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Title:
ROTOR FOR ANGULAR POSITION RESOLVER
Document Type and Number:
WIPO Patent Application WO/2019/166275
Kind Code:
A1
Abstract:
Rotor (10) for an angular position resolver, said rotor comprising a rotational body (1) defining an axis (3) of rotation, said rotational body comprising ferromagnetic material (2) defining on a radially outer surface of said rotational body a first region (4a), wherein at least an imaginary first circle (5) lies coaxially with said rotational body and wherein said first circle runs along said first region and along a second region (4b), which is devoid of ferromagnetic material. The invention is further directed to an angular position resolver comprising the rotor, to an angular position measuring arrangement comprising the angular position resolver and to a method of producing an angular position indicative signal, wherein the angular position measuring arrangement is used.

Inventors:
WYSS WALTER (CH)
Application Number:
PCT/EP2019/054053
Publication Date:
September 06, 2019
Filing Date:
February 19, 2019
Export Citation:
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Assignee:
ADMOTEC PREC AG (CH)
International Classes:
G01D5/22
Foreign References:
EP1739808A22007-01-03
DE102006024795A12007-11-29
EP2221945A22010-08-25
US6630763B12003-10-07
US20110109304A12011-05-12
EP0535181A11993-04-07
Attorney, Agent or Firm:
TROESCH SCHEIDEGGER WERNER AG (CH)
Download PDF:
Claims:
Claims

1. Rotor (10) for an angular position resolver, said rotor comprising a rotational body (1) defining an axis (3) of rotation, said rotational body comprising ferromagnetic material (2) defining on a radially outer surface of said rotational body a first region (4a) ,

wherein at least an imaginary first circle (5) lies

coaxially with said rotational body and wherein said first circle runs along said first region and along a second region (4b), which is devoid of ferromagnetic material.

2. Rotor (10) according to claim 1, wherein said

rotational body further comprises non-ferromagnetic

material (8) and wherein said ferromagnetic material (2) is arranged in the form of at least one island (6) being surrounded by said non-magnetic material or being arranged on said non-magnetic material.

3. Rotor (10) according to claim 2, wherein said at least one island (6) has an eye-shaped contour (7) .

4. Rotor (10) according to claim 1, wherein a radially oriented step in said ferromagnetic material defines a boundary between said first region and said second region.

5. Rotor (10) according to claim 4, wherein said

ferromagnetic material comprises layers of ferromagnetic sheet metal .

6. Rotor (10) according to claim 5, comprising a stack of coaxially arranged pieces of ferromagnetic sheet metal, wherein said pieces have identical geometry and each of said pieces is in a rotated position with regard to a neighboring piece, wherein said stack forms at its radially outer surface said first region and wherein said first region comprises at least one section (9) of trapezoidal form.

7. Rotor (10) according to any one of claims 1 to 6, wherein said first circle (5) is divided into first

sections crossing said first region and second sections crossing said second region, wherein pairs of adjacent first and second sections extend over an azimuthal angle = 360°/n with respect to said axis (3) of rotation, wherein n is an integral number.

8. Rotor (10) according to any one of claims 1 to 7, wherein said rotational body (1) has a central bore along said rotational axis, and wherein said rotational body in particular is a hollow cylinder.

9. Angular position resolver (100) comprising a rotor (10) according to any one of claims 1 to 8 and a stator (20), said rotor being rotatable around said axis (3) with respect to said stator, and wherein said stator comprises

- an exciting coil arrangement (P) configured to generate a magnetic field (H) entering into said rotational body at said first circle (5) , propagating across at least a part of said ferromagnetic material and emanating from said rotational body,

- a first measuring coil arrangement (SI) with at least one first coil facing towards said axis and

- a second measuring coil arrangement (S2) with at least one second coil facing towards said axis.

10. Angular position resolver (100) according to claim 9, wherein said stator (20) comprises a ring having a

multitude of axially oriented grooves, two neighboring grooves defining in between them a projection facing towards said axis and wherein coils of at least one of said exciting coil arrangement (P) , said first measuring coil arrangement (SI) and said second measuring coil arrangement (S2) are arranged in said grooves and around said

proj ections .

11. Angular position resolver (100) according to claim 9 or 10, wherein coils of at least one of said exciting coil arrangement (P) , said first measuring coil arrangement (SI) and said second measuring coil arrangement (S2) are

constructed as self-supporting air-core coils.

