An electromechanical switch (relay) is constructed using an axial reluctance for

Question

An electromechanical switch (relay) is constructed using an axial reluctance force actuator shown in the figure below (electrical contacts are not shown). The core is made from silicon sheet steel with a very high relative permeability, and all other parts of the relay are made from non-magnetic material. The reluctance of the highly permeable cores should be ignored. The lower of the two cores is fixed and the upper one moves up or down. In this analysis assume no fringing and leakage as well as that the cross-sectional area is constant in all parts of the core. Take the relaxed position of the springs to be x = 0. A positive displacement corresponds to the upper core moving down.

a) Draw the magnetic equivalent circuit for this axial reluctance force actuator.

b) Find the equivalent reluctance for the relaxed spring position (shown in figure) and for the closed central air gap (x = g2).

c) Express the inductance of the actuator as a function of x and calculate its maximum value.

d) Find the expression for reluctance force developed in the actuator. (It should include displacement, x, and current, I, as variables and all necessary parameters). Displacement is positive if the moving core goes down.

e) CalculatetheresistanceR,ofthecoilifthemaximumdevelopedforceisequalto200Ninthepositivexdirection when 48 V excitation is applied.

f) Calculate the voltage that has to be applied to hold the moving core at the displacement x = 1 mm.

Explanation / Answer

dd

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