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Title:
2-DOF VR RESOLVER FOR DETECTING LINEAR AND ROTATIONAL POSITIONS IN HELICAL MOTIONS
Document Type and Number:
WIPO Patent Application WO/2023/148562
Kind Code:
A1
Abstract:
A 2-degrees of freedom (DoF) variable reluctance (VR) resolver for detecting linear and rotational positions in a helical motion. The 2 -DoF VR resolver includes a rotor, a stator, and a variable air-gap between the rotor and the stator. A length of the variable air-gap varies in radial and axial directions.

Inventors:
NASIRI-GHEIDARI ZAHRA (IR)
ZARE FATEME (IR)
Application Number:
PCT/IB2023/050186
Publication Date:
August 10, 2023
Filing Date:
January 10, 2023
Export Citation:
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Assignee:
NASIRI GHEIDARI ZAHRA (IR)
ZARE FATEME (IR)
International Classes:
H02K24/00; G01B7/30; G01D5/20; H02K11/21; H02K19/06
Foreign References:
US20050168091A12005-08-04
Other References:
ZARE F.; TOOTOONCHIAN F.; DANIAR A.: "Highly Reliable Reduced Part Integrated 2DOF Helical Winding Resolver", 2021 IEEE 13TH INTERNATIONAL SYMPOSIUM ON DIAGNOSTICS FOR ELECTRICAL MACHINES, POWER ELECTRONICS AND DRIVES (SDEMPED), IEEE, vol. 1, 22 August 2021 (2021-08-22), pages 483 - 488, XP034026788, DOI: 10.1109/SDEMPED51010.2021.9605508
Attorney, Agent or Firm:
IDESAZAN ASR AFTAB (IR)
Download PDF:
Claims:
What is claimed is: 1. A 2-degrees of freedom (DoF) variable reluctance (VR) resolver for detecting linear and rotational positions in a helical motion, comprising: a rotor comprising a shape, each respective point of the shape defined by the following: X = (A − B sin(αu))(cos(u))(C − sin(βv)) Y = (A − B sin(αu))(cos(u))(C − sin(βv)) Z = Dv where: ^ is a horizontal component of each respective point of the shape, ^ is a vertical component of each respective point of the shape, ^ is an axial component of each respective point of the shape, ^ and ^ are independent variables where 0 ≤ u, v < 2ղ , α is a number of pole pairs of the rotor in a radial direction, β is a number of pole pairs of the rotor in an axial direction, and A, B, C, and D are constant parameters; a stator placed inside the rotor, the stator comprising: a stator core, the stator core comprising a plurality of horizontal slots and a plurality of vertical slots; an excitation winding placed in an excitation slots subset of the plurality of horizontal slots, coils of the excitation winding are placed in a first horizontal slot of the plurality of horizontal slots, a fourth horizontal slot of the plurality of horizontal slots, a seventh horizontal slot of the plurality of horizontal slots, and a tenth horizontal slot of the plurality of horizontal slots; a horizontal signal winding placed in a signal slots subset of the plurality of horizontal slots, the horizontal signal winding comprising: a plurality of horizontal sine coils placed in a third horizontal slot of the plurality of horizontal slots, a fifth horizontal slot of the plurality of horizontal slots, a ninth horizontal slot of the plurality of horizontal slots, and an eleventh horizontal slot of the plurality of horizontal slots; and a plurality of horizontal cosine coils placed in a second horizontal slot of the plurality of horizontal slots, a sixth horizontal slot of the plurality of horizontal slots, an eighth horizontal slot of the plurality of horizontal slots, and a twelfth horizontal slot of the plurality of horizontal slots; and a vertical signal winding placed in the plurality of vertical slots, the vertical signal winding comprising: a plurality of vertical sine coils placed in a first vertical slot of the plurality of vertical slots, a second vertical slot of the plurality of vertical slots, a third vertical slot of the plurality of vertical slots, a seventh vertical slot of the plurality of vertical slots, an eighth vertical slot of the plurality of vertical slots, and a ninth vertical slot of the plurality of vertical slots; and a plurality of vertical cosine coils placed in a fourth vertical slot of the plurality of vertical slots, a fifth vertical slot of the plurality of vertical slots, a sixth vertical slot of the plurality of vertical slots, a tenth vertical slot of the plurality of vertical slots, an eleventh vertical slot of the plurality of vertical slots, and a twelfth vertical slot of the plurality of vertical slots; and a variable air-gap between the rotor and the stator, a length of the variable air-gap varying in radial and axial directions, wherein: different coils of the excitation winding comprise an equal number of turns; different horizontal signal coils of the horizontal signal winding comprise an equal number of turns; and different vertical signal coils of the vertical signal winding comprise an equal number of turns. 2. A 2-degrees of freedom (DoF) variable reluctance (VR) resolver for detecting linear and rotational positions in a helical motion, comprising: a rotor; a stator; and a variable air-gap between the rotor and the stator, a length of the variable air-gap varying in radial and axial directions.

