介电型EAP换能器机电耦合特性研究
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摘要
作为一种新兴智能材料，介电型EAP（Electroactive Polymer,电活性聚合物）具有质量轻、应变大（最大应变380%）、能量密度高（3.4J/g）、效率高、响应速度快、环境适应性好等优点，其综合性能接近于生物肌肉。介电型EAP的研究已经成为国内外智能材料研究领域的热点问题。介电型EAP具有双向工作模式：驱动模式和发电模式，实现电能与机械能之间的相互转换。两种工作模式下的共性问题是电场环境中介电型EAP受力和变形之间的关系，即介电型EAP的机电耦合特性，因此可采用相同的方法对其进行建模分析。本文在国家自然科学基金项目（50975139）资助下深入研究介电型EAP的机电耦合特性，结合材料非线性、几何非线性对介电型EAP换能器进行理论建模与试验研究，为介电型EAP换能器的设计、制作提供依据与指导。
利用连续介质力学理论，推导出介电型EAP的应力、应变、运动平衡方程表示方法。基于介电型EAP是一种不可压缩材料的假设，分析其在电场环境中的受力情况，利用非线性弹性理论和Maxwell应力张量方法推导了介电型EAP的机电耦合本构方程。
利用建立的本构方程分析了电场激励下圆形介电型EAP驱动器的变形行为。建立了圆形介电型EAP驱动器的分析模型，利用Matlab求解微分方程边值问题，研究不同激励电压下预拉伸率、主动区域尺寸等因素对圆形驱动器变形的影响，并利用试验对理论分析结果进行验证，说明前面建立的介电型EAP本构方程是合理的。
应用弹性薄膜理论对锥形驱动器进行建模研究，给出了锥形驱动器的分析模型。结合介电型EAP驱动器工作原理，提出利用力—位移拉伸曲线来设计驱动器的方法。分析了基于正刚度预载荷（压缩弹簧）的锥形驱动器力、位移输出特性，试验结果与理论分析结果较吻合。为提高驱动器的输出位移，设计了一种半菱形式负刚度预载荷机构，对采用该预载荷机构的驱动器输出特性和效率进行详细分析。另外对介电型EAP驱动器的电学模型进行了分析。
分析了介电型EAP的几种失效模式：机械强度失效、介电击穿、pull-in现象(机电不稳定性)、起皱失效、系统不稳定性。确定各种失效模式的发生条件，并给出理想条件下介电型EAP驱动器工作时的安全区域。同时针对锥形驱动器的失效行为进行了深入讨论。
研究了介电型EAP的发电机理和工作过程，对恒电荷、恒电压、恒电场三种工作形式进行了详细比较。根据其能量转换原理，分析了介电型EAP的能量转换关系。基于建立的介电型EAP换能器模型，经过数值计算得到换能单元在断电拉伸和通电返回过程中的力—位移曲线，据此计算出介电型EAP换能器的发电量、能量转换效率，确定初始电压、拉伸位移为发电量、能量转换效率的主要影响因素，并通过试验验证了理论分析结果，进而对如何提高机电能量转换效率作了进一步研究，设计了多单元换能器的工作方案。
As a new kind of emerging smart material, dielectric electroactive polymer (EAP) hasdemonstrated low weight, large strain rate (up to380%), high energy density (3.4J/g), good efficiency,fast response and excellent environmental adaptability. The overall performance of dielectric EAP issimilar to that of biological muscle tissue. Nowdays, research on dielectric EAP has been becomingthe focus of intelligent material field wordwidely. It has two working modes including actuator modeand generator mode, which can transform electrical energy directly into mechanical work and viceversa. The common problem of two working modes is the relationship between force and deformationof dielectric EAP in the presence of electric field, named the electromechanical couplingcharacteristic of dielectric EAP. Thus the same method can be used to model dielectric EAPtransducer. Supported by National Natural Science Foundation of China (No.50975139), research onelectromechanical coupling characteristic of dielectric EAP transducer is performed based thematerial and geometrical nonlinearities in this dissertation. Theoretical modeling and experimentalanalysis on dielectric EAP transducer can contribute to the design of dielectric EAP transducer.
