is expressed by the following equations (6) to (11).

Here, H _rc , H _tc and H _zc are each component of the magnetic field vector in the cylindrical coordinate system.
j is the current density.

r _a , θ, and z _b are dimensions of the arc-shaped columnar conductor 45c, and R _c is an average value of the inner diameter and the outer diameter of the arc.

sgn is the sign of the _{Z k,} R _{j, Z k} is the upper limit of the integration represents the lower limit, the relationship shown in equation (12) holds.

  The above is the calculation procedure of the magnetic field vector created by the coil at an arbitrary point P.

  The control unit 3 of the arithmetic server 204 reads the position vector of the p point inside the polyhedron element having the center of gravity as the position vector of all particles constituting the magnetic body that has already been calculated and stored in the storage device 5.

Next, the control unit 3 converts the position vector of the point p into the local coordinate system (x _s , y _s , z _s ), calculates the dimensions of the rectangular parallelepiped conductor 45 a calculated and stored in the storage device 5, and step 101. Or the current density vector memorize | stored in the memory | storage device 5 as the input information 21 is read from step 117, and a magnetic field vector is calculated based on Formula (1)-(4).

  Next, the control unit 3 converts the magnetic field vector calculated by the equations (1) to (4) into the global coordinate system (x, y, z), and stores the converted magnetic field vector in the storage device 5.

  Thereby, the magnetic field vector which the energized rectangular parallelepiped conductor 45a produces in p point is calculated | required.

Further, the control unit 3 converts the position vector of the point p into the local coordinate system (x _c , y _c , z _c ), and further, the cylindrical coordinate system (bold) r _pc = (R _pc , φ _pc , Z _pc ). Convert to

Next, the control unit 3 reads the dimensions r _a , θ, z _b and R _c of the arc-shaped columnar conductor 45 _c calculated and stored in the storage device 5, and the control unit 3 inputs in step 101 or step 117. A current density vector stored in the storage device 5 as information 21 is read.

  The controller 3 calculates a magnetic field vector based on the equations (6) to (12).

  Next, the calculated magnetic field vector is converted into an orthogonal coordinate system, further converted into a global coordinate system (x, y, z), and stored in the storage device 5.

  As a result, a magnetic field vector created at the point p by the energized circular columnar conductor 45c is obtained.

  The above is the details of step 102 in FIG.

Next, similarly to step 102, the control unit 3 of the arithmetic server 204 calculates a magnetic field vector that the permanent magnet 39 creates on the particles constituting the magnetic body, and stores the magnetic field vector in the storage device 5.
The above is the details of step 103 in FIG.

Next, the control unit 3 of the arithmetic server 204 calculates the sum of the magnetic field vector calculated in step 102 and the magnetic field vector calculated in step 103.
The above is the details of step 104 in FIG.

  Next, the control unit 3 of the arithmetic server 204 uses the arithmetic program 19 to calculate the magnetic field vector after the virtual time step δt without considering the constraint condition from the motion equation of the magnetic field of the particles constituting the magnetic body, and stores it. Store in device 5.

  The Lagrangian of the N particles constituting the magnetic material is assumed to have a shape represented by the equations (13) to (15).

Here, in Expression (13), α is a virtual mass, bold r is a position vector, bold H is a magnetic field vector, bold bold H is a time derivative of the magnetic field vector, bold M is a magnetization vector, and bold n Is the normal vector of the polyhedral element boundary surface centered on the particle position vector, bold hex is the externally applied magnetic field vector, ΔS is the area of the element boundary surface of the polyhedral element centered on the particle position vector, ΔV is Polyhedral element boundary surface with the particle position vector as the center of gravity and polyhedral element volume with the particle position as the vertex, χ is the magnetic susceptibility, μ ₀ is the permeability of vacuum, λ is the Lagrange's undetermined constant, π is the circumference The rate, s, is the number of element boundary faces of a polyhedral element whose center of gravity is the particle position vector.

  The subscript ip of each physical quantity is the physical quantity of the p point in the polyhedron element whose center is the position vector of the i-th particle, and the subscript jq is the polyhedron element whose center is the position vector of the j-th particle. The physical quantity of q point is shown.

In equation (13), m is the mass of the particle, v is the velocity, and φ (r _i −r _j ) is the interaction potential energy between the i-th particle and the j-th particle. Subscripts i and j indicate physical quantities of the i and j-th particles, respectively.

Next, the canonical variables (in _{bold) H ip,} and (bold with _{neighbors) H ip,} and substituting Lagrangian of formula (13) to (15) to the Lagrange equation of motion, the motion equation of the magnetic field Can be described as in equation (16).

  Here, the second term on the right side of Equation (16) imposes a constraint condition (the divergence of the magnetization vector is 0) through Lagrange's undetermined constant.

  The third term on the right side of equation (16) is an attenuation term for quickly following when the externally applied magnetic field vector changes, and γ is an attenuation constant.

  In solving the equation of motion including the constraint condition shown in the second term on the right side of Equation (16), the present embodiment employs the SHAKE method, which is a generalized constraint condition introduction method.

  If equation (16) is discretized by the jumping method without considering the constraint condition, the following equations (17), (18), and (19) are obtained.

  Here, δt is a virtual time step used for calculating the convergence of the magnetization phenomenon.

  The subscript n is an arbitrary integer, a physical quantity at nδt, n−1 / 2 is a physical quantity at (n−1 / 2) δt, n + 1/2 is a physical quantity at (n + 1/2) δt, and n + 1 is (n + 1). This corresponds to the physical quantity at δt.

  The control unit 3 of the calculation server 204 reads the position vectors of the points p and q in the polyhedron element whose center of gravity is the particle position vector that has already been calculated and stored in the storage device 5.

  Next, the control unit 3 externally generates a magnetic field vector generated at the point p inside the polyhedron element whose center of gravity is the particle and the permanent magnet that are already calculated in step 104 and stored in the storage device 5. Read as the applied magnetic field vector.

  Further, the control unit 3 calculates the vertexes of the polyhedral element boundary surface having the center of gravity of the element boundary area, the normal vector, and the particle position vector of the particles constituting the magnetic body, which are already calculated and stored in the storage device 5. Read polyhedral element volume with particle position as vertex.

