JP4785051B2 - Electromagnetic field analysis method and electromagnetic field analysis program - Google Patents

Description

  The present invention relates to an electromagnetic field analysis method and an electromagnetic field analysis program, and is particularly suitable for obtaining a high-speed calculation and a reasonable solution even in nonlinear iterative calculation of a sliding mesh in electromagnetic field analysis of a rotating machine or the like using a finite element method. The present invention relates to an electromagnetic field analysis method and an electromagnetic field analysis program.

  In an electromagnetic field analysis using the finite element method, a transient response analysis having a calculation step at each of a plurality of time points in a time series and dealing with a material having nonlinear characteristics is usually performed at each of a plurality of times. The material characteristics are determined using a nonlinear iterative calculation method such as the Newton-Raphson method (hereinafter referred to as “N-R method”), and the electromagnetic field is calculated.

  FIG. 15 shows an example of a material having nonlinear characteristics. In the orthogonal biaxial coordinate system shown in FIG. 15, the horizontal axis indicates the magnetic field H, and the vertical axis indicates the magnetic flux density B. 15A is an overall view of nonlinear characteristics, and FIG. 15B is an enlarged view of a part 100 of FIG. The characteristic 101 has a non-linear characteristic. In order to determine the material characteristic value of a material having such a characteristic 101 at a certain time, as shown at points (1), (2), (3), (4) in FIG. Four iterations are performed to finally determine the point (4) as the material property value. In order to determine the material property value at each time, it is necessary to perform such a nonlinear iterative calculation, and the simultaneous linear equations must be solved a plurality of times. In the example of FIG. 15, an example of calculation four times (transition indicated by an arrow) is shown, but in practice, the number of calculations may reach several tens of times depending on the object of analysis. For this reason, the problem that analysis time becomes long is raised.

  In the case of the calculation by the above nonlinear iterative calculation method, in order to shorten the analysis time, it is desirable to appropriately determine the point (1) which is the initial value. If the initial value can be determined appropriately, it can be expected that the material characteristic value at a certain time t, that is, the number of nonlinear iterative calculations required to reach the point (4) will be reduced. From this point of view, based on the assumption that the material characteristics at the previous time are close to the material characteristics at the current time, a method has been proposed in which the solution of the previous time iteration calculation is used as the initial value of the current iteration iteration ( Non-patent documents 1, 2).

The above calculation method has the advantage that the first calculation can be omitted by the iterative calculation at each time, and the search can be performed from a place close to the material characteristic, so that the material characteristic can be reached quickly. .
Motomoto Yagawa / Ryuji Shioya, “Super Parallel Finite Element Analysis”, Asakura Shoten, first published in October 1998, pages 107-109 D. Kondrashov and D. Keefer, "A Maxwell's Equation Solver for 3-D MHD Calculations" IEEE Trans. On Magnetics Vol 33, No1, pp254-259, Jan. 1997

  The conventional calculation method using the solution of the previous time iteration as the initial value for the current time iteration includes a sliding mesh in a finite element mesh in an electromagnetic device such as a rotating machine having a movable part and a fixed part. In the case of things, there are cases where the number of nonlinear iterative calculations increases or an illegal solution that does not have physical meaning is reached. Examples of such cases will be described with reference to FIGS.

  FIG. 16 shows, as an example, a partial cross section (90 ° portion) of the movable part (rotor) 201 and the fixed part 202 forming the rotating machine 200, and a cross-sectional view perpendicular to the rotation axis 203. Yes. An air layer 204 exists between the movable 201 and the fixed portion 202, and the air layer 204 includes an air layer 204a on the movable portion side and an air layer 204b on the fixed portion side.

  When the rectangular area 205 in FIG. 16 is enlarged and an example of element division by the sliding mesh is shown, it becomes as shown in FIGS. Here, the “sliding mesh” is a finite element mesh created by applying the finite element method to the analysis target, and in particular, the air layer 204a and the air layer in the air layer 204 that forms the boundary between the movable part 201 and the fixed part 202. The mesh which comprises the contact surface of 204b is pointed out.