3. the 2-DoF VR resolver of claim 2, wherein the rotor comprises a shape, each respective point of the shape defined by the following: X = (A − B sin(αu))(cos(u))(C − sin(βv)) Y = (A − B sin(αu))(cos(u))(C − sin(βv)) Z = Dv where: X is a horizontal component of each respective point of the shape, Y is a vertical component of each respective point of the shape, Z is an axial component of each respective point of the shape, u and ^ are independent variables where 0 ≤ ^, ^ < 2^, α is a number of pole pairs of the rotor in a radial direction, β is a number of pole pairs of the rotor in an axial direction, and ^, ^, ^, and ^ are constant parameters. 4. the 2-DoF VR resolver of claim 2, wherein the rotor comprises a shape, each respective point of the shape defined by the following: X = (A − B sin(αu))(cos(u))(C − sin(βv)) Y = (A − B sin(αu))(cos(u))(C − sin(βv)) Z = Dv where: X is a horizontal component of each respective point of the shape, Y is a vertical component of each respective point of the shape, Z is an axial component of each respective point of the shape, u and ^ are independent variables where 0 ≤ u, v < 2ղ , α is a number of pole pairs of the rotor in a radial direction, β is a number of pole pairs of the rotor in an axial direction, and A, B, C, and D are constant parameters.

5. The 2-DoF VR resolver of claim 2, wherein the stator comprises a stator core, the stator core comprising a plurality of horizontal slots and a plurality of vertical slots. 6. The 2-DoF VR resolver of claim 5, wherein the stator further comprises: an excitation winding placed in an excitation slots subset of the plurality of horizontal slots; a horizontal signal winding placed in a signal slots subset of the plurality of horizontal slots; and a vertical signal winding placed in the plurality of vertical slots. 7. The 2-DoF VR resolver of claim 6, wherein the signal slots subset comprises an even number of horizontal slots of the plurality of horizontal slots. 8. The 2-DoF VR resolver of claim 7, wherein the horizontal signal winding comprises a plurality of horizontal sine coils and a plurality of horizontal cosine coils, a number of the plurality of horizontal sine coils equal to a number of the plurality of horizontal cosine coils. 9. The 2-DoF VR resolver of claim 8, wherein the vertical signal winding comprises a plurality of vertical sine coils and a plurality of vertical cosine coils, a number of the plurality of vertical sine coils equal to a number of the plurality of vertical cosine coils. 10. The 2-DoF VR resolver of claim 9, wherein coils of the excitation winding are placed in a first horizontal slot of the plurality of horizontal slots, a fourth horizontal slot of the plurality of horizontal slots, a seventh horizontal slot of the plurality of horizontal slots, and a tenth horizontal slot of the plurality of horizontal slots. 11. The 2-DoF VR resolver of claim 10, wherein the plurality of horizontal sine coils are placed in a third horizontal slot of the plurality of horizontal slots, a fifth horizontal slot of the plurality of horizontal slots, a ninth horizontal slot of the plurality of horizontal slots, and an eleventh horizontal slot of the plurality of horizontal slots.

12. The 2-DoF VR resolver of claim 11, wherein the plurality of horizontal cosine coils are placed in a second horizontal slot of the plurality of horizontal slots, a sixth horizontal slot of the plurality of horizontal slots, an eighth horizontal slot of the plurality of horizontal slots, and a twelfth horizontal slot of the plurality of horizontal slots. 13. The 2-DoF VR resolver of claim 12, wherein the plurality of vertical sine coils are placed in a first vertical slot of the plurality of vertical slots, a second vertical slot of the plurality of vertical slots, a third vertical slot of the plurality of vertical slots, a seventh vertical slot of the plurality of vertical slots, an eighth vertical slot of the plurality of vertical slots, and a ninth vertical slot of the plurality of vertical slots. 14. The 2-DoF VR resolver of claim 13, wherein the plurality of vertical cosine coils are placed in a fourth vertical slot of the plurality of vertical slots, a fifth vertical slot of the plurality of vertical slots, a sixth vertical slot of the plurality of vertical slots, a tenth vertical slot of the plurality of vertical slots, an eleventh vertical slot of the plurality of vertical slots, and a twelfth vertical slot of the plurality of vertical slots. 15. The 2-DoF VR resolver of claim 14, wherein: different coils of the excitation winding comprise an equal number of turns; different horizontal signal coils of the horizontal signal winding comprise an equal number of turns; and different vertical signal coils of the vertical signal winding comprise an equal number of turns. 16. The 2-DoF VR resolver of claim 2, wherein: the stator is placed inside the rotor; each of the stator and the rotor is made of a respective ferromagnetic material; and the rotor is filled with a solid material. 17. A method for detecting linear and rotational positions in a helical motion, the method comprising: placing a stator of a 2-degrees of freedom (DoF) variable reluctance (VR) resolver inside a rotor of a 2-degrees of freedom (DoF) variable reluctance (VR) resolver, the 2-degrees of freedom (DoF) variable reluctance (VR) resolver comprising a variable air-gap between the rotor and the stator, a length of the variable air-gap varying in radial and axial directions; placing an excitation winding and a horizontal signal winding in horizontal slots of the stator; placing a vertical signal winding in vertical slots of the stator; applying, utilizing a high-frequency voltage source, a high-frequency voltage to the excitation winding; obtaining, utilizing one or more processors, the linear position based on induced voltages on the horizontal signal winding; and obtaining, utilizing one or more processors, the rotational position based on induced voltages on the vertical signal winding. 18. The method of claim 17, wherein: placing the horizontal signal winding in the horizontal slots comprises placing a plurality of horizontal sine coils and a plurality of horizontal cosine coils in the horizontal slots, a number of the plurality of horizontal sine coils equal to a number of the plurality of horizontal cosine coils; and placing the vertical signal winding in the vertical slots comprises placing a plurality of vertical sine coils and a plurality of vertical cosine coils in the vertical slots, a number of the plurality of vertical sine coils equal to a number of the plurality of vertical cosine coils. 19. The method of claim 18, wherein obtaining the linear position comprises calculating the linear position according to an operation defined by the following: where: X is the linear position, VSin is an envelope of the first induced voltage on the plurality of horizontal sine, Vcos is an envelope of an induced voltage on the plurality of horizontal cosine coils, L is a length of the rotor, and β is a number of pole pairs of the rotor in an axial direction. 20. The method of claim 18, wherein obtaining the rotational position comprises calculating the rotational position according to an operation defined by the following: where: is the rotational position, VSin is an envelope of an induced voltage on the plurality of vertical sine coils, Vcos is an envelope of an induced voltage on the plurality of vertical cosine coils, and α is a number of pole pairs of the rotor in a radial direction.

