Freestanding Triboelectric Nanogenerator Research Articles

Nonlinear dynamics study of freestanding triboelectric nanogenerator system

As a nonlinear dynamic system, the dynamic equation of triboelectric nanogenerator system is not only difficult to accurately establish, but also difficult to solve. The output signals of triboelectric nanogenerator system depends on the initial conditions of the system, which reflects the dynamic behavior of the system. Currently, there is little research on using the output signals to study the dynamic behavior of triboelectric nanogenerator system. Therefore, a dynamic simulation model of a freestanding triboelectric nanogenerator (F-TENG) system was established using COMSOL software. The mathematical model of the F-TENG system was fitted. Using chaos theory and its phase-space reconstruction technology, the phase-space trajectories of the F-TENG system were reconstructed through voltage signals under external factors, and the dynamic behavior of the F-TENG system was discussed and studied. Finally, validation experiments were carried out. The research shows that with the variation of internal factors and operating frequency, the mathematical model of the F-TENG system remains basically unchanged, and the variation law of output characteristics also remains basically unchanged. The F-TENG system is in periodic motion; with the variation of external factors such as resistance and friction layer spacing, the mathematical model of the F-TENG system will evolve in a complex direction, and the output characteristics will gradually distort. The F-TENG system will evolve from periodic motion to chaotic motion. The research results not only reveal the dynamic behavior and enrich the nonlinear dynamic theory of triboelectric nanogenerator system, but also provide theoretical guidance for increasing the working bandwidth and stability of triboelectric nanogenerator system.

Controllable Manipulation of Large-Volume Droplet on Non-Slippery Surfaces Based on Triboelectric Contactless Charge Injection.

Controllable droplet manipulation is crucial in diverse scientific and engineering fields. Traditional electric-based methods usually rely on commercial high-voltage (HV) power sources, which are typically bulky, expensive, and potentially hazardous. The triboelectric nanogenerator (TENG) is a highly studied device that can generate HV output with limited current, showing great potential in droplet manipulation applications. However, current TENG-based approaches usually utilize traditional free-standing TENGs that produce short-pulsed alternating-current signals. This limitation hinders continuous electrostatic forces necessary for precise droplet control, leading to complex circuitry and suboptimal droplet motion control in terms of volume, distance, direction, and momentum. Here, a triboelectric contactless charge injection (TCCI) method employing a novel dual-functional triboelectric nanogenerator (DF-TENG), is proposed. The DF-TENG can produce both high voltage and constant current during unidirectional motion, enabling continuous corona discharges for contactless charge injection into the droplets. Using this method, a large-volume droplet (3000 µL) can be controlled with momentum up to 115.2 g mm s-1, quintupling the highest value recorded by the traditional methods. Moreover, the TCCI method is adaptable for a variety of non-slippery substrates and droplets of different compositions and viscosities, which makes it an ideal manipulation strategy for droplet transport, chemical reactions, and even driving solids.

Performance optimization and comparison of vertical motion-based triboelectric nanogenerators.

The vertical motion configuration is a common design in triboelectric nanogenerators (TENGs) for energy harvesting; however, the performance optimization and comparison are still vague between various vertical motion-based structures. In this paper, time-averaged power density is defined as a metric to compare the power output performances of vertically structured TENGs, including contact mode and freestanding mode. To ensure comparisons under the same circumstances, a novel sandwich-structured dielectric layer was designed to maintain a stable and consistent surface charge density, with an extra rotating triboelectric nanogenerator working as a charge pump. We also investigated the impact of parasitic capacitance, which is a primary source of error in theoretical optimization. The freestanding TENG (FTENG) with a single dielectric layer demonstrates superior power performance, even when accounting for the influence of parasitic capacitance. This work provides valuable insights and guidelines for the design of high-performance mechanical energy harvesting devices.

Maximizing the energy conversion of triboelectric nanogenerator through the synergistic effect of high coupling and dual-track circuit for marine monitoring

