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Universal Triboelectric Nanogenerator Simulation Based on Dynamic Finite Element Method Model

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Universal Triboelectric Nanogenerator Simulation Based on Dynamic Finite Element Method Model sensors Article Universal Triboelectric Nanogenerator Simulation Based on Dynamic Finite Element Method Model Jinkai Chen 1,* , Junchao Wang 1 , Weipeng Xuan 1, Shurong Dong 2 and Jikui Luo 1,2 1 Ministry of Education Key Lab of RF Circuits and Systems, College of Electronics & Information, Hangzhou Dianzi University, Hangzhou 310000, China; [email protected] (J.W.); [email protected] (W.X.); [email protected] (J.L.) 2 Key Lab of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310000, China; [email protected] * Correspondence: [email protected] Received: 26 July 2020; Accepted: 25 August 2020; Published: 27 August 2020 Abstract: The lack of a universal simulation method for triboelectric nanogenerator (TENG) makes the device design and optimization difficult before experiment, which protracts the research and development process and hinders the landing of practical TENG applications. The existing electrostatic induction models for TENGs have limitations in simulating TENGs with complex geometries and their dynamic behaviors under practical movements due to the topology change issues. Here, a dynamic finite element method (FEM) model is proposed. The introduction of air buffer layers and the moving mesh method eliminates the topology change issues during practical movement and allows simulation of dynamic and time-varying behaviors of TENGs with complex 2D/3D geometries. Systematic investigations are carried out to optimize the air buffer thickness and mesh densities, and the optimized results show excellent consistency with the experimental data and results based on other existing methods. It also shows that a 3D disk-type rotating TENG can be simulated using the model, clearly demonstrating the capability and superiority of the dynamic FEM model. Moreover, the dynamic FEM model is used to optimize the shape of the tribo-material, which is used as a preliminary example to demonstrate the possibility of designing a TENG-based sensor. Keywords: triboelectric nanogenerator; finite element model; dynamic behaviors; electrostatic induction 1. Introduction Scavenging environmental mechanical energy using triboelectric nanogenerators as energy sources [1–3] or self-powered sensors [4–11] for future maintenance-free applications has attracted much attention since the invention of the triboelectric nanogenerator (TENG) in 2012 [12]. The operating principle of TENGs is the combination effects of contact electrification and electrostatic induction. An in-depth understanding of these processes is essential for the design of high-performance TENGs and will help to promote practical applications of the TENGs. Various models for TENGs have been proposed and explored to explain the charge transfer process during the contact of two tribo-materials (i.e., the contact electrification) such as electron-cloud model [13–15], ion-transfer model [16], material-transfer model [17], etc. No matter which model is applied, a constant surface charge density is always assumed to quantitatively represent the transferred charges remaining on the surfaces of the tribo-materials, even after contact electrification. The surface charge density can be theoretically calculated using first-principle approaches [18,19]. However, from the contact electrification-based simulation, it is impossible to predict the charge transfer in the external circuit. Different from this, the electrostatic induction process reflects the redistribution of Sensors 2020, 20, 4838; doi:10.3390/s20174838 www.mdpi.com/journal/sensors Sensors 2020, 20, x FOR PEER REVIEW 2 of 14 Sensors 2020, 20, 4838 2 of 14 transfer in the external circuit. Different from this, the electrostatic induction process reflects the redistributioninduced charges of induced on the back charges electrodes on the of back TENG, elec astrodes well asof theTENG, charge as transferwell as processthe charge between transfer the processexternal between circuit andthe external back electrodes, circuit and rather back than electro triboelectricdes, rather chargethan triboelectric (i.e., surface charge charge (i.e., density surface on chargethe surface density of tribo-materials).on the surface of The tribo-materials). charge redistribution The charge is strongly redistribution related is to strongly material related properties, to materialdevice structureproperties, and device operational structure parameters and operational such as parameters movement, such contact as movement, force of the contact tribo-materials. force of theAs such,tribo-materials. analytical [20As– 22such,] and analytical numerical [[20–23–2522]] methodsand numerical