JP5439279B2 - Optimal design system for electromagnetic equipment - Google Patents

Description

  The present invention relates to an optimum design method for an electromagnetic device, and more particularly to an optimum design system for an electromagnetic device for performing optimization calculation at high speed while simultaneously solving a plurality of analysis methods.

  In recent years, a highly accurate optimization technique in which a plurality of analysis methods are coupled has been developed by improving the performance of a computer and increasing the recording capacity. For example, Patent Document 1 describes a method for performing optimization calculation in which a plurality of analysis methods such as structural analysis, thermal analysis, fluid analysis, and electromagnetic field analysis are coupled in order to improve the accuracy of optimization calculation. . The calculation order is as follows. (1) Input data necessary for analysis, (2) Couple multiple analyzes and solve simultaneously, (3) Optimize the obtained analysis results, (4) Optimization process and optimization The analysis conditions and shape data required for the results are changed. These series of operations are repeated until the optimization calculation converges.

JP 2007-122098 A

"Coupled analysis of heat, voltage, and magnetic field of small rotating machines considering demagnetization" Tadashi Yamaguchi, Junhiro Kawase, Masafumi Watanabe, Naotaka Hamada, Kazuya Nakamura, Eri Fukushima, Institute of Electrical Engineers of Japan Source, SA-06-91 / RM-06-93, 2006

  Non-Patent Document 1 shows a case where a coupled analysis of heat and magnetic field is performed. Since the three-dimensional finite element method is used for thermal analysis and magnetic field analysis, it takes about one month to calculate one coupled analysis. On the other hand, in Patent Document 1, since various quantities necessary for calculating the objective function are calculated by coupled analysis, it is assumed that it takes a considerable time for the optimization calculation to converge. In this way, the optimal design that combines coupled analysis and optimization has a problem of shortening the calculation time.

  In order to solve the above-described problem, an objective function calculation unit that receives a set of design variables, calculates a function value based on the set of design variables, and outputs the function value; and the design variable that has the maximum or minimum function value. In the optimum design system comprising optimization means for searching for pairs, the objective function calculation unit can input physical quantities such as dimension data and physical property values related to electromagnetic equipment from a history file, and the latest calculation calculated by reflecting these physical quantities. It is sufficient that the physical quantity is written in the history file, and the optimization means is based on a direct search algorithm.

  According to the present invention, optimization calculation can be performed at high speed.

BRIEF DESCRIPTION OF THE DRAWINGS Schematic which cut down the permanent-magnet-type synchronous motor which performs the miniaturization design which is the 1st Embodiment of this invention to the rotating shaft direction. FIG. 2 is a schematic diagram in which the permanent magnet type synchronous motor of FIG. 1 which is the first embodiment of the present invention is sectioned in a radial direction, and a part of the permanent magnet type synchronous motor is extracted. The schematic diagram which shows the view of the irreversible demagnetization on the demagnetization curve of the permanent magnet which is the 1st Embodiment of this invention. The figure which shows the whole flow of the optimization calculation which is the 1st, 3rd embodiment of this invention. The figure which shows the means to avoid the dimensional contradiction of the mesh which is the 1st Embodiment of this invention, and the interference of positional relationship. The figure which shows an example of a structure of the thermal model in the thermal equivalent network method which is the 1st Embodiment of this invention. The figure which shows the thermal model which modeled the electric motor of FIG. 1, FIG. 2 which is the 1st Embodiment of this invention with the heat | fever equivalent circuit network. The figure which shows the temperature characteristic of the stator winding | coil of the thermal model of FIG. 7 which is the 1st Embodiment of this invention. The figure which shows the optimization variable which is the 1st Embodiment of this invention. The figure which shows the optimization result (transition of an objective function and constraint conditions) which shortened the core thickness by reviewing the cross-sectional shape which is the 1st Embodiment of this invention, and the number of turns of a stator winding | coil. The figure which shows transition of the resistivity of the stator winding | coil in the calculation process of the optimization which is the 1st Embodiment of this invention, and the residual magnetic flux density of a permanent magnet. The axial direction sectional drawing of the permanent magnet synchronous machine which shows Embodiment 2 of this invention. The thermal circuit network (axial direction sectional drawing) of the rotary machine for implementing the thermal analysis in this invention. The result which shows the effect of Embodiment 4 of the present invention. Explanatory drawing of Embodiment 6 of this invention. The effect of Embodiment 6 of this invention. Explanatory drawing of Embodiment 9 of this invention. Explanatory drawing of Embodiment 10 of this invention.

  The optimum design of the permanent magnet type synchronous motor according to one embodiment of the present invention will be described with reference to FIGS.

[First Embodiment]
The downsizing design of an abduction type, multipole, concentrated winding permanent magnet type synchronous motor will be described with reference to FIGS.

(1) Configuration of Target Machine FIG. 1 is a schematic view of an abduction type, multi-pole, concentrated winding permanent magnet synchronous motor that is designed to be downsized according to the present invention in the direction of the axis of rotation.

  FIG. 2 is a schematic view in which the permanent magnet synchronous motor of FIG.

  1 to 2, an outer rotation type, multi-pole, concentrated winding permanent magnet type synchronous motor 101 includes a stator 102 and a rotor 103. The stator 102 is mainly composed of a stator core 104 and a stator winding 105. The stator core 104 is formed by stacking silicon steel plates by punching with a mold. The inner periphery of the stator core 104 includes a stator core back 201 constituting a stator magnetic path, and stator salient poles 202 extending radially from the stator core back 201 toward the outer periphery of the stator. As shown in the drawing, the space formed between the adjacent stator salient poles 202 and the stator core back 201 is a slot 203, which is a space for storing the stator winding 105. Here, it is assumed that one stator winding 105 is wound around each stator salient pole 202 as shown in the figure. The stator core 104 is fixed to an iron plate 107 standing on a surface plate 106 with bolts.

