EP3215964A2

EP3215964A2 - Calculation method for designing reluctance systems, and computer program

Info

Publication number: EP3215964A2
Application number: EP15778204.6A
Authority: EP
Inventors: Hans-Jürgen Remus
Original assignee: Individual
Current assignee: REMUS, HANS-JUERGEN
Priority date: 2014-08-12
Filing date: 2015-08-07
Publication date: 2017-09-13
Also published as: WO2016023627A2; WO2016023627A3; DE102014011911A1; US20170228340A1

Abstract

The invention relates to a calculation method for designing reluctance systems by balancing the inner and outer system energy using the equation W=½Λ (Θ_a ²+Θ_b ²+2Θ_aΘ_b), where 2Θ_aΘ_b≠0, according to claim 1. The invention further relates to a computer program comprising program code means, in particular a computer program stored on a machine-readable medium, for carrying out the disclosed calculation method when the computer program is executed on a computer.

Description

Calculation method for designing reluctance systems and a computer program

The invention relates to a calculation method for the design of reluctance systems by balancing the inner and outer

System energy is with, according to

first claim.

In addition, the invention relates to a computer program according to the tenth claim.

Between carriers of electric charges, between magnets, between current-carrying lines, and between magnetic poles and electrical line currents exist forces. The use of electric motors in the automotive sector is becoming increasingly important. Displace in transport technology

Linear motors conventional traction devices. To do so, there are more and more complex geometries

unconventional energy converters new calculation methods

to be provided.

It applies, such technical systems with complex geometry and under the influence of mag. Saturation to be optimally dimensioned.

To describe the static and dynamic properties of variable reluctance systems, there are currently three methods:

The calculation by using the Maxwellian stress tensor, the calculation by energy balancing, as well as an emanating from an equivalent circuit calculation.

The prerequisite of all three methods is to know the field distribution of the system in order to be able to calculate the forces and or moments. While with Maxwell's stress tensor the volume forces can be attributed to equivalent surface tensions, can be in the energy balance, the energy split by

Clearly describe volume integrals. The equivalent circuit as a discrete, idealizing idea of an energy distribution describes the technical system under restrictive

Requirements.

However, given the same conditions, the three deliver

Calculation approaches different results. The following will be the

Energy balancing explained in more detail following the state of science and technology.

So it is basically to determine that a

Calculation method of such reluctance systems can be set up as variable as possible, so that it can be assumed not by material constants, but by material functions. Here, an empirically given function D = D (E) or inverse E = E (D) is assumed as the electrification function. H = H (B) or also the inverse B = B (H), which is also empirical and as

Magnetizing function is assumed is used as the basis. (FIGS. 1, 2, 3) These functions are the foundations of a more general theory, such as the material-technical constants ε

(Permittivity) and μ (permeability) of the Proportionaltheorie are .. However, because of the nonlinearity of the

Soft iron magnetizing function does not apply the superposition principle. In the development of a corresponding

Calculation method will continue to be unique

Material functions assuming no hysteresis and isotropy. The general approach describes

- the proportionality theory with

- the magnetically soft substances with M = O, B = B (H) unique function with the point (O, O) positive functions

- The stabilized permanent magnets with

μ = const and the secondary loops with

- The remanentmagnetischen state curves with

Added the sizes:

where μ (Η) is the permeability, the function μ _d (Η) is the

differential permeability.

The same can be derived for the electrification function

The expressions for the functions from which the field forces as well as the inductance and capacitance coefficients are determined must be derived in terms of field theory, ie by Maxwell's equations and from the principle of the conservation of the total energy of a closed system. Prerequisite for this are in a finite volume τ carrier with electrical charges,

Line currents, permanent magnetization and the

Distributions of ε and μ. As the work of field forces at Deformations to determine the body is the Maxwell's equation in the form:

to be applied or in an advertised form:

Multiply the first equation from 004 by the second with and added

and integrate about the volume and applies the theorem of Gauss and takes for this the normal π of each surface element dÄ inward, one obtains following the state of science and technology:

Assuming that the envelope is infinite (the system itself is finite and complete) in the limit:

is the energy balance of the system:

Here is

as the total energy loss in volume by current heat t in the time span dt known. If one does not exclude quasi-stationary processes, then the two further integrals in the previous one can

Energy balance of the system can be explained as:

infinitasimale increase of the electric, the

magnetic field energy, infinitesimal work

ddeerr eelleekkttrriisscchheenn ,, magnetic field forces

displacements the carrier.

