JP5713572B2 - Magnetic field analysis device, magnetic field analysis method, and coupled analysis device - Google Patents

Description

  The present invention relates to a magnetic field analysis apparatus and a magnetic field analysis method.

  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

  However, since the static magnetic field analysis does not consider temporal variation, the electromagnetic behavior of the driven motor cannot always be sufficiently reflected. As a result, the accuracy of analysis tends to be insufficient. In addition, it is practically preferable that the time required for calculation is short.

  Accordingly, an object of the present invention is to provide a magnetic field analysis apparatus and a magnetic field analysis method that can obtain an analysis result at high speed and with high accuracy.

  According to one aspect of the present invention, a magnetic field analyzer for analyzing a magnetic field in a system including an object is provided. This device works on the object by dividing the object into a large number of particles and numerically solving 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 an equation of motion for each particle. A magnetic field calculation unit for calculating a magnetic field is provided. An adjustable parameter is introduced into the equation of motion of the magnetic field, and the magnetic field calculation unit adjusts the parameter so as to alleviate the influence of the nonlinearity of the magnetization curve of the object on the convergence of the numerical solution.

  According to this aspect, since the equation of motion is numerically solved, unlike the known magnetic field analysis method based on the finite element method, the calculation of the inverse matrix is unnecessary. For this reason, magnetic field analysis can be performed accurately with few calculation resources. Moreover, since the adjustable parameter is adjusted so as to reduce the influence of the nonlinearity of the magnetization curve on the convergence of the numerical solution, the convergence delay of the numerical solution due to magnetic saturation can be reduced.

  Another aspect of the present invention is a magnetic field analysis method. In this method, a magnetic field calculation step for numerically solving a motion equation of a magnetic field in which a magnetic field acting on an object including a material whose magnetization curve is nonlinear is to be satisfied is described in the form of a motion equation, and the motion equation of the magnetic field is An adjustment step of adjusting the introduced adjustable parameters so as to reduce the influence of the nonlinearity of the magnetization curve on the convergence of the numerical solution.

  An embodiment of the present invention may be a program for causing a computer to execute the magnetic field analysis method, or a computer-readable recording medium on which the program is recorded.

  Another aspect of the present invention is a coupled analysis device. This device includes a magnetic field analysis calculation unit that calculates a magnetic field based on a motion equation of a magnetic field that describes the relationship to be satisfied by the magnetic field acting on each particle constituting the object in the form of a motion equation for each particle, and the calculated magnetic field. And a mechanism analysis calculation unit that calculates the motion of the object based on the above.

  Another aspect of the present invention is an analysis device for analyzing characteristics of an object having a first physical quantity and a second physical quantity having a nonlinear relationship with the first physical quantity. The apparatus includes a numerical operation unit that numerically solves a relational expression to be satisfied by the first physical quantity described in the form of a motion equation, the relational expression including a term that depends on the second physical quantity, A term that does not depend on the physical quantity, and the coefficient of the term that does not depend on the second physical quantity is defined to be linked to the term that depends on the second physical quantity.

  According to the present invention, magnetic field analysis can be performed at high speed and with high accuracy.

It is a figure which shows the hardware constitutions of the magnetic field analyzer which concerns on one Embodiment of this invention. It is a figure which shows the memory | storage device of the magnetic field analyzer which concerns on one Embodiment of this invention. It is a figure which shows the outline of a structure of the SPM motor which concerns on one Embodiment of this invention. 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 magnetic field analyzer which concerns on one Embodiment of this invention. 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 the rectangular parallelepiped conductor which concerns on one Embodiment of this invention, and a local coordinate. It is a figure which shows the relationship between the circular-arc-shaped columnar conductor which concerns on one Embodiment of this invention, and a local coordinate. It is explanatory drawing of the element used for the magnetic field calculation of the magnetic body which concerns on one Embodiment of this invention. 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.

  DESCRIPTION OF EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail based on the drawings.

  First, a hardware configuration of the magnetic field analysis apparatus 1 according to the present embodiment will be described with reference to FIG.

  It should be noted that the hardware configuration in FIG. 1 is an example, and is not limited to this.

  As shown in FIG. 1, the magnetic field analysis apparatus 1 includes a control unit 3, a storage device 5, a media input / output unit 6, an input unit 7, a display unit 9, a printer port 11, and the like connected to each other via a bus 13.