  Further, the control unit 3 reads the attenuation constant, virtual mass, and virtual time increment stored in advance in the storage device 5.

  Next, the control unit 3 reads the magnetic field vector stored in advance in the storage device 5 and the initial value of the time differentiation of the magnetic field vector.

  In addition, the control part 3 reads the value, when the magnetic field vector and the time differentiation of the magnetic field vector are updated in step 106 mentioned later.

  Note that the magnetization vector is calculated by substituting the magnetic field vector into a function representing the magnetization curve stored in the storage device 5 as the input information 21 from step 101.

  The control unit 3 calculates the equations (17), (18), and (19) for all p points in the polyhedral element whose center of gravity is the position vector of the particles constituting the magnetic body. The stored magnetic field vector is stored in the storage device 5.

  The above is the details of step 105 in FIG.

  Next, the control unit 3 of the arithmetic server 204 restricts the magnetic field vector at the point p in the polyhedron element having the center of gravity of the position vector of the particles constituting the magnetic body, which is calculated in step 105 and stored in the storage device 5. And the calculated magnetic field vector is stored in the storage device 5.

  A constraint condition is applied to the magnetic field vector at point p in the polyhedron element whose center of gravity is the position vector of the particles constituting the magnetic body according to the following equations (20) and (21).

  Here, bold H is a magnetic field vector, α is a virtual mass, δt is a virtual time step, γ is an attenuation constant, N is the number of particles constituting the magnetic body, s is a position vector of the particles constituting the magnetic body, and the center of gravity. The subscript i is the physical quantity on the position vector of the i-th particle among the particles constituting the magnetic body, and ip is the i-th particle among the particles constituting the magnetic body. The physical quantity of point p in the polyhedron element whose center is the position vector of, iq is the physical quantity of point q in the polyhedron element whose center of gravity is the position vector of the i-th particle among the particles constituting the magnetic body, n is an arbitrary integer, and corresponds to a physical quantity at nδt, and n + 1 corresponds to a physical quantity at (n + 1) δt.

  The control unit 3 of the calculation server 204 uses the calculation program 19 to read the magnetic field vector at point p in the polyhedron element whose center of gravity is the particle constituting the magnetic material calculated in step 105 and stored in the storage device 5. .

  The control unit 3 reads the virtual mass, virtual time step, and attenuation constant stored in advance in the storage device 5.

  The control unit 3 performs a calculation based on Expression (20) and Expression (21) for each particle constituting the magnetic body, and stores the calculated magnetic field vector in the storage device 5.

  The above is the details of step 106 in FIG.

  Next, the control unit 3 of the arithmetic server 204 determines whether or not the magnetic field vector obtained in step 106 satisfies the constraint condition, and if satisfied, proceeds to the next step, and returns to step 106 if not satisfied.

  Specifically, the control unit 3 performs calculation based on the equation (22) using the magnetization vector calculated from the magnetic field vector of each of the particles constituting the magnetic body calculated in step 106 and stored in the storage device 5. .

  Here, the subscript n + 1 corresponds to the physical quantity at (n + 1) δt.

err _i is an error value with respect to the constraint condition of the i-th particle among the particles constituting the magnetic material.

  The magnetization vector (in bold) M is calculated in step 106 and the control unit 3 reads the magnetic field vector stored in the storage device 5 and substitutes it in the function representing the magnetization curve stored in the input information 21 from step 101. Calculated by

  For the normal vector (bold) n, the control unit 3 reads and substitutes what has already been calculated and stored in the storage device 5.

  If the error value does not satisfy the equation (23) for all particles, the control unit 3 returns to Step 106.

In Expression (23), A ₁ is an arbitrary error determination value, and an arbitrary value is stored in the storage device 5 in advance.

  The above is the details of step 107 in FIG.

  Next, the control unit 3 of the arithmetic server 204 determines whether the magnetization phenomenon of the magnetic material has reached a steady state, and proceeds to the next step if the condition is satisfied.

  Whether the particles constituting the magnetic material have reached a steady state is determined by the following equation (24).

Here, the bold letter H is the magnetic field vector, μ ₀ is the magnetic permeability of the vacuum, N is the number of particles constituting the magnetic body, and s is the number of faces of the polyhedral element whose center of gravity is the position vector of the particles constituting the magnetic body. The subscript ip is a physical quantity at the point p in the polyhedron element whose center of gravity is the position vector of the i-th particle among the particles constituting the magnetic body.

  Further, the subscript n is an arbitrary integer, which corresponds to a physical quantity at nδt, n−1 corresponds to (n−1) δt, and n + 1 corresponds to a physical quantity at (n + 1) δt.

A ₂ is an arbitrary error determination value for determining whether the magnetic field vector of the magnetic material has reached a steady state.

The control unit 3 of the arithmetic server 204 reads A ₂ and μ ₀ stored in advance in the storage device 5.

  Further, the control unit 3 reads the magnetic field vector at the point p in the polyhedron element having the center of gravity of the particles constituting the magnetic body, which is calculated in step 106 and stored in the storage device 5.

  Next, the control unit 3 calculates Expression (24). If Expression (24) is satisfied, the process proceeds to the next step. If not satisfied, the process returns to Step 105.

  The above is the details of step 108 in FIG.

  Next, the control unit 3 of the calculation server 204 calculates a magnetic field vector, a magnetization vector, and a magnetic flux density vector on the position vectors of all particles constituting the motor, and stores them in the storage device 5. That is, the control unit 3 of the calculation server 204 includes the magnetic field vector, the magnetization vector, the magnetic flux density vector on the position vector of all particles constituting the magnetic body, and the magnetic field vector on the position vector of all particles constituting the coil, The magnetic flux density vector is calculated and stored in the storage device 5.

(Particles constituting magnetic material)
The magnetic field vector on the position vector of the particles constituting the magnetic body is expressed by the following equation (25).

Here, (bold) e _x = (1,0,0), (bold) e _y = (0,1,0), (bold) e _z = (0,0,1).

  The bold letter H is a magnetic field vector, the bold letter n is a normal vector, the suffix i represents the physical quantity on the position vector of the i-th particle of the particles constituting the magnetic body, and the suffix ip is the magnetic body. Is a physical quantity of p point in the polyhedron element whose center of gravity is the position vector of the i-th particle.

