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, we we focusfocus onon the the research research of electrostaticof electrosta inductiontic induction for TENGs, for TENGs, and propose and propose a novel universala novel universalnumerical numerical method which method is capable which ofis calculatingcapable of dynamiccalculating behavior dynamic of TENGs behavior with of complex TENGs 2Dwith/3D complexgeometries 2D/3D under geometries practical movementsunder practical using movements ﬁnite element using method finite (FEM). element Byintroducing method (FEM). a moving By introducingmesh method a moving and air bumeshﬀer layersmethod in and TENG airsimulation, buffer layers the in unavoidable TENG simulation, topology-change the unavoidable issues in topology-changethe existing simulation issues modelsin the existing while dealing simulati withon models practical while movements dealing can with be practical eliminated. movementsThus, it is can be eliminated. Thus, it is possible to calculate the dynamic behavior of 2D/3D TENG geometries.

Sensors 2020, 20, 4838 3 of 14 possible to calculate the dynamic behavior of 2D/3D TENG geometries. The universal dynamic FEM numerical model is extremely beneﬁciary for the structural design of TENGs with practical experimental setup, combined with the ongoing in-depth research of the contact electriﬁcation, are expected to promote practical TENG applications.

2. General Theory The key problem for simulating time-varying behaviors of 2D/3D TENGs with practical experimental configuration using the FEM method is to solve the topology-change issues. In this research, we start with the most fundamental working modes (i.e., contact mode and sliding mode) for TENGs, the solution of which can be easily applied to other working modes such as the single electrode mode and freestanding mode. We first introduce the well-known general theory for dynamic TENG simulation based on FEM, then focus on how to solve the topology-change problems. The finite element method divides the TENG 2D/3D geometries into many basic elements (i.e., the meshing process), and each mesh element follows the same constitutive equations, which is based on Maxwell’s displacement current. The basic simulation flow for time-dependent TENG FEM model is similar to other researches [24,25], thus, we briefly introduce it here. The relationship between displacement field (D) and charge density (ρ) is described by the Maxwell–Poisson equation,

D = ρ (1) ∇· It should be noted that equation 1 is applicable to both tribo-material and back electrode; here, ρ represents the charge density of free charges on the back electrode as well as the triboelectric charges in the tribo-material. For a displacement ﬁeld (D), it can be related to the electric ﬁeld (E) using the following equation in an isotropic media:

D = εrε0E (2) where εr and ε0 represent permittivity of the dielectric material and vacuum, respectively. In the absence of magnetic ﬁeld, the electric ﬁeld (E) can be derived as follows:

E = φ (3) −∇ where φ represents the electric potential in the tribo-material. Combining Equations (1)–(3), the relationship between electric potential and charge density can be ﬁnally derived,

2 εrε φ = ρ (4) − 0∇ Based on the above electrostatic constitutive equation, the link between electric potential and surface charge density is established. The electric potential can be numerically obtained by combining the above equations with the moving meshes and boundary conditions, which will be detailed in the subsequent sections as the conﬁgurations for the contact and sliding modes are quite diﬀerent.

3. Results

3.1. Dynamic Behavior of Contact Mode TENGs The numerical calculation is carried out using COMSOL software. The boundary conditions for the contact mode TENG are shown in Figure2. The triboelectric surface charge densities on the contacting surfaces of Materials 1 and 2 are σ and σ, respectively. The back electrode of Material 2 is − set as the ground (i.e., voltage equals to 0), and the back electrode of Material 1 is set to be the terminal Sensors 2020, 20, 4838 4 of 14 for current to ﬂow to the external circuit, which is governed by the Kirchhoﬀ’s law. The output current (I) can be mathematically expressed as follows: Z dQ f ree D ndS = Q f ree; I = (5) s · dt

Sensorswhere 2020S and, 20, nx FORrepresent PEER REVIEW the back-electrode surface of Material 1 and the normal vector perpendicular4 of 14 to it, respectively. By integrating the normal component of electric displacement field over the electrodeback-electrode surface, surface, the free the charge free charge Qfree canQfree becan derived. be derived. Similarly, Similarly, by differentiating by differentiating it over it overtime, time, the outputthe output current current I canI becan obtained. be obtained. The rest The of rest the of boundari the boundarieses are set are as set zero as zerocharge. charge. Combining Combining with thewith electrostatic the electrostatic and andelectrical electrical relation relation formulas, formulas, both both the the voltage voltage potential potential distribution distribution and and the the dynamicdynamic voltage/current voltage/current outputs outputs can can be be simulated, simulated, and and the the power power output output under under different different external loadsloads can can also also be be derived. derived.

FigureFigure 2. ((aa)) BoundaryBoundary conditions conditions for fo contactr contact mode mode TENG. TENG. (b) Mesh(b) Mesh remains remains best quality best quality when contact when contactmode TENG mode is TENG moving is from moving state from I to III. state (c) The I to voltage III. (c) potential The voltage distribution potential and distribution the dynamic and voltage the dynamicoutput under voltage a 10-M outputΩ external under a load. 10-MΩ external load.