If one excludes such displacements preparatory: therefore everywhere in place d` / dt one obtains:

That means

the spatial density of the electrical and

the spatial density of the magnetic field energy The field energies are thus determined by:

Kicking displacements as a result of the FBld forces,

need for the determination of

Assumptions are made that

- the scalar μ

- The magnetization vector

- the spatial current density vector adhere to the matter. So you = 0 for constant H

where a fixed surface in matter called.

With respect to μ, this approach means neglecting the small changes, the μ by the change of shape of a

Body element experiences, and thus the low forces of

Magnetostriction. As far as M is concerned, this is an expression of a fact. In terms of is it a calculation rule; the actual process can be divided into two parts:

- Displacement of matter with adhering flow

- Shift of the flow against the matter.

Only the change of V _m is included in the calculation in the first sub-operation. These assumptions now apply to all further considerations. Similar considerations can then be made for the electric field.

Then in equations 009 the dW _el and dWn must unambiguously be the. Expressions found in equations Q10 to 013 ". Hence:

The calculation results

Analogy to the field energies is this too and denote V as the electrical, V as the magnetic el m

FORCE FUNCTION, because of these functions, the dV = dW, dV = dW from these functions, the field forces at thickening el el mec m mmec

calculates material body.

For the one hand, on the other hand applies after

And denote V _el as the electric, V _m as the magnetic

Forces function, because from these functions the field forces at displacements of material bodies are calculated via dVei = dWei mec dV _m = dW _m mec. For the W _el , V _el on the one hand, W _m , V _m on the other hand

If the thermal losses P _th dt = 0 in the energy balance Gl.007, according to the energy conservation law for a closed system dWeimec, the increase in the force of the field forces must be equal to the decrease in the field energies.

Out

in the cases ε = const, μ = const

The work is just as large as the increase in field energy: if energy is supplied to the incomplete system from the outside, the excess over the current heat loss energy is equally distributed to the work of the field forces and the propagation of the field energies. Starting from the derived energy balance (Eq.020) and the prerequisites met there, the mechanical forces of magnetic origin become stationary

magnetic field, determined using the principle of virtual displacement. The mechanical work involved in displacements of bodies as a result of the field forces is calculated from the force function.

If displacements occur in a constant external magnetic field (FIG. 4), it should be noted that the permeability μ changes in the fixed spatial point, despite the constant field

Indicates one

- the change in the fixed space point with

- the change in the fixed substantial point with d

- the infinitely small displacement with this results purely geometrically for a scalar u

and for a vector U, the already used expression in Eq.003

With

With the assumptions made under (Gl.003-007) and

since quasi-stationary processes were assumed results

So it's at constant magnetic field strength 8th

With

the mechanical work is calculated by

For the first term in the volume integral receives

The third link becomes too

Simplifies the second member of the volume integral

and add it, you get

With

which describes the force related to the volume unit.

It is composed of three parts: a force on electricity carriers

a force on carriers of magnetic quantities

- A force that acts on non-perfused and non-permanent magnetic bodies, but on bodies that are in their magnetic behavior of their environment

differ.

To establish an energy balance, the principle of virtual displacement is assumed. That requires one

Energy balance in the unfinished system.

Now, when the armature of the electromagnet (FIG 11) by a small distance _δ χ shifted and the current I kept constant in the winding, the magnetic flux Φ decreases at However, core, armature and the air gap by an amount δΦ and the magnetic flux density B ₂ by an amount δB ₂

As a result, a source voltage is induced in the circuit. To overcome this, the coil must do the electrical work be supplied. The magnetic energy stored in the soft iron core is

In the shift, it decreases by the amount

to.

As a result of the extension δ _x increases. internal energy by the amount:

In the air gap, the stored energy is increased due to the increase of Β ₁ and δΒ ₁ (Β ₁ = B ₂ ) and reduced by δ _χ due to the reduction of the air gap. Overall, this reduces the energy stored in the core and air gap

to.

Finally, in the displacement, the mechanical work

applied. The energy balance

results

It follows

Here, the specific area force p, at an interface between substances with different permeabilities, is equal to the difference of the energy densities in these permeable

Substances. Under these restrictive assumptions, the

Energy distribution in the electromagnet and the permanent magnet considered. It should be noted that in the permanent magnet, the internal energy has a greater influence on the force, as it is the case with the electromagnet. In order to study this energy distribution, one assumes the same hypotheses as initially described with a small air gap. In the case of the permanent-magnetic core, it is common practice in science and technology to distinguish between internal (index i) and external energy (index e) in general energy considerations (FIG. 5). For FIG.5 applies

A comparison of electrical and! Permanent magnet shows the present composition of field strengths:

From this follows the external and internal magnetic field strength

The air snap energy (external)

and Elektromagnet permanent magnet

The internal energy

With

The total energy (external + internal)

The different terms are now represented by the magnetic conductivities.