  FIG. 17A shows an example of sliding mesh division at time t, and FIG. 17B shows an example of sliding mesh division at time t + Δt. In FIGS. 17A and 17B, reference numeral 206 denotes a joint portion between the movable portion 201 and the fixed portion 202, which is shown separately in the figure, but actually overlaps. The joint portion 206 corresponds to the air layer 204 described above. In FIGS. 17A and 17B, numerals 1, 2, 3, 4, 5, 6, and 7 indicate numbers for distinguishing mesh elements, and the same numerals are used between (A) and (B). The attached mesh elements indicate the same parts. Black circles in the figure mean contacts. When (A) and (B) in FIG. 17 are compared, when the time changes from time t to time t + Δt, the mesh element of the fixed portion 202 does not change, and on the other hand, the position of the mesh element of the movable portion 201 is the movable portion 201. Rotate clockwise by one mesh element in accordance with the rotation operation, and its position changes. In this case, for example, when material properties are repeatedly calculated with each sliding mesh at time t + Δt, the material properties of the corresponding portion at time t are used as initial values of the first calculation.

  When the conventional calculation method using the solution of the previous time iteration calculation as the initial value of the current time iteration calculation is applied to the rotating machine 200 divided by the sliding mesh as described above, the calculation result as shown in FIG. can get. In the coordinate system of FIG. 18, the horizontal axis represents time and the vertical axis represents torque. In the graph shown in FIG. 18, 301 is a change characteristic of the material characteristic value obtained based on the result of the above iterative calculation using the solution at the previous time, and 302 is a change characteristic of the torque representing a physically correct state. is there. As a result of the calculation, the torque change characteristic 301 obtained as a solution indicates an incorrect solution. In this way, there arises a situation in which the result of the calculation is significantly different from the actual physical state.

  The above problem occurs because the solution on the sliding mesh largely changes depending on the time on the movable part 201 side and the fixed part 202 side, and the material property at the previous time is close to the material property at the current time. It is presumed that it is not established and the solution for the iterative calculation at the previous time cannot be set as the initial value of the iterative calculation at the current time. For this reason, there was room for sufficient consideration regarding the handling of solutions on the sliding mesh.

  An object of the present invention is an electromagnetic field analysis of a rotating machine or the like using a finite element method, and in the case where material properties are determined by a nonlinear iterative calculation method such as an NR method at each of a plurality of time steps. In non-linear iterative calculations using the time solution as the initial value of the current time, even for sliding meshes such as rotating machines, the number of iterative calculations is reduced, the calculation speed is increased, and the appropriateness is physically realistic. It is to provide an electromagnetic field analysis method and an electromagnetic field analysis program capable of obtaining a simple solution.

  In order to achieve the above object, an electromagnetic field analysis method and an electromagnetic field analysis program according to the present invention are configured as follows.

The first electromagnetic field analysis method (corresponding to claim 1) is:
The electromagnetic field characteristics of an electromagnetic device having a fixed part, a movable part, and a boundary part formed between the fixed part and the movable part are calculated on a computer by applying a finite element method to a plurality of time-series times. An electromagnetic field analysis method for performing analysis by performing nonlinear iterative calculation at each ,
The calculation means creates a finite element mesh based on the finite element method for each divided element of the fixed part and the movable part of the electromagnetic device, and a sliding mesh based on the finite element method for the divided element of the boundary part of the electromagnetic device. Step to make,
A time setting means for setting each of a plurality of times in a time series;
The initial value setting means sets a solution for nonlinear iterative calculation at a time before a certain time to an initial value for a finite element mesh when a time is set by the time setting means among a plurality of time-series times. And, for the sliding mesh, setting a value sufficiently smaller than 0 or a value obtained for a surrounding edge or node to an initial value;
Calculating means for performing nonlinear iterative calculation at a certain time using initial values respectively set for each of the finite element mesh and the sliding mesh;
It is comprised so that it may have.

