Research paperFractal structures in centrifugal flywheel governor system

- A new type of comb-shaped fractal structure with invariable periodic number in centrifugal flywheel governor is found.
- The mode-locking of the system are organized according to Stern-Brocot tree, which is a kind of more general tree, including Farey tree as a subtree.
- A new type of mixed-mode oscillations (MMOs), namely nonchaos-mediated MMO, is found in the periodic response.

The global structure of nonlinear response of mechanical centrifugal governor, forming in two-dimensional parameter space, is studied in this paper. By using three kinds of phases, we describe how responses of periodicity, quasi-periodicity and chaos organize some self-similarity structures with parameters varying. For several parameter combinations, the regular vibration shows fractal characteristic, that is, the comb-shaped self-similarity structure is generated by alternating periodic response with intermittent chaos, and Arnold's tongues embedded in quasi-periodic response are organized according to Stern-Brocot tree. In particular, a new type of mixed-mode oscillations (MMOs) is found in the periodic response. These unique structures reveal the natural connection of various responses between part and part, part and the whole in parameter space based on self-similarity of fractal. Meanwhile, the remarkable and unexpected results are to contribute a valid dynamic reference for practical applications with respect to mechanical centrifugal governor.