JPH0817562B2 - Reluctance resolver - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a rotor shape of a reluctance resolver configured to eliminate or reduce a harmonic component of a resolver function error.

(Prior Art) Generally, a resolver has a winding type resolver in which a winding is wound so that the magnetic flux distribution on the stator side has a sinusoidal shape, and a rotor and a stator each have a sinusoidal change in magnetic flux with respect to a rotation angle. There is a reluctance type resolver in which several protrusions are arranged on the circumference and a change in magnetic resistance is used.

Since a reluctance resolver has a simple structure, it has been easy to miniaturize and to have multiple poles as compared with a wire-wound resolver. However, the reluctance type resolver cannot reduce the function error due to the winding method of the winding wire like the winding type resolver, so that the projection shape on each circumference of the rotor and the stator must be devised. It is difficult to obtain such a rotor or stator projection shape with a small function error, and even if a shape with a small function error is known, it is often difficult to machine the shape, and machining accuracy cannot be obtained. This caused the function error to increase. Therefore, it is usually difficult for the reluctance resolver to achieve higher accuracy between the wire-wound resolver and the reluctance resolver having the same number of poles.

FIG. 4 shows a conventional reluctance type resolver having a shaft angle multiplier of 12 (hereinafter referred to as 12X), where 1 is a rotor and 2 is a stator, both made of magnetic material. Reference numerals 3 to 14 are rotor protrusions arranged on the outer periphery of the rotor 1 at regular intervals of 30 °, and 15 to 30 are stator protrusions disposed on the circumference of the stator 2 at regular intervals of 22.5 °. Is. 32 is SIN
COS coils, 31 are COS coils, SINωt,
By inputting the voltage of COSωt, one of the 16 stator protrusions 15 to 30 is SINωt, COSωt, −SINωt, −C
It is wound so as to excite in the order of OSωt. Reference numeral 33 is an output coil that is evenly wound around all of the stator protrusions 15 to 30.

Fig. 5 shows the 12X reluctance type resolver of Fig. 4
The rotation angle θ of the rotor 1 and the output coil 33 when only one of the OS winding 31 and the SIN winding 32 is excited by a sine wave.
₅ is a characteristic diagram showing an output voltage V ₀ of FIG. In the reluctance type resolver having the structure as shown in FIG. 4, the magnetic resistance changes due to the change in the air gap between the rotor protrusions 3 to 14 and the stator protrusions 15 to 30 depending on the rotation angle θ. When a sine wave voltage is input, an electromotive voltage whose amplitude changes in a 12-cycle sine wave for one rotation of the rotor 1 is generated in the output winding 33 as shown by the waveform a in FIG. Similarly SIN
When a sinusoidal voltage is applied to the winding 32 for use, as shown in the waveform b in FIG. 5, when one cycle of the waveform a is set to an electrical angle of 360 °, the electrical phase is 90 ° out of phase with the waveform a. An electromotive voltage whose amplitude changes in a 12-cycle sine wave is generated in the output winding 33.

From the above, when COSωt is input to the COS winding 31 and SINωt voltage is input to the SIN winding 32, assuming that the waveforms a and b in FIG. 5 are ideal sine waves, the output winding Line 3
When the output voltage V _{0 of} 3 is obtained, V ₀ = sin (12θ) · cosωt + cos (12θ) · sinωt = sin (ωt + 12θ) (1) In this way, the output voltage V ₀ of the output winding 33 changes in output waveform phase in proportion to 12 times the rotation angle θ of the rotor 1. That is, the rotation angle θ of the rotor 1 can be detected by detecting the phase shift of the output waveform with respect to the input waveform of the SIN winding 32, which is the principle of the reluctance resolver.

