DE102014203526A1 - Method for determining a design of a magnet arrangement, magnet arrangement and electrical machine - Google Patents

Abstract

A reliable method (100) optimizing a magnetic arrangement (200, 300) having a magnetic and / or mechanical design of a permanent magnet material (210, 310), in particular for electrical machines, for increased force action, efficiency, comprises: determining an initial design (201, 301) of the magnet arrangement in a given spatial area (202, 302), dividing the spatial area including magnet arrangement into a finite element model having a number of cells (209), determining magnetic and / or mechanical properties of each cell as optimization parameter, Defining a target function for magnet arrangement and spatial area describing a magnetic and / or mechanical property of the magnet arrangement as a function of the magnetic and / or mechanical properties of the cells, forming a gradient of the objective function after all optimization parameters, determining values of all optimization parameters at an extreme value of the objective function, smoothing contours of cells and / or groups of adjacent cells by adjusting the values of the optimization parameters of adjacent cells and / or groups of cells to each other, and forming the resulting magnetic and / or mechanical design of the magnet assembly.

Description

The invention relates to a method for determining a design of a magnet arrangement.

The invention further relates to a magnet arrangement designed in accordance with such a method and to an electrical machine having such a magnet arrangement.

State of the art

From the publication DE 698 23 239 T2 is a permanent magnet synchronous motor with a rotatably mounted rotor with a rotor iron core and arranged in the vicinity of the outer peripheral edge of the rotor iron core permanent magnet known. The permanent magnets each have a main magnetic pole section and auxiliary pole sections. The auxiliary pole portions are integrally formed at magnetic pole end portions each having one of the main magnetic pole portions and polarized to the same polarity as the main magnetic pole portion, so that the magnetic paths at the magnetic pole end portions are saturated by the magnetic fluxes flowing out of the auxiliary pole portions. In particular, the auxiliary pole sections have oblique sections. In several sections in the circumferential direction of the rotor iron core, the permanent magnet adapted openings are formed with oblique sections. The permanent magnets are arranged individually in the openings and are held by the oblique sections.

From the publication DE 10 2008 032 172 A1 For example, a permanent magnet electric machine is known which is said to have optimum efficiency in the engine operating mode and is particularly designed for use in a powertrain of a hybrid electric vehicle. In a rotor of the permanent magnet electric machine, an asymmetrical distribution pattern of a magnetic flux is generated. This is to improve the operating efficiency of the permanent magnet electric machine when it is in an engine operating mode. In detail, a rotor and a stator having electrical stator windings are provided for this purpose. A plurality of magnets are embedded in the rotor in close proximity to the stator windings. Provided in the rotor, substantially triangular openings designed for this flowing through a cooling medium and / or a weight reduction. The stator windings and the magnets each produce such mutually interacting magnetic flux distribution patterns that a resultant flux flow pattern is formed between each aperture and an adjacent magnet. The substantially triangular shape of the openings minimizes mean flux saturation of the magnetic flux per rotor length unit in areas on the rotor between the magnets and the openings and reduces rotational mass of the rotor.

A further optimization of the magnetic flux density in areas of the rotor between the openings and the magnets to improve the efficiency in operating the engine in an engine operating mode according to the statements in the document DE 10 2008 032 172 A1 be achieved in that the openings are arranged asymmetrically with respect to adjacent pairs of magnets. According to another measure described therein, a plurality of adjacently arranged pairs of magnets are provided and an opening adjacent each pair is arranged asymmetrically with respect to a line of symmetry passing through a geometric center of the opening. In this case, a tip of a substantially triangular-shaped opening is offset arcuately with respect to the symmetry line, whereby the effective liquid saturation in the flow flow path between the opening and an adjacent magnet is to be optimized to improve the efficiency in operating the engine in an engine operating mode. Also, an asymmetrical electrical flow flow path around the openings is to be constructed by arranging a plurality of adjacent pairs of magnets symmetrically with respect to a radial line of symmetry, the openings being arranged asymmetrically with respect to the line of symmetry. It is also intended to construct a flow flow pattern of optimum flux density in areas of the rotor between the openings and adjacent magnets during operation of the machine in a motor operating mode such that the plurality of adjacent pairs of magnets are symmetrically disposed with respect to a radial line of symmetry the openings are offset asymmetrically with respect to the line of symmetry. According to another measure, the pairs of magnets are arranged asymmetrically with respect to a radial symmetry line extending between the magnets of the pairs, whereby the flux density in areas of the rotor between the openings and the magnets to improve the efficiency in operating the machine in a Motor operating mode should be optimized.

In the known permanent magnet electric machines permanent magnets are used at least substantially parallelepiped with completely closed cross-section. This is how the document shows DE 10 2008 032 172 A1 a magnet having a rectangular cross section.

For innovative electric drives with permanent magnet synchronous motors permanent magnets are provided, which have a very high magnetization and are formed with special, very expensive materials. Therefore, conventionally designed permanent magnets make a serious cost share of such drives or motors. A further improvement in the efficiency or performance of the permanent magnet synchronous motors, as the numerous in the document DE 10 2008 032 172 A1 show individual measures, with elaborate optimizations of individual parameters of the motors, ie individual features, designs and dimensions connected. It is necessary to optimize both electrical and magnetic and mechanical properties of the engines. In particular, no construction could be found that would have led to a significant reduction in the cost of the permanent magnets.

