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The hysteresis model of giant magnetostrictive materials (GMMs) changes with model parameters: the excitation amplitude, bias condition and excitation frequency. The existing hysteresis model is unable to predict the effects of simultaneous changes in the three external conditions. In this paper, the hysteresis loss mechanism is explained by using the traditional Jiles-Atherton (J-A) dynamic model, and the relation equation is established according to the operating conditions and material properties to respond to the changes of external conditions. For the J-A model, the relationship equation related to the excitation amplitude is established, and the relationship equation relating the residual loss coefficient to the excitation amplitude and the bias condition is established for the residual loss, while the eddy current loss of the system is redefined by using the fractional order to obtain the modified hysteresis model. In the paper, the genetic algorithm is used to identify the model parameters of the test data under different operating conditions, and the corresponding correction coefficients are obtained according to the model parameters and the operating conditions. The accuracy of the modified model is verified by simulating the model and analyzing the influences of eddy currents and residual losses and their effects on the model predictions. The hysteresis model is evaluated to compare the hysteresis curves with the hysteresis losses in terms of errors. The results show that the modified model is capable of predicting various excitations with high accuracy, and that neglecting dynamic losses at low frequencies results in large errors. If the model order of the eddy current loss is smaller than the actual order of the material, the predicted hysteresis curve will be contracted inward and the predicted eddy current loss will be small; on the contrary, the predicted hysteresis curve will be expanded outward and the predicted eddy current loss will be large, and with the increase of the excitation frequency, both cases will cause the prediction error to become larger and larger. When the bias magnetic field is zero, the residual loss coefficient is unchanged; when the bias magnetic field is kept constant, the excitation amplitude increases and the residual loss coefficient decreases; when the excitation amplitude is unchanged, the bias magnetic field increases and the residual loss coefficient also increases. When both the bias magnetic field and the excitation amplitude change at the same time, it is necessary to conduct an actual analysis of their corresponding residual loss coefficients. Using hysteresis curves to evaluate hysteresis is more accurate.
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Keywords:
- giant magnetostrictive materials /
- Jiles-Atherton dynamic model /
- eddy current loss /
- residual loss
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图 1 GMM磁致伸缩原理
Figure 1. GMM magnetostrictive principle.
图 2 不同分数阶下的磁滞曲线特征 (a) f = 100 Hz; (b) f = 400 Hz
Figure 2. Characterization of hysteresis curves at different fractional orders: (a) f = 100 Hz; (b) f = 400 Hz.
图 3 GMA结构示意图
Figure 3. Schematic diagram of the GMA structure.
图 4 试验流程示意图
Figure 4. Schematic diagram of test procedure.
图 5 低频情况下涡流损耗和剩余损耗对磁滞特性的影响
Figure 5. Current loss and residual loss on low frequency hysteresis characteristics.
图 6 不同激励下GMM棒磁滞特性 (a) U (0—4 V); (b) U (0—3 V)
Figure 6. Hysteresis characteristics of the GMM rod under different excitations: (a) U (0–4 V); (b) U (0–3 V).
图 7 0—4 V激励下磁感应强度随频率变化动态特性 (a) f = 100 Hz; (b) f = 200 Hz; (c) f = 300 Hz; (d) f = 400 Hz; (e) f = 500 Hz; (f) f = 600 Hz
Figure 7. Dynamic characterization of magnetic inductance with frequency under 0–4 V excitation. (a) f = 100 Hz; (b) f = 200 Hz; (c) f = 300 Hz; (d) f = 400 Hz; (e) f = 500 Hz; (f) f = 600 Hz
图 8 0—3 V激励下磁感应强度随频率变化动态特性 (a) f = 200 Hz; (b) f = 400 Hz; (c) f = 600 Hz
Figure 8. Dynamic characterization of magnetic inductance with frequency under 0–3 V excitation: (a) f = 200 Hz; (b) f = 400 Hz; (c) f = 600 Hz.
图 9 0—4 V不同激励频率下的系统损耗 (a) 单位时间的系统损耗; (b) 单位周期的系统损耗
Figure 9. System losses at various excitation frequencies from 0–4 V: (a) System loss per unit time; (b) system loss per unit cycle.
表 1 GMA系统主要相关参数
Table 1. GMA system main relevant parameters.
名称 符号 单位 数值 GMM棒长 l m 0.08 GMM直径 D m 0.0128 GMM质量 m2 kg 0.12 GMM棒相对磁导率 μr — 9 GMM棒电阻率 ρ Ω·m 6×10–7 激励线圈匝数 N — 1000 真空磁导率 μ0 H·m–1 4π×10–7 漏磁系数 kg — 1.1 饱和磁滞伸缩系数 λs 10–6 1100 
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表 2 GMA系统主要相关参数
Table 2. Modified model parameter identification table.
系数 数值 系数 数值 系数 数值 α 0.01812 λα –0.613 kcl 8.533 c 0.3899 λc 2.393 ka 21.03 k 4407 λk –0.933 w1 9.35×108 a 16179 λa 0.7 w2 3.97 Ms 695000 p 1.07 w3 –29.35
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表 3 不同激励下的磁感应强度
Table 3. Magnetic induction at various excitations.
U/V f/Hz Bmin/T Bmax/T Bp/T Bd/T 0—5 20 0.066 0.7038 0.3189 0.3849 0—4 20 0.0504 0.669 0.3093 0.3597 0—4 100 0.056 0.661 0.3025 0.3585 0—4 200 0.059 0.66 0.3005 0.3595 0—4 300 0.09 0.676 0.293 0.383 0—4 400 0.124 0.65 0.263 0.387 0—4 500 0.153 0.636 0.2415 0.3945 0—4 600 0.182 0.612 0.215 0.397 0—3 20 0.0499 0.5686 0.25935 0.30925 0—3 200 0.0559 0.5832 0.26365 0.31955 0—3 400 0.107 0.536 0.2145 0.3215 0—3 600 0.16 0.48 0.16 0.32
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表 4 0—4 V不同频率激励下磁能损耗误差和磁滞曲线误差情况
Table 4. Magnetic energy loss error and hysteresis curve error under different frequency excitation from 0–4 V.
f/Hz ε Ref εemu1/% εemu2/% Ref1 Ref2 20 3.35 4.63 8×10–5 5.94×10–5 100 5.73 5.24 4.01×10–4 4.21×10–4 200 9.41 9.51 5.55×10–4 5.82×10–4 300 13.18 13.21 9.3×10–4 8.79×10–4 400 11.17 10.4 1.53×10–3 9.89×10–4 500 10.03 8.79 1.96×10–3 9.42×10–4 600 5.62 5.19 2.54×10–3 6.17×10–4 注: εemu1为参数未变化的相对损耗误差, εemu2为参数修正后的相对损耗误差, Ref1为参数未变化的磁滞曲线误差, Ref1为参数修正后的磁滞曲线误差.
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