WO2018098902A1 - 一种降低永磁同步电机转矩脉动的方法 - Google Patents

一种降低永磁同步电机转矩脉动的方法 Download PDF

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WO2018098902A1
WO2018098902A1 PCT/CN2017/072924 CN2017072924W WO2018098902A1 WO 2018098902 A1 WO2018098902 A1 WO 2018098902A1 CN 2017072924 W CN2017072924 W CN 2017072924W WO 2018098902 A1 WO2018098902 A1 WO 2018098902A1
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torque
offset
repeating unit
torque ripple
permanent magnet
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PCT/CN2017/072924
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English (en)
French (fr)
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刘国海
杜鑫鑫
赵文祥
陈前
胡德水
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江苏大学
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Priority to US15/772,433 priority Critical patent/US10530278B1/en
Publication of WO2018098902A1 publication Critical patent/WO2018098902A1/zh

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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple

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  • the invention relates to the design of a permanent magnet synchronous motor, in particular to a method for reducing the torque ripple of a permanent magnet synchronous motor, and belongs to the technical field of motor manufacturing.
  • permanent magnet motors have been widely used, and permanent magnet motors play a very important role in many fields from automotive to aerospace. This is mainly due to several notable features of permanent magnet motors, including high torque density, high efficiency, and small weight.
  • the permanent magnet motor replaces the traditional excitation winding with the magnetic material with high magnetic energy product, which not only eliminates the negative influence of the excitation winding, but also simplifies the mechanical structure of the motor, improves the reliability of the motor operation, and reduces the mechanical loss accordingly. small.
  • the prior art is only directed to the reduction of cogging torque.
  • the source of torque ripple is not limited to cogging torque, it may also be derived from permanent magnet torque and reluctance torque, and cogging torque. It occupies only a very small part of the total torque ripple. On this basis, analysis limited to cogging torque is not enough. Therefore, how to quickly and accurately reduce the main source components in torque ripple is a key research direction.
  • the technical solution adopted by the invention is: a method for reducing torque ripple of a permanent magnet synchronous motor, comprising the following steps:
  • Step 1 analyzing the pole slot ratio of the target motor, calculating the number of fluctuation cycles of the torque ripple in one electrical cycle according to the relationship between the number of rotor poles and the number of stator slots, and determining the overall fluctuation trend;
  • Step 2 Calculate the minimum number of poles N 0 that can produce the same torque, modularize the rotor and permanent magnets of the motor; through modular analysis, the permanent magnet poles in each module can generate the same torque, including the torque amplitude Value and phase, under this premise, to ensure that the number of poles in the module is the least, and as a basic repeating unit;
  • Step 3 combining two or more basic repeating units to form a new repeating unit, these new repeating units can also generate the same torque amplitude and waveform; determining the number of different new repeating units for magnetic pole bias Choose when moving;
  • Step 4 analyze the main source components of torque and torque ripple, and perform modular analysis on their generation, determine the basic repeating unit generated by each component in the torque ripple, and calculate the minimum number of magnetic poles N i0 in each basic repeating unit. ;
  • Step 5 comprehensively considering N 0 and each N i0 , reasonably selecting the offset repeating unit; and determining the number of repeating units q and the maximum number of possible offsets N according to the number of magnetic poles b in the selected repeating unit;
  • Step 6 in order to weaken the primary harmonic in the torque ripple, calculate the exact angle ⁇ 1 of the offset, and perform the first offset on the selected repeating unit;
  • Step 7 In order to weaken the second major harmonic in the torque ripple, calculate the exact angle ⁇ 2 of the secondary offset, and based on the first magnetic pole offset, re-divide the repeating unit and perform the new repeating unit.
  • Step 8 If the space permits, in order to weaken the n major harmonics in the torque ripple, calculate the exact angle ⁇ n of the n times of the offset, and perform the nth division of the repeating unit based on the first n-1 offsets. And perform the nth offset.
  • T ripple represents the number of fluctuation cycles of the torque ripple in one electrical cycle
  • N s represents the number of slots of the motor
  • N p represents the number of pole pairs of the motor
  • the basic repeating unit in the step 2 refers to the minimum number of permanent magnetic poles capable of generating the same torque waveform, and the torque waveforms have the same magnitude and phase.
  • N 0 represents the minimum number of permanent magnetic poles in the basic repeating unit
  • N s represents the number of slots of the motor.
  • the new repeating unit in the step 3 is composed of k basic repeating units, and the number of permanent magnetic poles thereof is kN 0 .
  • the main source components of the torque ripple in the step 4 include: cogging torque, reluctance torque and permanent magnet torque; the minimum number of permanent magnetic poles in the corresponding basic repeating units is respectively recorded as N 10 , N 20 , N 30 .
  • the number of magnetic poles b, the number of repeating units q and the number of maximum offsets N in the selected repeating unit satisfy the following relationship:
  • N takes an integer
  • the total torque of the motor can be expressed as the sum of the torques generated by the respective repeating units, that is, Where T i is the torque generated by each repeating unit.
  • step 6 the angle calculation process of the offset is:
  • step 6.1 the torque expression of the motor can be expressed as the sum of the torque average and the torque ripple, as follows:
  • T all_av represents the torque average value
  • T all_rip represents the torque ripple, and according to the periodicity of the torque ripple, it can be expressed as the above Fourier series form
  • the torque T of the motor can be expressed as the sum of the torques T i generated by the repeating units, and the components T i can also be expressed as the sum of the average value and the pulsation; on this basis, if a magnetic pole is repeated After the unit is offset by ⁇ , the torque generated by the repeating unit changes only in phase, ie
  • step 6.3 the final total torque ripple is superimposed on the torque ripple generated by the unshifted repeating unit and the shifted repeating unit:
  • Step 6.4 considering the average value of the torque, the output torque can be further expressed as
  • Step 6.5 after the permanent magnet repeating unit is offset, the rotor is slightly asymmetrical, and the average torque of each repeating unit has a slight change, but the change is small, far lower than the torque ripple content;
  • the relationship is as follows,
  • T r in the above formula is the main component of the torque ripple and should be used as the main analysis object; it is simplified by the trigonometric function formula:
  • Step 6.6 if you want to weaken the torque ripple, you need to make T r as small as possible.