In the electromagnetic field analysis method described above, in electromagnetic field analysis of electromagnetic equipment with rotational motion and translational motion, in non-linear iterative calculations executed at each of a plurality of times in a time series, only on a finite element mesh other than on a sliding mesh The nonlinear iteration is calculated with the previous time solution as the initial value of the current time, and the assumption that the previous time solution is close to the current time solution is not valid on the sliding mesh. Not set as initial value. Instead, for the sliding mesh, the initial value is set to 0 or a value sufficiently smaller than the value obtained for the surrounding side or node. As a result, it is possible to eliminate an increase in the number of non-linear iterative calculations due to the influence of the sliding mesh or an illegal solution having no physical meaning. In the nonlinear iterative calculation at each time, the initial value on the sliding mesh is set as described above, that is, the solution of the previous time is not used as the initial value in the finite element mesh in the portion where the abrupt change occurs. Even if the calculation is performed on a sliding mesh, the number of iterations can be reduced, the calculation can be speeded up, and a reasonable solution that is physically practical can be obtained.

In the second electromagnetic field analysis method (corresponding to claim 2), preferably, the boundary portion is an air layer .

In a third electromagnetic field analysis method (corresponding to claim 3 ), preferably, the nonlinear iterative calculation method is a Newton-Raphson method.

An electromagnetic field analysis program according to the present invention (corresponding to claim 4 ) is a program that causes a computer to execute the electromagnetic field analysis method described above.
First, a finite element mesh based on the finite element method is created for each divided element of the fixed part and the movable part of the electromagnetic device, and a sliding mesh based on the finite element method is created for the divided element of the boundary part of the electromagnetic device. Calculation means;
Time setting means for setting each of a plurality of times in a time series;
When a certain time among a plurality of times in the time series is set by the time setting means, for a finite element mesh, the solution of nonlinear iterative calculation at a time before a certain time is set to an initial value, and for a sliding mesh An initial value setting means for setting an initial value to a value sufficiently smaller than the value obtained for 0 or a surrounding edge or node;
Second calculation means for performing nonlinear iterative calculation at a certain time using initial values respectively set for each of the finite element mesh and the sliding mesh;
It is characterized by realizing.
In the above, further boundary is characterized by an air layer (corresponding to claim 5), or non-linear iterative calculation method is characterized by a Newton-Raphson method (corresponding to claim 6).

  The electromagnetic field analysis method according to the present invention is an electromagnetic field analysis of a device such as a rotating machine using a finite element method, and is initially performed by a non-linear iterative calculation method such as an NR method at each of a plurality of time steps. When determining the value, apply a non-linear iterative calculation with the solution at the previous time as the initial value of the current time on a finite element mesh other than the sliding mesh, and the initial value is 0 or a value close to 0 on the sliding mesh. Therefore, even in the case of the finite element method calculation with a sliding mesh, the number of iterations can be reduced, the calculation speeded up, and a reasonable solution that is physically realistic can be obtained.

  DESCRIPTION OF EMBODIMENTS Preferred embodiments (examples) of the present invention will be described below with reference to the accompanying drawings.

  An analysis target to which the electromagnetic field analysis method according to the embodiment of the present invention is applied is an electromagnetic device having a structural portion (slide portion) that performs a rotational motion or a translational motion. As a typical example of this electromagnetic device, an example of a rotating machine having a fixed part and a rotor (generally “movable part”) is used. In the rotating machine, the rotor performs a rotational motion with respect to the fixed portion as a relative motion. The rotor and the fixed part are separated, and a gap (gap) is formed between them. The gap that forms the boundary between the rotor and the fixed part is an air layer. When the finite element method is applied to the rotating machine, a large number of finite element meshes (mesh elements) are created for the fixed portion, the rotor, the boundary portion, and the like. The finite element mesh of the air layer that forms the boundary is a portion where a sudden change or a large change occurs, and is treated as a sliding mesh. An example of the element division of the sliding mesh is as shown in FIG.

