Resolver and motor

Abstract

Resolver (1) with a resolver rotor (2) fixed to a rotating shaft (4) and a resolver stator (3) arranged around the resolver rotor (2), wherein the resolver stator (3) has a plurality of projecting poles (31) provided on an annular stator core (30) projecting inward in the radial direction and arranged at equal distances in the circumferential direction, wherein the resolver rotor (2) has an outer peripheral surface (11) defined by an outer diameter obtained by combining a second function, in which the inverse of an air gap between the resolver rotor (2) and the salient poles (31) is proportional to a sinusoidal oscillation with respect to the angle (ϕ) of the resolver rotor (2), with a first function, in which the air gap is proportional to the sinusoidal oscillation, in a certain ratio, wherein the ratio is set to be greater than 0 and is set to a value which is greater the smaller a modulation is which represents a varying amplitude of an output signal of the resolver (1) with respect to the mean value of the output signal, and characterized in that the outer diameter is calculated based on the angle (ϕ), a stator inner diameter representing the length from the rotation center of the shaft (4) to the end face of the salient poles (31) on the radially inner side, the ratio, and a predetermined maximum (Gmax) and minimum (Gmin) air gap according to the following equation (A): Rm ( ∅ ) = Rs − { α × Gip ( ∅ ) + ( 1 − α ) × Gp ( ∅ )} where Gp ( ∅ ) = { ( Gmax − Gmin ) sin ∅} / 2 + ( Gmin + Gmax ) / 2 Gip ( ∅ ) = 1 [ { 1 Gmax − 1 Gmin 2} sin ∅ + 1 Gmin + 1 Gmax 2 ] Rm(ϕ): outer diameter ϕ: Angle in the coordinate system of the resolver rotor outer diameter Rs: Stator inner diameter α: ratio Gp(ϕ): first function Gip(ϕ): second function Gmax: Maximum value of the air gap Gmin: Minimum value of the air gap

Description

Technical FieldThe present invention relates to a resolver for detecting the rotation angle of a motor and a motor including the resolver.General State of the ArtUsually, a sensor that detects the rotational speed and the rotational angle (rotational position) of the motor is provided on a motor (in particular, a brushless motor). Such a sensor is a resolver, wherein a resolver is used in, for example, vehicle drive motors or power steering motors and the like due to its high angular resolution and robustness. As a structure of a resolver, it is known that, for example, a resolver rotor that rotates integrally with a rotation shaft of a motor and a resolver stator having a plurality of salient poles are provided, an exciting coil and two output coils are wound around the salient poles, respectively (see JP 3 309 025 B2).In the resolver of JP 3 309 025 B2, an outer circumferential shape of the resolver rotor that is offset by a certain amount with respect to a rotation axis has recess and protrusion portions smaller than the offset amount with respect to the round shape at a plurality of locations, such that a transmissivity error (harmonic distortion) of the detection waveform (output waveform of the detection coil) is compensated. Since the resolver rotor has this shape in JP 3 309 025 B2, the characteristic error included in the detection waveform can be reduced and at the same time the vibration of the fundamental wave component can be amplified.US 2005 / 0 023 921 A1 starts from a resolver in which the radius of the resolver rotor follows a function as a function of the inner stator radius and the minimum and maximum air gap in order to generate a sinusoidal output signal. KR 10 1 681 648 B1 discloses a resolver in which a certain ratio between the stator section area and the rotor section area is connected to the air gap that changes over the circumference.JP 2012-210 121 A teaches a prior art according to which the air gap changes sinusoidally over the circumference due to the selected resolver rotor shape. Thus, these three latter references each disclose a resolver according to the preamble of claim 1.Summary of the InventionObject of the present inventionHowever, it is known that the permeability is substantially proportional to the inverse of a distance between the salient poles of the resolver stator and the outer circumferential surface of the resolver rotor (hereinafter referred to as "air gap"). However, in JP 3 309 025 B2, since a resolver rotor is formed over the outer circumferential shape of which an Nth order waveform corresponding to the characteristic of the transmittance error component to be reduced (for example, the third or fifth order component) is stored, depending on the size of the air gap, it is not necessarily the case that the effect shown in FIG. 3 of JP 3 309 025 B2 is obtained. That is, there is a need for improvement in reducing the error (i.e., the permeability error) due to the harmonic component of the output waveform (the resolver signal) regardless of the size of the air gap.The present resolver is proposed in view of these