TheThe FEMFEM modelmodel divides divides the the TENG TENG 2D/3D 2D/3D geometries geomet intories many into basic many domains, basic domains, and for calculating and for calculatingthe time-varying the time-varying performance performance of a contact modeof a cont TENG,act mode some ofTENG, the meshed some of domains the meshed in TENG domains need bein TENGdeformed need to be simulate deformed the cyclic to simulate moving the process. cyclic However,moving process. the mesh However, topology the must mesh be kept topology unchanged, must bei.e., kept no meshunchanged, elements i.e., should no mesh be elements eliminated should or newly be eliminated created, for or convergencynewly created, of for the convergency FEM solver. ofTo the solve FEM this solver. problem, To solve an air this bu ffproblem,er layer isan introduced air buffer layer in the is modelintroduced as shown in the in model Figure as2a, shown and the in Figurethickness 2a, ofand which the thickness will not of shrink which to will zero not for shrink an unchanged to zero for topology.an unchanged The movingtopology. mesh The moving method meshis used method for the is moving used for mesh the movi nodalng points mesh throughoutnodal points the throughout region to the best region approximate to best approximate the updated thegeometry updated boundaries. geometry Theboundaries. boundary The conditions boundary for co thenditions moving for meshthe moving method mesh are also method illustrated are also in illustratedFigure2a.The in Figure meshinside 2a. The the mesh area ofinside Material the area 2 is fixed. of Material The mesh 2 is in fixed. Material The 1mesh is moving in Material as a whole 1 is movingand the as relative a whole positions and the of relative mesh nodal positions points of inme Materialsh nodal 1 points remain in unchanged. Material 1 remain For mesh unchanged. in the air Forbuff mesher layer, in the they air will buffer shrink layer, or expandthey will in shrink accordance or expand with in the accordance motions to with keep the the motions mesh topology to keep theunchanged mesh topology and to simulate unchanged the motionand to processsimulate of the the motion contact-separation process of the mode contact-separation TENG, thus, the modelmode TENG, thus, the model provides a free deformation configuration during simulation. The movement of the mesh nodal points inside the air buffer layer is governed by the following equation over time: ∂∂222rrr ∂∂ ∂∂ ++=0 (6) ∂∂∂∂∂∂Xt222 Yt Zt where r represents absolute coordinates of the mesh nodal points, and X, Y, Z represents the reference coordinates between mesh nodal points inside the air buffer layer. The moving mesh in the air buffer area at different operation times is illustrated in Figure 2b. The large red and blue rectangles represent Materials 1 and 2, respectively. Evenly mapped meshes

Sensors 2020, 20, 4838 5 of 14 provides a free deformation conﬁguration during simulation. The movement of the mesh nodal points inside the air buﬀer layer is governed by the following equation over time:

∂2 ∂r ∂2 ∂r ∂2 ∂r + + = 0 (6) ∂X2 ∂t ∂Y2 ∂t ∂Z2 ∂t where r represents absolute coordinates of the mesh nodal points, and X, Y, Z represents the reference coordinates between mesh nodal points inside the air buffer layer. The moving mesh in the air buffer area at different operation times is illustrated in Figure2b. The large red and blue rectangles represent Materials 1 and 2, respectively. Evenly mapped meshes are applied to all the areas of TENG. It can be seen that the mesh in the air buffer layer expands vertically when Material 1 moves from state I to III, while the number of mesh nodal points remains unchanged. The color bars on the right side represent the mesh element quality with the scale varying from 0 to 1, with 1 meaning the best mesh quality. Combining the moving mesh results with the electrostatic theory mentioned above, the voltage potential distribution and the dynamic voltage/current output can be calculated simultaneously, which is shown in Figure2c with a 10-M Ω external load. The color legends represent the electric potential. It can be easily summarized from Figure2c that the largest electric potential occurs when two tribo-materials separate the most at ~0.1 s, while the voltage output in the external circuit decreases to zero voltage at ~0.1 s. As Material 1 approaches Material 2 at 0.189 s, the electric potential in TENG decreases, but the voltage output reaches the negative maximum. After that, Material 1 contacts Material 2 and starts separation, which leads to a maximum voltage output at 0.215 s. It should be noted that the voltage output needs a relaxation time to reach a steady state as the external load hinders the charge transfer, and a larger external load leads to a longer relaxation time. Optimizations are carried out for the air buffer thickness and mesh density. The simulation parameters used during optimization are listed in the Supplementary Information, Table S1. As the mesh topology must remain unchanged throughout the simulation, the air buffer layer cannot be shrunk to zero, which differs slightly from real experimental configuration; therefore, the starting thickness of the air buffer layer is set to a value close to zero but not zero. Using Table S2 as an example, it is clear that a thicker air buffer layer will lead to a much shorter calculating time, but a worse consistency between experimental and simulated results, and vice versa. Thus, an optimal air buffer thickness should be determined first for our model. The voltage and power outputs with various external loads using different air buffer thicknesses are simulated, with the results shown in Figure3a,c, respectively. The summarized peak voltage at a 10-M Ω external load is shown in Figure3b, which remains almost unchanged (<1% discrepancy) when the thickness of the air buffer layer is less than 1 µm (1/100 of tribo-material thickness). If a 10% voltage discrepancy can be tolerated, then the thickness of the air buffer layer of ~5 µm can be used for simulation to save a lot of computing time, which is around 1/20 of the tribo-material thickness. The peak power and corresponding optimum load are shown in Figure3d, which experiences a similar trend as that of the voltage output. The peak power and optimum load remain almost unchanged for the air buffer layer thickness range from 1 to 6.3 µm. The thickness of the air buffer layer can further be increase to ~3.5 µm to reduce the computation time if a 10% voltage discrepancy can be tolerated. In most cases, the mesh density can affect the simulation accuracy significantly, but it is not practical to increase mesh density infinitely due to the limited computational capability. The optimal mesh density is investigated for the contact mode TENG, and the voltage and power outputs under different loads using various mesh densities are shown in Figure4. As mentioned before in Figure2b, mapped meshes are applied to all the areas of TENG, which divides the TENG geometry into many rectangular areas, and the mesh density is determined by the vertical and horizontal boundaries as shown in Figure4e. Figure4a,b shows that the simulated voltage and power peak outputs remain nearly identical when the mesh nodal points in the horizontal boundaries (2, 4, 6, and 7) increase from 10 to 90, and the same trend occurs when the mesh nodal points in the vertical boundaries (1, 3, 5, Sensors 2020, 20, 4838 6 of 14

