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Motor Fundamentals

Motor Fundamentals

Basic Magnetism

Electric motors derive their characteristic ability to convert electrical energy to mechanical energy from magneto static force. Magneto static forces result from electric charges in motion. These charges may flow freely through space, in a conductor,
or exist as spinning electrons of the atoms that make up magnetic materials.

As early as 640 B.C. certain natural
magnets were known to exist. Nearly 2000 years later, two simple laws governing their behavior were discovered:

  1. Like poles repel each other, while unlike poles attract.
  2. The force of attraction or repulsion is proportional to the inverse square of the distance between the poles.
Magnetic Field
An important property of magnets is that they can exert forces on one another without being in actual contact. This is explained by the existence of a magnetic field around a magnetized body. The magnetic field of the bar magnet (see figure below) is represented by the lines radiating out from the north pole and entering the south pole. Any other magnet placed in this magnetic field will experience a force. Forces will also be exerted on electrons moving through a magnetic field.
Flux Field Flux field pattern of a simple bar magnet.

Flux Density:
The magnetic field lines in Fig. 1-9 are collectively referred to as the magnetic flux. Magnetic flux density is the amount of magnetic flux passing through a unit area plane at a right angle to the magnetic field. It is a measure of how concentrated the magnetic field is in a given area. Magnetic flux density (B) is a vector quantity. That is, it has magnitude as well as direction.
Magnetism at the Atomic Level
While ferrous materials, like iron, are strongly magnetic, many materials show at least some magnetic properties. Paramagnetic
materials, mostly metals, exhibit very weak attraction to a magnet. The rest of the metals and nonmetals are diamagnetic
—very weakly repelled by a magnet. Only the ferrous materials, some specialized alloys, and ceramics have sufficiently strong
magnetic properties to be of commercial use.

No more than two electrons can share the same electron level or shell of an isolated atom. Diamagnetic materials have two electrons in each shell, spinning in opposite directions. See figure below (a).. Since the magnetic response of a material is dependent upon the net magnetic moment of the atoms, this balanced symmetrical motion produces a magnetic “moment” of near zero. Quite simply, the fields produced by the counter spinning electrons cancel each other.

For the paramagnetic elements in which the electron shells are naturally asymmetric (see figure below), each atom has a weak but significant magnetic field. However, few of the paramagnetic elements are magnetically very strong. These are called the ferromagnetic elements.

Ferromagnetism is the result of the asymmetrical arrangement of electrons in atoms in combination with a coupling or aligning of one atom’s magnetic field with that of an adjacent atom. This results in a strong magnetic response. This “exchange
coupling” occurs only in materials in which the spacing between atoms falls within a certain range.

In iron, cobalt, nickel and gadolinium, the net magnetic moment is strong enough, and the atoms close enough, for spontaneous
magnetic alignment of adjacent atoms to occur. Solid ferromagnetic materials conduct magnetic flux in the alignment direction.
Arrangement of electrons Arrangement of: a) electrons in diamagnetic materials (left), and b) electrons in magnetic materials (right).
Electric Current and Magnetic Fields
In 1820, Oersted discovered that an electric current passing through a conductor would establish a magnetic field. This discovery
of the relationship between electricity and magnetism led to the development of most of our modern electric machines.

The magnetic field around a current carrying straight conductor takes the form of concentric cylinders perpendicular to the conductor. In the figure below, the current is shown emerging from the page and the flux lines, shown as concentric circles, are flowing counterclockwise. When the direction of the current is reversed, the flux lines flow clockwise.
Direction of flux flow Direction of flux flow with a) current flowing out of page (left), and b) flux flow with current flowing into page (right).
The right-hand rule, shown below, can be used to determine either the direction of the magnetic field or the direction of current when the other one is known.
Right hand rule Right-hand rule: thumb points in direction of current, palm curls in direction of magnetic field.
When the current-carrying conductor is formed into a loop as shown below, the faces of the loop will show magnetic polarities. That is, all of the magnetic field lines enter the loop at one face and leave at the other, thus acting as a disc magnet.
Direction of the magnetic flux Direction of magnetic flux when an energized conductor is formed into a loop.
The polarities will be more pronounced and the magnetic field will be much stronger if we wind a number of loops into a solenoid (shown below).
Flux characteristics Flux characteristics in simple soleniod.
The magnetic field developed by the solenoid resembles that of a bar magnet. The flux lines form continuous loops, leaving the solenoid at one end and returning at the other, thus establishing north and south poles.

