EP2340601A2

EP2340601A2 - Rotating electric machine

Info

Publication number: EP2340601A2
Application number: EP09736392A
Authority: EP
Inventors: Lin Feuerrohr; Steven Andrew Evans
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 2008-10-21
Filing date: 2009-09-24
Publication date: 2011-07-06
Also published as: DE102008042976A1; CN102257710A; JP2012506683A; WO2010046196A3; JP5586613B2; WO2010046196A2

Abstract

The invention relates to a rotating electric machine (10) comprising a stator (20) having a plurality of poles (28), and a rotor (30) having a plurality of poles (32, 38), wherein at least either a first pole (28) of the stator (20) has a width that differs from a width of a second pole (28) of the stator (20), or a first pole (32, 38) of the rotor (30) has a width that differs from a width of a second pole (32, 38) of the rotor (30).

Description

description

title

Rotating electrical machine

The present invention relates to rotary electric machines which have a cogging torque, for example due to excitation by permanent magnets. Further, the present invention relates to a method of designing a rotary electric machine.

State of the art

For a number of technical, economic, environmental and social reasons, electric drives have a large and still rapidly growing distribution. In addition to track-bound and lane-bound land vehicles and watercraft, the first man-bearing aircraft are already electrically powered. Actuators that have been hydraulically realized in the past, for example, are increasingly being realized electrically.

A permanent magnet-excited rotating electrical machine has a cogging torque at least in the de-energized state. This cogging torque is a torque whose magnitude and direction depends on the angular position of the rotor. The rotor engages in those positions in which one or more pole transitions of the stator each lie opposite a pole transition of the rotor. In many applications, the cogging torque interferes or poses a safety risk. One example is an electric power steering system or steering power assistance of a motor vehicle. In case of failure of the electrical support, it should be possible to steer the motor vehicle with muscle power. A cogging torque is so disturbing that it increases the risk of accidents, which is already increased anyway at the moment of failure of the power steering, again significantly.

There are a number of measures to the cogging torque of an electric

Reduce machine, for example:

- axial skew or helical or helical configuration or gradation (in the form of a spiral staircase) of the permanent magnets and / or the slot slots between the winding teeth;

- Polabhebungen in the vicinity of Polübergänge;

- enlargement of the air gap;

- closed or very small slot slots.

Each of these measures has specific disadvantages, such as an increase in manufacturing costs, poor scalability, a reduction in the efficiency or a reduction in the achievable drive torque.

An object of the present invention is to provide a rotating electric machine with a reduced cogging torque and a method for arranging pole transitions on the stator and / or rotor of a rotating electrical machine.

This object is solved by the subject matters of the independent claims. Further developments of the present invention are defined in the dependent claims. Disclosure of the invention

The present invention is based on the recognition that the total cogging torque of a rotating electrical machine is the sum of individual cogging torques that arise in each case due to the meeting of a pole transition of the stator and a pole transition of the rotor. A Polübergang is, for example, a gap or a slot between two tooth tips or between two pole pieces. In many conventional rotating electrical machines, at certain angular positions of the rotor, several pole transitions of the stator each are opposite to a pole transition of the rotor at the same time. On this basis, exemplary embodiments of the present invention are based on the idea of varying the spacings of the pole junctions instead of a spacing between two adjacent pole junctions that is the same for all poles of the stator or of the rotor, so that at least one pole of the stator has a width which differs from the width of another pole of the stator, or that one pole of the rotor has a width that differs from the width of another pole of the rotor. The width of a pole can be defined, for example, as the distance between the centers of the two pole junctions adjacent to the pole or as the distance of the two boundaries of the pole. Furthermore, the width of a pole as

Angular dimension based on the axis of the electric machine or be defined as a linear measure.

By different widths of the poles of the stator and / or different widths of the poles of the rotor can be achieved with a suitable arrangement or distribution of the poles of different width, that the number of pole transitions of the stator, which are each opposite a pole of the rotor , and thus the cogging torque can be reduced.

An electric machine includes a stator having a plurality of poles and a rotor having a plurality of poles, wherein at least either a first pole of the stator has a width that is one width of a second PoIs of the stator is different, or a first pole of the rotor has a width which is different from a width of a second pole of the rotor.

In a method of designing an electric machine, a first width and a second width different from the first width are set, and then a pole of the first width and a pole of the second width on a stator or rotor of the rotating electrical Machine provided.

In a method of manufacturing an electric machine, the electric machine is designed according to the above-described method and then manufactured.