Description:
2-DOF VR RESOLVER FOR DETECTING LINEAR AND ROTATIONAL POSITIONS IN HELICAL MOTIONS TECHNICAL FIELD [0001] The present disclosure generally relates to electrical machines, and particularly, to resolvers. BACKGROUND ART [0002] Two-degrees of freedom (2-DoF) electrical machines may produce motion in two independent directions. Using 2-DoF electrical machines may reduce volume and mass compared to two separate electrical machines. However, 2-DoF electrical machines may need position sensors in their control loops. [0003] Common position sensors include encoders and resolvers. Although encoders are less expensive than resolvers, their performance may be affected in a polluted environment with a wide temperature variation or a high mechanical vibration. Therefore, resolvers may be a better choice in harsh applications. Robust performance of resolvers is due to their structures. They are two-phase synchronous generators with sinusoidal excitations on their rotors. To feed excitations, winding slip rings and brushes may be used in brushed resolvers [US Patents no. 10,627,258 B2 and 11,169,007 B2]. However, due to challenges of using brushes, brushed resolvers may be replaced with brushless resolvers [US Patents no. 10,508,931 B2 and 10,753,771 B2]. In brushless resolvers, an excitation winding is fed using a rotary transformer (RT). Primary coils of RTs are placed on stators and may be fed using high frequency voltages. Induced voltage on secondary coils (that is, rotating coils) may be used for feeding excitation windings of resolvers. Although using RTs may lead to brushless excitation of resolvers, they may cause challenges, such as leakage flux of RTs that may link with resolver signal windings and a phase shift between primary and secondary voltages of RTs. [0004] There is, therefore, a need for a 2-DoF resolver that may be able to simultaneously measure rotational and linear positions. There is also a need for a 2-DoF resolver for detecting rotational and linear positions without increasing volume, mass, or complexity of control systems. There is further a need for a 2-DoF resolver that may provide higher reliability of position determination. SUMMARY OF THE DISCLOSURE [0005] This summary is intended to provide an overview of the subject matter of the present disclosure, and is not intended to identify essential elements or key elements of the subject matter, nor is it intended to be used to determine the scope of the claimed implementations. The proper scope of the present disclosure may be ascertained from the claims set forth below in view of the detailed description below and the drawings. [0006] In one general aspect, the present disclosure describes an exemplary 2-degrees of freedom (DoF) variable reluctance (VR) resolver for detecting linear and rotational positions in a helical motion. An exemplary 2-DoF VR resolver may include a rotor, a stator, and a variable air-gap between the rotor and the stator. An exemplary length of the variable air-gap may vary in radial and axial directions. An exemplary stator may be placed inside the rotor. In an exemplary embodiment, each of the stator and the rotor may be made of a respective ferromagnetic material. An exemplary rotor may be filled with a solid material. [0007] An exemplary stator may include a stator core. An exemplary stator core may include a plurality of horizontal slots and a plurality of vertical slots. An exemplary stator may further include an excitation winding, a horizontal signal winding, and a vertical signal winding. An exemplary of excitation winding may be placed in an excitation slots subset of the plurality of horizontal slots. An exemplary horizontal signal winding may be placed in a signal slots subset of the plurality of horizontal slots. An exemplary vertical signal winding may be placed in the plurality of vertical slots. An exemplary signal slots subset may include an even number of horizontal slots of the plurality of horizontal slots. [0008] In an exemplary embodiment, the horizontal signal winding may include a plurality of horizontal sine coils and a plurality of horizontal cosine coils. An exemplary number of the plurality of horizontal sine coils may be equal to a number of the plurality of horizontal cosine coils. In an exemplary embodiment, the vertical signal winding may include a plurality of vertical sine coils and a plurality of vertical cosine coils. An exemplary number of the plurality of vertical sine coils may be equal to a number of the plurality of vertical cosine coils. [0009] In an exemplary embodiment, different coils of the excitation winding may include an equal number of turns. In an exemplary embodiment, different horizontal signal coils of the horizontal signal winding may include an equal number of turns. In an exemplary embodiment, different vertical signal coils of the vertical signal winding may include an equal number of turns. [0010] Other exemplary systems, methods, features and advantages of the implementations will be, or will become, apparent to one of ordinary skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description and this summary, be within the scope of the implementations, and be protected by the claims herein. BRIEF DESCRIPTION OF THE DRAWINGS [0011] The drawing figures depict one or more implementations in accord with the present teachings, by way of example only, not by way of limitation. In the figures, like reference numerals refer to the same or similar elements. [0012] FIG.1 shows a schematic of a cross-section of a 2-degrees of freedom (DoF) variable reluctance (VR) resolver, consistent with one or more exemplary embodiments of the present disclosure. [0013] FIG.2 shows a schematic of different shapes of rotors with a first structure, consistent with one or more exemplary embodiments of the present disclosure. [0014] FIG. 3 shows a schematic of different shapes of rotors with a second structure, consistent with one or more exemplary embodiments of the present disclosure. [0015] FIG. 4A shows a schematic of a stator core, consistent with one or more exemplary embodiments of the present