Sinusoidal surface of the rotor and stator

Abstract

The invention relates to an electric machine (1), comprising an axis of rotation (2) extending in the axial direction, a stator (3) which forms a lateral surface (4) spaced apart from the axis of rotation (2) in the radial direction, wherein the stator (3) has N teeth (5) in the circumferential direction, said teeth (5) having grooves (6), which are angularly equidistantly distributed and lie between them in the axial direction, for receiving windings. The electric machine (1) further comprises a rotor (7), which forms a lateral surface spaced apart from the axis of rotation (2) in the radial direction, wherein the rotor forms an even number of magnetic poles. The electric machine (1) further comprises an air gap formed between the lateral surfaces (4) spaced apart from one another in the radial direction, wherein one of the lateral surfaces (4) has a periodically variable radial distance (8) from the axis of rotation in the circumferential direction, wherein R is a constant nominal radius R, and r is a variable portion which has a sinusoidal function with an angular period of 720° / N or an integral multiple of N and an amplitude a, wherein the radial distance (8) in the circumferential direction results from a superimposition of R and the positive or negative portions of r.

Description

[0001] Sinusoidal surface of the rotor and stator

[0002] The present invention relates to an electrical machine comprising an axially extending axis of rotation, and a stator which forms a lateral surface spaced radially from the axis of rotation, wherein the stator has N teeth in the circumferential direction, which have angularly equidistantly distributed in the axial direction, forming slots between the teeth for receiving windings. Furthermore, the electrical machine comprises a rotor which forms a lateral surface spaced radially from the axis of rotation, wherein the rotor forms an even number of magnetic poles, and an air gap formed between the lateral surfaces spaced radially from one another, wherein one of the lateral surfaces has a radial distance from the axis of rotation that varies periodically in the circumferential direction.

[0003] Electric drives are increasingly being used in motor vehicles to create alternatives to combustion engines that require fossil fuels. Considerable efforts have already been made to improve the everyday suitability of electric drives and also to offer users the same driving comfort they are accustomed to.

[0004] Although electric motors used as traction machines generally emit less noise than comparable combustion engines in terms of performance, the specific noise behavior of electric motors in many applications – particularly in the field of electromobility – leads to reduced comfort and even acceptance problems. The reason for this lies primarily in the completely different noise characteristics of electric motors from those of combustion engines. Examples include the unsteady noise level and the very tonal, order-specific whine of electric motors, which is further amplified by the considerably wider speed range of electric motors (often greater than 10,000 rpm) combined with the high order numbers. The noise characteristics of conventional electric motors are very unfamiliar to car drivers and represent a major hurdle to the acceptance of electric vehicles.Optimizing the noise behavior of electric vehicles is therefore an important task for vehicle manufacturers and suppliers and is considered a major challenge.

[0005] The cause of the relatively high-frequency and tonal noise characteristics of electric motors is primarily related to the design-related change in the magnetic flux, which in permanent magnet motors leads to significant orders depending on the number of poles and windings. These changes in the magnetic flux generate predominantly radial, but also axial and tangential alternating forces on both the motor components (rotor, stator) and the motor housing or the coupled structures. In the literature, this is also referred to as torque ripple, i.e., a periodic increase or decrease in the output torque when the rotor rotates.

[0006] US2011043070 presents a rotor assembly for an electrical machine, in particular for a brushless synchronous machine excited by a permanent magnet with embedded permanent magnets. This rotor assembly is characterized by reduced cogging torque and torque ripple. The innovation of this rotor assembly lies in the specific design of the pole soles of the rotor segments, which are provided with an arc contour whose contour radius is smaller than the radius of the rotor assembly, thus forming a gap between two adjacent rotor segments.

[0007] US2021184520 presents an improved rotor design for reducing noise, vibration, and harshness (NVH) effects in an electrified powertrain using a rotating electric machine. The rotor of this system is designed to incorporate arc notches across the diameter of each rotor pole face, arranged symmetrically for each rotor pole. These notches can run along the entire axial length of the rotor or be limited to specific lamination layers. A key feature of the rotor design is the arrangement of at least three rotor notches on each magnetic pole, with additional pairs of rotor notches that can be added in other designs.

