Windage Power Loss Modeling of a Smooth Rotor Supported by Homopolar Active Magnetic Bearings

Rotors supported by active magnetic bearings (AMBs) can spin at high surface speeds with relatively low power losses. This makes them particularly attractive for use in flywheels for energy storage in applications such as electric vehicles and uninterruptible power supplies. In order to optimize efficiency in these and other applications, the loss mechanisms associated with magnetic bearings and rotating machinery must be well understood. The primary parasitic loss mechanisms in an AMB include complex magnetic losses, due to eddy currents and hysteresis, and windage losses along the entire rotor in nonvacuum environments. In low-loss magnetic bearing designs, the windage loss component along the rotor can become dominant at high speeds, and the need for accurate windage models becomes even more critical. This study extends previous AMB power loss work by evaluating five different windage loss models using the experimental rundown data from the previous work. Each of the five windage models, along with standard models of eddy current and hysteresis losses, are used to reduce the rundown data into the associated power loss components. A comparison is then completed comparing the windage power loss component extracted through the rundown data reduction scheme to the associated analytical windage prediction in order to identify the most accurate model for calculating windage losses along a smooth rotor. Five empirical flat-plate drag coefficient models are implemented, four turbulent and one laminar. An empirical flat-plate turbulent boundary layer formula (referred to here as “Model 2”) developed by Prandtl and Schlichting displayed the best agreement between experimentally extracted and analytically predicted windage loss values. The most accurate model formula (Model 2) dictates that the frequency dependency of windage loss is both logarithmic and power based and represents the minimum error between experimentally extracted and analytically predicted losses of all models in the study of high-speed power losses in a smooth rotor supported in AMBs.