(Problems to be Solved by the Invention) However, the waveforms a and b in FIG. 5 are not actually ideal sine waves, but generally include third-order, fifth-order, seventh-order, and other odd-order harmonics. The error for the sine wave is called the function error.
If this function error is large, the phase shift amount of the output waveform with respect to the input waveform of the SIN winding 32 is not faithfully proportional to 12 times the rotor rotation angle, and the detection error of the rotor rotation angle increases. Therefore, when improving the accuracy of the reluctance resolver, the shape of the rotor protrusion and the shape of the stator protrusion should be rounded with corners or several notches on the opposing surfaces of the rotor and stator protrusions. Adjusting the change of magnetic resistance with respect to the rotation angle θ by putting it in and devising,
It is necessary to reduce the function error. This involves many problems such as spending a lot of time to search for a good shape, difficult machining, and inability to obtain machining accuracy.

The present invention has been made under the circumstances as described above,
An object of the present invention is to provide a relatively simple reluctance resolver having a rotor structure capable of reducing a function error without devising the shape of protrusions of the rotor and the stator of the reluctance resolver.

(Means for Solving the Problem) The present invention relates to a reluctance resolver in which m projections are arranged on a rotor and 4n projections are arranged on the circumference of a stator. , M, n is G and the least common multiple is L, J = m / G, when G ≧ 2 and one of the m rotor protrusions is the reference position,
For each of the G protrusions that are continuously arranged around the predetermined direction from the reference position, (G-1) J protrusions are arranged at intervals of (360 / J) degrees, and With respect to the positional relationship of the G protrusions arranged around the predetermined direction from the reference position, the kth position from the reference position is {360 (k-1) / m + θ _k } degrees (where k is 1 ≦ k
≦ G, θ _k is k = 1, θ _k = 0, k ≧ 1, −180 / L <θ _k <18
0 / L) and at least one angle θ _k is other than 0 °.

(Operation) In the present invention, the reluctance type resolver has m rotor projections of the same shape and n stator projections of the same shape.
In each resolver, when the greatest common divisor of m and n is G and the least common multiple is L, J = m / G, this reluctance resolver is a resolver with a shaft multiplication angle L. If G ≧ 2, the stator is This is the same as in FIG. 4 of the related art, and even a reluctance type resolver having J rotor protrusions evenly arranged on the outer circumference of the rotor functions as a resolver with a shaft angle multiplier L. Therefore, the conventional reluctance type resolver (m =
12, n = 4, G = 4, L = 12, J = 3), the rotor protrusions 3 to 14
As shown in the figure, the positional relationship between the stator projections 15 to 30 for SIN excitation, COS excitation, −SIN excitation, and −COS excitation is Protrusion 4,7,10,1
3 and the rotor projections 5, 8, 11, and 14 have the same relationship in each set. Therefore, it can be considered that a J = 3 reluctance type resolver such as that shown in FIG. 1 in which one rotor protrusion is left from each set has almost the same characteristics as the conventional resolver, and the resolver of FIG. The rotor part of the resolver in Fig. 1 is composed of 4 sets, and each set has a rotor of 360 / m.
Only by a degree (an electrical angle of 360 °), the function error characteristics before and after the composition are almost the same.

Thus, the present invention focuses on the fact that the rotor of the conventional reluctance resolver with G ≧ 2 can be considered as a rotor having J independent rotor projections of G groups, and the separated G groups are separated. By changing the arrangement angle of each rotor from the conventional one, the phase of the output voltage characteristic with respect to the rotor rotation angle of each set is shifted, and the harmonic component of the function error is reduced from the combined characteristic.