[0008] LIS2019319503 presents an engine specifically designed to reduce gear rattle (cogging torque) by forming notches in areas where the stator and rotor face each other. Several notches are located on both the stator and rotor in a vertical direction perpendicular to the circumferential direction. These notches are specifically configured to significantly reduce gear rattle and thus significantly improve the NVH (noise, vibration, harshness) performance of the engine.

[0009] US2022181927 presents a rotor for an electric machine with permanent magnets. This document focuses on an innovative rotor design that enables improved torque generation and reduced torque fluctuations. The outer circumference of the rotor forms smooth spline curves within each pole arc angle, which slope radially inward relative to the outer diameter.

[0010] US5736803 presents a rotor for synchronous machines, specifically designed for use in high-speed synchronous machines. This configuration differs from conventional rotors with a constant magnetic air gap in that it features a variable magnetic air gap geometry. To achieve the progressive magnetic air gap, the rotor poles are specially shaped, with curved central areas and flat surfaces in the progressive magnetic air gap areas, complemented by sharp, beveled, or rounded edges.

[0011] US2018175682 describes an electric motor with a rotor containing a cavity that accommodates a magnet, an outer periphery, and an overlying bridge that includes at least two slots, each with a length in the radial direction. The maximum of the lengths is closer to a Q-axis and the minimum of the lengths is closer to a D-axis, resulting in a changing rate of change of the air gap flux density through the upper bridge during operation of the electric motor. This arrangement causes the waveform associated with the air gap flux density to increase and decrease in a stepped pattern, resulting in a reduction in torque ripple and iron losses. US2006250041 presents a rotating electric machine in which a plurality of permanent magnets are embedded as magnetic poles within a rotor that rotates within a stator.To suppress torque pulsation, several circumferential regions are defined along the outer circumference of the rotor, each corresponding to the magnetic pole centers. Between adjacent pairs of these circumferential regions, convex sections are provided that protrude radially outward and have several angled sections directed radially outward. This configuration aims to reduce the fluctuation range of the output torque (torque ripple) while also reducing noise and vibration.

[0012] US2018175685 describes a rotor for an electrical machine with permanent magnets. This rotor is characterized by a special configuration comprising a cavity for a magnet, an outer circumference, and an overlying bridge. The bridge defines at least two segments, each of which has a minimum width near a Q-axis and a maximum width near a D-axis and increases monotonically from the minimum to the maximum, so that the rate of change of the rotor air gap flux density is different for each segment during operation. This configuration enables a differentiated influence on the magnetomotive force and the air gap flux density, leading to a reduction in torque ripple and iron losses.

[0013] WO20260567 describes a stator for an electric machine, designed particularly for use in motor vehicles. The stator comprises an annular stator yoke with a plurality of circumferentially arranged teeth that extend radially toward the rotor of the electric machine and form slots for receiving coil windings. A key feature of the stator are the slot closures, which close the slots between two adjacent teeth and are arranged radially between the slots and the rotor. A slot closure has at least one radial notch, which can contribute to reducing electrical erosion within the electric machine.

[0014] DE102022001864 describes a rotor for an electric machine that is rotatable about a rotor axis and has an outer rotor circumference. The rotor is characterized by several bulges formed on the outer rotor circumference, which are distributed in the circumferential direction. This configuration aims to reduce audible or perceptible vibrations caused by the rotor or the electric machine.

[0015] WO10054992 describes an electrical machine comprising a rotor and a stator, wherein at least two recesses are arranged in the circumferential surface of the rotor and / or the stator. This configuration aims to reduce the disruptive cogging torque caused by the attraction between the armature teeth and the magnets. In contrast to previous solutions, such as those described in EP 1 542 335 A1, the recesses are distributed irregularly over the circumferential surface, which enables a more effective reduction of the cogging torque while simultaneously reducing the effective torque. The irregular arrangement of the recesses leads to a different influence on the magnetic flux, which minimizes the disruptive effects of the cogging torque.

