V型电热驱动器理论模型及动态特性

doi:10.16183/j.cnki.jsjtu.2020.216

摘要/Abstract

摘要：

为研究V型电热驱动器的动态响应特性,根据热传导理论和受迫振动方程分别建立驱动器电-热和热-力耦合模型,从而形成完整的一维V型电热驱动器多物理场耦合理论模型.采用正弦变换结合隐式差分法对电-热耦合模型求解并进行收敛性测试,正弦变换中,空间离散点数对温度求解结果的稳定性影响较小.电-热耦合模型在不同电压下,其瞬态和稳定温度分布与有限元仿真结果吻合得较好.通过实验和边缘检测算法获得驱动器在不同电压下的稳态位移,与热-力耦合模型的结果对比发现两者具有良好的一致性.基于该理论模型,分析驱动器在阶跃、正弦电压下的动态特性.研究结果表明:正弦电压幅值越大,V型电热驱动器中心处的温度与位移变化的幅度也就越大;当正弦电压作用时间大于5个周期,即50 ms后,驱动器中心处的温度与位移的平均值均等于驱动器在等效直流电压作用下的稳态温度和位移;在周期性电压加载下,驱动器会逐渐趋于周期性运动,其运动周期与电压周期相等.

关键词: 电热驱动器, 耦合, 正弦变换, 受迫振动, 边缘检测

Abstract:

To study the dynamic performance of the V-shaped electrothermal actuator, electrothermal and thermoelastic coupling models are established based on the heat transfer theory and the forced vibration equation, respectively. A one dimensional multi-physical field coupling theoretical model of the V-shaped electrothermal actuator is proposed. The electrothermal coupling model is solved by the method in which the sine transformation and the implicit difference are combined together. Then, a convergence test is performed. The number of discrete points in the sine transformation has less influence on the temperature stability. The transient and static temperature distributions of the model coincide with that of the finite element method (FEM) at different voltages. The static displacements gained by the experiment and the edge detection algorithm also match well with that gained by the thermoelastic coupling model at different voltages. Based on the proposed model, the dynamic performances of the actuator at step and sine voltages are analyzed. The research results indicate that changes of temperature and displacement in the middle of the V-shaped electrothermal actuator are larger with the amplitude of sine voltage increasing. When the loading time of sine voltage is larger than 5 periods (50 ms), the average temperature and displacement in the middle of the actuator are equal to those with equivalent direct voltage. When applied to a periodic voltage, the motion of the actuator is also gradually cyclical and has the same time period with the voltage cycle.

Key words: electrothermal actuator, coupling, sine transformation, forced vibration, edge detection

中图分类号:

陈浩, 王新杰, 王炅, 席占稳, 聂伟荣. V型电热驱动器理论模型及动态特性[J]. 上海交通大学学报, 2021, 55(10): 1263-1271.

CHEN Hao, WANG Xinjie, WANG Jiong, XI Zhanwen, NIE Weirong. Theoretical Model and Dynamic Performance of V-Shaped Electrothermal Actuator[J]. Journal of Shanghai Jiao Tong University, 2021, 55(10): 1263-1271.

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参数	取值
L/μm	1500
b/μm	45
d/μm	100
θ₀/(°)	1
g/μm	10

参数	取值
c/(J·m^-1·K^-1)	787
κ/(W·m^-1·K^-1)	60
k_v/(W·m^-2·K^-1)	70
ρ/(Ω·m)	2.3×10^-4
α/K^-1	2.56×10^-6
E/GPa	169
μ	0.28