(Embodiment) The resolver shown in FIG. 2 is obtained by improving the conventional reluctance type resolver shown in FIG. 4 into the rotor structure of the present invention, and all symbols in the figure correspond to those in FIG. Also,
The shapes of the stator protrusions 15 to 30, the arrangement angle of the stator 2 on the circumference, and the shapes of the rotor protrusions 3 to 14 are all the same as those in FIG. 4, and the rotor protrusions 3 to 14 are arranged on the outer circumference of the rotor. Only the arrangement angle is different from that in FIG. That is, the rotor protrusion
3,7,11, rotor protrusions 4,8,12 and rotor protrusions 5,9,13
, And the three rotor protrusions in each set of the rotor protrusions 6, 10, and 14 are arranged on the outer periphery of the rotor 1 at an interval of 360/3 = 120 degrees. Therefore, as described above, each set can be independently considered as a resolver having the same function error characteristic as the resolver of FIG. Further, when the arrangement angle of the rotor protrusion 3 with respect to the rotor 1 is 0 degree, the rotor protrusion 4,
5 and 6 are 27 degrees, 55 degrees, and 82 degrees (30 ° -180 ° / (12 ×
5), 30 ° × 2-180 ° / (12 × 3), 30 ° × 3-180 ° /
It is arranged at an angle of (12 × 5-180 ° / (12 × 3)). Here, when the resolver of FIG. 1 is excited only by the COS winding 31, the output voltage amplitude of the output winding 33 with respect to the rotor rotation angle θ is E (θ), and the amplitude of the fundamental wave is E ₁ , the function The amplitude of the 3rd harmonic in the error component is E ₃ , and the amplitude of the 5th harmonic is
If E ₅ and other function error components are e (θ), then E ′
When (θ) is calculated, E ′ (θ) = E ₁ · SIN (12θ) + E ₃ · SIN (12 × 3θ) + E ₅ · SIN (12 × 5θ) + e (θ) (2)

The resolver shown in FIG. 2 has four sets of the first set of rotors 1 of the resolver shown in FIG. 1 which are deviated from the rotor axis by 0 °, 27 °, 55 ° and 82 °.
Since it can be considered as a synthesis of a resolver having a function error characteristic equivalent to that in the figure, the resolver in FIG.
Output winding for rotor rotation angle θ when excited only
The output voltage amplitude E (θ) of 33 is calculated as follows: E (θ) ≈ E '(θ + 0) + E' (θ + 27) + E '(θ + 55) + E' (θ + 82) ≈ E ₁ · SIN (12 x (θ + 0)) ＋ E ₃・ SIN (12 × 3 (θ + 0)) ＋ E ₅・ SIN (12 × 5 (θ + 0)) + e (θ + 0) ＋ E ₁・ SIN (12 × (θ + 27)) ＋ E ₃・ SIN (12 × 3 (θ + 27)) ) + E ₅ · SIN (12 × 5 (θ + 27)) + e (θ + 27) + E ₁ · SIN (12 × (θ + 55)) + E ₃ · SIN (12 × 3 (θ + 55)) + E ₅ · SIN (12 × 5 (θ + 55) )) + E (θ + 55) ＋ E ₁・ SIN (12 × (θ + 82)) ＋ E ₃・ SIN (12 × 3 (θ + 82)) ＋ E ₅・ SIN (12 × 5 (θ + 82)) + e (θ + 82) ≒ E ₁・ SIN (12θ) ＋ E ₃・ SIN (36θ) ＋ E ₅・ SIN (60θ) ＋ e (θ) ＋ E ₁・ SIN (12θ−36 °) ＋ E ₃・ SIN (36θ−108 °) + E ₅・ SIN (60θ + 180 °) ＋ e (theta + 27 _{°) + E 1 · SIN (12θ} -60 _{°) + E 3 · SIN (36θ} + 108 _{°) + E 5 · SIN (60θ} + 60 °) + e (θ + 55゜) + E ₁・ SIN (12θ-96 °) ＋ E ₃・ SIN (36θ-108 ° + 180) ＋ E ₅・ SIN (60θ + 60 ° + 180 °) + e (θ + 82 °) ≈ 3.29 × E ₁・ SIN (12θ + 48 °) + e (Θ) + e (θ + 27 °) + e (θ + 55 °) + e (θ + 82 °) ... (3) From this equation (3), it can be understood that the resolver function error in FIG. 2 does not have a third-order harmonic component and a fifth-order harmonic component. Even if only the SIN winding 32 of the resolver shown in FIG. 2 is excited, the θ in equation (3) can be replaced by (θ + 90 ° / 4), and like the COS winding 31, the error in 3 It can be seen that there is no fifth and fifth harmonic components. Therefore, in the conventional reluctance type resolver of FIG. 4 having the same characteristics as the resolver of FIG. 1, the main component of the function error is reduced only by changing the arrangement angle of the rotor protrusion as shown in FIG. , You have got a high precision resolver.