[0016] WO12038377 presents a machine component for an electrical machine, in particular a rotor for a rotary electrical machine, with an optimized pole contour of the rotor poles. This machine component is essentially circular-cylindrical in design and has poles at which a magnetic field generated by at least one permanent magnet emerges. The special feature of this component lies in the pole contours of the poles, which deviate from a purely circular-cylindrical outer surface and have several sections in the axial direction over the length of the component that are offset in the circumferential direction. This configuration enables a significant reduction in cogging torques and torque ripple, which are a common problem in conventional electrical machines with permanent magnets.

[0017] The object of the present invention is therefore to reduce or completely avoid the described disadvantages of the prior art and to provide an electric machine with improved acoustic characteristics, particularly perceived as pleasant by a user, and with minimized torque ripple. This object is achieved by the electric machine with the features according to claim 1. Advantageous embodiments of the invention can be found in the dependent claims.

[0018] According to one aspect, an electric machine comprises an axially extending axis of rotation and a stator which forms a circumferential surface spaced radially from the axis of rotation. The stator has N teeth in the circumferential direction, which have grooves distributed angularly or equidistantly in the circumferential direction in the axial direction between the teeth for receiving windings. The electric machine further comprises a rotor which forms a circumferential surface spaced radially from the axis of rotation. The rotor forms an even number of magnetic poles. The electric machine further comprises an air gap formed between the circumferential surfaces spaced radially from one another.At least one of the lateral surfaces has a radial distance from the axis of rotation that varies periodically in the circumferential direction, where R is a constant nominal radius R and r is a variable component that has a sine function with an angular period of 7207N or an integer multiple of N and an amplitude a, where the radial distance in the circumferential direction results from a superposition of R and the positive or negative components of r.

[0019] The advantageous effect of this aspect, namely the reduction in torque ripple, arises particularly when the air gap is varied periodically with the teeth of the stator. In a preferred embodiment using the example of a rotor that runs inside the stator, corresponding reductions in torque ripple result if, compared to a cylindrical rotor, recesses on the outer diameter of the rotor are arranged such that, when the rotor is stationary, they each face a tooth of the stator. In the preferred embodiment, the period is therefore 7207N and the amplitude a is in particular smaller than the air gap. Particularly preferably, the period is 7207(2*N). Since only recesses are introduced into the rotor, thus only the negative component of r is taken into account, the amplitude a can also be larger than the air gap.Preferably, the radial distance of the rotor's outer surface can be formed by the positive components of r. In the preferred embodiment, the period is thus 7207N. Particularly preferably, the period is 7207(2*N). Then, for geometric reasons alone, it is essential that the amplitude a is smaller than a comparative air gap that would result if the rotor were formed solely by the constant nominal radius R. Particularly preferably, the two previously described embodiments can be combined, and the radial distance of the outer surface is formed by both the negative and the positive components of r.

[0020] In an alternative embodiment, the air gap is periodically varied across the lateral surface of the stator. In the preferred embodiment, the period is thus 7207N and the amplitude a is, in particular, smaller than the air gap. Particularly preferably, the period is 7207(2*N). Since only recesses are made in the stator, thus only the positive component of r is taken into account in an external stator, the amplitude a can also be larger than the air gap. Particularly preferably, the two previously described embodiments can be combined, and the radial distance of the lateral surface is formed by both the negative and the positive components of r.

[0021] Preferably, the radial distance of the lateral surface of the stator can be formed by the negative components of r. In the preferred embodiment, the period is thus 7207N. Particularly preferably, the period is 7207(2*N). Then, for geometric reasons alone, it is essential that the amplitude a be smaller than a reference air gap that would result if the stator were formed solely by the constant nominal radius R.

[0022] In the previously described embodiments, r is in particular selected such that r is equal to or less than 80% of the reference air gap, particularly preferably equal to or less than 50% of the reference air gap.

[0023] Optionally, r can have a positive or negative component c, which is smaller than the amplitude a. Particularly advantageously, the component c is selected such that c corresponds to half the radial extent of the air gap.

[0024] In other words, the radial distance of the lateral surface describes a sinusoidal oscillation that propagates in the circumferential direction. Depending on the design, this sinusoidal oscillation is formed completely or only in sections, depending on whether only the positive or negative components of r, or both components, are taken into account. The particular advantage of this design lies in the fact that it results in a geometry that is easy to parameterize and thus optimize with regard to specific torque fluctuations and their excitations, known as harmonics.

