JP2002119037A - Two-phase hybrid stepping motor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an effective vernier system, having higher degrees of freedom by elucidating the theory of a vernier system, because a vernier system which makes the pitch of a small tooth of a stator and the pitch of a small tooth of a rotor unequal has been investigated, in order to reduce cogging torque of a two-phase hybrid stepping motor, and the problem of insufficient investigation or effects being obtained. SOLUTION: It is considered that the cause of generation of the cogging torque in the two-phase hybrid type stepping motor is based on the regularities of changes where permeance between small teeth formed in a stator magnetic pole and a rotor magnetic pole changes, accompanying the rotation of the rotor. The small teeth, of multiples of 6 which are installed on the tip of the stator, are constituted by using 2 groups of sets of 3 small teeth. At least one pitch of the adjacent small teeth is made unequal to the pitch of other adjacent small teeth, in such a manner that the sum of third higher harmonic vectors of permeance of 3 small teeth of each of the sets is made substantially zero, and that the sum of vectors of permeance of two small teeth which become axial symmetry in a fourth higher harmonic plane of the two groups becomes substantially zero.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a two-phase hybrid type stepping motor, and more particularly to a two-phase hybrid type stepping motor having a structure capable of reducing cogging torque and improving a torque waveform.

[0002]

2. Description of the Related Art A conventional two-phase hybrid stepping motor is shown in FIGS. 1A, 1B and 1C.
As shown in FIG. 1, eight magnetic poles 2 are arranged at equal intervals on the inner periphery of an annular yoke 1, and windings 3 are wound around each of the magnetic poles 2 to form a two-phase winding. A stator 5 provided with six small teeth 4 at the tip and two rotor magnetic poles 7 provided with 50 small teeth 6 at an equal pitch on the outer periphery thereof are arranged at one pitch of the small teeth 6.
The rotor 9 is fixed to the end face of the permanent magnet 8 magnetized to the NS two poles in the axial direction by being shifted by a half pitch. The rotor 9 is rotatably supported on the rotor 9 through the air gap with the stator 5. It is opposed.

The winding 2 is wound across both poles of the NS, and is connected so that odd-numbered and even-numbered windings form two phases A and B, respectively. The flow of the magnet magnetic flux is N in the case of A phase.
The magnetic flux of the pole-side rotor magnetic poles enters the stator 5 from the N1 and N5 winding poles, flows in the S-pole direction, enters the stator 5 from the S3 and S7 winding poles, and enters the S-pole side rotor magnetic poles. And return to the permanent magnet 8. Since this magnetic flux does not flow through the B-phase side magnetic pole, the A-phase and the B-phase have no mutual interference and are magnetically independent.

[0004] The hybrid type switch shown in FIGS.
When considering the equivalent circuit of the magnetic circuit of a stepping motor
However, for simplicity, the equivalent circuit ignores the magnetic resistance in the iron core.
This is shown in FIG. In FIG. 2, F_iIs i
Magnetomotive force of the eye winding pole (where i is 1 to 8), P_iIs the i-th volume
Permeance on the N or S pole side of the wire pole (where i is 1 to
4), F _mAnd P_m Is the magnet's magnetomotive force and internal permeance
is there. The permeance of the winding pole at the axisymmetric position is
Since they are equal to each other, the same symbols are used. A phase
Speaking of windings, N1 and N5 poles are forward and N3 and N7 poles are reverse
Are connected in series in the
Magnetic force is the same size F_AAnd only the polarity changes
Become. As a result, FIG. 2 shows four branches (P₁And F_A, P_TwoWhen
F_B, P_ThreeAnd -F_A, P_FourAnd -F_B) Circuit group (sub)
Circuits) are in parallel, and two of them are arranged in series.
Is equivalent to one subcircuit by circuit theory
can do. This is shown in FIG.

[0005] Since the torque τ is given by the angular differentiation of the magnetic energy in the equivalent circuit of FIG.

[0006]

(Equation 1)

Here, F ₀ is the magnetomotive force drop of the air gap including the excitation, N _R is the number of rotor teeth, 2S is the number of winding poles (S = 4 in the figure), and θ _e is the electrical angle. .

Note that F ₀ is obtained from Norton's theorem as shown in Equation 2.

[0009]

(Equation 2)

It is assumed that each permeance has a phase difference of 90 degrees and is represented by a Fourier series of equations (3) and (4).

[0011]

(Equation 3)

[0012]

(Equation 4)

For example, P ₁ is as shown in Expression 5.

[0014]

(Equation 5)

[0015]

In the above-described two-phase hybrid type stepping motor, when the rotor is rotated without energizing the winding, torque is generated between the rotor and the stator. Is referred to as cogging torque.