An electric machine in the sense of the present invention can be, for example, a machine provided for direct current or alternating current and can have a commutator or be electronically commutated. The rotor of the electric machine can be designed as an internal rotor or as an external rotor. Both the stator and the rotor may be wholly or partially excited by permanent magnets, all or, for example, in a subsequent pole arrangement (English: consequent pole), only a part of the poles may have a permanent magnet. Permanent magnets can be designed as surface magnets, spoke magnets, buried magnets, etc., several magnets can be summarized in a one-piece component. The electric machine can be designed predominantly or exclusively for a generator operation or predominantly or exclusively for a motor operation or for both modes of operation.

In order to avoid induction of circulating currents within a parallel circuit of several windings and corresponding losses, it may be advantageous to switch windings which are assigned to the same phase not in parallel but in series. Brief description of the figures

Embodiments will be explained in more detail with reference to the figures. Show it:

Figure 1 is a schematic representation of an electrical machine;

Figure 2 is a schematic representation of an electrical machine;

Figure 3 is a schematic representation of an electrical machine;

Figure 4 is a schematic representation of an electrical machine. Embodiments of the invention

An electric machine has a stator with N _s poles and a rotor with N _R poles. Between two adjacent poles of the stator or the

Rotor is each a pole transition. In the following it is initially assumed that the angular distance a _s between two adjacent pole junctions for all pole transitions of the stator

360 °. 2π, _,. , α ₉ = or α ₉ = (Equation 1)

N _s N _s

is, and that the angular distance a _R between two adjacent pole transitions for all pole transitions of the stator

a "= or a" = (equation 2)

N N

is. The angular distance a of adjacent pole transitions is the angle between the centers of adjacent pole transitions with respect to the axis of the rotor. At a full revolution of the rotor, d. H. a rotation around

360 ° or 2π, each of the N _s pole transitions of the stator encounters each of the N _R pole transitions of the rotor exactly once. These are altogether N _s ^■ N _R

Encounters between each pole transition of the stator and a pole transition of the rotor.

The case is considered where, at the same time, u ₀ pole transitions of the stator each lie opposite a pole transition of the rotor. The angular distance δ between two pole transitions of the stator, which are each opposite a pole transition of the rotor, must be an integer multiple d _{s of} the angular spacing a _{s of} adjacent pole transitions of the stator, δ = d _s - a _s . At the same time, the angle δ must be an integer multiple d _{R of} the angular spacing a _{R of} adjacent pole transitions of the rotor, δ = d _R - a _R. The minimum angular distance S ₀ between two pole transitions of the stator, which are each opposite a pole transition of the rotor, is thus the smallest common multiple kgV (a _s , a _R ) of the angular distances a _s , a _{R of} adjacent pole transitions on the stator or Rotor,

δ ₀ = kgV {a _s , a _R ). (Equation 3)

For the product of the least common multiple kgV (x, y) and the largest common divisor gcd (x, y) of two numbers x, y applies in general

kgV {x, y) - gcd (x, y) = x - y. (Equation 4)

This general identity applied to the variables involved here

k ig WV [a _s , a _R ϊy ggT H [a _s , a _R \) = a _s - a _R = - ³⁶⁰ ° ³ - ⁶⁰ ° K or kgV {a _s , a _R ) - ggT {a _s , a _R ) = a _s - a _R = ^ ~. (Equation 5)

The number u _{0 of} the pole transitions of the stator, which are each opposite a pole transition of the rotor, is equal to Equation 3 360 ° 360 ° _u 2π 2π u _o = = -. r or u _o = - = ₇ r. (Equation 6) δ ₀ kgV {a _s , a _R ) δ ₀ kgV [a _s , a _R )

The larger the number u, the larger the cogging torque in the corresponding rotor positions. From equations 5 and 6 follows

U _n = R or u ₀ = ₍ ^π ; = gcd {a _s , a _R ) ^{s R.} (Equation 7) kgV {a _s , a _R ) 2π

For the number n _{r of} the rotor positions, in which a plurality of pole transitions of the stator each lie opposite a pole transition of the rotor, applies

n _r -u ₀ = N _s -N _R. (Equation 8)

From Equations 7 and 8 follows

N _s ^■ N _R 360 ° n = - - = -, r resp.

U ₀ ggT {a _s , a _R )

N _s -N "2π ._. , , n = - - - = ₇ r. (Equation 9)

U ₀ ggT {a _s , a _R )

For the angular distance p between two adjacent rotor positions, in which several pole transitions of the stator each have a pole transition of the stator

Rotor are opposite, applies

n _r -p = 360 ° or n _r -p = 2π. (Equation 10)

From Equations 9 and 10 follows (Equation 11)

The commutative law applies to both the least common multiple and the largest common divisor

kgV {y, x) = kgV {x, y) or ggT {y, x) = ggT {x, y) (Equation 12)

and the distributive law,

kgV {nx, ny) = n-kgV {x, y) or gcd {nx, ny) = n- gcT (x, y). (Equation 13)

