JP2015095968A - Dynamo-electric machine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a dynamo-electric machine in which the cogging torque due to the magnetic anisotropy of an armature core can be reduced, and the position of a groove can be limited.SOLUTION: In a dynamo-electric machine 1 including an armature core 4 having magnetic anisotropy, and a rotor 3 having magnetic poles of P poles (P is a multiple of 2) arranged oppositely, when the number of times of pulsation of the first cogging torque to be reduced is αP(α is a natural number), a groove 6 generating the second cogging torque for reducing the first cogging torque is provided at a position determined from the P and α on the salient pole of the armature core 4.

Description

  As a method for reducing the cogging torque of a rotating electric machine, a groove is provided on the surface of the armature salient pole part and facing the field, and the cogging torque generated by the groove cancels the cogging torque that originally exists. Thus, the present invention relates to a technique for reducing the total amount of cogging torque.

  In a motor having a permanent magnet, an armature-side salient pole is generated so that a cogging torque having a phase shifted by π (rad) is generated with respect to the phase of the fundamental wave of the cogging torque waveform generated by opening the slot on the armature side. A technique for providing a groove on an end surface of a portion is disclosed (for example, Patent Document 1).

JP 2009-189163 A (paragraphs [0008], [0054] to [0055], FIGS. 4 and 7)

  In the invention of Patent Document 1, a method for reducing a cogging torque waveform by opening a slot is shown, but a groove is provided at a position where a cogging torque having a phase shifted by π (rad) from the original cogging torque is generated. However, it does not disclose a specific position for providing the groove. In addition, a method for dealing with cogging torque generated by factors other than slot opening is not disclosed. The cogging torque generated by factors other than the slot open has a problem that the contribution of each factor varies depending on the product and it is difficult to deal with it in a unified manner.

  An object of the present invention is to provide a rotating electrical machine that can reduce the cogging torque caused by the magnetic anisotropy of the armature core and can limit the position of the groove.

  A rotating electrical machine according to the present invention includes an armature core having magnetic anisotropy configured to obtain a rotating magnetic field by sequentially energizing a plurality of coils wound around a plurality of salient poles, and an armature core And a P pole (P is a positive multiple of 2) arranged opposite to each other via a gap, and is configured to generate torque by electromagnetic force generated between the armature and the armature of the armature core. In the case of providing a rotor having magnetism and providing a groove on the salient pole of the armature core in order to reduce the first cogging torque due to the magnetic anisotropy of the armature core, the first cogging torque to be reduced When the number of pulsations is αP (α is a natural number), the position of the groove for generating the second cogging torque for reducing the first cogging torque is obtained from P and α on the salient poles of the armature core.

  Since the rotating electrical machine according to the present invention is configured as described above, when the first cogging torque to be reduced is αP (α is a natural number and P is the number of magnetic poles), the first cogging torque is reduced. In addition, the position of the groove can be limited by an expression represented by α and P.

It is sectional drawing of the electric motor which concerns on the rotary electric machine of Embodiment 1 of this invention. It is a schematic diagram for considering the force which acts on 1 pole of magnetic poles by the magnetic anisotropy concerning the rotary electric machine of Embodiment 1 of this invention. It is explanatory drawing of the change of the force which acts on 1 pole of magnetic poles by the magnetic anisotropy concerning the rotary electric machine of Embodiment 1 of this invention. It is a schematic diagram for considering the force which acts on 1 pole of magnetic poles by the groove | channel of the armature internal peripheral surface which concerns on the rotary electric machine of Embodiment 1 of this invention. It is explanatory drawing of the change of the force which acts on 1 pole of magnetic poles by the groove | channel of the armature internal peripheral surface which concerns on the rotary electric machine of Embodiment 1 of this invention. It is a groove process candidate position figure of the specific example which concerns on the rotary electric machine of Embodiment 1 of this invention. It is a vector diagram for the composition consideration which concerns on the rotary electric machine of Embodiment 1 of this invention. It is a combination figure of the control groove processing position of the example of Drawing 6 concerning the rotary electric machine of Embodiment 1 of this invention. It is a vector diagram of the cogging torque resulting from the groove | channel which concerns on the rotary electric machine of Embodiment 1 of this invention. It is a vector diagram showing the groove processing position which concerns on the rotary electric machine of Embodiment 1 of this invention. It is a groove process candidate position figure of the specific example which concerns on the rotary electric machine of Embodiment 1 of this invention. FIG. 12 is an optimum groove machining position diagram of the specific example of FIG. 11 relating to the rotary electric machine according to Embodiment 1 of the present invention; It is a vector diagram showing the groove processing position which concerns on the rotary electric machine of Embodiment 2 of this invention. It is a vector diagram showing the groove processing position which concerns on the rotary electric machine of Embodiment 3 of this invention.

Embodiment 1 FIG.
The first embodiment relates to a rotating electrical machine that can reduce cogging torque caused by magnetic anisotropy by providing a groove on a salient pole of an armature core and limit the machining position of the groove. In the first embodiment, groove processing for reducing cogging torque due to magnetic anisotropy with one groove, or cogging torque due to magnetic anisotropy with two grooves is reduced, and new separate harmonics are generated by the grooves. Groove machining that suppresses the generation of cogging torque and further increases the number of grooves without reducing the groove dimensions (groove design) in order to suppress variation in the reduction effect due to groove dimensional errors and machining variations Will be described.

  FIG. 1 is a cross-sectional view of a rotating electrical machine, and FIG. 1 is a schematic diagram for considering the force acting on one pole of a magnetic pole due to magnetic anisotropy, regarding the configuration and operation of the rotating electrical machine 1 according to Embodiment 1 of the present invention. FIG. 2 is an explanatory diagram of a change in force acting on one magnetic pole due to magnetic anisotropy, and FIG. 4 is a schematic diagram for considering the force acting on one magnetic pole due to the groove on the inner peripheral surface of the armature. FIG. 5 is an explanatory diagram of a change in force acting on one magnetic pole by a groove on the inner peripheral surface of the armature, FIG. 6 is a groove processing candidate position diagram of a specific example, FIG. 7 is an explanatory diagram of vector synthesis, FIG. FIG. 8 is a combination diagram of restraint groove machining positions, FIG. 9 is a vector diagram of cogging torque caused by the grooves, FIG. 10 is a vector diagram showing groove machining positions, and is a diagram of candidate positions for restraint groove machining in a specific example. 11 and FIG. 12, which is an optimum groove machining position diagram of a specific example, will be described.