DESCRIPTION OF THE INVENTION: Problem, Solution, Advantages

The invention has the object to provide a reliable, systematic method, with the permanent magnets or permanent magnetic material containing magnet assemblies, in particular for electric drives with permanent magnet synchronous motors of the type described, specifically further optimized in their design, i. be designed for a further increase in their power and thus in particular for a further improvement in the efficiency or performance of permanent magnet synchronous motors.

• i. in einem ersten Verfahrensschritt Festlegen einer Anfangsgestaltung der Magnetanordnung in einem vorgegebenen Raumbereich,
• ii. in einem zweiten Verfahrensschritt Gliedern des vorgegebenen Raumbereichs einschließlich der darin enthaltenen Magnetanordnung in ein eine Anzahl von Zellen aufweisendes Finite-Elemente-Modell,
• iii. in einem dritten Verfahrensschritt Festlegen vorgebbarer magnetischer und/oder mechanischer Eigenschaften für jede einzelne der Zellen des Finite-Elemente-Modells als Optimierungsparameter,
• iv. in einem vierten Verfahrensschritt Festlegen einer Zielfunktion für die Magnetanordnung und den vorgegebenen Raumbereich, wobei die Zielfunktion eine magnetische und/oder mechanische Eigenschaft der Magnetanordnung in Abhängigkeit von den vorgebbaren magnetischen und/oder mechanischen Eigenschaften der Zellen des Finite-Elemente-Modells beschreibt,
• v. in einem fünften Verfahrensschritt Bildung eines Gradienten der Zielfunktion nach den Optimierungsparametern aller Zellen,
• vi. in einem sechsten Verfahrensschritt Bestimmen von Werten für die Optimierungsparameter aller Zellen, bei denen die Zielfunktion einen Extremwert annimmt,
• vii. in einem siebten Verfahrensschritt Glätten von Konturen von Zellen und/oder von Gruppen, die eine vorgebbare Anzahl aneinander angrenzender Zellen umfassen, durch Anpassen der im Verfahrensschritt vi bestimmten Werte der Optimierungsparameter einzelner der Zellen und/oder einzelner Zellen der Gruppen von Zellen an Werte der Optimierungsparameter weiterer, den Zellen und/oder Gruppen von Zellen benachbarter Zellen und/oder Gruppen von Zellen, sowie
• viii. in einem achten Verfahrensschritt Bilden der daraus resultierenden magnetischen und/oder mechanischen Gestaltung der Magnetanordnung.

This object is achieved by a method for determining a magnetic and / or mechanical design of a magnet arrangement formed at least with permanent-magnetic material, in particular for an electrical machine, comprising the method steps:

• i. in a first method step, determining an initial design of the magnet arrangement in a predetermined spatial area,
• ii. in a second method step, dividing the predetermined spatial area including the magnet arrangement contained therein into a finite element model having a number of cells,
• iii. in a third method step, defining predefinable magnetic and / or mechanical properties for each of the cells of the finite element model as an optimization parameter,
• iv. in a fourth method step, specifying a target function for the magnet arrangement and the predefined spatial area, the objective function describing a magnetic and / or mechanical property of the magnet arrangement as a function of the predeterminable magnetic and / or mechanical properties of the cells of the finite element model,
• v. in a fifth method step, formation of a gradient of the objective function according to the optimization parameters of all cells,
• vi. in a sixth method step, determining values for the optimization parameters of all cells in which the objective function assumes an extreme value,
• vii. in a seventh method step, smoothing contours of cells and / or groups comprising a predeterminable number of contiguous cells by adapting the values of the optimization parameters of individual cells and / or individual cells of the groups of cells determined in method step vi to values of the optimization parameters another, the cells and / or groups of cells of adjacent cells and / or groups of cells, as well as
• viii. in an eighth method step, forming the resulting magnetic and / or mechanical design of the magnet assembly.

As an initial design, preference is given to defining a simple configuration of a magnet arrangement to be optimized, which has been gained from experience. In a predeterminable spatial region, this has a certain spatial distribution of a permanent magnetic material with a specific spatial distribution of a magnetization, i. a magnetic field or flux caused by the permanent magnetic material.

Furthermore, optionally a magnetically conductive material, ie a material with a high value of its relative magnetic permeability constants, eg iron, with a spatial distribution associated therewith in the predeterminable spatial region is present. In a modification, a plurality of permanent-magnetic materials or a plurality of magnetically conductive materials, each with an associated spatial distribution, may be provided in the predeterminable spatial region, or the magnetic properties The materials can vary within their spatial distributions specifiable. Sections of the predeterminable space range in which neither permanent-magnetic nor magnetically conductive materials are provided are assumed to be magnetically nonconductive, ie having a value of their relative magnetic permeability constants of at least nearly one, such as air or vacuum. In addition, the initial design assigned to the spatial distributions of the abovementioned materials in the predeterminable spatial area advantageously also includes a spatial distribution of mechanical properties of these materials, eg their weight and tensile strength.