The graphic representation (FIG. 6) alone shows the strong influence of the internal energy density in the permanent magnet, while it is negligible in the case of the electromagnet. If one applies the Maxwellian stress tensor to one of the separating surfaces of the magnet then the difference of the fictitious tensions becomes on the left and on the right side of the interface, to determine the perceptible force. The following expression for the force results:

since only normal components of the magnetic field strengths were assumed. The magnetic field strengths are now replaced by the sizes of the current source equivalent circuit diagram. Integration over the face gives the force:

Corresponding considerations resulted for the electromagnet

Following the current state of science and technology, in equation 058 a "correction term" appears, which is based exclusively on the geometric dimensions of the air gap μ _r and the Permanent magnet length depends. Following the state of science and technology, the forces overlap without influencing each other. To explain this, the permanent magnet is surrounded by a current-carrying coil (FIG 8). It is so excited that the field of the permanent magnet and the field of the coil in the air space are rectified.

Where:

The field equations are written for the normal components of the magnetic field strength

This is followed by the external and internal magnetic field strength

The comparison according to the state of science and technology shows:

The subfields that come from the coil (Θ _b ), and the

Subfields that originate from the permanent magnet (M) are superimposed without influencing each other:

For the air gap energy (external) one gets the state of science and technology following, thus the expression

The internal energy is then calculated as follows:

This results in the state of science and technology following the total energy (external + internal)

And as magnetic conductivities:

and thus

61066

When compared with Equation 065, the state of science and technology concludes that the total energy of the combined field is equal to the sum of the individual amounts of energy that result when first sets M = 0 and then Θ _b - 0. There is no mutual energy between coil and permanent magnet. To clearly illustrate the interaction of this electromechanical system in an equivalent circuit diagram (FIG. 10), the energy balance requires a combination of voltage source equivalent circuit for the circuit and a current source equivalent circuit for the permanent magnet. The energy distribution of the permanent magnet and the electromagnet alone are also included as special cases in it. In the usual

Equivalent circuit diagram (FIG. 10) applies to a mutual energy:

This is mentioned by Remus in "Analysis of Variable Reluctance Systems Using Integral Equations" on page 48. Fischer also teaches in "Demolition of Permanent Magnetic Resonance," p Energy balance., And comes, as Remus concludes _> that due to lack of mutual influence of electric and permanent magnet, the last term "2Θ _a Θ _b " of the energy balance is negligible, since it = 0.

This term is also neglected by Multon in ENS Cachan - Antenna de Bretagne "Application of the aimants aux machines electriques" p.6 2005.

The invention is based on the object, a precise

To provide calculation methods for designing reluctance systems. This object is according to claim 1 by a calculation method for the design of reluctance systems by balancing the internal and external energy system with

By design is meant: dimensioning of the permanent magnets (length, height, width, shape),

Material selection, dimensioning of the electromagnet consisting of coil and core (length, height, width, shape, number of turns,

Coil conductor thickness, choice of material), dimensioning of the air gap (positioning of permanent magnet and electromagnet to each other), energizing the electromagnet.

the magnetic flux of the permanent magnet is and Θ _b = NI is the magnetic flux of the electromagnet and Λ represents the permanence. Here, H _e and H * are contrary to the state of science and technology:

Contrary to the state of science and technology, the second term of the energy balance 2Θ _a Θ _{b is included} in the calculation. In many metrological publications it is pointed out that a certain relationship between air gap length and

Permanent magnet length exists. Nevertheless, in order to be able to calculate the force approximately, one led a "correction factor" - increase of the