Distributivity and commutativity are followed by general identity. (Equation 14)

From equations 4, 11 and 14 follows

360 ° _H. _{τ ΛT} x 360 ° p = gg ^τ {N _s , N _R ) = or

N _s -N _R ^ää * ' ^R) kgV (N _s , N _R ) p ₌ - * L-gg _T {N _s , N _R ) =? * (Equation 15)

N _s -N _R kgV (N _s , N _R )

From the equations 10 and 15 follows for the number n _{r of} the rotor positions in which a plurality of pole transitions of the stator are each opposite a pole transition of the rotor,

n _r = kgV {N _s , N _R ). (Equation 16) From the equations 4, 8 and 16 follows for the number u _{0 of} the pole transitions of the stator, which are each opposite to a pole transition of the rotor,

₌ N ₁₁ N ^ ₌ AT - N _{= (} y (Equation 17) n _r kgV {N _s , N _R )

Now consider an angle segment of the electric machine with the angular width δ ₀ . In this angle segment at most exactly one pole transition of the stator is opposite to a pole transition of the rotor. The electric machine comprises u ₀ equal such angle segments. If, in an angle segment, a pole transition of the stator is opposite a pole transition of the rotor, a pole transition of the stator is also opposite a pole transition of the rotor in each of the other angle segments.

As already mentioned, the greater the number u _{0 of} the pole transitions of the stator, which are each opposite to a pole transition of the rotor, is the greater the cogging torque. It follows from equation 17 that the cogging torque is smaller, the smaller the greatest common divisor gcd (N _s, N _R) of the number

N _{s is} the pole of the stator and the number N _{R of} the poles of the rotor. The cogging torque is therefore minimal when N _s and N _{R are} prime. The number

However, N _{s of} the poles of the stator and the number N _{R of} the poles of the rotor are seldom freely selectable. For example, the number of poles of a stator or rotor equipped with permanent magnets is usually straight, while the number of winding poles of a stator of a rotating field machine is often a multiple of three.

The statements made so far relate to an electrical machine in which the angular separation a _s between two adjacent pole junctions is the same for all pole transitions of the stator, and in which the angular spacing a _R between adjacent pole junctions for all pole transitions of the stator

Rotor is the same (compare equations 1 and 2). Deviating from this, the following explanations relate to an electrical machine in which the angular spacings of the pole transitions either at the stator or the rotor are not constant. For the sake of simplicity, it is assumed below that the angular distances vary with the stator and are constant in the rotor. By interchanging the terms and quantities relating to the stator and rotor, however, a description of a corresponding arrangement results in which the angular spacings in the stator are constant and vary in the rotor.

The stator is subdivided into u ₀ predetermined stator sections i, i = 1,..., U ₀ , each having the angular width δ _ι = δ ₂ =... = Δ _u = δ ₀ , the subdivision of the features described below no further physical features implied. For example, the stator can still be carried out in one piece without any problems or consist of several parts whose boundaries do not or only partially coincide with boundaries between the stator sections.

Within each stator section, the angular distance a _s between adjacent pole junctions is constant. However, the angular distance a _{S ι ι + ι} between adjacent pole transitions, which are not assigned to the same stator but adjacent stator sections i, i + l, deviates from the angular distance a _s between adjacent pole transitions within a Statorabschnitts, a _{S ι ι + ι} ≠ a _s . Let p ₀ be the angle between two nearest neighboring rotor positions in which, in the case defined by Equations 1 and 2 (all angular distances a _s between adjacent ones)

Pole transitions of the stator equal and all angular distances a _R between adjacent pole transitions of the rotor equal) several pole transitions of the

Stators at the same time each lie opposite a pole transition of the rotor. By equation 15 applies

360 °. 2π, _,. ,

P _n = -. r or O _n = -. r. (Equation 18)

u ₀ is the number of poles of the stator which, in the case defined by Equations 1 and 2 (all angular distances a _s between adjacent pole overlays) gears of the stator equal and all angular distances a _R between adjacent pole transitions of the rotor equal) at the same time each lie opposite a pole transition of the rotor. According to equation 17 applies

u _o = gcd {N _s , N _R ). (Equation 19)

If the difference a _{S l l + ι} - a _{s of} the angular distance a _{S l l + ι} at the boundary between two stator sections and the angular distance a _s within a Statorabschnitts is not a whole multiple of p ₀ ,

a S, ι, ι + l - (X c

^" - £ IN _O (Equation 20)

P ₀

If the positions of the rotor in which a pole transition of the stator in the stator section i is opposite to a pole transition of the rotor no longer coincide with the positions of the rotor in which the adjacent stator section