When a plurality of windings of a two-phase hybrid type stepping motor are sequentially energized and rotated, the torque generated in the rotor is a combined torque of the torque generated by energizing the windings and the cogging torque. However, since a large amount of pulsation is included in the resultant torque, there is a problem that vibration and noise are large.

It is an object of the present invention to provide a two-phase hub-lid type stepping motor having a structure capable of minimizing the cogging torque and reducing distortion of a torque waveform generated by energizing a winding.

Further, in order to reduce the cogging torque of the two-phase hybrid stepping motor, a vernier method in which the pitch between the small teeth of the stator and the small teeth of the rotor has been studied has been studied. Sufficient studies have not been made and sufficient effects have not been obtained. Therefore, in the present invention, it is an object of the present invention to elucidate the theory of the vernier system and obtain an effective vernier system having a higher degree of freedom.

In order to solve the problem, first, the state of generation of cogging torque will be examined. The cogging torque τ _c is
And the winding magnetomotive force is zero (F _A = F _B = 0).
Expressions 6 and 7 can be used.

[0020]

(Equation 6)

[0021]

(Equation 7)

In order to remove the cogging torque, the sum of the orders of P _i in Equation 6 should be zero.

When the harmonic components up to the fourth order of each Fourier series and their sum are obtained from i = 1 to 4, the results are as shown in Table 1.

[0024]

[Table 1]

Here, since the coefficient ρ _i is the same for each pole, it is omitted.

[0026] According to Table 1, the sum of P _i is the cogging torque contribution at 8 winding pole structure is zero in the third order or less. Usually, the higher the higher-order component, the smaller the value, so the fourth-order component remains as the largest influencing factor. This is why the fourth harmonic component appears in the cogging torque of the two-phase motor.

[0027] In order to remove the torque, it is necessary to zero the fourth harmonic components of each pole permeance P _i in each winding pole.

This means that ρ ₄ in Equation _{3 is set} to zero. Next, a method of eliminating ρ ₄ by the arrangement of the small teeth provided on the winding poles will be considered.

FIG. 4 shows an example of the configuration of the small teeth of the winding pole.
The permeance P _i of the winding pole is the permeance P _{ik of the} small teeth constituting it (i: the number of the winding pole, k: the number of the small teeth)
It is considered to be the sum of Here, assuming that the number of small teeth of the winding pole is Q, Equation 8 holds.

[0030]

(Equation 8)

Therefore, here, the permeance is calculated for each of the small teeth, and the permeance of the winding pole is obtained from the sum thereof.

FIG. 5 shows an example of the magnetic path of one small tooth portion when the assumption magnetic path method is used for calculating the permeance. In FIG. 5, 2T is a small tooth pitch of the rotor (magnetic pole pair pitch), α and β are ratios of the small tooth width of the stator and the rotor to the magnetic pole pair pitch, x is a rotational displacement, and so on are magnetic path types. Classification. Since handling these magnetic paths in detail is quite complicated, considering that the gap size is extremely small, here, for simplicity, only the permeance of the opposing flat portions will be described, and the others will be omitted.

The permeance P ₁₁ between the planes is calculated by equation (9).

[0034]

(Equation 9)

Here, μ ₀ is the vacuum permeability, w is the facing width,
t iron core stacking thickness, l _g is the gap length. Since P ₁₁ is determined by the opposing width w, when considered with reference to FIG. 5, the shape of FIG. In FIG. 6, the horizontal axis is the electrical angle, the point where the central axes of the small teeth of both the stator and the rotor coincide is 0, and π is T
Corresponding to

Table 2 shows γ, δ, A, and B in FIG. 6 arranged according to the relationship shown in FIG.

Note that min (α, β) is a function that takes the smaller one of α and β.

[0038]

[Table 2]

Normally, (α + β) ≦ 1, so that P11 can be Fourier-expanded into equations (10), ( ₁₁ ) and (12).

[0040]

(Equation 10)

[0041]

[Equation 11]

[0042]

(Equation 12)

From these relationships, it is understood that the value of each order component of permeance is determined by the tooth width ratios α and β in addition to the gap length l _g , the stack thickness t and the rotor tooth pitch 2T.

Therefore, if the fourth harmonic component of the permeance can be reduced to zero as shown in Expression 13 by combining the permeances of the small teeth, the cogging torque is minimized.

[0045]

(Equation 13)

In _Equation 13, P _ik4 is the fourth harmonic component of the permeance of the k-th small tooth, and can be generally represented by the vector form of _Equation 14 (hereinafter referred to as a permeance vector).