FIG. 1 is a cross-sectional view of a rotating electrical machine 1 according to Embodiment 1 of the present invention. In FIG. 1, a rotating electrical machine 1 to which the present invention is applied includes an armature 2 and a rotor 3.
The armature 2 includes an armature core 4, a groove 6 (not shown), and a slot 7. The rotor 3 includes a magnetic pole 5 and a rotor shaft 8.
The rotating electrical machine 1 according to the first embodiment is a permanent magnet type and field rotating type synchronous motor, and has P number of poles and S number of slots. The first embodiment will be described assuming a synchronous motor having P = 10 poles and S = 12.

The armature 2 is manufactured by laminating electromagnetic steel plates punched into a cylindrical shape using a mold and a press. In small and mass-produced motors, in order to increase the productivity of this process, a method called caulking with a progressive die is often employed. In this construction method, the magnetic steel sheet wound in a coil shape is fed into the mold at a constant pitch in synchronization with the stamping cycle of the press machine, and a predetermined portion is punched every time one pitch is advanced, and a plurality of times The magnetic steel sheets punched to the final shape after punching are pulled out to a portion called squeeze ring in the mold, and are laminated by being crimped onto the magnetic steel sheets that have been punched out one shot before.
In order to obtain a desired plate thickness, the electromagnetic steel plate has magnetic anisotropy under the influence of repeated rolling in the longitudinal direction. The magnetic anisotropy is the tendency that the permeability in the rolling direction is the highest and the permeability in the direction orthogonal to the rolling direction is the lowest.

FIG. 2 is a cross-sectional view of the rotating electrical machine 1 according to the first embodiment, and is a schematic diagram for excluding the influence of the magnetic resistance due to the slot 7 and considering the cogging torque due to the magnetic anisotropy. In order to simplify the explanation, attention is paid to one pole on the rotor shaft 8 and the force acting on the magnetic pole 5 is considered.
Here, one pole of the magnetic pole 5 means from a zero cross point having a fundamental wave of the magnetic flux density distribution on the surface of the rotor 3 to an adjacent zero cross point, and the peak position of the fundamental wave, that is, the maximum point or the minimum point is defined as the magnetic pole 5. The center of

The cogging torque resulting from the magnetic anisotropy will be described with reference to FIG. FIG. 3 is a diagram showing a state in which the force acting on one pole due to magnetic anisotropy changes as the magnetic pole rotates.
When the force in the rotating direction of the rotor 3 acting on the magnetic pole 5 due to the magnetic anisotropy is F (θ), the relative positional relationship between the magnetic anisotropy on the armature 2 side and the force acting on the magnetic pole 5 is as shown in the developed view of FIG. It is expressed as follows. The meaning of FIG. 3 is as follows.
The armature 2 according to the first embodiment has two positions where the magnetic permeability becomes maximum and minimum when the rotor 3 makes one rotation due to magnetic anisotropy. Now, assuming that one point of the position with the maximum magnetic permeability is a rotation angle 0 (rad), when the center of the magnetic pole 5 is at the position 0 (rad), the rotor 3 is in a stable position. The working rotational force is zero. Next, when the center of the magnetic pole 5 moves in the positive direction, a force is exerted on the magnetic pole 5 to return to the stable position of 0 degrees, so F (θ) takes a negative value. When the rotor 3 is further rotated in the positive direction, F (θ) takes the minimum value at any position. Thereafter, the magnetic flux 5 starts to increase, and the magnetic permeability becomes minimum at the center of the magnetic pole 5 at a position of π / 2 (rad), and F (θ) becomes zero.
This position is an unstable position. When the position is slightly shifted in the negative direction, a negative force is applied to the magnetic pole 5, and when the position is slightly shifted in the positive direction, a positive force is applied to the magnetic pole 5. When it is further rotated in the positive direction, F (θ) continues to take a positive value, F (θ) takes the maximum value at any position, and the permeability becomes maximum at the position where the center of the magnetic pole 5 is 180 degrees. (Θ) becomes zero.
The waveform of F (θ) from π (rad) to 2π (rad) is the same as that of 0 (rad) to π (rad) described above.

  Since F (θ) is a periodic function with a period of π (rad), it can be generally expressed as in equation (1) using a Fourier series.

  However,

From FIG. 3, since F (θ) is an odd function, a _k = 0 for all k, and equation (1) can be expressed by equation (3).

  Equation (3) is a rotational force acting on one pole of the magnetic pole 5. Using the equation (3), the sum T (θ) of the torque for the P pole can be expressed by the equation (4), where r is the radius of the rotor 3.

  Here, for a certain k,

Is a value other than 0 because of the nature of trigonometric functions, α is a natural number (2k) · (2π / P) = 2πα,

At the time. Substituting equation (5) into equation (4) yields equation (6).

From the equation (6), it can be seen that the number of pulsations per rotation of the rotor 3 of the cogging torque caused by the magnetic anisotropy in the first embodiment can take a value that is a natural number times the number of poles.
Which component of the number of pulsations prevails depends on the material and shape of the armature core 4 and therefore differs depending on the model of the rotating electric machine (electric motor).
The cogging torque T (θ) resulting from the magnetic anisotropy is the first cogging torque of the present invention.

Now, the number of pulsations that prevail is α ₁ P times, and this component is called the α ₁ P mountain component. It is considered based on FIG. 4 and FIG. 5 to cancel this component by providing a groove 6 extending in the direction of the rotation axis on the salient pole of the armature core and on the surface facing the magnetic pole 5.
FIG. 4 is a schematic diagram for considering the force acting on one pole of the magnetic pole 5 when the center of the groove 6 is at the position of φ (rad) on the inner periphery of the armature. However, in the figure, φ = 0.

