Mathematical Modeling and Scaling of the Friction Losses of a Mechanical Gyroscope

Abstract

Friction is a complicated phenomenon that plays a central role in a wide variety of physical systems. An accurate modeling of the friction forces is required in the model-based design approach, especially when the efficiency optimization and system controllability are the core of the design. In this work, a gyroscopic unit is considered as case study: the flywheel rotation is affected by different friction sources that needs to be compensated by the flywheel motor. An accurate modeling of the dissipations can be useful for the system efficiency optimization. According to the inertial sea wave energy converter (ISWEC) gyroscope layout, friction forces are modeled and their dependency with respect to the various physical quantities involved is examined. The mathematical model of friction forces is validated against the experimental data acquired during the laboratory testing of the ISWEC gyroscope. Moreover, in the wave energy field, it is common to work with scale prototypes during the full-scale device development. For this reason, the scale effect on dissipations has been correlated based on the Froude scaling law, which is commonly used for wave energy converter scaling. Moreover, a mixed Froude–Reynolds scaling law is taken into account, in order to maintain the scale of the fluid-dynamic losses due to flywheel rotation. The analytical study is accompanied by a series of simulations based on the properties of the ISWEC full-scale gyroscope.