V型电热驱动器的理论建模及位移响应特性

Theoretical modeling and displacement response characteristics of V-shaped electrothermal actuator

为了研究V型电热驱动器的位移响应特性,考虑到材料参数的温度非线性及数学模型中存在的非连续性边界问题,从理论、仿真和实验三个方面对V型电热驱动器进行研究。通过引入与温度相关的材料参数更新函数,建立V型电热驱动器的电-热-力耦合模型;利用改进型切比雪夫谱方法求解所构建的耦合模型,得到V型电热驱动器温度和瞬态位移表达式。然后,对V型电热驱动器温度和位移进行有限元仿真和理论分析。最后,搭建电热驱动器瞬态位移响应实验平台,将恒定电压激励下的V型电热驱动器位移响应实验结果与理论和仿真结果进行对比,并对周期性方波电压下V型电热驱动器的位移响应进行了测试。实验结果表明:在一段时间后,V型电热驱动器的位移响应呈现周期性变化,且周期与方波电压周期相等;在其他参数相同的条件下,峰峰值为14 V的周期方波电压作用下,电热驱动器位移均值为20μm,峰峰值为7 V的周期方波电压作用下,位移均值为28μm;频率为50 Hz的周期方波电压作用下,电热驱动器位移变化幅度比频率100 Hz下多7μm。V型电热驱动器的位移均值基本不变,但位移变化幅度与频率负相关。

To study the characteristics of displacement response for a V-shaped electrothermal actuator,considering that the material parameters are affected by temperature nonlinearity and discontinuous bound⁃ary problems in the mathematical model,the characteristics of displacement response for the V-shaped electrothermal actuator were studied in theory,simulation,and experiment.First,an electro-thermal-me⁃chanical coupling model of a V-shaped electrothermal actuator was established by introducing updating functions of a material parameter related to the temperature.Expressions for the temperature and transient displacement of the V-shaped electrothermal actuator were obtained using the improved Chebyshev spec⁃trum method to solve the constructed coupling model.Then,a finite element simulation and theoretical analysis of the temperature and displacement of the V-shaped electrothermal actuator were performed to verify the correctness of the model.Finally,an experimental platform for the transient displacement response of the electrothermal actuator was constructed.The experimental results of the displacement re⁃sponse for the V-shaped electrothermal actuator under constant voltage excitation were compared with the theoretical and simulation results.The displacement response of the V-shaped electrothermal actuator un⁃der a periodic square wave voltage was tested.The test results reveal the following:the V-shaped electro⁃thermal actuator performs periodic variation after a certain amount of time.The cycle is identical to that of the square wave voltage.Under similar conditions of other parameters,the average displacements of the electrothermal driver under the action of the peak-to-peak 14 V periodic square wave voltage are 20μm.Furthermore,the average displacements under the action of the peak-to-peak 7 V periodic square wave voltage are 28μm.The displacement variation of the electrothermal actuator under the action of a periodic square wave voltage with a frequency of 50 Hz is 7μm larger than that under a frequency of 100 Hz.The mean displacement is approximately equal.However,the variation range of displacement is negatively cor⁃related with frequency.