The wave energy harvesting efficiency (EHE) and electrical energy storage efficiency (ESE) significantly impact ocean power at the front-end and back-end stages, respectively. In this work, to maximize the overall energy conversion affected by these two factors, a clip-like structured pendulum coupled nanogenerator (CP-CNG) integrated with a dual-track circuit (DTC) is elaborately designed to address poor energy conversion of the TENGs for marine monitoring. The optimized EHE was realized through coupling one freestanding triboelectric nanogenerator (FR-TENG) unit and two electromagnetic generator (EMG) units into two contact-separation triboelectric nanogenerator (CS-TENG) units. The space utilization rate of CP-CNG can be as high as 91.9%. Meanwhile, increased ESE is achieved by integrating DTC as voltage regulators, which perform backend energy management for CS-TENG and EMG, respectively. It is worth noting that for a 1 mF capacitor, the stored energy via the cooperation of CP-CNG and DTC can reach 60.7 mJ in 110 s, which is about 164 times that of CS-TENG (0.37 mJ) coupling with FR-TENG and EMG and 1.6 times that of CS-TENG (36.8 mJ) with buck circuit, demonstrating excellent synergistic effects. Owing to the synergistic effect, one CP-CNG can continuously drive four thermohygrometers under simulated water wave conditions. In additional, a hazard alarm system, including an immersion sensor, Bluetooth and gateway support, can also be powered by one CP-CNG successfully. This work develops a state-of-the-art concept for maximum energy conversion of TENGs, which should have a profound impact on the design of high-performance TENGs in the future.

Investigation on the tribological properties and electrification performance of grease-lubricated triboelectric nanogenerators

Compared with lubricating oil, grease can firmly adhere to the lubricated surface without loss even on the vertical surface, which is more conducive to improving the durability of triboelectric nanogenerators (TENGs) in practical engineering applications by reducing material wear. However, the correlation between property parameters of grease and triboelectrification is still unclear. In this paper, rotary freestanding TENG with the most severe wear among the working modes of TENGs is taken as the research subject. First, the tribological properties and electrification performance of TENGs lubricated by different greases are studied, and then the effects of the dielectric constant, shear-thinning behavior and cone penetration on the electrical output as well as durability of TENG are explored to reveal the triboelectrification mechanism of the grease-lubricated interface. The results show that, the electrical output of TENG lubricated by the grease with a low dielectric constant can increase by more than 3.5 times compared to dry friction, where the thickener in the grease participates in triboelectrification at the grease-lubricated interface. With increasing sliding distance, the electrical output increases first and then decreases, and the durability is related to the shear-thinning behavior of grease. For greases with similar relative dielectric constant, with increasing cone penetration, the maximum electrical output of TENG decreases, but its durability is improved. This study provides a new approach to improve the electrical output and durability of TENG simultaneously, which further promotes the practical applications of TENGs.

A Self‐Decoupled and High‐Resolution 2D Displacement Sensor Based on Triboelectric Nanogenerator for Manipulator Precision Positioning

Abstract2D displacement sensor (2DDS) is significant in precision manufacturing positioning, machine condition monitoring, robotic manipulation, and human–computer interaction system. However, the reported 2DDSs have severe limitations, such as low accuracy, poor decoupling, and lack of smart signal analysis. Herein, a self‐decoupled and high‐resolution 2DDS based on two freestanding triboelectric nanogenerators (F‐TENGs) is presented. This sensor achieves self‐decoupling by two orthogonal and independent 1D displacement sensors with low‐cost grating‐structured PCB. The test results of the sensor exhibit a high accuracy ≥99.06% (1D) and 98.94% (2D). Also, the experimental and simulation results demonstrate that this sensor has a high resolution of 200 µm and the function of initial position identification. A 2D displacement sensing system is developed that is capable of collecting F‐TENGs’ open‐circuit voltages in real‐time and performing 2D trajectory synthesis and display. This work expands the potential application of the TENG‐based 2DDS in robotic precision machining.

Dual-mode sensor for intelligent solution monitoring: Enhancing sensitivity and recognition accuracy through capacitive and triboelectric sensing

Monitoring solution parameters is of utmost importance in various industries and daily applications. However, the challenge lies in using a single sensor to effectively monitor different parameters in the solution. In this study, a dual-mode sensor is proposed, capable of monitoring multiple solution parameters combined with deep learning method. The fabrication process of the dual-mode sensor is simple, involving a substrate, interdigital electrodes, and a dielectric layer. The sensitivity of the dual-mode sensor is improved by increasing the dielectric constant of the dielectric layer and optimizing the design of the interdigital electrodes. Under the capacitive sensing mode, the sensor effectively identifies solution type by detecting capacitance changes due to the conductivity of the mixed solution. Under the triboelectric sensing mode, the sensor exhibits high sensitivity to solution concentration through the coupling of the capacitive enhancement effect and the triboelectric effect. An electric switch is incorporated into the design to control the signal acquisition of the dual-mode sensor. By combining the deep learning method with the dual-mode sensor, high recognition accuracies have been achieved for both solution type and concentration, with average accuracies exceeding 95%. Furthermore, the dual-mode sensor is not limited to monitoring liquid droplets; it can also be used for monitoring the types of liquids in bottles. In addition, an intelligent system is developed to visualize the intelligent monitoring process. This work not only contributes to a better understanding of the underlying mechanisms of planar capacitive sensors (PCS) and free-standing triboelectric nanogenerators (FS-TENG), but also presents a promising method for intelligent solution monitoring.