[0047]

[Equation 14]

Here, P _10n is the n-th of the permeance of the small teeth.
The amplitude of the higher harmonic component, θ _k, is the position (electrical angle) of the k-th small tooth. θ _k is expressed by the following _equation (1) using the deviation δθ _k from the angle (reference angle) θ _k0 when the magnetic poles are arranged at the pitch of the magnetic pole pairs.
5 can be represented.

[0049]

(Equation 15)

In Expression 14, Expression 16 is obtained.

[0051]

(Equation 16)

[0052] The number 14 is also the same form by using the deviation angle δθ _k instead of θ _k. Therefore, when considered using the deviation angle δθ _k , it can be expressed as in Equation 17.

[0053]

[Equation 17]

In order to study the arrangement of the small teeth, first, FIG. 4 shows a hybrid type stepping motor having 50 rotor teeth and 8 stator winding poles shown in FIG. 1A. Consider an example in which the small teeth of one winding pole are arranged in a uniform pitch vernier arrangement. In the uniform pitch vernier arrangement, the small teeth of the stator are equally spaced at 6.9 degrees, which is smaller than the rotor tooth pitch angle of 7.2 degrees. The fourth harmonic component of the permeance vector of the small teeth is distributed as shown in FIG.

[0055] In Figure 7, to represent a vector P _IKN in V _k for ease of representation. The figures in parentheses in the figure are
The deviation angle (mechanical angle) corresponding to δθ _k is shown.

Since each harmonic component vector V _k of each small tooth is distributed by dividing the electrical angle 360 degrees into six equal parts, the total sum becomes zero. Since each vector rotates while maintaining this relationship, the balance is always established during rotation, and the cogging torque is minimized. This is the principle of reducing the cogging torque by the conventional equal pitch arrangement vernier method.

Looking closely at the vector arrangement in FIG.
It may be considered that “there are three pairs of vectors that are balanced at the axisymmetric position” or “there are two pairs of three vectors that are balanced at 120 ° intervals”. That is, in order to satisfy Expression 13, if all the vectors are partially balanced, it is not always necessary that all of the vectors are equally spaced.

This is the basic consideration of the irregular pitch arrangement method.
Is. 8A and 8B with 6 small teeth
Kind is conceivable. In FIG. 8A, V₁And V_Four, V_TwoAnd V_Five,
V_ThreeAnd V₆3 pairs are in axisymmetric position and balanced
In FIG. 8B, V₁, V_Three, V _FiveAnd V_Two, V_Four, V₆
Are balanced at equal intervals of 120 degrees.

In particular, in the case of FIG. 8A, two pairs form a pair.
As shown in the figure, the width of the small teeth can be changed within the pair.

As described above, since the unequal pitch arrangement method has more flexibility than the equal pitch arrangement, there is an advantage that consideration other than the cogging torque can be taken.

Next, consider the torque generated by the current flowing through the winding.

In FIG. 3, the A-phase winding is F₁And F_ThreeIs reversed
Since it is connected in series to the polarity, P₁And P_Three The difference in magnetic flux
Of the linkage flux. The same applies to the B phase.

Accordingly, from the table 1, it can be seen that even harmonics of each phase are canceled out, but odd harmonics are added. The first harmonic generates an induced voltage corresponding to the main torque of the sine wave, but the third harmonic is distorted and needs to be removed.

Here, a method for minimizing the third harmonic which affects the waveform distortion of the torque while minimizing the cogging torque by balancing the fourth harmonic will be examined.

When there are six small teeth, there is a method of balancing in two vectors as shown in FIG. 8A and a method of balancing in three vectors as shown in FIG. 8B. On the third harmonic plane, each corresponds to 3
It is necessary to balance both the intra-vector balance and the two-vector balance.

For the sake of simplicity, it is assumed in FIG. 8A that the small tooth width and therefore the vector length are equal, and considering that 180 degrees of the fourth harmonic plane corresponds to 135 degrees in the third plane, FIG.
A, a vector as shown in FIG. 9B is one solution.

As shown in FIG. 9A, in the third harmonic plane,
Is V₁, V_Two, V_FourAnd V_Three, V_Five, V ₆Each of the three vectors
Among them, as shown in FIG. 9B, in the fourth harmonic plane, V₁
And V_Three, V_TwoAnd V_Five, V_FourAnd V₆Vector in three pairs of
Is balanced.

