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Influence of turns on permeability test

1 introduction

as we all know, permeability μ It is a key technical index of soft magnetic materials. Relative permeability μ The measurement of is basically winding on the standard sample ring. Measure the inductance L of its winding coil, and then use L to calculate the permeability of the material. However, for the same sample ring, the number of test turns wound by different instruments or the same instrument is different, and the measured material permeability μ The difference may be great. Sometimes it will cause contradictions or disputes between the supplier and the demander. In particular, the number of coil turns is tested, and then the pressure is converted into the kinetic energy of jet mixing through a special nozzle μ Values are different, sometimes measured with more turns μ The value is low, but sometimes it is measured when the number of turns increases μ The value is higher. This will confuse some testers. This paper attempts to clarify the influence of different test instruments, test coil turns and calculation formulas on the permeability test according to the test principle

2 several related concepts of permeability

for a uniform magnetic medium, if it is magnetized in a uniform magnetic field H, the magnetic medium itself will produce an additional magnetic field H ', and the directions of H' and H are the same. The total magnetic field strength superimposed by H 'and H is called the magnetic flux density B of this magnetic material [1]. It can be seen that the magnetic flux density B and the magnetic field strength h are essentially physical quantities representing the strength of the magnetic field. However, the names and sizes of the units they use may be different. In the usual Gauss unit system, the unit of H uses OE and the unit of B uses GS. The names of these two units are different, but they are exactly the same size. In the international system of units now emphasized, the unit of B is Tesla (T), the unit of H is ampere per meter (a/m), and the units of B and H are no longer equal, 1a/m =4 × T。 The ratio of magnetic flux density to magnetic field strength is called the permeability of materials, and the ratio of their values is called absolute permeability μ Absolutely, the ratio of these two physical quantities is called relative permeability μ。 Obviously, in the Gaussian system of units, because the units of B and H are equal, the ratio of their values is equal to the ratio of their magnitudes. Therefore, in the Gaussian unit system, the relative permeability of the material is equal to the absolute permeability, and there is no need to distinguish between the absolute permeability and the relative permeability. For vacuum, it will not produce additional magnetic field, and B is equal to h, so the permeability of vacuum is equal to 1. In the international system of units, since the unit sizes of B and H are no longer equal, the ratio of their values μ It must not represent the ratio of their physical quantities μ， The relative permeability of the material is no longer equal to its absolute permeability. For vacuum, because no additional magnetic field can be generated, the two physical quantities b and H are equal, so the permeability of vacuum is equal μ Equal to 1. If the magnetic field intensity H at a point in vacuum is ya/m, the magnetic flux density B at that point should be 4 π y × T. Therefore, the ratio of the values of B and h at this point is the vacuum absolute permeability in the international system of units μ 0=4π × H/m。 The absolute permeability of general soft magnetic materials is divided by μ 0 to get its relative permeability μ= B/μ 0H。 Unless otherwise specified, the reference to permeability refers to relative permeability

DC magnetization curve b~h of general soft magnetic materials and its corresponding μ~ The H curve is shown in Figure 1. It can be seen from Figure 1 that the initial part of the b~h curve rises linearly, then rises steeply, and finally approaches the level. The permeability corresponding to the initial linear part of the b~h curve is a constant, which is called the initial permeability μ i。 From the origin to the b~h curve, when the sensor is subjected to the effect of tension P, a tangent line is introduced, and the permeability corresponding to its tangent point reaches the maximum, which is called the peak permeability μ m。 From initial permeability to peak permeability μ m. This section of permeability is also collectively referred to as amplitude permeability μ a。 obviously, μ A rises with the increase of magnetic field H

for soft magnetic materials under AC magnetic field, the μ "Negligible, μ' It is considered to be the AC permeability of the material μ。 AC magnetization curve of materials and corresponding μ~ H curve is very close to DC, and there are also μ i、 μ A and μ m. Figure 1 can still be used for similar explanation and explanation

3 permeability test instrument function

permeability measurement is an indirect measurement, which measures the inductance of the winding coil on the core, and then calculates the permeability of the core material with the formula. Therefore, the permeability test instrument is the inductance tester. It is emphasized here that for some simple inductance test instruments, the test frequency and test voltage cannot be adjusted. For example, for some bridges, the test frequency is 100Hz or 1kHz, and the test voltage is 0.3V. The given 0.3V is not the voltage at both ends of the inductance coil, but the voltage generated by the signal generator. As for the voltage at both ends of the measured coil, it is unknown. If high-end instruments are used to measure inductance, such as Agilent 4284A precision LCR tester, not only the test frequency is adjustable, but also the voltage and magnetizing current at both ends of the measured inductance coil are adjustable. Understanding these functions of the test instrument is very helpful for the correct measurement of permeability

4 material permeability the measurement method and principle of turning the knob to the corresponding range position

speaking of permeability μ It seems very simple to measure the inductance by winding a few turns of the coil on the material sample ring, and then finding a formula to calculate it. In fact, for the same sample ring, using different instruments, winding different turns, adding different voltages or using different frequencies, it is possible to measure the permeability with very different differences. The reason for the great difference in test results is that not every tester has the energy to figure it out. The influence of distributed capacitance on inductance and impedance measurement has been discussed in another article and may be published in the journal "magnetic materials and devices". This paper mainly discusses the influence of different turns and calculation formulas on the measurement of permeability

