Ball joints are components of the vehicle axle, and their friction characteristics must be considered when evaluating vibration behavior and ride comfort in driving simulator-based simulations. To model the three-dimensional friction behavior of ball joints, real-time capability and intuitive parameterization using data from standardized component test benches are essential. These requirements favor phenomenological modeling approaches. This paper applies a spherical, three-dimensional friction model based on the LuGre model, compares it with alternative approaches, and introduces a universal parameter estimation framework using machine learning. Furthermore, the kinematic operating ranges of ball joints are derived from vehicle measurements, and component-level measurements are conducted accordingly. The collected measurement data are used to estimate model parameters through gradient-based optimization for all considered models. The results of the model fitting are presented, and the model characteristics are discussed in the context of their suitability for online simulation in a driving simulator environment. We demonstrate that the proposed parameter estimation framework is capable of learning all the applied models. Moreover, the three-dimensional LuGre-based approach proves to be well suited for capturing the dynamic friction behavior of ball joints in real-time applications.