  • the one-time offset in the step 6 is to shift the selected repeating unit interval, and the offset angle is ⁇ 1 .
  • the secondary offset in the step 7 refers to dividing the repeated unit that has been offset and one of the adjacent ones that are not offset as a whole on the basis of one offset, and dividing into new ones. Repeat the unit; then shift the new repeating unit by an offset angle of ⁇ 2 ; the secondary offset must be in the same direction as the primary offset.
  • the permanent magnet synchronous motor of the present invention is not limited to reducing the torque ripple caused by the cogging torque after the magnetic pole shift, and can effectively reduce the torque caused by the permanent magnet torque or the reluctance torque. Pulsation, optimization of back EMF and reduction of final output torque ripple make the motor significantly improved in stability.
  • the magnetic pole offset method of the present invention which comprehensively considers the minimum number of magnetic poles N 0 in the basic repeating unit that generates the total torque and the minimum number of magnetic poles N i0 in the basic repeating unit of the respective source components that generate the torque ripple.
  • the average torque of the holding motor is hardly decreased, and the performance of the motor is improved comprehensively.
  • the motor pole shift method of the present invention includes various options for the offset repeating unit, and the offset repeating unit can be reasonably selected according to the main source component of the torque ripple, so that different motors can achieve similar effects.
  • the motor pole shifting method of the present invention includes multiple offset effects, which can reduce torque ripple according to the required depth by deeply weakening different types of harmonics in the torque ripple.
  • the motor pole shifting method performs magnetic pole shift by selecting a suitable repeating unit, and introduces the radial force of the motor as little as possible. Compared with the traditional magnetic pole shift method, the influence of rotor asymmetry on the vibration and noise of the motor can be effectively reduced.
  • FIG. 1 is a schematic diagram showing the selection of a motor pole offset method and a repeating unit in the present invention
  • (a) is a schematic diagram of a permanent magnet distribution of a primary motor
  • (b) is a schematic diagram of a permanent magnet distribution after a single offset
  • (c) is a secondary offset Schematic diagram of rear permanent magnet distribution.
  • FIG. 2 is a schematic structural view of a permanent magnet synchronous motor (original motor) according to the present invention.
  • Fig. 3 is a comparison diagram of the reluctance torque of the original motor and the original motor magnetic pole shift (the embodiment motor) of the present invention.
  • FIG. 4 is a diagram showing the reluctance torque harmonic analysis of the primary motor and the example motor of the present invention.
  • Fig. 5 is a comparison diagram of permanent magnet torque of the primary motor and the motor of the embodiment of the present invention.
  • Fig. 6 is a diagram showing the analysis of permanent magnet torque harmonics of the primary motor and the example motor of the present invention.
  • Fig. 7 is a comparison diagram of the back electromotive force of the primary motor and the motor of the embodiment of the present invention.
  • Figure 8 is a diagram showing the back-potential harmonic analysis of the primary motor and the embodiment motor of the present invention.
  • Fig. 9 is a comparison diagram of output torques of the primary motor and the motor of the embodiment of the present invention.
  • Fig. 10 is a diagram showing the harmonic analysis of the output torque of the primary motor and the motor of the embodiment of the present invention.
  • Fig. 11 is a diagram showing the analysis of the radial force harmonic of the motor in the prior art and the magnetic pole offset method of the present invention.
  • Figure 12 is a flow chart of the magnetic pole offset method of the present invention.
  • the three-phase integrated permanent magnet synchronous motor includes an outer stator 1 and an inner rotor 2; the outer stator 1 includes 48 stator slots and an armature winding 4 embedded therein; the inner rotor 2 includes Rotor core and 8 permanent magnet poles 3 and 6 vents 5.
  • the original motor has 8 magnetic poles (M1-M8), and each magnetic pole serves as a basic repeating unit, and has 8 basic repeating units.
  • the offset repeating unit is reasonably selected; and according to the number of magnetic poles b in the selected repeating unit, the number of repeating units q and the maximum number of possible offsets N are determined.
  • the total torque of the motor can be expressed as the sum of the torques generated by the respective repeating units, that is,
  • T i is the torque generated by each repeating unit.
  • the number of magnetic poles b, the number of repeating units q and the number of maximum offsets N in the selected repeating unit satisfy the following relationship:
  • N takes an integer.
  • the minimum permanent magnet pole number N 0 1 in the repeating unit in which the primary motor generates the total torque.
  • the angle ⁇ 1 of the offset is calculated, and the selected repeating unit is first offset.
  • the angle calculation process of the offset is:
  • step 6.1 the torque expression of the motor can be expressed as the sum of the torque average and the torque ripple, as follows:
  • T all_av represents the torque average value
  • T all_rip represents the torque ripple. According to the periodicity of the torque ripple, it can be expressed as the above Fourier series form
  • the torque T of the motor can be expressed as the sum of the torques T i generated by the repeating units, and the components T i can also be expressed as the sum of the average value and the pulsation; on this basis, if a magnetic pole is repeated After the unit is offset by ⁇ , the torque generated by the repeating unit changes only in phase, ie
  • step 6.3 the final total torque ripple is superimposed on the torque ripple generated by the unshifted repeating unit and the shifted repeating unit:
  • Step 6.4 on the basis of which, considering the average value of the torque, the output torque can be further expressed as
  • Step 6.5 after the permanent magnet repeating unit is offset, the rotor is slightly asymmetrical, and the average torque of each repeating unit has a slight change, but the change is small, far lower than the torque ripple content;
  • the relationship is as follows,
  • T r in the above formula is the main component of the torque ripple and should be used as the main analysis object; it is simplified by the trigonometric function formula:
  • ⁇ n 1
  • the magnetic pole offset ⁇ 1 can eliminate the primary harmonic in the torque ripple
  • the magnetic pole offset ⁇ 2 can eliminate the 2 major harmonics in the torque ripple.