problems, and one of its objects is to reduce the error due to the harmonic component of the resolver signal and to increase the detection accuracy of the rotation angle. An object of the present motor is to perform various control operations with high accuracy. The object of the present invention is not limited to the above objects, and it is another object to achieve effects that can be obtained from various embodiments of the invention described below and cannot be obtained in the related art.means for achieving the object(1) A resolver of the present disclosure includes a resolver rotor fixed to a rotating shaft and a resolver stator disposed around the resolver rotor, the resolver stator including a plurality of salient poles provided on an annular stator core so as to project radially inward and arranged so as to be equally spaced in the circumferential direction, the resolver rotor including an outer circumferential surface defined by an outer diameter obtained by combining a second function in which the reciprocal of an air gap between the resolver rotor and the salient poles is proportional to a sinusoidal vibration with respect to the angle of the resolver rotor with a first function in which the air gap is proportional to the sinusoidal vibration at a certain ratio. The angle is not the rotation angle of the resolver rotor, but an angle for setting the outer diameter of the resolver rotor (the angle from the rotation center of the shaft, that is, the angle in the polar coordinate system). The ratio is set to be larger than 0 and set to a value that is larger the smaller a modulation representing a varying amplitude of an output signal of the resolver with respect to the average value of the output signal is. The outer diameter is calculated based on the angle, a stator inner diameter representing the length from the rotational center of the shaft to the end face of the salient poles on the radially inner side, the ratio, and a predetermined maximum and minimum value of the air gap according to the following equation (A): whereinRm(φ): Outer diameterφ: Angle in Resolver Rotor Outer Diameter Coordinate SystemRs: Stator inner diameterα: ratioGp(φ): First functionGip(φ): Second functionGmax: Maximum value of air gapGmin: Minimum value of air gap(2) Preferably, the ratio is set to a value of 0.2 or greater and 1.0 or less.(3) Preferably, the wave angle multiplier of the resolver is 1.(4) The motor disclosed herein includes the resolver according to any one of (1) to (3), a rotor that rotates integrally with the shaft, and a stator fixed to a housing.Effect of the inventionAccording to the disclosed resolver, the outer circumferential surface of the resolver rotor is set by an outer diameter obtained by appropriately combining a second function with a first function at a certain ratio, thereby obtaining an output waveform that approximates an ideal inductance waveform without harmonic component, so that the error due to the harmonic component of the resolver signal is reduced. The detection accuracy of a rotation angle can be improved.According to the disclosed motor, various control operations such as position control or speed control can also be performed with high accuracy.Brief Description of the FiguresThe following are shown: FIG. 1 is a schematic plan view of a resolver according to an embodiment from the axial direction, only the shaft being shown in section; FIG. 2 is a schematic sectional view of a motor according to an embodiment; FIG. 3 is a circuit diagram illustrating the electrics of the resolver of FIG. 1 ; FIG. 4( a) is a graph illustrating the result of calculating an ideal inductance waveform when the resolver signal is a sinusoidal wave (calculation under the condition of a harmonic component of 0), and FIG. 4( b) is a graph illustrating the relationship of the air gap to an angle φ upon acquisition of the waveform of FIG. 4( a); and FIG. 5 is an exemplary graph showing measurement of a fourth-order component of an angular error and a total angular error as the ratio is changed.Embodiment of the InventionReferring now to the figures, an embodiment of a resolver and a motor will be described. The following embodiment is merely exemplary in nature and is not intended to exclude application of various modifications or techniques not set forth in the embodiment. The individual configurations of the present embodiment allow various modifications without departing from the scope thereof. Substitutions and omissions are also possible as needed, as are suitable combinations.1. Structure1-1. Basic Configuration of ResolverA resolver as discussed herein is configured such that a distance of a tubular outer circumferential surface of a resolver rotor, which is opposed to salient poles of a resolver stator, from the rotation center of a shaft is periodically changed in the circumferential direction, which is a variable reactance resolver (VR) in which a rotation angle is detected based on the change