基于等效热弹性应变能的智能变形蒙皮模拟分析及实验

张伟; 麻越垠; 蔡清青; 高鑫宇; 聂旭涛

doi:10.13224/j.cnki.jasp.20220976

基于等效热弹性应变能的智能变形蒙皮模拟分析及实验

doi: 10.13224/j.cnki.jasp.20220976

张伟^{1, 2,},
麻越垠^{1, 2},
蔡清青¹,
高鑫宇¹,
聂旭涛^1,*, ,

1.
国防科技大学空天科学学院，长沙 410073
2.
中国空气动力研究与发展中心设备设计与测试技术研究所，四川绵阳 621000

基金项目: 中国空气动力研究与发展中心基础和前沿技术研究基金探索项目（PJD20200240）

详细信息

作者简介:
张伟（1988-），男，工程师，主要从事变体飞行器。E -mail：zhangwei6103@126.com

通讯作者:
聂旭涛（1979-），男，副研究员，主要从事智能材料和飞行器方面的研究。E-mail：nie_xu_tao@163.com

中图分类号: V259
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- 被引次数: 0
出版历程
- 收稿日期: 2022-12-23
- 网络出版日期: 2024-05-17

Numerical and experiment of morphing skin based on equivalent thermoelastic energy method

ZHANG Wei^{1, 2
,},
MA Yueyin^{1, 2},
CAI Qingqing¹,
GAO Xinyu¹,
NIE Xutao^{1,*
, ,}

1.
College of Aero Space Science and Engineer，National University of Defense Technology，Changsha，410073，China
2.
Facility Design and Instrumentation Institute，China Aerodynamics Research and Development Center，Mianyang 621000，China

摘要

摘要:
为简化记忆合金建模，提出了一种等效模拟方法，将形状记忆合金相变能转化为弹性基体的热弹性应变能，并以温差形式表达。以形状记忆合金丝为对象，开展了该方法和Boyd-Lagoudas扩展模型的对比分析。基于Boyd-Lagoudas扩展模型编写的自定义物性子程序，除了常规的退孪马氏体和奥氏体，还考虑了孪生马氏体以提高模拟分析的准确性。等效模型的最大误差为9.8%，验证了方法的有效性和准确性。针对不锈钢及单程记忆合金组成的主动变形蒙皮，等效方法计算的机翼弧高变化幅值为4.03 mm，和实验值3.81 mm吻合，降低了数值模拟难度和计算消耗，表明该方法有助于开展机翼模型的全尺寸模拟研究，并用于设计快速迭代。
- 变形蒙皮 /
- 热弹性应变能 /
- 形状记忆合金 /
- 等效方法 /
- 有限元分析
Abstract:
To simplify the modeling, an equivalent simulation method was proposed to convert the transformation energy of SMA into the thermoelastic strain energy of elastic plate and express it by temperature difference. Firstly, the equivalent approach and Boyd-Lagoudas extended model were compared and analyzed for a SMA wire model. According to the compiled physical property subroutine of SMA based on the Boyd-Lagoudas extended model, twinned martensite other than conventional detwinned martensite and austenite was considered. The maximum error of the equivalent model was 9.8%, proving its effectiveness and accuracy. For the active morphing skin composed of stainless steel and one-way SMA, the variation magnitude of the wing arc height calculated by the equivalent approach was 4.03 mm, consistent with the experimental value of 3.81 mm. It indicated that the equivalent thermoelastic energy method was effective to carry out full-scale wing simulation and rapid design iteration.
- morphing skin /
- thermal elastic stress energy /
- shape memory alloy /
- equivalent method /
- finite element simulation

HTML

图 1 主动变形蒙皮结构示意

Figure 1. Schematic of active morphing skin

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图 2 主动变形蒙皮结构样件

Figure 2. Active morphing skin prototype

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图 3 三类晶体相相互转化示意

Figure 3. Schematic of phase transformation among three types

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图 4 SMA丝的应力应变关系

Figure 4. Stress-strain curve of SMA wire

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图 5 SMA棒材分析验证模型

Figure 5. Validation model of the SMA wire

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图 6 Boyd-Lagoudas扩展模型在步骤1的计算结果

Figure 6. Calculation results of step 1 of extended Boyd-Lagoudas model

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图 7 Boyd-Lagoudas扩展模型在步骤2的计算结果

Figure 7. Calculation results of step 2 of extended Boyd-Lagoudas model

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图 8 Boyd-Lagoudas扩展模型在步骤3的计算结果

Figure 8. Calculation results of step 3 of extended Boyd-Lagoudas model

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图 9 Boyd-Lagoudas扩展模型在步骤4的计算结果

Figure 9. Calculation results of step 4 of extended Boyd-Lagoudas model

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图 10 等效热弹性应变方法在步骤1的计算结果

Figure 10. Calculation results of step 1 of equivalent thermoelastic energy method

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图 11 等效热弹性应变方法在步骤2的计算结果

Figure 11. Calculation results of step 2 of equivalent thermoelastic energy method

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图 12 主动变形蒙皮数值模型

Figure 12. Numerical model of the active morphing skin

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图 13 初始状态下的位移及温度

Figure 13. Displacement and temperature distribution at the initial condition

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图 14 升温工况下变形蒙皮回复为平直状态

Figure 14. Morphing skin recovers to flat state under high-temperature condition

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图 15 实验中变形蒙皮回复为平直状态

Figure 15. Morphing skin recovers to flat state in the experiment

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图 16 降温工况下复合变形蒙皮弯曲变形

Figure 16. Morphing skin recovers to bending state under low-temperature condition

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图 17 变形蒙皮回复为弯曲状态

Figure 17. Morphing skin recovers to bending state in the experiment

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表 1 SMA棒材物性参数

Table 1. Material properties parameters for SMA wire

参数	数值
马氏体相变起始温度 M_s/K	302
马氏体相变结束温度M_f/K	291
奥氏体相变起始温度A_s/K	326
奥氏体相变结束温度 A_f/K	336
马氏体弹性模型 E_M/10⁴ MPa	2
奥氏体弹性模量 E_A/10⁴ MPa	4
泊松比 μ	0.33
马氏体热膨胀系数 α_M/10⁻⁵	3
奥氏体热膨胀系数 α_A/10⁻⁵	3
最大相变应变 H	0.034
马氏体退孪开始应力σ_s/MPa	100
马氏体退孪结束应力σ_f/MPa	200
应力影响系数ρΔs₀	-0.3131

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表 2 SMA棒材在高温状态下的计算结果

Table 2. Numerical results of SMA wire at high temperature

参数	Boyd-Lagoudas 扩展模型	等效模型	相对误差/%
最大等效应力/MPa	321	320	0.3
轴向变形/mm	1	0.99	1
孪晶马氏体体积分数	−0.063	−0.069	9.5
退孪马氏体体积分数	0.067	0.071	6
奥氏体体积分数	0.995	0.998	0.3

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表 3 SMA棒材在低温状态下的计算结果

Table 3. Numerical results of SMA wire at low temperature

参数	Boyd-Lagoudas 扩展模型	等效模型	相对误差/%
最大等效应力/MPa	127	130	2.3
轴向变形/mm	1.48	1.46	1.4
孪晶马氏体体积分数	0.75	0.73	2.7
退孪马氏体体积分数	0.28	0.27	3.6
奥氏体体积分数	−0.03	0

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