When the force acting on the magnetic pole 5 F ^* and ^(theta), the relative positional relationship between the armature 2 and F ^{* (theta)} is as shown in FIG. FIG. 5 shows a state in which the force acting on one magnetic pole is changed by the groove provided on the inner peripheral surface of the armature according to the rotation of the magnetic pole. The meaning of this figure is as follows.
When the center of the magnetic pole 5 is at the position of φ (rad), which is the center position of the groove 6, this position is an unstable point, and if the position slightly deviates from the center position in the negative direction, the force in the negative direction is positive. If it is shifted to, positive force will work. When the magnetic pole 5 is further advanced in the positive direction, F ^* (θ) takes the maximum value at a certain position in the vicinity of the groove 6, and then decreases and becomes 0 at the position of φ + π (rad). This point is a stable point, and F ^* (θ) takes a negative value when the magnetic pole 5 is further advanced in the positive direction. When the magnetic pole 5 comes to a certain position in the vicinity of the groove 6, F ^* (θ) takes the minimum value, and then becomes 0 at the position of 2π (rad). That is, F ^* (θ) has a point-symmetric waveform with respect to the position of φrad.
The center position of the groove is the center position when the distance from one edge of the groove to the other edge is measured.

When F ^* (θ) is expressed by a Fourier series, considering that the values of 0 to π (rad) and π to 2π (rad) are different, considering similarly to the derivation of F (θ), (7) The formula is obtained.

Here, b ^* _{k *} is expressed by equation (8).

Expression (7) is a rotational force acting on one pole of the magnetic pole 5. The sum T ^* (θ) of the torque for the P pole using the equation (7) is expressed by the equation (9) in the same way as the derivation of T (θ).

From the equation (9), the number of pulsations per rotation of the rotor 3 of the cogging torque T ^* (θ) caused by the groove can be a natural number times the number of poles. The magnitude and positive / negative of the amplitude b ^* _{α * P} of the pulsation component are determined by the mutual relationship between the waveform of F ^* (θ) and the waveform of sinα ^* P (θ−φ) depending on the width and depth of the groove (FIG. 5). (See F (θ) and sin2kθ). However, b ^* _{α * P} can be made positive if the depth of the groove is sufficiently small with respect to the arc length of half wavelength of sin α ^* P (θ−φ).
The cogging torque F ^* (θ) due to the groove is the second cogging torque of the present invention.

Of cogging torque due to the groove, with a component which is alpha ^{* =} alpha _1, for canceling the cogging torque due to magnetic anisotropy, consider the position of the groove.

T (theta) of alpha = alpha ₁ The components _T α1 (θ), if ^{T *} a (theta) of alpha ^* = alpha ₁ component and ^{T *} _{[alpha] 1} (theta), for all theta (10) formula It only has to be established.

  Equation (11) is derived from Equation (10).

  Equation (12) is derived from Equation (11).

  Since equation (12) always holds for θ, equation (13) is derived.

  Equation (14) is derived from Equation (13).

Here, case division occurs with respect to the sign of b ^* _α1P / _bα1P .
First, when (b ^* _α1P / _bα1P )> 0, equation (15) is derived from equation (14).

  Since the first term and the second term on the left side of the equation (15) are each 0 or more, the necessary and sufficient condition for satisfying the equation (15) is

It becomes.

Next, when (b ^* _α1P / _bα1P ) <0, Equation (17) is derived from Equation (14).

  Since the first term and the second term on the left side of the equation (17) are each 0 or more, the necessary and sufficient condition for satisfying the equation (17) is

It becomes.

The expression (16) or the expression (18) is a condition to be satisfied by the groove. Of these _| b ^* α1P _|, i.e. the magnitude of the amplitude, the magnetic field analysis and prototyping, alpha _{1 P} pile component of the cogging torque due to the grooves becomes the alpha _{1 P} mountains component equivalent to the magnitude of the torque that originally Adjust the width and dimensions of the groove as follows.
Regarding the position of the groove, first, the presence or absence of the cogging torque reduction effect is confirmed at the position of equation (16), and if the α ₁ P peak component is amplified, it is reliably reduced by changing to the position of equation (18). An effect is obtained. That is, since the position of the groove is limited to two types of the formula (16) or the formula (18), the number of calculations and prototypes can be reduced, which is efficient. In addition, m can take any integer mathematically, but when considering the groove machining position on the inner peripheral surface of the actual armature, m and m ± α ₁ P indicate the same position, so m can be taken. The value can be limited to an integer of 0 or more and α ₁ P−1 or less.

  In the invention of Patent Document 1, a groove is provided at a position where a cogging torque having a phase shifted by π (rad) from the original cogging torque is generated, but a specific position where the groove is provided is not disclosed. However, in the present invention, the position of the groove can be specifically limited.

If a groove is provided at any one of the α ₁ P candidate positions that satisfy Expression (16) or Expression (18), an equivalent reduction effect can be obtained.
As an example, FIG. 6 shows a candidate position (α ₁ P = 20) for grooving when P = 10, α ₁ = 2 and S = 12.

The groove processing candidate positions for suppressing the cogging torque caused by the magnetic anisotropy can be generalized as follows.
In a rotating electric machine having a P-pole rotor, in order to reduce the first cogging torque due to the magnetic anisotropy of the armature core, the number of pulsations of the first cogging torque to be reduced is expressed as αP (α is a natural number) ), A second cogging torque that cancels the first cogging torque can be generated by providing a groove at a position obtained from P and α on the salient pole of the armature core.
The position of the groove for generating the second cogging torque is the position at which the permeability in the linkage direction is maximum with respect to the armature coil on the opposing surface of the salient pole of the armature core in the rotational direction of the rotor. Is 0 (rad), and β integers (β is a natural number from 1 to αP) taking any value from 0 to αP−1 are m ₀ ,..., M _β−1 , There are β pieces, and the center position of each groove is ((2π / αP) · m ₀ ,..., (2π / αP) · m _β-1 ), or ((2π / αP) · m ₀ + (π / αP)),... ((2π / αP) · m _β-1 + (π / αP)).