of an output signal of the resolver (hereinafter, "resolver signal") due to a change in the distance (air gap) between the radially inner end surface of the salient poles and the tubular outer circumferential surface of the resolver rotor. Hereinafter, the term "rotational speed" denotes the number of rotations per unit time and corresponds to the rotational speed.FIG. 1 is a schematic plan view of a resolver 1 according to an embodiment from the axial direction, in which only one shaft 4 (rotation axis) is shown in section. In FIG. 1, hatching of the shaft 4 has been omitted. The resolver 1 of the present embodiment is integrated into a motor 9 as shown in FIG. 2, for example. The motor 9 is a brushless motor (for example, servomotor) including a stator 9A fixed to a housing 9C, a rotor 9B rotating integrally with the shaft 4, and the resolver 1 accommodated in the housing 9C. The resolver 1 is disposed on the shaft 4 of the motor 9 and detects a rotation angle (rotation position) of the motor 9. the present embodiment shows an example of a resolver 1 whose shaft angle multiplier is 1 (resolver 1 having a 1X structure).As shown in FIG. 1, the resolver 1 is fixed to the rotating shaft 4, and includes a resolver rotor 2 having a tubular outer circumferential surface 11 whose distance from a rotation center C of the shaft 4 in the circumferential direction periodically varies, and an annular resolver stator 3 having a wound coil 5. The distance of the outer peripheral surface 11 of the resolver rotor 2 from the central axis Ce thereof forms a shape offset from a specific reference cylindrical surface 12 (broken line in the figure). Hereinafter, when viewed from the axial direction, the radius Rr of the reference cylindrical surface 12 (eccentric circle) indicated by a broken line in the figure is referred to as "rotor reference radius Rr". The shape of the outer circumferential surface 11 of the resolver rotor 2 will be described later. Since the structure of the resolver 1 of the present embodiment is a 1X structure, the resolver rotor 2 is eccentrically disposed with respect to the rotation center C. Hereinafter, the axis center Ce of the reference cylindrical surface 12 is referred to as an "eccentric axis Ce".A round hole formed in the central portion of the resolver rotor 2 is a mounting hole 2 hinto which the shaft 4 is inserted, and its central axis coincides with the rotation center C. The resolver rotor 2 of the present embodiment is configured such that a plurality of high magnetic ring-shaped sheets (for example, steel sheets) are laminated on each other. The resolver rotor 2 is formed by, for example, press processing of sheets having a round hole at the center thereof, and a plurality of sheets having the same shape are laminated on each other.As shown in FIG. 1, a plurality of radially inwardly projecting poles 31 are provided on a substantially annular stator core 30 of the resolver stator 3. In the present embodiment, four salient poles 31A-31D of the same shape are arranged at equal intervals (phase offset by 90 degrees) in the circumferential direction. The salient poles 31A- 31D each have radially extending teeth 31 eand a wide wall portion 31 fprovided at a radially inner end portion of the teeth 31 eand widening in the circumferential direction, and are substantially T-shaped when viewed in plan view.On the teeth 31e of the four salient poles 31A-31D, coils 5A-5D are wound, respectively. The coils 5A- 5D are input coils to which current is applied, and are formed of the same winding wire and having the same winding number, but the winding direction at adjacent salient poles 31 is opposite, respectively. The wall portions 31 fare parts that receive magnetic flux, and extend from radially inner end portions of the teeth 31 eon both sides in the circumferential direction (rotational direction). The length of the wall portions 31 fin the rotational direction is provided to be equal.A radially inner end surface 31 gof the salient poles 31 (radially inward facing surface on the wall portion 31 f) is, as shown by the dot-dash line in FIG. 1, disposed on a radius Rs whose center is the rotation center C. That is, the end surfaces 31 gof the salient poles 31 in the present embodiment are each disposed at an equal distance from the rotation center C and form a circular arc with the rotation center C as a center. This radius Rs is hereinafter referred to as "stator inner diameter Rs". An air gap is provided between the end surfaces 31 gand the outer circumferential surface 11 of the resolver rotor 2.1-2. Circuit Configuration of ResolverAs shown in FIG. 3, one end 51a of the windings of the coils 5A-5D serving as input to the salient poles 31A-31D is connected to one terminal 40a of an AC power source 40, while the other end 51b of the windings of the coils 5A-5D is connected to the other terminal 40b of the AC power source 40 via sub resistors 41A-41D, respectively. Between the coils 5A-5D and their