disclosure. [0016] FIG. 4B shows a schematic of a horizontal winding, consistent with one or more exemplary embodiments of the present disclosure. [0017] FIG.4C shows a schematic of a vertical signal winding, consistent with one or more exemplary embodiments of the present disclosure. [0018] FIG.5A shows a diagram of an arrangement of a horizontal winding in a plurality of horizontal slots, consistent with one or more exemplary embodiments of the present disclosure. [0019] FIG.5B shows a diagram of an arrangement of a vertical signal winding in a plurality of vertical slots, consistent with one or more exemplary embodiments of the present disclosure. [0020] FIG.6 shows a flowchart of a method for detecting linear and rotational positions in a helical motion, consistent with one or more exemplary embodiments of the present disclosure. [0021] FIG. 7A shows a diagram of induced voltages on a horizontal signal winding, consistent with one or more exemplary embodiments of the present disclosure. [0022] FIG. 7B shows a diagram of envelopes of induced voltages on a horizontal signal winding, consistent with one or more exemplary embodiments of the present disclosure. [0023] FIG.7C shows a diagram of a linear position of a rotor, consistent with one or more exemplary embodiments of the present disclosure. [0024] FIG.8A shows a diagram of induced voltages on a vertical signal winding, consistent with one or more exemplary embodiments of the present disclosure. [0025] FIG.8B shows a diagram of envelopes of induced voltages on a vertical signal winding, consistent with one or more exemplary embodiments of the present disclosure. [0026] FIG.8C shows a diagram of a rotational position of a rotor, consistent with one or more exemplary embodiments of the present disclosure. [0027] FIG.9 shows a high-level functional block diagram of a computer system, consistent with one or more exemplary embodiments of the present disclosure. DESCRIPTION OF EMBODIMENTS [0028] In the following detailed description, numerous specific details are set forth by way of examples in order to provide a thorough understanding of the relevant teachings. However, it should be apparent that the present teachings may be practiced without such details. In other instances, well known methods, procedures, components, and/or circuitry have been described at a relatively high-level, without detail, in order to avoid unnecessarily obscuring aspects of the present teachings. [0029] The following detailed description is presented to enable a person skilled in the art to make and use the methods and devices disclosed in exemplary embodiments of the present disclosure. For purposes of explanation, specific nomenclature is set forth to provide a thorough understanding of the present disclosure. However, it will be apparent to one skilled in the art that these specific details are not required to practice the disclosed exemplary embodiments. Descriptions of specific exemplary embodiments are provided only as representative examples. Various modifications to the exemplary implementations will be readily apparent to one skilled in the art, and the general principles defined herein may be applied to other implementations and applications without departing from the scope of the present disclosure. The present disclosure is not intended to be limited to the implementations shown, but is to be accorded the widest possible scope consistent with the principles and features disclosed herein. [0030] Herein is disclosed an exemplary variable reluctance resolver that includes a stator, a rotor, and a variable air-gap between the stator and the rotor. An exemplary structure of the rotor may vary in axial and radial directions. As a result, an exemplary length of the air-gap may also vary in axial and radial directions, leading to variations of a reluctance of an exemplary resolver in axial and radial directions. Exemplary variations of the resolver’s reluctance in two different dimensions may result in a two degrees of freedom (2-DoF) resolver that may allow for determining the rotor’s linear and rotational positions utilizing a single excitation winding on the stator. For this purpose, exemplary signal windings may be placed in stator slots in horizontal and vertical directions. Arrangements of horizontal signal windings and vertical signal windings may allow for detecting rotor’s linear and rotational positions independently. To do so, an exemplary high-frequency voltage may be applied to the excitation winding and resulting induced voltages on horizontal signal windings and vertical signal windings on the stator may be measured. Exemplary linear and rotational positions of the rotor may be extracted from induced voltages on horizontal and vertical windings, respectively. [0031] FIG.1 shows a schematic of a cross-section of a 2-degrees of freedom (DoF) variable reluctance (VR) resolver, consistent with one or more exemplary embodiments of the present disclosure. An exemplary 2-DoF VR resolver 100 may be utilized for detecting linear and rotational positions in a helical motion. In an exemplary embodiment, 2-DoF VR resolver may include a rotor 102, a stator, and a variable air-gap 104. An exemplary stator may include a stator core 105, an excitation winding 106, and signal windings 107. In an exemplary embodiment, rotor 102 and stator core 105 may be made of ferromagnetic materials. In an exemplary embodiment, rotor 102 may be either hollow or filled with a solid material. In an exemplary embodiment, rotor 102 may be placed inside stator core 105. However, in an exemplary embodiment, stator core 105 may also be placed inside rotor 102 to facilitate the manufacturing process of 2-DoF VR resolver 100 since excitation winding 106 and signal windings 107 may be placed on stator core 105, as described below. [0032] In an exemplary embodiment, variable air-gap 104 may be formed between rotor 102 and stator core 105. An exemplary length ^ of variable air-gap 104 may vary in radial and axial directions. In an exemplary embodiment, a “radial direction” may refer to a direction 108 of a radius of a cross-section of stator core 