[0025] A further advantage is that the continuous shaping of the outer surface, in particular, prevents notch effects in the rotor. This is advantageous when the rotor is designed as a laminated rotor and thus has multiple electrical laminations, with the outer contour of the individual laminations forming the outer surface in the axial stacking direction.

[0026] According to one embodiment, r comprises at least one further sine function which has a further angular period of 7207N or an integer multiple of N and a further amplitude a.

[0027] Since more than one harmonic is often decisive for torque fluctuations, the radial distance of the stator or rotor surface for r can include more than just one sine function. The sine functions preferably differ in their periodicity and amplitude a. Higher harmonics are particularly important here.

[0028] According to a preferred embodiment, the lateral surfaces of the stator have a first radial distance from the axis of rotation that varies periodically in the circumferential direction, where R1 is a constant nominal radius R1 and r1 is a variable component that has a sine function with an angular period of 7207N or an integer multiple of N and an amplitude a1. The first radial distance in the circumferential direction results from a superposition of R1 and the positive components of r1. Furthermore, the lateral surfaces of the rotor of the preferred embodiment of the electric machine have a second radial distance from the axis of rotation that varies periodically in the circumferential direction, where R2 is a constant nominal radius R2 and r2 is a variable component that has a sine function with an angular period of 7207N or an integer multiple of N and an amplitude a2.The first radial distance in the circumferential direction results from a superposition of R2 and the negative components of r2. R1 is larger than R2.

[0029] Particularly preferably, the period is 7207(2*N). The advantageous effect of this design lies in the fact that, starting from the previously described reference air gap, which would result if the rotor were formed solely by the constant nominal radius R2 and the stator solely by the constant nominal radius R1, only the negative component of r2 and only the positive component of r1 are used to form the respective lateral surfaces. Thus, simply subtracting material in the radial direction away from the reference air gap means that no extensive changes to the original rotor or stator design need to be made. This applies in particular to the design as a so-called internal rotor, where the rotor is arranged in the stator.

[0030] Optionally, r1 or r2 can have a negative or positive component c1 or c2 that is smaller than the amplitude a1 or a2. Particularly advantageously, the component c1 or c2 is selected such that c1 or c2 corresponds to half the sum of R1 and R2.

[0031] According to a further preferred embodiment, the lateral surfaces of the stator have a first radial distance from the axis of rotation that varies periodically in the circumferential direction, where R1 is a constant nominal radius R1 and r1 is a component that varies according to a sine function and has an angular period of 7207N or an integer multiple of N and an amplitude a1. The first radial distance in the circumferential direction results from a superposition of R1 and the positive and negative components of r1. Furthermore, the lateral surfaces of the rotor have a second radial distance from the axis of rotation that varies periodically in the circumferential direction, where R2 is a constant nominal radius R2 and r2 is a component that varies according to a sine function and has an angular period of 7207N or an integer multiple of N and an amplitude a2.The first radial distance in the circumferential direction results from a superposition of R2 and the positive and negative components of r2. R1 is greater than R2. The maximum sum of r1 and r2 is smaller than the difference between R1 and R2.

[0032] Particularly preferably, the period is 7207(2*N). The advantageous effect of the embodiment lies in the fact that, starting from the previously described reference air gap, which would result if the rotor were formed solely by the constant nominal radius R2 and the stator were formed solely by the constant nominal radius R1, the lateral surfaces are now formed from the positive and negative components of r1 and r2, which brings about an improved reduction in torque ripple. Due to the change in the lateral surface in the radial direction into the reference air gap, it must be ensured when selecting the amplitudes a1 and a2 that the maximum sum of r1 and r2 is smaller than the reference air gap, which results from the difference between R1 and R2.The maximum sum of r1 and r2 results geometrically when the lateral surfaces of the rotor and stator are positioned opposite each other in such a way that the largest radial distance of the rotor and the smallest radial distance of the stator lie on an imaginary line which passes through the axis of rotation and is perpendicular to it.