  The electromagnetic field analysis method (torque calculation, etc.) of a rotating machine to which the finite element method in this embodiment is applied is, in principle, an analysis having a calculation step at each of a plurality of times in a time series, and has nonlinear characteristics. This is an analysis in the case of handling the material characteristics, and for each of a plurality of times, for example, the material characteristics are determined using a nonlinear iterative calculation method of the NR method, and the electromagnetic field is calculated.

  Furthermore, in the electromagnetic field analysis method, in the non-linear iterative calculation, regarding the determination of the initial value of the calculation, in the calculation on the finite element mesh other than the sliding mesh, the material property at the previous time is close to the material property at the current time. Based on the assumptions, the solution of the nonlinear iteration calculation at the previous time is set as the initial value of the nonlinear iteration calculation at the current time, while the value on the sliding mesh is set to 0 or a value close to 0 as the initial value of the nonlinear iteration calculation at the current time. Value.

  In a non-sliding calculation, on the finite element mesh other than the sliding mesh, the solution of the non-sliding calculation at the previous time is set as the initial value of the non-sliding calculation at the current time. Value. Accordingly, the number of nonlinear iterations can be reduced in each mesh element of the finite element mesh other than the sliding mesh in the nonlinear iteration calculation at each time, and the calculation efficiency can be improved.

  In addition, in the calculation on the sliding mesh, an abrupt change or the like occurs and the assumption that the solution at the previous time is close to the solution at the current time is not valid, so the solution of the nonlinear iteration calculation at the previous time is changed to the nonlinear iteration calculation at the current time. The process for setting the initial value is not performed, and a value close to 0 is set as an initial value for nonlinear iterative calculation at the current time. Thereby, a physically reasonable solution can be obtained in the calculation on the sliding mesh. In the above, the “value close to 0” is a value substantially corresponding to 0, and more specifically, “a value sufficiently smaller than the value obtained for the surrounding sides (or nodes)”. Meaning.

  Next, a calculation formula for nonlinear iterative calculation based on the NR method on a finite element mesh corresponding to nonlinear material elements (elements in the rotor and the fixed portion) at time t and time t + Δt will be described. Here, description will be made in relation to the points (1), (2), (3), and (4) shown in FIG.

  The expansion of the equations (1) and (2) shown in the following (Equation 1) is the first calculation equation at the time t, and corresponds to the calculation equation at the point (1). In the calculation formulas (1) and (2) shown in (Equation 1), “K” is a coefficient matrix of simultaneous linear equations, “A” is a solution vector of simultaneous linear equations, and “f” is a simultaneous linear equation. It is a load vector.

  The expansion of the equations (3), (4), and (5) expressed by the following (Equation 2) is the second calculation equation at the time t, and corresponds to the calculation equation at the point (2).

Thereafter, {A ^t } is iteratively calculated in the same manner, and a solution (solution corresponding to the point (4)) as a result of the nonlinear iterative calculation at time t is calculated. calculate.

Next, the expansion of the formulas (6) and (7) expressed by the following (Equation 3) is the first calculation formula at the time t + Δt, which is the next time, and the conventional method using {A ^{t + Δt} } as the initial value. It is an example.

However, as described above, according to the calculation by the electromagnetic field analysis method of the present embodiment, the initial value of the first calculation is determined on the finite element mesh other than the sliding mesh in the nonlinear iterative calculation at time t + Δt. Based on the assumption that the material property at the time is close to the material property at the current time, the solution of the nonlinear iterative calculation at the previous time is set as the initial value of the nonlinear iterative calculation at the current time. Therefore, instead of using {A ^{t + Δt} } as the initial value in the above calculation formula, the solution {A ^t } obtained by nonlinear iterative calculation at time t can be used, and the calculation of the result (Equation 3) can be omitted. As a result, the second calculation formula at time t + Δt is the formulas (8), (9), and (10) shown in the following (Equation 4).