12. Angular position measuring arrangement comprising

- an angular position resolver (100) according to any one of claims 9 to 11,

- an alternating current power supply operatively connected to said exciting coil arrangement (P) ,

- at least a first voltage meter operatively connected to said first measuring coil arrangement (SI), and

- a second voltage meter operably connected to said second measuring coil arrangement (S2) .

13. Method of producing an angular position indicative signal, wherein an angular position measuring arrangement according to claim 12 is used and wherein said signal is indicative for the angular position of said rotor with respect to said stator, the method comprising the steps of:

- applying an alternating current to said exciting coil arrangement (P) , thereby generating a magnetic field (H) entering into said rotational body (1) in a region of said first circle (5) , propagating across at least a part of said ferromagnetic material and emanating from said

rotational body (1),

- measuring a first voltage signal induced by said magnetic field in said first measuring coil arrangement (SI),

- measuring a second voltage signal induced by said

magnetic field in said second measuring coil arrangement

(S2) , - evaluating amplitudes and phases of said first and second voltage signals to derive said angular position indicative signal .

Description:
Rotor for angular position resolver

The invention addressed herein relates to a rotor for an angular position resolver. Under further aspects, the invention relates to an angular position resolver and to a method of operating the resolver.

In different applications resolvers for measuring an angular position or an angular velocity of e.g. a shaft are applied. One type of angular position resolvers uses an induced magnetic field between a stator and a rotor being rotatable around an axis with respect to the stator. The rotor may e.g. be arranged on the shaft, the angular position of which is to be measured. The rotation axis of the rotor defines a cylindrical coordinate system with an axial direction parallel to the axis, a radial direction orthogonal to the axis and an azimuthal direction along a circumference described by the rotation of the rotor around the axis. Such angular position resolvers, which determine the azimuthal angular position of the rotor with respect to the stator, have a rotor that creates or modifies a spatial distribution of a magnetic field in a way that is specific to the azimuthal position of the rotor. By measuring this magnetic field on the stator side, the azimuthal position of the rotor with respect to the stator can be determined. Such an arrangement may be seen as a sensor for measuring angular positions or revolutions using inductive coupling. An azimuthal position resolver for measuring an angular position using an induced magnetic field between a stator and a rotor is known e.g. from the document

EP 0 535 181 A1. The rotor of an azimuthal position

resolver according to this document comprises a loop of magnetic material extending around the axis of the rotor and being arranged along a geometric plane cutting the axis of the rotor under an oblique angle. This loop of magnetic material is placed between two hollow cylindrical bodies, which are made of non-magnetic material. The hollow

cylindrical bodies have faces running parallel to the geometric plane. These faces are in contact with the loop of magnetic material to hold the loop in place, such that the rotor as a whole has the form of a hollow cylinder having on its outer surface magnetic pole faces formed by the loop of magnetic material. A sinusoidally shaped form of this pole faces becomes apparent, if the cylinder surface in unrolled on a plane. Only the stator of an azimuthal position resolver according to EP 0 535 181 A1 is wound with an exciting coil and with measuring coils.

Generally, angular position information of high angular precision is considered as valuable, particularly in the field of industrial automation, where angular position resolvers are used in the context of motion control of robots. Furthermore, a general trend towards higher

rotational speed of electro-motors increases the need for angular position resolvers delivering highly precise signals over a wide range of rotational speeds. The object of the present invention is to provide an alternative angular position resolver, in particular to provide an angular position resolver alleviating or solving one or more of the problems of known angular position resolvers .

This object is achieved by a rotor according to claim 1.

The rotor according to the invention is a for an angular position resolver. The rotor comprises a rotational body defining an axis of rotation. The rotational body comprises ferromagnetic material defining on a radially outer surface of the rotational body a first region,

wherein at least an imaginary first circle lies coaxially with said rotational body and wherein the first circle runs along the first region and along a second region, which is devoid of ferromagnetic material.

The first region along the first circle (i.e. the region with ferromagnetic material) and the second region along the first circle (i.e. the region, where there is no ferromagnetic material) both may comprise unconnected parts or may comprise a single connected region. The

ferromagnetic material may extend into the interior of the rotational body or may be arranged on its surface only.