  On the other hand, the rotor 103 includes a rotor core 108 constituting a rotor magnetic path disposed on the outer periphery of the stator 102, a permanent magnet 109 disposed on the inner peripheral surface of the rotor core 108 at equal intervals, And a bowl-shaped drum 110 covering the child core 108 from the outer periphery. The rotor core 108 is configured by stacking silicon steel plates by punching with a mold or the like. The rotor core 108 is fixed to the inner peripheral surface of the drum 110 with bolts. A shaft 111 is connected to the center of the drum 110. The shaft 111 is connected to the stator 102 via a bearing 112 so that the rotor 103 can rotate. An encoder 113 that detects a position necessary for controlling the permanent magnet synchronous motor 101 is connected to a shaft 111 and fixed to an iron plate 107.

In the miniaturization design described in this embodiment, the core thickness L _c is shortened with respect to the predetermined outer diameter D _c of the rotor core 108 shown in FIG. 1 by the Rosen block method which is one of direct search methods. It is. Further, the outer diameter D _c of the rotor core 108 may be shortened by fixing the core thickness L _c .

The evaluation of the temperature of the stator winding 105 of the electric motor 101 is performed in the heat steady state of the heat run test. As a result of the performance test of the electric motor 101, it is known that the required performance is achieved, and there is a margin of about 10% (required specification value ratio) for the voltage and the stator winding 105 temperature. Therefore, when designing a miniaturization, the core product thickness L _c is shortened to the limit by using the margin of the voltage and the temperature of the stator winding 105.

(2) Setting Optimization Problem FIG. 3 is a schematic diagram showing the concept of irreversible demagnetization on the demagnetization curve of a permanent magnet.

  The problem with downsizing is the temperature inside the motor. As the motor size is reduced, the temperature rises due to the decrease in the cooling area. This causes dielectric breakdown of the stator winding and irreversible demagnetization of the permanent magnet (a phenomenon in which the magnetic force of the permanent magnet is greatly reduced and loses its original performance), and is not established as an electric motor. Therefore, it is important to know the temperature of the stator winding and the irreversible demagnetization of the permanent magnet when downsizing. Further, if the core thickness is reduced, the axial length of the permanent magnet is shortened, so that the amount of magnetic flux of the permanent magnet that contributes to the torque is reduced and the torque is reduced. Therefore, it is necessary to increase the torque by shortening the core thickness and changing the number of turns of the stator winding and optimizing the motor cross-sectional shape. This is equivalent to increasing the torque density. Furthermore, since there is an upper limit on the power supply capacity, it is necessary to grasp the line voltage of the motor when changing the number of stator winding turns or optimizing the motor cross-sectional shape.

When reworking this work into an optimization problem, "the objective function f (x) while imposing constraints (voltage, stator winding temperature, irreversible demagnetization of permanent magnets) on optimization variables x such as motor cross-sectional shape “Search for the optimum value x ^{* of the} variable that maximizes (torque density)”. This is formulated as follows.

Here, τ is the torque, D _c is the outer diameter of the rotor core, and L _c is the core thickness. τ and L _c are functions of x. Since the denominator of equation (1) represents volume, f (x) corresponds to the torque density. The constraint conditions are expressed by equations (2) to (4). Equation (2) relates to the voltage of the electric motor on the condition that the line voltage V is smaller than the upper limit value V _lim . The expression (3) imposes that the temperature rise T _c of the stator winding is not more than the upper limit value T _{c, lim} . Equation (4) corresponds to the condition that the permanent magnet is not irreversibly demagnetized.

A method for considering irreversible demagnetization will be described with reference to a schematic diagram of a demagnetization curve 301 of a permanent magnet shown in FIG. The demagnetization curve 301 is generally represented as shown in a coordinate space in which the horizontal axis indicates the strength of the magnetic field inside the permanent magnet and the vertical axis indicates the magnetic flux density (or magnetization) inside the permanent magnet. Often used to grasp. In this embodiment, it is assumed that the permanent magnet permeability (recoil permeability) equivalent to the slope of the demagnetization curve 301 is linear, the demagnetization curve 301 is placed on the a axis, and the a axis and the vertical axis The intersection point is defined as a = 0%, and the intersection point between the a axis and the horizontal axis is defined as a = 100%. Then, the distribution of a is obtained from the magnetic flux density distribution inside the permanent magnet calculated by the magnetic field analysis, and the operating point inside the permanent magnet is calculated by outputting this distribution as a histogram 302 shown in the figure. In Equation (4), a ₁ represents the position 303 of the operating point where a is the largest in the histogram, and a _knick represents the position of the _nick point (point where irreversible demagnetization starts) 304 of the permanent magnet. According to the equation (4), when the operating point 303 of the permanent magnet exceeds the knick point 304, the permanent magnet has caused irreversible demagnetization.

V, T _c and a ₁ are functions of x. Moreover, since a _knick has temperature dependence, it is indirectly a function of x.

  In order to solve the optimization problem with constraints described above by the Rosen block method, it is necessary to make it unconstrained. This is because the Rosen block method is an unconstrained local optimum solution search algorithm. For this reason, the constraints of the equations (2) to (4) are incorporated into the equation (1) by the outer point penalty function method, and the following extended objective function is maximized without the constraints:

  Here, p is a penalty coefficient. The second term on the right side of equation (5) is a penalty term. As a result, if any one of the constraints of the expressions (2) to (4) is not satisfied, a large handicap is added to the value of F (x) (here, the value of F (x) is f (x)). Will be greatly reduced). Therefore, the larger the penalty coefficient value, the less likely it is that the variable that breaks the constraint will be the optimal solution. As is clear from the form of equation (5), the continuity of the extended objective function F (x) is guaranteed in the entire region of the variable x.

On the other hand, the idea of the optimization problem is applicable not only to the electric motor but also to the generator. In the case of a permanent magnet synchronous generator, the objective function f (x (x) while imposing constraints (torque, stator winding temperature, irreversible demagnetization of the permanent magnet) on the optimization variable x such as the generator cross section ) Search for the optimum value x ^{* of the} variable that maximizes (output density).

(3) Flow of Optimization Calculation FIG. 4 is an overall flow of optimization calculation for downsizing the permanent magnet type synchronous motor that is one embodiment of the present invention.