  The magnetization vector of the particles constituting the magnetic material can be obtained by substituting the magnetic field vector into a function representing the magnetization curve.

  The magnetic flux density vector on the position vector of the particles constituting the magnetic body is expressed by Expression (26).

  Here, the bold letter B is the magnetic flux density vector, the bold letter H is the magnetic field vector, the bold letter M is the magnetization vector, and the suffix i is the position vector of the i-th particle among the particles constituting the magnetic body. Indicates the physical quantity.

μ ₀ is the vacuum permeability.

  The control unit 3 of the calculation server 204 reads the magnetic field vector at the point p in the polyhedron element whose center of gravity is the particle constituting the magnetic material, which has already been calculated, from the storage device 5.

  Next, the control unit 3 reads the normal vector already calculated and stored in the storage device 5, and calculates and stores the magnetic field vector on the position vector of the particles constituting the magnetic body based on the equation (25). Store in device 5.

  Further, the control unit 3 substitutes the magnetic field vector calculated in this step into a function representing the magnetization curve stored in the storage device 5 as the input information 21 from step 101, and the magnetization vector of the particles constituting the magnetic body. Is calculated and stored in the storage device 5.

  Next, the control unit 3 substitutes the magnetic field vector and the magnetization vector calculated in this step into Expression (26), calculates the magnetic flux density vector on the position vector of the particles constituting the magnetic body, and stores it in the storage device 5. .

  The control unit 3 reads the vacuum permeability stored in the storage device 5 in advance.

(Particulate particles)
The magnetic field vector on the position vector of the particles constituting the coil is described by Expression (27) and Expression (28).

  Here, the bold letter r is a position vector, the bold letter H is a magnetic field vector, N is the number of particles constituting the magnetic body, s and ΔS are the number of boundary faces and boundaries of the polyhedron element having the particle constituting the magnetic body as the center of gravity. Area, bold M is a magnetization vector, bold n is a normal vector, subscript i is a physical quantity on the position vector of the i-th particle among the particles constituting the coil, and j is a magnetic material Jq is the physical quantity on the position vector of the j-th particle, and jq is the physical quantity at the point q of the polyhedron element whose center of gravity is the position vector of the j-th particle among the particles constituting the magnetic body. Point to.

  The first term on the right side of Equation (27) is a term describing a magnetic field vector created on the position vector of the particles constituting the coil by the particles constituting the magnetic material, and is represented by Equation (28).

  The second term on the right side of the equation (27) is a magnetic field vector formed on the position vector of the particles constituting the coil by the particles constituting the coil, and is represented by equations (1) to (12).

  The control unit 3 of the calculation server 204 reads the position vector of the particles constituting the coil calculated and stored in the storage device 5 from the storage device 5.

  In addition, when the position vector of the particle | grains which comprise a coil is updated in step 114, the control part 3 reads the value.

  Next, the control unit 3 calculates the number of particles constituting the magnetic body and the number of faces of the polyhedron element stored in the storage device 5, and the position vector of the q point in the polyhedron element having the particle position vector as the center of gravity. And the polyhedral element boundary area.

  Further, the control unit 3 reads the magnetization vector of the particles constituting the magnetic body, which is calculated in this step and stored in the storage device 5.

  Further, the control unit 3 reads the coil size calculated and stored in the storage device 5 and the current density vector stored in the storage device 5 as the input information 21 in step 101 or step 117.

  Thereafter, the control unit 3 calculates the magnetic field vector on the position vector of the particles constituting the coil in accordance with the equations (27), (28), and (1) to (12), and stores them in the storage device 5.

The control unit 3 converts the magnetic flux density vector (bold) B _i on the position vector of the particles constituting the coil into the magnetic field vector on the position vector of the particles constituting the coil that has already been calculated, and the vacuum permeability. Multiply and store in the storage device 5.

  The magnetic permeability of the vacuum is stored in the storage device 5 in advance.

  The details of step 109 have been described above.

  Thus, the control unit 3 analyzes the magnetization phenomenon of the magnetic material by solving the motion equation of the magnetic field.

  Therefore, it is not necessary to divide the entire space into meshes unlike the finite element method, and the magnetic field analysis can be efficiently performed with sufficient accuracy for a system having a magnetic body.

  In addition, since the equation of motion is solved, a matrix is not handled and the amount of memory necessary for the calculation is proportional to the number of particles.

  Next, the control unit 3 of the calculation server 204 calculates a force vector acting on all the particles constituting the SPM motor 31 and stores it in the storage device 5.

(Force vector acting on particles constituting magnetic material)
The canonical variables bold r _i, and bold neighbor with r _i, substituting the Lagrangian of the formula (13) in the equation of motion of the Lagrangian.

  Then, the force acting on the particles constituting the magnetic material is described as shown in Expression (29).

Here, μ ₀ is the vacuum permeability, bold H is the magnetic field vector, bold M is the magnetization vector, bold r is the position vector, and ΔV is the vertex of the polyhedral element boundary surface and the particle centered on the particle position vector. The polyhedral element volume with the position at the apex, N is the number of particles constituting the magnetic body, and the subscripts i and j indicate the physical quantities of the i-th and j-th particles among the particles constituting the magnetic body. The letter ip indicates the physical quantity of the point p in the polyhedron element whose center of gravity is the position vector of the i-th particle among the particles constituting the magnetic body.

Φ (r _i −r _j ) is an interaction potential energy between the i-th particle and the j-th particle.

  In this embodiment, the SPM motor is a rigid body (relative distance between particles is unchanged).

  Assuming that the model is a rigid model, the force acting on the particles constituting the magnetic material is described as in equation (30).

  The control unit 3 of the calculation server 204 reads the magnetic field vector at the point p in the polyhedron element having the center of gravity of the particles constituting the magnetic body calculated and stored in the storage device 5.

  The control unit 3 calculates the magnetization vector at the p point by substituting the magnetic field vector at the p point into a function representing the magnetization curve stored in the storage device 5 as the input information 21 from step 101 to calculate the storage device 5. To remember.

  Further, the control unit 3 reads the polyhedron element volume having the vertex of the polyhedral element boundary surface having the gravity center as the position vector of the particle constituting the magnetic body calculated and stored in the storage device 5 and the vertex of the particle position.

