A multiphysics model for triboelectric nanogenerator design with explicit surface roughness representation

Abstract

The design of triboelectric nanogenerators (TENGs) for efficient energy harvesting requires predictive models that capture the interplay between surface roughness, real contact area, and electrostatic behaviour across diverse tribolayer materials and roughness levels. To address this demand, this paper presents a multiphysics finite element framework that couples mechanical contact analysis with electrostatic simulations, considering exact surface roughness representations rather than idealised statistical approximations. Compared with optical interference microscopy measurements, the framework predicts the real contact area ratio more accurately than analytical models. The proposed approach captures the electrostatic behaviour by scaling the TENG surface charge density with the real contact area ratio between the rough tribolayers, computed for a given mechanical load. This method improves agreement with experiments for open-circuit voltage and capacitance relative to approximate analytical models. To represent the TENG circuit, a time-dependent ordinary differential equation is integrated, enabling evaluation of electrical responses under varying load conditions and elucidating the roles of surface roughness, mechanical load, contact-separation frequency, and resistive load. The framework provides a robust, scalable tool for performance optimisation across dielectric materials, mechanical behaviours, and operating conditions and is readily extendable to other surface-dependent energy-harvesting devices.

Figures (49)

• Figure 1: Scope of a predictive multiphysics numerical framework for systematic TENG design and optimisation. Addressing the existing research gaps requires a predictive tool for investigating distinct physics, considering coupling between finite surface roughness, contact mechanics, triboelectric charge transfer, and electrostatics analyses within a single computational pipeline.
• Figure 2: Schematic of a contact-separation TENG with two dielectric layers (blue, red) and electrodes (green) showing a time-dependent open-circuit voltage $V_{OC}(t)$ and capacitance $C_T(t)$ in the external circuit where mechanical contact generates equal and opposite tribo-charges $\sigma_T^{+}$ and $\sigma_T^{-}$, while charges $Q^{+}$ and $Q^{-}$ are induced in the separation stage on the electrodes.
• Figure 3: TENG characteristics as functions of air gap using the material parameters reported in XUVoc, showing:(a) analytical approximations of the open-circuit voltage $V_{OC}$XUVocniu_Voc_linearguo2020derivation (b) effective capacitance $C_T$ derived from the analytical models niu_Voc_linearXUVocxiang2006electrostatic.
• Figure 4: Schematic of the simulation pipeline for TENG accounting for surface roughness, showing: (a) Layered TENG structure substrate (grey) at the top and bottom with attached electrodes (green) and triboelectric materials 1 and 2 in between. (b) Combined rough surface topography of both layers. (c) 3D finite element mesh upon projecting the measured surface height, used to compute the mechanical contact response upon indentation by a rigid counter-surface. (d) simulation result showing contact (black) and non-contact (white) zones, permitting the computation of $A_r/A_n$. (e) Electrostatic model with the TENG layers containing surface charge densities $\sigma^{\pm}$ scaled by the contact area fraction to evaluate the $V_{OC}$ and $C_T$. (f) Equivalent circuit model of the TENG, comprising a time-dependent $V_{OC}$ and $C_T$, delivering an output voltage $V$ and short-circuit current $I_{e}$ across a resistive load.
• Figure 5: Schematic of the contact problem with a rigid surface indenting on a deformable body with surface roughness, where fixed boundary conditions are applied at the bottom in addition to the symmetric boundary conditions to the vertical faces. A rough surface topology is introduced at the top of the deformable layer, where the active contact zone $\Gamma_c$ is a subset of the potential contact zone $\Gamma$ such that $\Gamma_c \subseteq \Gamma$.