  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. 2, the storage device 5 stores a control program 15 for driving and controlling each component of the magnetic field analysis device 1, 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, a procedure for analyzing a magnetic field using the magnetic field analyzer 1 will be described with reference to FIGS.

  Here, a magnetic field analysis of an SPM motor 31 (Surface Permanent Magnet Motor), which is a kind of permanent magnet motor, will be described as an example.

  First, an outline of the configuration of the SPM motor 31 will be described with reference to FIGS. 3 and 4.

  As shown in FIG. 3, the SPM motor 31 has a rotor 33 as a rotor (moving element) and a stator 35 as 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. 3 and 4, 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. 3 and 4. 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.

  First, the control unit 3 of the magnetic field analysis apparatus 1 activates the magnetic field analysis program 17 and functions representing the three-dimensional structure (shape, coordinate point), mass density, and magnetization curve of the magnetic material as analysis conditions of the SPM motor 31 to be analyzed. The current density vector of the conductor is stored as input information 21 of the storage device 5 (step 101 in FIG. 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.

  The above is the details of step 101 in FIG.

  Next, the control unit 3 of the magnetic field analysis apparatus 1 determines that the magnetic material is N particles (a polyhedral element whose center is the position vector of the particle (cubic element in this embodiment) from the information of the three-dimensional structure included in the input information 21. )), And the particle position vector is calculated and stored in the storage device 5 (step 102 in FIG. 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 102 in FIG.

  Next, the control unit 3 determines that the conductor (coil 45 shown in FIG. 6A) is a local conductor (rectangular conductors 45a and 45b) as shown in FIG. And arc-shaped columnar conductors 45c and 45d), the coefficient for calculating the magnetic field vector created by each conductor is calculated and stored in the storage device 5 (step 103 in FIG. 5).

  Here, step 103 in FIG. 5 will be specifically described.

  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 reads the three-dimensional structure of the conductor and the current density vector stored in the storage device 5 as the input information 21 from step 101, and a, b, c that are the dimensions of the local conductor (cuboid conductor 45a) and the particles The position vector is 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. 8) 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 reads the three-dimensional structure of the conductor and the current density vector stored in the storage device 5 as the input information 21 from step 101, and the dimensions r _a and z _{b of the} local conductor (arc-shaped columnar conductor 45c). , Θ, R _c and the particle position vector are calculated and stored in the storage device 5.

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

  The above is the details of step 103 in FIG.

  Next, the control unit 3 of the magnetic field analysis device 1 stores the position vector of N particles constituting the magnetic body calculated up to this step and stored in the storage device 5 and 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 body is calculated according to the shape of the polyhedral element and stored in the storage device 5 (step 104 in FIG. 5).

  Here, step 104 in FIG. 5 will be specifically described.

  When the divided polyhedral elements (cubic elements in this embodiment) are displayed two-dimensionally, the shape shown in FIG. 9 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 (cubic elements in the present embodiment) having the center of gravity of the particles) constituting the magnetic body calculated in step 102 and stored in the storage device 5.

  If the particle position vector is updated and stored in the storage device 5 in step 113, 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 the center of gravity, and the vertex of the boundary surface of the polyhedral element having the particle position vector as the center of gravity and the particle position as the vertex. The volume ΔV is calculated and stored in the storage device 5.

  The above is the details of step 104 in FIG.

  Next, the control unit 3 of the magnetic field analysis apparatus 1 uses the size of the coil stored in the storage device 5 in step 103 and the current density vector stored in the storage device 5 up to this step to perform bio-savart. Based on the analytical solution obtained by integrating the above law, 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 (step 105 in FIG. 5).

  Here, step 105 in FIG. 5 will be specifically described.

  Here, when it is assumed that an arbitrary position vector is a point P where the stator teeth 43 as a magnetic body in FIG. 4 are present, a procedure for calculating a magnetic field vector generated by the energized coil 45 on the position vector of the P point. 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.

  This local coordinate system is described in step 103.

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, r _ps (bold) is the position vector of the point P in the local coordinate system (x _s , y _s , z _s ), and x _ps , y _ps , z _ps are 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.

  This local coordinate system is described in step 103.

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 magnetic field analysis apparatus 1 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 already calculated in step 104 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 ), and calculates the dimensions of the rectangular parallelepiped conductor 45 a calculated in step 103 and stored in the storage device 5. From step 101, the current density vector stored in the storage device 5 as the input information 21 is read, and the magnetic field vector is calculated based on the equations (1) to (4).