8, 9 and 10) increase as shown in Figure4c,d. A higher mesh density will only lead to less output curve distortion. This trend can be attributed to the highly symmetric geometry of the contact mode TENG model. Combining with the symmetric mesh, the mesh quality remains at the highest rate of 1 and larger mesh density will not improve the simulation accuracy significantly. Thus, a moderate mesh density should be chosen for less curve distortion. Based on the systematical investigation above, optimal parameters can be obtained for the contact mode TENGs. For the air buffer layer, the optimum thickness is about 1 µm. For the vertical mesh density, the optimum density is about 50 with even distribution. As for the horizontal mesh density, three material areas have different mesh numbers; SensorsSensors 20202020,, 2020,, xx FORFOR PEERPEER REVIEWREVIEW 66 ofof 1414 the optimal mesh densities are about 5, 10, 25 for Material 1, the air buffer, and Material 2, respectively.

Figure 3. Simulated (a) voltage and (c) power output when the thickness of air gap increases from 0.1 FigureFigure 3.3. SimulatedSimulated ((aa)) voltagevoltage andand ((cc)) powerpower outputoutput whenwhen thethe thicknessthickness ofof airair gapgap increasesincreases fromfrom 0.10.1 to 100 µm; (b) summarized peak voltage at a 1-MΩ external load with increasing air gap thickness; toto 100100 μμm;m; ((bb)) summarizedsummarized peakpeak voltagevoltage atat aa 1-M1-MΩΩ externalexternal loadload withwith increasingincreasing airair gapgap thickness;thickness; and (d) summarized peak power and correspondence optimum load under increasing air gap. ((dd)) andand summarizedsummarized peakpeak powerpower andand correspondenccorrespondencee optimumoptimum loadload underunder increasingincreasing airair gap.gap.

Figure 4. Simulated (a) voltage and (b) power output with increasing mesh density in horizontal FigureFigure 4.4. SimulatedSimulated ((aa)) voltagevoltage andand ((bb)) powerpower outputoutput withwith increasingincreasing meshmesh densitydensity inin horizontalhorizontal boundaries; simulated (c) voltage and (d) power output with increasing mesh density in vertical boundaries;boundaries; simulatedsimulated ((cc)) voltagevoltage andand ((dd)) powerpower outputoutput withwith increasingincreasing meshmesh densitydensity inin verticalvertical boundaries. (e) The mapped mesh of contact mode TENG with vertical (1, 3, 5, 8, 9 and 10) and boundaries.boundaries. ((ee)) TheThe mappedmapped meshmesh ofof contactcontact modemode TENGTENG withwith verticalvertical (1,(1, 3,3, 5,5, 8,8, 99 andand 10)10) andand horizontal boundaries (2, 4, 6, and 7). (f) Comparison of experimental data and simulated results based horizontalhorizontal boundariesboundaries (2,(2, 4,4, 6,6, andand 7).7). ((ff)) ComparisonComparison ofof experimentalexperimental datadata andand simulatedsimulated resultsresults on the dynamic FEM model, analytical model. basedbased onon thethe dynamicdynamic FEMFEM model,model, analyticalanalytical model.model.

ToTo verifyverify thethe dynamicdynamic FEMFEM modelmodel forfor thethe contcontactact modemode TENG,TENG, thethe simulatedsimulated resultsresults basedbased onon thethe dynamicdynamic FEMFEM modelmodel areare comparedcompared withwith thethe experiexperimentalmental datadata andand analyticalanalytical simulatedsimulated resultsresults basedbased onon ourour previousprevious workwork [27],[27], asas shownshown inin FigureFigure 4f.4f. TheThe simulationsimulation parametersparameters forfor thethe dynamicdynamic FEMFEM modelmodel andand analyticalanalytical modelmodel areare listedlisted inin thethe SuSupplementarypplementary Information,Information, TableTable S3.S3. TheThe practicalpractical movementmovement waswas extractedextracted fromfrom thethe dynamicdynamic fatigufatiguee testertester (Popwil(Popwil Instrument,Instrument, Hangzhou,Hangzhou, China,China, ModelModel YPS-1)YPS-1) [27],[27], whichwhich isis listedlisted inin thethe SupplementarySupplementary Information,Information, TableTable S4.S4. TheThe experimentalexperimental voltagevoltage outputoutput waswas measuredmeasured usingusing anan oscilloscopeoscilloscope (Tektronix,(Tektronix, Beaverton,Beaverton, UnitedUnited States,States, MDO3022)MDO3022) withwith aa 100:1100:1 voltagevoltage probe,probe, andand oneone ofof thethe electrodeselectrodes ofof TENGTENG isis groundedgrounded duedue toto thethe voltagevoltage probe.probe. TheThe calculatedcalculated voltagevoltage underunder differentdifferent loadsloads usingusing thethe dynamicdynamic FEMFEM andand analyticalanalytical modelmodel isis highlyhighly