Scattering factors - one. The leakage fluxes are too big

as already observed on anisotropic materials. A look at the magnetization curve B over H clarifies the geometric conditions. (FIG. 12) The degrees of shear 2 connect the zero point to the point of the magnetization characteristic curve of the permanent magnet for I = 0. The result is the intersection point 3, which is referred to as the operating point. Zero point (B / H) operating point 3 and intersection of the magnetization line 1 with the ordinate B create a triangle. This triangle

describes the external energy (density) of the permanent magnet. in addition Now comes the external energy (density) of the electromagnet, which, however, affects the total energy of the permanent magnet, so that the total energy of the reluctance system consisting of the total energy of the permanent magnet and the total energy of the electromagnet by the amount 2Θ _a Θ _b grows. These are the two parallel loops with the width between the points 4 and 5. Where 6 represents the new operating point of the reluctance system, and 7 the value shifted on the abscissa H by Θ _b / I ₁ . FIG. 12 shows that two parallelograms 2Θ _a Θ _b are formed which span the surface 2Θ _a Θ _b . This has also confirmed measurement results (FIG 13). After a preferred calculation variant is doing the

magnetic potential of an electromagnet Θ _b , which is a value dependent on the current (I), chosen such that

and the following calculation steps are performed: a) Use of a starting value with 1 = 0 and a second one

Value I ₁ which is between 1 = 0 and I = I _saturation (for Θ _b ), b) calculation of an evaluation value Β ₁ , which is a measure for the leveling of the balancing between Θ _a and Θ _b with

c) Calculation of a second evaluation value B ₂ for an I ₂ with the assumption

I ₁ <I ₂ <I _saturation for Θ _b ,

d) at B ₂ <Β ₁ set B ₂ as the new valuation standard.

The aim of such a calculation is the calculation of a

Working point at the

(FIG. 13) A value that is approaching 1 is to be understood as minimum. The rating value is understood to be any value that increases as the sum of the energy balance increases. This can be done, for example, by multiplying at least one of the values by a random number or by adding a value to at least one of the values (I). The measure of

The change is proportional to the valuation value and inversely proportional to the number of changes, so that after a large number of changes, the optimization of the valuation pattern is almost completed. The significant change in arousal takes place at the beginning of the optimization. A fast changing one

Rating value delays the end of the optimization, but can also restart the near-completed optimization. If the rating is ideally minimal, then the energy balance goes to 1 and a new calculation no longer takes place. The operating point of a corresponding system has been determined according to the prior art by the point which is the intersection of shear rates and the magnetization characteristic of the permanent magnet, with the assumption that 1 = 0. Considering 2Θ _a Θ _b , the operating point is now searched for not on the magnetization curve but on the degrees of shearing.

According to another preferred embodiment, before the

described energy balance

a) an input of the data of the reluctance system partners,

b) a determination of the magnetic resistances as a function of the entered data,

c) output the values of the values obtained under b) as

spline functions,

d) a determination of the magnetic Zwischenereichu reluctances e) the establishment of at least one nonlinear

Equation system with the steps b) -d)

generated values,

f) a leveling of the nonlinearity of the system of equations according to e) made by a mathematical model to obtain the output values.

Consists e.g. a Relunktanzsystempartner from an electromagnet with a toothed structure, is after the

Integral equation method of the equivalent magnetic conductance or the attractive force and thrust known for a particular position. To get unknown intermediate values from these ordered

To obtain value pairs, an interpolation must be made. Compared to other interpolation methods, interpolation using spline functions shows significant advantages. By interpolation in the narrower sense, we mean the reconstruction of a function f (x) from values f (xi) given at discrete places xi. From the technical

The problem generally follows that there must be a continuous function f (x) for which f (xi) = »fi. Since f (x) is unknown except for the base values fi, one looks for a comparatively "simple" function for calculations at the interpolation points

While the error at the nodes x ₁

Nothing can be said about its course in the interval [a, b] iA. Thus one finds the assumption that / the unknown function f (x) approaches [a, b]. The determination of values (x) for arguments x ∈ [a, b], x x _i is referred to as interpolation. From a function f (x) j whose analytic form is unknown, from the interval [a, b] at finitely many nodes x _{i are given} their fundamental values fi in a Cartesian coordinate system.

It is defined that x _i grow monotonously. One way to connect these points by an often differentiable smooth curve, is the always existing LAGRANGE 'see

interpolation

or the algebraic polynomial

However, these polynomials vary with increasing number and choice of interpolation points. On the other hand, the smallest possible degree of polynomial between every two points is the polyline. Although the fluctuation of the interpolating function is minimal, but the

Discontinuity at the node begins at the first derivation; In addition, these curves are not smooth, as shown in FIG 16.