105 (or rotor 102). In an exemplary embodiment, an “axial direction” may refer to a direction 110 that may be perpendicular to the cross-section of stator 104 (or rotor 102). [0033] FIG. 2 shows a schematic of different shapes of rotors with a first structure, consistent with one or more exemplary embodiments of the present disclosure. An exemplary first structure of rotor 102 may be described according to the following equations: x = (A — B sin(αu))(cos(u))(C — sin(βv)) Equation (1a) y = (A — B sin(αu))(sin(u))(C — sin(βv)) Equation (1b) z = Dv Equation (1c) where x, y, and z represent horizontal, vertical, and axial components, respectively, of an arbitrary point (x, y, z) in the first structure in a Cartesian coordinate system. Parameters u and v are independent variables where 0 ≤ u, v < 2ղ , α is a number of pole pairs of rotor 102 in radial direction 108, p is a number of pole pairs of rotor 102 in axial direction 110, and A, B, C, and D are constant parameters. Exemplary values of A, B, C, and D may be determined based on geometrical dimensions of 2-DoF VR resolver 100. An exemplary shape of rotor 102 may vary with a and P according to Equations (la)-(lc). For example, a shape 202 may be obtained by setting a = 5 and p = 1, a shape 204 may be obtained by setting a = 3 and p = 3, and a shape 206 may be obtained by setting a = 3 and P = 5

[0034] FIG. 3 shows a schematic of different shapes of rotors with a second structure, consistent with one or more exemplary embodiments of the present disclosure. An exemplary second structure of rotor 102 may be described according to the following equations: x = (A — B sin(αu))(cos(u)) + (C sin(βv)) Equation (2a) y = (A — B sin(αu))(sin(u)) + (C sin(βv)) Equation (2b) z = Dv Equation (2c) where x, y, and z represent horizontal, vertical, and axial components, respectively, of an arbitrary point (x, y, z) of in the second structure in a Cartesian coordinate system. Parameters u and v are independent variables where 0 < u, v < 2ղ , α is a number of pole pairs of rotor 102 in radial direction 108, p is a number of pole pairs of rotor 102 in axial direction 110, and A , B , C , and D are constant parameters. Exemplary values of A , B , C , and D may be determined based on geometrical dimensions of 2-DoF VR resolver 100. An exemplary shape of rotor 102 may vary with a and P according to Equations (2a)-(2c). For example, a shape 302 may be obtained by setting a = 1 and p = 1, a shape 304 may be obtained by setting a = 5 and P = 1, and a shape 306 may be obtained by setting a = 1 and P = 3

[0035] FIG. 4A shows a schematic of a stator core, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1 and 4A, in an exemplary embodiment, stator core 105 may include a plurality of horizontal slots (for example, a horizontal slot 402) and a plurality of vertical slots (for example, a vertical slot 404). In an exemplary embodiment, stator core 105 may be made of a ferromagnetic material. [0036] FIG. 4B shows a schematic of a horizontal winding, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1 and 4B, in an exemplary embodiment, stator core 105 may further include horizontal windings 406. In an exemplary embodiment, horizontal windings 406 may include an excitation winding 106 and a horizontal signal winding. In an exemplary embodiment, different excitation coils of excitation winding 106 (for example, an excitation coil 408) may include an equal number of turns. In an exemplary embodiment, a “horizontal signal winding” may refer to signal winding that may be placed in the plurality of horizontal slots in a horizontal direction. In an exemplary embodiment, different horizontal signal coils of the horizontal signal winding may include an equal number of turns. An exemplary horizontal signal winding may be a two-phase winding and may have a s horizontal sine winding that may include a plurality of horizontal sine coils (for example, a horizontal sine coil 410) and a horizontal cosine winding that may have a plurality of horizontal cosine coils 412 (for example, a horizontal cosine coil 412). In an exemplary embodiment, a number of the plurality of horizontal sine coils may be equal to a number of the plurality of horizontal cosine coils. [0037] Referring again to FIGs. 4A and 4B, an exemplary plurality of horizontal slots may include an excitation slots subset and a signal slots subset. In an exemplary embodiment, each of the plurality of horizontal slots may belong to either the excitation slots subset or the signal slots subset. For example, horizontal slot 402 may belong to the excitation slots subset and a horizontal slot 414 may belong to the signal slots subset. In an exemplary embodiment, each of plurality of excitation coils 106 may be placed in a corresponding slot (also referred to as “tooth”) of the excitation slots subset. For example, excitation coil 408 may be placed in horizontal slot 402. In an exemplary embodiment, each of the horizontal signal coils may be placed in a corresponding slot of the signal slots subset. For example, horizontal sine coil 410 may be placed in horizontal slot 414. In an exemplary embodiment, the signal slots subset may include an even number of horizontal slots of the plurality of horizontal slots. As a result, half of the slots in the signal slots subset may be allocated to each of the plurality of horizontal sine coils and the plurality of horizontal cosine coils. [0038] FIG.4C shows a schematic of a vertical signal winding, consistent with one or more exemplary embodiments of the present disclosure. Referring to FIGs. 1 and 4C, in an exemplary embodiment, stator core 105 may further include a vertical signal winding 416. In an exemplary embodiment, signal windings 107 may consist of horizontal signal winding and vertical signal winding 416. In an exemplary embodiment, a “vertical signal winding” may refer to signal winding that may be placed in the plurality of vertical slots in a vertical direction. In an exemplary embodiment, different vertical signal coils of vertical signal winding 416 may include an equal number of turns. In an exemplary embodiment, vertical