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Minor loop dynamic Jiles-Atherton model in giant magnetostrictive actuator
GAO Xiaohui , LIU Yongguang , PEI Zhongcai
School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-12-09; Accepted: 2016-03-25; Published online: 2016-05-03 16:47
Foundation item: National Natural Science Foundation of China (11272026)
Corresponding author. PEI Zhongcai, Tel.:010-82339730, E-mail:peizc@buaa.edu.cn
Abstract: Hysteresis nonlinear relationship between input and output exists in giant magnetostrictive actuator (GMA). In order to lower hysteresis nonlinearity of material, minor hysteresis loops are often applied when the high frequency characteristics are studied. Therefore, it is very important to research the mathematic model of minor hysteresis loops. First, the dynamic hysteresis model is established combining Ampere circuital theorem with giant magnetostrictive material (GMM) and structural dynamic characteristic of GMA, which regards exciting current as input variable and strain as output variable. Then, the laws between model parameters and hysteresis loop characteristic are achieved by simulation and minor hysteresis loop dynamic Jiles-Atherton (J-A) model is proposed through modifying the model parameters according to the error characteristic between simulation and experiment waveform. Finally, the mathematic model is proved at different frequencies and exciting currents by experiment.
Key words: giant magnetostrictive actuator (GMA)     dynamic     Jiles-Atherton (J-A) model     minor hysteresis loop     parameter modification

1 GMA结构及工作原理

GMA的结构如图 1所示，其工作原理为GMM棒在励磁线圈产生动态驱动磁场的作用下产生伸缩位移，通过输出杆驱动其他装置运动。由于GMM自身的性能特点需要通过预压弹簧施加预应力来提高其磁致伸缩系数。采用环形外套式永磁体产生偏置磁场，一方面可以消除GMM自身的“倍频”特性实现双向位移输出，尽可能利用材料磁滞回线偏置磁场附近线性度较好的区域，降低材料自身非线性因素的影响，另一方面可提供较大的偏置磁场、能耗低、发热量小。在研究其中高频输出特性时，材料及结构的惯性、刚度和阻尼对位移输出产生一定的影响。

 图 1 GMA工作原理 Fig. 1 Working principle of GMA
2 GMA J-A建模 2.1 J-A动态磁滞模型

J-A模型是基于铁磁材料的磁畴理论建立起来描述材料内部特性的数学模型，认为材料中非磁性夹杂、晶界和内应力等牵制点的存在使畴壁取代的磁化过程受阻而导致磁滞。因此，将磁畴运动分为可逆和不可逆壁移和壁转运动，将磁化强度可分为可逆磁化强度和不可逆磁化强度[15]

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Bertotti损耗统计理论[17]认为铁磁性材料的能量损耗主要是由磁滞损耗Ehysteresis、涡流损耗Eeddy和异常损耗Eanomalous三部分组成，因此在动态环境下J-A模型的能量守恒方程为

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GMA在中高频工作时，激励磁场的动态输入导致GMM棒处于快速伸缩状态，其输出特性受材料自身惯性、刚度和阻尼的影响较大。因此，本文在考虑材料自身特性的基础上结合GMA非线性动力学方程建立以励磁电流为输入、应变为输出的磁滞非线性动态模型。

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 图 2 GMA等效力学模型 Fig. 2 Equivalent mechanical model of GMA

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2.2 模型参数特性分析

 图 3 磁滞回线特征参数 Fig. 3 Characteristic parameters of hysteresis loop

 图 4 J-A模型参数对磁滞回线特性影响 Fig. 4 Influence of J-A model parameters on hysteresis loop properties

 参数 初始斜率 斜率 饱和斜率 最大输出 最小输出 回线面积 a↑ ↓ ↓ ↓ ↓ ↓ - α↑ ↑ ↑ - ↑ ↑ ↓ c↑ ↑ ↑ - - ↓ ↓ k↑ ↑ - ↓ - ↑ - 注：↑表示该变量增大；↓表示该变量减小；-表示该变量保持基本不变的状态。

2.3 不饱和小回线模型参数修正

 图 5 J-A小回线实验与仿真波形 Fig. 5 J-A minor loop experiment and simulation waveform

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3 实验验证

GMA实验台主要是由GMA、激光位移传感器以及测控实验台组成(如图 6所示)，采用RTX为下位机、LabWindows为上位机的测控系统，采样周期为1 ms。选用日本电子技研工业(DENSHIGIKEN)株式会社生产的V100-MS激光位移传感器，可实现对位移、速度以及加速度的实时监测，位移测量精度高达5 μm/V。选用桂林风得控公司生产的ISF20DA250电流伺服驱动器，可实现电流反馈闭环控制，驱动频率高达15 kHz，幅值可达10 A。首先通过旋转螺塞压缩碟簧将初始预压力调整为6 MPa，工作台附近应保持安静的工作环境，防止周边的环境噪声对信号采集产生干扰。一切准备就绪之后给电流伺服驱动器下发激励电流幅值为2 A、频率为10 Hz的正弦信号指令，同时利用激光位移传感器采集GMA输出位移，并将采集信号记录保存。此组测试完成之后需将GMM棒取出放置在无磁环境中静置2 h方可重新进行实验，此组实验需重复3次取平均值方可得到激励电流幅值为2 A、频率为10 Hz时GMA输出位移波形曲线。J-A模型修正前后与实验波对比波形和磁滞回线特征参数分别如图 7表 2所示，由此可以看出修正后模型磁滞回线的特征参数与实验数据比较接近，大大优于修正前模型，从而证明了该小回线模型的正确性。

 图 6 GMA实验台 Fig. 6 GMA test bed
 图 7 J-A模型修正前后和实验对比 Fig. 7 Comparison between J-A model before and after modification and experiment loop

 参数 数值 实验 模型修正前 模型修正后 初始斜率/(10-4A-1) 2.08 1.00 2.00 斜率/(10-4A-1) 3.4 2.8 3.4 饱和斜率/(10-4 A-1) 1.0 0.7 1.0 最大输出应变/10-4 5.2 4.7 5.2 最小输出应变/10-4 -5.54 -5.4 -5.5

4 结论

1) 在综合考虑GMA材料和结构动力学特性的基础上结合安培环路定理提出以励磁电流为输入、应变为输出的动态J-A模型。

2) 引入磁滞回线特性参数得出J-A模型参数对磁滞回线特性影响规律。

3) 根据不饱和小回线仿真与实验波形的偏离特性，通过增大参数αc减小参数ak来实现对J-A模型修正得到不饱和小回线动态J-A模型。

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文章信息

GAO Xiaohui, LIU Yongguang, PEI Zhongcai

Minor loop dynamic Jiles-Atherton model in giant magnetostrictive actuator

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(12): 2648-2653
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0815