Magnetic Circuits - Magnetic Circuit with an Air Gap

Summary

This lecture delves into the significance of air gaps in magnetic circuits, highlighting their role in electrical machines and inductors. It explains how air gaps increase reluctance, necessitating higher magnetizing currents for equivalent magnetic field density. The lecture contrasts circuits with and without air gaps, emphasizing the substantial current increase required for those with gaps. It also discusses the fringing effect, which alters the effective cross-sectional area of the air gap, and concludes by illustrating the disproportionate magnetomotive force distribution between the core and air gap, with most energy stored in the latter.

Takeaways

• 🧲 The presence of an air gap in a magnetic circuit significantly increases the reluctance, necessitating a higher magnetizing current to achieve the same magnetic field density as a circuit without an air gap.
• 🔌 Air gaps are a natural part of some structures, such as in electrical machines where the rotor and stator are separated by an air gap, and are also intentionally designed into circuits to prevent saturation.
• ⚙️ In applications like reactors or inductors, air gaps are added to extend the range of excitation current before saturation occurs, thus protecting against loss of permeability and power.
• 📉 The addition of an air gap flattens the magnetization curve, indicating a reduced rate of change in magnetic field density with respect to the magnetizing force.
• 🔗 The fringing effect, where magnetic field lines spread out in the air gap, increases the effective cross-sectional area of the air gap compared to the magnetic material.
• 🔄 To mitigate the fringing effect, air gaps in practice are often divided into several smaller gaps.
• 📊 The magnetomotive force (MMF) required for the air gap is much higher compared to the magnetic core, even with a smaller physical length, indicating most of the energy is stored in the air gap.
• 🔋 Air gaps are crucial for applications needing high current or energy storage without the risk of saturation, as they allow for a controlled increase in MMF.
• ⚠️ Abnormal operating conditions can lead to saturation and damage in magnetic circuits, and air gaps can serve as a protective measure against such conditions.
• 🔬 The script provides a practical example comparing the excitation current required for magnetic circuits with and without air gaps, highlighting the substantial increase in current needed with an air gap.

Q & A

What is the primary impact of an air gap in a magnetic circuit?

The primary impact of an air gap in a magnetic circuit is to increase the reluctance of the circuit, which requires a higher magnetizing current to achieve the same magnetic field density compared to a circuit without an air gap.

Why is an air gap typically included in the design of a magnetic circuit?

An air gap is often included in the design of a magnetic circuit to prevent saturation, which can lead to a loss of permeability, an increase in current, and a loss of power. It also extends the range of excitation current before saturation occurs.

How does the presence of an air gap affect the magnetization curve of a magnetic circuit?

The presence of an air gap causes the magnetization curve to have a less steep slope compared to one without an air gap, indicating that a higher magnetizing current is required for the same magnetic field density.

What is the practical implication of the fringing effect in magnetic circuits?

The fringing effect causes the magnetic field lines to spread out in the air gap, effectively increasing the cross-sectional area of the air gap. This results in a decrease in the magnetic field density in the air gap compared to the core material.

Why might an air gap be divided into several small gaps in a magnetic circuit?

An air gap might be divided into several small gaps to reduce the fringing effect, which can cause an increase in the effective cross-sectional area of the air gap and affect the overall magnetic field distribution.

How does the magnetomotive force (MMF) distribute between the air gap and the magnetic core in a circuit with an air gap?

In a circuit with an air gap, most of the magnetomotive force is used at the air gap, even if the air gap is much smaller in length compared to the core. This means that most of the energy is stored in the air gap.

What is the role of an air gap in protecting magnetic circuits from abnormal conditions?

An air gap can protect magnetic circuits from abnormal conditions by preventing saturation, which can be caused by high currents or energy storage, and by mitigating the effects of abnormal operating conditions that could damage the circuit.

What is the relationship between the cross-sectional areas of the magnetic material and the air gap in a magnetic circuit?

In an idealized magnetic circuit without considering fringing effects, the cross-sectional areas of the magnetic field densities of the magnetic material and the air gap are assumed to be the same. However, in practice, due to fringing, the effective cross-sectional area of the air gap is greater than that of the magnetic material.

How does the length of the air gap affect the required magnetizing current in a magnetic circuit?

The length of the air gap directly affects the required magnetizing current; a longer air gap increases the reluctance of the circuit, thus requiring a higher magnetizing current to achieve the same magnetic field density.

What is the significance of the difference in excitation current between a magnetic circuit with an air gap and one without?

The difference in excitation current between a magnetic circuit with an air gap and one without highlights the increased energy requirement to maintain the same magnetic field density in the presence of an air gap, emphasizing the impact of air gaps on circuit design and operation.

Outlines

00:00

🧲 Impact of Air Gap in Magnetic Circuits

This paragraph discusses the role and impact of air gaps in magnetic circuits. The lecturer explains that air gaps can be inherent in the structure of some applications like electrical machines, where the rotor is separated from the stator by an air gap. In other applications, such as reactors or inductors, air gaps are intentionally introduced to prevent saturation, which can lead to loss of permeability and power. The air gap increases the reluctance of the circuit, requiring a higher magnetizing current to achieve the same magnetic field density. The concept is illustrated with a comparison of magnetization curves for circuits with and without air gaps. The lecturer also touches on the protective role of air gaps against abnormal conditions that could lead to saturation and damage.