[0033] According to one embodiment, r1 comprises at least one further sine function, which has a further angular period of 7207N or an integer multiple of N, as well as a further amplitude a1. Preferably, r2 also comprises at least one further sine function, which has a further angular period of 7207N or an integer multiple of N, as well as a further amplitude a2. Advantageously, the torque ripple can thus be adjusted either by designing the rotor surface or by designing the stator surface.

[0034] According to one embodiment, R1 is 0.2 to 5 mm larger than R2.

[0035] According to a further embodiment, maximum values ​​of r1 and r2 are equal. This advantageously results in a mirror-symmetrical design of the lateral surfaces in the air gap between the lateral surfaces of the rotor and stator if the lateral surfaces of the rotor and stator are positioned opposite each other in such a way that the greatest radial distance of the rotor and the smallest radial distance of the stator lie on an imaginary line which runs through the axis of rotation and is arranged perpendicular to it. According to one embodiment, each of the N teeth of the stator is designed symmetrically in the circumferential direction to a plane running through the axis of rotation. Furthermore, the radial distance of the lateral surface of the stator in the circumferential direction is symmetrical to each of these planes. According to one embodiment, each of the magnetic poles of the rotor is designed symmetrically in the circumferential direction to a plane running through the axis of rotation.Furthermore, the radial distance of the rotor's outer surface is circumferentially symmetrical to each of these planes. This advantageously results in a rotation-independent design for the electric machine, so that the machine can be reliably used in both directions of rotation, both as a motor and as a generator, without there being a preferred direction of rotation for one or the other operating mode. Depending on the requirements of the electric machine, however, deviations from the symmetry can be made for the rotor or stator. The symmetry for the stator is circumferentially based on the extension of the tooth, while the symmetry of the rotor is based on the extension of a magnetic pole.

[0036] The individual elements of the claimed subject matter of the invention are explained below

[0037] Electrical machines are used to convert electrical energy into mechanical energy and / or vice versa, and usually comprise a stationary part known as a stator, stand or armature and a part known as a rotor or runner which is arranged to be movable relative to the stationary part.

[0038] In the case of electrical machines designed as rotating machines, a distinction is made in particular between radial flux machines and axial flux machines. A radial flux machine is characterized by the fact that the magnetic field lines in the air gap formed between the rotor and stator extend in the radial direction, whereas in the case of an axial flux machine, the magnetic field lines in the air gap formed between the rotor and stator extend in the axial direction. It is preferred to use the method according to the invention in conjunction with stators for radial flux machines.

[0039] In connection with the invention, it is advantageous that the electrical machine is a radial flux machine.

[0040] The electric machine is particularly intended for use within a drive train of a hybrid or fully electric motor vehicle. In particular, the electric machine is dimensioned such that vehicle speeds greater than 50 km / h, preferably greater than 80 km / h, and in particular greater than 100 km / h can be achieved. The electric motor particularly preferably has an output greater than 30 kW, preferably greater than 50 kW, and in particular greater than 70 kW. It is further preferred that the electric machine provides speeds greater than 5,000 rpm, particularly preferably greater than 10,000 rpm, and most particularly preferably greater than 12,500 rpm. According to a further preferred embodiment of the subject matter of the invention, it can be provided that the electric machine can be operated at 1,000-20,000 rpm.The stator of a radial flux machine is typically cylindrical and consists of electrically insulated, layered, and stacked laminations. This design minimizes the eddy currents caused by the stator field in the stator. Distributed around the circumference, grooves or circumferentially closed recesses are cut into the lamination, running parallel to the rotor shaft. These grooves accommodate the stator winding or parts of the stator winding. Depending on the design, the grooves can be closed toward the surface with locking elements, such as locking wedges or covers, to prevent the stator winding from becoming detached.

[0041] A rotor is the rotating part of an electrical machine. The rotor comprises a rotor shaft and one or more rotor bodies mounted on the rotor shaft in a rotationally fixed manner. The rotor shaft can be hollow, which reduces weight and allows for the supply of lubricant or coolant to the rotor body.

