The constant damping, defined by the instantaneous velocity and damping ratio, falls short in accurately describing damping in gear systems due to its oversimplified assumptions about complex energy dissipation mechanisms. Therefore, a non-viscous damping approach is required to capture these mechanisms effectively. This research illustrates a spur gear pair system incorporating a parametric exponential non-linear damping model under time-varying stiffness. The non-linear damping model fully captures the velocity history by integrating kernel functions through a convolution process. To demonstrate the impact of nonlinearity on damping, the transmission error obtained with nonlinear damping is compared to that with constant damping, using a numerical integration method implemented through a Python algorithm.