The inventor has recognized that with this rotor, a

component for an angular position resolver is provided, which is easy to fabricate. It provides a low-cost alternative to previously known rotors. Furthermore, the rotor according to the invention enables to implement various geometries of the first and second region by simple fabrication steps. It enables further improvements by designing the geometries of the first and second region such that a resolver equipped with the rotor produces clean signals, i.e. signals free of unwanted higher order

harmonics, as defined in the embodiments still to be addressed .

Embodiments of the rotor are defined by the features of claims 2 to 8.

In one embodiment of the rotor according to the invention, which may be combined with any of the embodiments still to be addressed unless in contradiction, the rotational body further comprises non-ferromagnetic material and the ferromagnetic material is arranged in the form of at least one island being surrounded by said non-magnetic material or being arranged on said non-magnetic material.

A rotor according to this embodiment may be manufacture in a particularly simple way, for example in the following steps: turning a ring-shaped body of non-ferromagnetic material, e.g. of austenitic steel, brass or bronce;

coating the ring-shaped body with a layer of ferromagnetic material, e.g. by galvanically depositing the ferromagnetic material; milling away the ferromagnetic material in the second region and retaining the ferromagnetic material in the first region. The milling may be performed on a numerically controlled machine tool, such that any desired geometry of the first and second regions may be realized with high precision.

In one embodiment of the rotor according to the invention, which may be combined with any of the preaddressed

embodiments and any of the embodiments still to be

addressed unless in contradiction, the at least one island has an eye-shaped contour.

With this embodiment of the rotor, particularly clean electrical signals may be received in an angular position resolver. The islands of ferromagnetic material having eye shaped contour provide for a smooth transition from angular positions, where there is no ferromagnetic material

present, to angular positions, where the first region reaches its maximum axial extension, i.e. the ferromagnetic islands have their maximum width. The eye-shaped contour may as an example be defined by sections of sine functions along said first circle. The specific geometry of the eye shaped contour may be adapted such that the fraction of higher harmonics in a signal indicative for the angular position of the rotor is kept low. This may be achieved by superposing higher harmonic sine functions, e.g. sine functions with periodicity 3 or 5 to the first order sine function. The superposed sine functions may be phase shifted with respect to the first order sine function. This way, a continuous curve defining the eye-shaped contour with high precision may defined. The adaptations to the eye-shaped contour may be developed in an iterative manner by determining undesired higher order harmonics from a realization of a resolver with the inventive rotor and by applying a correction to the eye-shaped contour, which defines the geometry of the first region. The correction may correspond in its form to the undesired harmonics, but has opposite phase. This contour may e.g. be produced by numerically controlled machine tools, such that a precisely defined continuous curve results.

In one embodiment of the rotor according to the invention, which may be combined with any of the preaddressed

embodiments and any of the embodiments still to be

addressed unless in contradiction, a radially oriented step in the ferromagnetic material defines a boundary between the first region and the second region.

On one side of the radially oriented step, the

ferromagnetic material is recessed from the first circle.

As a result, a salient magnetic pole results in the first region. Magnetic fields generated by the stator of an angular position resolver are guided into the salient magnetic poles.

In one embodiment of the rotor according to the invention, which may be combined with any of the preaddressed

embodiments and any of the embodiments still to be

addressed unless in contradiction, the ferromagnetic material comprises layers of ferromagnetic sheet metal. The layers of ferromagnetic sheet metal may for example be layers of a non-oriented grain electrical sheet metal. A commercially available non-oriented grain electrical sheet metal suitable for this purpose carries the designation "N020 " .

In one embodiment of the rotor according to the invention, which may be combined with any of the preaddressed

embodiments and any of the embodiments still to be

addressed unless in contradiction, the rotor comprises a stack of coaxially arranged pieces of ferromagnetic sheet metal. The pieces have identical geometry and each of the pieces is in a rotated position with regard to a

neighboring piece. The stack forms at its radially outer surface the first region. The first region comprises at least one section of trapezoidal form.

The stack for a rotor of this embodiment may e.g. be fabricated by the steps of punching identical pieces of sheet metal, stacking them coaxially and completely

overlapping and then twisting the stack with respect to the rotational axis. As final step the stack is packetized such that a stable configuration results. The last step may e.g. be realized by applying a thermally bonding varnish and baking the stack. Another option would be to connect the pieces by welding.

