Lecture 02 Electro Mechanical System 1

Assignment 1

• Page 46, Problem 2.4, 2.5, 2.7 & 2.8• Due Date: Tuesday 1st Feb, 2011

Lecture 02 Electro Mechanical System 2

Residual Flux Metals that have a strong magnetic

attraction can be modeled as being composed of many molecular size magnets.• Orientation of the magnets are normally

random.• By applying an external magnetic field (e.g.

using a coil with a current flow), the molecular size magnets will align themselves with the external field.

Lecture 02 Electro Mechanical System 3

Residual Flux When the external magnetic field decreases,

the magnetic domains tend to retain their original orientation.• This is called residual induction.

Lecture 02 Electro Mechanical System 4

Hysteresis Loop To eliminate the

residual flux, a reverse coil current is required to generate a field H in the opposite direction.• The magnetic domains

gradually change their previous orientation until the flux density becomes zero.

• HC is the coercive force • Energy is required to

overcome the molecular friction of the domains to any changes in direction.

Lecture 02 Electro Mechanical System 5

Hysteresis Loop AC magnets have ac flux

changing continuously and will map out a closed curve call a hysteresis loop.

With an external ac flux, the B/H characteristics of a magnetic material traces out a curve from:

(+Bm ,+Hm) to (+Br ,0) to (0, -Hc) to (-Bm ,-Hm) to (-Br ,0) to (0 ,+Hc)

Lecture 02 Electro Mechanical System 6

Hysteresis Losses Magnetic material

absorbs energy during each cycle and the energy is dissipated as heat. The heat released per

cycle [J/m3] is equal to the area [T-A/m] of the hysteresis loop.

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Hysteresis Losses caused by rotaiton Hysteresis losses are

also produced when piece of iron rotates in a permanent magnetic field

Consider an iron armature AB revolves in a field of permanent magnets N, S

As the armature rotates N pole of domain points towards A and then B

Reversal occur half cycle

Hysteresis losses occur as in an ac magnetic field

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Eddy Currents An ac flux linking a

rectangular-shaped conductor induces an ac voltage E across its terminals

If the conductor terminals are shorted, a substantial current flows.

The same flux linking smaller coils induce lesser voltages and lower currents.

A solid metal plate is basically equivalent to a densely packed set of rectangular shaped coils.

The induced currents flowing inside the plate are eddy currents, and flow to oppose the change in flux.

Lecture 02 Electro Mechanical System 9

Eddy Current Losses Eddy currents become a

problem when iron must carry an ac flux Eddy currents flow

throughout the entire length of the iron core.

Resistance in the iron causes energy to be dissipated as heat.

Losses can be reduced by splitting the core into sections (lamination) Subdividing causes the

losses to decrease progressively

Varnish coatings insulate the laminates from current flows.

Silicon in the iron increases the resistance.