signal winding 416 may be a two-phase winding and may have a vertical sine winding that may include a plurality of vertical sine coils (for example, a vertical sine coil 418) and a vertical cosine winding that may include a plurality of vertical cosine coils (for example, a vertical cosine coil 420). An exemplary number of the plurality of vertical sine coils may be equal to a number of the plurality of vertical cosine coils. In an exemplary embodiment, each coil of vertical signal winding 416 may be placed in a corresponding vertical slot of the plurality of vertical slots. For example, vertical sine coil 418 may be placed in vertical slot 404. [0039] FIG.5A shows a diagram of an arrangement of a horizontal winding in a plurality of horizontal slots, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, coils excitation winding 106 may be placed in a first (1 st ) horizontal slot of the plurality of horizontal slots, a fourth (4 th ) horizontal slot of the plurality of horizontal slots, a seventh (7 th ) horizontal slot of the plurality of horizontal slots, and a tenth (10 th ) horizontal slot of the plurality of horizontal slots. In an exemplary embodiment, the plurality of horizontal sine coils may be placed in a third (3 rd ) horizontal slot of the plurality of horizontal slots, a fifth (5 th ) horizontal slot of the plurality of horizontal slots, a ninth (9 th ) horizontal slot of the plurality of horizontal slots, and an eleventh (11 th ) horizontal slot of the plurality of horizontal slots. In an exemplary embodiment, the plurality of horizontal cosine coils may be placed in a second (2 nd ) horizontal slot of the plurality of horizontal slots, a sixth (6 th ) horizontal slot of the plurality of horizontal slots, an eighth (8 th ) horizontal slot of the plurality of horizontal slots, and a twelfth (12 th ) horizontal slot of the plurality of horizontal slots. FIG. 5B shows a diagram of an arrangement of a vertical signal winding in a plurality of vertical slots, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, the plurality of vertical sine coils may be placed in a first (1 st ) vertical slot of the plurality of vertical slots, a second (2 nd ) vertical slot of the plurality of vertical slots, a third (3 rd ) vertical slot of the plurality of vertical slots, a seventh (7 th ) vertical slot of the plurality of vertical slots, an eighth (8 th ) vertical slot of the plurality of vertical slots, and a ninth (9 th ) vertical slot of the plurality of vertical slots. In an exemplary embodiment, the plurality of vertical cosine coils may be placed in a fourth (4 th ) vertical slot of the plurality of vertical slots, a fifth (5 th ) vertical slot of the plurality of vertical slots, a sixth (6 th ) vertical slot of the plurality of vertical slots, a tenth (10 th ) vertical slot of the plurality of vertical slots, an eleventh (11 th ) vertical slot of the plurality of vertical slots, and a twelfth (12 th ) vertical slot of the plurality of vertical slots. [0040] FIG.6 shows a flowchart of a method for detecting linear and rotational positions in a helical motion, consistent with one or more exemplary embodiments of the present disclosure. An exemplary method 600 may include applying a high-frequency voltage to the excitation winding (step 602), obtaining the linear position based on induced voltages on the horizontal signal winding (step 604), and obtaining the rotational position based on induced voltages on the vertical signal winding (step 606). [0041] Referring to FIGs. 1 and 6, in an exemplary embodiment, step 602 may include applying a high-frequency voltage ^ ^^^ to excitation winding 106. An exemplary high- frequency voltage source may be coupled to excitation winding 106 to generate and apply high- frequency voltage ^ ^^^ to excitation winding 106. [0042] In further detail with respect to step 604, FIG.7A shows a diagram of induced voltages on a horizontal signal winding, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, high-frequency voltage ^ ^^^ may induce voltages on the horizontal signal winding. An exemplary voltage signal 702 may be induced on the plurality of horizontal sine coils and an exemplary voltage signal 704 may be induced on the plurality of horizontal cosine coils. In an exemplary embodiment, induced voltages due to a linear motion on the horizontal signal winding may be amplitude modulated (AM) voltages, whereas induced voltages due to a linear motion on vertical signal winding 416 may have constant amplitudes. Therefore, in an exemplary embodiment, a linear position in a helical motion may be obtained by extracting envelopes of induced voltages on the horizontal signal winding. [0043] FIG. 7B shows a diagram of envelopes of induced voltages on a horizontal signal winding, consistent with one or more exemplary embodiments of the present disclosure. An exemplary envelope signal 706 may be an envelope of voltage signal 702 and an exemplary envelope signal 708 may be an envelope of voltage signal 704. In an exemplary embodiment, envelope signal 706 may be estimated as follows: E quation (3a) where V Sin is an envelope of voltage signal 702 that is induced on the plurality of horizontal sine coils, V M is an amplitude of envelope signals 706 and 708, ^ is the linear position, and l is a length of rotor 102 in axial direction 110. [0044] Similarly, in an exemplary embodiment, envelope signal 708 may be estimated as follows: E quation (3b) where V cos is an envelope of voltage signal 704 that is induced on the plurality of horizontal cosine coils. [0045] According to Equations (3a) and (3b), an exemplary linear position may be calculated as follows: Equation (4) [0046] FIG.7C shows a diagram of a linear position of a rotor, consistent with one or more exemplary embodiments of the present disclosure. An exemplary linear position 710 of rotor 102 may be estimated by measuring voltage signal 702 and 704 utilizing a voltage sensor and applying Equation (4) to envelopes of measured voltages. [0047] Referring again to FIG. 6, in an exemplary embodiment, step 606 may include obtaining the rotational position based on induced