In one embodiment of the rotor according to the invention, which may be combined with any of the preaddressed

embodiments and any of the embodiments still to be addressed unless in contradiction, the first circle is divided into first sections crossing the first region and second sections crossing the second region, wherein pairs of adjacent first and second sections extend over an azimuthal angle = 360°/n with respect to the axis of rotation. The number n is an integral number, i.e. n = 1, n=2, n=3, n=4, etc.

By selecting a specific number n, the rotor may be adapted to a corresponding stator in an angular position resolver having the same number n of pole pairs arranged on a circumference of the stator. In the case of n = 1, there exist exactly one first section and one second section of the imaginary first circle around the rotor and the first and the second section together cover the complete circle, i.e. extend over 360°. For n = 2 and higher, a pattern of first and second sections is repeated n times over the complete circle.

In one embodiment of the rotor according to the invention, which may be combined with any of the preaddressed

embodiments and any of the embodiments still to be

addressed unless in contradiction, the rotational body has a central bore along the rotational axis. In particular, the rotational body may be a hollow cylinder. This

embodiment of the rotor is e.g. suited to be mounted on a shaft, the angular position of which is to be detected.

Further in the scope of the invention lies an angular position resolver according to claim 9. An angular position resolver according to the invention comprises a rotor according to the invention. The angular position resolver further comprises a stator. The rotor is rotatable around the axis with respect to the stator. The stator comprises

- an exciting coil arrangement configured to generate a magnetic field entering into the rotational body in the region of the first circle, propagating across at least a part of the ferromagnetic material and

emanating from the rotational body,

- a first measuring coil arrangement with at least one first coil facing towards the axis and

- a second measuring coil arrangement with at least one second coil facing towards the axis.

As an example, the exciting coil arrangement, the first or the second measuring coil arrangement may comprise coils, e.g. saddle coils, defining areas each surrounded by a respective number of coil windings being an approximation to a sine or cosine function of the azimuthal position of the area multiplied by a factor common to all the coils of the respective coil arrangement. The inventor has

recognized that this embodiment leads to a filtering out of harmonic distortions of higher order. This is particularly useful in the case, where first, second and higher order time derivatives are calculated based on the azimuthal position of the rotor to derive angular speed, angular acceleration and angular jerk. The latter quantities are highly sensitive to irregularities in the basic signal describing the azimuthal position. Particularly clean signals are achieved, if the coil windings approximate a sinusoidal distribution with respect the azimuthal

direction .

Embodiments of the angular position resolver are defined by the features of claim 10 and 11.

In one embodiment of the angular position resolver

according to the invention, which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in contradiction, the stator comprises a ring having a multitude of axially oriented grooves, two neighboring grooves defining in between them a projection facing towards the axis of the rotor. The coils of at least one of the exciting coil arrangement, the first measuring coil arrangement and the second measuring coil arrangement are arranged in the grooves and around the proj ections .

The projections and grooves may in particular provide a common support structure for all of the coil arrangements. The ring may comprise magnetic material, such that magnetic fields are efficiently guided through the coils of the coil arrangements .

In one embodiment of the angular position resolver

according to the invention, which may be combined with any of the preaddressed embodiments and any of the embodiments still to be addressed unless in contradiction, coils of at least one of the exciting coil arrangement, the first measuring coil arrangement and the second measuring coil arrangement are constructed as self-supporting air-core coils .

This embodiment makes possible a very compact design of the angular position resolver.

Further in the scope of the invention lies an angular position measuring arrangement according to claim 12.

Such an angular position measuring arrangement comprises

- an angular position resolver according to the invention,

- an alternating current power supply operatively connected to the exciting coil arrangement,

- at least a first voltage meter operatively connected to the first measuring coil arrangement, and

- a second voltage meter operably connected to the second measuring coil arrangement.

The invention is further directed to a method of producing an angular position indicative signal according to

claim 13.

In the method, an angular position measuring arrangement according to the invention is used. The signal produced by the method is indicative for the angular position of the rotor with respect to the stator. The method comprises the steps of:

- applying an alternating current to the exciting coil arrangement, thereby generating a magnetic field entering into the rotational body in a region of the first circle, propagating across at least a part of the ferromagnetic material and emanating from the rotational body,

- measuring a first voltage signal induced by the magnetic field in the first measuring coil arrangement,

- measuring a second voltage signal induced by the magnetic field in the second measuring coil arrangement,

- evaluating amplitudes and phases of the first and second voltage signals to derive the angular position indicative signal .