In the above calculation, the condition for making the α ₁ P peak component zero with one groove is obtained, but this may be performed with a plurality of grooves. When β is a natural number equal to or less than α ₁ P, β grooves such that | b _α1P | = β | b ^* _α1P | are represented as the candidate positions of α ₁ P locations in the equation (16) or (18). The same effect can be obtained even if distributed at any one of the β points.

As described above, it has been clarified that the α ₁ P peak component of the cogging torque caused by the magnetic anisotropy can be offset by the groove designed by the equation (16) or (18) as described above.
However, there is a possibility that an α _γ P mountain component (α _γ is a natural number and α _γ ≠ α ₁ ) is newly generated by this groove. In particular, when α ₁ is 2 or more, the components of α _γ = 1 are the same as the number of poles, so even if the magnetomotive force distribution of the rotor 3 is composed only of the fundamental wave, it is generated not a little. Therefore, it is necessary to suppress the generation of at least α _γ = 1 component, that is, the P mountain component.

Now let α _{1 be} an integer greater than or equal to 2. From the equations (16) and (18), there are α ₁ P locations for each 2π / α ₁ P (rad) as groove processing candidate positions for reducing the α ₁ P peak component. With respect to the α ₁ P peak component, the cogging torque can be reduced regardless of which location is selected.

Here, it is assumed that α ₁ groove is used to cancel the P peak component.
The cogging torque P peak component generated by a certain groove is a component of α ^* = 1 in the equation (9) and can be expressed by the equation (19).

Here, t = rPb _P , δ is the center position of this groove.
Α ₁ −1 taking any value from 0 to P−1 is assumed to be λ ₁ , λ ₂ ,..., Λ _α1-1, and [(2π / α ₁ P) + ( 2π / P) λ ₁ ] (rad), [(2π / α ₁ P) · 2 + (2π / P) λ ₂ ] (rad),..., [(2π / α ₁ P) · (α ₁ − 1) + (2π / P) λ _α1-1 ] (rad) Each cogging torque P mountain component when one groove of the same size is provided at a position separated from each other is expressed by equation (20). The

(19) the sum of the expressions of formulas and (20), a P mountain component alpha ₁ single groove is generated, which is referred to as ^T _{* 1} (theta). _Considering that the terms related to λ ₁ , λ ₂ ,..., Λ _{α1-1 in the} equation (20) can be eliminated from the periodicity of the P mountain component, T ^* ₁ (θ) is expressed by the equation (21) Become.

FIG. 7 shows each term on the right side of equation (21) corresponding to each point on the circumference according to the definition of the sine function. Since T ^* ₁ (θ) corresponds to the sum of vectors connecting the origin of FIG. 7 and each point on the circumference, equation (22) is established from the symmetry of the figure.

Next, components other than α _γ = 1 are considered inductively. When _one α groove is provided, α _γ P mountain component T _αγ (θ) is expressed by equation (23).

When the equation (23) also vectorially discussed on the circumference and 7, A vector corresponding to each term of the right side, corresponds to the point where the circumference on the road alpha _gamma rotations of alpha ₁ aliquoted Therefore, as long as α _γ is not an integral multiple of α ₁ , the right side of equation (23) is also zero.

Eventually, the only component that may be newly generated by the groove other than the α ₁ P peak component that was originally targeted for reduction is the qα ₁ P peak component (q is an integer of 2 or more). The closer it is, the smaller the amplitude tends to be.
In other words, it is possible to suppress the generation of another harmonic cogging torque due to the groove.
The position of the α ₁ groove derived in the above description is hereinafter referred to as “180 degree reduced position”.

As an example, FIG. 8 shows a 180 degree reduction position when P = 10, α ₁ = 2, S = 12, and (b ^* _α1P / _bα1P )> 0. Specifically, FIG. 8 shows a combination of machining positions that can suppress the occurrence of a new extra cogging torque of another component due to the groove among the groove machining candidate positions in FIG. In FIG. 8, the 20q peak component can be reduced by selecting the same number of ● and ■.
It should be noted that n combinations (n is a natural number from 1 to P) can be made as combinations of α ₁ grooves represented by the expressions (19) and (20). That n [alpha Qa _{1 P} mountain component with _one groove (q is an integer of 2 or more) it is possible to suppress the occurrence of non.

The 180 degree reduction position of the groove for suppressing the cogging torque due to the magnetic anisotropy can be generalized as follows.
With respect to the rotation direction of the rotor, nα integers (n is 1 to P) taking any value from 0 to P−1 with respect to the armature coil on the opposing surface of the salient pole of the armature core. natural number) the _m 10 _{up, ···, m 1 (α-} 1), ···, m n0, ···, when the _{m n (α-1),} the number of the grooves nα number exists The center position of each groove is (2π / αP) · (0 + αm ₁₀ ),..., (2π / αP) {(α-1) + αm _{1 (α-1)} },. / ΑP) · (0 + αm _n0 ),..., (2π / αP) {(α-1) + αm _{n (α-1)} }, or (2π / αP) · (0 + αm ₁₀ ) + (π / αP),..., (2π / αP) {(α-1) + αm _{1 (α-1)} } + (π / αP),..., (2π / αP) _{· (0 + αm n0) +} ( / ΑP), ···, (2π / αP) {(α-1) + αm n (α-1)} + (π / αP) become consists of nα of grooves.

By the way, the cogging torque caused by the magnetic anisotropy is generated in the same size for any individual unless the dimensions and materials of the armature core and the rotor are changed. For this reason, once the dimensions and position of the groove are determined by trial manufacture, a product having a small α ₁ P mountain component is obtained by preparing a groove shape in the mold in advance in the punching process of the armature core during mass production. Can do.