  • the secondary offset refers to dividing the repeated unit that has been offset and its adjacent one of the unrepeated repeating units as a whole into a new repeating unit on the basis of one offset; then repeating the new repeat
  • the cell spacing is offset by an angle of ⁇ 2 .
  • the repeated units (M1, M2) that have been shifted and one of the adjacent repeating units (M3, M4) that are not offset are taken as a whole. , divided into quadratic repeating units (M1, M2, M3, M4).
  • M5, M6, M7, M8) is another secondary repeating unit.
  • the quadratic repeating unit interval shift, that is, (M1, M2, M3, M4) is additionally shifted by the angle ⁇ 2 .
  • M5, M6, M7, M8) The state after one offset is maintained.
  • the secondary offset must be in the same direction as the primary offset.
  • the angle of the offset required for the repeating unit is as shown in Table 2 below.
  • FIG. 2 is a schematic structural view of a surface-embedded permanent magnet synchronous motor.
  • the present invention uses the same as a primary motor, and performs magnetic pole offset on the basis of the present invention.
  • the motor of the embodiment is obtained, and the performances of the two are compared to illustrate the beneficial effects of the present invention.
  • Figures 3 and 4 show the reluctance torque (one of the main sources of torque ripple) and its harmonic analysis in the original motor and the embodiment motor, respectively.
  • the peak-to-peak value of the reluctance torque of the motor of the embodiment is significantly reduced from the original 52.5 Nm to 25.2 Nm.
  • the peak-to-peak value of the reluctance torque was further reduced from 25.2 Nm to 14.2 Nm.
  • a major harmonics (6 th harmonic) and two major harmonics (12 th harmonic) are eliminated successively.
  • Figures 5 and 6 show the comparison of the permanent magnet torque (another major source of torque ripple) and its harmonic analysis of the original motor and the embodiment motor, respectively.
  • the peak-to-peak value of the permanent magnet torque of the embodiment motor was significantly reduced compared with the original motor, from the original 49.1 Nm to 11.9 Nm.
  • the main-order harmonic (harmonic TH 6) is eliminated.
  • Figures 7 and 8 show a comparison of the back electromotive force and its harmonic analysis of the original motor and the embodiment motor, respectively.
  • the sinusoidality of the motor back EMF of the embodiment has been significantly improved compared to the original motor.
  • the amplitude of the fundamental wave remains almost unchanged from the original motor, which means that the motor is in torque ripple. While the performance has been greatly improved, the average torque remains basically unchanged.
  • Figures 9 and 10 reflect a comparison of the final output torque and its harmonic analysis of the original motor and the embodiment motor. It can be seen from Fig. 9 that the effect is obvious after the magnetic pole shift. In the embodiment, the torque ripple of the motor is greatly reduced. After applying the pole shift method, the torque ripple is reduced from 35.9% to 12.7%. After applying the secondary magnetic pole shift method, the torque ripple was further reduced from 12.7% to 7.9%. Also it can be seen from FIG. 10, a major harmonics (6 th harmonic) and two major harmonics (12 th harmonic) are eliminated successively.
  • Figure 11 is a comparison of the radial force harmonic analysis of the motor in the prior art and in the magnetic pole offset method of the present invention. It can be seen from Fig. 11 that in the prior art, after the magnetic pole offset is used to weaken the cogging torque, the lowest harmonic order of the radial force of the motor is lower, which is the third harmonic, and the other higher harmonic amplitudes are compared. High; while the magnetic pole offset in the present invention attenuates the pulsation caused by the reluctance torque and the permanent magnet torque, the lowest harmonic of the radial force of the motor is the 5th harmonic, and the harmonic amplitude is smaller than the present There is a corresponding amplitude in the technical pole shift method.
  • the example motor of the present invention has a harmonic order that is much less than the prior art example motor after the pole offset. Therefore, the magnetic pole offset method of the present invention can effectively reduce the motor caused by the asymmetry of the rotor. Vibration noise.
  • the present invention discloses a magnetic pole offset method for a permanent magnet synchronous motor, which is offset by selecting a suitable repeating unit to reduce the main source of torque ripple of the motor, optimize the back electromotive force, and ensure that the overall output torque ripple is almost constant.
  • the magnetic pole offset method is adopted, which includes: a method of selecting a permanent magnet magnetic pole repeating unit, an offset method and an angle calculation of a primary offset and a secondary offset. These offset methods are applied to the repeating unit of the permanent magnet poles individually or multiple times, and can be used to reduce the torque ripple caused by different torque components (cogging torque, reluctance torque or permanent magnet torque), and improve the motor's performance.
  • the permanent magnet synchronous motor can quickly calculate the angle of the magnetic pole offset by properly selecting the offset magnetic pole. After the offset, the sinusoidality of the back EMF waveform is effectively increased, and the peaks and valleys between the torque ripples generated by the respective repeating units are eliminated to reduce the content of various subharmonics, thereby reducing the overall torque ripple. purpose. At the same time, in the case of ensuring that the output torque value of the motor is almost constant, the introduction of the radial force can be minimized, and the vibration noise of the motor caused by the asymmetry of the rotor can be effectively reduced, and the optimal effect can be achieved.