3 (A) and 3 (B) show the present invention as a 10X reluctance type resolver (m = 10, n = 2, G = 2, L) having a three-dimensional magnetic path structure.
= 10, J = 5). In the figure, 1 is a rotor, 2 is a stator, both made of magnetic material, 31 is a coil for COS, 32 is a coil for SIN, one of which is excited by COSωt, SINωt The amplitude of the magnetic flux passing through the central portion of the stator 2 as shown by the arrow 34 in the figure (B) is sine corresponding to the change in the air gap between the stator protrusions 15 to 22 and the rotor protrusions 3 to 12 as the rotor 2 rotates. It has become wavy. When the COS winding 31 and the SIN winding 32 are both excited by COSωt and SINωt, respectively, the magnetic flux passing through the center of the stator 2 is detected by the output winding 33, which is a reluctance resolver. In FIG. 3 (A), the rotor projections 3, 5, 7, 9, 11 and the rotor projections 4, 6, 8, 10, 12 each have five projections of 360/5 =
They are arranged on the outer circumference of the rotor 1 at intervals of 72 degrees,
Further, since this resolver has G = 2 and J = 5, the rotor 1 includes the rotor consisting of five rotor protrusions 3, 5, 7, 9, and 11, and the rotor protrusions 4, 6, and 6. It can be independently considered as two sets of rotors having the same characteristics consisting of five rotor projections 8, 10, and 12. Further, when the arrangement angle of the rotor protrusion 3 to the rotor 1 is 0 degree, the rotor protrusion 4 is arranged at an angle of {36-18 / 7 ° (36 ° -180 ° / (10 × 7))}. Has been done. Where the rotor protrusions 3, 5, 7, 9,
When only the COS winding 32 is excited by the rotor consisting of 11,
The output voltage amplitude of the output winding 33 with respect to the rotor rotation angle θ is E ′ (θ), the fundamental wave amplitude is E ₁ , the third harmonic amplitude in the function error component is E ₃ , and the fifth harmonic is Set the wave amplitude to E ₅ , 7
The amplitude of the second harmonic is E ₇ , the other function error component is e (θ)
When E '(θ) is calculated, E' (θ) = E ₁ · SIN (10θ) + E ₃ · SIN (10 × 3θ) + E ₅ · SIN (10 × 5θ) + E ₇ · SIN (10 × 7θ) + e
(Θ) ………… (4) According to the formula (4), the rotor consisting of the rotor projections 3, 5, 7, 9, 11 and the rotor projections deviated from this rotor by (36-18 / 7) degrees. The output voltage amplitude E of the output winding 33 with respect to the rotor rotation angle θ when only the COS winding 31 is excited by the resolver of FIG. 3 having the combined characteristics of the rotor composed of 4,6,8,10,12 When (θ) is calculated, E (θ) ≒ E '(θ) + E' (θ + 36 ° -18 ° / 7) ≒ 1.94 x E ₁ · SIN (10θ-1.29 °) +1.56 x E ₃ · SIN ( 30θ−38.6 °) + 0.868 × SIN (50θ−64.3 °) + e (θ) + e (θ + 33.4 °) ……… (5) As can be seen from this equation (5), equation (4) It can be understood that the third and fifth harmonics in the function error component are reduced by about 20% and about 65% with respect to the fundamental wave, respectively, and the seventh harmonic component is eliminated, compared with the resolver of.