[0042] The rotor can, in particular, consist of a substantially cylindrical or hollow-cylindrical rotor body, which is rotationally fixedly connected to a rotor shaft. For the purposes of the invention, a rotor body is understood to mean the rotor without a rotor shaft. The rotor body is therefore composed, in particular, of the rotor core and the magnetic elements incorporated into the pockets of the rotor core or peripherally fixed to the rotor core, as well as any axial cover parts for closing the pockets and the like.

[0043] A rotor lamination stack is a plurality of laminated individual laminations or rotor laminations, usually made of electrical steel, which are layered and packaged on top of one another to form a stack, the so-called rotor lamination stack. The individual laminations can then be held together in the lamination stack by gluing, welding, or screwing. In general, the surface of cylinders is defined by the outer surface and cover surfaces. The cover surfaces are arranged perpendicular to a rotational axis of the cylinder, while the outer surface is spaced around the rotational axis. Following this logic, a hollow cylinder has two outer surfaces: a radially inner one, which delimits the hollow cylinder in the radial direction towards the rotational axis, and a radially outer one, analogous to the outer surface of a solid cylinder.In an arrangement of an electrical machine in which the stator encloses the rotor in the radial direction, the rotor thus has a radially outer surface, whereas the stator has a radially inner surface.

[0044] In electrical engineering, an air gap in the context of magnetic circuits refers to the space or distance between two opposing surfaces that carry a magnetic flux. In an electrical machine, the air gap is formed between the outer surfaces of the stator and rotor. Typical air gaps range from 0.2 to 5 mm.

[0045] The invention will be explained in more detail below with reference to figures without limiting the general inventive concept.

[0046] The terms "radial," "axial," "tangential," and "circumferential direction" used in this application always refer to the rotational axis of the rotor of the electric machine. The terms "left," "right," "top," "bottom," "above," and "below" serve only to clarify which areas of the figures are currently being described in the text. The later embodiment of the invention can also be arranged differently. Furthermore, the invention is not limited to the embodiments illustrated in the figures. The above description is therefore not to be regarded as limiting, but as explanatory. The following patent claims are to be understood in such a way that a named feature is present in at least one embodiment of the invention. This does not exclude the presence of further features.Where the patent claims and the above description define 'first' and 'second' features, this designation serves to distinguish between two similar features without establishing a priority. It shows:

[0047] Figure 1 shows a schematic section through an electrical machine and a more detailed section of the electrical machine,

[0048] Figure 2 two embodiments of an electrical machine,

[0049] Figure 3 shows two further embodiments of an electrical machine.

[0050] Figure 1 shows in Fig. 1a) a schematic section through an electrical machine 1. The electrical machine 1 is designed as an internal rotor, the stator 3 encloses the rotor 7, which is mounted so as to be rotatable about a rotation axis 2, so that the outer surface 4 of the rotor 7 and the outer surface 4 of the stator 3 are aligned concentrically to one another. The outer surface 4 of the stator 3 is initially shown as cylindrical, which is why the radial distance 8, see Fig. 1b), of the outer surface 4 of the stator 3 corresponds to the nominal radius R1 in the circumferential direction. Likewise, the outer surface 4 of the rotor 7 is initially shown as cylindrical, which is why the radial distance 8, see Fig. 1b), of the outer surface 4 of the rotor 7 corresponds to the nominal radius R2 in the circumferential direction.

[0051] Figure 1 b) shows a more detailed view of the electrical machine 1 according to Fig. 1 a), wherein the curvature of the lateral surfaces 8 and thus the nominal radii R1 and R2 are shown as parallel straight lines. The stator 3 has a plurality of teeth 5, between which slots 6 are formed, which are designed to accommodate windings. The windings are not shown. Depending on the design of the teeth 5, the windings can preferably be designed as hairpin or wave windings. The lateral surface in the sense of the application is to be understood as the sum of the surfaces of the stator teeth facing radially towards the axis of rotation, but not correspondingly aligned surfaces of the slots. The rotor 7 comprises an even number of poles and is preferably permanently excited. Thus, the poles are preferably formed by buried permanent magnets. The permanent magnets are not shown.