based on [23–25] the electrostatic methods induction based on process the electrostatichave also been induction developed process and have successfully also been applied developed for TENGs and successfully of different workingapplied for modes TENGs such of as differentthe contact working mode modes [20], sliding such as mode the contact [23], freestanding mode [20], modesliding [26 mode], etc., [23], but freestanding they are limited mode to some[26], etc.,simple but cases.they are The limited existing to methodssome simple have cases. limitations The existing in calculating methods complex have limitations cases, and in the calculating problems complexassociated cases, include and the problems following: associated include the following: (1)(1) Analytic Analytic methods methods can can easily easily obtain obtain accurate accurate dy dynamicnamic voltage/current voltage/current outputs outputs (i.e., (i.e., I(t) I(t) or or V(t)) V(t)) forfor some some specific specific operation operation mode mode TENGs TENGs with with simple simple geometries, geometries, but but can can hardly hardly deal deal with with the the sliding sliding modemode TENG, TENG, or or TENGs TENGs with with complex complex 2D 2D or or 3D 3D geometries. geometries. (2)(2) Numerical Numerical methods methods can can easily easily simulate simulate contact/sliding contact/sliding mode mode TENGs TENGs with with complex complex 2D/3D 2D/3D geometries,geometries, but thethe achievable achievable results results are are mostly mostly limited limited to steady to steady state potential state potential distribution. distribution. Although Althoughsome recently some developedrecently developed numerical numerical methods meth are capableods are ofcapable simulating of simulating the time-varying the time-varying behavior behaviorof TENGs of with TENGs 3D geometrieswith 3D geometries with limited with movement limited rangemovement (i.e., tworange tribo-materials (i.e., two tribo-materials should not be shouldfully separated not be fully from separated each other) from [each24,25 other)], they [2 cannot4,25], they simulate cannot dynamic simulate voltage dynamic/current voltage/current outputs of outputsTENGs of under TENGs practical under movements practical (i.e.,movements tribo-materials (i.e., tribo-materials are fully separated) are fully due separated) to the topology-change due to the topology-changeproblems. The topology-change problems. The issuestopology-change in contact and issues sliding in modecontact TENGs and sliding are highlighted mode TENGs in Figure are1 . highlightedIt is clear in in Figure Figure1a 1. that It is the clear air layerin Figure (yellow) 1a that vanishes the air (i.e., layer topology (yellow) changed) vanishes when (i.e., thetopology upper changed)tribo-material when (red)the upper finally tribo-material contacts with (red) the lower finally tribo-material contacts with (blue); the lower for the tribo-material sliding mode (blue); TENG, forthe the overlapped sliding mode boundary TENG, (green) the overlapped also vanishes boundary when the (green) upper also tribo-material vanishes when (red) moves the upper from tribo- state I materialto III as (red) shown moves in Figure from1 b.state I to III as shown in Figure 1b. FigureFigure 1. 1. PracticalPractical movement movement of of contact contact and and slidin slidingg mode mode TENG TENG makes makes the the FEM FEM geometry geometry have have topologytopology change change issues. issues. (a ()a )The The topology topology of of contact contact mode mode TENG TENG changes changes due due to to the the vanish vanish of of air air layer layer (yellow)(yellow) when when upper upper tribo-material tribo-material (r (red)ed) moving moving from from state state I Ito to III. III. (b (b) )The The topology topology of of sliding sliding mode mode TENGTENG changes changes due due to to the the vanish vanish of of the the overlapped overlapped boundary boundary (green) (green) when when upper upper tribo-material tribo-material (red) (red) movingmoving from from state state I Ito to III. III. AlthoughAlthough the the existing existing models models are are useful useful for for pa partiallyrtially understanding understanding the the principle/operation principle/operation of of TENGs,TENGs, the the lack lack of of an an adequate adequate approach approach for for simu simulatinglating the the time-varying time-varying and and dynamic dynamic behaviors behaviors of TENGsof TENGs with with complex complex geometries geometries under under practical practical movements movements prevents prevents in-depth in-depth understanding understanding of TENGsof TENGs in operation in operation and further and further development development of high-performance of high-performance TENGs TENGsor TENG-based or TENG-based sensor devices.sensor devices. Here,Here,
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