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  • Engineering & Computer Science (AREA)
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  • Permanent Field Magnets Of Synchronous Machinery (AREA)
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Abstract

一种降低永磁同步电机转矩脉动的方法，包括：合理选择永磁磁极重复单元的方法，一次偏移和二次偏移的偏移方式和角度计算。将偏移单独或多次施加于永磁磁极（3）的重复单元，提升电机的性能。该方法能运用于表贴、表嵌式和内嵌式永磁电机，可用于降低来源于不同转矩成分所引起的转矩脉动。永磁同步电机通过合理选择偏移单元，能够快速计算出磁极偏移的角度（θ1，θ2）。偏移之后，有效的提升反电势波形的正弦度，通过各重复单元所产生转矩脉动之间的峰谷相消以减小转矩脉动各类次谐波含量，达到减小整体转矩脉动的目的。同时，在保证电机输出转矩值几乎不变的情况下，能够尽量少地引入电机振动噪声，实现最优的效果。

Description

一种降低永磁同步电机转矩脉动的方法 技术领域
本发明涉及到永磁同步电机的设计，特别是永磁同步电机转矩脉动的降低方法，属于电机制造的技术领域。
背景技术
现如今永磁电机已经得到了广泛的应用，从汽车到航空航天的众多领域，永磁电机都扮演着十分重要的角色。这主要得益于永磁电机的几个显著特点，包括高转矩密度、高效率以及重量体积小等。永磁电机采用了高磁能积的磁性材料取代了传统的励磁绕组，不仅消除了励磁绕组带来的负面影响，而且简化了电机的机械结构，使电机运行可靠性提高，机械损耗也相应的减小。
虽然永磁电机拥有一系列的优点，但对于要求苛刻的高性能应用，如电动转向系统、伺服电机、风力发电机、电动汽车驱动系统等应用仍然面临许多困难。这些应用对电机的工作稳定性方面提出了很高的要求，即电机的输出转矩脉动要尽可能小，从而实现平稳精确的推力传动，因此研究削减齿槽转矩和输出转矩脉动是非常具有价值的。
目前，对于转矩脉动的抑制，国内外都有比较深入的研究，如优化极弧系数、在转子或转子槽表面开孔、转子静态偏心等方法。这些方法普遍的一个缺点，就是电机的平均转矩会随着转矩脉动的减小而大幅下降，也就是说转矩脉动和平均转矩是两个相互掣肘的性能指标。所以，在准确分析转矩脉动来源成分的基础上减小转矩脉动的同时，如何保持转矩密度的性能不下降或者尽量将平均转矩下降值减小到最低，是需要重点研究的方向。
其次，对于磁极偏移法，现有技术只针对于齿槽转矩的降低。而在目前应用广泛的内嵌式或表嵌式电机当中，转矩脉动的来源不仅仅局限于齿槽转矩，它还可能来源于永磁转矩和磁阻转矩，而齿槽转矩只占据总转矩脉动的极小部分。在此基础上，只局限于齿槽转矩的分析是远远不够的。所以，如何快速准确有效地降低转矩脉动中的主要来源成分，是需要重点研究的方向。
发明内容
本发明的目的是，提出了一种尽量减少平均转矩损失的转矩脉动抑制方法。在 准确分析转矩脉动来源成分的基础上，合理选择永磁磁极的重复单元并将其间隔性偏移，在有效降低转矩脉动的基础上，综合考虑永磁转矩和磁阻转矩成分，削弱转子不对称对转矩出力的影响，减小平均转矩的损失。同时，有效地降低不对称转子对电机的振动噪声产生的影响。
本发明采用的技术方案是：降低永磁同步电机转矩脉动的方法，包括以下步骤：
步骤1，对目标电机的极槽配比进行分析，根据转子极数和定子槽数的关系，计算一个电周期内转矩脉动的波动周期数，确定其总体波动趋势；
步骤2，计算能够产生相同转矩的最小磁极数N0，将电机转子和永磁体模块化；通过模块化分析，使得每个模块中的永磁磁极能够产生相同的转矩，包括转矩幅值和相位，在此前提下，保证模块中的磁极数最少，并以此作为一个基本重复单元；
步骤3，将两个或多个基本重复单元合并，组成新的重复单元，这些新的重复单元同样可以产生相同的转矩幅值和波形；确定不同新重复单元的个数，以供磁极偏移的时候选择；
步骤4，分析转矩及转矩脉动主要来源成分，并对它们的产生进行模块化分析，确定转矩脉动中各个成分所产生的基本重复单元，计算各个基本重复单元中的最小磁极数Ni0；
步骤5，综合考虑N0和各个Ni0，合理选择偏移重复单元；并根据所选重复单元内磁极数量b，确定重复单元数q和最大可偏移次数N；
步骤6，为了削弱转矩脉动中的1次主要谐波，计算一次偏移的准确角度θ1，对所选的重复单元进行第一次偏移；
步骤7，为了削弱转矩脉动中的2次主要谐波，计算二次偏移的准确角度θ2，在第一次磁极偏移的基础上，重新划分重复单元，对新的重复单元进行第二次偏移；
步骤8，如果空间允许，为了削弱转矩脉动中的n次主要谐波，计算n次偏移的准确角度θn，在前n-1次偏移的基础上，进行第n次划分重复单元，并进行第n次偏移。
进一步，所述步骤1中的转矩脉动的波动周期数计算公式为：
Figure PCTCN2017072924-appb-000001
其中，Tripple表示一个电周期内转矩脉动的波动周期数；Ns表示电机的槽数，Np表示电机的极对数，Nps表示电机槽数与极数的最小公倍数Nps＝LCM(Ns，2Np)。
进一步，所述步骤2中基本重复单元是指能够产生相同转矩波形的最小永磁磁极数，这些转矩波形具有相同的幅值和相位。
进一步，所述步骤2中基本重复单元内最小永磁磁极数的计算公式为：
Figure PCTCN2017072924-appb-000002
其中，N0表示基本重复单元内的最小永磁磁极数，Ns表示电机的槽数。
进一步，所述步骤3中的新的重复单元是由k个基本重复单元所组成，其永磁磁极数为kN0。
进一步，所述步骤4中的转矩脉动主要来源成分包括：齿槽转矩、磁阻转矩和永磁转矩；它们相对应的基本重复单元中的最小永磁磁极数分别记为N10，N20，N30。