Particularly useful is a compromise between polygon and interpolation polynomial higher degree: thereby

low-grade and therefore weakly fluctuating polynomials to a function which is as often as possible differentiable throughout the interval [a, b] connected. The application of the rational spline function shows the edge and longitudinal effects of the linear motor. (FIG. 17) When designing a corresponding reluctance system, it is particularly advantageous to level the occurring nonlinearities by a mathematical model. This becomes true when using the integral equation method

provided that the boundary conditions are known and the space to be considered is linear.

In the cases considered, this space is represented by the air gap zone. The edge is formed by the stator and rotor surfaces. On the surfaces are then the

Specify boundary conditions. In general:

Since stator and rotor in the cases considered

Ferromagnetic materials are made, the surfaces are considered from the outset as "non-linear edges". This means that the boundary conditions to be specified depend on the saturation state. Preferably, in the course of a

Computation method a leveling of the nonlinearity of the equation system by using the derived

stress tensor performed

In order to be able to theoretically detect the nonlinearities of the derived stress tensor for nonlinear

Material functions of the relationship:

went out. Where:

With this tensor p, the fictitious stress state in the nonlinear medium can be described as follows: For each area unit perpendicular to the field H, a normal train of magnitude acts along the field lines:

and on each surface unit parallel to the field H, a normal pressure of the magnitude acts across the field lines:

Thus, in the ordinary non-linear magnetizing functions, the transverse pressure is always greater than the longitudinal tension (FIGS. 18, 19). Tensile and compressive stresses are therefore different from each other.

L + Q = B H

It is L the magnetic energy density w and Q the

magnetic force density function v. w + v = B H

everywhere where the Nagnetisierungsfunktion is linear, is

Only the fictitious magnetic tensile and compressive stresses are the same for a straight-line magnetization function. If you place now arbitrarily a surface - in any position - with the

Area normal in the magnetic field H, the stress tensor p can be represented by different expressions:

This is true if α is the angle between the magnetic field strength H and the unit normal n. The vector diagram (FIG. 20) shows this relationship. The comparison with the as constant

assumed magnetization function shows that not only the amount of p changes. Also, the angle β between p and the magnetic field strength H is at a common

Magnetizing function always be greater than the angle α between the magnetic field strength H and the

Area unit norms n. To the mechanical stresses

magnetic origin at a separation surface, formed by two bodies with different nonlinear magnetization functions., be able to determine surface currents and magnetic

Area charges excluded.

As the normal component of the magnetic flux density and the tangential component of the magnetic field strength On both sides of the surface each have the same values, you get

as a perceptible force on the area unit

The perceptible force is directed perpendicular to the separation surface, a thrust does not occur. Considering the case in which the body (2) is iron and the body (1) is air, we obtain

If α ₂ does not come too close to a right angle, w ₂ and V _{2 are} small compared to W ₁ = v ₁ and the first term outweighs W ₁ , ie

When the lines of force in the iron are grazing into the surface (α ₂ approximately 90 °), the density of the direct line in the iron becomes considerably greater than in the air; W ₂ and V ₂ are therefore next

W ₁ = v ₁ . The field lines in the air then form almost a right angle with those in the iron, and the transverse pressure of the field lines in the iron supports the almost rectilinear longitudinal course of the

Field lines in the air, which in ordinary cases alone

is perceived, now considerably (FIG. 22)

This explains that with electromagnets, the tensile forces so often exceed expectations. The non-linear magnetization function of the iron causes the amount of p ₂ and the

Increase supplementary angle ß for this angle of incidence α ₂ . On the resulting vector p _21, the increase in amount acts in the same direction; she supports him. This is the explanation that in saturated materials one can obtain a greater force or a greater moment, as with many

electromechanical systems were observed. It can be clearly seen that the properties which are fully symmetrical with constant permeability are lost due to the non-linear magnetization function. Advantageously, the reluctance system consists of rotor and stator of an electric motor. Of course, the term "electric motor" also includes linear motors. Another particularly advantageous embodiment is described by a calculation method wherein the determination of the Zwischenbereichsreluktanzen by determining the Luftspaltreluktanzen depending on the rotor position α _{n is} replaced and last n-fold repetition of the calculation steps with the now obtained values for each rotor position α _n follows. This is exemplified by a

Differential reluctance three-phase motor, the stator lamination shown in FIG 23 has twelve toothed poles with ten teeth each. The resulting tooth pitch corresponds to a total number of teeth of 132 teeth, since the gap between each two poles equals a Statorzahnteilung. The in the

Statornuten housed three-phase winding generated under

Addition of diodes a four-pole rotating field.