In the invention of Patent Document 1, the dimensions of the groove for reducing the cogging torque are preferably a width of 0.5 mm or less and a depth of 0.3 mm. However, a method for dealing with variations in the reduction effect due to groove processing errors has not been clarified.
The armature core of a rotating electrical machine that is mass-produced is manufactured by punching electromagnetic steel sheets into a desired shape with a mold and a press machine and laminating them, and the thickness of the electromagnetic steel sheet is 0.5 mm or 0.3 mm. There are many cases. In general, it is considered difficult to control the dimension below the plate thickness in the punching process using a press die, and therefore, it is considered that the grooving process with the above dimension has a large variation.
In the invention of Patent Document 1, since the cogging torque generated by the groove is shifted by 180 degrees with respect to the phase of the original cogging torque, the influence due to the variation in the groove dimension is directly connected to the total amount of the cogging torque. For example, when the groove machining dimension is swung to the larger side, the amplitude of the cogging torque due to the groove exceeds the amplitude of the original cogging torque, and a cogging torque having a phase opposite to that of the original cogging torque is generated.

However, as described in Patent Document 1, the dimensions of these grooves are often on the order of a few millimeters of commas based on experience, and the effect of reducing cogging torque due to punching and die machining errors and chipping in the mold. Variation occurs. In order to reduce the influence of variation, it is effective to increase the number of grooves, that is, to provide _one groove of sα (s is an integer of 2 or more), but the size of the α ₁ P peak component to be reduced is Since it is constant, the amount of cogging reduction per groove is reduced, so that the groove size is further reduced and machining becomes difficult.

Therefore, a method for increasing the number of grooves without reducing the size of the grooves is examined.
Expressions (16) and (18) are necessary and sufficient conditions for canceling the cogging torque caused by the magnetic anisotropy at one groove. At this time, the α ₁ P peak component of the cogging torque caused by the groove T ^* _α1 (θ) is expressed by equation (24).

  The necessary and sufficient condition for satisfying the equation (24) is the equation (25) or the equation (26).

Now, let us consider generating the torque of equation (24) in two grooves. The circumference in FIG. 9 is equivalent to 2π / α ₁ P (rad), and the position on the circumference and 0 (rad) is a vector representing the α ₁ P peak component of the original cogging torque. . At this time, T ^* _α1 (θ) is represented by a vector a in FIG.
Here, consider vectors b and c that are separated from the vector a by + ζ (rad) and −ζ (rad), respectively. The sum of vectors b and c is in the same direction as vector a.
Here, ζ is a shift angle, which is a real number.
These can be expressed as follows: _Assuming that the cogging torques corresponding to the vectors b and c are T ^* _bα1 (θ) and T ^* _cα1 (θ), respectively, T ^* _bα1 (θ), T ^* _cα1 (θ) and their sum T ^* _bα1 (θ) + T ^* _cα1 (θ) is expressed as shown in equations (27) to (29).

  The necessary and sufficient condition for the expression (29) to be equal to the expression (24) is the expression (30).

That is, if the dimensions of the two grooves and the groove position ζ are adjusted so that the expression (30) is satisfied, the effect equivalent to that of the groove at the 180 ° reduction candidate position can be obtained with respect to the reduction of the α ₁ P peak component. it can. In particular, if ζ = π / 3, then 2 cos ζ = 1, and therefore equation (31) is established.

That is, the groove having the same size as the groove determined at the 180 degree reduction candidate position, and using two grooves, the same effect (reducing the cogging torque due to the magnetic anisotropy and the qα ₁ P peak component ( q is an integer greater than or equal to 2), and the generation of cogging torque due to grooves other than grooves) can be obtained.

By the way, similarly to the fact that the 180 degree reduction candidate positions are α ₁ P places for every 2π / α ₁ P (rad), the groove candidate positions for the shift angle ζ (rad) are α ₁ P places in the b direction, There are α ₁ P locations in the c direction.
That is, choose the location of the beta from 180 degrees reduce candidate positions alpha _{1 P} point number (beta is alpha _{1 P} following a natural number), can offset the alpha _{1 P} pile component of the cogging torque in beta of grooves of the same dimensions If the grooves satisfying the expression (30) are provided at the positions of 2β positions shifted by ζ / α ₁ P (rad) in the + direction and the − direction, respectively, with respect to the positions of these grooves, 180 degrees. The same effect can be obtained with a groove twice as large as the groove at the reduction candidate position.

In particular, β = α ₁ and a 180 degree reduction position, that is, α ₁ −1 integers taking any value from 0 to P−1 are defined as λ ₁ , λ _{2 ,.} , 180 degrees reduction candidate position, and from this groove (2π / α ₁ P + (2π / P) λ ₁ ) (rad), ((2π / α ₁ P) · 2 + (2π / P ) Λ ₂ ) (rad) ((2π / α ₁ P) · (α ₁ −1) + (2π / P) λ _α1-1 ) (rad) One groove of the same size at each position When imagining the case of providing them one by one (however, it is not actually provided), 2α ₁ pieces shifted by (ζ / α ₁ P) (rad) in the + direction and − direction, respectively, from the position of these α ₁ grooves. Even when the groove is provided, the same effect as the 180-degree reduction position, that is, components other than the qα ₁ P peak component (q is an integer of 2 or more) Can be killed. Here, FIG. 10 is shown as an example.
It should be noted that 2α ₁ groove combinations expressed as described above can be made n sets (n is a natural number from 1 to P) for a certain ζ. That 2nα qα _{1 P} mountain component with _one groove (q is an integer of 2 or more) it is possible to suppress the occurrence of non. In FIG. 10, α _{1 is set} to 4.

10 is equivalent to (2π / α ₁ P) (rad), and the α ₁ P mountain component of the cogging torque that originally has a position of 0 (rad) on the circumference is defined as Let the vector represent. The group of α ₁ grooves at the 180-degree reduction position is referred to as group A for convenience. The α ₁ P peak component generated by the groove of the A group is a sum of α ₁ vectors (A in FIG. 10) whose size is 1 / α ₁ of the radius of the circle and whose angle is π (rad).

Here, consider vectors such as group B and group C instead of group A. That is, if the sum of the vectors of the B group and the C group becomes equal to the vector sum of the A group, an equivalent reduction effect can be obtained.
The B group and the C group are each composed of α ₁ grooves, and their positions are shifted by + π / 3 (rad) and −π / 3 (rad) on the FIG.
Since the circle in FIG. 10 corresponds to (2π / α ₁ P) (rad), the actual groove position is + (π / 3α ₁ P) (rad), − (π / 3α ₁ P) (rad) is shifted.