进一步，所述步骤5中：
所选重复单元内磁极数量b，重复单元数q和最大偏移次数N满足以下关系：
Figure PCTCN2017072924-appb-000003
N取整数；
所选重复单元内磁极数量b，重复单元数q和最大偏移次数N确定之后，则电机总转矩则可表示为各重复单元所产生的转矩之和，即
Figure PCTCN2017072924-appb-000004
其中，Ti为各重复单元所产生的转矩。
进一步，所述步骤6中，偏移的角度计算过程为：
步骤6.1，电机的转矩表达式可表示为转矩均值和转矩脉动之和，具体如下：
Figure PCTCN2017072924-appb-000005
其中，Tall_av表示转矩平均值，Tall_rip表示转矩脉动，根据转矩脉动的周期性，可以将其表示成为上述傅里叶级数形式；
步骤6.2，电机的转矩T可表示为各重复单元所产生的转矩Ti之和，而各分量Ti也可表示为平均值和脉动之和；在此基础上，若某个磁极重复单元被偏移θ之后， 该重复单元所产生的转矩仅在相位上发生改变，即
Figure PCTCN2017072924-appb-000006
步骤6.3，最终的总的转矩脉动则为未被偏移的重复单元和已被偏移的重复单元分别产生的转矩脉动相叠加：
Figure PCTCN2017072924-appb-000007
步骤6.4，考虑转矩的平均值，则输出转矩可进一步表示为
Figure PCTCN2017072924-appb-000008
其中，Tpavj表示第j个重复单元产生的平均转矩，在磁极偏移之前，各重复单元产生的平均转矩相同，即Tpavj＝Tpav；
步骤6.5，永磁体重复单元被偏移之后，使得转子稍有不对称，每个重复单元的平均转矩有微小的变化，但是这种变化很小，远远低于转矩脉动的含量；具体关系如下，
Figure PCTCN2017072924-appb-000009
其中，
Figure PCTCN2017072924-appb-000010
上式中的Tr即为转矩脉动的主要成分，应作为主要分析对象；利用三角函数公式，将其化简得：
Figure PCTCN2017072924-appb-000011
步骤6.6，若想削弱转矩脉动，则需要使得Tr尽可能小，在极限情况下，Tr＝0，则有偏移的角度为：
Figure PCTCN2017072924-appb-000012
或
Figure PCTCN2017072924-appb-000013
其中，θn表示消除转矩脉动中n次谐波时需要重复单元偏移的角度；当n＝1时，磁极偏移θ1可消除转矩脉动中的1次主要谐 波；当n＝2时，磁极偏移θ2可消除转矩脉动中的2次主要谐波。
进一步，所述步骤6中的一次偏移是将选择的重复单元间隔性偏移，偏移角度为θ1。
进一步，所述步骤7中的二次偏移是指在一次偏移的基础上，将已被偏移的重复单元以及其相邻的一个未被偏移的重复单元作为整体，划分为新的重复单元；然后将新的重复单元间隔性偏移，偏移角度为θ2；二次偏移必须与一次偏移同方向。
本发明采用的有益效果是：
1.本发明中的永磁同步电机进行磁极偏移后，不局限于降低齿槽转矩带来的转矩脉动，还能够有效地减小永磁转矩或磁阻转矩带来转矩脉动，优化反电势以及减小最终的输出转矩脉动，使电机在稳定性方面有明显的提升。
2.本发明的磁极偏移法，综合考虑产生总转矩的基本重复单元中最小磁极数N0和产生转矩脉动各个来源成分的基本重复单元中最小磁极数Ni0。在减小输出转矩脉动的情况下，保持电机的平均转矩几乎没有下降，比较全面的提高电机的性能。
3.本发明的电机磁极偏移法中包含偏移重复单元的多种选择，能够根据转矩脉动的主要来源成分，合理的选择偏移重复单元，使得不同的电机可以达到类似的效果。
4.本发明的电机磁极偏移法中包含多次偏移效果，能够通过深入削弱转矩脉动中的不同类次谐波，根据需求深度降低转矩脉动。
5.本发明中电机磁极偏移法通过选择合适的重复单元进行磁极偏移，尽可能少地引入电机的径向力。与传统的磁极偏移法相比，可以有效降低转子不对称对电机的振动噪声产生的影响。
附图说明
图1为本发明中电机磁极偏移法以及重复单元的选取示意图；(a)为原电机永磁体分布示意图；(b)为一次偏移后永磁体分布示意图；(c)为二次偏移后永磁体分布示意图。
图2为本发明中永磁同步电机(原电机)的结构示意图。
图3为本发明中原电机和原电机磁极偏移(实施例电机)的磁阻转矩比较图。
图4为本发明中原电机和实例电机的磁阻转矩谐波分析图。
图5为本发明中原电机和实施例电机的永磁转矩比较图。
图6为本发明中原电机和实例电机的永磁转矩谐波分析图。
图7为本发明中原电机和实施例电机的反电势比较图。
图8为本发明中原电机和实施例电机的反电势谐波分析图。
图9为本发明中原电机和实施例电机的输出转矩比较图。
图10为本发明中原电机和实施例电机的输出转矩谐波分析图。
图11为现有技术和本发明中磁极偏移法的电机径向力谐波分析图。
图12为本发明磁极偏移法的流程图。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述。
下面通过参考附图描述的实施例是示例性的，仅用于解释本发明，而不能理解为对本发明的限制。
如图2所示，三相表嵌式永磁同步电机包括外定子1和内转子2；所述外定子1包括48个定子槽和嵌在其中的电枢绕组4；所述内转子2包括转子铁芯和8个永磁磁极3和6个通风孔5。
下面以三相表嵌式永磁同步电机为例，其方法步骤如图12所示。
1)对目标电机的极槽配比进行分析，根据转子极数和定子槽数的关系，计算一个电周期内转矩脉动的波动周期数，确定其总体波动趋势。转矩脉动的波动周期数计算公式为：
Figure PCTCN2017072924-appb-000014
转矩脉动的波动周期数计算结果为Tripple＝12。其中，Ns＝48，Np＝4；Nps＝LCM(48，8)＝48。该目标电机包括：表贴式、表嵌式和内嵌式永磁同步电机。