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To verify the dynamic FEM model for the contact mode TENG, the simulated results based on the dynamic FEM model are compared with the experimental data and analytical simulated results based on our previous work [27], as shown in Figure4f. The simulation parameters for the dynamic FEM model and analytical model are listed in the Supplementary Information, Table S3. The practical movement was extracted from the dynamic fatigue tester (Popwil Instrument, Hangzhou, China, Model YPS-1) [27], which is listed in the Supplementary Information, Table S4. The experimental voltage output was measured using an oscilloscope (Tektronix, Beaverton, OR, USA, MDO3022) with a 100:1 voltage probe, and one of the electrodes of TENG is grounded due to the voltage probe. The calculated voltage under different loads using the dynamic FEM and analytical model is highly identical, which is reasonable as the basic constitutive relations are exactly the same. Both of them are close to the measured voltage output of the TENG, clearly demonstrating that the dynamic FEM model can be used to calculate the contact mode TENG accurately. The discrepancy between experimental and FEM/analytical results can be attributed to three reasons. Firstly, the simulation parameters extracted from experiments are not perfectly accurate. Secondly, the experimentally measured voltage output curve under a low external load can be very unstable, which leads to much larger discrepancy under a relatively lower eternal load. Lastly, the analytical and FEM results are calculated under the bases that the electric potential has a uniform distribution horizontally. Since the length and width of the tribo-plate are much larger than the maximum displacement in vertical, the TENG is normally treated as a device with two infinite plates with a uniform electric potential between the plates. However, a faint edge effect will still exist in experimental results, which also leads to a discrepancy of the experimental and FEM/analytical results.

3.2. Dynamic Behavior of Sliding Mode TENG Owing to the symmetric geometry of contact mode TENGs, the mesh quality remains very high during movements. However, the case for sliding mode TENGs is quite different due to its asymmetric geometry, thus needs different geometry, meshing method, boundary conditions and optimizations to solve the topology-change issues for accurate simulation. For the existing simulation methods for sliding mode TENGs, the general approach is to assume two materials contact directly with each other and only the non-overlapped areas have surface charge [23,25]; additionally, during simulation, the two tribo-materials must not be totally separated from each other as disappearance of the overlapped areas will result in the topology-change issue as well as the convergence problems. Therefore, a new approach is needed to simulate sliding mode TENGs, particularly the rotating (sliding) mode TENGs, as the moving tribo-material in sliding mode TENGs is periodically totally separated from the fixed one. Similar to what we used in the contact mode case, here we introduce the moving mesh method and air buffer layers for sliding mode TENG simulation. The boundary conditions for the sliding model are illustrated in Figure5a; Materials 1 and 2 have similar configurations as those for the contact mode TENG with an air buffer layer (the 1st air buffer layer) between them. In addition, an extra 2nd air buffer layer is introduced in the model which surrounds Material 1 as shown in Figure5a. The 2nd air bu ffer layer can be divided into three regions: the ones on the left and right sides of Material 1, and the ones above and below Material 1. The air buffer layers above and below Material 1 are meshed with fixed mesh nodal points and the meshes move together with Material 1 during sliding movements, while those meshes in the air buffer layers on the left and right sides of Material 1 deform freely following the rules governed by Formula (6); they expand on one side and shrink on the other side accordingly, with the mesh nodal points remained unchanged when Material 1 moves horizontally, thus eliminating the topology-change issue. The moving mesh of the sliding mode TENG model at different times is illustrated in Figure5b, showing that the meshes in the 2nd air buffer layer of the left side expand and those on the right side shrink when Material 1 moves from state I to III which allows an unchanged topology to be achieved. Sensors 2020,, 20, x 4838 FOR PEER REVIEW 88 of of 14 14