In the above equation (Equation 4), the solution {A ^t } at time t, which is the previous calculation step, is used as the initial value of time t + Δt, which is the current calculation step.

On the other hand, according to the calculation by the electromagnetic field analysis method of the present embodiment, in the non-linear iterative calculation at time t + Δt, regarding the determination of the initial value of the first calculation, the material property at the previous time is the current time on the sliding mesh. Since the assumption that the material properties are close is not established, 0 or a value close to 0 is substituted into the initial value (the part of the term {A ^t }) in the above calculation formula (Formula 4).

Thereafter, {A ^{t + Δt} } is iteratively calculated to calculate a solution as a result of the nonlinear iterative calculation at time t + Δt, thereby determining material characteristics and calculating an electromagnetic field. A non-linear iterative calculation is similarly performed at each of a plurality of subsequent times to calculate a solution.

  An apparatus configuration and functional blocks for implementing the electromagnetic field analysis method will be described.

  FIG. 1 shows a computer system. 11 is a computer main body, 12 is a storage device, 13 is an input device, and 14 is a display device (output device). The computer main body 11 reads and executes the electromagnetic field analysis program 12a stored in the storage device 12, and performs the calculation related to the electromagnetic field analysis method. Thus, an apparatus for performing electromagnetic field analysis based on the computer main body 11 and the like is realized. FIG. 2 is a block diagram showing a configuration relating to each function of the electromagnetic field analysis apparatus.

  In FIG. 2, 21 is a time setting means for determining a plurality of time-series times, and 22 is a calculation means for performing nonlinear iterative calculation at each of a plurality of time-series times based on time information given from the time setting section 21. , 23 is a nonlinear iterative calculation at each time, and on the finite element mesh other than the sliding mesh, the solution of the previous time is set as the initial value of the current time, thereby changing the material property of the previous time to the initial of the material property of the current time. And an initial value determining means for determining the initial value of the material property at the current time by setting the value to 0 or a value close to 0 on the sliding mesh as the initial value of the current time. The calculation means 22 outputs the calculation result at each calculation step. This calculation result is stored in the calculation result storage means 24. The time setting unit 21 supplies time information of each calculation step to the calculation unit 22 and the initial value setting unit 23. The calculation means 22 receives the time information and starts nonlinear iterative calculation. At this time, in the first calculation, the initial value setting means 23 gives the data related to the initial value to the calculation means 22 at an appropriate synchronized timing. At this time, the initial value setting means 23 takes out the calculation result in the previous calculation step stored in the calculation result storage means 24 on the finite element mesh other than the sliding mesh, supplies it as initial value data, and supplies the sliding mesh. For the above, 0 or a value close to 0 is supplied. Each of these means is realized by the electromagnetic field analysis program 12a.

  Next, FIG. 3 shows an example of verification of calculation results (solution is torque) based on the electromagnetic field analysis method according to the present embodiment. In FIG. 3, the horizontal axis represents calculation steps (1 to 12), and the vertical axis represents torque (Nm).

  This verification result shows that when calculating the torque value of an SPM (Surface Permanent Magnet) motor, (1) characteristics C1 by an original calculation method (hereinafter referred to as “original”) that gives a physically correct result, (2) Characteristic C2 by calculation method (a) in which the initial calculation value on the sliding mesh is set to 0 by setting the previous calculation step as the initial value of the current calculation step, and (3) the previous calculation step as the initial value of the current calculation step. The characteristic C3 by the calculation method (b) which delivers the solution of the previous time as the initial value of the present time only for the initial value of calculation on the finite element mesh related to the nonlinear material in the calculation to be the value is shown. FIG. 3 shows a verification result that these characteristics C1, C2, and C3 are substantially the same.

  As is clear from the above results, according to the electromagnetic field analysis method of the present invention having the above characteristics, the number of iterations can be reduced by the nonlinear iterative calculation method by the NR method, and the overall calculation speed can be increased. Furthermore, a physically reasonable solution can be obtained.