In the second method step, the predetermined spatial area, including the magnet arrangement contained therein, is divided into the cells of a finite element model taking into account, in particular, boundaries between the individual spatial distributions of the different materials. Such cells are hexahedral shaped in a preferred embodiment quadrangular or spatially viewed. This makes it easy to assign the individual cells the different magnetic or mechanical properties of the initial design.

For each of these cells of the finite element model, the predetermined magnetic or mechanical properties are determined according to the above-described initial design in the third method step. These magnetic or mechanical properties of the individual cells form optimization parameters of the finite element model for the subsequent method steps, i. the intended optimization of the magnet arrangement or its design is carried out by varying the optimization parameters. The optimization parameters also include material properties of the aforementioned materials, such as magnetic permeability, magnetization according to magnitude and spatial orientation, and mechanical strength.

By setting the target function for the magnet arrangement and the predetermined spatial area in the fourth method step, the goal of the desired optimization of the magnet arrangement is determined. The objective function generally describes a magnetic or mechanical property of the magnet arrangement or a combination of both properties in dependence on the predetermined magnetic or mechanical properties of the cells of the finite element model. The objective function is thus a function preferably of the predetermined magnetic and mechanical properties of the cells of the finite element model in combination, so that both a magnetic and a mechanical optimization are combined by the desired optimization. This is a particularly advantageous feature of the method according to the invention, because it allows a much more direct, streamlined and shortened process sequence compared to a formation of an objective function with either exclusively magnetic or exclusively mechanical properties. In the latter case, e.g. An optimization of the magnetic properties can not provide a final design of the magnet arrangement, but it must first be followed by an optimization of the mechanical properties subsequently. However, since this usually changes the magnetic properties and thus leaves the optimal magnetic design again, a further, repeated, re-optimization of the magnetic properties would have to follow, which would in turn be followed by further optimization of the mechanical properties, etc. These repeated Mutual optimization runs can be avoided by defining the target function as a function of the given magnetic and mechanical properties.

As an example of the above-described training, the magnetization of the permanent magnetic material as a magnetic property and the mechanical strength, advantageously the tensile strength, of the permanent magnetic material is specified as a mechanical property of each of the cells of the finite element model. The objective function is then, e.g. The magnetic force of the magnet assembly or the output power or the output torque of the machine in which the magnet assembly is used.

The formation of the gradient of the objective function according to the optimization parameters of all cells in the fifth method step aims at a particularly simple implementation of the optimization of the magnet arrangement, which is carried out in the sixth method step by determining the extreme value of the objective function as a function of the optimization parameters of all cells. Such an extreme value can be determined very simply by finding the zeros of the gradient of the objective function. As such an extreme value, in the aforementioned example of an objective function, a maximum of the magnetic force of the magnet assembly and the output torque of the machine in which the magnet assembly is used is advantageously formed.

By consistently carrying out the described optimization, a variation of the magnetic and mechanical properties of each of the cells to achieve the extreme value of the target function is feasible and is generally carried out, in principle, no approximation of the magnetic or mechanical properties of adjacent cells is made. As a result of the method steps described so far, in particular of the sixth method step, a design of the magnet assembly may result in a spatial distribution of the different materials, which represents a magnetic or mechanical optimum, but from a manufacturing point of view very unfavorable, ie with available manufacturing means, ie Tools and machines, not or can be very expensive to produce. In order to achieve a design that is both magnetically and mechanically as optimal as possible, but at the same time favorable to manufacture, in the seventh process step, smoothing of contours of the spatial distributions of the individual materials of the magnet assembly by the optimization parameters of adjacent individual cells or groups of cells of the finite Element models are adapted to each other so that there are simplistic spatial contours for the spatial distributions of the individual materials of the magnet assembly. The spatial extension over which this adaptation takes place is selectable, so that, depending on the desired compromise between optimum magnetic or mechanical properties on the one hand and simple production on the other hand, different degrees of smoothing of the contours takes place.

With the contours smoothed in this way, in the eighth method step, the resulting magnetic or mechanical configuration of the magnet arrangement, i. the design or shaping of individual parts of the magnet assembly of different materials, formed, this step may optionally include a further smoothing and simplification of the contours.

The invention thus enables a simple and direct optimization of the magnet arrangement, i. a design for maximum magnetic force and at the same time maximum mechanical strength and optimum manufacturability. In this way, it is preferable to further build up efficiency-enhanced permanent magnet synchronous machines and other electrical machines of similar design. Due to the direct procedure, this optimization is simple, fast, inexpensive and comprehensively executable; It will be avoided so far necessary, lengthy and expensive stages of development.