The method may be executed by applying an alternating current having a frequency in the range from Hz to MHz. In Particular, the alternating current may have a frequency in the range from 2 kHz to 10 kHz.

Dimensions of the rotor and/or materials used to build the rotor may be adapted to the frequency of the alternating current, that will be applied when executing the method.

The invention shall now be further exemplified with the help of figures. The figures show:

Fig. 1 a perspective view of a rotor according to the invention;

Fig. 2 a functional diagram of an angular position resolver;

Fig. 3 different views of a rotational body of an embodiment of the rotor in Figs. 3. a) to 3.d); Fig. 4 an unrolled surface of an embodiment of the rotor together with a schematic configuration of coil windings on a stator of an angular position resolver;

Fig. 5 schematic configurations of coil winding on a stator of an embodiment of an angular position

resolver;

Fig. 6 a cross-section through an embodiment of an angular position resolver;

Fig. 7 different views of a rotational body of an embodiment of the rotor in Figs. 7. a) and 7.b);

Fig. 8 different views of a rotational body of a further embodiment of the rotor in Figs. 8. a) and 8.b) .

Fig. 1 shows a perspective view of an embodiment of a rotor according to the invention. The rotor 10 comprises a rotational body 1. In the embodiment shown here, the rotational body has the form of a hollow cylinder. The rotational body has an axis 3 of rotation corresponding to the cylinder axis and running through the central bore of the hollow cylinder. The axis 3 of rotation is indicated as dash-dotted line. The rotor comprises ferromagnetic

material 2, indicated by diagonal hatching. On the radially outer surface of the rotational body, there is a first region 4a, which is covered by ferromagnetic material 2. There is also a second region 4b, which is devoid of ferromagnetic material. Here, the rotor comprises non ferromagnetic material 8, indicated by white color. In the embodiment shown here, most of the rotational body is built from non-ferromagnetic material, which for example may be austenitic steel, brass or bronze. An imaginary first circle 5 lying coaxial the rotational body is indicated by a dashed line. This first circle runs along the first region 4a as well as the second region 4b. In the

embodiment shown here, the first region 4a comprises unconnected parts of the region, which are arranged like islands in the second region 4b. These parts of the first region are arranged along the first circle and form

magnetic pole faces. Specifically, in the embodiment shown here, these islands have an eye-shaped contour.

Fig. 2 shows a functional diagram of an angular position resolver. The angular position resolver comprises a rotor 10 and a stator 20. The rotor 10 is rotatable around axis 3, which in this view lies perpendicular to the plane of the figure. The stator comprises three types of coil arrangements: an exciting coil arrangement P, a first measuring coil arrangement SI and a second measuring coil arrangement S2. Each of these coil arrangements, which are symbolically indicated, has electrical ports, which are symbolically indicated as circles. At these ports, an alternating current power supply may be connected to said exciting coil arrangement P, a first voltage meter may be connected to said first measuring coil arrangement SI and a second voltage meter may be connected to said second measuring coil arrangement S2, such that an angular

position measuring arrangement results. The rotor 10 is rotatable around the axis 3 with respect to the stator 20. The angular position of the rotor (azimuthal position Q) is detected by angular position resolver due to the fact that the flux linkage of the coil arrangement is varied depending on the azimuthal position Q of the rotor relative to the stator. The rotor comprises ferromagnetic material 2, here symbolized by the vertically hatched part.