/ + 1 a Polübergang the stator is a Polübergang the rotor opposite, together. Relative only to these two adjacent stator sections so that the number of locking positions have doubled and reduces the cogging torque. An equivalent to Equation 20 description is that the pole transitions within the stator z, / + 1 by a displacement angle S ₁ and ε _{1 + ι} from the positions of the equations

1 and 2 defined are shifted, wherein the displacement angle S ₁ is the same for all Polübergänge within the Statorabschnitts i, and wherein the displacement angle ε _{1 + ι} for all Polübergänge within the stato cut / + 1 is the same, but the displacement angle S ₁ , ε _{1 + ι} are different from each other and their difference is not an integer multiple of p ₀ ,

^ε ' ^ε ' ^{+ ι} £ IN ₀ . (Equation 21)

po In extension of the stator for two adjacent described pole transitions can within each stator z, z, M may be ₀ shifted by a shift angle S ₁ = 1, ..., being constant within a stator, the angle S _1, but the displacement angle S ₁ , ε _{J ≠ ι} in different stator sections i ≠ j are different from each other, S ₁ ≠ S _j Vz ≠ j. If the difference S ₁ -ε _{J ≠ 1 of} the displacement angle S _{1 of} different stator sections z, j ≠ i is not a whole multiple of p ₀ ,

^S ' ^Sj € IN ₀ Vz ≠ j (Equation 22)

po

If the positions of the rotor in which in a stator section i a pole transition of the stator is opposite to a pole transition of the rotor no longer coincide with the positions of the rotor in which in any other stator section i + 1 a pole transition of the stator corresponds to a pole transition of the rotor Rotor is opposite, together. Thus, the number of locking positions is maximized and the cogging torque at least significantly reduced. Only by an unfavorable superposition of cogging moments to close to adjacent positions of the rotor can still arise positions with unnecessarily high cogging torque.

To avoid such unfavorable overlays, the locking positions of the rotor can be evenly distributed over 360 ° or 2π. For this purpose, the displacement angle S ₁ are chosen so that applies

ε -ε. uo -e {1,2, ..., u ₀ -l} Vz ≠ j. (Equation 23)

po

It would be possible in greater generality, the condition

s - su ₀ - ^J - G {1,2, ..., u ₀ -l, u _o + 1, ..., 2u ₀ -l, 2u ₀ + 1, ...} Vz ≠ j. (Equation 24)

po However, this can lead to unnecessarily large and unnecessarily small angular spacings between adjacent pole junctions, which are undesirable in some applications at the boundaries between stator sections /, / + 1, as well as other disadvantages.

In a simple example, the displacement angles are

ip ₀ . 360 °. 360 °.

S ₁ = - ^ - = i -. r ₇ r = i or

U ₀ kgV {N _s , N _R _g gT {N _s , N _R ) N _S , N _R ∈ = IA = i ¹ JL = _t . _≥L_. (Equation 25) u ₀ kgV (N _s , N _R ) -ggT (N _s , N _R ) N _S , N _R

In this example, the angular distances a are _{Sιι + ι} between adjacent pole transitions of the stator at the boundaries between the stator sections i, i + l (i = 1,2, ..., M ₀ -I)

a _{Sιι + ι} = a _s + ^ - with (/ = 1,2, ..., M ₀ -I). (Equation 26)

M _n

With equations 18 and 19 follows

360 ° 360 ^c

S ₉ ,, _+! = + _{? \?} T with (/ = 1,2, ..., M ₀ -I) or s''' ^{1 + 1} ^~ NÜT _s ⁺ kkggVV {{NN _ss ,, NN _sR ) yg _g ggTT ({NN _ss ,, NN _sR )) with ( ^Z = 1,2, ..., ^M ₀ - 1).

(Equation 27)

With equation 4 follows

360 ° _Λ \ Λ. _t,. ... _{λ u} α ,,, ₊ , = + 1 + with (z = 1,2, ..., M ₀ -I) or

"J NV _x \ ^ N JV _Ä J \ ''' ^{O /} a _{Sιι + χ} = - + ^2π = - - l + - with (/ = 1,2, ..., M ₀ -I). (Equation 28) s''' ^{1 + ι} N _s N _S -N _R N _s \ N _R " The angular distances a _{S l l + l} between adjacent pole transitions of the stator at the boundary between the stator sections i = u ₀ and i = \ are in this example

α S, M ₀ , 1 = a _s - = a, - Po -A (Equation 29)

With equations 18 and 19 follows

360 ° 360 ^c 360 ° α 5> ₀ , l: + - or

N _s kgV {N _s , N _R ) ^' kgV {N _s , N _R ) - gCT {N _s , N _R )

2π 2π 2π α S, u _o , l - + (Equation 30)

N _s LCM {N _s, N _R) LCM {N _s, N _R) - gcd {N _s, N _R) ^'

With equations 4 and 19 follows

α S, u _o , l or

α S, u _o , l (Equation 31)

As mentioned, all angular distances are a _s between adjacent pole transitions of the stator within a stator same.