4.1 influence of calculation formula

as you know, measuring permeability μ The general method is to measure the inductance L by winding an n-turn coil on the sample ring, because the expression of l can be deduced as [1]:

l= μ 0 μ N2a/l (1)

therefore, the calculation formula of magnetic permeability derived from formula (1) is:

μ= Ll/μ 0n2a (2)

where: l is the magnetic circuit length of the magnetic core, and a is the cross-sectional area of the magnetic core

for a ring magnetic core with rectangular cross-section, if its average magnetic circuit length l= π (d+d)/2 is taken as the magnetic circuit length L of the magnetic core, and the cross-sectional area a=h (D-D)/2, μ 0=4π × All of them are substituted into formula (2) to get: (3)

, where D is the outer diameter of the ring, D is the inner diameter, and H is the height of the ring, as shown in Figure 2. Substitute the inner diameter of the ring d=d-2a into formula (3) to get: (4)

where: A is the wall thickness of the ring

for the ring magnetic core with small inner diameter, the inner diameter is not as easy to measure as the wall thickness, so formula (4) is more convenient. (4) Equation (3) is equivalent to equation (3), and their origin is that the average magnetic circuit length of the ring is taken as the magnetic circuit length of the magnetic core. The permeability calculated by them is called the ring permeability of the material. Some people say that the permeability measured by ring samples is called ring permeability, which is incorrect. In fact, the ring permeability is higher than the real permeability of the material, and the thicker the wall of the sample ring, the greater the error

for the sample ring, the magnetization field is uneven in the radial direction under the same ampere turn magnetomotive force excitation. The closer to the outer side of the ring wall, the weaker the magnetic field. Permeability throughout the sample ring μ Under constant conditions, the closer to the outside of the ring wall, the lower the magnetic flux density B of the ring. In order to eliminate the influence of this uneven magnetization on the measurement, we regard the sample ring as consisting of an infinite number of thin-walled rings with radius R and wall thickness Dr. According to formula (1), the inductance DL produced by each thin-walled ring can be written as:

in the above formula: D is the outer diameter of the sample ring, and D is the inner diameter. Replace the natural logarithm with the common logarithm, and equation (8) is changed into: (9)

if the sample ring is composed of the same material, the permeability calculated by equation (7), (8) or (9) is the true permeability of its material μ。 It is slightly lower than its ring permeability

4.2 influence of the number of turns n of the test coil

since the inductance L is directly proportional to the number of turns N 2, it is reasonable to use the permeability calculated by formula (9) μ It should no longer be related to the number of turns n, but in fact it is often related

generally, the test frequency used for the measurement of material permeability is not high, and it is often tested at the frequency of 1kHz or 10kHz. Generally, sinusoidal signal is used as the test signal. Because the frequency is not high, the resistance part of the sample surrounding coil impedance can be ignored. The winding coil is regarded as a pure inductance L connected to the measuring instrument. The test equivalent circuit is shown in Figure 3. The effective value of the voltage generated by the instrument signal source is u, and RI is the output impedance of the signal source. It is easy to write the expression of magnetizing current from Figure 3:

in the above formula, ω Is the angular frequency of the instrument signal source, and l is the inductance of the sample surrounding the group coil

L= μ 0 μ In n2ae/le (11)

(11), AE is the effective cross-sectional area of the magnetic core, and le is the effective magnetic circuit length of the magnetic core. If AE and le of the ring core are substituted, the result of equation (11) will become the same as that of equation (6)

the above formula tells us that when the number of turns of the test coil is small, the strength of the test magnetic field is directly proportional to the number of turns. As the number of turns increases, when（ ωμ 0 μ AE) when 2n4 is much larger than le2ri2, equation (13) can be approximated as: (15)

from equation (15), when the number of turns of the test coil is too many, the strength of the test magnetic field will be inversely proportional to the number of turns

from the above analysis, when measuring the permeability, the magnetization field intensity in the sample ring is related to the number of turns of the test coil. When the number of turns is a certain value, the magnetic field intensity will reach the strongest value. The permeability of the material is closely related to the magnetization field strength, so the measurement of permeability is related to the number of turns of the test coil. Now we will discuss the influence of turns on permeability test in combination with figure 1

4.2.1 low test voltage U

as mentioned above, for high-end instruments, such as Agilent 4284A precision LCR tester, its test voltage can be adjusted very low, so that when the test magnetic field intensity reaches the maximum with the change of turns, it still does not exceed the starting area shown in Figure 1. At this time, the initial permeability of the material is always measured μ i. It is independent of the number of turns n of the test coil. With the same instrument, if the test voltage is adjusted higher, it can no longer be guaranteed that the permeability measured by different turns is the initial permeability. At this time, the measured permeability will be related to the number of turns of the test coil

4.2.2 the test voltage u cannot be adjusted

most simple instruments for measuring inductance cannot flexibly adjust the test voltage and frequency. For example, the test frequency of 2810 LCR bridge is 100Hz or 1kHz, and the test voltage is less than 0.3V. (to be continued) (end)

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