# 4 Effects of Induction Hardening You Should Know

## 1. Skin effect

Skin effect is also called surface effect.

When direct current passes through a conductor, the current density is equal across the conductor section.

When alternating current passes through the conductor, the current density on the cross-section of the conductor is small in the middle and large on the surface.

When the current frequency is quite high, there may be no current in the center of the conductor and all the current is concentrated on the surface layer of the conductor.

This phenomenon is called the surface effect of high-frequency current.

The skin effect of high-frequency current on the cylindrical conductor is shown in Fig. 1.

Fig. 1 skin effect of high frequency current

The reason for the skin effect is that when the alternating current passes through the conductor, the magnetic field surrounding the conductor is generated at the same time.

This magnetic field generates the self induced electromotive force on the conductor.

The direction of the self induced electromotive force is opposite to the original electromotive force.

The self induced electromotive force is the strongest at the center of the cylindrical conductor and the weakest at the surface.

As a result of the cancellation of the self induced electromotive force against the original electromotive force, the surface of the high-frequency current is the largest and the center is the smallest, forming a skin effect.

Due to the skin effect, the current density on the cross-section of the conductor decreases exponentially from the surface to the center.

The current density IX at the position x from the surface is shown in Formula 1, that is:

Where,

• I0 – surface current density (maximum)
• C – speed of light
• μ – Permeability of conductor material
• ρ – Resistivity of conductor material
• f – Current frequency

In engineering, the depth from the conductor surface to the point where the amplitude of IX decreases to 1 / e of I0 (e = 2.718, then 1 / e ≈ 36.79%) is called the current penetration depth, which is expressed by δ and calculated by formula 2:

It can be seen from the above formula that the current penetration depth δ is related to ρ, μ and f;

When ρ increases and μ and f decrease, δ will increase.

According to the theoretical calculation, the heat generated by the current accounts for 86.5% of the total heat generated by the current in the electric penetration depth a layer.

It can also be seen from equation 2 that when the current frequency f is constant, as long as ρ and μ change, there can be different current penetration depths.

Materials have different ρ and μ at different temperatures, so there are different current penetration depths at different temperatures.

Fig. 2 Relationship between magnetic permeability, resistivity and heating temperature of steel

Fig. 2 shows the relationship between the magnetic permeability μ and the resistivity ρ of steel and the heating temperature.

It can be seen that the resistivity of steel increases with the increase of heating temperature.

At 800-900 ℃, the resistivity of all kinds of steel is basically the same, about 10-4 Ω· cm;

The magnetic permeability μ is basically unchanged when the temperature is lower than the magnetic transition point A2 or the ferrite austenite transition point, but decreases sharply when it exceeds A2 or is transformed into austenite.

Substituting the values of ρ and μ at room temperature or 800-900 ℃ into formula 2, the following simple formula can be obtained:

At 20 ℃,

At 800 ℃,

Generally, the current penetration depth at 20 ℃ is called “cold current penetration depth”, and the current penetration depth δ800 at 800 ℃ is called “hot current penetration depth”.

## 2. Proximity effect

The distribution of the alternating current in the conductor is affected by the alternating current in the adjacent conductor.

This phenomenon is called proximity effect.

There are two main cases of proximity effect in practical application.

(1) When two parallel conductors are fed with alternating current with opposite directions and equal magnitude, the current is concentrated in the inner surface layer of the two conductors and flows.

The magnetic field strength between the two conductors is strengthened on the surface of the magnetic field, and the magnetic field strength outside the two conductors is weakened.

As shown in Fig. 3a, it is a reverse current.

Fig. 3 performance of proximity effect on rectangular bus bar

a – reverse current;  b – current in the same direction

(2) When two parallel conductors are fed with alternating current with the same direction and the same size, the current concentrates on the outer surface layer of the two conductors and flows.

The magnetic field shows that the magnetic field strength between the two conductors is the weakest, and the magnetic field outside the two conductors is strengthened due to mutual superposition.