Advantageous embodiments of the invention are characterized in the subclaims. According to a preferred embodiment of the method according to the invention, in the fourth method step, the target function as a magnetic and / or mechanical property of the magnet assembly at least a set of permanent magnetic material with which the magnet assembly is formed, comprising, and includes the assumed in the sixth step by the objective function Extreme value is a minimum of this amount of permanent magnetic material with which the magnet assembly is formed. According to this development, the objective function is thus advantageously formulated in such a way that the amount of the permanent magnetic material used in the magnet arrangement, which constitutes a magnetic or mechanical property of the magnet arrangement, is minimized. In other words, the quantity of the permanent magnetic material is part of the target function or comprises it. In a modification of this development, optionally or additionally, the amount of a magnetically conductive material used in the magnet assembly, i. a material having a high value of its relative magnetic permeability constants, e.g. Iron, a magnetic or mechanical property of the magnet assembly, so that by optimizing the target function also optimizes the amount of magnetically conductive material used in the magnet assembly, i. their minimization is achieved.

In a further preferred embodiment of the method according to the invention, at least the determination of values for the optimization parameters of all cells in which the objective function assumes an extreme value is carried out according to the sixth method step by means of an iteration, preferably according to a so-called SNOPT method.

At this point it should be mentioned that from the publication " SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization ", published in 2005 by the Society for Industrial and Applied Mathematics (SIAM) in SIAM REVIEW, Vol. 47, No. 1, pp. 99-131 , or electronically under the Internet address http://www.siam.org/journals/sirev/47-1/44609.html , a calculation and optimization method called "Sparse Nonlinear Optimizer (SNOPT)". According to this publication, so-called "sequential quadratic programming (SQP)" methods have proven to be highly effective for solving optimization tasks with limit conditions with smoothed nonlinear functions in objective function and limit conditions. The paper deals with problems with general inequality limit conditions - linear and nonlinear. It depends on the requirement assume that first derivatives are available and that the gradients of the limiting conditions are sparsely distributed. Furthermore, it is assumed that second derivatives are either not available or too expensive to calculate. The publication presents an SQP method which uses a smoothed, enhanced Lagrangian merit function and makes explicit provision for inability to perform the original task and for the applicability of so-called quadratic programming (QP) sub-tasks. The Hesse matrix of Lagrange's merit function is approximated by using a memory-constrained quasi-Newton method.

As for this from the Internet encyclopedia "Wikipedia" - cf. the internet appearance " http://de.wikipedia.org/wiki/Hesse-Matrix ", Read on 18.12.2013 at 10:46 - The Hesse matrix in multidimensional real analysis is an analogue to the second derivative of a function: Hessian matrices play a role in the approximation of multi-dimensional functions, among others in context with the optimization of multi-parameter systems in engineering.

Furthermore, the Internet encyclopedia "Wikipedia" - cf. the internet appearance " http://de.wikipedia.org/wiki/Quasi-Newton-Verfahren ", Entry read at 18.12.2013 at 10:57 - it can be seen that Quasi-Newton's method is a class of numerical methods for solving nonlinear minimization problems.The methods are based on the Newton method, calculate the inverse of the Hesse matrix, however, not directly, but approach it only to reduce the computational effort per iteration.

Furthermore, from the Internet encyclopedia "Wikipedia" - cf. the internet appearance " http://de.wikipedia.org/wiki/Newton-Verfahren ", Read on 18/12/2013 at 11:03 am - can be deduced that the Newton method is a standard mathematical method for the numerical solution of nonlinear equations and systems of equations In the case of an equation with a variable can be added to a given continuously differentiable function The basic idea of this method is to determine the tangent of the function in a starting point and to use the tangent of the tangent as an improved approximation of the function's zero, which serves as the starting point for a further improvement step In this way, an iteration is carried out until the change in the approximate solution has fallen below a specified limit.

Finally, the internet encyclopedia "Wikipedia" - cf. the internet appearance " http://en.wikipedia.org/wiki/Sequential_quadratic_programming ", Read on 17.12.2013 at 14:29 - can still be deduced that the so-called" sequential quadratic programming (SQP) "method is an iterative method for nonlinear optimizations SQP methods are used for tasks, for SQP methods solve a series of optimization sub-tasks, each of which optimizes a quadratic model of the objective function as a function of a linearization of the constraint conditions, and if the task is not subject to limit conditions, the SQP method is reduced. Method to the Newton Method for Finding a Point at which the Gradient of the Target Function Disappears If the task has only equality constraint conditions, the SQP method is equivalent to applying the Newton method to the first-order optimality conditions of the task ng. SQP methods are carried out in the context of the aforementioned SNOPT method.

According to the above-mentioned publication "SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization", this SNOPT method is a special implementation which uses a reduced Hesse semi-determined QP solution method - abbreviated to SQOPT - for the QP method. Sub-tasks used. It is said to be designed for tasks with many thousands of limit conditions and variables, but is best suited for tasks with an average number of degrees of freedom, i. until about 2000.

The aforementioned preferred embodiment of the invention now makes use of this method and uses it for optimizing the magnetic and / or mechanical properties of the magnet arrangement, preferably for a combined optimization of both the magnetic and the mechanical properties to achieve the highest possible magnetic force effect at the same time the highest possible mechanical strength of the magnet assembly. In this case, use is advantageously made of the fact that at least essential magnetic and mechanical properties obey similar or identifiable physical-mathematical laws, whereby the method of designing the magnet arrangement can be combined to save both magnetic and mechanical properties.