Grease-lubricated triboelectric instantaneous angular speed sensor integrated with signal processing circuit for bearing fault diagnosis

The triboelectric sensor can be integrated with the rolling bearing to diagnose bearing faults by monitoring the periodic fluctuation of instantaneous angular speed, yet continuous dry friction between materials will reduce its signal-to-noise ratio (SNR). Moreover, the signal processing modules used by previous triboelectric sensors need additional wires to transmit the signal, and thus affect the reliability of the system. In this manuscript, a wireless grease-lubricated triboelectric instantaneous angular speed sensor (GL-TEIASS) integrated with the signal processing circuit for bearing fault diagnosis is proposed based on rotary freestanding triboelectric nanogenerators (TENGs). First, electrical insulating grease is presented as an ideal candidate lubricant used in the GL-TEIASS. Next, by establishing the charge density-dependent electromechanical model of grease-lubricated TENG, optimal structural parameters for maximum signal-to-noise ratio and angular resolution as well as minimum friction torque of the GL-TEIASS can be obtained. Moreover, the kurtosis-guided local polynomial fitting method is employed to extract the signal fluctuation caused by bearing faults. The results show that, compared to dry friction, the mass loss of the polymer under grease lubrication decreases by 91.7 % and the electrical output increases by 4.0 times. The durability of the GL-TEIASS in fault diagnosis is improved by at least 2.8 times compared with that of the sensor operating under dry friction. The error between the angular speed measured by the GL-TEIASS and a commercial sensor is less than 0.731 %, and the SNR of the output signal from in-situ monitoring by the GL-TEIASS can reach 39.1 dB, which is 4.9 times higher than that of vibration signal commonly used in fault diagnosis. The designed GL-TEIASS has good application prospects in self-sensing and self-diagnosis of operation state for smart bearings.

High-performance omnidirectional-sliding hybrid nanogenerator for self-powered wireless nodes

Energy-autonomous smart electronics have been the focus of the next generation of the Internet of Things. Recently, advanced power technology with sustainable energy supply and pollution-free characteristics has become a research hotspot. Herein, to realize a reliable and unattended power unit, we propose a high-performance omnidirectional-sliding triboelectric-electromagnetic hybrid nanogenerator (OS-TEHNG) to convert the mechanical energy into electricity. The free-standing triboelectric nanogenerator (TENG) achieves a charge transfer of 24.4 μC in one cycle and a short-circuit current of 0.36 mA after optimizing the electrode structure. The TENG with 130 kΩ impedance allows efficient charging of energy storage units without complex power management modules (PMMs). The electromagnetic part achieves an open-circuit voltage of 300 V after optimization. OS-TEHNG achieves a peak power density of 1568.4 W/m3 and an average power density of 352.3 W/m3 at 2 Hz. As a result, OS-TEHNG charges a 1 mF capacitor to 46 V within 8 s. The strong power supply capability allows OS-TEHNG to charge smartwatches and phones. Furthermore, a completely self-powered wireless keyboard with a PMM and an energy storage unit based on OS-TEHNG is developed. The wireless self-powered keyboard sends data 213 times after only sliding the OS-TEHNG once. Finally, OS-TEHNG is successfully demonstrated to drive a 40 mW wireless sensor node with a 1.3-inch OLED screen in continuous operation. This work represents a significant advance toward self-powered microsystems and practical power sources.

Structure-Crack Detection and Digital Twin Demonstration Based on Triboelectric Nanogenerator for Intelligent Maintenance.