In FIG. 4, the inside of the broken line is the extended objective function F (x) of the formula (5). From the top, the physical property value calculation, automatic mesh creation, magnetic field analysis, motor loss calculation, thermal resistance calculation, thermal analysis, motor characteristics Consists of calculations. Define this as a command file. Here, since the finite element method is used for the magnetic field analysis, it is necessary to create a mesh, and since the thermal equivalent circuit method is used for the thermal analysis, a thermal resistance calculation is required. The optimization engine 403 finds the optimum value x ^{* of the} variable that starts from an appropriate variable initial value x ⁰ and sequentially maximizes the objective function while sequentially executing the objective function described above.

  Hereinafter, the calculation procedure in the extended objective function F (x) will be described in detail in time series order.

First, the optimization variable x is input, and the temperature of the stator winding and permanent magnet obtained in the previous calculation is read from the temperature history file 401. (i) Using these, the physical property value (the resistivity of copper wire and the permanent value) Calculate the residual magnetic flux density and irreversible demagnetization characteristics of the magnet. Next, (ii) create a two-dimensional mesh to be used in the magnetic field analysis based on the variable x, and (iii) perform a two-dimensional magnetic field analysis by the finite element method, and then obtain from the accumulated thickness history file 402 in the previous calculation. Load the core lamination thickness L _c was to calculate the copper loss with iron loss, the shape of the mesh by post-treatment (iv) the magnetic field analysis result. Next, (v) based on the variables x and a core lamination thickness L _c, to calculate the thermal resistance in the heat equivalent circuit model, calculating the temperature distribution in the thermal steady state based on the loss calculated on (vi) To do. The obtained temperature of the stator winding and permanent magnet is added to the temperature history file 401 as the latest value. (Vii) Calculate the torque, voltage, operating point of the permanent magnet, and core thickness, and add the core thickness to the thickness history file 402 as the latest value. Finally, the extended objective function F (x) of the equation (5) is calculated from the various quantities obtained above and output. It is also possible to apply a magnetic circuit method to the magnetic field analysis and a finite element method to the thermal analysis.

  Originally, the thermal-magnetic field coupled analysis is a technique for calculating a physical property value by using the temperature obtained in the thermal analysis of the previous step in the time step in the calculation of the transient state and converging the temperature. Therefore, in the optimization calculation of FIG. 4 described above, the calculation of the thermal steady state is performed, so the magnetic field analysis and the thermal analysis are not directly coupled and solved. However, each time the value of the objective function F (x) is calculated in the iteration of optimization, the motor characteristics are calculated reflecting the previous thermal analysis result, and the thermal analysis result is updated to the latest value. The process is repeated. As a result, if the iterative calculation of optimization is close to convergence (when the change in the motor cross-sectional shape has settled), it is possible to solve the coupled analysis of the thermal steady state and the magnetic field analysis.

(4) Mesh Creation Method FIG. 5 is a schematic diagram showing a means for avoiding dimensional inconsistency and positional relationship interference leading to the cause of mesh shape and mesh creation failure.

  The point regarding the mesh creation of FIG. 4 will be described. The optimization engine searches for a solution by reviewing the variable x regardless of the validity of the mesh. Therefore, consideration must be given to unintended mesh shapes and mesh creation failures in the optimization calculation process.

  As a countermeasure for this, the mesh creation method of this optimization calculation employs a method of defining a mesh creation procedure as a program and creating a two-dimensional mesh by the Delaunay method. Because it is a program-based method, it is relatively easy to foresee dimensional discrepancies and positional interference (compare and judge the positional relationship from the dimensions calculated in the program and take appropriate measures). Is possible.

As a means for avoiding this, it is most convenient to use the “reverse” operation 501 shown in FIG. The example of FIG. 5 represents a situation where the variable x ₁ must not exceed a502. This is equivalent to imposing a constraint x ₁ −a ≦ 0. Now, assume that the value of the variable x ₁ is b (> a) 503, which is unexpected. In the mesh creation program described above, when such a situation occurs, the variable x ₁ is forcibly set to 2a-b 504 and a mesh is created using the revised x ₁ . In the processing described above, the mirror 505 is placed at the position of x ₁ = a, and the b value of the variable x ₁ is replaced with the mirror image coordinates 2a-b. From the standpoint of the optimization program, the search range of the variable x ₁ is still the entire range on the x ₁ axis.

The continuity of the objective function and the discontinuity of the derivative when the “invert” operation 501 is performed will be described. When the variable x ₁ approaches the a 502 from the right side of the mirror 505 in FIG. 5, the value of the processed variable x ₁ approaches the a 502 from the left side of the mirror 505 as much as possible. Therefore, according to this method, the continuity of the objective function is guaranteed. On the other hand, the objective function is clearly not smooth at x ₁ = a, and the derivative of the objective function with respect to x ₁ is discontinuous at this point. Therefore, due to the nature of this objective function, an optimization algorithm that requires a derivative cannot be used. On the other hand, in the direct search method, a solution can be searched if the continuity of the objective function is guaranteed.

  The above mesh creation method does not need to incorporate dimensional constraints into the extended objective function F (x) of equation (5), and does not perform useless calculation (variables violated dimensional constraints) in optimization calculation. Therefore, the calculation time is shortened.

(5) Temperature Calculation Method FIG. 6 shows an example of the configuration of a thermal model in the thermal equivalent network method.

  The thermal analysis method shown in FIG. 4 employs a thermal equivalent network method. This is aimed at shortening the calculation time and simplifying the configuration within the broken line in FIG.

The thermal equivalent network method uses an analogy of heat flow and current flow in an electric circuit. For this purpose, the flow of heat in the target object is analyzed, nodes 601 are provided at each part, and a heat resistance 602 connecting them is provided with a heat capacity 603 and a heat source 604 at each node. FIG. 6 shows the surrounding thermal circuit by focusing on the n-th node (temperature is T _n , heat capacity is C _n ) among these nodes. Q _n heat flows from the heat source 604 to the node 601 per unit time. This node is connected to the surrounding nodes (temperature is T _{n, i} ) through a total of m thermal resistors R _{n, i} . Here, in order to obtain the node temperature as a function of time, the time t is divided into equal intervals at intervals Δt (t _k = t ₀ + kΔt). Further, with respect to the heat source, Q _n > 0 when t ≧ t ₀ , and Q _n = 0 when t <t ₀ . Further, all the node temperatures are set to T ⁰ (environment temperature) before the start of heat generation.