[0052] Fig. 1 c) shows ideal-typical curves of the radial distances 8 between the rotor and stator, depending on the nominal radii R1 and R2 as well as the variable components r1 and r2, which are shown in the positive radial direction corresponding to the amplitudes a1 and a2 of a respective sine function with an angular period. As shown in Figs. 2b) and 3b), the radial distance 8 and thus in particular the variable component r1 or r2 are preferably formed from several sine functions with corresponding amplitudes a1 and a2 and corresponding angular periods.

[0053] Figure 2 shows in Fig. 2a) a detailed view corresponding to Fig. 1 b), wherein the outer surface 4 of the stator 3 has a first radial distance 8. This first radial distance 8 results from the nominal radius R1 and the variable component r1, or more precisely, only the positive components of the variable component of r1. The variable component r1 corresponds to a sine function with a period of 7207(2*N), where N is the number of teeth 5 of the stator 3. The outer surface 4 of the rotor 7 has a second radial distance 8, wherein this second radial distance results from the nominal radius R2 and the variable component r2, or more precisely, only the negative component of the variable component of r2. This results in cutouts in the teeth 5 of the stator 3, which are formed in a positive radial direction. Correspondingly, recesses are created in the rotor 7 in the negative radial direction.

[0054] Fig. 2b) shows a further embodiment of the electric machine. The variable component r1 corresponds to the sum of a first sine function with a first period of 7207(2*N) and a first amplitude a1, and a second sine function with a second period of 7207(8*N) and a second amplitude a1. The same applies to the variable component r2, which corresponds to the sum of a first sine function with a first period of 7207(2*N) and a first amplitude a2, and a second sine function with a second period of 7207(8*N) and a second amplitude a2. The outer surface 4 of the stator 3 has a first radial distance 8. As in the embodiment of Fig. 2a), for the further embodiment of Fig. 2b) the first radial distance 8 results from the nominal radius R1 and the variable component r1, or more precisely, only the positive components of the variable component of r1.The outer surface 4 of the rotor 7 has a second radial distance 8. As in the embodiment of Fig. 2a), for the further embodiment of Fig. 2b), the second radial distance 8 results from the nominal radius R2 and the variable component r2, or more precisely, only the negative component of the variable component of r2.

[0055] Figure 3 shows in Fig. 3a) a detailed view corresponding to Fig. 1b), wherein the outer surface 4 of the stator 3 has a first radial distance 8. This first radial distance 8 results from the nominal radius R1 and the variable component r1. In contrast to the embodiment of Fig. 2a), both the negative and the positive components are taken into account. The outer surface 4 of the rotor 7 has a second radial distance 8, wherein this second radial distance results from the nominal radius R2 and the variable component r2. In contrast to the embodiment of Fig. 2a), both the negative and the positive components are taken into account. This results in cutouts in the teeth 5 of the stator 3 which are formed in the positive radial direction as well as components which protrude from the teeth 5 in the negative radial direction, compared to Fig. 1b).Correspondingly, there are recesses in the rotor 7 in the negative radial direction as well as portions that protrude from the rotor in the positive radial direction, compared to Fig. 1 b).

[0056] Fig. 3b) shows a further embodiment of the electric machine. The variable component r1 corresponds to the sum of a first sine function with a first period of 7207(2*N), and a first amplitude a1 and a second sine function with a second period of 7207(8*N), and a second amplitude a1. The same applies to the variable component r2, which corresponds to the sum of a first sine function with a first period of 7207(2*N), and a first amplitude a2 and a second sine function with a second period of 7207(8*N), and a second amplitude a2. The outer surface 4 of the stator 3 has a first radial distance 8. As in the embodiment of Fig. 3a), for the further embodiment of Fig. 3b) the first radial distance 8 results from the nominal radius R1 and the variable component r1. The outer surface 4 of the rotor 7 has a second radial distance 8. As in the embodiment of Fig.3a), for the further embodiment of Fig. 3b), the second radial distance 8 results from the nominal radius R2 and the variable component r2. The embodiments of Figs. 2a), 2b), 3a) and 3b) have in common that each of the N teeth of the stator is designed to be symmetrical to a plane running through the axis of rotation 2 in the circumferential direction, so that the radial distance 8 of the outer surface 4 of the stator 3 in the circumferential direction with respect to the extension of the tooth 5 in the circumferential direction is symmetrical to each of these planes. Furthermore, each of the magnetic poles of the rotor is designed to be symmetrical to a plane running through the axis of rotation 2 in the circumferential direction, and the radial distance 8 of the outer surface 4 of the rotor 7 in the circumferential direction is symmetrical to each of these planes with respect to the extension of the magnetic pole in the circumferential direction.