sub resistors 41A-41D, output terminals 42A-42D are provided, respectively.At this time, a sine wave signal is output from the output terminal 42A of the coil 5A, a sine wave signal whose phase is opposite to the output terminal 42A is output from the output terminal 42C of the coil 5C, a cosine wave signal is output from the output terminal 42B of the coil 5B, and a cosine wave signal whose phase is opposite to the output terminal 42B is output from the output terminal 42D of the coil 5D.The sine wave signals and cosine wave signals output from the output terminals 42A- 42D of the coils 5A- 5D are input to an R / D (resolver digital) conversion section 6. In the R / D conversion section 6, an operational amplifier 61 as a first differential amplifier, an operational amplifier 62 as a second differential amplifier, a phase shifter 63 and an adder 64 are provided, and as a step subsequent to the adder 64, various processings such as digitalizing of the input analog signal are performed by an A / D conversion device (not shown).The salient pole 31A and the salient pole 31C having the coils 5A, 5C which are arranged 180 degrees out of phase with each other and both output a sinusoidal oscillation signal form a first salient pole pair 31S1 (see FIG. 1 ), and the output terminal 42A of the coil 5A of the salient pole 31A is connected to the positive input terminal of the operational amplifier 61, while the output terminal 42C of the coil 5C of the salient pole 31C is connected to the negative input terminal of the operational amplifier 61.Also, the salient pole 31B and the salient pole 31D with the coils 5B, 5D which are arranged 180 degrees out of phase with each other and both output a cosine wave signal form a second salient pole pair 31S2 (see FIG. 1), and the output terminal 42B of the coil 5B of the salient pole 31B is connected to the positive input terminal of the operational amplifier 62, while the output terminal 42D of the coil 5D of the salient pole 31D is connected to the negative input terminal of the operational amplifier 62.To the output terminal of the operational amplifier 62, the phase shifter 63 which makes a phase shift of 90 degrees is connected, and to the output terminal of the operational amplifier 61, a first input terminal of the adder 64 is connected, while to the output terminal of the phase shifter 63 a second input terminal of the adder 64 is connected.In this manner, the following processing is performed at the R / D conversion section 6.1-3. Processing by Resolver CircuitsIn the resolver signal (wave voltage) V of the output terminals 42A- 42D, an error component due to the harmonic component of the resolver signal is included, respectively.When the resolver signal V output from the output terminal 42A is 0 the resolver signal V output from the output terminal 42B is 90 the resolver signal V output from the output terminal 42C is 180 and the resolver signal V output from the output terminal 42D is 270 the resolver signal V 0, V 180, V 90, V 270 of the output terminals 42A, 42C, 42B, 42D is respectively expressed by the following equations (1)-(4).In Equations (1)-(4), a is an average value of the resolver signal, b is a variable amplitude of the resolver signal, c is a variable amplitude of the second-order harmonic component of the resolver signal, and d is a variable amplitude of the third-order harmonic component of the resolver signal. As shown in FIG. 1, θ is a rotation angle with a reference position of the resolver rotor 2 of 0 degrees. The rotation angle θ is represented by the value of the time integral of the angular velocity ωm of the resolver rotor 2 (motor 9) (product of the angular velocity ωm and the time t: ωmt). Although there are also harmonic components of the fourth and other orders, since their amplitude is small, their influence is so weak that it can be ignored.Ωe is the angular velocity (ωe=2πfe) corresponding to the frequency fe of the excitation source, where t is the time at the reference time. The frequency fe is, for example, about 5 kHz.In addition, there is a phase difference α between the sinusoidal wave voltage due to the error component and the voltage of the actual sinusoidal wave (hereinafter referred to as the fundamental wave) corresponding to the variation of the gap G. [Equation 2]As mentioned above, since the influence from the fourth-order harmonic component is slight, omitting it from the above equations (1)-(4) yields the following equations (1A)-(4A). [Equation 3]Processing is performed at the operational amplifier 61 with the sides of the equation (1A) subtracted from the sides of the equation (2A), while processing is performed at the operational amplifier 62 with the sides of the equation (3A) subtracted from the sides of the equation (4A).In this way, odd-order components are computed out of symmetry, so that the output of the operational amplifier 61 is shown by the right side of the following equation (5) and the output of the