2)对计算转子上能够产生相同转矩的最小磁极数N0，将电机转子和永磁体模块化。通过模块化分析，使得每个模块中的永磁磁极能够产生相同的转矩，包括转矩幅值和相位，在此前提下，保证模块中的磁极数最少，并以此作为一个基本重复单元。基 本重复单元内最小永磁磁极数的计算公式为：
Figure PCTCN2017072924-appb-000015
其中，N0表示基本重复单元内的最小永磁磁极数，Ns表示电机的槽数。
所述步骤2)中根据重复单元中的最小永磁磁极数的计算公式计算得出N0＝1。
所述步骤2)中的磁极数2Np＝8，根据重复单元中的磁极数N0p，将电机转子模块化，将电机转子划分为8个基本模块，每个基本重复单元为一个基本模块。如图1(a)所示，原电机共有8个磁极(M1-M8)，每个磁极作为一个基本重复单元，共有8个基本重复单元。
3)将两个或多个基本重复单元合并，可组成新的重复单元，这些新的重复单元同样可以产生相同的转矩幅值和波形。确定不同重复单元的个数，以供磁极偏移的时候选择。
所述步骤3)中的“新的重复单元”是由k个基本重复单元所组成，所以其永磁磁极数为kN0，k＝1，2，4。共有3种不同的重复单元可供选择。
4)分析转矩及转矩脉动主要来源成分，并对它们的产生进行模块化分析，确定转矩脉动中各个成分所产生的基本重复单元，计算各个基本重复单元中的最小磁极数Ni0。原电机各转矩成分如下表1所示，原电机的转矩脉动为35.9％，其中的齿槽转矩百分比仅为1.3％，而磁阻转矩和永磁转矩脉动比例分别为22％和12％。由此可见，原电机的转矩脉动主要来源成分是磁阻转矩和永磁转矩。
表1
Figure PCTCN2017072924-appb-000016
所述步骤4)中的产生磁阻转矩的基本重复单元中最小磁极数N20＝1，产生永磁转矩的基本重复单元中最小磁极数N30＝2。
5)综合考虑N0和各个Ni0，合理选择偏移重复单元；并根据所选重复单元内磁极数量b，确定重复单元数q和最大可偏移次数N。
该步骤中所选重复单元内磁极数量b，重复单元数q和最大偏移次数N确定之后，则电机总转矩则可表示为各重复单元所产生的转矩之和，即
Figure PCTCN2017072924-appb-000017
其中，Ti为各重复单元所产生的转矩。
所选重复单元内磁极数量b，重复单元数q和最大偏移次数N满足以下关系：
Figure PCTCN2017072924-appb-000018
N取整数。
所述步骤2)中原电机产生总转矩的重复单元中最小永磁磁极数N0＝1。
所述步骤4)中的产生磁阻转矩的基本重复单元中最小磁极数N20＝1，产生永磁转矩的基本重复单元中最小磁极数N30＝2。
综合分析N0、N20和N30，为了综合考虑磁阻转矩和永磁转矩，选取2个基本重复单元(最小磁极数2)作为一次偏移的重复单元，即b＝2。
在此基础上，所述步骤5)中的最大偏移次数N＝2，最多可以偏移2次。
如图1(b)所示，选取一对永磁磁极(即2个基本重复单元)，则共有4个一次重复单元，即(M1，M2)，(M3，M4)，(M5，M6)，(M7，M8)。此重复单元是为了消除转矩脉动中的第1次主要谐波含量，故称为一次重复单元。
6)为了削弱转矩脉动中的1次主要谐波，计算一次偏移的角度θ1，对所选的重复单元进行第一次偏移。偏移的角度计算过程为：
步骤6.1，电机的转矩表达式可表示为转矩均值和转矩脉动之和，具体如下：
Figure PCTCN2017072924-appb-000019
其中，Tall_av表示转矩平均值，Tall_rip表示转矩脉动。根据转矩脉动的周期性，可以将其表示成为上述傅里叶级数形式；
步骤6.2，电机的转矩T可表示为各重复单元所产生的转矩Ti之和，而各分量Ti也可表示为平均值和脉动之和；在此基础上，若某个磁极重复单元被偏移θ之后，该重复单元所产生的转矩仅在相位上发生改变，即
Figure PCTCN2017072924-appb-000020
步骤6.3，最终的总的转矩脉动则为未被偏移的重复单元和已被偏移的重复单元分别产生的转矩脉动相叠加：
Figure PCTCN2017072924-appb-000021
步骤6.4，在此基础上，考虑转矩的平均值，则输出转矩可进一步表示为
Figure PCTCN2017072924-appb-000022
其中，Tpavj表示第j个重复单元产生的平均转矩，在磁极偏移之前，各重复单元产生的平均转矩相同，即Tpavj＝Tpav；
步骤6.5，永磁体重复单元被偏移之后，使得转子稍有不对称，每个重复单元的平均转矩有微小的变化，但是这种变化很小，远远低于转矩脉动的含量；具体关系如下，
Figure PCTCN2017072924-appb-000023
其中，
Figure PCTCN2017072924-appb-000024
上式中的Tr即为转矩脉动的主要成分，应作为主要分析对象；利用三角函数公式，将其化简得：
Figure PCTCN2017072924-appb-000025
步骤6.6，若想削弱转矩脉动，则需要使得Tr尽可能小，在极限情况下，Tr＝0， 则有
Figure PCTCN2017072924-appb-000026
或
Figure PCTCN2017072924-appb-000027
其中，θn表示消除转矩脉动中n次谐波时需要重复单元偏移的角度。当n＝1时，磁极偏移θ1可消除转矩脉动中的1次主要谐波；当n＝2时，磁极偏移θ2可消除转矩脉动中的2次主要谐波。
该步骤中的一次偏移的磁极偏移角度是指，当n＝1时，经计算所得θ1＝180°/48＝3.75°。然后，将所选的一次重复单元间隔性偏移。如图1(b)所示，一次重复单元(M1，M2)和(M5，M6)被逆时针偏移θ1角度，(M3，M4)和(M7，M8)保持不变。
7)为了削弱转矩脉动中的2次主要谐波，计算二次偏移的额外角度θ2，在第一次磁极偏移的基础上，对重复单元进行第二次偏移。二次偏移是指在一次偏移的基础上，将已被偏移的重复单元以及其相邻的一个未被偏移的重复单元作为整体，划分为新的重复单元；然后将新的重复单元间隔性偏移，偏移角度为θ2。