  When the current density vector is updated in step 116 and stored in the storage device 5, the control unit 3 reads the value.

  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 in step 103 and stored in the storage device 5, and the control unit 3 inputs in step 101. A current density vector stored in the storage device 5 as information 21 is read.

  When the current density vector is updated in step 116 and stored in the storage device 5, the control unit 3 reads the value.

  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 105 in FIG.

  Next, the control unit 3 of the magnetic field analysis apparatus 1 uses the calculation program 19 to calculate the magnetic field vector after the virtual time step δt without considering the constraint from the motion equation of the magnetic field of the particles constituting the magnetic body, and stores it. It memorize | stores in the apparatus 5 (step 106 of FIG. 5).

  Here, step 106 in FIG. 5 will be specifically described.

  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.

  The points p and q are described in step 104.

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 (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 shown in the second term on the right side of Expression (16), the present embodiment employs the SHAKE method, which is a generalized constraint introduction method.

  When equation (16) is discretized by the jumping method without considering the constraint, 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 magnetic field analysis apparatus 1 reads the position vectors of the p point and the q point in the polyhedron element whose center of gravity is the particle position vector already calculated in step 104 and stored in the storage device 5.

  Next, the control unit 3 generates a magnetic field vector generated at the point p inside the polyhedron element whose center of gravity is the particle constituting the magnetic body, which is already calculated in step 105 and stored in the storage device 5. Read as a vector.

  Further, the control unit 3 calculates the polyhedral element boundary surface having the centroid of the element boundary area, normal vector, and particle position vector of the particles constituting the magnetic body, which are already calculated in step 104 and stored in the storage device 5. The volume of a polyhedron element whose vertex is the particle position is read.

  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 107 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 details of step 106 in FIG. 5 have been described above.

  Next, the control unit 3 of the magnetic field analysis device 1 is bound to the magnetic field vector at the point p in the polyhedron element having the center of gravity as the position vector of the particles constituting the magnetic material, which is calculated in step 106 and stored in the storage device 5. A force is applied, and the calculated magnetic field vector is stored in the storage device 5 (step 107 in FIG. 5).

  Here, step 107 in FIG. 5 will be specifically described.

  A binding force is applied to the magnetic field vector at the point p in the polyhedron element with the position vector of the particle constituting the magnetic body as the center of gravity 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 magnetic field analysis apparatus 1 uses the calculation program 19 to calculate the magnetic field vector at the point p in the polyhedron element with the particle constituting the magnetic body calculated in step 106 and stored in the storage device 5 as the center of gravity. Read.

  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 107 in FIG.

  Next, the control unit 3 of the magnetic field analysis apparatus 1 determines whether or not the magnetic field vector obtained in step 107 satisfies the constraint condition, and if satisfied, proceeds to the next step, and if not satisfied, returns to step 107 (FIG. 5 step 108).

  Specifically, the control unit 3 performs the 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 107 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 for the binding condition of the i-th particle among the particles constituting the magnetic material.

  The magnetization vector (bold) M is calculated in step 107 and the magnetic field vector stored in the storage device 5 is read by the control unit 3 and substituted 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 the one already calculated in step 104 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 107.

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 108 in FIG.

Next, the control unit 3 of the magnetic field analysis apparatus 1 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. (Step 109 in FIG. 5)
Here, step 109 in FIG. 5 will be specifically described.

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 magnetic field analysis apparatus 1 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 107 and stored in the storage device 5.

  Next, the control unit 3 calculates Expression (24), and proceeds to the next step if Expression (24) is satisfied, and returns to Step 106 if not satisfied.

The above is the details of step 109 in FIG.

  Next, the control unit 3 of the magnetic field analysis apparatus 1 performs 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 on the position vector of all particles constituting the coil. The vector and the magnetic flux density vector are calculated and stored in the storage device 5 (step 110 in FIG. 5).

  Step 110 will be specifically described below.

(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 magnetic field analysis apparatus 1 reads the magnetic field vector at the point p in the polyhedron element with the particle constituting the magnetic body as the center of gravity calculated up to step 110 from the storage device 5.