  Next, the control unit 3 calculates the partial differentiation of the magnetic field vector at the point p in the polyhedral element with the particle constituting the magnetic body as the center of gravity, and calculates the force vector from the equation (30) based on the value. Store in the storage device 5.

(Force vector acting on the particles constituting the coil)
Of the particles constituting the coil, the position vector of the i-th particle is bold r _i , the current unit vector at that position vector is bold t _i , the magnetic flux density vector is bold B _i , and the current flow direction When the length of the coil and L _i, of the particles constituting the coil, the force vector acting on the i-th particle is described by the following equation (31).

  The control unit 3 of the calculation server 204 reads the position vector of the particles constituting the coil that is calculated and stored in the storage device 5.

  If the position vector of the particles constituting the coil has been updated in step 114, the control unit 3 reads the value.

  Further, the control unit 3 reads the dimensions of the coil calculated and stored in the storage device 5.

  Next, the control unit 3 reads the current density vector of the coil stored in the storage device 5 as the input information 21 from step 101 or step 117.

  The control unit 3 calculates a force vector acting on the particles constituting the coil based on the equation (31) and stores the force vector in the storage device 5.

  The above is the details of step 110 in FIG.

Next, the control unit 3 of the arithmetic server 204 outputs the calculation results up to that time from the printer 12 via the printer port 11 as necessary.
The above is the details of step 111 in FIG.

Next, the control unit 3 of the calculation server 204 calculates the sum of the torque or force vector acting on the particles constituting the movable unit.
The above is the details of step 112 in FIG.

  Next, the control unit 3 of the arithmetic server 204 calculates the rotation amount, angular velocity, translation of the movable part (moving element) from the sum of the torque or force vector acting on the particles constituting the movable part (moving element) calculated in step 112. The amount and the translation speed are calculated and stored in the storage device 5.

  The equation of motion of the translational motion of the rigid body is expressed by equation (32).

Here, m _tot constitutes the mass of the movable portion (movable element), the position vector of the representative point arbitrarily determined in bold r _c is the movable portion (movable element), bold F movable portion (slider) The force vector acting on the particles, N, is the number of particles constituting the movable part (moving element).

  Next, the equation of motion of the rotational motion around an arbitrary fixed point is expressed by Equation (33-1), Equation (33-2), and Equation (33-3).

Here, I ₁ , I ₂ , and I ₃ are the main inertia moment of the rigid body, ω ₁ , ω ₂ , and ω ₃ are the angular velocities in the inertial principal axis coordinate system, and N ₁ , N ₂ , and N ₃ are the inertial principal axis coordinate systems. Torque.

  The rotor 33 of the SPM motor 31 of this embodiment is fixed to a certain rotating shaft through the rotor shaft 41.

  Assuming that the fixed rotation axis is the z-axis, the motion of the rotor 33 is calculated as follows.

  Since the rotor 33 is fixed to the z-axis through the rotor shaft 41, the motion of the rotor 33 is calculated by solving the motion equation of the rotational motion around the z-axis.

  The equation of motion of the rotational motion of the rotor 33 around the z-axis is expressed by equation (34).

Here, I _z is the moment of inertia of the rotor 33, ω _z is the angular velocity in the z direction, and N _z is the torque in the z direction.

  When the equation (34) is discretized by the flying method, the following equations (35) and (36) are obtained.

  Here, θz is a rotation amount around the z axis, and dt is a minute time step.

  The subscripts n−1 / 2, n, n + 1/2, and n + 1 correspond to physical quantities in (n−1 / 2) dt, ndt, (n + 1/2) dt, and (n + 1) dt, respectively. Yes.

  The control unit 3 reads the time step width in which an arbitrary value is stored in the storage device 5 in advance.

  Initial values of the rotation amount and the angular velocity are stored in the storage device 5 in advance in the storage device 5.

  If the rotation amount and angular velocity of the rotor 33 have already been updated in step 113, those values are used.

  The controller 3 calculates the moment of inertia based on the three-dimensional structure and mass density of the rotor 33 stored in the storage device 5 as the input information 21 from step 101.

  Further, the control unit 3 calculates the equations (35) and (36) based on the position vector of the particles constituting the rotor 33 and the force vector acting on the particles constituting the rotor 33 calculated and stored in the storage device 5. ) And the rotation amount and angular velocity of the rotor 33 after dt seconds are calculated and stored in the storage device 5.

  The above is the details of step 113 in FIG.

Next, the control unit 3 of the arithmetic server 204 calculates and stores the position vector of the particles constituting the moving element based on the rotation amount after a minute time calculated in step 113 and the movement amount of the center of gravity.
The above is the details of step 114 in FIG.

Next, the control unit 3 of the arithmetic server 204 determines whether or not a predetermined end condition (time, movement amount, etc.) is satisfied. If it is satisfied, the analysis is terminated, and if not, the process proceeds to step 116.
The above is the details of step 115 in FIG.

The communication unit 201 of the arithmetic server 204 transmits the position vector, velocity vector, force vector, and command for coupled analysis obtained so far to the first design terminal 206a in the form of a packet. That is, the communication unit 201 of the calculation server 204 receives the position vector, velocity vector, and force vector calculated by the calculation server 204 as input to the first design terminal 206a, and the current density vector of the current flowing through the coil of the motor to be analyzed. It can be said that it is calculating.
The above is the details of step 116 in FIG.

  The above is the magnetic field analysis procedure in the arithmetic server 204.

  As described above, according to the calculation server 204 of the coupled analysis system 200 according to the embodiment, the calculation server 204 obtains the movement amount of the rotor 33 that is a moving element based on the magnetic field analysis of the SPM motor 31.

  Therefore, in this embodiment, the interaction between the magnetic field and the motion can be calculated, and the magnetic field analysis and the mechanism can be coupled.

  In the present embodiment, the analysis can be performed while updating the current density vector flowing in the coil 45 by the first design terminal 206a.

  Therefore, the analysis can be performed while changing the current flowing through the coil, and the magnetic field analysis can be performed with higher accuracy than in the past.

  In the above description, the case where the magnetization phenomenon of the magnetic material is calculated by solving the equation of motion of the magnetic field derived from the Lagrangian of the particles constituting the magnetic material has been described, but the present invention is not limited to this. Any equation other than that derived from the Lagrangian may be used as long as it is an equation of motion.