Figs. 3. a) to 3.d) shows different views of a rotational body 1 of an embodiment of the rotor as shown in Fig. 1. Fig. 3. a) shows a front view of the rotational body 1;

Fig. 3.b) shows a side view of the rotational body 1;

Fig. 3.c) shows the radially outer surface of the

rotational body 1 unrolled into a plane;

Fig. 3.d) shows a perspective view of the rotational body 1

In Figs. 3. a) to 3.d), the rotational body has

substantially the shape of a hollow cylinder with an inner diameter ID and outer diameter OD. On its radially outer surface, three islands 6 of ferromagnetic material slightly protrude over the radially outer surface. These islands 6 define the first region. The reminder of the rotational body is made of non-ferromagnetic material 8. The height of the islands as shown here may be selected to be t,

corresponding to a thickness t of a ferromagnetic layer deposited onto the non-ferromagnetic material. As an example, the height or the thickness, respectively, could be selected to be in the range t = 50 micrometers to t =

100 micrometers. The ferromagnetic material of the islands 6 may e.g. be Nickel. The islands 6 define the first regions of the rotor. As apparent from Fig. 3.c), the first circle 5 has first sections crossing said first region and second sections crossing said second region, wherein pairs of adjacent first and second sections extend over an azimuthal angle = 360°/3 = 120°, thus being suited for a configuration having n=3 pole pairs. The islands 6 have contours 7, which contours have eye-shaped geometry. The contour may be defined by sections of sine functions along the unrolled first circle indicated by dashed lines. In the present case, these are two sine functions showing three complete oscillations over the complete circle. A first sine

function defines the contour by its positive sections, a second sine function defines the contour by its negative sections. The other sections of the sine functions are not displayed. The two sine functions have a mutual phase shift of 180°. Thus, same pattern is repeated three times. At their largest azimuthal extension, the ferromagnetic islands 6 extend over an angle of 60°.

Fig. 4 shows in its lower part an unrolled radially outer surface of an embodiment of the rotor. The horizontal direction in the figure corresponds to the azimuthal direction with respect to the axis of the rotor. The second region 4b, shown in dark, is devoid of ferromagnetic material and the first region 4a, shown in white, is the region, where ferromagnetic material is present, i.e. the region where magnetic pole faces can be established by applying a magnetic field. The first region 4a has an eye- shaped contour. This contour may e.g. be produced by numerically controlled machine tools. The eye-shaped contour may be adapted such that the fraction of higher harmonics in a signal indicative for the angular position of the rotor is kept low. In three rows in the upper part of the figure, schematic configurations of coil windings on a stator of an angular position resolver are shown, thereby Nref indicates number and winding direction of an exciting coil arrangement P, Nsin indicates number and winding direction of a first measuring coil arrangement SI and Ncos indicates number and winding direction of a second

measuring coil arrangement S2. The coil arrangements as shown here may be wound on projections on a stator ring.

The present figure shows the configuration for n=2 pole pairs. The basic building block, which covers an azimuthal angle denoted by "360°el" may be repeated several times over the complete circumference of the stator, such that n=2, 3, 4, 5, ... pole pairs result. According to the choice of n, the azimuthal angle "360°el" corresponds to a

geometrical angle 360°/n, i.e. to 180°, 120°, 90°, 72°, etc. A rotation of the rotor by 360°/n results in a 360° phase shift of the electrical signals obtained by measuring the voltage induced in SI and S2. A further possibility would be to select "360°el" to cover a geometrical angle of 360°, i.e. the complete circumference of the rotor, which corresponds to n=l . In the latter case, only the left half of Fig. 4 describes the outer surface of the rotor and a suitable coil configuration of the stator.

The coil distributions shown in Fig. 4 may be realized by winding coils around protrusions or notches on ring with grooves separating these protrusions. In the case shown, four protrusions cover an azimuthal angle corresponding to "360°el". The coil distributions can be seen as rough approximation to sine or cosine distributions. A better approximation to sine or cosine distribution may be

achieved by increasing the number of protrusions covering the azimuthal angle corresponding to "360°el" to, as an example, eight or twelve protrusions.

Fig. 5 shows schematic configurations of coil windings on a stator of an angular position resolver, similar to the ones shown in Fig. 4, but suited for coil arrangements that are constructed as self-supporting air-core coils. In each of the Figs. 5. a) to 5,c) a building block covering an

azimuthal angle "360°el" corresponding to a geometrical angle 360°/n is shown. In the upper part of each figure, the pattern of winding number and winding direction is indicated. In the lower part of each figure, a schematic coil arrangement implementing the corresponding pattern. Building blocks of the coils arrangement may be connected in series by connecting the coil ends indicated as circles. Fig. 5. a) shows a building block suitable for an exciting coil arrangement P, Fig. 5.b) shows a building block suitable for a first measuring coil arrangement SI and Fig. 5.c) shows a building block suitable for a second measuring coil arrangement S2. A better approximation to sine or cosine distributions may be achieved in an analogous way as mentioned in connection with Fig. 4 for self-supporting air-core coils as well. Fig. 6 shows a cross-section through an embodiment of an angular position resolver, cutting through a part of the stator 20, which carries coil arrangements P, SI, S2, and a part of the rotor 10. Crosses and dots indicate the winding directions of the individual wires of the coil