operational amplifier 62 is shown by the right side of the following equation (6A). [Equation 4]In the equation (6A), since the cosine phase of the equation (6A) output from the operational amplifier 62 is delayed by the angle of 0.5 π of the AC excitation current (90 degrees), "sin ωet" shifts to "-coswet" at the phase shifter 63, so that the output of the phase shifter 63 is represented by the following equation (6).The angular velocity ωm (≅rotation frequency fmof the motor) at which the rotation angle θ of the resolver rotor 2 (motor 9) is changed is sufficiently small (i.e., ωm<ωe or fm<fe) compared to the angular velocity ωe of the excitation source (frequency fe of the excitation source), and therefore the change of sin θ, cos θ by the phase shifter 63 can be ignored. [Equation 5]Since the output of the operational amplifier 61 and the output of the phase shifter 63 are added at the adder 64, processing of adding the sides of the equation (5) and the sides of the equation (6) takes place so that the output of the adder 64 is represented by the right side of the following equation (7). [Equation 6]Here, ωe is the angular velocity (ωe=2πfe) corresponding to the frequency fe of the excitation source, and θ is the product of the angular velocity ωm(ωm=2πfm) corresponding to the frequency fm of the resolver rotor 2 (motor 9) and the time t (θ=2πfmt), and therefore, when the angular velocities ωe, ωm in the equation (7) are replaced by the frequencies fe, fm, the following equation (8) is obtained. [Equation 7]When the output of the adder 64 is subjected to frequency analysis, a peak can be detected at fe+fm and fe+3fm, respectively. From fe+fm and fe+3fm and the peak values, the maximum amplitude |-2b| can be derived from the first right-hand term of equation 8 [-2b·cos2πt(fe+fm)] and the maximum amplitude |-2d| from the second right-hand term of equation 8 [-2d·cos2πt(fe+3fm)].The second term of the right side of Equation 8 [-2d·cos2πt(fe+3fm)] is the error component due to the harmonic component of the resolver signal (third-order harmonic component) and is the error component in the detection angle of the resolver 1. The third order harmonic component is correlated with the fourth order component of the angular error.As mentioned above, since the amplitude of the fourth-order harmonic components is small, among the odd-order harmonic components, the fifth-order harmonic component can be ignored, while it is critical for enhancing the detection accuracy of the rotation angle how far the third-order harmonic component can be reduced.1-4. Configuration of Resolver RotorThe outer circumferential surface 11 of the resolver rotor 2 of the present embodiment is configured so that the third-order harmonic component can be reduced. More specifically, the resolver rotor 2 has an outer circumferential surface 11 defined by an outer diameter Rm(φ) obtained by combining a second function Gip(φ) in which the reciprocal of the air gap is proportional to the sinusoidal wave with respect to the angle φ of the resolver rotor 2 (i.e., sin φ) with a first function Gp(φ) in which the air gap is proportional to the sinusoidal wave with respect to the angle φ (i.e., sin φ) at a certain ratio α. The angle φ is an angle for setting the outer diameter Rm(φ) of the resolver rotor 2, and is an angle in the case where the outer diameter of the resolver rotor 2 is represented in a polar coordinate system with the reference position at 0 degrees. That is, this angle φ is different from the rotation angle θ of the resolver rotor 2 of the signal output of the resolver 1.The first function Gp(φ) is a function of the air gap on the assumption that the resolver rotor 2 is an eccentric circle. That is, the first function Gp(φ) is a function representing the length of the air gap in the radial direction, assuming that the outer circumferential surface 11 of the resolver rotor 2 coincides with the reference cylindrical surface 12 (the eccentric circle represented by a broken line in FIG. 1 ). When it is assumed that the resolver rotor 2 is the eccentric circle, the size of the air gap (length in the radial direction) is proportional to sinφ.The resolver rotor 2 of the present embodiment has an axis-symmetric shape with respect to the axis of symmetry indicated by the dot-and-dash line Z in FIG. 1 as viewed in the axial direction, and in the state (rotational position) shown in FIG. 1, the air gap is set to be maximum on the right side of the figure and the air gap is set to be minimum on the left side of the figure. The maximum value of the air gap (maximum distance) is referred to as "maximum gap Gmax", and the minimum value of the air gap (minimum distance) is referred to as "minimum gap Gmin".In the resolver rotor 2, since the shaft angle multiplier is 1, in the case where an offset amount of the eccentric axis Ce from the rotation center C is y, the maximum gap Gmax and the minimum gap Gmin are respectively represented by the following