On the other hand, since the positional relationship of the grooves in the group is the same as the positional relationship of the grooves in the equations (19) and (20), no component other than the qα ₁ P mountain component is generated by these grooves. By disposing the grooves at the positions of the B group and the C group instead of the grooves of the A group, the number of grooves can be doubled with the same size as when the grooves are provided in the A group. For this reason, since it is possible to reduce the degree of influence on the α ₁ P peak component per groove portion, it is possible to obtain the armature 2 having a small cogging torque and strong against variations in groove dimensions.
As an example, FIG. 11 shows grooving candidate positions of the B group and the C group when P = 10, α ₁ = 2 and S = 12.
In FIG. 11, by selecting the same number of ●, ■, ○, and □, the cogging torque peak component due to magnetic anisotropy can be reduced, and the cogging torque other than the qα ₁ P peak component due to the provided groove is Does not occur.

The number of grooves in FIG. 10 is an example of _one 2.alpha, if we reduce the groove dimensions as long as the machining accuracy _{permits, 2nα 1 (n = 1,2,} ···, P) also of grooves It is feasible. FIG. 12 shows, as an example, groove processing positions of the B group and the C group when P = 10, α ₁ = 2 and S = 12. From the candidate positions shown in FIG. 11, the numbers ●, ■, ○, and □ are the same, the number of grooves per salient pole is the same, and the processing position close to the slot 7 is avoided.
The reason why the number of grooves per salient pole is the same is to avoid the occurrence of torque ripple due to imbalance in the rotating magnetic field created by the three-phase alternating current. The reason why the machining position close to the slot is avoided is to stabilize the effect of the groove.

In order to suppress the cogging torque caused by magnetic anisotropy, the grooves are processed when grooves of group B and group C are provided for grooves (group A) satisfying the condition of equation (16) or (18). The position can be generalized as follows.
With respect to the rotation direction of the rotor, 2β integers taking any value from 0 to αP-1 with α being a certain natural number for the coil of the armature on the opposing surface of the salient pole of the armature core (β is a natural number from 1 to αP) is m ₀ ,..., m _β−1 , λ ₀ ,... λ _β−1, and a real number ζ satisfies 0 <ζ <π / 2 The number of the grooves is 2β, and the center position of each groove is ((2π / αP) · λ ₀ + ζ / αP), ..., ((2π / αP) · λ _β-1 + ζ / αP). Β grooves and (β (2π / αP) · m ₀ −ζ / αP),..., ((2π / αP) · m _β−1 −ζ / αP) Β grooves that satisfy or ((2π / αP) · λ ₀ + ζ / αP + π / αP), ..., ((2π / αP) · λ _β-1 + ζ / αP + π / αP) and ( (2π / αP) · m ₀ −ζ / αP + π / αP),..., ((2π / αP) · m _β−1 −ζ / αP + π / αP).

In addition, with respect to the groove at the 180 degree reduction position (group A) for suppressing the cogging torque caused by the magnetic anisotropy, the groove machining positions when the grooves of the group B and group C are provided are as follows. Can be generalized to:
With respect to the rotation direction of the rotor, 2nα integers that take any value from 0 to P−1, where α is a certain natural number for the armature coil on the opposing surface of the salient pole of the armature core. (where n is any natural number from 1 to P) m ₁₀ ,..., m _{1 (α-1)} ,..., m _n0 , ..., m _{n (α-1)} , λ ₁₀ ,..., Λ _{1 (α-1)} ,..., Λ _n0 ,..., Λ _{n (α-1)} , and when a real number ζ satisfies 0 <ζ <π / 2, the number 2nα, and the center position of each groove is (2π / αP) · (0 + αλ ₁₀ ) + ζ / αP,..., (2π / αP) · {(α-1) + αλ _{1 (α-1)} } + Ζ / αP, ..., (2π / αP) · (0 + αλ _n0 ) + ζ / αP, ..., (2π / αP) {(α-1) + αλ _{n (α-1)} } + ζ / αP Nα grooves and (2π / αP) · ( 0 + αm ₁₀ ) −ζ / αP,..., (2π / αP) · {(α−1) + αm _{1 (α−1)} } −ζ / αP,..., (2π / αP) · (0 + αm _n0 ) −ζ / αP,..., (2π / αP) {(α−1) + αm _{n (α−1)} } −ζ / αP, or (2π / αP) ) · (0 + αλ ₁₀ ) + ζ / αP + π / αP, ..., (2π / αP) · {(α-1) + αλ _{1 (α-1)} } + ζ / αP + π / αP, ..., (2π / αP ) · (0 + αλ _n0 ) + ζ / αP + π / αP,..., (2π / αP) {(α-1) + αλ _{n (α-1)} } + ζ / αP + π / αP and (2π / (αP) · (0 + αm ₁₀ ) −ζ / αP + π / αP,..., (2π / αP) · {(α−1) + αm _{1 (α−1)} } −ζ / αP + π / αP,. 2π / αP) · (0 + αm n0) ζ / αP + π / αP, ···, it consists of a (2π / αP) {(α -1) + αm n (α-1)} -ζ / αP + π / αP become nα of grooves.

  As described above, the rotating electrical machine of the first embodiment can reduce the cogging torque caused by magnetic anisotropy by providing a groove on the salient pole of the armature core, and can limit the machining position of the groove. is there.

If groove processing for reducing cogging torque due to magnetic anisotropy with a single groove is applied to a rotating electrical machine, cogging torque due to magnetic anisotropy can be reduced by performing minimum groove processing.
In addition, if the groove machining for reducing the cogging torque caused by the magnetic anisotropy in the two grooves is applied to the rotating electrical machine, it is possible to suppress the generation of a new separately harmonic cogging torque due to the grooves.
Furthermore, in order to increase the number of grooves without reducing the size of the groove, the groove processing is rotated by providing two grooves that are vector-equal to the cogging torque by the groove that reduces the cogging torque due to magnetic anisotropy. When applied to an electric machine, it is possible to suppress variations in the reduction effect due to groove dimensional errors and groove machining variations.
Further, as described above, in the rotating electrical machine of the first embodiment, the rotating electrical machine can be reduced in size and the production process can be simplified.

