Analytical calculation no-load air-gap flux density of air-core compensated pulsed alternator with double layer Halbach
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摘要: 采用空芯式结构的补偿脉冲发电机，克服了铁磁材料磁场饱和对电机磁场强度和转速的限制，可显著提高电机储能密度和功率密度。Halbach永磁阵列具有磁屏蔽作用，可省去转子铁芯，并能产生正弦度较好的气隙磁密波形。首先，本文将结构简单、整体性强、易于优化的双层Halbach永磁阵列转子应用于空芯补偿脉冲发电机的拓扑结构中。其次，在不考虑磁场饱和的情况下，在极坐标下采用子域模型的方法，建立了空芯式补偿脉冲发电机内的空载电磁场解析计算模型。该方法从电磁场的基础理论出发，运用矢量磁位法分别对四个子区域建立拉普拉斯方程（无旋场）或泊松方程（旋度场），结合相邻子区域间的边界条件，将各个方程联合求解，得到了电机空载气隙磁密的数学表达式，并对空载气隙磁场的分布情况进行了分析。解析计算结果和有限元仿真结果的对比，验证了该方法的精确性，其计算结果能够较为真实的反应电机的静态及稳态性能。最后，研究了电机的四个主要参数与空载气隙磁密径向分量和切向分量的幅值和正弦度之间的变化关系，可为后续电机空载气隙磁场的优化和进一步计算设计提供技术支持。Abstract:
Background The compensated pulsed alternator (CPA) is a pulsed power source that integrates rotor inertial energy storage, electromechanical energy conversion and power regulation. It connects the prime mover and the electromagnetic launch load directly as a “unit component”, reducing many intermediate links. It has the advantages of high output voltage, high power density, high frequency of repetition and long service life, and is regarded as the most promising pulsed power source for electromagnetic launch systems.Purpose The air-core CPA (ACCPA) overcomes the limitations of ferromagnetic material saturation on magnetic field strength and rotational speed, significantly improving the motor’s energy storage density and power density. The Halbach permanent magnet array (HPMA) possesses a magnetic shielding, eliminating the need for a rotor core while generating an air-gap magnetic flux density (AGMFD) waveform with good sinusoidal characteristics. Therefore, this paper investigates the application of a double-layer HPMA rotor, which is simple in structure, strong in integrity, and easy to optimize, in the topological structure of ACCPA.Methods Without considering magnetic saturation, an analytical calculation model for the no-load electromagnetic field in an ACCPA was established using the subdomain model method in polar coordinates. Starting from the basic theory of electromagnetic fields, this method used the vector magnetic potential method to establish Laplace’s equations (for no- curl fields) or Poisson’s equations (for curl fields) for four subdomains respectively. By combining the boundary conditions between adjacent subdomains, the equations were solved jointly to obtain the mathematical expression for the no-load AGMFD of the motor, and the distribution of the no-load AGMFD was analyzed.Results This analytical model could directly reflect the relationship between the no-load AGMFD distribution of the motor and its design parameters. The analytical model’s calculation results were highly consistent with the results of finite element analysis, verifying the accuracy of the analytical model. Its calculation results could relatively accurately reflect the static and steady-state performance of the motor.Conclusions The relationship between the four main parameters of the motor and the amplitude and sinusoidal characteristics of the radial and tangential components of the no-load AGMFD is studied, which can provide technical support for the subsequent optimization of the motor’s no-load air-gap magnetic field and further calculation design. -
图 1 空芯双层Halbach永磁阵列转子拓扑结构图
Figure 1. Rotor topology with double layer Halbach permanent magnet array
图 2 双层永磁体共作用时空载气隙磁密分布的对比情况
Figure 2. Comparison between analytically and FE predicted no-load air-gap flux density waveforms
图 4 空载气隙磁密分布随极对数P和永磁体厚度比ht的变化规律
Figure 4. Changing laws of no-load air-gap flux density distribution with P and ht
图 5 空载气隙磁密分布随上下层极弧系数$ {\alpha }_{u} $和$ {\alpha }_{d} $的变化规律
Figure 5. Changing laws of no-load air-gap flux density distribution withP $ {\alpha }_{u} $ and $ {\alpha }_{d} $
表 1 空芯双层Halbach阵列CPA的主要参数
Table 1. Main Parameters of air-core CPA with double layer Halbach
number
of
phasesnumber
of pole
pairsstator inner
diameter/
mmrotor inner
diameter/
mmmagnet thickness
of downer
layer PM/mmmagnet thickness
of upper layer
PM/mmpole-arc to
pole-pitch ratio
of downer layerpole-arc to
pole-pitch ratio
of uper layerrated
speed/
(r·mim−1)2 2 80 26 9 3 0.8 0.31 10000 
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