  A verification example (simulation model) based on the electromagnetic field analysis method according to this embodiment described above is shown in Table 1 below. Table 1 shows the calculation speed improvement ratio between the original and the calculation method (a) for the six verification examples of model numbers 1 to 6. Model number 1 is an SPM motor model (three-dimensional), model number 2 is a claw pole type stepping motor model (including two element types), and model number 3 is a thin IPM (Interior Permanent Magnet) motor. Model (3 dimensions, including two element types), model number 4 is an IPM motor model (including two element types), model number 5 is an SPM motor model (two dimensions), Model number 6 is an IPM motor model (two-dimensional). On the horizontal axis, in addition to the items “original” and “speed improvement ratio by this method”, the items “dimension”, “element type”, “number of elements”, and “number of nodes” are shown as related items. .

  According to the verification example of Table 1, the calculation speed improvement ratio is found to be greatly improved even in the case of the SPM motor of model number 1 and in the case of the second to sixth other motors. To do. According to the calculation method (a) of the electromagnetic field analysis method according to the above embodiment, the calculation speed can be greatly increased.

  Next, the verification results of some of the six verification examples shown in Table 1 are shown in the figure.

  FIG. 4 shows a characteristic curve 41 of a nonlinear material, which is a verification result in the verification example of model number 1. In the coordinate system of FIG. 4, the horizontal axis indicates the magnetic field (A / m), and the vertical axis indicates the magnetic flux density (T). The main structure of the verification example of model number 1 is shown in FIGS. FIG. 7 shows a perspective view of the main part of the SPM motor in a mesh division state, and FIG. 8 shows a circuit diagram of the voltage driving unit.

  In FIG. 7, a plurality of symbols 51 in the motor structure 50 indicate coils on the fixed portion side, and a symbol 52 indicates a magnet on the rotor side. In the motor structure 50, the magnet 52 is provided to rotate around the axis 53 in the space inside the coil 51. The portion indicated by reference numeral 54 in the motor structure 50 is a non-linear material, and the portion indicated by reference numeral 55 is a gap (gap). As shown in FIG. 7, the motor structure 50 is drawn with a finite element mesh. Further, as shown in FIG. 8, in the voltage drive unit of the SPM motor, an alternating current is supplied from each of the three alternating current sources 56 to the corresponding coil 51 via the switch element 57.

  According to the characteristic curve 41 described above, especially for the calculation of the curve portion representing the non-linear characteristic, the number of repeated calculations is reduced, the calculation speed is increased, and a reasonable solution that is physically realistic is obtained. It has been.

  FIG. 5 shows a characteristic curve 42 of the nonlinear material, which is the verification result of the verification example of model number 3. In the coordinate system of FIG. 5, the horizontal axis indicates the magnetic field (A / m), and the vertical axis indicates the magnetic flux density (T). The main structure of the verification example of model number 3 is shown in FIGS. FIG. 9 is a perspective view of a main part of the thin IPM motor in a mesh division state, and FIG. 10 is a circuit diagram of a three-phase current driving unit.

  In FIG. 9, a plurality of reference numerals 61 in the motor structure 60 indicate slots on the fixed portion side, and a plurality of reference numerals 62 indicate magnets on the rotor side. On the fixed part side, the inside of the slot 61 is handled as a coil 63. In the motor structure 60, the magnet 62 is provided so as to rotate around the axis 64 in the space inside the coil 63. A portion indicated by reference numeral 65 in the motor structure 60 is a non-linear material, and a portion indicated by reference numeral 66 is a gap (gap). As shown in FIG. 9, the motor structure 60 is drawn with a finite element mesh. Further, as shown in FIG. 10, in the three-phase current drive unit of the thin IPM motor, the AC current of each phase is supplied from the three-phase AC current source 67 to the coil 63 of each phase.