所述步骤7)中的二次偏移是为了消除转矩脉动中的第2次主要谐波含量，故磁极偏移的额外角度是指，当n＝2时，经计算所得θ2＝180°/2×48＝1.875°。
如图1(c)所示，在一次偏移的基础上，将已被偏移的重复单元(M1，M2)和与其相邻的一个未被偏移的重复单元(M3，M4)作为整体，划分为二次重复单元(M1，M2，M3，M4)。(M5，M6，M7，M8)是另外一个二次重复单元。然后，将二次重复单元间隔性偏移，即(M1，M2，M3，M4)额外地偏移θ2角度。(M5，M6，M7，M8)保持一次偏移之后的状态不变。二次偏移必须与一次偏移同方向。
重复单元所需偏移的角度具体如下表2所示。
表2
Figure PCTCN2017072924-appb-000028
图2为表嵌式永磁同步电机的结构示意图，本发明以其为原电机，在此基础上进行 磁极偏移，得到实施例电机，将两者的性能相比较，说明本发明的有益效果。图3和图4分别表示原电机和实施例电机的磁阻转矩(转矩脉动的主要来源之一)及其谐波分析方面的比较。由图3可知，在运用一次磁极偏移法之后，与原电机相比，实施例电机的磁阻转矩峰峰值有了大幅的降低，从原来的52.5Nm下降到了25.2Nm。在运用二次磁极偏移法之后，磁阻转矩峰峰值有了进一步的降低，从25.2Nm下降到了14.2Nm。同时，从图4也可以看出，1次主要谐波(6th谐波)和2次主要谐波(12th谐波)依次被消除。
图5和图6分别表示原电机和实施例电机的永磁转矩(转矩脉动的另一主要来源)及其谐波分析方面的比较。如图5所示，在运用二次磁极偏移法之后，与原电机相比，实施例电机的永磁转矩峰峰值有了大幅的降低，从原来的49.1Nm下降到了11.9Nm。同时，从图6也可以看出，主要阶次谐波(6th谐波)被消除。
图7和图8分别表示原电机和实施例电机在反电势及其谐波分析方面的比较。如图7所示，实施例电机反电势正弦度相比于原电机有了明显的提升。除此之外，如图8所示，电机进行磁极偏移后，不仅次谐波的含量减少了，而且基波的幅值几乎与原电机保持不变，这表示电机在转矩脉动方面的性能有了很大的提升的同时，平均转矩基本保持不变。
图9和图10反映了原电机和实施例电机在最终的输出转矩及其谐波分析方面的比较。由图9可知，经过磁极偏移之后，效果明显。实施例电机的转矩脉动有了大幅的降低，在运用一次磁极偏移法之后，转矩脉动从原来的35.9％下降到了12.7％。在运用二次磁极偏移法之后，转矩脉动有了进一步的降低，从12.7％下降到了7.9％。同时从图10也可以看出，1次主要谐波(6th谐波)和2次主要谐波(12th谐波)依次被消除。
图11反映了现有技术中和本发明中磁极偏移法的电机径向力谐波分析方面的比较。由图11可知，现有技术中采用磁极偏移削弱齿槽转矩之后，电机的径向力存在的最低谐波阶数较低，为3次谐波，且其他高次谐波幅值较高；而本发明中采用磁极偏移削弱磁阻转矩和永磁转矩所产生的脉动之后，电机的径向力存在的最低谐波为5次谐波，并且其谐波幅值小于现有技术磁极偏移法中的相应幅值。此外，从总体上看本发明中的实例电机在磁极偏移之后，存在的谐波阶数远少于现有技术的实例电机。所以，本发明中的磁极偏移法，可以有效降低转子不对称带来的电机的 振动噪声。
综上，本发明公开了永磁同步电机的磁极偏移法，通过选择合适的重复单元进行偏移，以减小电机的转矩脉动主要来源、优化反电势，且保证整体输出转矩脉动几乎不变。在基于电动汽车应用设计的永磁同步电机的基础上，采用磁极偏移法，具体包括：合理选择永磁磁极重复单元的方法，一次偏移和二次偏移的偏移方式和角度计算。这些偏移法单独或多次施加于永磁磁极的重复单元，可用于降低不同转矩成分(齿槽转矩、磁阻转矩或永磁转矩)所引起的转矩脉动，提升电机的性能。永磁同步电机通过合理选择偏移磁极，能够快速计算出磁极偏移的角度。偏移之后，有效的提升反电势波形的正弦度，通过各重复单元所产生的转矩脉动之间的峰谷相消以减小各类次谐波的含量，达到减小整体转矩脉动的目的。同时，在保证电机输出转矩值几乎不变的情况下，能够尽量减少径向力的引入，有效降低转子不对称带来的电机的振动噪声，实现最优的效果。
在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示意性实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。
尽管已经示出和描述了本发明的实施例，本领域的普通技术人员可以理解：在不脱离本发明的原理和宗旨的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由权利要求及其等同物限定。

Claims (10)

  1. 一种降低永磁同步电机转矩脉动的方法，其特征在于，包括以下步骤：
    步骤1，对目标电机的极槽配比进行分析，根据转子极数和定子槽数的关系，计算一个电周期内转矩脉动的波动周期数，确定其总体波动趋势；
    步骤2，计算能够产生相同转矩的最小磁极数N0，将电机转子和永磁体模块化；通过模块化分析，使得每个模块中的永磁磁极能够产生相同的转矩，包括转矩幅值和相位，在此前提下，保证模块中的磁极数最少，并以此作为一个基本重复单元；
    步骤3，将两个或多个基本重复单元合并，组成新的重复单元，这些新的重复单元同样可以产生相同的转矩幅值和波形；确定不同新重复单元的个数，以供磁极偏移的时候选择；
    步骤4，分析转矩及转矩脉动主要来源成分，并对它们的产生进行模块化分析，确定转矩脉动中各个成分所产生的基本重复单元，计算各个基本重复单元中的最小磁极数Ni0；
    步骤5，综合考虑N0和各个Ni0，合理选择偏移重复单元；并根据所选重复单元内磁极数量b，确定重复单元数q和最大可偏移次数N；
