Question

b) A portion of a solenoid is shown as in Figure Q3(b). The magnetic circuit comprises of cast iron yoke, sheet steel plunger, cast steel plunger and air gaps. The yoke and plunger have a cross section area of 4.8x10 m´and 4.5x10m respectively. A coil is wound on the center of the yoke. The effective length of the cast iron yake, sheet steel plunger and cast steel plunger are la = 0.25 m; 4 = 0.12 m and l = 0.05 m respectively, Neglect any magnetic leakage and fringing effect. Used the BH characteristic curve given in Appendix 1. i Draw the equivalent Ampere's Circuital Law model. (5 marks) SULIT SULIT (BEKG 2433 BEKP 2323) ii. If the magnetic flux in the cast iron yoke is 28x10-*Wb, determine the number of tums required in a coil to generate the magnetic flux (15 marks) lagt 2.5 mm Cast ironyok 1-4.42A Sheet punger luga= 1.2 mm Cast Steel leg22.8mm Figure Q3 (b)

Answer 1

i Equivalent Ampere's circuital Low model ! -- Rci Ragan Rss m NE Rag3 Rcs Raga 1 Given : = 4.22 A (current) Ayoke Aplunger 4.8x10-4 m² (A sea of yoke) 4.5x10-4 m? ( Area of plunger ) = Reluctance of each poth, RA ;) air as well as Let us find Reluctances of each ison and steel path gapes for this have to get relative permeability from B-H Sheet -steel Molle 6 X10-3 [slope in we curve, SS O.G linear region cs Cast steel Hollro -0.0016 500 slope from graph given (in linear my wys ) ) O. 4 x 10"3 Cast ison Moun Oo lci Reluctance of cast iron (Roi) = Mci A goke 0.25 4X10-3 *4.8 x 10-4 130208.33 AT/Wb lss Reluctance of Sheet Steel plunger CRss) - uss A plunger D.12 6xlo 3x4.5X1.-4 4 4 4 4 4.44 AT wb les Mes A plungen cast steel plonger Plunger (Rab) Reluctance of 0,05 a.vol6X4,5X10-4 69 444.44 Reluctance of ais gap combined ( Rage + Rogz & Raga) lag, + laga lag3 + Mo A yoke Mo A plongeer + (2.5+ 2.8) x 10 1.2 x 10-3 4tX lo x 4.8 x 10-4 YAX10²4.50104 Rag 87,868 los Atwo From magnetic circuit, it t's and fringing being neglected, flux flow at element will be Reluctance of magnetic cismit (Re) clear that it leakage each ir as they series, some are Re: Rci + Rag & Rss + Res wb Re 90.3 x105 Atl that he know Net Flux $2 Net mmb (NI) Net Reluctance Cre) + NI Re Re 90.3X10S AT/ Wb 4.420 N 90.3 xlos 2.0 X16.4 572 Tuyns 5 72-04 N