Question

Please do all parts

Problem 2- Lateral Reluctance Actuator 20 ptsl The actuator shown below has a core and movable section of steel. The moveable section is supported by bearings with permeability u o, with Hr. All parts of the actuator extend a depth "a" into the page The rest of the parameters for the actuator N-150 a-5 cm a x a cross section b- 25 cm g 2 cm K-40 Nm Equilibrium position of the steel, xi = 4 cm Spring Constant depth "a" into page N tuns Neglect fringing around the air-gaps and mechanical losses. Assume that the moveable section is long enough so that the narrower section of the core always provides an area of a nomal to the a) Draw the magnetic equivalent circuit of the above actuator. Neglect the reluctances of the b) Calculate the equivalent reluctances, based on the equivalent circuit in part(a), as function c) From part(b), calculate the total inductances L(x) as a function of displacement "x", for (1) flux flow core in your equivalent circuit. ofx" for both (1) positive and (2) negative"x positive and (2) negative "x". d) Calculate the current required to hold the steel section at a displacement of x = 2 cm.

Answer 1

Protom 2 Soluhon; Reder to the given figure for the actuaton Consideγ all the given valuu, Ca) the majnetic eauivalent ciruit of the actvator RA Rb FIQURE! Fmas fk fm FURE2Bynejudog ona uistena wil steel movinj hrechon for both vegative calculate the length of the core. C From the siven Valwex

Calculate the ,Yeluctance mean length 아the Ore Ra subaStutut巳the values. Calculate the YelMC七ance Rb. R mean length Substitute the values. 25 Xt0 4 Cal ulate the reluctano Raytotal mean length For the Pasiaivex" -1 g/ total 4- Ry,total = 1 = 15.9 MH

Caltulate the total inductanes LCx) fr osb ve and Foy-the neghve"x 150 5 9X10 Calculate the required ument to hod the stel Secton at displacement x=2 cm The expressoh fothe Yeni red cunrent is, Cub Stitute the Valveg 40 = 20 GA.