  In the above description, the present invention is used for the magnetic field analysis of the SPM motor 31. However, the present invention is not limited to this, and analyzes the magnetic field at an arbitrary point in the space where the magnetic body is arranged. If there is, for example, a motor other than the SPM motor 31 such as a linear motor, or a magnetic shield surrounding the space with a magnetic material, it may be used for magnetic field analysis in the space shielded by the magnetic material.

  As described above, according to the calculation server 204 of the coupled analysis system 200 according to the embodiment, in order to perform the analysis of the magnetic field acting on the object and the mechanism analysis of the motion of the object caused by the magnetic field. A device is provided. That is, this apparatus includes a magnetic field analysis calculation unit and a mechanism analysis calculation unit. In one embodiment, the control unit 3 may include a magnetic field analysis calculation unit and a mechanism analysis calculation unit. The magnetic field analysis calculation unit calculates a magnetic field based on a motion equation of a magnetic field in which a relationship to be satisfied by a magnetic field acting on each particle constituting the object is described in the form of a motion equation for each particle. The mechanism analysis calculation unit calculates the motion of the object based on the calculated magnetic field, and updates the position of each particle of the object. The communication unit 201 transmits the updated position vector and the like to the first design terminal 206a. The magnetic field analysis calculation unit further recalculates the magnetic field based on the updated position of each particle and the current density vector updated in the first design terminal 206a. Analysis can be performed by repeating magnetic field analysis and mechanism analysis for each particle in this way. Hereinafter, for convenience, the magnetic field analysis calculation unit is also referred to as a magnetic field calculation unit, and the mechanism analysis calculation unit is also referred to as a position calculation unit.

  Here, as described above, the magnetic field calculation unit divides the object into a large number of particles, and numerically expresses the equation of motion of the magnetic field describing the relationship to be satisfied by the magnetic field acting on each particle in the form of the equation of motion for each particle. The magnetic field acting on the object is calculated by solving. The analysis target object may include a material whose magnetization curve is non-linear. For example, a magnetic material may be used as the analysis target object. The present inventor succeeded in describing the governing equation of the magnetic field acting on each particle of the object in the form of the equation of motion using a so-called analytical mechanics method. In the above-described embodiment, by substituting the Lagrangian defined in the above equation (13) into the Lagrangian equation of motion, the magnetic field acting on each particle is described in the form of the equation of motion as in equation (16). is doing.

  A magnetic field calculation part calculates | requires the magnetic field which acts on an object by solving the equation of motion of a magnetic field numerically. Specifically, for example, the magnetic field calculation unit first substitutes the initial value of the magnetic field and its time derivative into the discretized motion equation of the magnetic field to obtain the magnetic field and its time derivative after a lapse of a minute time. Here, the minute time may be a virtual time used for performing the convergence calculation of the magnetic field. In other words, this virtual time is different from the actual elapsed time. The magnetic field calculation unit determines whether the calculated magnetic field after a lapse of a minute time satisfies a convergence criterion. The convergence determination condition is given by Expression (24) in one embodiment. The magnetic field calculation unit obtains a numerical solution of the magnetic field by repeatedly calculating the discretized motion equation of the magnetic field until the convergence criterion is satisfied.

  According to this method, unlike the known analysis method based on the finite element method, the calculation of the inverse matrix is unnecessary, which is preferable in that the magnetic field analysis can be executed with a small amount of calculation resources. This method is also preferable in that a highly accurate analysis result can be obtained without dividing the entire system including the object to be analyzed and its surrounding space into meshes as in the finite element method.

  In the present embodiment, the above-described coupled analysis is used for the magnetic field analysis of the motor. According to the verification by the present inventor, it has been found that when the convergence determination condition is set to a high accuracy level required for the magnetic field analysis of the motor, the time required until the end of the calculation may be relatively long. This convergence delay is considered to be caused by magnetic saturation in the object to be analyzed. In other words, the nonlinearity of the magnetization curve affects the convergence of the numerical solution of the magnetic field.

  FIG. 12 is a diagram schematically illustrating an example of a magnetization curve of a magnetic material (for example, iron). The horizontal axis of FIG. 12 indicates the magnetic field H, and the vertical axis indicates the magnetization M. As shown in FIG. 12, the magnetization M is proportional to the magnetic field H when the magnetic field H is small. As the magnetic field H increases, the proportionality constant (so-called magnetic susceptibility) between the magnetization M and the magnetic field H gradually decreases. The proportionality constant when the magnetic field H is small (for example, point A in the figure) can be about 1000 times the proportionality constant when the magnetic field H is large (point B in the figure). Thus, the magnetization curve of the magnetic material is non-linear.

The equation of motion of the magnetic field includes not only the magnetic field and its time derivative term but also a magnetization dependent term that depends on the magnetization. The magnetization dependence term in the equation of motion of the magnetic field for a certain particle is, for example, a term representing a magnetic field that acts on the particle due to the magnetization of another particle. The term representing such an interaction explicitly includes the magnetization M as shown in, for example, the equation (14). Therefore, it can be said that the equation of motion of the magnetic field shown in Expression (16) includes a term that changes nonlinearly as the convergence calculation proceeds. Since the initial value of the magnetic field for the convergence calculation is usually a small value (for example, zero), H (r _ip ) in Expression 14 can be a value about 1/1000 smaller at the time of completion compared to the beginning of the convergence calculation. This large nonlinearity in the equation is thought to delay the convergence of the numerical solution.

  An adjustable parameter that can be arbitrarily set can be introduced into the equation of motion of the magnetic field. For example, in the equation of motion of the magnetic field shown in Equation (16), the virtual mass α and the damping constant γ are adjustable parameters. If importance is attached to simplifying the parameter setting operation, these adjustable parameters may be set to constant values. In this case, the adjustable parameters are unchanged during the convergence calculation. On the other hand, the magnetic field calculation unit may change the adjustable parameter during the convergence calculation.

  The equation of motion of the magnetic field generally takes the form of a second-order linear ordinary differential equation unless constraints are taken into account. This form is common to the fundamental equation of vibration with one degree of freedom. Therefore, the convergence characteristic of the motion equation of the magnetic field corresponds to the damping characteristic of the fundamental equation of vibration. From this, it is possible to adjust to the desired convergence characteristic by changing the adjustable parameter of the motion equation of the magnetic field according to the fact that the damping characteristic changes according to the coefficient of each term of the equation of vibration. .

