Fig. 4 Mechanical Sub-block The mechanical model takes into account the movement of the floating magnet along three coordinate axes. After a preliminary investigation, the rotation around the axes has been considered negligible. The resultant 3-dof model is = + + + + = = air em bump fric C z C y C x mz F F F F F my F mx F && && && (1) where C iF is the input force along the i th direction, fric F is the force due to dry friction, bump F is the Kelvin–Voigt elastodissipative force due to the bumpers, em F is the magnetic force, air F is the force due to pneumatic effect. The mechanical dynamic sub-block is shown in Fig. 4. Parametric analysis of non-linear elements Magneto-elastic effect From the mechanical point of view, the electromagnetic simulation provides two force contributions: elastic and dissipative. The elastic component is due to the position of the floating magnet during its movement along the guide with respect to the preload magnet and it is dependent only on the z coordinate. The force values are estimated by a finite element model or from experimental measurements and can fit a negative exponential function in the empirical form: ( ) n B z em elastic F z Ae − = (2) where coefficient A, B and n can be estimated in a least-mean-square algorithm. A comparison between FEM force values and the negative exponential characteristic is shown in Fig. 5 (a). 342
RkJQdWJsaXNoZXIy MTMzNzEzMQ==