As described above, even if θ _k is not specified as 180 / (3L) or 180 / (5L) so as to cancel the amplitude E _{3 of the third} harmonic and the amplitude E ₅ of the _fifth harmonic, Can reduce E ₃ and E ₅ . In this respect, G is a multiple of 2 and G / 2 rotor protrusions (m / 2 rotor protrusions as a whole) are {360 (K-1) / with respect to the remaining G / 2 rotor protrusions. An example will be described in which the difference is m + θ ₂ }. First, expressing the relationship between the fundamental wave of one G / 2 rotor protrusion and the X-order harmonic component with an equation, E '(θ) = E ₁ · SIN (L · θ) + Ex · SIN (L · X
θ) + e (θ) (6) (E1: Amplitude of fundamental wave, Ex: Amplitude of Xth harmonic, e (θ):
Other harmonic components) Based on the equation (6), the overall characteristics including the other G / 2 rotor protrusions are obtained. E (θ) = E ′ (θ) + E ′ (θ + θ ₂ ) = E ₁ · SIN (L · θ) + Ex · SIN (L · X · θ)
+ E (θ) + E ₁ · SIN (L (θ + θ ₂ )) + Ex · SIN (L · X (θ + θ ₂ )) + e (θ + θ ₂ ) ...
... (7) (7) to extract only the fundamental wave component from the _{formula, E 1 · SIN (L ·} θ) + E 1 · SIN (L (θ + θ 2)) = E 1 · 2COS (L · θ 2/2) · SIN (L (θ + θ 2/2)) ...
To become ... (8) (8) the amplitude of the fundamental wave from the equation _{E 1 · 2COS (L · θ} 2/2). Also, if only the X-order harmonic component is extracted from equation (7), Ex · SIN (L · X · θ) + Ex · SIN (L · X (θ +
_{θ 2)) = Ex · 2COS} (L · X · θ 2/2) · SIN (L · X (θ + θ 2 /
2)) (9) From equation (9), the amplitude of the X-order harmonic is Ex · 2COS (L · X · θ).
_2/2) and a. Therefore, the ratio of the Xth harmonic to the fundamental wave is given by the following equation.

| (Ex · 2COS (L · X · θ 2/2)) / (E1 · 2COS (L · θ 2/2)) | = (Ex / E 1) · | COS (L · X · θ 2/2 _{) / COS (L · θ 2} /2) | ...
(10) In the formula (10), when the value of the ratio Ex / E ₁ of the conventional resolver with θ ₂ = 0 to the fundamental wave of the X-order harmonic is 1 is shown in the graph, the graph of FIG. 6 is obtained.

As can be understood by looking at the graph, θ ₂ other than 0 is −
If the value is larger than 180 / L and smaller than 180 / L, there is a wide range of values that can be reduced (where the ratio is less than 1) or canceled by the harmonic order compared to the conventional resolver (θ ₂ = 0). .

Also, when G is a multiple of 3, the G / 3 rotor protrusion and the other two G / 3 rotor protrusions are each {360 (K-1) / m + θ.
_2} and {360 (K-1) / m + θ 3}, θ 3 = 2 · θ 2
Taking the case of deviation as an example, when the ratio of the X-order harmonic to the fundamental wave is calculated based on equation (6), the following equation is obtained.

(Ex / E ₁ ) ・ | (1 + 2COS (L ・ X ・ θ ₂ )) / (1 + 2COS (L ・ θ ₂ ))
| (11) As in the case of Fig. 6, when the ratio of the X-order harmonic of the conventional resolver to the fundamental wave is set to 1 in the same way as in Fig. 6, the graph in Fig. 7 is obtained. As you can see from the graph, θ ₂ , θ ₃
Is a value other than 0, conventional resolvers (θ ₂ , θ ₃ =
There is a wide range of values that can be reduced or canceled depending on the order of higher harmonics than 0). This makes G 2
It means that the effect of the present invention can be obtained without being limited to a multiple of, and it is important that G is 2 or more and θ ₂ is at least in the range of −180 / L <θ _k <+ 180 / L, _To make a rotor with _k ≠ 0.

In order to easily improve the function error of the resolver by using the present invention, G is set to a multiple of 2 or 3 and the predetermined harmonics that are problematic in use are reduced or canceled according to the graphs of FIGS. 6 and 7. θ _k can be chosen. Further, even if G is any other number, the formula of the ratio of the X-order harmonic to the fundamental wave is derived based on the formula (6), a graph or the like is created from the formula, and θ _k is obtained. The characteristic resolver can be improved.