A further advantageous embodiment of the method according to the invention is characterized by an objective function according to the formulas

aus den elektromagnetischen Feldgrößen berechnen lässt, und S der Poynting’sche Vektor, der sich nach S = E × H ergibt. Dabei ist mit

• F

  die Kraft,

  q

  die Ladung,

  E

  die elektrische Feldstärke,

  E_i

  eine erste Komponente der elektrischen Feldstärke E,

  E_j

  eine zweite Komponente der elektrischen Feldstärke E,

  v

  die Geschwindigkeit,

  B

  die magnetische Flussdichte,

  B_i

  eine erste Komponente der magnetischen Flussdichte B,

  B_j

  eine zweite Komponente der magnetischen Flussdichte B,

  O

  die Oberfäche,

  V

  das Volumen ([V] = 1m³),

  µ₀

  die absolute Permeabilitätskonstante,

  e₀

  die absolute Dielektrizitätskonstante,

  d_ij

  das Kronecker-Delta und

  H

  die magnetische Feldstärke

bezeichnet. Where T is the Maxwellian stress tensor, which follows

from the electromagnetic field quantities and S the Poynting vector, which follows S = E × H results. It is with

• F

  the power

  q

  the charge,

  e

  the electric field strength,

  E _i

  a first component of the electric field strength E,

  E _j

  a second component of the electric field strength E,

  v

  the speed,

  B

  the magnetic flux density,

  B _i

  a first component of the magnetic flux density B,

  B _j

  a second component of the magnetic flux density B,

  O

  the surface,

  V

  the volume ([V] = 1m ³ ),

  μ ₀

  the absolute permeability constant,

  e ₀

  the absolute dielectric constant,

  d _ij

  the Kronecker delta and

  H

  the magnetic field strength

designated.

Thus, the objective function is either described by the Lorentz force, which can be formulated as the product of charge q multiplied by the strength of the electric field E added to the force component on the charge resulting from the movement in the magnetic field B at the velocity v. Alternatively, a force can be determined by integration of Maxwell's stress tensor T over the surface of the considered body. The temporal change of the Poynting vector in volume must also be taken into account. In both cases, therefore, the objective function can be formulated as a function of the electromagnetic field variables.

The above object is further achieved by a magnet assembly which is designed according to a method of the type and design described above. This magnet arrangement is simple and directly designed and constructed and ensures a high magnetic force effect with the most economical and efficient material use.

Furthermore, the above object is achieved by an electric machine with at least one magnet arrangement of the type and design described above. Such a machine allows a maximum of output or torque output and energy efficiency with minimum material usage and weight as well as cost-effective development and production.

In addition, the above object is achieved by a computer program product having program parts for carrying out a method of the type described above, by a machine-readable, in particular computer-readable, data structure generated by such a method and / or by at least one computer program product of the aforementioned type, as well as by a machine-readable, in particular computer-readable, data carrier on which at least one computer program product of the type described above is recorded and / or stored and / or on which at least one data structure of the type described above is kept ready for retrieval.

Brief description of the drawings

Embodiments of the invention are illustrated in the drawings and will be described in more detail below, with matching elements in all figures are given the same reference numerals and a repeated description of these elements is omitted. Show it:

1 1 is a rough flowchart of a method sequence of an embodiment of a method according to the invention;

2a to 2e a first example of a design of a magnet assembly with the embodiment of the inventive method according to 1 , and

3a and 3b a second example of a design of a magnet assembly with the embodiment of the inventive method according to 1 ,

Preferred embodiment of the invention

The 1 shows a by the reference numeral 100 referred to, rough schematic flow diagram of a process flow of an embodiment of the method according to the invention, which is set up here for determining a magnetic and mechanical design of a magnet assembly, both permanent magnetically as well as magnetically conductive and magnetically non-conductive material in each of the materials associated spatial distributions in a given Space is formed. Such a magnet arrangement is preferably intended for use in an electrical machine.

After the beginning 101 In the first method step i of the method sequence, an initial design of the magnet arrangement is defined in the predetermined spatial area. This area of space preferably encloses the entire magnet arrangement as well as its spatial environment, insofar as this is significant for the formation of essential sections or portions of a magnetic field or flux caused or influenced by the magnet arrangement. The initial design of the magnet assembly and any counter magnets to form mutual magnetic force effects is preferably chosen intuitively based on experience and has in particular simple, straight and smooth contours of the spatial distributions of permanent magnetic, magnetically conductive and magnetically non-conductive materials.

In the second method step ii, the predetermined spatial area, including the magnet arrangement contained therein, is subdivided into a finite element model having a number of cells. For each of these cells of the finite element model, predetermined magnetic and / or mechanical properties are defined as optimization parameters in the third method step iii, e.g. the strength and direction of a magnetic flux, the relative magnetic permeability constant, the mechanical tensile strength of the material.

