The present invention relates to permanent magnet motors, and specifically to permanent magnet motors for servomotors and electric power steering motors etc., with reduced cogging torque.
There has been a demand for miniaturized and low-loss servomotors and electric power steering motors, and by employing a motor in which armature windings are concentratedly wound around respective salient magnetic poles of a stator, the amount of the windings that extend beyond an end portion of the stator is reduced, and thus the length of the motor and copper loss in the windings are reduced. Also, there has been a strong demand for reducing the cogging torque of motors in order to improve positioning accuracy and to reduce noise and vibrations.
As a method for reducing the cogging torque of a concentrated winding permanent magnet motor, Japanese Patent No. 2135902, which is herein incorporated by reference, describes a method in which the relationship between the number P of poles of a rotor and the number M of salient stator poles is made to satisfy P=6n±2 and M=6n, wherein n is an integer of 2 or more, or P=3m±1 and M=3m, wherein m is an odd number of 3 or more. The permanent magnet motor has a cogging torque that pulsates, the number of which is the least common multiple of the number P of poles and the number M of salient poles per revolution of the rotor, and the magnitude of the cogging torque decreases as the number of pulsations increases. Based on this principle, the permanent magnet motor has the combination of the number P of poles and the number M of salient poles such that the least common multiple of the number P of poles of the rotor and the number M of salient poles of the stator increases under the condition that a three-phase winding connection is possible. Table 1 shows a summary of specific combinations of the number P of poles and the number M of salient poles.
TABLE 1Number ofNumber ofNumber of coggingpoles Psalient poles Mtorque pulsationsn210, 141260, 84316, 2018144, 180m3 8, 10972, 90514, 1615210, 240
A permanent magnet motor having the combination of P=10 and M=12 shown in Table 1 was designed. FIG. 11 shows a schematic cross-sectional view of the permanent magnet motor having 10 poles and 12 slots, in a plane perpendicular to the axis of the permanent magnet motor. In FIG. 11, the motor includes: a rotor 10 in which ten neodymium magnets (M1 to M10) having a residual magnetic flux density of 1.26 Tesla are disposed on a rotor yoke 11 made of low carbon steel S45C at even intervals such that the polarities of the magnets alternate in the circumferential direction; and a stator 20 having a stator yoke 22 that is opposed to the permanent magnets and that is formed from an isotropic silicon steel sheet 35A300 on which twelve salient magnetic poles 21 are disposed at even intervals in the circumferential direction, ten-turn armature windings 23, which are wound around the magnetic poles and which are serially connected in each of the U, V and W phases that are three-phase connected. In FIG. 11, the direction of magnetization of the permanent magnets is indicated by an arrow in each permanent magnet. Moreover, at the center of the rotor, the direction of revolution of the rotor is indicated by an arrow. The permanent magnets have a shape in which the thickness of the permanent magnets is reduced at both end portions. FIG. 12 shows a specific shape of the permanent magnets. In FIG. 12, Ri=23 mm, Ro=10 mm, D=15 mm, and W=12 mm. By reducing the thickness of a permanent magnet at both end portions, the distribution of the magnetic flux density at an air gap is smoothed, and thus an effect of reducing the cogging torque is achieved. The rotor and the stator have a length of 40 mm in the axial direction, and the air gap between the rotor magnets and the stator magnetic poles is 1 mm. In FIG. 11, symbols shown in the windings indicate the directions of the windings: a solid circle (●) indicates the direction emerging from the paper surface and a cross (×) indicates the direction entering the paper surface. The rated torque was set to be 2 Nm (newton meter) when the motor is driven with a sinusoidal current having an effective value of 20 A (ampere).
The cogging torque of the above-described permanent magnet motor was calculated assuming that there was no variation in the characteristics and the dimensions of the magnets and that all factors were in an ideal state. It was found that the cogging torque had a waveform having a peak value of 0.0003 Nm and 60 pulsations per revolution of the rotor. Since the cogging torque is expressed as the difference between the maximum and the minimum points of the waves, in this case, the cogging torque was 0.0006 Nm, which was 0.03% of the rated value, that is, a very small value. In the case of permanent magnet motors such as for electric power steering, a weak cogging torque affects the steering feel, so it is desirable that the cogging torque is no greater than 0.5% of the rated torque (in the present case, no greater than 0.01 Nm).
Next, as Comparative Example 1, the designed motor was actually fabricated, and the cogging torque of that motor was measured. Neodymium magnets were used as the permanent magnets, which were made by filling a die having a Japanese roof tile-like shape with magnet powder, pressing the die in a transverse magnetic field, sintering the pressed magnetic powder, and subjecting the sintered product to heating and which were then ground to precision of 0.05 mm or less using a whetstone. Moreover, a dedicated jig was prepared to position the permanent magnets on the rotor yoke, and the positioning was performed with a precision of 0.05 mm or less. The stator yoke was made by laser cutting out pieces of 0.35 mm silicon steel sheet to a predetermined shape, and laminating the pieces with a laminating method, referred to as “parallel laminating method”, in which the pieces are laminated with their rolling directions in a uniform direction. After the lamination, the pieces were fastened at eight points on a peripheral portion of the stator yoke by laser welding, and the inner surface of the stator yoke opposed to the permanent magnets was ground to increase dimensional accuracy.