As shown in Fig. 3b, the current is in the same direction.

Fig. 4 performance of proximity effect in induction heating

• a-monopole round tube conductor for heating flat plate
• b-unipolar square tube conductor for heating flat plate
• c – heating solid cylindrical parts when the gap of cylinder inductor is equal
• d – heating solid cylindrical parts when the gap of cylinder inductor is not equal

The proximity effect is also shown between the inductor and the parts to be induction heated, as shown in Fig. 4.

Fig. 4a shows that when the effective conductor is a monopole round pipe wire used for heating a flat plate, the eddy current on the flat plate is in a circular arc shape, which corresponds to the current distribution on the round pipe wire;

Fig. 4b shows that the eddy current layer on the flat plate is flat when the effective conductor is a unipolar square tube conductor used for heating the flat plate;

Fig. 4c is a diagram of heating a solid cylindrical part when the gap of the round tube inductor is equal.

Because the gap of the round tube inductor is equal, the current layer and the eddy current layer on the inductor and the workpiece are flat and equal;

Fig. 4d shows that in the cylindrical inductor, the cylindrical parts are inclined, resulting in different gaps.

In the places with small gaps, the current layer on the inductor and the eddy current layer on the workpiece are thick, and in the places with large gaps, both are thin.

## 3. Ring effect

When a high-frequency current passes through a circular conductor, the maximum current density is distributed inside the circular conductor.

This phenomenon is called ring effect.

The essence of the ring effect is the proximity effect of the ring inductor.

Fig. 5 is a schematic diagram of the ring effect.

Fig. 5 Schematic diagram of ring effect

Based on the principle of ring effect, we can explain the reason why the heating efficiency of the cylindrical parts and the inner surface of the inner hole parts are greatly different when the same ring inductor is used to heat the outer surface of the cylindrical parts and the inner surface of the inner hole parts respectively.

As shown in Fig. 6, the ring inductor is used to heat the cylindrical parts and the cylindrical parts respectively.

Fig. 6 heating cylindrical parts and round hole parts with ring inductors

b1 – heating width of cylindrical surface

b2 – heating width of inner hole surface

a – clearance; φ- Magnetic flux

When heating the outer surface of cylindrical parts, the workpiece is heated violently and rapidly, and the heating area is wider than b1.

When the inner surface of the round hole is heated, the heating is gentle, the temperature rise is slow, and the heating zone is narrow to B2. It can be seen from the figure that b1 ≥ b2.

Although the gap in both cases is a, due to the ring effect, the high-frequency current is concentrated on the inner side of the inductor.

When the inner hole surface is heated, the real gap is much larger than a.

Therefore, the eddy current intensity of the inner hole surface will be much smaller than that of the cylindrical surface, resulting in a moderate heating of the inner surface of the circular hole.

## 4. Notch effect of magnetic conductor

A copper conductor with rectangular cross-section is placed in the slot of the conductor.

When high-frequency current passes through the conductor, the current will only flow through the conductor surface layer at the opening of the conductor.

This phenomenon is called the slot effect of the conductor.

The slot effect is shown in Fig. 7.

Fig. 7 notch effect of magnetic conductor

H – magnetic field strength; I-high frequency current

The conductive magnet has a high permeability and a small magnetic resistance.

The magnetic force lines generated by the conductive conductor will be concentrated through the conductive magnet at the bottom of the slot.

Although the conductor at the bottom of the slot links the most magnetic flux and generates a lot of self induced electromotive force, similarly, the conductor at the opening of the slot generates the smallest self induced electromotive force, so the high-frequency current is forced to flow here.

Fig. 8 effective coil, conductive magnet and current distribution of inductor

1-conductive magnet

2-effective coil of inductor

3-current

By using the notch effect of the magnet, we can expel the high-frequency current to the outer surface of the ring inductor, which can improve the heating efficiency of the inner hole surface. The effective coil of the inductor, the magnet and the current distribution are shown in Fig. 8.

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