In the fourth method step iv, an objective function for the magnet arrangement and the predetermined spatial area is defined. In this case, the objective function describes a magnetic or a mechanical, but preferably at least one magnetic and additionally at least one mechanical property of the magnet arrangement as a function of the predefinable magnetic or mechanical properties, i. the optimization parameters, the cells of the finite element model. The objective function is thus described as a function of the optimization parameters. By way of example, the objective function as a magnetic property comprises a magnetically induced force effect of the magnet arrangement or, as a mechanical property, a mechanical strength or rigidity of the magnet arrangement. A quantity of the permanent magnetic or the magnetically conductive material, with which the magnet arrangement is formed, or the quantities of both materials preferably form secondary conditions.

In the fifth method step v, a gradient of the objective function is formed according to the optimization parameters of all cells. This serves to prepare for the sixth method step vi, in which now values for the optimization parameters of all cells, at which values of the optimization parameters the objective function Extreme value assumes, be determined. Such an extreme value can be easily determined by the fact that the gradient disappears there. If, for example, the objective function includes a magnetically induced force effect of the magnet arrangement as the magnetic property, a maximum of this force effect is determined as a function of all optimization parameters.

The sixth method step vi is preferably carried out iteratively with the aforementioned "SNOPT" method, indicated in FIG. 1 by the reference symbol 102 , It is in an in 1 not shown embodiment, the fifth step v included in the iterative runs.

In the seventh method step vii, smoothing of contours of cells and / or of groups comprising a predeterminable number of contiguous cells is undertaken. This is done by adjusting the values determined in the sixth method step vi of the optimization parameters of individual ones of the cells and / or individual cells of the groups of cells to values of the optimization parameters of further cells and / or groups of cells of neighboring cells and / or groups of cells. The aim is a production-related smoothing of the contours of the spatial distributions of the different materials, so that simple shapes are formed from the different materials that make up the magnet assembly. In a modification, the seventh method step vii can be combined directly with the sixth method step vi in such a way that the smoothing is included in the iteration sequence.

In the eighth method step viii, from the magnetic and / or mechanical design of the magnet arrangement, as resulting from the seventh method step vii, a final, resulting magnetic and / or mechanical design of the magnet arrangement is formed such that forms that are easy to manufacture are formed from the different materials are from which the magnet assembly can be easily assembled in the production. This is the end 103 of the procedure achieved.

The 2a . 2 B . 2c . 2d and 2e show a first example of a design of a magnet assembly 200 with the embodiment 100 of the inventive method 1 in a rough schematic sectional view. This is in 2a an initial design 201 the magnet arrangement 200 in a given space area 202 shown. The initial design 201 is formed with simple contours and includes a massive iron core 203 as a magnetically conductive material and two counter magnets 204 . 205 oppositely oriented magnetization as a permanent magnetic material. Opposite this is a horseshoe magnet 206 arranged, whose legs 207 . 208 the counter magnet 204 . 205 magnetized oppositely, so that a repulsive force effect between the horseshoe magnet 206 and the initial design 201 the magnet arrangement 200 results. The representation according to 2a corresponds to the result of the first method step i.

2 B shows an outline of the given space area 202 including the magnet assembly contained therein 200 or their initial design 201 in a number of cells 209 having finite element model as a result of the second method step ii. To every single one of these cells 209 In the third method step iii, magnetic and mechanical properties are determined as optimization parameters, in particular the magnetization of the counter magnets 204 . 205 and the horseshoe magnet 206 , the relative magnetic permeability of the iron core 203 and the one of the counter magnets 204 . 205 , the horseshoe magnet 206 and the iron core 203 within the given space 202 surrounding material, here air, as well as the mechanical tensile strength of the listed materials.

In 2c is the design of the magnet assembly 200 shown how they are after determining the objective function in the fourth step iv to describe the magnetic and mechanical properties of the magnet assembly 200 depending on the given magnetic and mechanical properties of the cells 209 of the finite element model as optimization parameter, formation of a gradient of the objective function according to the optimization parameters of all cells 209 in the fifth method step v and determining those values for the optimization parameters of all cells 209 in which the objective function assumes an extreme value, in the sixth method step vi results in its end. It can be clearly seen that in this stage of the process no smoothing of the contours of cells 209 or groups of cells 209 or spatial distributions of the different materials, namely the permanent magnetic material 210 , the magnetically conductive material 211 and the magnetically non-conductive material 212 , has taken place. It should be noted that the contours and the magnetic and mechanical properties of the horseshoe magnet 206 as well as the horseshoe magnet 206 and the initial design 201 the magnet arrangement 200 surrounding material, here also the magnetically non-conductive material 212 attributed air, by an appropriate definition of the objective function in the optimization of Magnet arrangement have not been changed. In a modification of the method 100 can also be used for these parts of the room area 202 to perform an optimization.

Since the in 2c illustrated contours of the spatial distributions of the permanent magnetic material 210 , the magnetically conductive material 211 and the magnetically non-conductive material 212 are too irregular for cost-effective production, takes place in the seventh process step vii a production-related smoothing, the result 2d shows. Compared to the result of the design 2c are in 2d a predeterminable size underrun areas of the spatial distributions of each of the materials 210 . 211 . 212 adjacent spatial distributions of other materials 210 . 211 . 212 been affiliated, so that larger-scale contours of the spatial distributions of the materials 210 . 211 . 212 be formed. Due to the resulting design with manufacturing reference, an approximation to an easily manufacturable shape is obtained. In this case, in the present example, a combination of the sixth and seventh method step vi, vii already in the optimization of the contours and the objective function has been made, resulting in already from the outset different contours than in the case in which starting from the result 2c only small areas of spatial distribution of materials 210 . 211 . 212 be cleaned up. This results in an improved optimization despite simple contours.