  According to the above-described characteristic curve 42, the calculation of the curve portion representing the non-linear characteristic is reduced, the number of repeated calculations is reduced, the calculation is speeded up, and a reasonable solution that is physically realistic is obtained. It has been.

  FIG. 6 shows a characteristic curve 43 of the nonlinear material, which is the verification result of the verification examples of model numbers 5 and 6. In the coordinate system of FIG. 6, the horizontal axis indicates the magnetic field (A / m), and the vertical axis indicates the magnetic flux density (T). Further, the main structure of the verification example of model number 5 is shown in FIGS. FIG. 11 is a cross-sectional view of the main part of the two-dimensional SPM motor, and FIG. 12 is a circuit diagram of the voltage driving unit. Furthermore, the principal part structure of the verification example of the model number 6 is shown in FIG. 13 and FIG. FIG. 13 is a cross-sectional view of the main part of the two-dimensional IPM motor, and FIG. 14 is a circuit diagram of the current driving unit.

  In FIG. 11, a plurality of reference numerals 71 in the motor structure 70 indicate coils on the fixed portion side, and a reference numeral 72 indicates a magnet on the rotor side. In the motor structure 70, the magnet 72 is provided to rotate around the axis 73 in the space inside the coil 71. The portion indicated by reference numeral 74 in the motor structure 70 is a non-linear material, and the portion indicated by reference numeral 75 is a gap (gap). As shown in FIG. 11, the motor structure 70 is drawn with a finite element mesh. Also, as shown in FIG. 12, in the voltage drive unit of the SPM motor, an alternating current is supplied from each of the three alternating current sources 76 to the corresponding coil 71 via the switch element 77.

  In FIG. 13, a plurality of reference numerals 81 in the motor structure 80 indicate slots on the fixed portion side, and a reference numeral 82 indicates a magnet on the rotor side. On the fixed part side, the inside of the slot 81 is handled as a coil 83. In the motor structure 80, the magnet 82 is provided to rotate around the axis 84 in the space inside the coil 83. The portion indicated by reference numeral 85 in the motor structure 80 is a non-linear material, and the portion indicated by reference numeral 86 is a gap (gap). As shown in FIG. 13, the motor structure 80 is drawn with a finite element mesh. Further, as shown in FIG. 14, in the current drive unit of the IPM motor, the AC current of each phase is supplied from the three-phase AC current source 87 to the coil 83 of each phase.

  According to the characteristic curve 43 described above, the number of iterations for the calculation of a curve portion or the like representing a nonlinear characteristic is reduced, the calculation speed is increased, and a reasonable solution that is physically realistic is obtained. It has been.

  The configurations, shapes, sizes, and arrangement relationships described in the above embodiments are merely schematically shown to the extent that the present invention can be understood and implemented, and numerical values are merely examples. Therefore, the present invention is not limited to the described embodiments, and can be modified in various forms without departing from the scope of the technical idea shown in the claims.

  The present invention is used to achieve efficient calculation by reducing the number of non-linear iterative calculations in electromagnetic field analysis of electromagnetic equipment including structural parts that perform rotational motion and translational motion, and in addition to obtain a valid solution. The

