JP2606214B2 - Permanent magnet rotating machine - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION A. Industrial Field of the Invention The present invention relates to a permanent magnet type rotating machine, which is devised so as to eliminate generation of cogging torque.

B. Prior Art Three-phase brushless DC motors have been used as floppy disk driver motors, VTR cylinder motors, and spindle motors for hard disk drivers. In a three-phase brushless DC motor, a current switched by an inverter is passed through an armature winding of a stator, and a rotor is provided with a permanent magnet as a field source.

C. Problems to be Solved by the Invention By the way, in the three-phase brushless DC motor, the action of the magnetic flux density of the permanent magnet which is the field source and the magnetic resistance of the armature slot allows the armature current not to flow. Torque is generated depending on the position of the armature. This torque is called cogging torque. The cogging torque causes uneven rotation and reduces the starting torque.

In order to reduce the cogging torque, conventionally, auxiliary grooves are provided in the armature core, skew is provided in the grooves of the armature core, and the magnetic flux density distribution is made closer to a sine wave to reduce high frequency components. Measures were taken. Although these measures are effective in reducing the cogging torque, they were not able to eliminate the cogging torque.

The present invention has been made in view of the above-described related art, and provides a permanent magnet type rotating machine having no cogging torque.

D. Means for Solving the Problems The present invention for solving the above problems, in the permanent magnet type rotating machine, the magnetic flux distribution of each permanent magnet, flat in the center,
It is characterized in that it changes in a cosine wave on both sides. E. Embodiments The present invention will be described below. In the following description, (I) cogging torque, (II) optimum magnetomotive force distribution, and (III) permanent magnet shape will be described theoretically in order, and then specific examples will be described. For a part of the theoretical explanation, reference was made to the document "The Institute of Electrical Engineers of Japan, RM-85-52".

(I) Cogging torque In a motor using a permanent magnet as a field source, an attractive force is exerted by a magnetic flux distribution of the permanent magnet and a slot of a stator core. This component is called a cogging torque. This occurs even when the armature current is zero, and varies depending on the angle of the rotor. This torque may cause uneven rotation or cause a torque shortage at a torque valley at the time of startup.

In the analysis of the cogging torque (considering the magnetic flux distribution of the permanent magnet), it is necessary to be able to grasp the spatial magnetic flux distribution without dealing with energy alone in a gap such as an induction machine. Therefore, it cannot be handled analytically,
Generally, an analysis method using a finite element method or the like is used.

As a qualitative explanation, the model in which the magnetic flux is perpendicular to the gap plane and a magnet is used as a magnetomotive force source will be examined.

The cogging torque T _c is the total energy in the gap ∫E _t
This occurs because (θ, φ) dφ changes depending on the position of the armature.

K ₁ : Constant E _t : Energy distribution in the gap P: Number of poles θ: Rotation angle of the rotor φ: Gap space angle Magnetic flux density distribution of the gap by the permanent magnet (when the stator is smooth) B (φ) is the spatial harmonic component It can be expressed as follows.

B (φ): Gap magnetic flux density distribution B _n : nth-order spatial magnetic flux density harmonic component A groove function is defined to obtain an energy fluctuation component due to the slot opening end.

Groove function with one slot Groove function with all slots The magnetic flux density distribution when this slot opening end exists is: Here, the first term has nothing to do with torque The opening width is narrow, the _{(1-u t (θ,} φ)) center value of expression slot .SIGMA.B _n · sin be approximated by the value and the product of w of _{(n · φ) ∫ΣB n ·} sin ( n ・ φ) u (θ, φ) dφ ≒ ΣB _n・ sin
_{(N · φ) · u t} (θ, φ) × w u (θ, φ) = grooves function u _t (θ, φ) = a function therefore torque component only take 1 when the center of the slot, different orders of Considering that when integrated over the entire circumference of the product of the components, it becomes 0 The above equation (1-3) means that the total energy obtained by multiplying the energy component of each order by the number of grooves changes with the rotation of the rotor. From this, it can be seen that in order to reduce the cogging torque, it is necessary to provide a sinusoidal magnetic flux density distribution that does not include a higher-order component, or to perform a groove arrangement that becomes zero when the higher-order components are combined.

FIG. 1 shows a model in the case of three slots per pole pair. Here, the energy reduced by the groove is a portion hatched to each component. Here, as for the fundamental wave order, the combined value of the three slots is always a constant value. Therefore, no synchronous torque of the basic component is generated.

Next, the third-order component and the sixth-order component have the same phase in all three slots, and the amount of change in energy is large due to the rotation of the rotor. This indicates that torque unevenness components of 6 steps and 12 steps are generated.

As shown in FIG. 2, when a magnetic flux distribution having a waveform obtained by combining a sine wave and a straight line is obtained, one of the three grooves of the armature core is
The change in magnetic energy is zero at the flat portion of the magnetic flux distribution of the field permanent magnet, the remaining two grooves are at opposite phases of the sine wave, and the combined value of the two magnetic energies is always constant. As a result, if the magnetic flux density distribution is as shown in FIG. 2, the cogging torque becomes zero.

