Electric Machines I Introduction to Machinery

Principles

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Dr. Firas Obeidat

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Table of contents

1 • The Magnetic Field

2 • The Magnetic Circuit

3 • Faraday's and Lenz's laws

Dr. Firas Obeidat Faculty of Engineering Philadelphia University

3 Dr. Firas Obeidat Faculty of Engineering Philadelphia University

The Magnetic Field

Magnetic fields are the fundamental mechanism by which energy is converted from one form to another in motors, generators, and transformers. Four basic principles describe how magnetic fields are used in these devices

• A current-carrying wire produces a magnetic field in the area around it.

• A time-changing magnetic field induces a voltage in a coil of wire if it passes through that coil. (This is the basis of transformer action.)

• A current-carrying wire in the presence of a magnetic field has a force induced on it. (This is the basis of motor action.)

• A moving wire in the presence of a magnetic field has a voltage induced in it. (This is the basis of generator action.)

4 Dr. Firas Obeidat Faculty of Engineering Philadelphia University

The Magnetic Field

The basic law governing the production of a magnetic field by a current is

Ampere's law:

𝐻. 𝑑𝑙 = 𝐼𝑛𝑒𝑡

where H is the magnetic field intensity produced by the current Inet and dl is a

differential element of length along the path of integration. In SI units, I is

measured in amperes and H is measured in ampere-turns per meter.

If the core is composed of iron or certain

other similar metals (collectively called

ferromagnetic materials) , essentially all

the magnetic field produced by the current

will remain inside the core, so the path of

integration in Ampere's law is the mean

path length of the core lc. The current

passing within the path of integration Inet is

then Ni, since the coi1 of wire cuts the path

of integration N times while carrying

current i.

5 Dr. Firas Obeidat Faculty of Engineering Philadelphia University

The Magnetic Field

Ampere's law thus becomes

𝐻𝑙𝑐 = 𝑁𝑖

The strength of the magnetic field flux produced in the core also depends on

the material of the core.

The relationship between the magnetic field intensity H and the resulting

magnetic flux density B produced within a material is given by

𝐵 = 𝜇𝐻

H = magnetic field intensity

𝜇 = magnetic permeability of material

B = resulting magnetic flux density produced

𝜇 = 𝜇𝑜𝜇𝑟

𝜇o = 4π×10-7 H/m 𝜇r = relative permeability

Now the total flux in a given area is given by

𝜙 = 𝐵. 𝑑𝐴 =𝐵𝐴 dA: is the differential unit of area0

A: is the cross-sectional area of the core .

𝜙 =𝜇𝑁𝑖𝐴

𝑙𝑐

6 Dr. Firas Obeidat Faculty of Engineering Philadelphia University

The Magnetic Circuit

In the electric circuit, it is the voltage or electromotive force that drives the

current flow. By analogy, the corresponding quantity in the magnetic circuit is

called the magnetomotive force (mmf) . The magnetomotive force of the

magnetic circuit is equal to the effective current flow applied to the core.

𝑉 = 𝑅𝐼 𝔉 = 𝑁𝑖 𝔉 = ℜ𝜙

𝔉 = magnetomotive force of circuit

𝜙 = flux of circuit

ℜ = reluctance of circuit

V=voltage

I=current

R= resistance

ℜ =𝑙𝑐

𝜇𝐴

7 Dr. Firas Obeidat Faculty of Engineering Philadelphia University

Faraday's and Lenz's laws

Faraday's law states that if a flux passes through a turn of a coil of wire, a

voltage will be induced in the turn of wire that is directly proportional to the

rate of change in the flux with respect to time.

𝑒 =𝑑𝜙

𝑑𝑡

If a coil has N turns and if the same flux passes through all of them, then the

voltage induced across the whole coil is given by

𝑒 = 𝑁𝑑𝜙

𝑑𝑡

e= voltage induced in the coil

N=number of turns of wire in coil

ϕ=flux passing through coil

Lenz's law states that the direction

of the voltage buildup in the coil is

such that if the coil ends were short

circuited, it would produce current

that would cause a flux opposing the

original flux change.

𝑒 = −𝑁𝑑𝜙

𝑑𝑡

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