  Next, the control unit 3 reads the normal vector already calculated in step 104 and stored in the storage device 5, and calculates the magnetic field vector on the position vector of the particles constituting the magnetic body based on the equation (25). Calculate and store in the storage 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 magnetic field analysis apparatus 1 reads the position vector of the particles constituting the coil calculated in step 103 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 113, 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 calculated from step 102 and stored in the storage device 5, and q points in the polyhedron element having the particle position vector as the center of gravity. Read the position vector and 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 in step 103 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.

  If the current density vector is updated in step 116, the control unit 3 reads the value.

  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 110 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 magnetic field analysis apparatus 1 calculates a force vector acting on all the particles constituting the SPM motor 31 and stores it in the storage device 5 (step 111 in FIG. 5).

  The step 111 in FIG. 5 will be specifically described below.

(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 magnetic field analysis apparatus 1 reads the magnetic field vector at the point p in the polyhedron element with the particle constituting the magnetic body calculated up to step 110 and stored in the storage device 5 as the center of gravity.

  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 calculates the polyhedral 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 in step 104 and stored in the storage device 5 and the vertex of the particle position. Read.

  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 magnetic field analysis apparatus 1 reads the position vector of the particles constituting the coil calculated in step 103 and stored in the storage device 5.

  If the position vector of the particles constituting the coil has been updated in step 113, the control unit 3 reads the value.

  Further, the control unit 3 reads the dimensions of the coil calculated in step 103 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.

  Note that if the current density vector of the coil is updated in step 116, the control unit 3 uses the value.

  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 111 in FIG.

  Next, the control unit 3 of the magnetic field analyzer 1 calculates the rotation amount, angular velocity, translation amount, translation of the movable unit (moving element) from the force vector acting on the particles constituting the moving part (moving element) calculated in step 111. The speed is calculated and stored in the storage device 5 (step 112 in FIG. 5).

  The step 112 in FIG. 5 will be specifically described below.

  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 112, 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 uses the position vector of the particles constituting the rotor 33 and the force vector acting on the particles constituting the rotor 33 calculated in step 111 and stored in the storage device 5, based on the equation (35), Equation (36) is calculated, 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 112 in FIG.

  Next, the control unit 3 of the magnetic field analysis apparatus 1 calculates and stores the position vector of the particles constituting the moving element based on the rotation amount after a minute time and the movement amount of the center of gravity calculated in step 112 ( Step 113 in FIG.

  Next, the control unit 3 of the magnetic field analyzer 1 outputs the position vector, force vector, magnetic field vector, magnetic flux density vector, and magnetization vector of the particles constituting the SPM motor 31 from the printer 12 via the printer port 11 as necessary. (Step 114 in FIG. 5).

  Next, the control unit 3 of the magnetic field analysis apparatus 1 determines whether or not a predetermined end condition (time, amount of movement, etc.) is satisfied. If it is satisfied, the analysis ends, and if not, the process proceeds to step 116. (Step 115 in FIG. 5).

  Next, the control unit 3 of the magnetic field analysis apparatus 1 updates the current density vector flowing in the coil 45 as necessary, and returns to Step 104 (Step 116 in FIG. 5).

  The above is the magnetic field analysis procedure according to the present embodiment.

  As described above, according to the present embodiment, the magnetic field analysis device 1 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.

  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-described embodiment, the case where the magnetization phenomenon of the magnetic material is calculated by solving the motion equation of the magnetic field derived from the Lagrangian of the particles constituting the magnetic material has been described. Without being limited thereto, any equation other than that derived from Lagrangian may be used as long as it is an equation of motion.

  In the above-described embodiment, 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 the magnetic field at an arbitrary point in the space where the magnetic body is arranged is analyzed. 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 may be used for magnetic field analysis in the space shielded with the magnetic material.

  As described above, according to one embodiment of the present invention, there is provided a coupled analysis device for performing coupled analysis of magnetic field analysis on a magnetic field acting on an object and mechanism analysis on motion of the object generated by the magnetic field. Provided. That is, the coupled analysis device 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 magnetic field analysis calculation unit further recalculates the magnetic field based on the updated position of each particle. Thus, coupled analysis is possible by repeating magnetic field analysis and mechanism analysis for each particle. 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). 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 one embodiment, the above 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. 10 is a diagram schematically illustrating an example of a magnetization curve of a magnetic material (for example, iron). The horizontal axis in FIG. 10 indicates the magnetic field H, and the vertical axis indicates the magnetization M. As shown in FIG. 10, when the magnetic field H is small, the magnetization M is proportional to the magnetic field H. 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, in one embodiment of the present invention, the magnetic field calculation unit adjusts 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. May be. 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 109 in FIG. 5), 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.