Further, the balance in each of the two vectors is calculated by the third order.
Fourth harmonic balance between the harmonic plane and the balance in each of the three vectors
FIG. 10A and FIG.
There is 10B. Third harmonic plane as shown in FIG. 10A
Then V₁And V_Three, V_TwoAnd V_Five, V_FourAnd V₆Within three pairs of
As shown in FIG. 10B, in the fourth harmonic plane, V₁,
V _Two, V_FourAnd V_Three, V_Five, V₆The three vectors are
Balanced.

[0069]

A two-phase hybrid type stepping motor according to the present invention has a plurality of magnetic poles arranged at equal intervals on the inner periphery of a substantially annular yoke, and windings are wound around each of the magnetic poles. A stator having a two-phase winding formed thereon and having a small number of teeth at a multiple of 6 provided at the tip of the magnetic pole, and two rotor magnetic poles having a plurality of small teeth provided at an equal pitch on the outer periphery thereof; A rotor fixed to the end face of a permanent magnet magnetized into two poles NS in the axial direction by shifting the pitch of the small teeth by ピ ッ チ pitch, wherein the rotor is opposed to the stator via an air gap. In the phase hybrid type stepping motor, at least six small teeth provided at the tip of the stator magnetic pole are replaced with two sets of three small teeth.
The sum of the third harmonic vectors of the permeance of the three small teeth of each set is substantially zero, and 2
The pitch of at least one adjacent small tooth is adjusted so that the sum of the vectors of the permeances of the two small teeth that become axially symmetric in the fourth harmonic plane of the group is substantially zero. The feature is that it is different from the tooth pitch.

The two-phase hybrid type stepping motor according to the present invention comprises a plurality of magnetic poles arranged at equal intervals on the inner periphery of a substantially annular yoke, and a winding wound around each of the magnetic poles. And a rotor provided with a small number of teeth at a multiple of 6 at the tip of the magnetic pole and two rotor magnetic poles provided with a plurality of small teeth at an equal pitch on the outer periphery of the stator. 1/2 of installation pitch
A two-phase hybrid type stepping motor comprising: a rotor fixed to an end face of a permanent magnet magnetized to NS2 poles in the axial direction with a pitch shift, wherein the rotor is opposed to the stator via a gap. At least six small teeth provided at the tip of the magnetic pole are constituted by three groups of two sets of small teeth, and the sum of the third harmonic vector of the permeance of the two small teeth of each set is substantially determined. And at least one adjacent small tooth such that the vector of permeance vectors of three small teeth arranged at 120 degrees in each of the fourth harmonic planes of the three groups is substantially zero. Is different from the pitch of other adjacent small teeth.

The two-phase hybrid type stepping motor according to the present invention has a plurality of magnetic poles arranged at equal intervals on the inner periphery of a substantially annular yoke, and a winding is wound around each of the magnetic poles. And a rotor provided with a small number of teeth at a multiple of 6 at the tip of the magnetic pole and two rotor magnetic poles provided with a plurality of small teeth at an equal pitch on the outer periphery of the stator. 1/2 of installation pitch
A two-phase hybrid type stepping motor comprising: a rotor fixed to an end face of a permanent magnet magnetized to NS2 poles in the axial direction with a pitch shift, wherein the rotor is opposed to the stator via a gap. At least six small teeth provided at the tip of the magnetic pole are composed of two groups of three small tooth sets, and the fourth harmonic vector sum of the permeance of the three small teeth in each set is substantially equal to the total number. The pitch of at least one adjacent small tooth is made different from the pitch of another adjacent small tooth so as to be zero.

[0072]

Embodiments of the present invention will be described below with reference to the drawings.

In the first embodiment of the present invention, a two-phase hybrid type stepping motor has a plurality of magnetic poles 2 arranged at equal intervals on the inner periphery of a substantially annular yoke 1, and a winding 3 is provided on each of the magnetic poles 2. And a stator 5 having six small teeth 4 provided at the tip of the magnetic pole and a plurality of small teeth 6 provided at equal pitches on the outer periphery thereof. The rotor pole 7 of
A rotor 9 fixed to an end face of a permanent magnet 8 magnetized into two NS poles in the axial direction by being shifted by a half pitch of the arrangement pitch of the small teeth, and the rotor 9 is rotatably supported by the rotor 9. Then, the six small teeth 4 provided at the front end of the stator magnetic pole 2 are opposed to the stator 5 via a gap, and the three small teeth 2
The sum of the third harmonic vectors of the permeance of the three small teeth of each set is substantially zero, and 2
The pitch of at least one adjacent small tooth is adjusted so that the sum of the vectors of the permeances of the two small teeth that become axially symmetric in the fourth harmonic plane of the group is substantially zero. Different from the tooth pitch.