The bladed rotor (FIG 24) with its 130 teeth, which carries neither a winding nor a cage rotates with synchronous

Angular velocity of n = 23.08 1 / min. As a result of this tooth structure defined from the outset, the rotor angular velocity can thus be reduced without additional gear. An engine with these characteristics is called a differential reluctance motor. In this case, a common rotor and Statorabwicklung is determined. FIG. 25 shows the partial development of rotor and stator. In the air gap zone 1, the teeth of rotor and stator are exactly opposite. For this position, the magnetic conductance reaches its maximum value. Now moves the rotor from stator tooth 1 to stator tooth 2, the shifts

magnetic axis to the air gap zone 2 out. The rotor has the way

covered, while the magnetic axis around the

Statorzahnstellung has moved on. Substituting in equation 078 the number of teeth of the rotor N _r and the stator N _s , forms the quotient of the rotating field speed of the magnetic axis and the rotor speed, we obtain

This reduction factor R is dependent exclusively on the number of rotor and stator teeth, which results in a synchronous rotor speed which represents a fraction of the rotating field speed of the stator.

For the concrete calculation of this differential reluctance motor, the following assumptions are made: The material used is homogeneous and isotropic

- The permeability in iron is infinite

- The occurring asynchronous torque is negligible

- The air gap can be divided into constant air gap zones, from which the magnetic conductance can be calculated

- Scattering influences are negligible. Under these conditions, the magnetic conductance of each

Calculated air gap zone; with a hatched area in FIG. 4 FIG. 25, with a certain rotor position for which the equivalent magnetic conductance can now be calculated according to the integral equation method. To obtain the associated analytical expression, these calculated guide values are interpolated by means of a compensating periodic spline function.

The measured static torque is plotted for different currents as a function of angle. For I = 600 mA, the maximum torque is T = 14.10 Nos. The calculation gives T = 15.48 N · m for the same current. (FIG 26)

For the dynamic behavior, the current was measured and

calculated. The rotor moves two steps further. The stationary current is 1 = 600 mA. Thus there is one

Match between calculation and measurement. (FIG. 27)

According to a preferred variant of the invention, following the n-fold repetition of the calculation of the air gap resistances with the now obtained values for each rotor position, the previous calculation step follows the determination of its torque by the induced voltage of the electric motor. This has the advantage, in particular for geometrically complex reluctance systems, that all reluctance components are taken into account in the calculation. In the same way, you can reverse the calculation so that you can calculate various possibilities to geometrically design a reluctance system so that the motor achieves the required performance characteristics. Under performance characteristics is thereby achievement and

Torque of the engine to understand. Following a particularly advantageous embodiment becomes Determining the spline functions uses an equivalent circuit diagram, which consists of a combination of voltage source equivalent circuit diagram and power source equivalent circuit diagram. Here are preferred the inner and outer energy, as well as the total energy in the

Equivalent circuit diagram shown; The respective magnetic conductivities represent the corresponding energies. Following the state of science and technology, it can be seen that the permanent magnet circuit as a voltage source equivalent circuit is incomplete in terms of internal energy and overall energy balance.

A corresponding equivalent equivalent circuit is shown in FIG 29, 30. Based on the tensile force exerted on the one half of the ring of the permanent magnet, the representation of the energy densities., Based on the permanent magnet volume, in the B (H) diagram proves to be advantageous to compare the energy ratios of the electromagnet and permanent magnet can. For this purpose, the equations (063) to (066) are used and the energies on the

Relative permanent magnet volume.

These energy densities are shown in FIGS. 31, 32. If one now assumes the energy balance in the incomplete system, taking into account the assumptions assumed to be linear

Material functions, as shown in FIG 33, 34 for the mechanical work related to the magnetic volume

Charts. The object mentioned above is also by a

Computer program with program code means, in particular a computer program stored on a machine-readable carrier, for

Implementation of the method according to one of the preceding

Claims when the computer program is run on a machine is solved. The computer may in particular be a microprocessor or microcontroller. Accordingly, the computer program is then executed on this computer software. The

Computer program can then be stored in a memory of the microprocessor or the microcontroller. The computer program may also be stored on other machine-readable carriers, e.g. on removable carriers such as CD-ROM or memory stick.

The invention is explained in more detail below with reference to examples and associated figures. This alone serves the

Illustrate the invention without limitation

General public.

1, 2, 3 show the magnetization functions of the air gap, soft iron and permanent magnet.

FIG. 4 shows the change in permeability despite a constant external field.

5 shows a comparison of electric and permanent magnet.

