NONLINEAR ELECTROMECHANICAL MODELING OF PENDULUM-TYPE TRIBOELECTRIC NANOGENERATORS
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摘要: 面向摆式摩擦发电机结构优化设计需求, 开展非线性机电耦合建模与参数敏感性分析, 以推动其向工程实用化方向发展. 在摩擦发电机理分析的基础上, 构建等效电容拟合函数; 结合能量原理和等效电路法, 建立了考虑摆角非线性变化的机电耦合模型. 利用谐波平衡法, 解析求解摆式摩擦发电机的周期稳态输出, 并判断结果稳定性. 结合数值积分和动态测试两种手段, 验证谐波平衡分析的准确性. 与线性模型结果进行深入对比, 并考察了不同设计参数对摆式摩擦发电机输出特性的影响. 考虑非线性效应, 模型预估的工作带宽显著增加(相对增量83%). 文章提出的机电耦合模型能够有效避免线性模型对工作带宽的低估问题, 显著提升输出性能估计的准确性; 增加激励幅值、降低系统阻尼或减小电极夹角, 均有助于提升摆式摩擦发电机的输出表现; 在实际设计时, 需综合考虑间隙长度和摩擦力幅值, 以使摆式摩擦发电机输出表现处于较优状态; 构建多种拟合模型用于表征设计参数与输出性能的关系, 可作为摆式摩擦发电机输出性能设计的依据.Abstract: By reasonably designing the pendulum length, the natural frequency of a pendulum structure can be effectively reduced, so that it can realize resonance under low frequency (even ultra-low frequency) vibration excitation, and then greatly improve the energy conversion performance. The pendulum-type triboelectric nanogenerator (P-TENG) has naturally become the focus of academic attention. In this study, nonlinear electromechanical coupling modeling and parameter sensitivity analysis are conducted to optimize the structural design of the P-TENG, so as to promote its development towards engineering practicability. Based on the analysis of power generation mechanism, an equivalent capacitance model is proposed. Combined with the energy principle and equivalent circuit method, an electromechanical coupling model considering the nonlinear variation of pendulum angle is established. Using the harmonic balance method and alternated frequency/time domain technique, the steady-state output of the P-TENG is solved analytically, and the stability of the results is determined. Numerical integration and dynamic tests are conducted to verify the accuracy of analytical model. The results are compared with the linear model and the influence of various design parameters on the output characteristics of the P-TENG is investigated. Considering the nonlinear effects, the estimated operating bandwidth of the model increases significantly (by a relative increment of 83%). The proposed model can effectively avoid the underestimation of the operation bandwidth and significantly improve the accuracy of the P-TENG performance estimation. Increasing the excitation amplitude, reducing the damping ratio, and minimizing the electrode angle can improve the output performance of the P-TENG. Various fitting models have been proposed to model the relationship between design parameters and output performance. The fitting coefficients obtained from the parameter influence discussion can be used as the basis for the P-TENG output performance design.
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图 5 等效电容仿真模型 (单位: mm)
Figure 5. The three-dimensional capacitance simulation model based on COMSOL (unit: mm)
图 7 单摆最大摆角随激励频率变化曲线
Figure 7. Pendulum angle vs. excitation frequency solved by HBM and NI
图 8 P-TENG表面摩擦电荷随激励频率变化曲线
Figure 8. Surface charge vs. excitation frequency solved by HBM and NI
图 11 考虑非线性效应与否对摆动角位移的影响
Figure 11. Comparison of the influence of the consideration of the nonlinear effect for pendulum angle response curves
图 12 摆动角位移波形和频谱的对比
Figure 12. Comparison of the influence of the consideration of the nonlinear effect
图 13 非线性效应对P-TENG输出特性的影响
Figure 13. Comparison of the influence of the consideration of the nonlinear effect
图 14 激励幅值对输出电流均方根值影响的瀑布图
Figure 14. Waterfall map for the effect of excitation amplitude an on the output performance of the P-TENG
图 15 工作带宽和最大电流随激励幅值变化曲线及拟合结果
Figure 15. Variation curves of operation bandwidth and maximum output current with excitation amplitude and fitting results
图 16 阻尼比对输出电流均方根值影响的瀑布图
Figure 16. Waterfall map for the effect of damping ratio an on the output performance of the P-TENG
图 17 工作带宽和最大电流随阻尼比变化曲线及拟合结果
Figure 17. Variation curves of operation bandwidth and maximum output current with damping ratio and fitting results
图 18 间隙长度对输出电流均方根值影响的瀑布图
Figure 18. Waterfall map for the effect of gap length an on the output performance of the P-TENG
图 19 工作带宽和最大电流随间隙长度变化曲线及拟合结果
Figure 19. Variation curves of operation bandwidth and maximum output current with gap length and fitting results
图 20 电极夹角对输出电流均方根值影响的瀑布图
Figure 20. Waterfall map for the effect of electrode angle an on the output performance of the P-TENG
图 21 工作带宽和最大电流随电极夹角变化曲线及拟合结果
Figure 21. Variation curves of operation bandwidth and maximum output current with electrode angle and fitting results
表 1 电容仿真时P-TENG结构参数
Table 1. Structural parameters of the simulated P-TENG
electrode outer diameter/mm 60 electrode inner diameter/mm 10 electrode thickness/mm 0.050 electrode angle/(°) 0.95 center angle of the pendulum/(°) 46 pendulum outer diameter/mm 55 pendulum thickness/mm 5 
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