equations (9A), (9B). As mentioned previously, Rs is the stator inner diameter and Rr is the rotor reference radius. The thickness of the resolver rotor 2 (length in the axial direction) is constant. [Equation 8]A representation of the first function Gp(φ) as a formula yields the following equation (10). The maximum gap Gmax and the minimum gap Gmin are set in advance based on the specifications for the resolver 1. [Equation 9]On the other hand, the second function Gip(φ) is a function in which the reciprocal of the air gap (i.e., "1 / air gap") is proportional to sinφ, and is represented by the following equation (11). [Equation 10]The air gap Gm(φ) in the case where the second function Gip(φ) is combined with the first function Gp(φ) with a certain ratio α is represented by equation (12). Hereinafter, the air gap Gm(φ) is referred to as "air gap Gm(φ) after assembling". [Equation 11]Therefore, the outer diameter Rm(φ) defining the outer circumferential surface 11 of the resolver rotor 2 can be obtained by subtracting the air gap Gm(φ) after assembling from the stator inner diameter Rs. That is, the outer diameter Rm(φ) is calculated based on the stator inner diameter Rs, the ratio α, the first function Gp(φ), and the second function Gip(φ) (angle φ, and predetermined maximum air gap Gmax and minimum air gap Gmin) from the following equation (13). [Equation 12]The reason why, in the resolver rotor 2 having the outer circumferential surface 11 defined by the outer diameter Rm(φ) obtained by combining the second function Gip(φ) with the first function Gp(φ) at the specific ratio α, the third-order harmonic component can be reduced is explained below.The permeability of the resolver magnetic circuit is determined by the air gap, and as the air gap increases, the permeability decreases, while as the air gap decreases. That is, the permeability is proportional to the inverse of the air gap, and therefore the first function Gp(φ) can be described as a function in which the permeability is proportional to the inverse of sin φ (1 / sin φ), while the second function Gip(φ) can be described as a function in which the permeability is proportional to sin φ. Also, the permeability is in a proportional relationship to the inductance, and therefore the first function Gp(φ) can also be described as a function in which the inductance is proportional to the inverse of sinφ (1 / sinφ), while the second function Gip(φ) can be described as a function in which the inductance is proportional to sinφ.However, when an ideal inductance waveform in which the resolver signal is a sine wave (i.e., the harmonic component should be 0) is calculated back, approximately a sine wave shape is obtained as shown in FIG. 4( a). However, the shape of the inductance waveform varies depending on the magnitude of modulation m(=b / a) representing a varying amplitude b of the resolver signal with respect to the average value a of the resolver signal. More specifically, the lower the modulation m is, the closer the inductance waveform is to the sine wave, and the stronger the modulation m is, the more an inductance waveform in which the sine wave deforms to abruptly increase with the angle at which the air gap becomes smaller is obtained. Since the inductance is in proportional relationship to the permeability and the permeability is proportional to the inverse of the air gap, the air gap is given a relationship shown in FIG. 4(b) when the inductance waveform is as in FIG. 4(a). That is, the high modulation shape m approximates the waveform of the second function Gip(φ), while the low modulation shape m approximates the waveform of the first function Gp(φ).Thus, by appropriately combining the second function Gip(φ) in which the inductance is proportional to sinφ with the first function Gp(φ) in which the inductance is proportional to the inverse of sinφ, an inductance waveform approximating the ideal can be obtained, as a result of which the errors due to the harmonic component of the resolver signal can be reduced. The distribution ratio α is set such that the lower the modulation m is, the larger the value is, and the smaller the stronger the modulation m is. Thus, in order to obtain a resolver signal having few harmonic components, the lower the modulation m is, the more priority should be given to the second function Gip(φ), while the higher the modulation m is, the more priority should be given to the first function Gp(φ).FIG. 5 shows measurement results of the fourth-order component of the angular error and the total angular error when the ratio α is changed from -2.0 to 3.0 to obtain an optimum value for the ratio α. As shown in FIG. 5, the ratio α is not limited to a positive value, and a negative value may be applied. However, the second function Gip(φ) is not combined at a ratio α of 0, and therefore the ratio α must be set to a value other than 0, preferably to a value greater than 0. In the graph of FIG. 5, the rotor reference radius Rr and