In the first embodiment of the present invention, as shown in FIG. 9A, the vectors on the third harmonic plane are V ₁ , V
_{The two} vectors V ₂ , V ₄ are arranged at equal intervals of 120 degrees and are balanced, and the three vectors V ₃ , V ₅ , V ₆ are arranged at equal intervals of 120 degrees and are balanced. Balanced.

FIG. 11 shows the arrangement of the small teeth for realizing this balance relationship.

In the vector diagram of FIG. 9A, the vertices V ₁ , V ₂ , V ₃ , V ₄ , V ₅ , and V ₆ of each vector are each a small tooth t.
₁ , t ₂ , t ₃ , t ₄ , t ₅ , and t ₆ indicate the positions, and the number in parentheses on the side indicates the deviation angle δ from the reference position.
θ (mechanical angle).

Therefore, when the position of each small tooth is calculated from the value of the deviation angle, the result is as shown in FIG.

In the arrangement of the small teeth shown in FIG.
₁ and intervals of t ₂ is 6.4 degrees, 7.1 degrees between t ₂ and t _3, t ₃
And 6.5 degrees between t _4, is 7.1 degrees between t ₄ and t _5, t ₅ and t
The interval between ₆ is 6.4 degrees.

As shown in FIG. 9B, the vectors of the fourth harmonic plane are V ₁ and V ₃ , V ₂ and V ₅ , V ₄ and V
₆ and each are symmetrical and balanced,
Balance as a whole.

[0080] When the verify the correspondence between the vector of the vector and 9B of Figure 9A, in the V ₁ and V ₃ in the fourth harmonic plane vector of Figure 9B the position of the position or 180 degrees of symmetry, 9A Must be 135 degrees between V ₁ and V ₃ in the third harmonic plane vector.

Since the other relationships between V ₂ and V ₅ and between V ₄ and V ₆ are the same, the third harmonic plane vector in FIG. 9A is 135 degrees.

Therefore, in the first embodiment shown in FIGS. 9A and 9B, the vectors of the fourth harmonic and the third harmonic can be both balanced, so that the cogging torque is reduced and the torque waveform is improved. Can be.

In the second embodiment of the present invention, a two-phase hybrid type stepping motor has a plurality of magnetic poles 2 arranged at equal intervals on the inner periphery of a substantially annular yoke 1, and windings 3 are provided on each of the magnetic poles 2. And a stator 5 having six small teeth 4 provided at the tip of the magnetic pole and a plurality of small teeth 6 provided at equal pitches on the outer periphery thereof. The rotor pole 7 of
A rotor 9 fixed to the end face of a permanent magnet 8 magnetized into two NS poles in the axial direction while being shifted by a half pitch of the arrangement pitch of the small teeth, and rotatably supporting the rotor 9 ,
The stator 5 is opposed to the stator 5 via an air gap, and
Are formed in three groups of two sets of small teeth, and the sum of the third harmonic vector of the permeance of the two small teeth of each set is substantially determined. And at least one adjacent small tooth such that the sum of the vectors of the permeances of the three small teeth arranged at 120 degrees in the fourth harmonic plane of the three groups is substantially zero. Make the pitch different from the pitch of other adjacent small teeth.

FIG. 12 shows an arrangement of small teeth provided at the tip of the winding pole according to the second embodiment of the present invention.
A, which corresponds to the vector diagram shown in FIG. 10B.

The arrangement of the small teeth shown is t ₁ , t ₂ and t ₃
, And between t ₄ and t ₅ and t ₆ are both 6.6 degrees, and t ₃
And between t ₄ and 7.2 degrees, which is the same as the rotor tooth pitch. Accordingly, the small teeth are arranged symmetrically about the center 0 degree between t ₃ and t ₄ . Examining the relationship between the arrangement of the small teeth shown in FIG. 12 and the third harmonic plane vector shown in FIG. 10A, the interval between t ₁ and t ₃ is 6.6 × 2.
= 13.2 degrees and becomes, in the vector diagram of FIG. 10A are balanced because becomes 180 degrees, between t ₄ and t _6, like
At 13.2 degrees, the position is 180 degrees in the vector diagram of FIG. Also, between t ₂ and t ₅ is 13.2 degrees, which is the position of 180 degrees in the vector diagram of FIG.

Further, while the balance of the third harmonic plane vector is shown by the vector shown in FIG. 10A, the fourth harmonic plane vector shown in FIG.
_1, 3 vector of V _2, V ₄ and V _3, V _5, V ₆ are balanced respectively.

That is, in FIG. 10A, the relationship between V ₁ , V ₂ and V ₄ is 90 degrees in the third harmonic plane vector, whereas FIG. 10B is the fourth harmonic plane vector. From this, the angle between the respective vectors is 90 × 4/3 = 120 degrees, and in the third harmonic plane vector shown in FIG. 10A, the interval between V ₁ , V ₂ and V ₄ is equal at 120 degrees. You are balanced.