Using a continuum mechanics theory, the stress, strain description and equations of equilibriumof dielectric EAP are deduced. The stress analysis of dielectric EAP activated by electrical field isexecuted. The constitutive equation of the dielectric EAP is determined by a superposition of themechanical stress due to the nonlinear elastic theory and the Maxwell stress due to the electrostaticfield.
Based on the proposed electromechanical constitutive equations of dielectric EAP, themechanical behavior of circular dielectric EAP actuator under electrical field is analyzed. With thedeveloped analytical model of circular actuator, the impacting of pre-stretch ratio and area of activeregion to the circular actuator’s deformation under different applied voltages has been achieved bysolving the differential equations with boundary value problem by Matlab. The theoretical results arevalidated by experiments, which verify the of electromechanical constitutive equations of dielectricEAP.
Using elastic theory of membrane, a model that describing conically-shaped dielectric EAPactuator is founded. Combing the working principle and process of dielectric EAP actuator, a methodof designing actuator is proposed by using the force-displacement curve of actuator. The force outputand displacement output of actuator with positive stiffness preload mechanism (compressive spring) are determined and validated by the experiments. To improve the displacement output, a negativestiffness preload mechanism with half diamond is presented. Actuation characteristics and efficiencyof conically-shaped dielectric EAP actuator with negative stiffness preload mechanism are analyzedin detail. Moreover, the electrical model of dielectric EAP actuator is discussed.
Several failure mechanisms of dielectric EAP actuator including mechanical strength, dielectricbreakdown, pull-in phenomena (electromechanical instability), wrinkling phenomena and systeminstability are investigated, and the safe working area of ideal dielectric EAP actuator is determined.In addition, the failure behavior of conically-shaped actuator is discussed in detail.
The energy harvesting mechanisms and working cycles of dielectric EAP transducer areinvestigated. Three different cycles including constant charges, constant electric voltage and constantelectrical field are compared. Based on the working cycles, the energy conversion betweenmechanical energy inputted and electrical energy generated have been studied. With the proposedmodel of dielectric EAP transducer, the force-stroke of generator unit in the stretching process withvoltage on and the retracting process with voltage off are determined. With the force-stroke ofgenerator unit, the energy generated and energy conversion efficiency are calculated. It isdemonstrated that the stretch displacement of dielectric EAP generator and bias voltage are the mainfactors influencing the amount of electrical energy generated and the efficiency of energy conversion.In addition, the theoretical analysis results are validated by the experiments. To improve theefficiency of energy conversion, a scheme of a generator with multiple dielectric EAP units isdeveloped.
利用连续介质力学理论，推导出介电型EAP的应力、应变、运动平衡方程表示方法。基于介电型EAP是一种不可压缩材料的假设，分析其在电场环境中的受力情况，利用非线性弹性理论和Maxwell应力张量方法推导了介电型EAP的机电耦合本构方程。
利用建立的本构方程分析了电场激励下圆形介电型EAP驱动器的变形行为。建立了圆形介电型EAP驱动器的分析模型，利用Matlab求解微分方程边值问题，研究不同激励电压下预拉伸率、主动区域尺寸等因素对圆形驱动器变形的影响，并利用试验对理论分析结果进行验证，说明前面建立的介电型EAP本构方程是合理的。
应用弹性薄膜理论对锥形驱动器进行建模研究，给出了锥形驱动器的分析模型。结合介电型EAP驱动器工作原理，提出利用力—位移拉伸曲线来设计驱动器的方法。分析了基于正刚度预载荷（压缩弹簧）的锥形驱动器力、位移输出特性，试验结果与理论分析结果较吻合。为提高驱动器的输出位移，设计了一种半菱形式负刚度预载荷机构，对采用该预载荷机构的驱动器输出特性和效率进行详细分析。另外对介电型EAP驱动器的电学模型进行了分析。
分析了介电型EAP的几种失效模式：机械强度失效、介电击穿、pull-in现象(机电不稳定性)、起皱失效、系统不稳定性。确定各种失效模式的发生条件，并给出理想条件下介电型EAP驱动器工作时的安全区域。同时针对锥形驱动器的失效行为进行了深入讨论。
研究了介电型EAP的发电机理和工作过程，对恒电荷、恒电压、恒电场三种工作形式进行了详细比较。根据其能量转换原理，分析了介电型EAP的能量转换关系。基于建立的介电型EAP换能器模型，经过数值计算得到换能单元在断电拉伸和通电返回过程中的力—位移曲线，据此计算出介电型EAP换能器的发电量、能量转换效率，确定初始电压、拉伸位移为发电量、能量转换效率的主要影响因素，并通过试验验证了理论分析结果，进而对如何提高机电能量转换效率作了进一步研究，设计了多单元换能器的工作方案。