Figure 5. (a) Boundary conditions for sliding mode TENG. (b) Mesh quality deteriorates when Material Figure1 moving 5. from(a) Boundary state I to III.conditions (c) The meshed for sliding geometry mode of TENG. sliding ( modeb) Mesh TENG. quality deteriorates when Material 1 moving from state I to III. (c) The meshed geometry of sliding mode TENG. As emphasized by the black dashed lines in state I of Figure5b, the large translational motion in theThe sliding simulation mode parameters TENG will for lead mesh to meshdensity discontinuity and air gap thickness (i.e., mesh optimizations nodal points are discontinued), listed in the Supplementarywhich happens betweenInformation, top air Table and S5 2nd. The air definitions buffer, as well for the as between air gap and 1st andmesh 2nd density air bu areffer. illustrated The mesh indiscontinuity Figure 5c. The will airlead gap thickness to failure represents of calculation the di whenstance the between electrostatic two tribo-materials, constitutive similar equations to that are forapplied the contact for modelling. mode TENG Here, simulation. we introduce The the mesh charge density continuity for thecondition sliding mode to mitigate TENG theis varied problem by changingas schematically the mesh shown nodal in points Figure on5a. the The correspon charge densityding horizontal remains identical boundaries, and which continuous are marked along the by yellowmoving circles interfaces in Figure no matter 5c. Although where Material thinner 1 moves.air gap thickness and denser mesh nodal points will resultAs inshown more accurate in stateIII simulation of Figure 5results,b, the mesh it takes quality much deteriorates more simulation significantly resources; when therefore, Material 1a trade-offleaves Material is needed. 2, which is different from that of the contact mode TENG simulation due to asymmetric geometryFor the and optimization movement. of Therefore, mesh density, mesh densityvoltage and output air bu underffer thickness different optimization loads with various are necessary mesh densitiesfor accurate is shown simulation. in Figure 6a. The mesh density is determined by the number of the mesh nodal pointsThe at simulationspecific boundaries parameters as the for meshyellow density circles andmarked air gap in Figure thickness 5c. optimizationsIt is clear that aredenser listed meshes in the canSupplementary lead to higher Information, voltage output Table S5.as summarized The definitions in forFigure the air6b, gapwhich and is mesh obtained density using are illustrateda 100-GΩ externalin Figure load.5c. The Moreover, air gap thickness with denser represents meshes, the the distance voltage betweencurve over two time tribo-materials, becomes smoother, similar towhich that experiencesfor the contact more mode spikes TENG with simulation. smaller amplitude The mesh as sh densityown in for Figure the sliding6c. The modeeffect of TENG mesh is density varied on by powerchanging output the meshis shown nodal in points Figure on 6d. the Although corresponding the optimal horizontal load boundaries,remains unchanged which are for marked different by meshyellow densities, circles in the Figure peak5c. power Although slightly thinner increases air gap with thickness denser and meshes, denser as mesh shown nodal in Figure points will6e. result in more accurate simulation results, it takes much more simulation resources; therefore, a trade-off is needed. For the optimization of mesh density, voltage output under different loads with various mesh densities is shown in Figure6a. The mesh density is determined by the number of the mesh nodal points at specific boundaries as the yellow circles marked in Figure5c. It is clear that denser meshes can lead to higher voltage output as summarized in Figure6b, which is obtained using a 100-G Ω external load. Moreover, with denser meshes, the voltage curve over time becomes smoother, which experiences more spikes with smaller amplitude as shown in Figure6c. The e ffect of mesh density on power output is shown in Figure6d. Although the optimal load remains unchanged for di fferent mesh densities, the peak power slightly increases with denser meshes, as shown in Figure6e.

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Figure 6. The simulated (a) voltage and (d) power output with increasing mesh density. (b) The

summarized peak voltage at a 100-GΩ external load with increasing mesh density. (e) The Figure 6. The simulated (a) voltage and (d) power output with increasing mesh density. (b) The Figuresummarized 6. The peak simulated power (outputa) voltage with and increasing (d) power mesh output density. with (c) increasingThe voltage mesh curve density. under different (b) The summarized peak voltage at a 100-GΩ external load with increasing mesh density. (e) The summarized summarizedmesh density. peak voltage at a 100-GΩ external load with increasing mesh density. (e) The peak power output with increasing mesh density. (c) The voltage curve under different mesh density. summarized peak power output with increasing mesh density. (c) The voltage curve under different The voltage output under an open-circuit condition (100 GΩ) with different air gap thicknesses meshThe voltagedensity. output under an open-circuit condition (100 GΩ) with different air gap thicknesses is is shown in Figure 7a. The spiked voltage outputs under movement are attributed to the limited mesh shown in Figure7a. The spiked voltage outputs under movement are attributed to the limited mesh densityThe applied voltage foroutput less undersimulation an open-circuit time. As summ conditionarized (100 in GFigureΩ) with 7b, different the open-circuit air gap thicknesses voltage at density applied for less simulation time. As summarized in Figure7b, the open-circuit voltage at isdifferent shown inair Figure gap thicknesses7a. The spiked increases voltage dramaticaloutputs underly from movement 511.3 V are to attributed 2042.4 V towhen the limited the air mesh gap different air gap thicknesses increases dramatically from 511.3 V to 2042.4 V when the air gap increases densityincreases applied from 2.2 for μ mless (1% simulation of material time. thickness) As summ to 440arized μm in at Figure0.08 s. If7b, a the5% simulationopen-circuit discrepancy voltage at from 2.2 µm (1% of material thickness) to 440 µm at 0.08 s. If a 5% simulation discrepancy in voltage differentin voltage air can gap be thicknessestolerated, the increases optimal dramaticalthickness ofly airfrom gap 511.3 can Vbe toset 2042.4 to ~8.8 V μ whenm for thean accurateair gap can be tolerated, the optimal thickness of air gap can be set to ~8.8 µm for an accurate simulation and increasessimulation from and 2.2 relatively μm (1% shorter of material calculation thickness) time. to 440 μm at 0.08 s. If a 5% simulation discrepancy relatively shorter calculation time. in voltage can be tolerated, the optimal thickness of air gap can be set to ~8.8 μm for an accurate simulation and relatively shorter calculation time.