That is, by arranging the six small teeth as shown in FIG. 12, the third harmonic vectors can be expressed as V ₁ and V ₃ , V ₂ and V ₅ , V ₄ as shown in FIG. 10A. The three pairs of V ₆ can be arranged at 180 ° positions and balanced so that the third harmonic can be reduced from the torque waveform, and the fourth harmonic vector can be reduced as shown in FIG. 10B. V _1, V _2, V ₄ and V _3, V _5, each 3 vector of V ₆ can reduce the cogging torque are balanced at 120 degree intervals.

In the third embodiment of the present invention, a two-phase hybrid type stepping motor is provided in which a plurality of magnetic poles 2 are arranged at equal intervals on the inner periphery of a substantially annular yoke 1, and a winding 3 is provided on each of the magnetic poles 2. To form a two-phase winding, and to provide a stator 5 having six small teeth 4 at the tip of the magnetic pole 2 and a plurality of small teeth 6 at an equal pitch on the outer periphery of the stator 5. Rotor poles 7
Is shifted by １ ／ of the arrangement pitch of the small teeth 6,
A rotor 9 fixed to an end face of a permanent magnet 8 magnetized to NS 2 poles in the axial direction, rotatably supporting the rotor 9, facing the stator 5 via an air gap, and The six small teeth 4 provided at the tip of the magnetic pole 2 are divided into two sets of three small teeth.
Two sets, each group consisting of three small teeth having a permeance of the fourth harmonic vector sum substantially equal to zero and being axially symmetrical in the third harmonic plane of the two groups. At least one so that the sum of
The pitch of one adjacent tooth is different from the pitch of the other adjacent tooth. The number of small teeth 4 in each of the above embodiments may be a multiple of six.

It has been found that by arranging the small teeth as described above, the cogging torque can be reduced and the torque waveform can be improved. The effect will be examined by two-dimensional FEM simulation.

[0091] Since it is difficult to make prototypes of the various tooth arrangement methods described above on a real machine, it is verified by simulation. However, three-dimensional magnetic field analysis is originally desirable. Then, an approximate analysis was performed using a two-dimensional finite element method. This is a method in which a portion corresponding to N1 in the equivalent circuit of FIG. 2 is cut out, a magnetic field analysis is performed by a two-dimensional FEM, and a cogging torque and a linkage magnetic flux are obtained from the result.

The calculation method is as follows.

(1) The model in FIG. 13 from which the N1 part in FIG. 2 is extracted is set as a calculation target.

(2) The cogging torque τ _c1 (θ) and the linkage flux φ ₁ (θ) of the N1 part are calculated by magnetic field analysis using a two-dimensional FEM.

(3) The cogging torque τ is obtained from the equation (18).
_{Find c1} (θ).

[0096]

(Equation 18)

(4) The A-phase linkage flux Ф
Find _A (θ).

[0098]

[Equation 19]

In FIG. 11, a periodic model in which the polarity is reversed in the circumferential direction is used for convenience of calculation. Therefore, unlike the case where all the N poles in FIG. 1A have the same pole, the calculation takes a form in which one of the different poles is taken out, but it is considered that there is no large error because the gap is extremely small. The winding current is
Since the magnetomotive force applied to the air gap by the permanent magnet was imitated, a constant current value such that the air gap magnetic flux density was 1.6 T, which is close to the actual value, was used.

The cogging torque was calculated by the Maxwell stress method while rotating the rotor to one tooth pitch (7.2 degrees). For the Maxwell stress, a triangular mesh equally divided into three layers in the radial direction at the center of the gap and 0.15 degrees in the circumferential direction was used.

The Maxwell stress was calculated using the average value of the magnetic flux densities of the triangular elements adjacent in the radial direction at the center of the gap.

FIG. 14 shows an example of calculating the cogging torque in the equal pitch arrangement method.

In FIG. 14, τ _c1 , τ _c2 , τ _c3 , τ _c4
Are the respective torques within the Σ of equation (18). From this, it can be seen that most of the torques of the respective poles cancel each other, and the remainder forms a cogging torque.

FIG. 15 shows the calculated values of the cogging torque waveform in the arrangement of small teeth examined in the above equation 13 and after, in comparison with those without vernier. Each of the arrangements is significantly reduced compared to the case without the vernier. In an actual motor, since various dimensional errors all lead to an increase in cogging torque, it is considered that such a difference is buried in the variation and there is no great difference.