Therefore, the magnetic field calculation unit may adjust the adjustable parameter introduced in the equation of motion of the magnetic field so as to reduce the influence of the nonlinearity of the magnetization curve on the convergence of the numerical solution. The magnetic field calculation unit may change the adjustable parameter so as to suppress the influence of the magnetization dependence term on the convergence of the numerical solution. In one embodiment, the magnetic field calculation unit performs a coefficient adjustment process for changing the adjustable parameter when it is determined that the convergence determination criterion is not satisfied in the convergence determination process for determining whether or not the convergence determination criterion is satisfied. May be executed. In the above-described embodiment, when the control unit 3 determines that the error value exceeds the error determination value A ₂ (No in step 108 in FIG. 7), the coefficient adjustment that adjusts the virtual mass α and the attenuation constant γ. Steps may be performed.

The equation of motion of the magnetic field H acting on the particles of a certain object is generally expressed by equation (37). Here, the coefficient C _M denotes the coefficient of second order time derivative term of the magnetic field H, the coefficient C _D represents the coefficient of first-order time derivative term of the magnetic field H, factor C _K represents the coefficient of the term of the magnetic field H. The coefficients C _M , C _D , and C _K are all parameters that can be adjusted by the analyst. On the other hand, the coefficient F _NL depends on the proportionality constant between the magnetic field H and the magnetization M. H ₀ represents an externally applied magnetic field.

Therefore, by adjusting the coefficients C _M and C _D that are adjustable parameters based on the magnetization curve, it is possible to eliminate the influence of the nonlinearity of the magnetization curve on the convergence of the numerical solution. That is, the coefficients C _M and C _D of the time differential term of the magnetic field H are defined as C _M 'F _NL and C _D ' F _NL using the magnetization dependence coefficient F _NL as shown in the equation (38). If the time change rate of the magnetization dependence coefficient F _NL is sufficiently small, the influence of the nonlinearity of the magnetization curve on the convergence of the numerical solution can be virtually eliminated.

A common parameter F _NL that changes nonlinearly with respect to the magnetic field H is introduced into the magnetic field term and the time derivative term of the equation (38). That is, the convergence characteristic of the equation of motion of the magnetic field shown in the equation (38) is substantially equal to the convergence property of the equation of motion (39) having no common magnetization dependence coefficient _FNL .

Magnetic field H and the coefficient C _M of the time derivative term of equation _{(39) ', C D'} , and C _K are both independent on the magnetization M, it is a parameter that can be analyzed user to arbitrarily set. Therefore, even if the magnetization dependence coefficient F _NL changes for each convergence calculation in the equation (38), a constant convergence characteristic determined from the coefficients C _M ′, C _D ′, and C _K can be obtained. In this case, it is preferable to set the coefficients C _M ′, C _D ′, and _CK in advance so as to provide desired convergence characteristics.

  The present invention is not limited to the embodiment that excludes the influence of the nonlinearity of the magnetization curve from the convergence characteristics of the motion equation of the magnetic field. The present invention can also be applied to a numerical equation method of motion equation type when the coefficient of a variable of a basic equation changes nonlinearly with respect to the variable. For example, it may be applicable to so-called large deformation analysis.

  In one embodiment, an analysis device is provided for analyzing characteristics of an object having a first physical quantity and a second physical quantity having a non-linear relationship with the first physical quantity. For example, in the above-described embodiment, the first physical quantity and the second physical quantity correspond to the magnetic field and the magnetization, respectively. This analysis apparatus includes a numerical operation unit that numerically solves a relational expression that the first physical quantity described in the form of the equation of motion should satisfy. This relational expression includes a term that depends on the second physical quantity and a term that does not depend on the second physical quantity, and the coefficient of the term that does not depend on the second physical quantity is linked to a term that depends on the second physical quantity. Is defined as In one embodiment, an interlocking portion interlocking with the second physical quantity may be commonly introduced in each coefficient of the first physical quantity and its time derivative term.

  The adjustable parameter is preferably defined using a value derived in the process of numerically solving the motion equation of the magnetic field. That is, the magnetic field calculation unit may execute the coefficient adjustment process using the value calculated in the magnetic field calculation process. In this way, the adjustable parameter can be adjusted using the calculated value obtained in the process of solving the motion equation of the magnetic field. Since it is not necessary to perform a new operation for setting the adjustable parameter, the calculation cost can be reduced. Therefore, the time required for the convergence calculation can be shortened.

Therefore, the adjustable parameter may be adjusted in conjunction with a term representing a magnetic field acting on the particle due to the magnetization of another particle. In the above-described embodiment in which the magnetic field is obtained by solving Expression (16), for example, the virtual mass α _ip is defined as a variable amount by Expression (40) and Expression (41). Since the coefficient k _ip is defined by using the term of H (r _ip ) existing in the equation of motion of the magnetic field, it is not necessary to perform a new calculation for setting the adjustable parameter. The coefficient α ₀ is a parameter that can be arbitrarily set by the analyst.

It will be described that the influence of the nonlinearity of the magnetization curve is excluded from the convergence characteristic of the motion equation of the magnetic field by the virtual mass α _ip . Considering solving the equation (16) by applying the SHAKE method as described above, the second term on the right-hand side of the equation (16) converges to 0, and is expressed as the equation (42).

From the equations (14) and (41), H (r _ip ) is represented by the equation (43).

By substituting Equation (40) and Equation (43) into Equation (42), the equation of motion of the magnetic field is expressed by Equation (44). A common parameter (1-k _ip ) that changes nonlinearly with respect to the magnetic field H is introduced into the magnetic field term and the time derivative term of the equation (44). Therefore, the convergence characteristic of the motion equation (44) of the magnetic field is substantially equal to the convergence characteristic of the expression (45) that does not have the common parameter (1-k _ip ). Therefore, even if the coefficient k _ip (H (r _ip ) in the equation (16)) changes during the convergence calculation due to magnetic saturation, the convergence characteristic of the magnetic field equation of motion (44) does not change. By setting the coefficients α ₀ and γ in advance, desired convergence characteristics can be realized.

