Similarity modulation mechanism in triboelectric nanogenerators

The central open question in triboelectric nanogenerators is not how much power they can deliver, but what dynamic principle governs the conversion from motion to charge. We answer this by establishing a similarity modulation mechanism that extends the classical V-Q-x relation into a predictive dynamic law. A single similarity descriptor S_m = ω₀T organizes the electromechanical response across device geometries and operating modes under a clearly stated condition where dielectric relaxation and charge decay are slow relative to motion. Within this conditional similarity, normalized outputs collapse onto universal curves that reveal three regimes with simple design rules: a low frequency growth region, a resonance near S_m ≈ 2π that captures impedance alignment, and a high S_m ceiling where average power becomes frequency independent due to incomplete charge refresh per cycle. The framework also ranks input waveforms and shows why compact top hat profiles outperform sinusoids at fixed amplitude, and it provides explicit guidance for load matching and storage-oriented operation without introducing new empirical parameters. This theory converts scattered models into a single map that explains published trends, exposes real limits, and supplies a compact rule set for rational TENG design and scalable energy management.