Focusing on the node n, the conservation of heat in the time interval [t _k−1 , t _k ] is expressed by an equation:

が得られる。左辺第１項は熱容量Ｃ_nへ流れ込む熱量、第２項は周りの節点へ流れる熱量、これらの和が右辺の発熱量に等しいことを表している。（６）式を書き直して、

Is obtained. The first term on the left side represents the amount of heat flowing into the heat capacity C _n , the second term represents the amount of heat flowing to the surrounding nodes, and the sum of these is equal to the amount of heat generated on the right side. (6) Rewrite the equation,

の形に整理する（左辺に時刻ｔ_kにおける節点温度を集約）。全部の節点について（７）式と同様の関係式が成立するので、これらを統合すると、時刻ｔ_kの各節点温度に関する連立１次方程式が得られる。時刻ｔ_k-1における各節点の温度がわかっていれば、この連立方程式を解いて時刻ｔ_kの各節点温度を求めることができる。したがって、初期条件の時刻ｔ₀においてすべての節点温度がＴ⁰であることからスタートして、上記連立１次方程式を順次解くことにより各時刻の節点温度を求めることができる。

(The node temperatures at time t _k are aggregated on the left side). Since the same relational expression as Expression (7) is established for all the nodes, when these are integrated, simultaneous linear equations relating to the temperature of each node at time t _k are obtained. If the temperature of each node at time t _k-1 is known, this simultaneous equation can be solved to obtain the temperature of each node at time t _k . Therefore, starting from the fact that all the node temperatures are T ⁰ at time t ₀ of the initial condition, the node temperatures at each time can be obtained by sequentially solving the simultaneous linear equations.

In the optimization calculation of the present invention, the thermal steady state is targeted. Therefore, there is no heat flow that flows into the heat capacity. In this case, since there is no heat capacity, it is only necessary to set the environmental temperature T ⁰ and solve the simultaneous linear equations only once by setting C _n = 0 in the equation (7).

(6) Method for calculating motor characteristics (iii) Two-dimensional magnetic field analysis and (vii) motor characteristics calculation shown in FIG. 4 will be described in detail.

In order to calculate the objective function, the following two cases of two-dimensional magnetic field analysis are performed: (1) Analysis of the load state when a predetermined current is applied. (2) Analysis for demagnetization evaluation. The analysis of (1) is for calculation of voltage, eddy current loss generated in the permanent magnet, and iron loss generated in the stator core and the rotor core. Here, since various quantities per unit length in the axial direction are obtained, they are converted by multiplying the previous core thickness. The iron loss is obtained by post-processing the magnetic field analysis results. In the analysis of (2), the phase in which the direction of the magnetic flux generated by the stator winding current is opposite to the direction of the magnetic flux generated by the permanent magnet (in the technical terminology, the phase in the negative direction of the d axis) and (1) A current twice as large as the predetermined current is applied. This analysis result is post-processed to obtain the operating point a ₁ of the permanent magnet shown in FIG. The permanent magnet operating point a ₁ is compared with the _knick point position a _knick obtained from the previously calculated temperature of the permanent magnet to determine irreversible demagnetization of the permanent magnet.

Handling iron loss is a problem when calculating the motor characteristics using the analysis results described above. For copper loss, the voltage drop due to resistance is added to the voltage obtained by magnetic field analysis in a vector-like manner, and matching between the input, output, and loss can be established (energy conservation law is established). Since the eddy current loss generated inside the permanent magnet is directly obtained by magnetic field analysis, there is no particular problem. However, the iron loss is obtained by post-processing the analysis result of (1). For this reason, it is difficult to calculate a voltage in consideration of iron loss in the above calculation. Therefore, the voltage obtained by adding the voltage drop corresponding to the stator winding resistance to the voltage obtained by the magnetic field analysis of (1) is the line voltage of the constraint equation g ₁ (x) of equation (2). V (Ignore the effects of iron loss). As for torque, assuming that the actual motor output is obtained by subtracting iron loss and mechanical loss from the motor output due to the torque obtained in the magnetic field analysis of (1), the torque is reviewed as follows:

Here, τ is the revised torque, ω _r is the angular velocity of the rotor, τ ^* and _Wi are torque and iron loss calculated using the previous thickness, and W _m is mechanical loss.

  Since the motor shape changes in the process of repeated optimization calculation, the above-examined torque does not necessarily match the target torque. Therefore, it is necessary to review the core thickness considering the excess and deficiency for the next calculation. This includes

を用いた。ここで、Ｌ′_cは見直し後のコア積厚、Ｌ_cは前回のコア積厚、τ_gは目標トルクである。電動機特性の計算終了後、（９）式で求めた見直し後のコア積厚を積厚履歴ファイルに最新値として追加記載する。最適化の繰り返しの中で目的関数Ｆ（ｘ）の値を毎回計算する際に、上記のコア積厚の見直しを行うことで、コア積厚は目的関数のトルク密度の上昇と連動して減少していく。そして、最適化の繰り返し計算が収束したときのコア積厚の値が、小形化の限界値を示している。
（７）熱モデル
図７は、図１，図２の電動機を熱等価回路網でモデル化した熱モデルである。

Was used. Here, L ′ _c is the core thickness after review, L _c is the previous core thickness, and τ _g is the target torque. After the calculation of the motor characteristics is completed, the revised core thickness obtained by the equation (9) is additionally described as the latest value in the thickness history file. When the value of the objective function F (x) is calculated every time during the optimization iteration, the core thickness is reduced in conjunction with the increase in the torque density of the objective function by reviewing the core thickness described above. I will do it. The core thickness value when the optimization iteration calculation converges indicates the limit value for miniaturization.
(7) Thermal Model FIG. 7 is a thermal model obtained by modeling the electric motor of FIGS. 1 and 2 with a thermal equivalent circuit network.

  FIG. 8 is a temperature characteristic of the stator winding of the thermal model of FIG.