The magnetic flux (Φ) of a given solenoid is directly proportional to the current (I) it carries. The same holds true for a straight conductor or a single loop of wire. For solenoids with different numbers of turns and currents, the magnetic flux is proportional
to the product of the number of turns and the amount of current.

Properties of Magnetic Materials:
When a ferromagnetic material, like an iron bar, is placed in a magnetic field, it presents a low resistance path to the flow of flux. This results in a “crowding effect,” as flux seeks to flow through it and flux density increases in the gaps at the ends of the bar. See figure below. Iron, cobalt, nickel, some rare earth metals and a variety of other ferromagnetic alloys and compounds are excellent magnetic conductors with high permeability.
Effect of an iron bar on a magnetic field.

Permeability and Magnetic Field Strength:
Permeability (μ) is a measure of how well a material will conduct magnetic flux. It is related to magnetic flux density (B) and magnetic field strength (H) in the following equations:
where μo = 4π x 10-7 (in SI units) and μr is the relative permeability with a value of unity (1) in free space.

The magnetic field strength (H) is measured in amperes per meter. The following formula shows that for a solenoid (conductor loop) with length (1) and a number of turns (N), the magnetic field strength within the solenoid is proportional to the current (I):
For a given solenoid and current, H remains the same regardless of any material placed inside the solenoid. However, the magnetic flux density (B) will be directly proportional to the permeability (μ) of the material.

Magnetization, Demagnetization and Hysteresis:
If a piece of iron is used as the core of a solenoid and the current is increased slowly (increasing the magnetic field strength, H), the iron will be magnetized and follow the magnetization curve (abcd) as shown below.

The magnetization curve shows how the flux density (B) varies with the field strength (H). And since B = μH, it also shows how the permeability (μ) varies with the field strength. When H is gradually increased, the flux density (B) increases slowly at first (section ab of the curve). Then, as H is further increased, the curve rises steeply (bc of the curve). Finally, magnetic saturation is approached (near d) where the curve flattens out.

If the current is then gradually decreased, flux density (B) will decrease but the demagnetization curve will not retrace the path (dcba). Instead, it will follow a path de, where at point e, even though the current has been reduced to zero, there is some residual magnetism. If we then gradually increase the current in the reverse direction, creating -H, the iron will be completely demagnetized at point f. By further increasing the current and then slowly decreasing it, we will go through points g, h, i and d. The complete loop (defghi) is called a hysteresis loop and represents a virtual “fingerprint” for the material being used. See figure below.
Magnetization curve Magnetization curve and hysteresis loop.
As iron is magnetized and demagnetized, work must be done to align and realign its atoms, and this work takes the form of heat. In alternating current machines (i.e., motors and generators), the magnetizing and demagnetizing process takes place many times a second and hysteresis loss (heat) may be considerable, resulting in lower operating efficiency. The hysteresis loss for one cycle of alternating current is equal to the area enclosed by the hysteresis loop.

Motor Action:
If we place a current- carrying conductor (see figure below - a) between opposite magnetic poles (see figure below - b), the flux lines below the conductor will move from left to right, while those above the conductor will travel in the opposite direction (see figure
below - c). The result is a strong magnetic field below the conductor and a weak field above, and the conductor will be pushed in an upward direction. This is the basic principle of electric motors and is sometimes called “motor action.”
a) Flux pattern around an energized conductor (left), b) flux between two
magnetic poles (center), and c) effect of placing an energized conductor in a uniform magnetic field (right).
The force (F) on the conductor is a product of the magnetic flux density (B), the conductor’s current(I) and the length of the conductor(I):
where we have assumed that the conductor is at a right angle to the magnetic flux density (B).