Embodiment 2. FIG.
In the rotating electrical machine of the first embodiment, in order to increase the number of grooves without reducing the size of the grooves that reduce the cogging torque due to the magnetic anisotropy, the groove machining is performed by providing two grooves that are identical in vector. In the above, an example in which the shift angle ζ is π / 3 has been described. In the second embodiment, the shift angle ζ is 0 <ζ <π / 3.

  Hereinafter, the configuration and operation of the rotating electrical machine according to the second embodiment will be described with a focus on differences from the first embodiment, based on FIG. 13 which is a vector diagram showing a groove processing position related to the rotating electrical machine.

FIG. 13 is a vector diagram showing the groove machining position according to the second embodiment. In FIG. 10 of the first embodiment, the processing dimensions of the grooves are the same for the A, B, and C groups. However, in actuality, the position of the A group is not grooved, and the same as the A group is a virtual expression when considering the grooving of the B and C groups.
In the second embodiment eliminates the constraint, by shifting the groove machining position from _{± (π / 3α 1 P)} (rad), and an object thereof is to suppress the generation of 2.alpha _{1 P} mountain. In particular, in the second embodiment, it is considered to narrow the groove processing position from (π / 3α ₁ P) (rad). In FIG. 13, α _{1 is set} to 4.

In FIG. 13, the 2α ₁ P component of the cogging torque generated due to the grooves in the B group and the C group can be expressed as α ^* = 2α _{1 in} the equation (9), and the equations (32) and (33) Can be expressed as

When these sums are taken, equation (34) is obtained.

When the expression (34) becomes 0, that is, the necessary and sufficient condition for canceling the 2α ₁ P peak component is expressed by the expression (35).

  Equation (36) is obtained from Equation (35).

Here, n is an integer.
In other words, the 2α ₁ P mountain component is canceled by shifting the B group by − (π / 4α ₁ P) (rad) and the C group by + (π / 4α ₁ P) (rad) from the 180 degree reduction position. Here, as shown in FIG. 13A, when the sizes of the grooves of the B and C groups are the same as in FIG. 10 of the first embodiment, the size of the combined vector of the B and C groups is A It will be bigger than the group. Therefore, as shown in FIG. 13 (b), the groove processing dimension can be made smaller than that in the first embodiment, thereby reducing the α ₁ P peak component and further suppressing the generation of 2α ₁ P peak as the next order. Placement is realized.

As described above, the rotating electric machine according to the second embodiment has two grooves that are the same in vector as the second cogging torque due to the groove for reducing the first cogging torque caused by magnetic anisotropy. And the shift angle ζ is 0 <ζ <π / 3. For this reason, the cogging torque resulting from magnetic anisotropy can be reduced similarly to the rotary electric machine of Embodiment 1.
Furthermore, it is possible to increase the number of grooves without reducing the size of the grooves, and it is possible to suppress variations in the reduction effect due to groove dimensional errors and groove processing variations.

Embodiment 3 FIG.
In the rotating electrical machine of the first embodiment, in order to increase the number of grooves without reducing the size of the grooves that reduce the cogging torque due to the magnetic anisotropy, the groove machining is performed by providing two grooves that are identical in vector. , The shift angle ζ is π / 3, and in the second embodiment, the shift angle ζ is 0 <ζ <π / 3. In the rotating electrical machine of the third embodiment, the shift angle ζ is π / 3 <ζ <π / 2, and the number of grooves is twice or more.

  Hereinafter, the configuration and operation of the rotating electric machine according to the third embodiment will be described with a focus on differences from the first and second embodiments based on FIG. 14 which is a vector diagram showing a groove machining position related to the rotating electric machine.

FIG. 14 is a vector diagram showing a groove machining position according to the third embodiment. Unlike Embodiment 2, the object is to double the number of grooves while maintaining the same dimensions as when grooves were provided in group A.
By moving the groove processing position of group B and group C in a direction further widening than ± (π / 3α ₁ P) (rad), the number of grooves can be reduced to 2n ^* α ₁ (n ^* = 1, 2, ..., P) times. In FIG. 14, α _{1 is set} to 4.
Assuming that the machining position at this time is ± (ζ ^* / α ₁ P) (rad), the cogging torque α ₁ P mountain component due to the grooves of the B group and the C group is expressed by the expressions (37) to (39). .

Here, the dimension of the groove is the same as the group A
d _α1P = b ^* _α1P
It is. Under this condition, the necessary and sufficient condition that the right side of the equation (39) is equal to the combined vector of the group A is expressed by the equation (40). (41)

  The equation (41) is obtained from the equation (40).

In the case of the _first embodiment, by increasing the number of grooves by an integer multiple of α ₁ , the occurrence of components other than the qα ₁ P peak component (q is an integer of 2 or more) is suppressed, and the influence of variations in groove dimensions is Than can be reduced.

As described above, the rotating electrical machine of the third embodiment is provided with two grooves that are vector-equal to the cogging torque due to the grooves that reduce the cogging torque caused by magnetic anisotropy, and this shift angle ζ is set to π / 3 <ζ <π / 2. For this reason, the cogging torque resulting from magnetic anisotropy can be reduced similarly to the rotary electric machine of Embodiment 1.
Furthermore, the number of grooves can be increased by a factor of two or more without reducing the size of the grooves, and variations in the reduction effect due to groove dimensional errors and groove processing variations can be suppressed.

  Note that the present invention can be freely combined with each other within the scope of the invention, and the embodiments can be modified or omitted as appropriate.

1 rotary electric machine, 2 armature, 3 rotor, 4 armature core, 5 magnetic poles, 6 grooves,
7 slots, 8 rotor shafts.

