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Modeling dry friction is a challenging task. Accurate models must incorporate hysteretic rise of force across displacement and non-linearity from the Stribeck effect. Though sufficiently accurate models have been proposed for simple friction systems where these two effects dominate, certain rotational friction systems introduce self-energizing and accompanying backlash effects. These systems are termed self-energizing systems. In these systems, the friction force is amplified by a mechanical advantage which is charged through motion and released during reversing the direction of travel. This produces energized and backlash regimes within which the friction device follows different dynamic behaviors. This paper examines self-energizing rotational friction, and proposes a combined physics and machine learning approach to produce a unified model for energized and backlash regimes. In this multi-process information fusion methodology, a classical LuGre friction model is augmented to allow state-dependent parameterization provided by a machine learning model. The method for training the model from experimental data is given, and demonstrated with a 20 kN banded rotary friction device used for structural control. Source code replicating the methodology is provided. Results demonstrate that the combined model is capable of reproducing the backlash effect and reduces error compared to the standard LuGre model by a cumulative 32.8%; in terms modeling the tested banded rotary friction device. In these experimental tests, realistic pre-defined displacements inputs are used to validate the damper. The output of the machine learning model is analyzed and found to align with the physical understanding of the banded rotary friction device.