For the arrangement of the example defined by equation 25, the number of latching positions of the rotor is maximum, namely N _S - N _R , the latching positions are equally distributed or the distance of the next adjacent latching positions of the rotor is always the same. Consequently, the cogging torque is minimal at each detent position.

In a variant of the example defined by equation 25, the stator sections / are permuted. In this variant, too, all angular distances a _s between adjacent pole transitions of the stator are within a stator. section of the same value. Unchanged from the one with the

Equation 25 defined example, the number of locking positions of the rotor maximum, namely N _S - N _R , and the cogging torque at each locking position minimal.

In another example, all the pole transitions of the stator are divided into groups g (g = 1,..., N ₀ ) so that the next adjacent pole transitions of the stator within a group g are approximately the distance

(Equation 32)

have, in the case defined by the equations 1 and 2 (equal to all angular distances a _s between adjacent pole transitions of the stator and all angular distances a _R between adjacent pole transitions of the rotor) pole transitions of the stator, which are each opposite a pole transition of the rotor (see equation 3). In other words, each group comprises exactly those pole transitions which, in the case defined by equations 1 and 2, are simultaneously opposite a pole transition of the rotor. Where n _{0 is} defined as

n _o = kgV {N _s , N _R ). (Equation 33)

Thus, n _{0 is} the number of detent positions or rotor positions in which, in the case defined by equations 1 and 2, a plurality of pole transitions of the stator each face a pole transition of the rotor (compare equation 16).

Within each group g, the pole transitions are numbered consecutively with i = \, ..., u ₀ . Notwithstanding that defined by equations 1 and 2

If any pole transition is around the shift angle z - p _n . 360 °. i - O _n . 2π ._. , , , ..

S ₁ = - - = ι or S ₁ = - - = ι (equation 34) u ₀ N _S - N _R N ₅ - N _R

relative to the positions of the pole junctions in the case defined by Equations 1 and 2 (see Equation 25). If all pole transitions having the same number i but originating from different groups g are arranged in a stator section with the angular width S ₀ , the case defined by equation 25 or its variant with permuted stator sections also described above is present.

However, the pole transitions within a group g need not be consecutively numbered. In other words, the shift angles S ₁ need not increase from pole to pole transition within a group g. Rather, the different displacement angles S ₁ = i - p _o / u _o (Z = 1,... M ₀ ) can be arbitrarily distributed to the pole transitions within a group, as long as each shift angle S ₁ = i ^■ p _o / u _o

(z = 1, ..., M ₀ ) occurs exactly once. Also, the shift angles need not be evenly distributed in all groups g. Rather, within each group g, the different displacement angles S ₁ = i - p _o / u _o (Z = 1,..., M ₀ ) can be arbitrarily distributed to the pole transitions, as long as each shift angle S ₁ = i - p _o / u _o (z = 1, ..., M ₀ ) occurs exactly once in each group g. If each shift angle S ₁ = i - p _o / u _o (z = 1, ..., M ₀ ) occurs exactly once in each group g, the number of detent positions are maximum, the detent positions evenly distributed and the cogging torque at each detent position minimal. The angular distances between adjacent pole transitions of the stator vary accordingly from pole to pole. This can be used, for example, to spectrally broaden a torque ripple resulting from the different widths of the poles during a motor operation or to generate a predetermined torque curve.

The Polübergänge on the stator of an electric machine can also according to the shift angles ^ε , = η - - - with η <\. (Equation 35)

be arranged. The detent positions in this case form groups within which the angle between two detent positions is η- 360 ° / (N _s -N _R ), and between which there are corresponding gaps. Within the groups and between the groups, a particularly low cogging torque of the electric machine can be achieved, at the edges of the groups occurs in each case a substantially one-sided cogging torque.

The angular dependence of the cogging torque of the electric machine is a

Function of the angle dependencies of the cogging torques of the individual pole transitions. The angular dependence of the cogging torque of the individual pole transition is influenced by the widths and geometries of the gaps or payload slots between the poles of the stator and between the poles of the rotor. By a corresponding shape of the individual pole transitions

Stator and rotor, the angular dependencies of the cogging torques of the individual Polübergänge can be designed so that together with the high number N _s - N _R and correspondingly small distances of the locking positions in I-dealfall no cogging torque occurs more.

As already mentioned, the examples of electrical machines described above are not limited to a variation of the angular spacings of the pole junctions of the stator. By interchanging the terms and quantities related to the stator and rotor, one obtains electrical machines in which the angular distances of the pole transitions of the rotor vary. Furthermore, the angular spacings of the pole transitions of the stator and the angular spacings of the pole transitions of the rotor can simultaneously vary.