the displacement amount y are constant, and only the ratio α is changed. Since the rotor reference radius Rr and the offset amount y are constant, the maximum gap Gmax and the minimum gap Gmin are also constant, and the modulation m(=b / a) is also substantially constant. The thickness of the resolver rotor 2 is also constant.As described above, the second term of the right side of Equation 8 [-2d·cos2πt(fe+3fm)] is the error component due to the harmonic component of the resolver signal (third-order harmonic component), and when it is included, the error component (fourth-order component of the angular error) of the angle detected by the resolver 1 results. Thus, in order to reduce the total angular error of the resolver 1, it is important to reduce the fourth-order component of the angular error, as shown in FIG. 5 with white circles.As shown by the graph of FIG. 5, compared to the cases where the ratio α is less than 0 (a negative value) and greater than 1.0, the fourth-order component of the angular error is small in the cases where the ratio α is between 0.2 inclusive and 1.0 inclusive, and the total angular error is also small. Therefore, the ratio α is set to a value between 0.2 inclusive and 1.0 inclusive. Preferably, the ratio α is also set suitably within this range (0.2≤α≤1.0) in consideration of the modulation m. Preferably, adjustment is made such that when, for example, the modulation m is low (for example, 0.07), the ratio α is set to a large value, and when the modulation m is strong (for example, 0.5), the ratio α is set to a small value.2. Mode of action and effect(1) In the resolver 1 described above, the outer circumferential surface 11 of the resolver rotor 2 is set by the outer diameter Rm(φ) obtained by appropriately combining the second function Gip(φ) with the first function Gp(φ) at a certain ratio α. In this way, an output waveform close to an ideal inductance waveform without harmonic component can be obtained, so that the error due to the harmonic component of the resolver signal is reduced, and the detection accuracy of the rotation angle can be improved. (2) In the resolver 1 described above, the modulation m is larger than 0, and the ratio α is set to a larger value the lower the modulation m is, and the ratio α is set to a smaller value the inversely the larger the modulation m is. By adjusting the ratio α in this manner according to the modulation m, a resolver signal having a few harmonic components can be obtained, and the detection accuracy of the rotation angle can be improved. (3) When the ratio α is set to a value between 0.2 inclusive and 1.0 inclusive, the fourth-order component of the angle error can be reduced, so that the detection accuracy of the rotation angle can be improved. (4) In the resolver 1 described above, the resolver rotor 2 has the outer circumferential surface 11 determined by the outer diameter Rm(φ) calculated from Equation (13). Since the stator inner diameter Rs, the maximum air gap Gmax, and the minimum air gap Gmin are predetermined values, by adjusting the ratio α, a resolver rotor 2 (resolver 1) having an outer circumferential surface 11 that is determined by an optimum outer diameter Rm(φ) can be constructed. (5) In the resolver 1 described above, the shaft angle multiplier 1 is 1, so that the structure of the resolver 1 can be simplified. With the resolver 1, it is possible to detect an absolute angle, and it can be applied to motors 9 having different pole numbers. That is, regardless of the pole number of the motor 9, a resolver 1 having identical specifications may be applied. (6) In a motor 9 including the resolver 1 described above, the rotation angle of the resolver rotor 2 (i.e., the shaft 4) can be detected with high accuracy, so that various control operations such as position control or speed control can be performed with high accuracy.In the resolver 1 described above, since only the input coil 5 is wound around the salient poles 31 of the resolver stator 3, the winding structure can be simplified compared to a general resolver also having an output coil. When the winding wire of the resolver is not wound equally at all salient poles, the magnetic flux amount that concatenates the winding wires is different depending on the position of the winding wire (salient pole), which results in rotation angle detection errors. Therefore, in a resolver of a complicated winding structure (for example, a resolver having input and output windings), labor and equipment for uniformly winding winding winding wire around all salient poles become more complex, which is highly likely to result in increase in manufacturing cost. In the resolver 1 having its simple winding structure, on the other hand, the detection accuracy of the rotation angle can be increased.3. Otherwise,The configuration of the resolver 1 described above is merely an example, and is not limited thereto. For example, the above-described structure of the resolver rotor 2 may also