Figure 7. (a) The simulated voltage output and (b) summarized peak voltage under a 100-GΩ external Figureload. ( c7.) The(a) The comparison simulated of voltage calculated output results and based(b) summarized on dynamic peak FEM voltage model under and previous a 100-GΩ published external load.model, (c) demonstrating The comparison excellent of calculated consistency. results based on dynamic FEM model and previous published Figuremodel, 7.demonstrating (a) The simulated excellent voltage consistency. output and (b) summarized peak voltage under a 100-GΩ external load.For accurate (c) The comparison simulation of and calculated a reasonable results simulationbased on dynamic time, anFEM air model gap thickness and previous of 11 publishedµm and base horizontalmodel,For accurate meshdemonstrating nodalsimulation points excellent and of 60 consistency.a arereasonable then chosen simulation for the time, following an air simulation. gap thickness The of sliding 11 μm mode and baseTENG horizontal results based mesh on nodal the analytical points of calculation,60 are then thatchosen have for already the following been veriﬁed simulation. with experimental The sliding moderesultsFor TENG [23 accurate], are results used simulation to based compare onand withthe a reasonable ouranalytical simulation simulationcalculation, results astime, that depicted anhave air in gapalready Figure thickness7 c,been showing ofverified 11 excellentμm withand baseexperimentalconsistency horizontal between results mesh them,[23], nodal are demonstrating points used toof compare60 are the then high with chosen accuracy our simulation for of the the following dynamic results as FEMsimulation. depicted model. in The It Figure should sliding 7c, be modeshowingnoted thatTENG excellent in thisresults analyticalconsistency based calculationon between the analytical them, and numerical demonst calculation,rating simulation, that the highhave the accuracy tribo-materialsalready ofbeen the dynamicverified of the sliding FEMwith experimentalmodel.mode TENG It should areresults notbe [23], separatednoted are that used totally in tothis compare because analytical thewith calculation analytical our simulation method and numerical results is unable as depictedsimulation, to deal within Figurethe the tribo- total 7c, showingmaterialsseparation excellent of situation. the sliding consistency mode TENG between are them,not separated demonst totallyrating becausethe high the accuracy analytical of the method dynamic is unable FEM model.to dealFor withIt better should the demonstration total be notedseparation that of situation. thein this advantages analytical of thecalculation dynamic and FEM numerical model, a 3Dsimulation, rotating-type the TENGtribo- materialsis simulatedFor better of the as shownslidingdemonstration inmode Figure TENG 8ofa, the which are advantages not utilizes separated nylon of thetotally and dynamic PTFE because as FEM arrayed the analyticalmodel, bar typea method3D tribo-materials rotating-type is unable toTENGin deal air atmosphere. iswith simulated the total Theas separation shown PTFE in is situation.Figure ﬁxed and 8a, nylonwhich rotatesutilizes anticlockwise. nylon and PTFE The as voltagearrayed outputbar type under tribo- a For better demonstration of the advantages of the dynamic FEM model, a 3D rotating-type TENG is simulated as shown in Figure 8a, which utilizes nylon and PTFE as arrayed bar type tribo-

Sensors 2020, 20, x FOR PEER REVIEW 10 of 14

Sensorsmaterials2020 ,in20 ,air 4838 atmosphere. The PTFE is fixed and nylon rotates anticlockwise. The voltage output10 of 14 under a 50-MΩ external load is shown in Figure 8b, which varies periodically as the top tribo-layer rotates.50-MΩ externalInset images load isillustrate shown inthe Figure top 8tribo-barb, which variesposition periodically and the electric as the toppotential tribo-layer distribution rotates. between two tribo-materials over one rotation. This clearly shows the capability of calculating Inset images illustrate the top tribo-bar position and the electric potential distribution between two complex 2D/3D geometries dynamically, demonstrating the superiority of our dynamic FEM model. tribo-materials over one rotation. This clearly shows the capability of calculating complex 2D/3D Multiple spikes in the voltage output curve are generated when the arrayed bar type tribo-material geometries dynamically, demonstrating the superiority of our dynamic FEM model. Multiple spikes in approaches and leaves. the voltage output curve are generated when the arrayed bar type tribo-material approaches and leaves.

Figure 8. (a) The illustration of a 3D disk TENG with a bar type tribo-material. (b) The voltage output Figure 8. (a) The illustration of a 3D disk TENG with a bar type tribo-material. (b)The voltage output and electric potential distribution under a 50-MΩ external load. and electric potential distribution under a 50-MΩ external load. 3.3. Design of TENG Performance by the Dynamic FEM Model 3.3. Design of TENG Performance by the Dynamic FEM Model As shown above, the dynamic FEM model can be used to simulate the output power of TENGs as powerAs sources shown asabove, did bythe most dynamic of the FEM previous model work. can be Here, used weto simulate will show the the output extra power capability of TENGs of the asdynamic power FEMsources model as did which by canmost be of utilized the previous for designing work. Here, a TENG we with will dishowfferent the performance extra capability/properties of the dynamicor a new typeFEM of devicemodel for which sensing can application. be utilized for designing a TENG with different performance/propertiesRectangular shapes or are a commonlynew type of used device for for most sensing TENG-based application. sensors owing to the easiness of designRectangular and fabrication, shapes we are will commonly show that used the for dynamic most TENG-based FEM model allowssensors us owing to design to the a easiness triangular- of designshaped and TENG fabrication, sensor with we betterwill show performance. that the dy Thenamic geometry FEM model of a common allows TENGus to design is shown a triangular- in inset of shapedFigure9 aTENG used sensor in our FEMwith model.better performance. Material 1 (blue) The geometry is fixed, and of a Material common 2 (red)TENG is is sliding shown forward in inset ofand Figure backward 9a used laterally. in our FEM Figure model.9a shows Material the output1 (blue) voltageis fixed, of and the Material TENG with2 (red) an is external sliding forward load of 10and12 backwardΩ (near an laterally. open circuit Figure condition), 9a shows andthe output the dynamic voltage process of the TENG can be with seen an in external the Supplementary load of 1012 ΩInformation, (near an open Movie circuit S1. Thecondition), peak and and valley the dynamic voltage outputsprocess occurcan be when seen twoin the materials Supplementary are fully Information,overlapped and Movie separated, S1. The respectively. peak and Itvalley is clear voltage that the outputs voltage occur output when curves two are materials highly symmetric, are fully overlappedi.e., the voltage and curves separated, are identical respectively. when theIt is two clear materials that the approach voltage to output and leave curves from are each highly other. symmetric,Figure9b is thei.e., comparisonthe voltage ofcurves the two are halvesidentical of awh voltageen the output two materials pulse. The approach blue curve to and represents leave from the voltageeach other. output Figure when 9b theis the two comparison materials move of the from two the halves most of separated a voltage position output topulse. the fully The overlappedblue curve position,represents and the the voltage red curve output represents when the the two voltage materials output move under from opposite the most movement. separated position to the fully However,overlapped when position, the and external the red load curve decreases represents to 10 the11 voltageΩ, the output shape ofunder voltage opposite output movement. curve is deformed, as shown in Figure9c. Although the peak voltage still occurs when the two materials are fully overlapped, the voltage output curves are significantly different when the two materials approach to (blue) and leave (red) from each other, as shown in Figure9d. The discharge e ffect of the external load is severer when the two materials separate from each other. This can be utilized to design a sensor to detect whether the object is moving away or approaching. However, due to the symmetric structures