voltages on vertical signal winding 416. FIG.8A shows a diagram of induced voltages on a vertical signal winding, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, high- frequency voltage V exc may induce voltages on vertical signal winding 416. An exemplary voltage signal 802 may be induced on the plurality of vertical sine coils and an exemplary voltage signal 804 may be induced on the plurality of vertical cosine coils. In an exemplary embodiment, induced voltages due to a rotational motion on vertical signal winding 416 may be AM signals, whereas induced voltages due to a rotational motion on the horizontal signal winding may have constant amplitudes. Therefore, in an exemplary embodiment, a rotational position in a helical motion may be obtained by extracting envelopes of induced voltages on vertical signal winding 416. [0048] FIG.8B shows a diagram of envelopes of induced voltages on a vertical signal winding, consistent with one or more exemplary embodiments of the present disclosure. An exemplary envelope signal 806 may be an envelope of voltage signal 802 and an exemplary envelope signal 808 may be an envelope of voltage signal 804. In an exemplary embodiment, envelope signal 806 may be estimated as follows: Equation (5a) where V Sin is an envelope of voltage signal 802 that is induced on the plurality of vertical sine coils, V M is an amplitude of envelope signals 806 and 808, and ^ is a rotational position of rotor 102 in the cross-section of stator core 105. [0049] Similarly, in an exemplary embodiment, envelope signal 808 may be estimated as follows: Equation (5b) where V cos is an envelope of voltage signal 804 that is induced on the plurality of vertical cosine coils. [0050] According to Equations (5a) and (5b), an exemplary rotational position may be calculated as follows: E quation (6) [0051] FIG.8C shows a diagram of a rotational position of a rotor, consistent with one or more exemplary embodiments of the present disclosure. An exemplary rotational position 810 of rotor 102 may be estimated by measuring voltage signal 802 and 804 utilizing a voltage sensor and applying Equation (6) to envelopes of measured voltages. [0052] FIG.9 shows an example computer system 900 in which an embodiment of the present invention, or portions thereof, may be implemented as computer-readable code, consistent with exemplary embodiments of the present disclosure. For example, different steps of method 600 may be implemented in computer system 900 using hardware, software, firmware, tangible computer readable media having instructions stored thereon, or a combination thereof and may be implemented in one or more computer systems or other processing systems. [0053] If programmable logic is used, such logic may execute on a commercially available processing platform or a special purpose device. One ordinary skill in the art may appreciate that an embodiment of the disclosed subject matter can be practiced with various computer system configurations, including multi-core multiprocessor systems, minicomputers, mainframe computers, computers linked or clustered with distributed functions, as well as pervasive or miniature computers that may be embedded into virtually any device. [0054] For instance, a computing device having at least one processor device and a memory may be used to implement the above-described embodiments. A processor device may be a single processor, a plurality of processors, or combinations thereof. Processor devices may have one or more processor “cores.” [0055] An embodiment of the invention is described in terms of this example computer system 300. After reading this description, it will become apparent to a person skilled in the relevant art how to implement the invention using other computer systems and/or computer architectures. Although operations may be described as a sequential process, some of the operations may in fact be performed in parallel, concurrently, and/or in a distributed environment, and with program code stored locally or remotely for access by single or multi- processor machines. In addition, in some embodiments the order of operations may be rearranged without departing from the spirit of the disclosed subject matter. [0056] Processor device 904 may be a special purpose (e.g., a graphical processing unit) or a general-purpose processor device. As will be appreciated by persons skilled in the relevant art, processor device 904 may also be a single processor in a multi-core/multiprocessor system, such system operating alone, or in a cluster of computing devices operating in a cluster or server farm. Processor device 904 may be connected to a communication infrastructure 906, for example, a bus, message queue, network, or multi-core message-passing scheme. [0057] In an exemplary embodiment, computer system 900 may include a display interface 902, for example a video connector, to transfer data to a display unit 930, for example, a monitor. Computer system 900 may also include a main memory 908, for example, random access memory (RAM), and may also include a secondary memory 910. Secondary memory 910 may include, for example, a hard disk drive 912, and a removable storage drive 914. Removable storage drive 914 may include a floppy disk drive, a magnetic tape drive, an optical disk drive, a flash memory, or the like. Removable storage drive 914 may read from and/or write to a removable storage unit 918 in a well-known manner. Removable storage unit 918 may include a floppy disk, a magnetic tape, an optical disk, etc., which may be read by and written to by removable storage drive 914. As will be appreciated by persons skilled in the relevant art, removable storage unit 918 may include a computer usable storage medium having stored therein computer software and/or data. [0058] In alternative implementations, secondary memory 910 may include other similar means for allowing computer programs or other instructions to be loaded into computer system 900. Such means may include, for example, a removable storage unit 922 and an interface 920. Examples of such means may include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an