<p>Due to manufacturing and assembly errors, backlash acts as an uncertain but bounded parameter, exhibiting interval properties. Consequently, this paper examines the interval characteristics of backlash and assembly errors, as well as their coupling effects, and proposes a nonlinear interval dynamic model for the gear pair. First, a backlash correction model that considers the surface topography and assembly errors is developed based on fractal theory. The dynamics of the gear system are then modeled, and an interval method using Chebyshev functions is employed to determine the bounds of the dynamic response. The effectiveness of the interval method is validated through a comparison with the scanning method. Numerical simulations show that the interval characteristics and coupling effects of fractal backlash and assembly errors significantly influence the dynamic behavior of the uncertain system. As the interval range of uncertain parameters increases, the interval of dynamic transmission error also widens. The uncertainty of center distance assembly has the most significant effect on the system, followed by the initial backlash error, while the vertical assembly error has a negligible impact. Experiments on backlash uncertainty further validate the model's accuracy, indicating it predicts uncertain dynamic behavior better than the conventional model. Additionally, the mean value is a key indicator for assessing dynamic response uncertainty, while the Shape better identifies the lower bound of the interval. Kurtosis, Skewness, and Peak-to-Peak values are more suitable for cases with low assembly errors and large backlash.</p>