arrangements, which correspond to the coil arrangements shown in Figs. 5. a) to 5.c) . The cross-section is cut along the imaginary first circle surrounding the rotor. The rotor comprises a rotational body 1 comprising ferromagnetic material 2 (shown diagonally hatched) . Rotor and stator are separated by an air gap 21 and rotatable with respect to each other. A single field line of a magnetic field H is schematically shown. By applying an alternating current to the exciting coil arrangement P, such a magnetic field may be generated. The magnetic field H enters into the

rotational body 1 in the region of the first circle, i.e. in the cutting plane of the present cross-section, the magnetic field H propagates across at least a part of the ferromagnetic material 2 and emanates from the rotational body. The magnetic field alternates as the alternating current applied to the exciting coil arrangement P and thereby induces voltages in the first and second measuring coil arrangements SI and S2. The amplitude of the induced voltage depends on the amount of ferromagnetic material that is traversed by the magnetic field H and of the geometry of field line of the magnetic field, which is guided by the ferromagnetic material. This amplitude of the induced voltage depends on the position of the first and second regions of the rotor with respect to the exciting coil arrangement P and thus on the angular position of the rotor with respect to the stator.

Fig. 7. a) shows a side view of a rotational body built as stack of coaxially arranged pieces of ferromagnetic sheet metal. The pieces are made of ferromagnetic material 2 and have a radially protruding portion which establishes the first region of the rotor. The pieces of sheet material have identical geometry and each of said pieces is in a slightly rotated position with regard to a neighboring piece, such that sections of trapezoidal form 9 results at the outer radius of the rotational body.

Fig. 7.b) shows a top view of one of the pieces of

ferromagnetic sheet metal 2 from the stack shown in Fig.

7. a) . The position of an imaginary first circle 5 is shown in dashed line for easier orientation. The piece of

ferromagnetic sheet metal has the form of a ring with a circular inner hole and an outer contour which has three protruding regions touching the first circle 5. The

protruding regions are separated by three recessed regions. In the complete stack, the protruding regions establish the first regions 4a of the rotor and the recessed regions establish the second regions 4b of the rotor. The

protruding regions of individual pieces partially overlap with the corresponding protruding region of the neighboring piece in order to form the trapezoidal section 9 visible in Fig. 7. a) . The first regions 4a may be seen as salient poles of the rotor. Fig. 8. a) shows a side view of a rotational body build from non-ferromagnetic material 8, which carries on a radially outer surface ferromagnetic material 2 (shown in black color) . In the embodiment shown here, the ferromagnetic material 2 is structured as eye-shaped island.

Fig. 8.b) shows a top view of the rotational body shown in Fig. 8. a) . Three sections of ferromagnetic material 2

(shown in black color) are arranged along the circle 5. In these sections the first region 4a is established. Three sections, which are free of ferromagnetic material, separate the sections, where ferromagnetic material is present, and establish the second region 4b on the radially outer surface of the rotational body. In the embodiment shown here, the rotational body has substantially the form of a hollow cylinder.

List of reference signs

1 rotational body

2 ferromagnetic material

3 axis

4a first region (of radially outer surface)

4b second region (of radially outer surface)

5 first circle

6 island (of ferromagnetic material, on rotational body)

7 eye-shaped contour

8 non-ferromagnetic material

9 section of trapezoidal form

10 rotor

20 stator

21 air gap

100 angular position resolver

360°el azimuthal angle corresponding to 360° electrical phase shift

ID inner diameter (of hollow cylinder)

OD outer diameter (of hollow cylinder)

t thickness (of layer of ferromagnetic material)

P exciting coil arrangement

51 first measuring coil arrangement

52 second measuring coil arrangement

Nref number of coils of exciting coil arrangement

Ncos number of coils of first measuring coil arrangement Nsin number of coils of second measuring coil arrangement Q angular (azimuthal) position of the rotor