EPROM, or PROM) and associated socket, and other removable storage units 922 and interfaces 920 which allow software and data to be transferred from removable storage unit 922 to computer system 900. [0059] Computer system 900 may also include a communications interface 924. Communications interface 924 allows software and data to be transferred between computer system 900 and external devices. Communications interface 924 may include a modem, a network interface (such as an Ethernet card), a communications port, a PCMCIA slot and card, or the like. Software and data transferred via communications interface 924 may be in the form of signals, which may be electronic, electromagnetic, optical, or other signals capable of being received by communications interface 924. These signals may be provided to communications interface 924 via a communications path 926. Communications path 926 carries signals and may be implemented using wire or cable, fiber optics, a phone line, a cellular phone link, an RF link or other communications channels. [0060] In this document, the terms “computer program medium” and “computer usable medium” are used to generally refer to media such as removable storage unit 918, removable storage unit 922, and a hard disk installed in hard disk drive 912. Computer program medium and computer usable medium may also refer to memories, such as main memory 908 and secondary memory 910, which may be memory semiconductors (e.g. DRAMs, etc.). [0061] Computer programs (also called computer control logic) are stored in main memory 908 and/or secondary memory 910. Computer programs may also be received via communications interface 924. Such computer programs, when executed, enable computer system 900 to implement different embodiments of the present disclosure as discussed herein. In particular, the computer programs, when executed, enable processor device 904 to implement the processes of the present disclosure, such as the operations in method 600 illustrated by the flowchart of FIG.6 discussed above. Accordingly, such computer programs represent controllers of computer system 900. Where an exemplary embodiment of method 600 is implemented using software, the software may be stored in a computer program product and loaded into computer system 900 using removable storage drive 914, interface 920, and hard disk drive 912, or communications interface 924. [0062] Embodiments of the present disclosure also may be directed to computer program products including software stored on any computer useable medium. Such software, when executed in one or more data processing device, causes a data processing device to operate as described herein. An embodiment of the present disclosure may employ any computer useable or readable medium. Examples of computer useable mediums include, but are not limited to, primary storage devices (e.g., any type of random access memory), secondary storage devices (e.g., hard drives, floppy disks, CD ROMS, ZIP disks, tapes, magnetic storage devices, and optical storage devices, MEMS, nanotechnological storage device, etc.). [0063] The embodiments have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. [0064] While the foregoing has described what may be considered to be the best mode and/or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications and variations that fall within the true scope of the present teachings. [0065] Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain. [0066] The scope of protection is limited solely by the claims that now follow. That scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows and to encompass all structural and functional equivalents. Notwithstanding, none of the claims are intended to embrace subject matter that fails to satisfy the requirement of Sections 101, 102, or 103 of the Patent Act, nor should they be interpreted in such a way. Any unintended embracement of such subject matter is hereby disclaimed. [0067] Except as stated immediately above, nothing that has been stated or illustrated is intended or should be interpreted to cause a dedication of any component, step, feature, object, benefit, advantage, or equivalent to the public, regardless of whether it is or is not recited in the claims. [0068] It will be understood that the terms and expressions used herein have the ordinary meaning as is accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise been set forth herein. Relational terms such as first and second and the like may be used solely to distinguish one entity or action from another without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “a” or “an” does not, without further constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. [0069] The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various implementations. This is for purposes of streamlining the disclosure, and is not to be interpreted as reflecting an intention that the claimed implementations require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed implementation. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter. [0070] While various implementations have been described, the description is intended to be exemplary, rather than limiting and it will be apparent to those of ordinary skill in the art that many more implementations and implementations are possible that are within the scope of the implementations. Although many possible combinations of features are shown in the accompanying figures and discussed in this detailed description, many other combinations of the disclosed features are possible. Any feature of any implementation may be used in combination with or substituted for any other feature or element in any other implementation unless specifically restricted. Therefore, it will be understood that any of the features shown and/or discussed in the present disclosure may be implemented together in any suitable combination. Accordingly, the implementations are not to be restricted except in light of the attached claims and their equivalents. Also, various modifications and changes may be made within the scope of the attached claims.