Hereinafter, an alternative approach to the previous embodiments will be described. This approach is based on a step-by-step reduction of the number u of pole transitions of the stator, which are each opposite to a pole transition of the rotor, by a factor. This approach can be used Two or more pole transitions of the stator are at the same time each opposite to a pole transition of the rotor in any rotor position.

For example, for any electrical machine with an arbitrary number N _s poles of the stator, an arbitrary number N _R poles of the rotor and an even number u _{0 of} the pole transitions of the stator, which are each opposite a pole transition of the rotor, (w _o / 2 = gcd (N _s , N _R ) / 2G N) by providing only two different tooth head angles

, 360 ° 360 ° a _κι = a _sι -a _N = - a _N ,

N _s U ₀ ^■ n _r

360 ° 360 °. a _{κ 2} = a _S2 -a _N = 1 a _N (Equation 36)

N ^' s U ₀ -n _r

the number u ₀ is reduced by a factor of 2, whereby at the same time the number of detent positions n _r increases by a factor of 2 and the cogging torque of the electric machine decreases. Ct ^ ₁ , a _{S2 are} the modified angular distances between the centers of the pole transitions or payload slots adjacent to a tooth tip and a _N the angular width of a pole transition or slot slot. If the number ₀ and a multiple of 3 (M _0/3 = GCD (N _s, N _R) / 3 € N) u can be ₀ reduced by a factor of three the number by three different tooth tip angle

360 ° 360 ° aK, l = - ^a N>

NN _s s U ₀ ^■ n _r 360 ° 360 ^c

«AA _κ 'T.3 ₃ == - h --- ^ a _N (Equation 37)

N s U ₀ ^■ n _r

be provided. Corresponding statements apply if the number u _{0 is} a multiple of ze N, z> 3. After the number u of the pole transitions of the stator, the same time one each

Pole transition of the rotor are opposite, was reduced by providing a corresponding factor of u ₀ to u by providing a plurality of different tooth angles, the remaining number u of the pole transitions of the stator, which are each opposite a pole transition of the rotor, still greater than 1 be (u> 1). In this case, the number u can be further reduced by further varying the tooth head angles α _K (obtained, for example, according to Equation 37 or 38). If, for example, the number u is a multiple of 2, by varying the tooth tip angle a _{K ι again} according to equation 36

360 ° a K, i, l = ^a κ, _t - - u - n _r 360 ° a _{K l 2} = ^a _{K l} ⁺ - (Equation 38) u - n.

the number of pole transitions of the stator, which are each opposite to a pole transition of the rotor, be halved again, u "^' = u' / 2.

When distributing the tooth head angle obtained, for example, with Equation 36, 37 or 38, care must be taken that no groove positions arise which superimpose their cogging torque. Furthermore, care should be taken that the flow is balanced. Not every tooth-head angle has to occur the same number of times. To verify that with the chosen distribution of the head angle the number of pole transitions of the

Stators, which are each opposite to a pole transition of the rotor, not larger than necessary, of all the resulting slot positions V ₁ integer multiples of δ ₀ = kgV {360 ° / N _s , 360 ° / N _R ) or ^ o ⁼ kgV (2π / N _s , 2π / N _R ) are subtracted,

V ₁ = V ₁ mod ^ o. (Equation 39) Of the groove positions V ₁ thus obtained, no more should be the same as necessary. Ideally, V ₁ ≠ v _'m \ / l ≠ m or V ^ ₁ mod v ₀ ≠ _m modδ ₀ \ / l ≠ m applies.

Also, the alternative approach represented by equations 36, 37 and 38 is not based on a variation of the angular distances of the pole transitions of the

Stators limited. By interchanging the terms and quantities relating to the stator and rotor, geometries result where the angular spacings of the pole junctions of the rotor vary. Furthermore, the angular spacings of the pole transitions of the stator and the angular spacings of the pole transitions of the rotor can simultaneously vary.

Figures 1 to 4 show schematic representations of electrical machines 10 each in a cross section perpendicular to the axis of the electric machine. Each of these electric machines 10 may be, for example, part of an actuator of an electric power steering system of a motor vehicle, another actuator of a land, water or aircraft, an actuator for a stationary application or a drive for a vehicle or other device.

In the example illustrated in FIG. 1, the electric machine 10 has a stator 20 with six stator teeth 22 and a rotor 30 with four permanent magnets 34. The stator teeth 22 form at their inner ends facing the rotor 30 poles 28. Each permanent magnet 34 of the rotor 30 is associated with a pole 38 which faces the stator 20. The polyvinyl Ie 28 of the stator 20 have widths b _κ linear and angular widths a _κ on.