In FIG. 7, the main path of heat generated in the motor is roughly divided into two: (1) stator winding 105 -stator core 104 -iron plate 107 / surface plate 106 -air; (2) permanent magnets. 109-rotor core 108-drum 110-air. Therefore, the heat generated in the stator winding 105 and the stator core 104 is radiated mainly from the surfaces of the iron plate 107 and the surface plate 106, and the heat generated in the permanent magnet 109 and the rotor core 108 is mainly used for the surface of the drum 110. Radiated from the heat. Also, when going to shorten the core lamination thickness L _c by miniaturization, heat becomes difficult to flow in the radial direction, it tends to flow in the opposite axial direction.

  We set the thermal conductivity of the material and the heat transfer coefficient of the material surface by parameter tuning based on the results of the actual heat run test. The numerical value of the temperature increase of the stator winding in FIG. 8 is normalized by the numerical value when the temperature increase reaches almost steady state. In FIG. 8, since the temperature rise between the actual measurement result and the calculation result shows a nearly similar transition, the thermal model has sufficient accuracy.

  The thermal equivalent network method can be easily applied to modeling electromagnetic devices such as generators and transformers, and can calculate the temperature rise faster than the finite element method. As described above, improvement in analysis accuracy must be dealt with by performing parameter tuning from the result of the temperature test of the actual machine.

(8) Conditions for Optimization Calculation FIG. 9 shows optimization variables x in the expressions (1) to (5).

The optimization variables x, torque and impact of the temperature rise of the stator winding 105 is large, the gap radius x _1, teeth width x _2, teeth length x _3, selected four stator winding turns x ₄ It is. The gap radius x ₁ is directly related to the torque increase (assuming that Maxwell stress in the gap is constant, the torque is proportional to the square of the gap radius). Expected to be highly effective. For the stator winding turns x _4, since the stator winding space factor is assumed to be constant, the stator winding diameter and the stator winding turns is increased is set to be smaller. In addition, although the number of stator winding turns x ₄ is an integer, it is treated as a real number in this calculation. The initial values of the above variables are set to the design values of the target motor shown in FIGS. Further, the “invert” operation of FIG. 5 was applied to the cross-sectional shape variables x ₁ , x ₂ , and x ₃ in order to prevent the mesh creation failure. The required specification values of the target motor shown in FIGS. 1 and 2 are set as the upper limit values of the line voltage and the stator coil temperature rise. In calculating the knick point of the permanent magnet, a function obtained by reading the knick point for a certain temperature from the catalog and approximating it with a polynomial was used. The penalty coefficient p in equation (5) is set to 1000 by comparing the order of the objective function and the constraint function value.

(9) Results of Optimization Calculation FIG. 10 shows the results of optimization (transition of objective function and constraint conditions) in which the core thickness L _c was shortened by reviewing the cross-sectional shape and the number of turns of the stator winding.

  FIG. 11 is a transition of the resistivity of the stator winding and the residual magnetic flux density of the permanent magnet in the optimization calculation process.

  The results shown in FIGS. 10 and 11 confirm that the optimization calculation has almost converged, and the search is terminated after about 200 searches. The calculation time is about 50 hours on a PC equipped with a 3.7 GHz CPU.

In FIG. 10, (a) objective function, (b) line voltage, (c) temperature rise of the stator winding, (d) demagnetization resistance, and (e) variables are shown from the top. The horizontal axis represents the number of searches for the Rosen block method. The objective function, core thickness, and variable values are normalized with initial values, and the line voltage and stator winding temperature rise are normalized with the upper limit. From the transition of the core thickness shown in the figure, it can be seen that the core solution thickness L _{c in} FIG. 1 is reduced by about 10% in the optimum solution. On the other hand, with regard to the constraint conditions, the line voltage coincided with the upper limit value, and the temperature of the stator winding and the irreversible demagnetization of the permanent magnet resulted in a margin. Variables are x ₁ (gap radius) + 1.7%, x ₂ (tooth width) + 14%, x ₃ (tooth length) + 3%, x ₄ (number of stator winding turns) + 6% of the initial value doing. The gap radius x ₁ and the teeth width x ₂ are the maximum amount of change that does not cause positional relationship interference.

The main reason of the core lamination thickness 10% reduction (torque density is increased by 10%), increase of the torque due to the increase of the gap radius x _1, relaxation of the magnetic saturation in the teeth due to increased teeth width x _2, the stator winding increase of the induced voltage is inferred by an increase in the line winding number x _4. The reason for not using up the temperature of the stator winding and the irreversible demagnetization of the permanent magnet is that the number of turns of the stator winding, which has a large effect on the temperature rise of the stator winding, is further affected by voltage restrictions. This is because the size of the permanent magnet was not made a variable.

Results of the optimization calculations of the present embodiment, the cross-sectional shape (gap radius, slot-shaped) that there is a possibility that the core lamination thickness L _c can be shortened by about 10% by optimizing the number of turns of the stator winding Show. In addition, because there is room for stator coil temperature and permanent magnet irreversible demagnetization, new variables (gap width, stator core back thickness, permanent magnet thickness, permanent magnet width, etc.) can be set. It has also been shown that the core thickness can be further shortened by the introduction.

  FIG. 11 shows (a) the resistivity of the stator winding and (b) the residual magnetic flux density of the permanent magnet from the top. The horizontal axis is the number of searches. The numerical values on the vertical axis are normalized with the initial values. It can be seen that the resistivity of the stator winding and the residual magnetic flux density of the permanent magnet change following the temperature rise and converge to a value near the optimal solution. At the initial stage of the search with a large change in the motor cross-sectional shape, the fluctuation of the temperature rise is also large, so the coupling of heat and magnetic field is not established. However, in the vicinity of the optimal solution, the coupling of heat and magnetic field is established.

  At the end of the present embodiment, the optimization system of the present invention is used not only for the miniaturization design of the electric motor and generator described here but also for the case where it is desired to maximize the efficiency of an energy converter such as a transformer. Optimization calculations taking into account the temperature rise of the wire can be performed.