(III) Calculation of torque ripple by change in groove energy (optimum magnet distribution) (II-1) FIG. 3 shows an analysis model.

Number of poles: 4P Rotational speed: 3600 (rpm) Number of windings: 48 (T) Armature current: 0.8 (A) Residual magnetic flux density: 0.38 (T) Analysis conditions (1) Model developed in plane on stator core gap surface I do.

(2) The magnetic flux is generated only by the permanent magnet, and has only a component perpendicular to the gap.

(3) Ignore iron loss and saturation.

(4) The drive current is a 120 ° square wave, and the effect of the armature reaction is ignored.

(5) It is rotating at a constant rotation speed.

(6) In order to represent the shape of the permanent magnet, the half pole is divided into nine parts and given by data of ten points, and the breakpoint is approximated (see FIG. 4).

(7) Calculation of spatial magnetic flux density Ignore magnetic flux leakage and magnet loss (if necessary, Br
Consider in). The magnetic flux density is given by the following equation.

Br: Residual magnetic flux density of the permanent magnet μ _m : Relative permeability of the permanent magnet H _g : Distance between the rotor yoke and the stator core (II-2) Calculation method The calculation is the model in Fig. 3, o-2π (electrical angle) section Is divided into (NP-1), and the magnetic flux density at each point is converted into discrete values by linear interpolation from the dot data shown in FIG. The movement of the rotor may be considered to be that the armature relatively moves in the opposite direction, and the winding and the groove move on the fixed magnet magnetic flux and pass on each discrete point. The winding is ideally wound around both ends of the gap surface of the slot, and the magnetic flux density represented by discrete values is linked.

(II-3) Calculation method of induced electromotive force No-load induced electromotive force is only a component generated by the magnetic flux density of the permanent magnet. Voltage of one phase is a synthetic winding sides A and B in Figure 5, the magnetic flux density of each side B _A, When B _B, the voltage of this phase, N _t : Number of turns per tooth L: Shaft length ω: Rotational angular velocity P: Number of poles Other phase voltages are obtained from the magnetic flux density at points shifted by NP / 3 and 2NP / 3. The line voltage is obtained from the combination of the inter-phase voltages. E _uv = E _u (θ) −E _v (θ) If the no-load induced power is applied only in the section of the maximum value of the line voltage, E _uv (2π / 3 to 4π / 3) is obtained by copying six times periodically.

(How to find discrete points A and B) θ _A : Spatial angle (rotation angle) W _S : Slot opening width N _P : Total number of divisions (II-4) Motor torque If the inter-phase voltage and no-load voltage are obtained, the motoring torque T _mot is as follows.

A _mp : energizing current (A) E _R : current value of no-load induced inter-power ω: rotational angular velocity (II-5) cogging torque The magnetic flux distribution at the slot opening end is not only reduced actually between teeth. In addition, the bending of the magnetic path increases the magnetic flux at the teeth. Therefore, it is meaningless to simply represent the slot by the gap length.

The value of the magnetic flux in the slot portion should be obtained by calculating the integrated value of the magnetic flux density for about one tooth pitch, and calculating the integrated value from the amount of change caused by the presence of the slot. From this, it is assumed that the gap length of the slot portion is increased by the Carter coefficient (see FIG. 6).

(III) Permanent magnet shape The magnetic flux density distribution that reduces cogging torque
This can be obtained from the term I), but this is only valid on a model developed in a plane.

In a cylindrical model like an actual machine, the magnetic path is different,
Since there is an inclination between the magnetization direction and the magnetic path due to anisotropy and a leakage component between the magnet poles, it is necessary to determine the magnet shape by analyzing the spatial magnetic flux distribution using the finite element method.

(III-1) Analysis Model FIG. 7 shows the element division of the analysis model. The stator is assumed to be smooth without slots, and is treated in a linear system with μ _A = 7000.

(III-2) Magnet study model For permanent magnets, the thickness of the magnet is determined in the following two ways to compensate for the leakage between the poles of the magnet and the decrease in magnetic flux due to the difference between the magnetization direction and the magnetic path direction. An analysis was performed.

The magnetization direction was assumed to be fully magnetized in the complete radial direction (see FIG. 8).

(III-3) Gap Magnetic Flux Density Distribution and Evaluation FIGS. 9 and 10 show the magnetic flux density distribution on the stator gap surface obtained from the analysis results.

As a result, it can be understood that the model A well matches the target distribution, and the model B has too strong correction between the poles.

From the above, (Model A) is determined to be a magnet shape that results in this study.

(IV) Specific Examples and General Formulas Next, specific examples of the present invention will be described. FIG. 11 shows the inside of a three-phase 120-degree conducting brushless DC motor to which the present invention is applied. The motor shown in FIG. 1 has four poles, and four permanent magnets 12 are provided on the inner peripheral surface of the rotating rotor yoke 11 (only one is shown in the figure). At the center of the rotor yoke 11, an armature iron core 13 serving as a stator is provided. In this motor,
Armature core for one pair of permanent magnets, that is, for one pole pair
Thirteen grooves are opposed to each other. Of course, the grooves are formed at equal pitch intervals.