While smoothing the contours of the spatial distributions of materials 210 . 211 . 212 in the seventh process step vii is preferably already carried out in the optimization of the objective function, takes place separately and the seventh process step vii downstream in eighth process step viii from the result of optimizing the objective function or the smoothing of the contours forming the resulting magnetic and mechanical design of the magnet assembly 200 , In this eighth process step, once again a simplification and smoothing of the contours of the spatial distributions of the materials takes place 210 . 211 . 212 , but not now with the inclusion of the optimization of the objective function, but only according to manufacturing aspects, ie to achieve as simple as possible, ie easy to produce contours. It is thus a straightening or cleansing of the design 2d , The result of this eighth process step viii is exemplified in 2e shown. In this case, although a slight deterioration of the magnetic or mechanical properties of the magnet assembly 200 occur, but since in the preceding process steps a very large optimization of the magnet assembly 200 achieved, this deterioration does not significantly affect the final result.

In the example of the design of the magnet assembly 200 to 2a to 2e is reflected in the design 2e towards those after 2a an increase in the magnetic repulsion force between the magnet assembly 200 and the horseshoe magnet 206 by 2.7 times and a reduction in the mass of the magnetically conductive material 211 achieved by 62%, the mass of the permanent magnetic material 210 conditionally remains unchanged by a corresponding determination of the objective function.

The 3a and 3b show a second example of a design of a magnet assembly 300 with the embodiment of the method according to the invention 100 to 1 in a rough schematic sectional view. This is in 3a an initial design 301 the magnet arrangement 300 in a given space area 302 shown. The initial design 301 is formed with simple contours and includes a massive iron core 303 as a magnetically conductive material and two counter magnets 304 . 305 oppositely oriented magnetization as a permanent magnetic material. Opposite this is a horseshoe magnet 306 arranged, whose legs 307 . 308 the counter magnet 304 . 305 magnetized oppositely, so that a repulsive force effect between the horseshoe magnet 306 and the initial design 301 the magnet arrangement 300 results. The representation according to 3a corresponds to the result of the first method step i. Besides, the initial design is 301 to 3a identical to the initial design 201 to 2a selected.

3b shows for this second example the resulting magnetic and mechanical design of the magnet assembly 300 after completion of the eighth step viii of the procedure 100 , In this second example, the amounts of materials formulated as constraints were reduced. While in the example after the 2a to 2e the mass of the permanent magnetic material 210 remains constant in the optimization and a maximum of the force is determined, the example 3a and 3b the optimization task is based, for example, with 36% of the mass of the permanent magnetic material 310 the initial design 301 an optimal structure of the magnet arrangement 300 to accomplish. Starting from the initial design 301 the magnet arrangement 300 according to 3a results after carrying out the eighth process step viii for the resulting magnetic and mechanical design of the magnet assembly 300 to 3b a reduction in the mass of the permanent magnetic material 310 around 64% and of the magnetically conductive material 311 75% while still achieving an increase in magnetic repulsion to 1.4 times.

As a result, a reliable method, optimizing a magnetic and / or mechanical design of a permanent magnet material having magnet assembly, in particular for electrical machines, for increased power, efficiency and performance is thus provided, which comprises:

• Setting an initial design of the magnet arrangement in a predetermined spatial area,
• Dividing the space area including magnet arrangement into a number of cells having finite element model,
• Determining the magnetic and / or mechanical properties of each cell as an optimization parameter,
• Setting a magnetic and / or mechanical target function describing a magnetic and / or mechanical property of the magnet arrangement as a function of the magnetic and / or mechanical properties of the cells;
• Formation of a gradient of the objective function according to all optimization parameters,
• Determining values of all optimization parameters at an extreme value of the objective function,
• Smoothing contours of cells and / or groups of contiguous cells by adjusting the values of the optimization parameters of adjacent cells and / or groups of cells to each other, as well
• - Forming the resulting magnetic and / or mechanical design of the magnet assembly.