An easy way to remember the direction of motion is to apply the right-hand rule, shown below.
Right hand rule Right-hand rule for force on a conductor in a magnetic field.
Induced EMF
In general, if a conductor cuts across the flux lines of a magnetic field or vice versa, an emf is induced in the conductor. If the direction of the flux lines and the conductor are parallel, there is no induced emf.

Generator Action:
If the conductor in the figure below is moved vertically up or down in the magnetic field, an electromotive force is generated in the conductor. If the conductor is connected to a closed circuit, current will flow. This is the basic principle of electric generators and is also called “generator action.”
Direction of induced emf in a conductor-cutting flux.
The induced emf is a product of the velocity of the motion (v), the magnetic flux density (B), and the length of the conductor (l):
The relationship is valid only if the motion of the conductor is perpendicular to the flux lines.

The direction of induced emf depends on the direction of motion of the conductor and the direction of the magnetic field. This relationship can be shown by Fleming’s left-hand rule for electromagnetism.

Faraday’s Law:
We have seen that any conductor cutting across a magnetic field will produce an emf. However, this is only a special case of the more general law of induction established by Faraday in 1831: “If the total flux linking a circuit changes with time, there will be an induced emf in the circuit.”

If we were to wind two coils around a steel bar, as in the figure below, connecting one to a battery with a simple on/off switch and the other to a sensitive galvanometer, the effect of closing the switch would produce a change in current and a change in the field thereby inducing a current in Coil 2. Similarly, if we were to open the circuit, a current would again register in Coil 2.
Magnetically coupled coils Magnetically coupled coils wound around a steel bar.
The induced emf in Coil 2 is mathematically related to the change of flux as follows:
Where N2 is the number of turns in Coil 2 and dφ/dt is the rate of change of flux, the minus sign indicates that the induced current
in Coil 2 will flow in such a way as to oppose the change of flux due to the change of current in Coil 1.

Since both coils are wound in the same direction, the induced current will flow in the direction shown in the figure above when the switch is closed. This induced current in Coil2 sets up a magnetic field opposes the sudden increase of flux created by
current flowing in Coil 1. If the switch is then opened, the current in Coil 2 will flow in the opposite direction creating a flux that
opposes the sudden decline of flux from Coil 1.
Inductance (L)
The change of magnetic flux due to switching in the figure above would also produce a counter emf (cemf) in Coil 1 itself. The cemf opposes the build-up or decline of current in the same circuit. The ability of a coil to store energy and oppose the buildup of current is called inductance.

For a given coil, the change of magnetic flux is proportional to the change of current. Thus, the cemf may be expressed as follows:
where L is called the inductance of the coil. A coil or circuit is said to have an inductance of one Henry when a current changing at the rate of one ampere/second induces one volt in it.

RL Circuit:
In the section Basic Electricity we learned that there is a delay in the rise or fall of the current in an RC circuit. The RL circuit, shown below, has a similar property.
Basic RL Circuit Basic RL circuit.
When the switch (S) is closed at a, the current in the resistor starts to rise. However, the cemf presented by the inductor (L) opposes the rise of the current, thus the resistor responds to the difference between the battery voltage(V) and the cemf of hte indicator. As a result, the current rises exponentially as shown figure below.
Current rise in RL Circuit Current rise in RL circuit.
If we allow enough time for the current to reach V/R and then close the switch at b, current will continue to flow but diminish
as the stored magnetic field energy is dissipated through the resistor.

RL Time Constant:
The time constant is the time at which te current in the circuit will rise to 63% of its final value (V/R) or decay to 37% of its initial value. It
is represented by the formula:
The time constant can be controlled by varying the resistance or inductance of the circuit. Decreasing the circuit resistance increases the time constant. Increasing the inductance will also increase the time constant. Thus, the larger the time constant, the longer it takes the current to reach its final value. The current in an RL circuit will rise or fall to its final value after five time constants (within 99.3%).
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