    步骤6，为了削弱转矩脉动中的1次主要谐波，计算一次偏移的准确角度θ1，对所选的重复单元进行第一次偏移；
    步骤7，为了削弱转矩脉动中的2次主要谐波，计算二次偏移的准确角度θ2，在第一次磁极偏移的基础上，重新划分重复单元，对新的重复单元进行第二次偏移；
    步骤8，如果空间允许，为了削弱转矩脉动中的n次主要谐波，计算n次偏移的准确角度θn，在前n-1次偏移的基础上，进行第n次划分重复单元，并进行第n次偏移。
  2. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤1中的转矩脉动的波动周期数计算公式为：
    Figure PCTCN2017072924-appb-100001
    其中，Tripple表示一个电周期内转矩脉动的波动周期数；Ns表示电机的槽数，Np表示电机的极对数，Nps表示电机槽数与极数的最小公倍数Nps＝LCM(Ns，2Np)。
  3. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤2中基本重复单元是指能够产生相同转矩波形的最小永磁磁极数，这些转矩波形具有相同的幅值和相位。
  4. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤2中基本重复单元内最小永磁磁极数的计算公式为：
    Figure PCTCN2017072924-appb-100002
    其中，N0表示基本重复单元内的最小永磁磁极数，Ns表示电机的槽数。
  5. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤3中的新的重复单元是由k个基本重复单元所组成，其永磁磁极数为kN0。
  6. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤4中的转矩脉动主要来源成分包括：齿槽转矩、磁阻转矩和永磁转矩；它们相对应的基本重复单元中的最小永磁磁极数分别记为N10，N20，N30。
  7. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤5中：
    所选重复单元内磁极数量b，重复单元数q和最大偏移次数N满足以下关系：
    Figure PCTCN2017072924-appb-100003
    N取整数；
    所选重复单元内磁极数量b，重复单元数q和最大偏移次数N确定之后，则电机总转矩则可表示为各重复单元所产生的转矩之和，即
    Figure PCTCN2017072924-appb-100004
    其中，Ti为各重复单元所产生的转矩。
  8. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤6中，偏移的角度计算过程为：
    步骤6.1，电机的转矩表达式可表示为转矩均值和转矩脉动之和，具体如下：
    Figure PCTCN2017072924-appb-100005
    其中，Tall_av表示转矩平均值，Tall_rip表示转矩脉动，根据转矩脉动的周期性，可以将 其表示成为上述傅里叶级数形式；
    步骤6.2，电机的转矩T可表示为各重复单元所产生的转矩Ti之和，而各分量Ti也可表示为平均值和脉动之和；在此基础上，若某个磁极重复单元被偏移θ之后，该重复单元所产生的转矩仅在相位上发生改变，即
    Figure PCTCN2017072924-appb-100006
    步骤6.3，最终的总的转矩脉动则为未被偏移的重复单元和已被偏移的重复单元分别产生的转矩脉动相叠加：
    Figure PCTCN2017072924-appb-100007
    步骤6.4，考虑转矩的平均值，则输出转矩可进一步表示为
    Figure PCTCN2017072924-appb-100008
    其中，Tpavj表示第j个重复单元产生的平均转矩，在磁极偏移之前，各重复单元产生的平均转矩相同，即Tpavj＝Tpav；
    步骤6.5，永磁体重复单元被偏移之后，使得转子稍有不对称，每个重复单元的平均转矩有微小的变化，但是这种变化很小，远远低于转矩脉动的含量；具体关系如下，
    Figure PCTCN2017072924-appb-100009
    其中，
    Figure PCTCN2017072924-appb-100010
    上式中的Tr即为转矩脉动的主要成分，应作为主要分析对象；利用三角函数公式，将其化简得：
    Figure PCTCN2017072924-appb-100011
    步骤6.6，若想削弱转矩脉动，则需要使得Tr尽可能小，在极限情况下，Tr＝0， 则有偏移的角度为：
    Figure PCTCN2017072924-appb-100012
    或
    Figure PCTCN2017072924-appb-100013
    其中，θn表示消除转矩脉动中n次谐波时需要重复单元偏移的角度；当n＝1时，磁极偏移θ1可消除转矩脉动中的1次主要谐波；当n＝2时，磁极偏移θ2可消除转矩脉动中的2次主要谐波。
  9. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤6中的一次偏移是将选择的重复单元间隔性偏移，偏移角度为θ1。
  10. 根据权利要求1所述的一种降低永磁同步电机转矩脉动的方法，其特征在于：所述步骤7中的二次偏移是指在一次偏移的基础上，将已被偏移的重复单元以及其相邻的一个未被偏移的重复单元作为整体，划分为新的重复单元；然后将新的重复单元间隔性偏移，偏移角度为θ2；二次偏移必须与一次偏移同方向。
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