  It should be noted that the above-described parameter update is also effective when the target object of the magnetic field analysis includes substances with different magnetic susceptibility. For example, it is also effective when the object includes a magnet and iron. This is because the difference in magnetic susceptibility for each particle due to different materials is handled in the above-mentioned equation of motion of the magnetic field, similarly to the difference in magnetic susceptibility depending on whether or not magnetic saturation occurs.

FIG. 13 is a flowchart for explaining magnetic field calculation processing according to an embodiment of the present invention. As shown in FIG. 13, the control unit 3 of the calculation server 204 first creates an equation of motion of the magnetic field (S10). In one embodiment, the control unit 3 creates the equation of motion (16) of the magnetic field by executing steps 101 to 102 shown in FIG. Here, the virtual mass α _ip is defined as a variable amount by the equations (40) and (41).

  Next, the control part 3 calculates a magnetic field based on the equation of motion of a magnetic field (S11). In one embodiment, the control unit 3 calculates the magnetic field based on the equation of motion (16) of the magnetic field by executing steps 105 to 107 shown in FIG. The controller 3 determines whether or not the calculated magnetic field satisfies the convergence criterion (S12). The convergence criterion is the same as in step 108 shown in FIG. 7, for example, and the control unit 3 determines whether or not the error satisfies the error determination value.

When determining that the convergence criterion is not satisfied (No in S12), the control unit 3 updates the adjustable parameter (S13), and performs the magnetic field calculation based on the magnetic field equation of motion again (S11). . The control unit 3 repeats the update of the adjustable parameter and the magnetic field calculation until the convergence criterion is satisfied. The control unit 3 updates the virtual mass α _ip as an adjustable parameter. That is, the control unit 3 updates the coefficient k _ip .

  When determining that the convergence criterion is satisfied (Yes in S12), the control unit 3 calculates the motion of the analysis target object based on the calculated magnetic field (S14). In one embodiment, the control unit 3 executes steps 109 to 114 shown in FIG. Next, the control unit 3 determines whether or not a predetermined end condition is satisfied (S15), and ends the analysis when it is determined that the predetermined end condition is satisfied (Yes in S15). When the control unit 3 determines that the termination condition is not satisfied (No in S15), the communication unit 201 of the calculation server 204 transmits the calculation result to the first design terminal 206a (S16). In this way, the control unit 3 performs analysis of the magnetic field acting on the object and the movement of the object caused thereby.

14 and 15 are diagrams showing examples of magnetic field calculation according to an embodiment of the present invention. FIG. 14 shows the relationship between the magnetic field H and the virtual time δt when the virtual mass α _ip is fixed to a constant value, and FIG. 15 shows the convergence calculation while updating the virtual mass α _ip using the coefficient k _ip as described above. Shows the relationship between the magnetic field H and the virtual time δt. The example of the magnetic field calculation in FIGS. 14 and 15 is performed on an object composed of 10 particles arranged in one dimension. Particles 1 and 10 are both ends of the object. Compared to the calculation result of FIG. 14, the calculation result of FIG. 15 shows that the magnetic field has reached a steady state in a short time. By performing the convergence calculation while updating the virtual mass α _ip , it is possible to reduce the convergence delay due to the magnetic saturation of the numerical solution of the motion equation of the magnetic field.

  FIG. 16 is a chart showing a series of processes in the coupled analysis system 200. When performing a coupled motor analysis using the first design terminal 206a and the calculation server 204, communication is first established between the first design terminal 206a and the calculation server 204 (S302a, S302b). After establishing communication, the first design terminal 206a transmits a setting file for coupled analysis to the calculation server 204 (S304). When the calculation server 204 receives the setting file, the calculation server 204 performs initial setting of the analysis target system, in this case, the motor, based on the received setting file (S306). When the initial setting is completed and the preparation on the calculation server 204 side is completed, the calculation server 204 notifies the first design terminal 206a that the preparation is completed. Upon receiving the notification, the first design terminal 206a transmits the initial value of the current density vector of the current flowing through the motor coil to the calculation server 204 (S308). The calculation server 204 calculates a magnetic field based on the received initial value of the current density vector (S310). The calculation server 204 calculates a force vector based on the calculated magnetic field (S312). The calculation server 204 calculates a velocity vector based on the calculated force vector (S314). The calculation server 204 calculates a position vector based on the calculated velocity vector (S316). The calculation server 204 transmits the calculation result, that is, the calculated position vector, the calculated force vector, and the calculated speed vector to the first design terminal 206a (S318). The first design terminal 206a calculates a current density vector based on the received force vector, velocity vector, and position vector (S320). The first design terminal 206a transmits the calculation result, that is, the calculated current density vector, to the calculation server 204 (S322). The calculation server 204 calculates a magnetic field based on the received current density vector (S310). Similarly, steps S310, S312, S314, S316, S318, S320, and S322 are repeated.

  According to the coupled analysis system 200 according to the embodiment, the calculation server 204 calculates a physical quantity by numerically solving a governing equation with a control quantity calculated and sent from the first design terminal 206a as an input. To do. In addition, the first design terminal 206a calculates the control amount of the system to be analyzed with the physical quantity calculated and sent from the calculation server 204 as an input. Accordingly, by causing the control system simulation and the physical calculation simulation to be calculated by different devices, the respective calculation loads can be distributed. From the experience of the inventor as a person skilled in the art, the communication processing and communication load at this time are only negligible compared with the simulation time. Therefore, the simulation time can be shortened by distributing the calculation load.

  In particular, when the control calculation unit 210 is realized by using a general-purpose design tool in the first design terminal 206a, in order to keep such a design tool usable in the terminal, a large number of memory areas and CPUs are usually used. Occupying time. Therefore, if the calculation of the physical quantity is also performed by the first design terminal 206a, the amount of calculation resources that can be used for the calculation is limited, and the calculation of the physical quantity is relatively slow. Therefore, in the present embodiment, by leaving the calculation of the physical quantity to the calculation server 204, more calculation resources can be devoted to the calculation of the physical quantity, so that the entire simulation becomes faster.

  Further, from the experience of the present inventor as a person skilled in the art, the time required for the calculation of the physical quantity in the calculation server 204 is often considerably longer than the time required for the calculation of the control system in the first design terminal 206a. Therefore, in the coupled analysis system 200 according to the present embodiment, the designer can consider various designs at the first design terminal 206a while the calculation of the physical quantity is advanced at the calculation server 204. As a result, the designer can design more efficiently.