[Second Embodiment]
FIG. 12 shows a schematic diagram of a permanent magnet type synchronous motor according to the present invention and variables used for optimum design. FIG. 12 shows a central portion of the electric motor, which includes a stator core 1201, a stator winding 1202, a rotor core 1203, and a rotor permanent magnet 1204. Ten dimensions x1 to x10 shown in FIG. 12 are used as variables, and these variables are prepared in advance in a text file or the like as numerical values, each separated by a space or a line feed. The dimensions required for the motor shown in FIG. 12 other than the stator and rotor (for example, the dimensions of the motor housing, end plate, shaft, bearing, etc.) are similarly separated in advance in a text file or the like by spaces or line feeds. Or prepare it in the calculation program. In the present embodiment, the necessary dimensions other than the stator and the rotor are described as constant values, but they can also be handled as variables. In that case, since the numerical value is not a constant value but only a variable, the above processing does not change. In addition, the thermal conductivity, specific heat, and density, which are the physical properties necessary for calculating the temperature, are incorporated into the calculation program as values obtained from a science chronology, etc., or can be entered when the calculation program is executed. . A thermal-magnetic field coupled optimization calculation program is prepared in advance in consideration of the above variables and constants. This completes the input variables, constants, and calculation program necessary for the calculation, and executes the thermal-magnetic field coupled optimization calculation program. Two-dimensional magnetic field analysis by the finite element method (FEM) is applied to the magnetic field analysis, and thermal analysis using the thermal equivalent network method is applied to the thermal analysis. In the optimization calculation, the variables x1 to x10 change from moment to moment, the optimum shape is automatically searched so as to satisfy the target characteristics, and the shape that is one solution finally optimized by the convergence calculation Can be obtained. The optimization variables listed here are 10 x1 to x10, but the calculation can be performed with less or more than 10 variables. In addition, various calculation methods such as a finite element method and a magnetic circuit method can be applied to both magnetic field analysis and thermal analysis.

[Third Embodiment]
FIG. 4 shows an algorithm for downsizing a permanent magnet synchronous motor according to the present invention. In this algorithm, an optimization calculation method based on mathematical programming is applied. Mathematical programming is a method of obtaining a solution by functionalizing several variables as objective functions and minimizing or maximizing the functions by adding constraints. The variable corresponds to the optimization variable described in the first embodiment. In this embodiment, the objective is to reduce the size of the motor, and the objective function created from the variables is the torque density. The torque density is a value obtained by dividing the torque representing the rotational force of the motor by the volume of the motor. That is, by calculating so that this torque density is maximized, it is possible to calculate an optimum shape that can output a large torque with a small physique. For the calculation, an optimization program based on the Rosen block method is applied.

Hereinafter, the calculation procedure in the objective function F (x) will be described in time series. First, the optimization variable x is input, and the winding and magnet temperatures obtained in the previous calculation are read from the temperature history file 401 (the first calculation is arbitrarily given: it may be determined according to the environment in which the motor is used) (I) Using these, the physical property values (resistivity of copper wire, residual magnetic flux density of permanent magnet, irreversible demagnetization characteristics) are calculated. Each physical property value calculated in (i) is defined as a function of temperature from catalog data or the like so that the characteristics for each temperature can be calculated. Next, (ii) a two-dimensional mesh for magnetic field analysis is created based on the variable x, and (iii) a two-dimensional magnetic field analysis by the finite element method is performed. Load the core lamination thickness L _FE determined in the previous calculation from giving), the calculation of the copper loss with iron loss, the shape of the mesh by post-treatment (iv) the magnetic field analysis result. Next, (v) the variable x and the core lamination thickness L _FE calculate the thermal resistance in the heat equivalent circuit model based on, to calculate the temperature distribution on the basis of the loss determined in (vi) above. As shown in FIG. 13, the thermal equivalent circuit model is shown in the axial sectional view of the motor. , A housing 1308, an end plate 1309, a flange 1310 (a portion to which an electric motor is attached), a bench 1311 (a portion in contact with an object to which the electric motor is attached), and an outside air 1312, and (i) Thermal analysis can be performed using the thermal resistance between the nodes calculated from the dimensions and physical property values obtained in (ii) and the motor loss calculated in (iv) as input values. Here, the influence of the air between the windings caused by the winding space factor is taken into account when calculating the thermal resistance. Further, by providing more nodes than the number of nodes listed here, it is possible to improve the calculation accuracy. Thus, the obtained temperature of the winding and magnet is added to the temperature history file 401 as the latest value. (Vii) The torque, voltage, magnet operating point, and core stack thickness are calculated, and the core stack thickness is additionally described in the stack thickness history file 402 as the latest value. Finally, the objective function F (x) is calculated from the quantities obtained above and output. The variables are automatically adjusted so that the torque density, which is the objective function output here, is maximized by the optimization engine 403. In the above calculation, it is stated that the previously calculated values for temperature and thickness are used. However, this calculation is based on the assumption that the calculation is repeated. Even if the difference is minimized and the previously calculated value is used, the coupled analysis can be established, and finally one optimal shape solution can be obtained.

  Here, the constraint conditions important for the optimization calculation will be described. In general, when a motor is miniaturized, the heat generation density increases, and the problem of temperature rise increases. A heat-resistant temperature is defined for the winding used in the electric motor, and the electric motor cannot be established unless it is added as a constraint so as not to exceed the temperature. In addition, the permanent magnet causes a phenomenon of demagnetization due to the temperature and the external magnetic field generated by passing a current through the winding, and the residual magnetic flux density of the permanent magnet is lowered. As the external magnetic field is strengthened, the residual magnetic flux density decreases. When the external magnetic field is weakened, the original residual magnetic flux density is restored. However, if the external magnetic field is strengthened too much and exceeds a certain critical point, a phenomenon called irreversible demagnetization occurs. Irreversible demagnetization is a phenomenon that does not return to the original residual magnetic flux density even if the magnetic field is weakened. Therefore, it is necessary to add as a constraint condition not to cause irreversible demagnetization. Furthermore, since there is an upper limit value of the voltage in the inverter for driving, it is necessary to add that the voltage is not exceeded as a constraint condition. In this way, when an optimum shape search is attempted with respect to the target characteristic, an optimization calculation is performed by setting items that become constraints.