FIG. 6

Shows a graphic representation of the mechanical work related to the magnetic volume of permanent and electromagnet.

FIG. 7 - Missing

8 shows a simple sketch of a permanent magnet with exciting coil.

9 FIG.

FIG. 10 shows a spare diagram to be counted with the state of the art in science and technology with Θa and Θb which has hitherto been used. FIG. 11

Shows a model of an electromagnet.

FIG 12 shows the magnetization characteristics of electric and permanent magnet, and the shear line with the corresponding geometric relationships.

FI6 13 also shows the magnetization characteristic of electric and

Permanent magnet as well as the shear line and measured values for different air gap sizes.

FIG. 14 shows a variant of a flowchart for calculating

Reluctance system partners.

FIG. 15 shows a further variant of a flowchart for calculating the reluctance system partners.

FIG. 16 shows a compilation of polygonal and

Interpolation.

FIG. 17

Representation of a modulation function by six partial polynomials.

FIGS. 18, 19 show the occurrence of transverse pressure and longitudinal tension in relation to the magnetization function.

FIG. 2O, 21

Represents the linear case and the nonlinear case of a

Magnetization in a vector diagram opposite.

FIG. 22 shows a two-dimensional vector diagram for a non-linear magnetization function of iron.

FIG. 23 shows a stator lamination section of a three-phase motor.

FIG. 24 Shows a partial section of a stator pole and an opposite rotor.

25 shows a stator / rotor development,

FIG. 26 shows the statically measured torque which has been plotted over various currents as a function of the angle α.

FIGS. 27, 28 show the current profile over the time that was related to the motor steps.

29 shows the conventional representation of voltage sources and power source replacement diagram.

30 shows the equivalent circuit diagram, which influences the

Reluctance system partners considered. FI6 31, 32 shows the energy density distribution of electric and permanent magnet.

33, 34 shows the mechanical work related to the magnetic volume of the electric and permanent magnet.

1, 2, 3 show the magnetization functions of the air gap, soft iron and permanent magnet. 1 shows a linear magnetization function in the air, FIG. 2 shows a non-linear magnetization function for soft iron, and FIG. 3 shows a permanent magnetization function for permanent magnets.

4 shows the change in permeability despite a constant external field. In the case of displacements in a constant external magnetic field, the permeability μ in the fixed spatial point changes with a constant magnetic field

FIG. 5 shows a comparison of electric and permanent magnet. With the air gap dimensions l _e / 2 and the inner dimension l _i / 2 at a current I and a number of turns N. The same also applies to the permanent magnet.

6 shows a graphic representation of the mechanical work related to the magnetic volume of the electric and permanent magnet, which are compared here.

FIG. 7 - Missing

8 shows a simple sketch of an electromagnet.

9 FIG.

FIG. 10 shows a spare diagram to be counted in the state of science and technology with Oa and Ob which has hitherto been used.

FIG. 11 Shows a model of an electromagnet with a yoke 1, a core 2 and two anchors 3,4 and an air gap 5.

It is

1 intersection between the magnetization characteristic of the permanent magnet and the abscissa, 2 is the shear rate of the reluctance system,

3 is the intersection between magnetization characteristics of

Permanent magnets and shear rates with I = O,

4 is the point on the degrees of shear with the point 5

geometric ob corresponds. 5 is the corresponding point on the ordinate.

6 is the newly calculated operating point of the reluctance system in which the energy balance is minimal.

7 is the shifted lower vertex of the parallelogram 4-5 6-7 of width Θb and height Θa (or vice versa).

13 shows the ratios obtained by measurement of a

Reluctance system with 1 magnetization characteristic permanent magnet with a shear rate

2 for an air gap width of 2 mm

3 is the magnetization characteristic el. Magnet

4 the degrees of shear a reluctance system with a

Air gap width of 4 mm.

5 shows a collection of measurements on the

Magnetizing function of the permanent magnet with an air gap width of 2 mm

6 are the measured values of the magnetization function of the

Electromagnet.

7 shows the intersection of the magnetization function with the ordinate.

8 is the measured external operating point el. Magnet

9 is the conventionally calculated working point of duration and el. Magnet 10 saturation point of the el. Magnet

11 is the measured operating point of duration and el. Magnet

FIG. 14 shows a flowchart of a calculation algorithm with which geometrically complex reluctance systems can be calculated.