[0057] List of reference symbols Electric machine Rotation axis Stator Shell surface Tooth Groove Rotor radial distance

Claims

Patent claims 1. An electrical machine (1) comprising: an axially extending axis of rotation (2), a stator (3) forming a lateral surface (4) spaced radially from the axis of rotation (2), the stator (3) having N teeth (5) in the circumferential direction, which have angularly equidistantly distributed slots (6) located between the teeth (5) in the axial direction for receiving windings; a rotor (7) forming a lateral surface spaced radially from the axis of rotation (2), the rotor forming an even number of magnetic poles; an air gap formed between the lateral surfaces (4) spaced radially from one another; one of the lateral surfaces (4) having a radial distance (8) from the axis of rotation that varies periodically in the circumferential direction, characterized in that R is a constant nominal radius R and r is a variable component having a sine function with an angular period of 7207N or an integer multiple of N and an amplitude a, wherein the radial distance (8) in the circumferential direction results from a superposition of R and the positive or negative components of r.

2. Electrical machine (1) according to claim 1, wherein r comprises at least one further sine function which has a further angular period of 7207N or an integer multiple of N and a further amplitude a.

3. Electrical machine according to claim 1, wherein the lateral surfaces of the stator have a circumferentially periodically variable first radial distance from the axis of rotation, wherein R1 is a constant nominal radius R1 and r1 is a variable component which has a sine function with an angular period of 7207N or an integer multiple of N and an amplitude a1, wherein the first radial distance in the circumferential direction results from a superposition of R1 and the positive components of r1, wherein the lateral surfaces of the rotor have a circumferentially periodically variable second radial distance from the axis of rotation, wherein R2 is a constant nominal radius R2 and r2 is a variable component having a sine function with an angular period of 7207N or an integer multiple of N and an amplitude a2, wherein the first radial distance in the circumferential direction results from a superposition of R2 and the negative components of r2, wherein R1 is greater than R2.

4. Electrical machine according to claim 1, wherein the lateral surfaces of the stator have a circumferentially periodically variable first radial distance from the axis of rotation, wherein R1 is a constant nominal radius R1 and r1 is a component which varies according to a sine function and has an angular period of 7207N or an integer multiple of N and an amplitude a1, wherein the first radial distance in the circumferential direction results from a superposition of R1 and the positive and negative components of r1, wherein the lateral surfaces of the rotor have a circumferentially periodically variable second radial distance from the axis of rotation, wherein R2 is a constant nominal radius R2 and r2 is a component which varies according to a sine function and has an an- gular period of 7207N or an integer multiple of N and an amplitude a2, wherein the first radial distance in the circumferential direction results from a superposition of R2 and the positive and negative components of r2, wherein R1 is greater than R2, and the maximum sum of r1 and r2 is smaller than the absolute value of the difference between R1 and R2.

5. Electrical machine according to claim 3 or 4, wherein r1 comprises at least one further sine function which has a further angular period of 7207N or an integer multiple of N and a further amplitude a1, or r2 comprises at least one further sine function which has a further angular period of 7207N or an integer multiple of N and a further amplitude a2.

6. Electrical machine according to claim 3, 4, 5 wherein R1 is 0.2 to 5 mm larger than R2.

7. Electrical machine according to claim 3, 4, 5, 6, wherein maximum values ​​of r1 and r2 are equal.

8. Electrical machine according to one of the preceding claims, wherein each of the N teeth of the stator is formed symmetrically in the circumferential direction to a plane passing through the axis of rotation, and the radial distance of the lateral surface of the stator in the circumferential direction is symmetrical to each of these planes.

9. Electrical machine according to one of the preceding claims, wherein each of the magnetic poles of the rotor is formed symmetrically in the circumferential direction to a plane passing through the axis of rotation, and the radial distance of the rotor surface in the circumferential direction is symmetrical to each of these planes.

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