[Fourth Embodiment]
FIG. 14 shows the effect of the fourth embodiment. In the present embodiment, an example in which optimization calculation for the purpose of downsizing the electric motor described in the third embodiment is performed using the optimization variable in FIG. 12 described in the second embodiment is taken as an example. I will explain. As shown in FIG. 12, since the outer diameter of the motor is not included in the optimization variable, the calculation is performed with a constant value. In such a case, the optimum shape is different from the shape having a different outer diameter. Considering miniaturization, the optimum shape is calculated for each of the four types of outer diameters, and the physique and mass are different. As shown in FIG. 14, the horizontal axis represents the motor flatness, which is a value obtained by dividing the outer diameter of the motor by the axial length (where the axial length includes the end of the winding), and the vertical axis represents the electric motor. When taking the physique and mass of each, the relationship between the physique and the mass with respect to the flatness of the motor becomes clear for each optimum shape. The physique is the diameter of the motor ² x the axial length (including the end of the winding). Thus, it is possible to compare the optimum shapes calculated for each outer diameter. As a result, it is possible to find the most effective point for the purpose in several types of optimum shapes, and it can be applied as an application example of optimization calculation. In this case, a value that minimizes the physique and mass, and a shape in which the flatness of the electric motor is about 2.3 is most effective as a miniaturized design.

[Fifth Embodiment]
In this embodiment, a combination of materials will be described. In the second to fourth embodiments, the material to be used is determined at the time of starting the calculation, and the value quoted from the catalog value or the like is used as the characteristic. As shown in the third embodiment, when the electric motor is miniaturized, the heat generation density is increased, and the problem of temperature rise is enlarged. A heat-resistant temperature is defined for the winding used in the electric motor, and the electric motor cannot be established unless it is added as a constraint so as not to exceed the temperature. In addition, the permanent magnet causes a phenomenon of demagnetization due to the temperature and the external magnetic field generated by passing a current through the winding, and the residual magnetic flux density of the permanent magnet is lowered. As the external magnetic field is strengthened, the residual magnetic flux density decreases. When the external magnetic field is weakened, the original residual magnetic flux density is restored. However, if the external magnetic field is strengthened too much and exceeds a certain critical point, a phenomenon called irreversible demagnetization occurs. Irreversible demagnetization is a phenomenon that does not return to the original residual magnetic flux density even if the magnetic field is weakened. Therefore, it is necessary to add as a constraint condition not to cause irreversible demagnetization. Furthermore, since there is an upper limit value of the voltage in the inverter for driving, it is necessary to add that the voltage is not exceeded as a constraint condition. Thus, the optimization calculation is performed in consideration of the above three as constraint conditions. That is, at least one of these three constraints is a constraint, and the optimal shape is determined. When only one of the constraint conditions becomes a design constraint, the other two constraint conditions have not yet reached the constrained condition, and the design has a margin for the constraint. For example, there are limits that limit the winding temperature, and the following combinations exist as effective ways to use materials when the design has a margin for permanent magnet irreversible demagnetization restrictions. To do.

  First, a permanent magnet material having a small coercive force can be applied in a design that has a margin for the irreversible demagnetization restriction of the permanent magnet. Since a permanent magnet material having a small coercive force generally has a high residual magnetic flux density, a large torque can be expected with a small current. Furthermore, by applying a permendule known as a material having the highest saturation magnetic flux density among magnetic materials as an iron-cobalt alloy as a material of an electric motor core that is most suitable for the permanent magnet material, a small current can be obtained. The effect of a large torque characteristic can be enhanced, and the combination with the permanent magnet material is optimal.

[Sixth Embodiment]
The sixth embodiment will be described with reference to FIG. In FIG. 15, considering the constraint condition in the electric motor, the torque characteristics under the constraint condition are calculated for each constraint condition using the thermal-magnetic field coupled analysis. First, start with the number of revolutions in the low speed region. Determine the rotation speed and current value and use them as inputs. A magnetic field analysis is performed on a certain shape from these input values. Next, as shown in the third embodiment, thermal analysis is performed using the loss calculated by post-processing of the magnetic field analysis as an input value. The temperature rises due to the calculated loss, and the physical property value changes accordingly, so the calculation is repeated until the temperature-dependent physical property value converges. Next, convergence calculation is performed for each constraint condition while updating the current value until it is within the convergence determination value ± ε. When the convergence calculation is completed, a torque value near the constraint condition is calculated. By performing such a calculation, a torque value in the vicinity of each constraint condition can be calculated. The convergence calculation of the temperature-dependent physical property value shown above converges automatically as the current value is updated, so it can be considered in the loop for updating the current value. Time can also be shortened. When the calculation of the torque is finished, the rotation speed is changed and the same calculation is executed. The calculation ends when the number of rotations in the high speed range to be considered is calculated. The results obtained in this way are shown in FIG. As shown in FIG. 16, the maximum outputable torque can be clarified as the rotational speed-torque characteristic with respect to each of the winding temperature constraint, irreversible demagnetization constraint, and voltage constraint. As is apparent from this figure, it can be understood that the irreversible demagnetization constraint has a margin in the torque limit value with respect to the winding temperature constraint. As shown in the fifth embodiment, the torque limit value for each constraint condition is set to the same value by changing the combination of materials or conducting a parameter survey of dimensions not included in the optimization variable. be able to. By doing so, it is possible to perform limit design with respect to the constraint condition, and there is no variation with respect to the torque limit value for each constraint condition, and a balanced design with no material or design waste becomes possible.

[Seventh Embodiment]
In the second to sixth embodiments, the optimum design method for miniaturization has been described. However, by searching the optimum function described in the third embodiment, it is possible to search for the optimum shape for different purposes. For example, in an electrical device, not only miniaturization but also high efficiency is an important point of view. In this case, the objective function is defined as efficiency. As described in the third embodiment, in the optimization calculation, the magnetic field analysis and the thermal analysis are coupled. Considering the dimensions and physical properties calculated from optimization variables that change from moment to moment in these coupled analyses, a high value that assumes the actual driving state from the loss, torque value, and rotation speed obtained by post-processing of the magnetic field analysis Accurate efficiency can be calculated. Using the calculated efficiency as an objective function, an optimal shape that maximizes the efficiency can be calculated by performing optimization calculation that maximizes the efficiency. Furthermore, as shown in the fourth embodiment, by changing the dimensions that are not included in the optimization variable and calculating the optimum shape for each of the changed dimensions, the point with the highest performance as the most efficient design is obtained. It becomes possible to explore.