(Effect of the Invention) As described above, according to the present invention, it is possible to reduce the function error mainly by a simple method of changing the arrangement angle of the rotor protrusion to the outer circumference of the rotor without devising the shape of the rotor protrusion or the shape of the stator protrusion. It is possible to obtain a highly accurate reluctance type resolver by reducing the components.

[Brief description of drawings]

FIG. 1 is a structural diagram of a reluctance type resolver for explaining the present invention, FIG. 2 is a structural diagram showing an embodiment of a reluctance type resolver of the present invention, and FIGS. 3 (A) and 3 (B) are the present invention. FIG. 4 is a structural diagram showing an embodiment of a reluctance type resolver having a three-dimensional magnetic path structure, FIG. 4 is a conventional reluctance type resolver having a shaft angle multiplier of 12, and FIG. 5 is a characteristic diagram of the reluctance type resolver of FIG. And FIG. 7 is a diagram showing the ratio of the X-order harmonic of the conventional resolver to the fundamental wave. 1 ... Rotor, 2 ... Stator, 3-14 ... Rotor protrusion, 15-30 ... Stator protrusion, 31 ... COS winding, 32
...... SIN winding, 33 …… Output winding.

Claims (7)

[Claims] 1. A reluctance resolver in which m projections are arranged on a rotor and 4n projections are arranged on the circumference of a stator. In a reluctance resolver, the greatest common divisor of m, n is G and the least common multiple is L, J. = M /
If G, then G ≧ 2 and 1 of m rotor protrusions
When one is set as the reference position, (G-
1) J protrusions arranged in a row are arranged at an interval of (360 / J) degrees, and the positional relationship of G protrusions arranged around the predetermined direction from the reference position is 0. The degree of the kth from the reference position is {360 (k-1) / m + θ _k }
Degree (where k is 1 ≦ k ≦ G, θ _k is k = 1 and θ _k = 0, k
If it is ≧ 1, -180 / L <θ _k <180 / L) and arrange it so that the angle θ _k is at least one and more than 0 degrees, then eliminate or reduce the harmonic component of the resolver function error. A reluctance type resolver characterized in that 2. An output winding is arranged in the center of the stator, and the stator protrusion has SIN, COS, -SIN,
The reluctance resolver according to claim 1, wherein a coil for COS is wound and a magnetic path is passed through a rotor shaft. 3. The SIN, COS, -SIN on the stator protrusion
2. The reluctance type resolver according to claim 1, wherein a flat magnetic path structure is provided in which an output winding connected to all of the stator projections is wound, and a -COS winding is wound. 4. The SIN, COS, -SIN for the stator protrusion.
2. The reluctance type structure according to claim 1, wherein a plane magnetic path structure is formed by winding one winding for the COS and one winding for the -COS in order, and winding the output winding connected in series to all the remaining protrusions. Resolver. 5. G is a multiple of 2, wherein {360 (k-1) / m
+ Theta _k} there G number in formula _{θ k (1 ≦ k ≦ G} ) of G / 2
Each one has a rotor shape corresponding to the other G / 2 pieces by 180 / 3L = 60 / L degrees in a one-to-one correspondence, and reduces the third harmonic component in the resolver function error. The reluctance type resolver according to claim 1. 6. G is a multiple of 2, wherein {360 (k-1) / m
+ Theta _k} there G number in formula _{θ k (1 ≦ k ≦ G} ) of G / 2
Wherein each of the G has a rotor shape corresponding to one-to-one with a 180/3 (5L) degree shift with respect to the remaining G / 2, and reduces the fifth harmonic component in the resolver function error. Item 1. The reluctance type resolver according to Item 1. 7. G is a multiple of 2, wherein {360 (k-1) / m
+ Theta _k} there G number in formula _{θ k (1 ≦ k ≦ G} ) of G / 2
The number of the rotors has a rotor shape that corresponds to the remaining G / 2 units by 180/3 (7L) degrees and has a one-to-one correspondence, and reduces the seventh harmonic component in the resolver function error. Item 1. The reluctance type resolver according to Item 1.