Friction-induced vibration (FIV), which leverages friction for excitation to achieve close to resonant frequency vibration, presents an efficient solution for vibration-based piezoelectric energy harvesting. Previous experimental dynamic responses exhibited variability due to uncertainties in the properties of frictional material. This study conducts uncertainty analysis of frictional parameters on energy output for a magnet-engaged nonlinear piezoelectric energy generator utilizing FIV. An electromechanical model depicts the dynamics, and the energy output is evaluated through transient charging simulation. Employing the root mean square (RMS) charging power \({P}_{\text{e}}^{\text{rms}}\) as the performance function for uncertainty analysis, the Morris One-At-a-Time (MOAT) method, coupled with Latin hypercube sampling, evaluates the parametric influence induced by uncertainty on the system output. Notably, among the friction model parameters, sliding velocity \({v}_{0}\) exhibits the predominant elementary effect on energy generation performance. Increased variation ratio \({v}_{\text{rt}}\) and decreased linear spring stiffness \({k}_{\text{l}}\) increase the system's sensitivity to external parameter uncertainties. The observed trends in elementary effects for all the studied parameters reflect higher uncertainty sensitivity, when the initial state is near the stable region with reduced FIV. Future investigation could extend this research with a comprehensive uncertainty analysis of complicated energy generation systems under FIV for performance optimization.