A reduced order model of contact state and charge extraction in manually tapped contact separation triboelectric nanogenerators

Manual tapping of PVDF/PTFE contact-separation triboelectric nanogenerators cannot be completely described by the ideal voltage–charge–displacement (V–Q–x) relations alone. These relations provide the classical electrostatic basis for contact-separation TENG analysis, but they are commonly applied with complete contact, fixed surface charge, negligible residual separation, and idealized terminal charge extraction. Under manual excitation, the effective contact state depends on the applied tapping force, polymer-surface roughness, interfacial compliance, and incomplete microscopic contact formation. Finite residual separation, humidity-assisted retained-charge loss, and finite-rate circuit relaxation can further modify the measured terminal response. In this work, a reduced-order continuous-electrode model is developed for a PVDF/PTFE contact-separation TENG driven by prescribed tapping waveforms. Each tap’s peak force determines a charge generation participation factor at maximum compression, which remains constant during the release stroke that follows. This treatment preserves the charge state established during PVDF/PTFE contact while allowing the separation-dependent capacitance, open-circuit voltage, and circuit-accessible charge target to evolve during release. The model combines finite residual-gap closure, cumulative humidity-induced retained-charge loss, and a variable-capacitance load circuit within a unified analytical–numerical framework. Terminal charge, current, voltage, and cycle energy are calculated from the coupled mechanical, material-state, electrostatic, and circuit variables. Classical electrostatic limits, finite-load limits, and time-step convergence are verified to check the internal consistency of the formulation. Agreement between the time-integrated load energy and the closed (V L )–(Q) loop area is used as an additional internal energy-accounting check. The results are presented as internally verified, parameter-specified comparative scenarios for manually tapped PVDF/PTFE devices. The framework is therefore intended for comparative mechanistic analysis and parameter screening rather than device-specific absolute prediction. Clinical trial Not applicable.