For each position of the electromagnet is a new

Solved equation system, because for each position different

Air gap reactances must be considered. It starts with Entering the geometries of the positions of the system partners (angle and distance) taking into account the respective model. The result is a frame file that determines resistance in the iron parts. After input, these are output as constant values or as spline functions. Based on the considered rotor position a _n , the air gap resistances are determined. All resistors and magnetic voltage sources serve as input data for the calculation program. The calculation of the nonlinear

The system of equations takes place in an outsourced calculation file which is called by the frame file and which receives the energetically balanced relevant quantities. Subsequently, an evaluation of the values obtained, which results in either the calculation of the paged calculation file is terminated or takes place again with a new starting value. In several

Iterationsschritten while the equation system can be solved. The start value is the zero vector. The output values include potentials, flux values and resistances of the magnetic circuit. This is repeated for every angle. At the conclusion of the calculation, all results are summarized and the voltage induced in the coils and strings as well as the torque of the system are determined.

FIG. 15 shows the more concrete variant for calculating a

The electric motor.

FIG. 16 Vendeutlicht the discontinuity of a traverse to the final derivative.

FI6 17

Create a modulation function by six partial polynomials

FIG. 18, 19 shows the unfreezing of quench and longitudinal traction with respect to the magnetizing function B, H.

Dnuck voltages of one another are different.

FIGS. 2O, 21 illustrate the linear case and the nonlinear case of FIG

Magnetizing in a vector diagram.

FIG. 22 shows a two-dimensional vector diagram for a nonlinear magnetization function of iron.

FIG. 23 shows a staton plate section of a diphasic motone.

FIG. 24 shows a partial section of a stator pole and an opposite rotor.

FIG. 25 shows a stator / rotor development.

FIG. 26 shows the statically measured torque that has been plotted over various currents as a function of the angle α.

FIGS. 27, 28 show the current variation over time, which was related to the motor steps.

29 shows the representation of voltage sources and

Current source replica graph that takes into account the internal energy densities under mutual influence.

30 shows the equivalent circuit diagram, which influences the

Reluctance system partners considered.

FIG. 31, 32 shows the energy density distribution of electric and permanent magnet.

where:

Claims

claims

1. Calculation method for the design of reluctance systems by balancing the internal and external energy system with

2. Calculation method according to the preceding claim, wherein the magnetic potential of an electromagnet Θ _{b is} a current dependent on the current (X) value to be chosen so that is minimal but> 1

with the steps: a) using a starting value with I = 0 and a second value I ₁ which lies between I = 0 and I = I _saturation (for Θ _b ),

b) calculation of a score Β ₁ , which is a measure of the

Leveling the balance between Θ _a and Θ _b is with

c) Calculation of a second evaluation value B. for an I. with the assumption

I ₁ <I ₂ <I _saturation for Θ _b ,

d) at B ₂ <Β ₁ set B ₂ as the new valuation standard.

3. Calculation method according to at least one of the preceding claims, wherein prior to energy balancing a) an input of the data of the reluctance system partners,

b) a determination of the magnetic resistances as a function of the entered data, c) an output of the values of the values obtained under b) as spline functions,

d) a determination of the magnetic intermediate region reluctances, e) the establishment of at least one non-linear system of equations with the values generated by steps b) -d),

f) a leveling of the nonlinearity of the system of equations according to e) by a mathematical model is carried out in order to obtain the output values.

4. calculation method according to the preceding claim, wherein the.

Leveling the non-linearity of the equation system according to claim 3 f) by using the derived stress tensor

he follows .

5. calculation method according to at least one of the preceding

Claims, wherein the reluctance system is an existing of rotor and stator electric motor.

6. calculation method according to at least one of the preceding

Claims 3,4 o. 5, wherein

the method step d) of the third claim by a

Determination of the air gap resistances as a function of

Rotor position α _{n is} replaced and the last step of the third claim an n-fold repetition of the calculation of

Air gap reactances with the values now obtained for each rotor position α _n follows.

7. Calculation method according to the preceding claim, wherein the last step is followed by a further step, by which the induced voltage of the electric motor and its torque is determined.

The calculation method of claim 3, wherein the last step is followed by a further step by which the dimensioning of the permanent magnet is made.

9. A calculation method according to at least one of claims 3,4,5,6,7 or 8 wherein for determining the spline functions a

Substitute circuit diagram is used, which consists of a combination of voltage source equivalent circuit diagram and power source equivalent circuit diagram.

10. Computer program with program code means, in particular computer program stored on a machine-readable carrier, for carrying out the method according to one of the preceding

Claims when the computer program is run on a computer.