be applied to a resolver whose shaft angle multiplier is not 1. In a resolver whose shaft angle multiplier is not 1, the central axis of the resolver rotor is provided in correspondence with the rotation center C, and the maximum air gap Gmax and the minimum air gap Gmin are set. In this case, since the resolver rotor has an outer circumferential surface set by the outer diameter Rm(φ) obtained by combining the second function Gip(φ) in which the inverse of the air gap is proportional to the sine wave (sinφ) with the first function Gp(φ) in which the air gap is proportional to the sine wave (sinφ) in the ratio α, the same effect as in the above-described embodiment can be obtained. The above-described manner of determining the ratio α is an example, and is not intended to be limited thereto.For example, it may be a shape in which the end surfaces 31 gof the vanes 31 fof the teeth 31 eare not constant spaced apart from the rotation center C as a whole (non-circular arc shape). In this case, the outer circumferential surface of the resolver rotor 2 may be configured to be set by an outer diameter Rm(φ) obtained by combining the first function Gp(φ) in which the air gap between the end surfaces 31 gand the resolver rotor 2 on a tooth center line of the end surfaces 31 gof the teeth 31 e(line passing through the rotation center C) is proportional to the sinusoidal vibration (sin φ) with the second function Gip(φ) in which the inverse of the air gap is proportional to the sinusoidal vibration (sin φ) in the ratio α.The structure of the resolver stator 3 described above is only an example, and the salient poles 31A- 31D may have a shape other than the described one, for example. In the above-described embodiment, a resolver rotor 2 having a laminated structure has been exemplified, but the resolver rotor 2 does not need to have a laminated structure. Also, the above-described circuit configuration is only an example, and other circuit configuration than the above-described circuit configuration may be provided.Explanation of Reference Numerals1 Resolver 2 Resolver rotor 3 Resolver stator 4 Shaft 9 Motor 9A Stator 9B Rotor 9C Housing 11 Outer peripheral surface 12 Reference cylindrical surface 31A- 31D Salient Pole C Rotation Center Gm(φ) Air Gap after Assembling Gmax Maximum Air Gap (Maximum Value of Air Gap) Gmin Minimum Air Gap (Minimum Value of Air Gap) Gp(φ) First Function Gip(φ) Second Function Rm(φ) Outer Diameter Rr Rotor Reference Radius Rs Stator Inner Diameter α Ratio θ Resolver rotor rotation angle φ Angle in the polar coordinate system of the resolver rotor outer diameter

Claims

A resolver (1) comprising a resolver rotor (2) fixed to a rotating shaft (4) and a resolver stator (3) disposed around the resolver rotor (2), the resolver stator (3) having a plurality of salient poles (31) provided on an annular stator core (30) to project inward in a radial direction and arranged to be equally spaced in a circumferential direction, the resolver rotor (2) having an outer circumferential surface (11) defined by an outer diameter obtained by combining a second function in which the reciprocal of an air gap between the resolver rotor (2) and the salient poles (31) is proportional to a sinusoidal wave with respect to the angle (φ) of the resolver rotor (2) with a first function in which the air gap is proportional to the sinusoidal wave in a certain ratio, wherein the ratio is set larger than 0 and set to a value larger the smaller a modulation representing a varying amplitude of an output signal of the resolver (1) with respect to the average value of the output signal, and characterized in that the outer diameter is set based on the angle (φ), a stator inner diameter representing the length from the center of rotation of the shaft (4) to the end face of the salient poles (31) on the radially inner side, The outer diameter φ: angle in the coordinate system of the air gap is calculated from the ratio and a predetermined maximum value (Gmax) and minimum value (Gmin) of the air gap according to the following equation (A): Rm ( )=Rs - { α×Gip ( )+(1-α)×Gp ( ) } wherein Gp ( )={(Gmax-Gmin) sin } / 2+(Gmin+Gmax) / 2 Gip ( )=1 [{ 1 Gmax - 1 Gmin 2} sin + 1 Gmin+1 Gmax 2] Rm(φ): Outer diameter φ: angle in the coordinate system of the air gap. Resolver rotor outer diameter Rs: Stator inner diameter α: ratio Gp(φ): First function Gip(φ): Second function Gmax: Maximum value of air gap Gmin: Minimum value of air gapThe resolver (1) according to claim 1, further characterized in that the ratio is set to a value of 0.2 or greater and 1.0 or less.The resolver (1) according to claim 1 or 2, further characterized in that the wave angle multiplier of the resolver (1) is 1.A motor (9) comprising a rotor (9B) rotating integrally with the shaft (4) and a stator (9A) fixed to a housing (9C), characterized in that it comprises a resolver (1) according to any one of claims 1 to 3.

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