05:03

🌀 Fringing Effect and Magnetizing Current

The second paragraph delves into the concept of fringing, which is the spreading out of magnetic field lines as they pass through an air gap, increasing the effective cross-sectional area of the gap. The lecturer notes that this effect can be neglected if the air gap is very small. The paragraph continues with an example comparing two magnetic circuits: one without an air gap and one with a small air gap. The example demonstrates that the circuit with an air gap requires a significantly higher excitation current to achieve the same magnetic field density as the one without an air gap. The lecturer concludes by emphasizing that even a small air gap can concentrate a large portion of the magnetomotive force, indicating that most of the energy is stored in the air gap.

Keywords

💡Magnetic Circuit

A magnetic circuit is a closed path through which magnetic flux passes, typically consisting of a magnetic core and an air gap. In the video, the magnetic circuit is central to understanding how energy conversion occurs, especially when discussing the impact of an air gap. The script mentions that the magnetic field lines flow through both the magnetic material and the air gap, highlighting the importance of the magnetic circuit in maintaining the field.

💡Air Gap

An air gap is a physical separation between two components of a magnetic circuit, which can be a natural part of the structure or intentionally added for design purposes. The script explains that in electrical machines, the air gap exists between the rotor and the stator, and it requires more magnetomotive force to maintain the same magnetic field lines, which is crucial for the operation of such machines.

💡Magnetomotive Force (MMF)

Magnetomotive force is the driving force that creates a magnetic field in a magnetic circuit. The script uses the term to illustrate that an air gap in a magnetic circuit necessitates a higher MMF to achieve the same magnetic field density as a circuit without an air gap, demonstrating the increased effort required to maintain the magnetic field across the gap.

💡Reluctance

Reluctance is a measure of how much a material opposes the establishment of a magnetic field and is the magnetic equivalent of electrical resistance. The video script mentions that adding an air gap increases the reluctance of the magnetic circuit, which in turn requires a higher magnetizing current to achieve the same magnetic field density.

💡Saturation

Saturation in a magnetic circuit refers to the point at which the magnetic material can no longer increase its magnetization even with an increase in magnetizing force. The script explains that an air gap can be added to a magnetic circuit to avoid saturation, which can lead to loss of permeability and power.

💡Magnetic Field Density (B)

Magnetic field density, often represented by the symbol B, is a measure of the strength of the magnetic field. The script uses the term to discuss the requirement of a higher magnetizing current in a magnetic circuit with an air gap to achieve the same magnetic field density of 0.6 Tesla as compared to a circuit without an air gap.

💡Magnetic Field Intensity (H)

Magnetic field intensity, often represented by the symbol H, is a measure of the force that a magnetic field exerts on a magnetic material. The video script uses this term to calculate the excitation current required for both magnetic circuits with and without an air gap, showing that the intensity is determined by the material's characteristics.

💡Fringing

Fringing refers to the spreading out of magnetic field lines at the edges of a magnetic circuit, particularly at an air gap. The script describes how fringing increases the effective cross-section area of the air gap, which affects the overall behavior of the magnetic field within the circuit.

💡Magnetization Curves

Magnetization curves are graphical representations showing the relationship between the magnetizing force (H) and the magnetic flux density (B) in a magnetic material. The script uses these curves to compare the performance of magnetic circuits with and without air gaps, illustrating the increased reluctance and the need for higher magnetizing current in the presence of an air gap.

💡Exciting Current

Exciting current, also known as magnetizing current, is the current required to establish a magnetic field in a magnetic circuit. The script provides an example where the exciting current for a circuit with an air gap is significantly higher than that for a circuit without an air gap, emphasizing the impact of the air gap on the circuit's performance.

💡Abnormal Operating Conditions

Abnormal operating conditions refer to situations that deviate from the normal or expected operating parameters of a system. The script mentions that an air gap can protect magnetic circuits from damage due to saturation caused by such abnormal conditions, highlighting the design consideration of robustness in magnetic circuits.

Highlights

The air gap in a magnetic circuit can either be part of the natural structure or added intentionally to avoid magnetic saturation.

In electrical machines, an air gap naturally exists between the rotating rotor and stationary parts to maintain magnetic field flow.

The air gap requires significantly higher magnetomotive force (MMF) compared to the magnetic core material to maintain the same magnetic field.

For reactors or inductors, an air gap is added to prevent saturation, ensuring better performance and efficiency in high-energy conditions.

The air gap increases the circuit's reluctance, allowing higher excitation current before saturation.

Magnetization curves show that circuits with an air gap have less slope, indicating higher magnetizing current is needed for the same magnetic field density.

Adding an air gap helps in handling high currents or storing energy in the magnetic circuit without risking saturation.

Air gaps can be implemented to protect magnetic circuits from abnormal operating conditions that could lead to saturation.

The magnetic field in an air gap spreads out due to the fringing effect, increasing the effective cross-sectional area of the air gap.