Between the poles 28 of the stator 20 are slot slots 26 with the linear width b _N and the angular width a _N. Each payload slot forms a pole transition of the stator 20. The distance between two adjacent pole transitions of the stator 20 is a _s = a _κ + a _N. Corresponding sizes at the poles of the rotor 30 are not shown for reasons of clarity. For the geometry shown in Figure 1, N _s = 6, N _R = 4, u ₀ = gcd {N _s , N _R ) = 2, n _r = kgV {N _s , N _R ) = 12. By using

Tooth angle

a _κ = a _s -a _N = ± a _N = 60 ° ± 15 ° -α _jV (Equation 40)

N ^' s U ₀ ^■ n _r

can the number of locking positions increased and the cogging torque can be reduced in each individual locking position. At the same time, the number u of the pole transitions of the stator 20, which at the same time each lie opposite a pole transition of the rotor 30, is reduced from 2 to 1.

For N _s = 9 stator teeth, and N _R = 6 rotor poles, u ₀ = gcT (N _s , N _R ) = 3, n _r = kgV (N _s , N _R ) = 18. By using tooth head angles according to Equation 37,

360 ° 360 ° a _{κ ι} = a _N = 40 ° -6.67 ° -a _N ,

N _s U ₀ ^■ n _r

360 ° aK, 2 = - ^a N = ^{40 "} « AM

360 ° 360 ° a _{κ 3} = + a _N = 40 ° + 6.67 ° -a _N , (Equation 41)

N _s U ₀ ^■ n _r

can be achieved with a corresponding distribution of the tooth head angle that in any position of the rotor simultaneously two or more pole transitions of the stator are each opposite a pole transition of the rotor, and that all locking positions have a uniform angular distance from each other. FIG. 2 shows a schematic representation of an electric machine 10 with these tooth head angles. It will be the same reference numerals as in

Figure 1 used. The tooth heads 22 are identified by the letters "s", "m" and "b", which indicate the dentition angles Ct ^ ₁ (narrow), a _{κ 2} (middle) and a _{κ i} (wide) respectively Windings 24. The

Windings 24 are labeled with digits "1", "2" and "3" indicating the membership of phases "1", "2" and "3". For N _s = 12 stator teeth, N _R = 8 rotor poles, u ₀ = ggT {N _s , N _R ) = 4, n _r = kgV (N _s , N _R ) = 24. By using tooth head angles according to Equation 36,

360 ° 360 ° a _{κ ι} = a _N = 30 ° - 3.75 ° -a _N ,

N _s U ₀ ^■ n _r

360 ° 360 ° _{aK 2} = ^ - + ^ ia _N = 30 ° + 3.75 ° -a _N , (Equation 42)

N _s U ₀ ^■ n _r

can be achieved with a corresponding distribution of the tooth head angle, that in each position of the rotor at most two pole transitions of the stator are each opposite to a pole transition of the rotor. The head angles according to equation 42 can be further varied according to equation 38. This results in tooth head angle, can be achieved with their proper distribution that in each position of the rotor at most one Polübergang the stator is a Polübergang of the rotor opposite.

FIG. 3 shows an example of an electric machine 10 with N _s = 12 stator teeth and N _R = 8 rotor poles in a follower pole arrangement. In contrast to the examples shown above with reference to FIGS. 1 and 2, all poles 28 of the stator here have the same width or all pairs of adjacent ones

Pole transitions on the stator 20 at the same distance, and the distances of the Polübergänge 36 on the rotor 30 are different. Here, the widths of the poles 32 equipped with permanent magnets 34 are equal to each other while the widths of the follower poles 38 vary. Letters "s", "m" and "b" in turn denote small, medium or large distances of adjacent pole junctions 36. Two pole junctions 36 adjacent to the same pole 32 equipped with a permanent magnet 34 always have the mean spacing while two follow the same pole In the illustrated geometry, exactly two pole transitions 26 of the stator 20 are located opposite a pole transition 36 of the rotor 30 in each detent position of the rotor Machine with symmetrical stator and symmetrical rotor, the number of detent positions are doubled and halved the number of simultaneously opposite each pole transition of the rotor pole junctions of the stator. This also reduces the cogging torque.