Sensors 2020, 20, 4838 11 of 14 of the two tribo-plates, it is still not possible to distinguish whether the object (i.e., the tribo-material) is moving from the leftmost or rightmost position as shown in Figure9a,c, as the curve shapes of every cycleSensors are 2020 exactly, 20, x FOR the PEER same. REVIEW 11 of 14

Figure 9.9. The voltagevoltage outputoutput ofof the the rectangular rectangular patterned patterned TENG TENG under under external external load load of (ofa) ( 10a)12 10and12 and (c) 10(c)11 10Ω11. Ω The. The voltage voltage output output of of one one cycle cycle under under external external load load of of (b ()b 10) 101212and and ( d(d)) 10 101111 ΩΩ,, demonstrating the voltagevoltage changechange of rectangularrectangular patterned TENG under lower external load and can be used in sensing applicationsapplications to to decide decide whether whether the the moving moving tribo-material tribo-material is under is under approaching approaching or leaving or leaving state. state. Through the simulations using the dynamic FEM model, the shape of the tribo-plate is found to changeHowever, the shape when of voltage the external output load curves, decreases so that theto 10 approaching11 Ω, the shape from of di ffvoltageerent directions output curve can beis distinguisheddeformed, as shown as shown in Figure in Figure 9c. Although10a inset. the All peak the simulation voltage still configurations occurs when arethe thetwo same materials as those are infully Figure overlapped,9 except thatthe thevoltage fixed output tribo-plate curves has aare triangular significantly shape. different The output when voltage the two curve materials under aapproach 1012 Ω external to (blue) load and leave is shown (red) in from Figure each 10 other,a, and as the shown dynamic in Figure process 9d. The can bedischarge clearly effect seen inof the Supplementaryexternal load is Information,severer when Movie the two S2. Thematerials peak andsepa valleyrate from voltage each output other. still This occur can atbe almost utilized fully to overlappeddesign a sensor and to separated detect whether positions, the respectively.object is moving However, away or the approaching. curve shapes However, for different due period to the (Peaksymmetric 1 and structures 2) are slightly of the ditwofferent tribo-plates, under the it is 10 still12 Ω notload possible as shown to distinguish in Figure whether10b. For the a clearer object demonstration,(i.e., the tribo-material) the voltage is moving output underfrom the a 10 leftmost11 Ω is shown or rightmost in Figure position 10c and as the shown voltage in Figure output 9a,c, curves as arethe showncurve shapes in Figure of every 10d whencycle are the exactly upper tribo-platethe same. approaches from the leftmost position (blue), leavesThrough to the rightmost the simulations position using (red), the approaches dynamic fromFEM themodel, rightmost the shape position of the (green) tribo-plate and leaves is found to the to leftmostchange the position shape (magenta).of voltage output The reason curves, why so curve that the shape approaching changes in from Figure different 10b,d is directions that the charges can be transferdistinguished quicker as undershown a in smaller Figure load, 10a inset. which All means the simulation the charge configurations flow (voltage output are the curve) same isas muchthose morein Figure sensitive 9 except to structural that the fixed shape tribo-plate of TENGs. has When a triangular the upper shape. tribo-plate The output approaching voltage from curve rightmost under a or1012 leftmost Ω external position, load itis will shown experience in Figure diff 10a,erent and incoming the dynamic shapes process of the lower can be triangular clearly seen tribo-plate, in the andSupplementary the charge flow Information, can sense Movie the subsequent S2. The peak electric and potential valley voltage distribution output change still occur better at duealmost to lower fully eternaloverlapped load. and It is clearseparated that more positions, information respectively. can be obtainedHowever, from the thecurve voltage shapes output for curvesdifferent by period TENG shape(Peak optimization,1 and 2) are slightly which can different easily distinguishunder the 10 the12 movingΩ load as situations. shown in All Figure the results 10b. For have a provenclearer thatdemonstration, the dynamic the FEM voltage model output can accurately under a simulate1011 Ω is theshown time-varying in Figure performance10c and the ofvoltage TENGs output with complexcurves are structures. shown in Furthermore,Figure 10d when based the on upper this universal tribo-plate FEM approaches model, the from genetic the algorithmleftmost position can be applied(blue), leaves to automatically to the rightmost design theposition TENG (red), structure approaches for tuned from output the curve rightmost in multi-functional position (green) sensing and applications,leaves to the leftmost which is position under research. (magenta). The reason why curve shape changes in Figure 10b,d is that the charges transfer quicker under a smaller load, which means the charge flow (voltage output curve) is much more sensitive to structural shape of TENGs. When the upper tribo-plate approaching from rightmost or leftmost position, it will experience different incoming shapes of the lower triangular tribo-plate, and the charge flow can sense the subsequent electric potential distribution change better due to lower eternal load. It is clear that more information can be obtained from the voltage output curves by TENG shape optimization, which can easily distinguish the moving situations. All the results have proven that the dynamic FEM model can accurately simulate the time-