When the air gap is small, the fringing effect can be neglected, allowing the cross-sectional area of the air gap to be assumed equal to that of the magnetic core.

Multiple small air gaps can be used to reduce the fringing effect in practical designs.

Magnetic circuits with air gaps require significantly higher current to achieve the same magnetic field density, such as 5.1 amperes with an air gap compared to 0.328 amperes without.

The magnetomotive force (MMF) in a magnetic circuit with an air gap is primarily concentrated in the air gap itself.

Even a small air gap length (0.4 cm) requires much higher MMF compared to the magnetic core, showing that most of the energy is stored in the air gap.

Magnetic circuits are highly sensitive to the presence of an air gap, significantly impacting energy storage, magnetizing current, and circuit efficiency.

Transcripts

welcome back to the energy conversion

lectures

in this lecture

i will give some details about the

impact of an air gap in a magnetic

circuit

in some applications

the air gap can be part of the nature

structure of the magnetic circuit

in other types of applications

the air gap could be added to the

magnetic circuit as part of its design

let's give some examples to these two

cases

the first type of applications such as

electrical machines

the rotating part which called rotor

is physically isolated from the

stationary part by an air gap

practically the same magnetic field

lines flowing through the magnetic

material and air gap

to maintain same magnetic field lines

the air gap will require much more

magnetomotive force comparing with the

core or the magnetic materials

the second type of applications

such as reactor or inductor

the air gap is mostly added to avoid the

risk of saturation

that cause loss of permeability

increase of current and loss of power in

the magnetic circuit

implementing an air gap in a magnetic

circuit

adding additional reluctance to the

magnetic circuit

this will extend the range of the

excitation current before magnetic

saturation

occurs

to elaborate on this concept

let's look at this figure that shows the

magnetization curves of two magnetic

circuits

one with air gap and other without air

gap

it is very clear

that the curve with an air gap

has less slope comparing with the one

without an air gap

the air gap causes an increase of the

reluctance

that means a higher magnetizing current

i

is required to obtain same magnetic

field density b

comparing with the non air gap

magnetization curve

basically

if you have a magnetic circuit and you

need to apply high current or store high

energy

without the risk of saturation

you need to add an air gap to your

design of the magnetic circuit

it should be noted here that abnormal

operating condition can also lead to the

saturation and cause damage to the

magnetic circuits

therefore air gap can also be

implemented to protect the magnetic

circuits from the saturation and

abnormal conditions

to understand how the magnetic field

behaves when there is an air gap in a

magnetic circuit

let's assume we have the following

magnetic circuit that consists of a

magnetic core and an air gap

in the previous lectures we assume that

the magnetic field lines

are confined and uniformly distributed

within the magnetic materials

and air gap

therefore

the cross-section areas of the magnetic

field densities

of the magnetic material and the air gap

are same

in other words

ac equal to ag

and bc equal to bg

if you remember

because of this assumptions we were able

to represent the magnetic field lines of

the magnetic circuit by the mean

magnetic field path phi

any practice

the magnetic field lines phi

that flow

through the air gap is spread out as

shown

this behavior

known as fringing of the magnetic field

lines

the flinging behavior

cause an increase in the effective

cross-section area of the air gap

in other words

the cross-section area of the air gap

will be greater than the cross-section

area of the magnetic material

or

a g greater than ac

and therefore bg less than bc

it should be noted here that if the air

gap is very small

the fringing effect can be neglected

therefore

we can assume that a g equal to ac

and therefore

bg equal to bc and equal to phi over ac

any practice

if we need to add an air gap to a

magnetic circuit

the air gap will be divided into several

small air gaps

to reduce the fringing effect

now let's assume we have these two

magnetic circuits

and try to determine

the excitation or magnetizing current i

for both circuits

as you can see

circuit a

is implemented without air gap and

circuit b

is implemented with

a small air gap

since the magnetic field density b

is known and equal to 0.6 tesla

the magnetic field intensity sc

for the soft cast steel core

can be determined for both circuits from

the bh curve

and it is equal to

325 ampere turns over meter

let's start with the circuit that has no

air gap

the excitation current can be determined

as follows and it is equal to 0.328

amperes

using the same procedure the excitation

current

for the magnetic circuit with air gap

can be determined as follows

and it is equal to

5.1 amperes

actually i provided this example

to highlight the following two points

the first point is that the magnetic

circuit with the air gap will require

higher current of

5.1 amperes

to achieve magnetic density of 0.6 tesla

however

the magnetic circuit without air gap

will require only 0.328

amps

to achieve magnetic density of 0.6 tesla

these results confirm what i have

explained at the beginning

of this lecture

the second point is that the

magnetomotive force of the air gap of

circuit b

is equal to 1909.8

ampere turns

while the magnetomotive force of the

magnetic

core

of the same circuit is equal to 130

ampere turns

that means

even with a small air gap of 0.4

centimeter length compared with 40

centimeter core length

most of the mmf

or magneto motor force is used at the

air gap

in other words

most of the energy

is stored in the air gap

now let's conclude this lecture at this

point and will continue in the next

lecture

thanks for your attention i am essan and

nebby and it was a pleasure sharing this

lecture with you thank you