The accomplishment of condition monitoring and intelligent maintenance for cantilever structure-based energy harvesting devices remains a challenge. Here, to tackle the problems, a novel cantilever-structure freestanding triboelectric nanogenerator (CSF-TENG) is proposed, which can capture ambient energy or transmit sensory information. First, with and without a crack in cantilevers, the simulations are carried out. According to simulation results, the maximum change ratios of natural frequency and amplitude are 1.1% and 2.2%, causing difficulties in identifying defects by these variations. Thus, based on Gramian angular field and convolutional neural network, a defect detection model is established to achieve the condition monitoring of the CSF-TENG, and the experimental result manifests that the accuracy of the model is 99.2%. Besides, the relation between the deflection of cantilevers and the output voltages of the CSF-TENG is first built, and then the defect identification digital twin system is successfully created. Consequently, the system is capable of duplicating the operation of the CSF-TENG in a real environment, and displaying defect recognition results, so the intelligent maintenance of the CSF-TENG can be realized.

Integrated Real-Time Pneumatic Monitoring System With Triboelectric Linear Displacement Sensor

With the continuous development of mechanical automation field, its monitoring technology is also changing with each passing day. Pneumatic technology is one of the important ways to realize mechanical automation. Here, the integrated real-time pneumatic monitoring system (PMS) is proposed, which is composed of a triboelectric linear displacement sensor (TLDS) and a cylinder. The resolution of TLDS is 100 µm, which is composed of a slider and a stator. According to theory of freestanding triboelectric nanogenerator, the working principle of TLDS is explained. Therefore, the proposed PMS can realize displacement and speed monitoring of the full stroke of the cylinder. The experiment results show that the PMS enabled accurate monitoring of cylinder displacement and speed under different pressure conditions, and the mean error rate of PMS is less than 2%. In addition, to fulfill the actual demands of the pneumatic industry, the real-time hardware processing module is designed to realize real-time monitoring. Finally, the PMS still has stable monitoring performance after 6 h (about 4 km) continuous operation. This work successfully explored the application of triboelectric sensors in pneumatic system and reached the requirements of industrial applications.

A cantilever-structure triboelectric nanogenerator for energy harvesting and defect detection via long short-term memory network.

The electric signals of cantilever energy harvesting devices with/without a crack were mainly obtained by external sensors, so detecting device damage on a large scale is difficult. To tackle the issue, a cantilever-structure freestanding triboelectric nanogenerator (CSF-TENG) device was proposed, which can scavenge ambient energy and act as a self-powered sensor. Firstly, the relation between the peak-to-peak voltage and amplitude of the CSF-TENG was established. Next, the output performance of the CSF-TENG was measured. Then, depending on electric signals output by the CSF-TENG, a cantilever defect identification model was built by using the wavelet packet and long short-term memory (LSTM) algorithms. The experimental results manifest that the accuracy of the model is about 98.6%. Thus, the CSF-TENG with a crack can be detected timely due to its self-monitoring ability, which is of great significance for the development of self-powered sensor networks.

Quantifying Output Power and Dynamic Charge Distribution in Sliding Mode Freestanding Triboelectric Nanogenerator

AbstractThe general concept of dielectric polarization density (P) is a macroscopic description of the underlying microscopic structure in the presence of an external electric field and polarized materials itself. A time‐dependent polarization PS induced by a non‐electric field also exists in practice due to the mechanically driven relative motion of media owing to the effects of contact electrification or piezoelectricity. In this work, the starting point is to consider the difference between P and PS, and how PS enters into the governing equations, since it describes the dielectric polarization density without an applied electric field, finally modifying the constitutive relations, Faraday's law, and Maxwell's equations. On this background, a 3D mathematical‐physical model for the sliding mode freestanding triboelectric nanogenerators (TENGs) is established that is taken as an example to confirm the relationship of free charge distribution and dynamics of output power. What needs to be emphasized is that the method of segmented uniform charge distribution is effective and the physical basis for modeling construction and analysis. Finally, we summarized the mathematical‐physical models of TENGs in rectangular coordinates, cylindrical coordinates, and spherical coordinates, building a bridge to reveal the underlying principle behind the microscopic polarization and energy conversion.

A Periodic Wetting Surface Driven by Triboelectric Nanogenerator for Efficient Postimpact Droplet Collection

AbstractThe phenomenon of droplet impact is widely observed in nature and industrial processes. No matter the intrinsic wettability (hydrophobic, hydrophilic, and superhydrophobic) of the surface, the postimpact droplets tend to rebound or splash. The droplet impact dynamics have been well investigated but the inhibition of the rebounding or splashing of the postimpact droplet requires further exploration. This paper proposes a periodic wetting surface (PWS) driven by a triboelectric nanogenerator (TENG) for efficient postimpact droplet collection. With the high‐voltage electric signal generated from a rotating freestanding triboelectric nanogenerator (RF‐TENG), the wettability of an interdigital electrodes‐based electrowetting‐on‐dielectric (EWOD) surface can be changed periodically. The droplet impacts on the PWS show oscillating sliding motion that compensates the kinetic energy for droplet rebounding or splashing. As compared to pure hydrophobic or hydrophilic surfaces, the PWS shows the best droplet collection performance. The effects of the electric signal of the RF‐TENG such as open‐circuit voltage (0.44–3.00 kV) and frequency (0–60 Hz), droplet contents such as ions type and concentration of the droplet on the postimpact droplet collection efficiency are discussed. Finally, a practical application is demonstrated by the TENG driven PWS for real‐time and high‐efficiency collection of multiple postimpact droplets.