It is a block diagram of the computer system with which the electromagnetic field analysis method concerning this invention is implemented. It is a functional block diagram which shows the apparatus structure for enforcing the electromagnetic field analysis method of this invention. It is a graph which shows an example of the verification result by the electromagnetic field analysis method of this invention. It is a graph which shows the characteristic curve of the nonlinear material which is the verification result in the verification example of the model number 1. It is a graph which shows the characteristic curve of the nonlinear material which is a verification result in the verification example of model number 3. It is a graph which shows the characteristic curve of the nonlinear material which is a verification result in the verification example of the model numbers 5 and 6. It is a perspective view which shows the mesh division | segmentation state of the principal part of the SPM motor which concerns on the verification example of the model number 1. FIG. It is a circuit diagram of the voltage drive part in the SPM motor which concerns on the verification example of the model number 1. FIG. It is a perspective view which shows the mesh division | segmentation state of the principal part of the thin IPM motor which concerns on the verification example of the model number 3. FIG. It is a circuit diagram of the current drive part in the thin IPM motor which concerns on the verification example of the model number 3. FIG. It is a perspective view which shows the mesh division | segmentation state of the principal part of the SPM motor which concerns on the verification example of the model number 5. FIG. It is a circuit diagram of the voltage drive part in the SPM motor which concerns on the verification example of the model number 5. FIG. It is a perspective view which shows the mesh division | segmentation state of the principal part of the thin IPM motor which concerns on the verification example of the model number 6. FIG. It is a circuit diagram of the current drive part in the thin IPM motor which concerns on the verification example of the model number 6. FIG. It is a figure which shows the graph for demonstrating the problem in the nonlinear iterative calculation by the conventional electromagnetic field analysis method, and a search process. It is sectional drawing for demonstrating the example which implements a finite element method with respect to the rotor and fixed part in a rotary machine. It is the elements on larger scale of the cross section shown in FIG. It is a graph for demonstrating the problem in the nonlinear iterative calculation by the conventional electromagnetic field analysis method.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 Computer main body 12 Storage device 12a Electromagnetic field analysis program 21 Time setting means 22 Calculation means 23 Initial value setting means 24 Calculation result storage means

Claims (6)

The electromagnetic field characteristics of an electromagnetic device having a fixed part, a movable part, and a boundary part formed between the fixed part and the movable part, and applying a finite element method on a computer to calculate a plurality of time series An electromagnetic field analysis method for performing nonlinear iterative calculation at each time for analysis,
The calculation means creates a finite element mesh based on the finite element method for each of the fixed elements and the movable part of the electromagnetic device, and for the divided elements of the boundary portion of the electromagnetic device. Creating a sliding mesh based on the finite element method;
A time setting means for setting each of the plurality of times in time series;
When the initial value setting means sets a certain time among the plurality of times in the time series by the time setting means, the nonlinear iterative calculation at the time before the certain time is performed for the finite element mesh. Setting the solution to an initial value, and setting the initial value to a value that is sufficiently smaller than 0 or a value obtained for a surrounding edge or node for the sliding mesh;
The calculating means performing the nonlinear iterative calculation at the certain time using the initial values respectively set for the finite element mesh and the sliding mesh;
An electromagnetic field analysis method characterized by comprising: The electromagnetic field analysis method according to claim 1, wherein the boundary portion is an air layer . 3. The electromagnetic field analysis method according to claim 1, wherein the nonlinear iterative calculation method is a Newton-Raphson method. By applying a finite element method to the electromagnetic field characteristics of an electromagnetic device having a fixed part, a movable part, and a boundary part formed between the fixed part and the movable part on a computer, a plurality of time series It is a program that executes an electromagnetic field analysis method for performing analysis by performing nonlinear iterative calculation at each.
In the computer,
A finite element mesh based on the finite element method is made for each divided element of the fixed part and the movable part of the electromagnetic device, and the finite element method is applied to the divided element of the boundary part of the electromagnetic device. A first calculation means for creating a sliding mesh based thereon;
Time setting means for setting each of the plurality of times in time series;
When a certain time among the plurality of times in the time series is set by the time setting means, the solution of the nonlinear iterative calculation at the time before the certain time is set as an initial value for the finite element mesh An initial value setting means for setting the sliding mesh to an initial value that is sufficiently smaller than 0 or a value obtained for a surrounding edge or node;
Second calculation means for performing the nonlinear iterative calculation at the certain time using the initial values respectively set for each of the finite element mesh and the sliding mesh;
An electromagnetic field analysis program characterized by realizing the above. The electromagnetic field analysis program according to claim 4, wherein the boundary portion is an air layer . The nonlinear iterative calculation method according to claim 5 Symbol mounting the electromagnetic field analysis program characterized in that it is a Newton-Raphson method.

Images