[Eighth Embodiment]
Similarly to the seventh embodiment, the cost is an important point of view if the electric motor is particularly mass-produced. Therefore, the value that can calculate the amount of electrical steel sheet, the amount of permanent magnet, the amount of copper wire, and the grade of material can be set in the optimization variable, and it can be converted into the total cost from the price per unit amount. . In this embodiment, cost is an objective function, and optimization calculation that minimizes cost is performed. Considering dimensions and physical properties calculated from optimization variables that change from moment to moment in the optimization calculation, the motor shape is converted into the cost for one motor. By performing optimization calculation that minimizes this cost, it is possible to design an inexpensive motor.

[Ninth Embodiment]
FIG. 17 shows an explanatory diagram used in the ninth embodiment. In the present invention, by considering the heat capacity at each node shown in FIG. 13, it can be reproduced with high accuracy including the transient temperature rise from the initial temperature to the thermal equilibrium state. Thereby, it is possible to calculate the characteristic in accordance with the driving time of the electric motor and to calculate the optimum shape of the state. The third embodiment will be described as an example. In the optimization calculation, the temperature and the thickness are calculated using the previous values, but the difference between the previous values is minimized by repeated calculation, It is a mechanism that can establish a coupled calculation. Therefore, in the finally obtained shape, the coupling is established, and by considering the heat capacity at each node in the cross-sectional view shown in FIG. Temperature can be calculated with high accuracy. By using this, it is possible to search for the optimum point at that time by specifying the temperature to be extracted in the optimization calculation as the temperature of a certain time, and optimization of continuous operation and short-time operation in the motor Is possible. For example, if it is an application that is rarely used for continuous operation such as a servo motor, it is optimal for searching for the optimum point in short-time operation, and can be applied to special applications such as electric power steering It becomes. In these embodiments, the embodiments shown in Nos. 2 to 7 can be applied.

[Tenth embodiment]
FIG. 18 shows an output format of the optimum design system of the present invention. Since the present invention employs the direct search method for the optimization algorithm, it is possible to create a graph in the figure with the horizontal axis representing the number of searches and the vertical axis representing the objective function, constraints, and variables. Thereby, it is possible to confirm the convergence status of the optimization calculation, the status of the constraint condition, and the status of the transition of the variable. In addition, since the temperature dependence of the physical property value is taken into consideration in the present invention, a graph in the figure is also created in which the horizontal axis represents the number of searches, the vertical axis represents the resistivity of the stator winding, and the residual magnetic flux density of the magnet. be able to. Thereby, it can be confirmed whether the coupling | bonding of a heat | fever and a magnetic field is materialized. In order to create these graphs, each time the objective function is calculated in the optimization calculation, various quantities necessary for creating the graph are written to a file.

Claims (8)

An objective function calculation unit that receives a set of design variables, calculates a function value based on the set of design variables, and outputs the function value;
In an optimal design system comprising optimization means for searching for the set of design variables in which the function value is maximized or minimized,
The objective function calculation unit can input physical quantities including dimension data and physical property values related to electromagnetic equipment from a history file, and
Has the function of writing the latest physical quantity calculated by reflecting this physical quantity to the history file,
Every time the objective function calculation unit calculates the objective function in the repetition of optimization of the magnetic field analysis and thermal analysis of the electromagnetic equipment, the temperature is calculated by the thermal analysis based on the loss calculated by the magnetic field analysis. And has the function of
An optimal design system for electromagnetic equipment, wherein the optimization means is based on a direct search algorithm. In the optimal design system of the electromagnetic device according to claim 1 ,
An optimum design system for electromagnetic equipment, wherein at least a history of the thermal analysis is stored in the history file. In the optimal design system of the electromagnetic device according to claim 2 ,
The magnetic field analysis means is a finite element method,
An optimal design system for electromagnetic equipment, wherein the thermal analysis means is a thermal equivalent network method. In the optimal design system of the electromagnetic device according to claim 3 ,
The optimal design system for an electromagnetic device, wherein the function value output from the objective function calculation unit is calculated from a torque per unit volume of the electromagnetic device. In the optimal design system of the electromagnetic device according to claim 4 ,
An optimum design system for electromagnetic equipment, wherein at least a history of core thickness of the electromagnetic equipment is stored in the history file. In the optimal design system of the electromagnetic device according to claim 3 ,
An optimal design system for an electromagnetic device, wherein the function value output from the objective function calculation unit is calculated from the efficiency of the electromagnetic device. Using the optimum design system according to any one of claims 1 to 5 ,
Applying the optimum design system to each of the dimensions or physical property values that do not become the design variables according to claim 1 ,
A design method characterized by comparing optimum shapes for each dimension or physical property value and selecting the most effective shape. A design method of a permanent magnet synchronous motor, wherein the design method of a permanent magnet synchronous motor is calculated by the following steps.
(1) Use the dimensions and physical properties of each part of the permanent magnet synchronous motor as variables or constants as input values,
(2) Divide the elements of the analysis target machine from the input value,
(3) Read the temperature of the winding and permanent magnet from the temperature history file prepared in advance, calculate the resistance value of the winding at that temperature and the residual magnetic flux density of the permanent magnet as a function of temperature,
(4) Perform a two-dimensional magnetic field analysis,
(5) Read the result of (4) and the thickness of the permanent magnet type synchronous motor from a thickness history file prepared in advance, and use them to calculate the loss of the permanent magnet type synchronous motor,
(6) Calculate the thermal resistance between each node from the nodes set in advance for analysis from the dimensions and physical properties,
(7) Perform thermal analysis using the loss and thermal resistance obtained from (5) and (6) as input values, update the temperature at each obtained node to the temperature history file,
(8) Calculate the thickness of the permanent magnet type synchronous motor so as to obtain the required torque value, update the new thickness to the thickness history file,
(9) Automatically adjust the variables entered in (1) so that the torque density that is the objective function is maximized ,
An analysis method having a feature that enables heat and a magnetic field to be solved simultaneously by repeating (1) to (9).

Images