A Self-Powered Dielectrophoretic Microparticle Manipulation Platform Based on a Triboelectric Nanogenerator.

Lab-on-a-chip systems aim to integrate laboratory operations on a miniaturized device with broad application prospects in the field of point-of-care testing. However, bulky peripheral power resources, such as high-voltage supplies, function generators, and amplifiers, hamper the commercialization of the system. In this work, a portable, self-powered microparticle manipulation platform based on triboelectrically driven dielectrophoresis (DEP) is reported. A rotary freestanding triboelectric nanogenerator (RF-TENG) and rectifier/filter circuit supply a high-voltage direct-current signal to form a non-uniform electric field within the microchannel, realizing controllable actuation of the microparticles through DEP. The operating mechanism of this platform and the control performance of the moving particles are systematically studied and analyzed. Randomly distributed particles converge in a row after passing through the serpentine channel and various particles are separated owing to the different DEP forces. Ultimately, the high-efficiency separation of live and dead yeast cells is achieved using this platform. RF-TENG as the power source for lab-on-a-chip exhibits better safety and portability than traditional high-voltage power sources. This study presents a promising solution for the commercialization of lab-on-a-chip.

Improved pharmacodynamics of epidermal growth factor via microneedles-based self-powered transcutaneous electrical stimulation

Epidermal growth factor is an excellent drug for promoting wound healing; however, its conventional administration strategies are associated with pharmacodynamic challenges, such as low transdermal permeability, reduction, and receptor desensitization. Here, we develop a microneedle-based self-powered transcutaneous electrical stimulation system (mn-STESS) by integrating a sliding free-standing triboelectric nanogenerator with a microneedle patch to achieve improved epidermal growth factor pharmacodynamics. We show that the mn-STESS facilitates drug penetration and utilization by using microneedles to pierce the stratum corneum. More importantly, we find that it converts the mechanical energy of finger sliding into electricity and mediates transcutaneous electrical stimulation through microneedles. We demonstrate that the electrical stimulation applied by mn-STESS acts as an “adjuvant” that suppresses the reduction of epidermal growth factor by glutathione and upregulates its receptor expression in keratinocyte cells, successfully compensating for receptor desensitization. Collectively, this work highlights the promise of self-powered electrical adjuvants in improving drug pharmacodynamics, creating combinatorial therapeutic strategies for traditional drugs.

Ultra-high-speed hybrid ceramic triboelectric bearing with real-time dynamic instability monitoring

The reliability and stability of bearing operation are crucial factors limiting the performance of high-speed rotating machinery. In this study, an ultra-high-speed hybrid ceramic rolling element triboelectric bearing (US-HCTEB) was developed to provide real-time dynamic behavior and stability monitoring. Herein, we adopted a floating rolling–sliding combination freestanding mode that ensures bearing structural integrity. Furthermore, a crown-shaped cage was employed with an opening, allowing the ceramic rolling element to be used as a dielectric material that was coupled with a sector-shaped interdigital electrode set on the bearing end cover to form a floating freestanding triboelectric nanogenerator (TENG). The rolling element self-rotated and revolved owing to the traction of the raceways, sweeping the electrodes to generate an alternating current. Additionally, the superiority and reliability of the US-HCTEB were demonstrated using a 30 million cycle durability test and an ultra-high rotating speed test at 16000 rpm, which far exceeds the capabilities of previously reported triboelectric bearings. The US-HCTEB output was then evaluated considering variable working conditions, structural optimization, and the surrounding environment. Dry contact lubrication and low humidity were found to be beneficial for the output performance. The spectra of the output current and the statistics describing the rolling element instantaneous speed suggest that the high-speed heavy radial load of the US-HCTEB could reduce overall skidding at the cost of increased instability. Subsequently, an extremely fast acceleration and deceleration test program was conducted on the US-HCTEB to evaluate its performance under the complex and nonstationary conditions in which high-speed bearings operate. The results revealed that the US-HCTEB not only achieved real-time and high-resolution dynamic behavior identification but also exhibited high reliability as it functioned appropriately until bearing failure. Thus, the proposed high-precision US-HCTEB can serve as an essential basis for the development of smart rolling bearings.