Claims (8)

An armature core having magnetic anisotropy configured to obtain a rotating magnetic field by sequentially energizing a plurality of coils wound around a plurality of salient poles, and opposed to the armature core via a gap A rotor having a magnetic field having a P pole (P is a positive multiple of 2) and configured to generate torque by an electromagnetic force generated between the armature and the armature of the armature core. In the rotating electrical machine provided,
When providing a groove on the salient pole of the armature core in order to reduce the first cogging torque due to the magnetic anisotropy of the armature core,
When the number of pulsations of the first cogging torque to be reduced is αP (α is a natural number),
The position of the groove for generating the second cogging torque for reducing the first cogging torque is the rotating electric machine obtained from the P and the α on the salient pole of the armature core. The groove for generating the second cogging torque is
With respect to the rotation direction of the rotor, the position where the permeability in the linkage direction is maximum with respect to the coil of the armature is 0 rad on the opposing surface of the salient pole of the armature core, and 0 to αP−1 Where β integers (β is a natural number from 1 to αP) are m ₀ ,..., M _β−1 , the number of the grooves is β, The center position of the groove comprises (2π / αP) · m ₀ ,..., (2π / αP) · m _β-1
Or ((2π / αP) · m ₀ + (π / αP)), ..., ((2π / αP) · m _β-1 + (π / αP)) Item 2. The rotating electrical machine according to Item 1. The groove for generating the second cogging torque is
With respect to the rotation direction of the rotor, the position where the permeability in the linkage direction is maximum with respect to the coil of the armature is 0 rad on the opposing surface of the salient pole of the armature core, and 0 to P-1 either take the value nα integers of (n is a natural number from 1 to P) and _{m 10, ···, m 1 (} α-1), ···, m n0, ···, m n _{When (α-1)} , the number of the grooves is nα, and the center positions of the grooves are (2π / αP) · (0 + αm ₁₀ ), ..., (2π / αP) {(α -1) + αm _{1 (α-1)} }, ..., (2π / αP) · (0 + αm _n0 ), ..., (2π / αP) {(α-1) + αm _{n (α-1)} } Or nα grooves,
Or (2π / αP) · (0 + αm ₁₀ ) + (π / αP),..., (2π / αP) {(α-1) + αm _{1 (α-1)} } + (π / αP), (2π / αP) (0 + αm _n0 ) + (π / αP), ..., (2π / αP) {(α-1) + αmn _(α-1) } + (π / αP) The rotating electrical machine according to claim 1, comprising nα grooves. The groove for generating the second cogging torque is
With respect to the rotation direction of the rotor, the position where the permeability in the linkage direction is maximum with respect to the coil of the armature is 0 rad on the opposing surface of the salient pole of the armature core, and 0 to αP−1 2β number of integer (β is a natural number of from 1 to αP) the _m 0 to take one of the _{values, ···, m β-1,} λ 0, ···, and λ _β-1, there is a real number ζ When 0 <ζ <π / 2, there are 2β grooves, and the center positions of the grooves are ((2π / αP) · λ ₀ + ζ / αP), (, (2π / αP) · λ _β-1 + ζ / αP) and ((2π / αP) · m ₀ −ζ / αP), ..., ((2π / αP) · m _β-1 Whether it is composed of β grooves of −ζ / αP),
Or ((2π / αP) · λ ₀ + ζ / αP + π / αP), ..., ((2π / αP) · λ _β-1 + ζ / αP + π / αP) and ((2π / αP) 2. The (αP) · m ₀ −ζ / αP + π / αP),..., ((2π / αP) · m _β−1 −ζ / αP + π / αP). Rotating electric machine. The groove for generating the second cogging torque is
With respect to the rotation direction of the rotor, the position where the permeability in the linkage direction is maximum with respect to the coil of the armature is 0 rad on the opposing surface of the salient pole of the armature core, and 0 to P-1 of 2nα integers take one of the values a (n is any natural number from 1 to _{P) m 10, ···, m} 1 (α-1), ···, m n0, ··· , M _{n (α-1)} , λ ₁₀ ,..., Λ _{1 (α-1)} ,..., Λ _n0 , ..., λ _{n (α-1),} and a real number ζ is 0 < When ζ <π / 2 is satisfied, the number of the grooves is 2nα, and the center position of each of the grooves is (2π / αP) · (0 + αλ ₁₀ ) + ζ / αP, ..., (2π / αP) · {(α-1) + αλ 1 (α-1)} + ζ / αP, ···, (2π / αP) · (0 + αλ n0) + ζ / αP, ···, (2π / αP) {(α- 1) _{αλ n (α-1)}} + ζ / αP and the nα of grooves made (2π / αP) · (0 + αm 10) -ζ / αP, ···, (2π / αP) · {(α-1) + αm _{1 (α-1)} } − ζ / αP,..., (2π / αP) · (0 + αm _n0 ) −ζ / αP,..., (2π / αP) {(α-1) + αm _{n (α -1)} Is it composed of n? Grooves that become-? /? P?
Or (2π / αP) · (0 + αλ ₁₀ ) + ζ / αP + π / αP,..., (2π / αP) · {(α-1) + αλ _{1 (α-1)} } + ζ / αP + π / αP,. , (2π / αP) · (0 + αλ _n0 ) + ζ / αP + π / αP,..., (2π / αP) {(α−1) + αλ _{n (α-1)} } + ζ / αP + π / αP (2π / αP) · (0 + αm ₁₀ ) −ζ / αP + π / αP,..., (2π / αP) · {(α-1) + αm _{1 (α-1)} } − ζ / αP + π / αP , ..., (2π / αP) · (0 + αm _n0 ) −ζ / αP + π / αP,..., (2π / αP) {(α-1) + αmn _(α-1) } − ζ / αP + π / The rotating electrical machine according to claim 1, comprising nα grooves serving as αP. The rotating electrical machine according to claim 4, wherein the ζ is ζ = π / 3. The rotating electrical machine according to claim 4, wherein the ζ is 0 <ζ <π / 3. The rotating electrical machine according to claim 4, wherein the ζ satisfies π / 3 <ζ <π / 2.

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