Since the torque due to the current is generated by the product of the back electromotive force of the phase winding and the current, here, the evaluation is made based on the harmonic distortion of the interlinkage magnetic flux based on the back electromotive force. FIG. 16 shows a calculation example of the linkage flux in the uniform pitch arrangement method. In FIG. 16, Φ ₁ and Φ ₃ are magnetic fluxes in parentheses in Expression 19. Φ ₁ ,
Looking at [Phi _3, many DC component flux, about 2/3 of the magnet flux
It turns out that they cancel each other out and are wasted. This shows that the leakage magnetic flux is large due to the structure of the hybrid type stepping motor.

The phase A magnetic flux waveform of FIG. 16 was decomposed into a Fourier series, and harmonic distortion was calculated from coefficients up to the 15th harmonic. Based on these results, FIG. 17 shows the relationship between the fundamental wave of the linkage magnetic flux and the harmonic distortion for each arrangement method.

FIG. 17 shows the results of the cogging torque shown in FIG. 15 in an organized manner.

FIG. 17 shows that the magnetic flux waveform distortion rate is about 5% in the non-vernier method, while it is about 2.5% in the fourth harmonic canceling method, and the fourth and second harmonics are simultaneous. The offset method has improved to around 2%.
On the other hand, the magnitude of the magnetic flux fundamental wave is about 7% and about 19%, respectively.
Is decreasing. The effect of improving the linkage magnetic flux waveform by canceling the third harmonic is recognized, but it is not so large.

[0109]

Since the hybrid type stepping motor according to the present invention has the above-described structure, the arrangement of the small teeth provided at the ends of the winding poles is changed in accordance with a certain theory to reduce the cogging torque and simultaneously reduce the cogging torque. There is an effect that the torque waveform can be improved.

[Brief description of the drawings]

FIG. 1A is a longitudinal sectional front view of a conventional two-phase hybrid type stepping motor.

FIG. 1B is a left side view (N-pole side) of the two-phase hybrid type stepping motor shown in FIG. 1A.

FIG. 1C is a right side view (S pole side) of the two-phase hybrid type stepping motor shown in FIG. 1A.

FIG. 2 is an equivalent magnetic circuit diagram of a two-phase eight-winding-pole hybrid type stepping motor.

FIG. 3 is an equivalent magnetic circuit diagram showing the circuit of FIG. 2 with one sub-circuit;

FIG. 4 is an explanatory diagram of arrangement of small teeth of a winding pole.

FIG. 5 is a diagram illustrating an assumed magnetic path between magnetic poles in which small teeth of a stator and a rotor face each other.

FIG. 6 shows the general form of one permeance change of a small tooth.

FIG. 7 is a vector diagram of a fourth harmonic plane in an equal pitch arrangement system.

FIG. 8A is a diagram showing a two-vector balance of a fourth harmonic plane in an unequal pitch arrangement system.

FIG. 8B is a diagram showing a three-vector balance of a fourth harmonic plane in an unequal pitch arrangement system.

FIG. 9A is a vector diagram of a third harmonic plane in the two-phase hybrid type stepping motor of the present invention.

FIG. 9B is a vector diagram of a fourth harmonic plane in the two-phase hybrid type stepping motor of the present invention.

FIG. 10A is a vector diagram for explaining the balance of the third harmonic in the two-phase hybrid type stepping motor of the present invention.

FIG. 10B is a vector diagram for explaining the balance of the fourth harmonic in the two-phase hybrid type stepping motor of the present invention.

FIG. 11 is an explanatory diagram showing an arrangement of small teeth for realizing the vector diagrams shown in FIGS. 9A and 9B.

FIG. 12 is an explanatory diagram showing an arrangement of small teeth for realizing the vector diagrams shown in FIGS. 10A and 10B.

FIG. 13 is an explanatory diagram of a local model for two-dimensional magnetic field analysis.

FIG. 14 is an explanatory diagram showing calculation of cogging torque based on the sum of magnetic pole torques.

FIG. 15 is an explanatory diagram showing a calculation result of a cogging torque.

FIG. 16 is an explanatory diagram showing a relationship between a magnetic flux generated by a winding and an effective magnetic flux.

FIG. 17 is an explanatory diagram showing a general summary of effects of the small tooth arrangement method.