Grating‐Structured Freestanding Triboelectric Nanogenerator for Self‐Powered Acceleration Sensing in Real Time

AbstractAcceleration sensors have wide applications in earthquake warning, human motion recognition, vehicle restraint system, etc. However, the existing commercial acceleration sensors have some limitations on needing an external power supply, high fabrication cost, and small signal when self‐powered. Here a grating‐structured freestanding triboelectric nanogenerator (GF‐TENG) capable of sensing displacements, velocities, and accelerations in real‐time is presented with self‐powered, low cost, and sufficiently large signal. The slider with grating‐structured electrodes of GF‐TENG sliding over the stator with another grating‐structured electrode generates the periodic open‐circuit voltage due to electrostatic induction. By recognizing the shape of open‐circuit voltage, it could sense the acceleration in real time even at scales down to hundred microns through systematic optimization of simulations and experiments. Furthermore, the acceleration sensing range could be expanded to the desired ranges, such as 5.0 to 45.0 m s–2, by assembling springs and GF‐TENG into a grating‐structured TENG‐based acceleration sensor (GTAS). Moreover, GTAS is demonstrated to sense the vehicle motion and be a part of the vehicle restraint system on a model car. This work reports a new self‐powered acceleration sensor with sufficiently large outputs for real‐time motion sensing and collision detection, which could be further applicated for robotics and human motion recognition.

Self-Powered Flexible Sensor Based on Triboelectric Nanogenerators for Noncontact Motion Sensing

Flexible sensors with surface suitability for complex-shaped objects generally sense object motion through a contact mode, which limits their application range and shortens their service life. The development of flexible sensors with noncontact working modes can overcome these shortcomings. Herein, superhydrophobic and self-powered flexible sensors based on a triboelectric nanogenerator (TENG) were fabricated by a step-by-step swelling-permeation method to prepare natural latex films with carbon black and silica nanoparticles embedded on their inner and outer surfaces, respectively. In addition to sensing object motion through contact, the TENG-based sensor can also sense charged object motion in noncontact mode based on the principle of electrostatic induction. The TENG-based sensor can sense horizontal and vertical movements of objects above it and can even detect the movement of objects with speeds as low as 0.04 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}/\text{s}$ </tex-math></inline-formula> . Interestingly, the sensor’s ability to monitor object motion in noncontact mode remains unchanged even at 70% strain. The TENG-based sensor can also be used to distinguish the type and amount of charge carried by an object and can harvest energy from moving objects in noncontact mode. Combining a single-electrode TENG with a freestanding TENG allows monitoring of the motion direction of an object loading an unknown type of charge in a noncontact mode. Based on the characteristics of our TENG-based flexible sensors to sense moving objects in both contact and noncontact modes, they have potential applications for human-machine interfaces, smart wearable devices, and flexible robots.

Three-dimensional mathematical modelling and dynamic analysis of freestanding triboelectric nanogenerators

Energy harvesting system based on triboelectric nanogenerators (TENGs) has aroused wide interest from many researchers since it integrates multiple disciplines together including electromagnetics, electric circuit theory, materials science and mechanical engineering. Accurate modeling of a TENG is an indispensable part for revealing the relationships and interactions among physical quantities from different areas. Here, a three-dimensional mathematical model of a contact-mode freestanding TENGs (CF-TENGs) is built with a combination of physical abstraction and geometry configuration, which makes it possible to dynamically analyze the variations of the field and circuit quantities. An accurate Norton’s equivalent circuit model that consists of a current source in parallel with a pure capacitive reactance is proposed. Based on this model the reason for identifying the displacement current as the driving force of TENGs is elucidated, and quantitatively determine the current flowing through the external load resistor and the internal equivalent capacitor. More importantly, a universal dynamic simulation model consisting of a quasi-electrostatic model and a circuit model for the TENG-based energy harvesting system is presented. The presented composite model exhibits an obvious advantage in terms of revealing the dynamic output of TENGs with arbitrary geometry and charge distribution. Finally, based on the characteristics of linearity and time-invariance of the CF-TENG, general optimization strategies are pinpointed, which allow us to accurately predict the maximum output efficiency (close to 82.5%).