LIST OF REFERENCE NUMBERS

100

Method and its flow chart

101

Start of the procedure

102

Iterative execution of the "SNOPT" method

103

End of the procedure

200

Magnet arrangement ( 2 )

201

Initial design of 200

202

Preset space area

203

Iron core as a magnetically conductive material

204

First counter magnet as permanent magnetic material

205

Second counter magnet as permanent magnetic material

206

Horseshoe magnet

207

First leg of 206

208

Second leg of 206

209

Cells of the finite element model of 202

210

Permanent magnetic material

211

Magnetically conductive material

212

Magnetically non-conductive material or air

300

Magnet arrangement ( 3 )

301

Initial design of 300

302

Preset space area

303

Iron core as a magnetically conductive material

304

First counter magnet as permanent magnetic material

305

Second counter magnet as permanent magnetic material

306

Horseshoe magnet

307

First leg of 306

308

Second leg of 306

310

Permanent magnetic material

311

Magnetically conductive material

i

First process step

ii

Second process step

iii

Third procedural step

iv

Fourth process step

v

Fifth process step

vi

Sixth procedural step

vii

Seventh process step

viii

Eighth process step

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 69823239 T2 [0003]
• DE 102008032172 A1 [0004, 0005, 0006, 0007]

Cited non-patent literature

• SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization ", published in 2005 by the" Society for Industrial and Applied Mathematics (SIAM) "in SIAM REVIEW, vol. 47, no. 1, pages 99 to 131 [0022]
• http://www.siam.org/journals/sirev/47-1/44609.html [0022]
• http://en.wikipedia.org/wiki/Hesse-Matrix [0023]
• http://en.wikipedia.org/wiki/Quasi-Newton- method [0024]
• http://en.wikipedia.org/wiki/Newton-Method [0025]
• http://en.wikipedia.org/wiki/Sequential_quadratic_programming [0026]

Claims (9)

Procedure ( 100 ) for determining a magnetic and / or mechanical design of at least one permanent-magnetic material ( 210 . 310 ) formed magnet assembly ( 200 . 300 ), in particular for an electrical machine, comprising the method steps: i. in a first process step, defining an initial design ( 201 . 301 ) of the magnet arrangement ( 200 . 300 ) in a given space area ( 202 . 302 ii. in a second method step, members of the predetermined spatial area ( 202 . 302 ) including the magnet arrangement contained therein ( 200 . 300 ) into a number of cells ( 209 ), finite element model, iii. in a third method step, predeterminable magnetic and / or mechanical properties for each of the cells ( 209 ) of the finite element model as an optimization parameter, iv. in a fourth method step, determining a target function for the magnet arrangement ( 200 . 300 ) and the given space area ( 202 . 302 ), wherein the objective function is a magnetic and / or mechanical property of the magnet arrangement ( 200 . 300 ) as a function of the predefinable magnetic and / or mechanical properties of the cells ( 209 ) of the finite element model, v. in a fifth method step, formation of a gradient of the objective function according to the optimization parameters of all cells ( 209 ), vi. in a sixth method step, determining values for the optimization parameters of all cells ( 209 ), where the objective function takes an extreme value, vii. in a seventh method step smoothing contours of cells ( 209 ) and / or groups having a predeterminable number of contiguous cells ( 209 ) by adjusting the values determined in step vi for the optimization parameters of individual cells ( 209 ) and / or individual cells ( 209 ) of the groups of cells ( 209 ) values of the optimization parameters of further cells ( 209 ) and / or groups of cells ( 209 ) of adjacent cells ( 209 ) and / or groups of cells ( 209 ), as well as viii. in an eighth method step, forming the resulting magnetic and / or mechanical design of the magnet arrangement ( 200 . 300 ). Procedure ( 100 ) according to claim 1, characterized in that in the fourth method step, the objective function as a magnetic and / or mechanical property of the magnet arrangement ( 200 . 300 ) at least a quantity of the permanent magnetic material ( 210 . 310 ), with which the magnet arrangement ( 200 . 300 ), is set comprehensively, and that the extreme value assumed by the objective function in the sixth method step is a minimum of this quantity of the permanent magnetic material ( 210 . 310 ), with which the magnet arrangement ( 200 . 300 ) is formed comprises. Procedure ( 100 ) according to claim 1 or 2, characterized in that at least determining values for the optimization parameters of all cells ( 209 ), in which the objective function assumes an extreme value, according to the sixth method step (vi) by means of an iteration ( 102 ), preferably according to a so-called SNOPT method. Procedure ( 100 ) according to claim 3, characterized by an objective function according to the formulas

where T is the Maxwellian stress tensor that follows

calculated from the electromagnetic field quantities, S is the Poynting vector, which follows S = E × H gives, and where with F the force, q the charge, E the electric field strength, E _i a first component of the electric field strength E, E _j a second component of the electric field strength E, v the velocity, B the magnetic flux density, B _i a first component of the magnetic flux density B, B _j a second component of the magnetic flux density B, O the surface area, V the volume ([V] = 1m ³ ), μ ₀ the absolute permeability constant, e ₀ the absolute dielectric constant, d _ij the Kronecker delta and H the magnetic field strength. Magnet arrangement ( 200 . 300 ), designed according to a method ( 100 ) according to one or more of the preceding claims. Electric machine, characterized by at least one magnet arrangement ( 200 . 300 ) according to claim 5. Computer program product comprising program parts for carrying out a method ( 100 ) according to at least one of claims 1 to 4. Machine-readable, in particular computer-readable, data structure generated by a method ( 100 ) according to at least one of claims 1 to 4 and / or by at least one computer program product according to claim 7.  Machine-readable, in particular computer-readable, data carrier on which at least one computer program product according to claim 7 is recorded and / or stored and / or on which at least one data structure according to claim 8 is kept ready for retrieval.

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