Sensors 2020, 20, x FOR PEER REVIEW 12 of 14 varying performance of TENGs with complex structures. Furthermore, based on this universal FEM model, the genetic algorithm can be applied to automatically design the TENG structure for tuned outputSensors 2020 curve, 20, 4838in multi-functional sensing applications, which is under research. 12 of 14

Figure 10. Voltage output of the triangular patterned TENG under an external load of (a) 1012 and Figure 10. Voltage output of the triangular patterned TENG under an external load of (a) 1012 and (c) (c) 1011 Ω. Voltage output of two different cycles under an external load of (b) 1012 and (d) 1011 Ω, 1011 Ω. Voltage output of two different cycles under an external load of (b) 1012 and (d) 1011 Ω, demonstrating the voltage curve of triangular patterned TENG contains more information than that demonstrating the voltage curve of triangular patterned TENG contains more information than that of rectangular patterned TENG, and the dynamic FEM model can be used to optimize the TENG of rectangular patterned TENG, and the dynamic FEM model can be used to optimize the TENG tribo- tribo-material shape in sensing applications for multi-functional purposes. material shape in sensing applications for multi-functional purposes. 4. Conclusions 4. Conclusions A universal dynamic FEM model has been proposed, which is capable of simulating TENGs with complexA universal 2D/3D geometries dynamic FEM for time-varying model has electricbeen propos outputs.ed, Awhich FEM modelis capable based of onsimulating an air buff TENGser layer withand movingcomplex mesh 2D/3D method geometries are used for to time-varying eliminate the electric topology-change outputs. A issuesFEM duringmodel based simulation on an with air bufferpractical layer movements. and moving Then, mesh the method dynamic are FEM used model to eliminate is systematically the topology-change optimized with issues different during air simulationbuffer thicknesses with practical and mesh movements. densities. The Then, simulated the dynamic results FEM are compared model is withsystematically the experimental optimized data withand calculatingdifferent air results buffer based thicknesses on other and methods, mesh densi showingties. The excellent simulated consistency. results are A 3Dcompared disk TENG with with the experimentala bar type tribo-plate data and iscalculating dynamically results simulated based on to furtherother methods, demonstrate showing the capabilityexcellent consistency. of calculating A 3Dcomplex disk TENG 3D TENG with geometries. a bar type Moreover,tribo-plate a is dynamic dynamically output simulated simulation to basedfurther on demonstrate rectangular andthe capabilitytriangular of shaped calculating tribo-plates complex has 3D been TENG carried geometries. out to present Moreover, the possibilitya dynamic of output purposely simulation tuned basedTENG on electric rectangular output and curves triangular for multi-functional shaped tribo-plat sensinges has applications been carried using out to the present dynamic the FEM possibility model. ofAll purposely results show tuned that TENG the dynamicelectric output FEM curves model fo hasr multi-functional the potential in sensing assisting applications structural using design the of dynamicTENGs with FEM practical model. experimentalAll results show setups, that asthe well dynamic as accelerating FEM model the proceedinghas the potential of practical in assisting TENG structuralapplications design in the of future.TENGs with practical experimental setups, as well as accelerating the proceeding of practical TENG applications in the future. Supplementary Materials: The following are available online at http://www.mdpi.com/1424-8220/20/17/4838/s1, SupplementaryTable S1: Parameters Materials: used forThe contact following mode are simulationavailable online in cosine at www.mdpi.com/xxx/s1, movement, Table S2: Simulation Table S1: Parameters time under different air gap thickness. (Simulation is processed using parameters shown in Table S1 with 10 MΩ external usedload. for The contact mapped mode mesh simulation for vertical in and cosine horizontal movement boundary, Table is 10S2: and Simulation 50, respectively.), time under Table different S3: Parameters air gap thickness.used for contact (Simulation mode is simulation processed in using practical parameters movement, shown Table in S4:Table Fitted S1 with curve 10 formulas MΩ external for practical load. The movement, mapped meshTable for S5: vertical Parameters and usedhorizontal for sliding boundary mode is simulation 10 and 50 in, respectively.), cosine movement, Table Video S3: Parameters S1: The rectangular used for contact shaped modeTENG simulation dynamic process in practical and voltage movement, output Table under S4: 1 TFittΩedload, curve Video formulas S2: The for triangular practical shaped movement, TENG Table dynamic S5: Parametersprocess and used voltage for outputsliding under mode 1 simulation TΩ load. in cosine movement, Video S1: The rectangular shaped TENG dynamicAuthor Contributions: process and voltageJ.C.: Conceptualization, output under 1 TΩ Methodology, load, Video Writing—OriginalS2: The triangular draft shaped preparation. TENG dynamic J.W.: Validation. process andW.X.: voltage Writing—Reviewing output under 1 and TΩEditing. load. S.D., J.L.: Supervision. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the following programs: National Key R&D Program of China (no.2018YFB2002500), National Natural Science Foundation of China (no. 61904042, 61974037). Sensors 2020, 20, 4838 13 of 14

Conflicts of Interest: The authors declare no conflict of interest. Availability of Data: The data that support the findings of this study are available from the corresponding author upon reasonable request.

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