[Explanation of symbols]

A Winding phase B Winding phase F ₁ Magnetizing force of winding pole F ₂ Magnetizing force of winding pole F ₃ Magnetizing force of winding pole F ₄ Magnetizing force of winding pole F ₅ Magnetizing force of winding pole F ₆ Magnetomotive force of winding pole F ₇ Magnetomotive force of winding pole F ₈ Magnetomotive force of winding pole N ₁ N pole side winding pole N ₂ N pole side winding pole N ₃ N pole side winding Pole N ₄ N pole winding pole N ₅ N pole winding pole N ₆ N pole winding pole N ₇ N pole winding pole N ₈ N pole winding pole S ₁ S pole Side winding pole S ₂ S pole side winding pole S ₃ S pole side winding pole S ₄ S pole side winding pole S ₅ S pole side winding pole S ₆ S pole side winding pole S ₇ S pole side winding pole S ₈ S pole side winding pole P ₁ Permeance of winding pole P ₂ Permeance of winding pole P ₃ Permeance of winding pole P ₄ Permeance of winding pole N _R rotor internal voids containing teeth F ₀ excitation magnetomotive force drops 2S winding number theta _e electrical angle tau _C cogging torque 2T rotor teeth pole repetition pitch F _m magnet magnetomotive force P _m magnets Miansu t ₁ teeth t ₂ teeth t ₃ teeth t ₄ teeth t ₅ small teeth t ₆ small teeth theta ₁ position theta positions theta ₄ teeth positions theta ₃ teeth positions theta ₂ small teeth of small teeth ₅ Small tooth position θ ₆ Small tooth position V ₁ vector V ₂ vector V ₃ vector V ₄ vector V ₅ vector V ₆ vector 1 Annular yoke 2 Magnetic pole 3 Winding 4 Small tooth 5 Stator 6 Small tooth 7 Rotor Magnetic pole 8 Permanent magnet 9 Rotor

Claims (3)

[Claims] A plurality of magnetic poles are arranged at equal intervals on the inner periphery of a substantially annular yoke, and a winding is wound around each of the magnetic poles to form a two-phase winding. A stator provided with a small number of teeth of a multiple of the above and two rotor magnetic poles provided with a plurality of small teeth on the outer periphery thereof at an equal pitch are shifted from each other by a half pitch of the arrangement pitch of the small teeth. A rotor fixed to an end face of a permanent magnet magnetized to two poles in the NS direction, wherein the rotor is provided at the tip of the stator magnetic pole in a two-phase hybrid type stepping motor facing the stator via a gap. At least six small teeth are composed of two groups of three small teeth sets,
The sum of the third harmonic vector of the permeance of the three small teeth of each set is substantially zero, and the fourth group of the two groups
If the pitch of at least one adjacent small tooth is different from the pitch of other adjacent small teeth such that the sum of the vectors of the permeances of the two small teeth that are each axially symmetric in the second harmonic plane is substantially zero. A two-phase hybrid type stepping motor characterized in that: 2. A two-phase winding is formed by arranging a plurality of magnetic poles at equal intervals on an inner periphery of a substantially annular yoke, winding a winding around each of the magnetic poles, and forming a six-phase winding at the tip of the magnetic pole. A stator provided with a small number of teeth of a multiple of the above and two rotor magnetic poles provided with a plurality of small teeth on the outer periphery thereof at an equal pitch are shifted from each other by a half pitch of the arrangement pitch of the small teeth. A rotor fixed to an end face of a permanent magnet magnetized to two poles in the NS direction, wherein the rotor is provided at the tip of the stator magnetic pole in a two-phase hybrid type stepping motor facing the stator via a gap. At least six small teeth are composed of three groups of two small teeth sets,
The sum of the third harmonic vectors of the permeance of the two small teeth in each set is substantially zero, and the fourth group of the three groups
3 placed at each 120 degrees in the second harmonic plane
The pitch of at least one adjacent small tooth is made different from the pitch of another adjacent small tooth so that the sum of the permeance vectors of the plurality of small teeth becomes substantially zero.
Phase hybrid type stepping motor. 3. A plurality of magnetic poles are arranged at equal intervals on an inner periphery of a substantially annular yoke, and a winding is wound around each of the magnetic poles to form a two-phase winding. A stator provided with a small number of teeth of a multiple of the above and two rotor magnetic poles provided with a plurality of small teeth on the outer periphery thereof at an equal pitch are shifted from each other by a half pitch of the arrangement pitch of the small teeth. A rotor fixed to an end face of a permanent magnet magnetized to two poles in the NS direction, wherein the rotor is provided at the tip of the stator magnetic pole in a two-phase hybrid type stepping motor facing the stator via a gap. At least six small teeth are composed of two groups of three small teeth sets,
Making the pitch of at least one adjacent small tooth different from the pitch of the other adjacent small teeth such that the fourth harmonic vector sum of the permeance of the three small teeth of each set is substantially zero. A two-phase hybrid type stepping motor characterized by the following: