1. Skin effect
The skin effect is also known as the surface effect.
When direct current flows through a conductor, the current density at all points of the conductor's cross section is equal.
However, when alternating current flows through a conductor, the current density in the cross-section of the conductor is lowest in the middle and highest at the surface.
When the current frequency is high enough, the center of the conductor may have no current and all the current is concentrated in the surface layer of the conductor.
This phenomenon is known as high-frequency current surface effect, and the skin effect of high-frequency current in a cylindrical conductor is shown in Figure 1.
Fig. 1 Skin effect of high frequency current
The reason for the skin effect is that when alternating current flows through a conductor, it simultaneously produces a magnetic field around the conductor.
This magnetic field generates a self-induced electromotive force in the conductor, which has a direction opposite to the original electromotive force.
The self-induced electromotive force is strongest at the center of the cylindrical conductor and weakest at the surface.
The cancellation of the original electromotive force by the self-induced electromotive force results in maximum surface current density and minimum center current density for high-frequency current, creating the skin effect.
Due to the skin effect, the current density in the cross-section of the conductor decreases exponentially from the surface to the center.
The current density I x at a distance x from the surface is given by Equation 1.
Where,
- EU 0 – surface current density (maximum)
- C – speed of light
- μ – Permeability of the conductive material
- ρ – Resistivity of the conductive material
- f – Current frequency
In engineering, the depth from the surface of the conductor to the point where the amplitude of I x falls to 1/e of I0 (where e=2.718, so 1/e ≈ 36.79%) is called current penetration depth, denoted by δ. It can be calculated using Equation 2.
As shown in the above equation, the current penetration depth δ is related to ρ, μ and f. When ρ increases and μ, f decreases, δ will increase. Theoretical calculations show that within the current penetration depth layer of δ, the heat generated by the current represents 86.5% of the total heat generated by the current.
Equation 2 also shows that when the current frequency f remains constant, different current penetration depths can be achieved as long as ρ and μ change. Materials have different ρ and μ at different temperatures, resulting in different current penetration depths at different temperatures.
Fig. 2 The relationship between magnetic permeability, electrical resistivity of steel and heating temperature.
Figure 2 shows the relationship between the magnetic permeability μ and the electrical resistivity ρ of the steel and the heating temperature.
It can be observed that the electrical resistivity of steel increases with increasing heating temperature. At 800-900°C, the resistivity of various types of steel is basically the same, around 10-4 Ω·cm. The magnetic permeability μ remains basically unchanged below the A2 magnetic transformation point or the ferrite-austenite transformation point, but drops sharply when it exceeds A2 or transforms to austenite.
Substituting the values of ρ and μ at room temperature or 800-900°C into Equation 2, the following simplified expression can be obtained:
At 20ºC,
At 800℃,
The current penetration depth at 20°C is generally referred to as “cold state current penetration depth”, while the current penetration depth at 800°C, denoted as δ800, is referred to as “current penetration depth”. in the hot state.” .
2. Proximity effect
The distribution of alternating current within a conductor is influenced by alternating current in nearby conductors, a phenomenon known as proximity effect.
In practical applications, the proximity effect manifests itself mainly in two situations.
(1) When two parallel conductors carry equal alternating currents in opposite directions, the current is concentrated on the inner surface layer of the two conductors, and the magnetic field is strengthened between the two conductors, while the magnetic field on the outer side of the conductors is weakened. Figure 3a shows the case of opposite currents.
Figure 3 Manifestation of the proximity effect in a rectangular bus.
a – Opposing Currents
b – Currents in the same direction
(2) When two parallel conductors carry equal alternating currents in the same direction, the current is concentrated on the outer surface layer of the two conductors, and the magnetic field between the two conductors is weaker, while the magnetic field on the outer side of the conductors is weaker. reinforced due to mutual superposition. Figure 3b shows the case of currents in the same direction.
Fig. 4 Proximity effect performance in induction heating
- A-monopole round tube conductor for flat plate heating
- b-unipolar square tube conductor for flat plate heating
- c – heating of solid cylindrical parts when the cylinder inductor gap is equal
- d – heating of solid cylindrical parts when the cylinder inductor clearance is not equal
The proximity effect also manifests itself between the induction coil and the part being heated, as shown in Figure 4 for proximity effect during induction heating.
Figure 4a shows the arc-shaped eddy current on a flat plate heated by a unipolar circular tubular wire, corresponding to the current distribution in the circular tubular wire;
Figure 4b shows the straight layer of eddy currents on the flat plate heated by a unipolar square tubular wire;
Figure 4c shows the even current and eddy current layers in a solid cylindrical part heated by a circular coil, with equal gaps between the coil and the part at all locations;
Figure 4d shows the uneven current and eddy current layers due to uneven gaps between the cylindrical part and the circular coil, with thicker current and eddy current layers at locations with smaller gaps and thinner layers at locations with larger gaps.
3. Ring effect
When high-frequency current flows through a circular ring-shaped conductor, the maximum current density is distributed on the inner side of the ring-shaped conductor, a phenomenon known as skin effect. The skin effect is essentially the proximity effect of a circular ring inductor.
Figure 5 shows a schematic diagram of the skin effect on a circular ring.
Fig. 5 Schematic diagram of the ring effect
Using the principle of skin effect, we can explain the significant difference in heating efficiency when using the same circular inductor to heat the outer surface of a cylindrical part and the inner surface of a cylindrical part with a through hole, as shown in Figure 6.
Figure 6 shows the use of a circular inductor to heat a cylindrical part and a cylindrical part with a through hole separately. The heating efficiency of the two workpieces is significantly different due to the skin effect.
Fig. 6 Heating of cylindrical parts and round hole parts with ring inductors
b1 – heating width of the cylindrical surface
b2 – heating width of the inner surface of the hole
the Liberation; φ- Magnetic flux
When heating the outer surface of a cylindrical part, the heating is intense and the temperature increases rapidly, resulting in a wider heating area of b1. On the other hand, when heating the inner surface of a cylindrical part with a through hole, the heating is smooth and the temperature increases slowly, resulting in a narrower heating area of b2. From the figure it can be seen that b1 ≥ b2, although the gaps in both cases are equal to a.
Due to the skin effect, the high frequency current is concentrated on the inner side of the inductor. When heating the inner surface of a cylindrical part, the true gap between the part and the inductor is much greater than that, resulting in a significantly lower eddy current intensity on the inner surface of the through hole compared to the outer surface of the cylindrical part. . This leads to smoother heating of the inner surface of the through hole.
4. Magnetic core slot effect
When a rectangular copper conductor is placed in the slot of a magnetic core, high-frequency current flows only through the surface layer of the conductor at the opening of the magnetic core. This phenomenon is known as the magnetic core slot effect, as shown in Figure 7.
Fig. 7 notch effect of magnetic conductor
H – magnetic field intensity; High frequency I-current
The magnetic core has high magnetic permeability and low magnetic resistance. The magnetic flux generated by the current-carrying conductor will be concentrated through the magnetic core at the bottom of the groove.
Although the conductor at the bottom of the groove has the largest magnetic flux connection, it also generates a large amount of self-induced electromotive force.
Likewise, the conductor at the gap opening generates the smallest self-induced electromotive force. As a result, high frequency current is forced to flow through this area.
Fig. 8 Effective coil, conductive magnet and inductor current distribution
Magnet 1 conductor
Effective inductor coil 2
3 chains
By utilizing the slit effect of the magnetic core, we can direct the high-frequency current to the outer surface of the circular inductor, thereby improving the heating efficiency of the inner surface of the through hole. The effective turns of the inductor, the magnetic core and the current distribution are shown in Figure 8.