As a new kind of emerging smart material, dielectric electroactive polymer (EAP) hasdemonstrated low weight, large strain rate (up to380%), high energy density (3.4J/g), good efficiency,fast response and excellent environmental adaptability. The overall performance of dielectric EAP issimilar to that of biological muscle tissue. Nowdays, research on dielectric EAP has been becomingthe focus of intelligent material field wordwidely. It has two working modes including actuator modeand generator mode, which can transform electrical energy directly into mechanical work and viceversa. The common problem of two working modes is the relationship between force and deformationof dielectric EAP in the presence of electric field, named the electromechanical couplingcharacteristic of dielectric EAP. Thus the same method can be used to model dielectric EAPtransducer. Supported by National Natural Science Foundation of China (No.50975139), research onelectromechanical coupling characteristic of dielectric EAP transducer is performed based thematerial and geometrical nonlinearities in this dissertation. Theoretical modeling and experimentalanalysis on dielectric EAP transducer can contribute to the design of dielectric EAP transducer.
Using a continuum mechanics theory, the stress, strain description and equations of equilibriumof dielectric EAP are deduced. The stress analysis of dielectric EAP activated by electrical field isexecuted. The constitutive equation of the dielectric EAP is determined by a superposition of themechanical stress due to the nonlinear elastic theory and the Maxwell stress due to the electrostaticfield.
Based on the proposed electromechanical constitutive equations of dielectric EAP, themechanical behavior of circular dielectric EAP actuator under electrical field is analyzed. With thedeveloped analytical model of circular actuator, the impacting of pre-stretch ratio and area of activeregion to the circular actuator’s deformation under different applied voltages has been achieved bysolving the differential equations with boundary value problem by Matlab. The theoretical results arevalidated by experiments, which verify the of electromechanical constitutive equations of dielectricEAP.
Using elastic theory of membrane, a model that describing conically-shaped dielectric EAPactuator is founded. Combing the working principle and process of dielectric EAP actuator, a methodof designing actuator is proposed by using the force-displacement curve of actuator. The force outputand displacement output of actuator with positive stiffness preload mechanism (compressive spring) are determined and validated by the experiments. To improve the displacement output, a negativestiffness preload mechanism with half diamond is presented. Actuation characteristics and efficiencyof conically-shaped dielectric EAP actuator with negative stiffness preload mechanism are analyzedin detail. Moreover, the electrical model of dielectric EAP actuator is discussed.
Several failure mechanisms of dielectric EAP actuator including mechanical strength, dielectricbreakdown, pull-in phenomena (electromechanical instability), wrinkling phenomena and systeminstability are investigated, and the safe working area of ideal dielectric EAP actuator is determined.In addition, the failure behavior of conically-shaped actuator is discussed in detail.
The energy harvesting mechanisms and working cycles of dielectric EAP transducer areinvestigated. Three different cycles including constant charges, constant electric voltage and constantelectrical field are compared. Based on the working cycles, the energy conversion betweenmechanical energy inputted and electrical energy generated have been studied. With the proposedmodel of dielectric EAP transducer, the force-stroke of generator unit in the stretching process withvoltage on and the retracting process with voltage off are determined. With the force-stroke ofgenerator unit, the energy generated and energy conversion efficiency are calculated. It isdemonstrated that the stretch displacement of dielectric EAP generator and bias voltage are the mainfactors influencing the amount of electrical energy generated and the efficiency of energy conversion.In addition, the theoretical analysis results are validated by the experiments. To improve theefficiency of energy conversion, a scheme of a generator with multiple dielectric EAP units isdeveloped.
引文
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