  In the coupled analysis system 200 according to the embodiment, exclusive processing for access to the data file 218 is performed in the first design terminal 206a. Normally, when the calculation function of the design terminal accesses a file accessed by the communication function of the design terminal, the calculation function cannot read the file. In some cases, the coupled analysis may stop there. In particular, when the design terminal uses Simulink, Simulink always reads the file during the coupled analysis, so that the fear of stopping the operation due to the collision of access to the file is increased. However, since the exclusive process is performed in the first design terminal 206a according to the present embodiment, the possibility that the coupled analysis stops due to the collision of access to the data file 218 can be reduced.

  If abnormal data is input to the control calculation unit 210 during the coupled analysis, the control calculation in the control calculation unit 210 does not converge, and the coupled analysis may stop midway as an exception error. In this case, since the coupled calculation that has been performed for a long time is stopped, the simulation performed so far is wasted. Therefore, in the coupled analysis system 200 according to the present embodiment, whether or not the first design terminal 206a satisfies the convergence criterion before the position vector, the force vector, and the velocity vector are registered in the data file 218. Is determined. As a result, the data can be interlocked so that illegal data is not passed to the control arithmetic unit 210. As a result, it is possible to reduce the possibility that the coupled calculation stops midway due to abnormal data input.

  In the coupled analysis system 200, in terms of the client-server relationship, the calculation server 204 that performs magnetic field calculation is the server side, and the design terminal that performs control calculation is the client side. In this case, if the client design terminal is connected to the network 202, the client analysis terminal can be connected to the computation server 204 of the coupling destination and the coupled analysis can be performed regardless of the client design terminal. Therefore, the coupled analysis can be performed while performing the control design on the PC terminal of each individual who is involved in the design, so that the restriction on the design place is relaxed.

  Coupled calculations often take several days. In this case, the coupled calculation is automatically continued at night after the user of the coupled analysis system returns home. Here, if the coupled calculation stops due to some error when there is no user, the machine time until the next user is wasted. Therefore, in the coupled analysis system 200 according to the embodiment, the resume unit 220 is provided in the first design terminal 206a, and the calculation is automatically restarted even when the calculation is stopped. Thereby, machine time can be used more effectively.

  The configuration and operation of the coupled analysis system 200 according to the embodiment have 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 the coupled analysis system 200 includes three design terminals has been described. However, the present invention is not limited to this, and the number of design terminals is not limited.

  In the embodiment, the case where the calculation server 204 calculates the magnetic field of the motor has been described, but the present invention is not limited to this. For example, the calculation server may perform calculations using the molecular dynamics method.

  In the embodiment, the case has been described in which the first design terminal 206a performs the exclusion process with a file, but the present invention is not limited to this. For example, the first design terminal 206a may perform exclusive processing using a shared memory or mail.

  In the embodiment, before the communication unit 208 of the first design terminal 206a registers the extracted position vector, force vector, and velocity vector in the data file 218, they are converged by the control operation in the control operation unit 210. However, the present invention is not limited to this. For example, the communication unit 201 of the calculation server 204 may make the same determination.

  DESCRIPTION OF SYMBOLS 1 Magnetic field analyzer, 3 Control part, 5 Storage device, 7 Input part, 9 Display part, 11 Printer port, 12 Printer, 13 Bus | bath, 31 SPM motor, 33 Rotor, 35 Stator, 37 Rotor core, 39 Permanent magnet, 41 Rotor Shaft, 43 stator teeth, 44 core back, 45 coils, 46 frames, 200 coupled analysis system, 202 network, 204 arithmetic server, 206a first design terminal.

Claims (9)

An arithmetic unit that calculates a physical quantity by numerically solving a governing equation;
A design device connected to the arithmetic device via a network and calculating a control amount of a predetermined system using a physical quantity calculated by the arithmetic device as an input;
The arithmetic unit calculates a physical quantity using a control amount calculated by the design apparatus as an input, and is a coupled analysis system.   The arithmetic unit divides an object included in the system into a large number of particles, and numerically solves the equation of motion of the magnetic field describing the relationship to be satisfied by the magnetic field acting on each particle in the form of the equation of motion for each particle. The coupled analysis system according to claim 1, wherein a magnetic field acting on the object is calculated by the calculation.   The arithmetic device is connected to a plurality of design devices via the network, calculates a physical quantity according to a request from each design device, and provides the calculated physical quantity to the design device. Or the coupled analysis system of 2. The design apparatus includes:
A communication unit that communicates with the arithmetic device via the network and registers the physical quantity calculated by the arithmetic device in an electronic file;
A control calculation unit that calculates a control amount of the system using a physical quantity registered in the electronic file as an input,
4. The coupled analysis system according to claim 1, wherein access to the electronic file by the control calculation unit is restricted while the communication unit is accessing the electronic file. 5. The design apparatus includes:
A communication unit that communicates with the arithmetic device via the network and registers the physical quantity calculated by the arithmetic device in an electronic file;
A control calculation unit that calculates a control amount of the system using a physical quantity registered in the electronic file as an input,
Before registering in the electronic file, the communication unit determines whether or not the physical quantity calculated by the calculation device satisfies a predetermined criterion in consideration of convergence of calculation in the control calculation unit. The coupled analysis system according to any one of claims 1 to 3. The design device accumulates a history of operations,
6. The coupled analysis system according to claim 1, wherein when the calculation is stopped, the design apparatus restarts the calculation with reference to the accumulated history.   An analysis system that uses two operations each having an output value of each other as input values, wherein the two operations are executed in separate devices. Calculating a physical quantity by numerically solving an equation in the first device;
In a second device different from the first device, a step of calculating a control amount of a predetermined system using a physical quantity calculated by the first device as an input;
And a step of numerically solving the equation using the control amount calculated by the second device as an input in the first device. A function of calculating a physical quantity by numerically solving an equation in the first device;
A function of causing a second device different from the first device to calculate a control amount of a predetermined system using a physical quantity calculated by the first device as an input;
In the first apparatus, the first apparatus causes the first apparatus to realize a function of numerically solving the equation using a control amount calculated by the second apparatus as an input.