The thickness H _m of the permanent magnet 12 is adapted to satisfy the following equation at each interval. In FIG. 11, the angle is shown as a geometric angle, and the center position of the permanent magnet 12 with respect to the rotation direction of the armature core 13 is set to an angle of 0 °.

(I) Section Hm of −45 ° ≦ θ ≦ −15 ° H _m = 1.0 + 1.5cos [(θ + 15 °) × 3.0] [mm] (11) (II) Section H of −15 ° <θ <15 ° _m = 2.5 [mm] ... (12) (III) Section of 15 ° ≤ θ ≤ 45 ° H _m = 1.0 + 1.5 cos [(θ-15 °) x 3.0] [mm] ... (13) Because the thickness is as described above,
The magnetic flux density B (θ) at the angle θ of the permanent magnet 12 is as shown in FIG. That is, if the angle θ is represented by an electrical angle, the magnetic flux density B (θ) will be as follows in each section. However, B _m is constant.

(I) -90 ° ≦ theta ≦ -30 ° interval B (θ) = B _m cos [(theta + 30 °) × 1.5] [T] ... (21) (II) -30 ° <theta <30 ° intervals B (θ) = B _m [T] (22) (III) Section of 30 ° ≦ θ ≦ 90 ° B (θ) = B _m cos [(θ−30 °) × 1.5] [T] (23) Since the magnetic flux density B (θ) of the permanent magnet 12 has the above-described value, no cogging torque is generated for the reason described in the theoretical explanation.

The shape of the permanent magnet 12 can be easily formed by polishing.

In the above embodiment, the thickness of the permanent magnet was adjusted in order to obtain the magnetic flux density distributions represented by Equations (21), (22), and (23). However, the magnetization orientation of the permanent magnet was adjusted while keeping the thickness constant. Thus, a required magnetic flux density distribution may be obtained.

The present invention is not limited to the specific examples described above, and various types of permanent magnets of a type in which 3 m (m is a positive integer) slots of an armature iron are arranged at equal intervals facing a pair of permanent magnets. Applicable to rotating machines (for example, inner rotor type brushless DC motor, PM motor, etc.). That is, the following equations (31) and (3
The cogging torque can be eliminated by obtaining a magnetic flux density distribution (see FIG. 13) satisfying (2) and (33). Note that the angles in equations (31), (32), and (33) are electrical angles.

In (I) -90 ° ≦ θ ≦ θ ₂ of section (II) In the section of θ ₂ <θ <θ ₁ B (θ) = B _m [T] (32) (III) In the section of θ ₁ ≦ θ ≦ 90 ° Equations (21), (22), and (23) in the specific examples described above correspond to general equations (31), (32), and (33) where m = 2 and n = 2.

F. Effects of the Invention As described above in detail with the embodiment, according to the present invention, among the 3m grooves, the m grooves are located on the flat portion of the magnetic flux and do not generate cogging torque, and the other The set of m pieces and the other set of m pieces are located in the magnetic flux portions having opposite phases, and the cogging torques cancel each other. As a result, there is no cogging torque as a whole. Therefore, a motor having less torque unevenness and less decrease in starting torque can be obtained. Of course, skew is not required, and assembly is facilitated.

Further, since the total magnetic flux amount is larger than that having a sinusoidal magnetic flux distribution, a large torque can be obtained.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory view showing a model and energy distribution of 3 slots per pole pair, FIG. 2 is an explanatory view showing a magnetic flux density distribution for making cogging torque zero, and FIG. FIG. 4 is an explanatory diagram showing a breakpoint approximation, FIG. 5 is an explanatory diagram showing a state of a winding edge, FIG. 6 is an explanatory diagram showing a magnetic flux state at a slot end, FIG. Is an explanatory diagram showing the element division of the analysis model, FIG. 8 is an explanatory diagram showing the magnetized state, FIG. 9 and FIG.
The figure is a characteristic diagram showing the magnetic flux density distribution on the stator gap surface,
FIG. 11 is a configuration diagram showing a specific example of the present invention, FIG. 12 is a characteristic diagram showing a magnetic flux density distribution of the specific example, and FIG. 13 is a characteristic diagram showing a general form of the magnetic flux distribution of the present invention. In the drawing, 11 is a rotor, a yoke, 12 is a permanent magnet, and 13 is an armature core.

Claims (1)

(57) [Claims] 1. A rotating machine in which a field is formed by permanent magnets, and 3m (m is a positive integer) slots of an armature iron core are arranged at equal intervals with respect to a pair of permanent magnets. In the above, when the central position of the permanent magnet is set to 0 ° with respect to the rotation direction, the magnetic flux density B (θ) at each angle θ (angle is an electrical angle) of each permanent magnet is expressed by: (I) −90 ° ≦ θ ≦ in θ ₂ of section (II) In the section of θ ₂ <θ <θ ₁ B (θ) = B _m (III) In the section of θ ₁ ≦ θ ≦ 90 ° A permanent magnet type rotating machine characterized by using a permanent magnet having a shape or a magnetization orientation such that