  Moreover, in one Example, it is preferable that the adjustable parameter is defined using the value derived | led-out in the process of solving the equation of motion of a magnetic field numerically. 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.

Thus, in one embodiment, the adjustable parameter may be adjusted in conjunction with a term representing a magnetic field acting on the particle due to the magnetization of the other 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. 11 is a flowchart for explaining magnetic field calculation processing according to an embodiment of the present invention. As shown in FIG. 11, the control unit 3 of the magnetic field analysis apparatus 1 first creates a motion equation of a magnetic field (S10). In one embodiment, the control unit 3 creates the motion equation (16) of the magnetic field by executing steps 101 to 105 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 106 to 108 shown in FIG. The controller 3 determines whether or not the calculated magnetic field satisfies the convergence criterion (S12). The convergence determination criterion is the same as that in step 109 shown in FIG. 5, 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 110 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 it is determined that the termination condition is not satisfied (No in S15), the control unit 3 calculates the magnetic field again based on the new position of the object to be analyzed by the motion. In this way, the control unit 3 executes a coupled analysis between the magnetic field acting on the object and the movement of the object caused thereby.

12 and 13 are diagrams showing examples of magnetic field calculation according to an embodiment of the present invention. FIG. 12 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. FIG. 13 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. 12 and 13 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. 12, the calculation result of FIG. 13 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.

  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.

Claims (10)

A magnetic field analyzer for analyzing a magnetic field in a system including an object,
Divide the object into a large number of particles, and calculate the magnetic field acting on the object by numerically solving the motion equation of the magnetic field describing the relationship that the magnetic field acting on each particle should satisfy in the form of the equation of motion for each particle With a magnetic field calculator,
Adjustable parameters are introduced into the equation of motion of the magnetic field,
The magnetic field analysis device, wherein the magnetic field calculation unit adjusts the parameter so as to alleviate the influence of the nonlinearity of the magnetization curve of the object on the convergence of the numerical solution. The equation of motion of the magnetic field includes a magnetic field term and its time derivative term,
The magnetic field analysis apparatus according to claim 1, wherein the parameter includes a coefficient of the time derivative term, and the coefficient is adjusted based on the magnetization curve.   2. The equation of motion of the magnetic field includes a term representing a magnetic field acting on the particle due to magnetization of another particle, and the parameter is adjusted in conjunction with the term. The magnetic field analysis apparatus according to 2.   The magnetic field analysis apparatus according to claim 1, wherein the parameter is defined using a value derived in a process of numerically solving the equation of motion of the magnetic field. A position calculator that updates the position of each particle of the object based on the calculated magnetic field;
The magnetic field analysis device according to claim 1, wherein the magnetic field calculation unit recalculates the magnetic field based on the updated position of each particle. A magnetic field calculation step for numerically solving the equation of motion of the magnetic field describing the relationship to be satisfied by the magnetic field acting on the object including the material whose magnetization curve is nonlinear, in the form of the equation of motion;
An adjusting step for adjusting an adjustable parameter introduced in the equation of motion of the magnetic field so as to mitigate the influence of nonlinearity of the magnetization curve on the convergence of the numerical solution, and a magnetic field analysis method comprising: .   A program for causing a computer to execute the method according to claim 6.   A computer-readable recording medium on which the program according to claim 7 is recorded. A magnetic field analysis calculation unit that calculates the magnetic field based on the equation of motion of the magnetic field in which the relationship that the magnetic field acting on each particle constituting the object should satisfy in the form of the equation of motion for each particle;
A mechanism analysis calculation unit that calculates the motion of the object based on the calculated magnetic field,
The magnetic field analysis calculation unit adjusts the adjustable parameter of the equation of motion of the magnetic field so as to reduce the influence of nonlinearity of the magnetization curve of the object on the convergence of the numerical solution of the equation of motion. Coupled analysis device. An analysis device for analyzing characteristics of an object having a first physical quantity and a second physical quantity having a nonlinear relationship with the first physical quantity,
A numerical operation unit for numerically solving a relational expression to be satisfied by the first physical quantity described in the form of the equation of motion;
Wherein in the equation, each of the coefficients of the first physical quantity of claims and their time differential term, the product of the common part and optionally settable parameters in each term a part linked to the second physical quantity in the represented analyzer according to claim Rukoto.