Nonlinear Models for Magnet Placement in Individually Actuated Magnetic Cilia Devices

Abstract

This paper presents a model for predicting the optimal magnet placement in magnetic cilia devices that achieve individual control via localization of the driving magnetic field. In this configuration, each cilium is controlled by a magnetic field source which is limited in spatial extent, and the cilia are spaced sufficiently far apart that the control remains uncoupled. An implementation is presented using an electromagnetic field source to attain large-deformation actuation (transverse deflections of 47% of the length). The large deformations are achieved by exploiting the nonlinear response of a flexible cantilever in a nonuniform magnetic field. However, the same nonlinearities also pose a modeling challenge: the overall performance is sensitive to the location of the electromagnet and the location that produces the largest deflections is nonlinearly dependent on the strength of the magnetic field. The nonlinear displacement of the cilium is predicted using a finite element model of the coupled magnetic–structural equations for static inputs at varying field strengths and magnet positions. The deflection at the model-predicted optimal placement is within 5% of the experiment-predicted optimal placement. Moreover, actuator placement using a model that does not include the nonlinearities is estimated to result in performance loss of about 50% peak deflection. This result emphasizes the importance of capturing nonlinearities in the system design.