Figure 4 shows an example of an electrical machine 10 having stator teeth 9 N _s = N and _R = 6 rotor poles. Also in this example all poles are pointing

28 of the stator on the same width, and the distances of the Polübergänge 36 on the rotor 30 are different. The poles 32 of the rotor 30 are formed here by the permanent magnets 34 formed as surface magnets. Pole transitions 36 are formed by gaps between the permanent magnets 34. The permanent magnets 34 have different widths. Letters "s", "m" and "b" in turn denote narrow, medium or wide permanent magnets 34 and small, medium or large distances of nearest adjacent pole junctions 36. In the illustrated geometry, only one pole transition 26 is located in each detent position of the rotor of the stator 20 opposes a pole transition 36 of the rotor 30. Compared with a conventional electric machine with a symmetrical stator and a symmetrical rotor, the number of latching positions is maximized and the number of simultaneously opposite each pole transition of the rotor

Polübergänge the stator minimized. Thus, the detent torque in each detent position is at least reduced.

Claims

claims

1. Electric machine (10) with:

a stator (20) having a plurality of poles (28);

a rotor (30) having a plurality of poles (32, 38);

wherein at least one of a first pole (28) of the stator (20) has a width that is different from a width of a second pole (28) of the stator (20), or a first pole (32, 38) of the rotor (30). has a width that is different from a width of a second pole (32, 38) of the rotor (30).

2. Electrical machine (10) according to the preceding claim, wherein in a latching position of the rotor (30), in the at least one Polübergang

(26) of the stator (20) is opposite a pole transition (36) of the rotor (30), the number of Polübergänge (26) of the stator (20), each opposite a pole transition (36) of the rotor (30), smaller as the largest common divisor is the number of poles (26) of the stator (20) and the number of poles (36) of the rotor (30).

3. Electrical machine (10) according to any one of the preceding claims, wherein in all locking positions of the rotor (30), in which in each case at least one pole transition (26) of the stator (20) a pole transition (36) of the rotor (30) opposite , the number of pole transitions (26) of the stator

(20), which are each opposite a pole transition (36) of the rotor (30), smaller than the largest common divisor of the number of poles (26) of the stator (20) and the number of poles (36) of the rotor (30) is.

4. Electrical machine (10) according to one of the preceding claims, wherein in all latching positions of the rotor (30), in which in each case at least one pole transition (26) of the stator (20) a pole transition (36) of the rotor (30) opposite , the number of pole transitions (26) of the stator

(20), which are each a pole transition (36) of the rotor (30) opposite, is the same.

5. Electrical machine (10) according to one of the preceding claims, wherein in all latching positions of the rotor (30), in which in each case at least one pole transition (26) of the stator (20) a pole transition (36) of the rotor (30) opposite , exactly one pole transition (26) of the stator (20) is opposite a pole transition (36) of the rotor (30).

6. Electrical machine (10) according to any one of the preceding claims, in which all locking positions of the rotor (30) have equal distances.

7. Electrical machine (10) according to one of the preceding claims, wherein at least either for each pole (28) of the stator (20) or for each pole (32, 38) of the rotor (30) holds that a difference between the

Angular distance between the centers of two pole junctions (26, 36) adjoining the pole (28, 32, 38) and a quotient of 360 ° and the number of poles (28, 32, 38) is a whole multiple of the quotient of 360 ° and Product of the number of poles (28) of the stator (20) and the number of poles (32, 38) of the rotor (30) is.

8. Electrical machine (10) according to one of the preceding claims, wherein in each case within a portion of the stator (20) or the rotor (30) having an angular width which is the least common multiple of the quotient of 360 ° and the number of poles ( 28) of the stator (20) and the quotient of 360 ° and the number of poles (32, 38) of the rotor (30), all pairs of adjacent pole junctions (26; 36) have the same distance.

An electric machine (10) according to the preceding claim, wherein all pairs of adjacent pole junctions (26; 36) of different sections are spaced apart from pairs of nearest adjacent pole junctions (26; 36) within a section.

10. Electrical machine (10) according to one of the preceding claims, wherein in each case all Polübergänge (26; 36) within a group of Polübergängen (26; 36) whose mutual distance is approximately a common multiple of the quotient of 360 ° and the number of Pole (28) of the stator (20) and the quotient of 360 ° and the number of

Pole (32, 38) of the rotor (30) is, compared to symmetrical positions whose distances are common multiples of the quotients of 360 ° and the number of poles (28) of the stator (20) and the quotient of 360 ° and the number of poles (32, 38) of the rotor (30) is shifted to different degrees.

11. The electrical machine according to claim 1, wherein at least one of the stator and the rotor comprises a permanent magnet.

12. A method of designing an electrical machine (10), comprising the following steps:

Defining a first width and a second width different from the first width;

Arranging a pole (26; 36) of the first width and a pole (26; 36) of the second width on a stator (20) or rotor (30) of the electrical machine (10).

A method according to the preceding claim, wherein an electric machine (10) is designed according to one of the preceding device claims.

14. A method of manufacturing an electric machine (10), comprising the following steps:

Designing the electric machine (10) according to a method according to one of the preceding method claims;

Finishing the electric machine (10).