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We report developments in the modeling of bearing force and torque for a toothless self-bearing servomotor (TSBS), a permanent-magnet synchronous machine that utilizes the Lorentz force for levitation and torque simultaneously. The contactless nature and toothless construction of the device results in smooth torque production, making the TSBS ideal for precision pointing and slewing applications. We present, for the first time, nonlinear analytical expressions for force and torque based on first principle modeling. The parameters are identified from system data using linear least squares. The resulting nonlinear model aligns very well with finite-element analysis predictions. This approach has advantages over previous modeling efforts, which were purely analytical and always yielded linearized force and torque expressions.