hw3 - Continued on back Problem 13 Calculation of Field...

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EE321 Spring 09 Homework 3 Problem 11 – UI Inductor Analysis Consider the UI inductor design we did in class. Recall we had N = 260 Turns d = 8.4857 cm g = 13.069 mm w = 1.813 cm a w = 21.5181 mm 2 d s = 8.94 cm w s = 8.94 cm In our design, we assumed that the permeability of the material was infinite. Compute (a) the inductance, (b) the flux density in the magnetic material, (c) the flux density in the air gap, (d) the field intensity of the magnetic material, and (e) the field intensity in the air gap if we assume that the relative permeability of the magnetic material is 5000. Finally compute (f) the percentage error between the desired inductance and the inductance that we calculate assuming a relative permeability of 5000. Assume the current is 40 A. Problem 12 – UI Inductor Analysis Energy stored in a magnetic field may be expressed: = volume dv E H B 2 1 For our inductor design (minimum cost), again assuming a magnetic permeability of 5000 and a current of 40 A, how much energy is stored in the air gap region and how much energy is stored in the magnetic material.
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Unformatted text preview: Continued on back Problem 13 Calculation of Field Energy An electromechanical device has the following flux linkage equations: 2 2 1 2 2 2 2 1 1 1 4 ) 1 )( sgn( 7 . 5 . 4 ) 1 )( sgn( 7 . 2 3 . 2 1 2 1 x e i x e x i +-+ + = +-+ + + = +-+- Note ) sgn( u is 1 if u and -1 if < u and 0 if = u . However, you need only consider the positive current/flux linkage case. Compute the field energy as a function of 1 and 2 . Problem 14 Calculation of Force from Field Energy Suppose that the field energy of is given by ( 29 x x W f + + + + + = 2 3 2 2 2 1 1 7 5 3 . Derive an expression for the electromagnetic force. Problem 15 Calculation of Co-Energy Consider the following system: x e i x e i x e i i i i i i i i i i +-+ = +-+ = +-+ = + +-+ +-+ +-7 ) 1 ( 2 7 ) 1 ( 4 2 7 ) 1 ( 2 5 ) 2 ( 3 3 ) 2 ( 2 2 ) 2 ( 1 1 3 2 1 3 2 1 3 2 1 Compute the co-energy assuming all currents are positive....
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hw3 - Continued on back Problem 13 Calculation of Field...

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