FIG. 13 shows an actually-measured waveform of the cogging torque of the permanent magnet motor according to Comparative Example 1 (parallel-laminated stator). The measured cogging torque waveform according to Comparative Example 1 was a waveform having 10 pulsations per revolution of the rotor. The entire waveform is shifted to the negative side due to a force working against revolution, which is called “loss torque”. This is caused by the hysteresis loss of the stator yoke. Since the cogging torque is expressed as the difference between the maximum and the minimum points of the waves, the cogging torque of Comparative Example 1 shown in FIG. 13 was 0.0274 Nm. FIG. 14 shows the results of a Fourier analysis in which the cogging torque waveform according to Comparative Example 1 was divided into components of respective orders of the waveform. Here, “order” is the number of pulsations that appear during one revolution of the rotor. For example, “duodenary component” is a component having twelve pulsations during one revolution of the rotor. Regarding the components of the cogging torque of Comparative Example 1 shown in FIG. 13, the denary component is 0.0061 Nm, the duodenary component is 0.0077 Nm, the vigenary component is 0.0016 Nm, and the twenty-fourth order component is 0.0007 Nm. It should be noted that the order components shown in FIG. 14 represent the peak values of the respective order components, which are values half the cogging torque. Checking the order components of the cogging torque waveform makes it possible to know what the cogging torque is attributed to. In the case of the permanent magnet motor according to Comparative Example 1, it is believed that the denary, vigenary, and thirtieth order components, whose orders correspond to multiples of the number of poles, are caused by variations in the stator yoke, and the duodenary, twenty-fourth order, and thirty-sixth order components, whose orders correspond to multiples of the number of salient poles, are caused by variations in the permanent magnets. If there is no variation in the permanent magnets, the positional relationship between the stator yoke and the permanent magnets has rotational symmetry with respect to the magnetic pole pitch angle, so that the cogging torque caused by variations in the stator yoke has a waveform in which the number of cycles of the fundamental wave corresponds to the number of poles per revolution. Similarly, if there is no variation in the stator, the positional relationship between the stator and the magnets has rotational symmetry with respect to the salient pole pitch angle, so that the cogging torque caused by variations in the magnets has a waveform in which the number of cycles of the fundamental wave corresponds to the number of salient poles per revolution. The sixtieth order, which corresponds to the least common multiple of the number of poles and the number of salient poles, is the cogging torque when the permanent magnet motor was an ideal permanent magnet motor. The cogging torque of Comparative Example 1 shown in FIG. 13 has large components of orders of multiples of 10. Since even an isotropic steel sheet has some magnetic anisotropy in the rolling direction, when the stator yoke is made by the parallel laminating method in which rolling directions of the pieces are made uniform, the magnetic anisotropy remains. It appears that the influence of this residual magnetic anisotropy causes the cogging torque.
In order to eliminate the magnetic anisotropy of the stator yoke, in “Measurement of Cogging Torque of Permanent Magnet Motor Due to Magnetic Anisotropy of Non-oriented Electrical Steel Sheet”, Proceedings of the National Convention of the Institute of Electrical Engineers of Japan, 5-016., which is herein incorporated by reference, a method in which lamination is performed such that the rolling direction successively rotates, which is called “rotational laminating method”, is used. As Comparative Example 2, a permanent magnet motor having a rotational-laminated stator was fabricated. The rotor and the method for making the stator yoke except for the laminating method were the same as in Comparative Example 1. FIG. 15 shows an actually-measured waveform of the cogging torque of the permanent magnet motor according to Comparative Example 2 (rotational-laminated stator). Moreover, FIG. 14 also shows the results of a Fourier analysis in which the cogging torque waveform according to Comparative Example 2 was divided into components of respective orders of the waveform. In Comparative Example 2, as compared to Comparative Example 1, the denary, vigenary, and thirtieth order components were significantly reduced to less than 0.0002 Nm, and the cogging torque was 0.0122 Nm. In this way, the cogging torque attributed to the stator yoke can be reduced.
However, even with such a method, the duodenary, twenty-fourth order, and thirty-sixth order components, which are attributed to the permanent magnets, cannot be eliminated. In particular, when the permanent magnet motor is used for electric power steering motors, lower order components greatly affect the steering feel, so that it is desirable to reduce the duodenary component.
In order to eliminate an order component (duodenary component, in the comparative example) of the cogging torque caused by the permanent magnets, a method has been used in which each of the permanent magnets of the rotor are divided into a plurality of magnets in the axial direction and are skewed. In this case, the skew angle is 360°/the number of salient poles (30°, in the comparative example). However, in the case of the permanent magnet motor in which a reduced cogging torque is achieved by using any of the combinations of the number of poles and the number of salient poles shown in Table 1, the difference between the number of poles and the number of salient poles is small, so that when skewing is performed, different magnetic poles come to be opposed to one salient pole at the same time, and thus driving torque is not generated. Accordingly, there has been no effective measure for reducing such cogging torque caused by permanent magnets, and there has been a problem in that there are practical limitations to industrial processes for reducing the cogging torque by suppressing variations in the permanent magnets.
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