Anisotropy of Permanent Magnet Shape and Demagnetization Field and Demagnetization Factor

Anisotropy of Permanent Magnet Shape and Demagnetization Field and Demagnetization Factor

Make the permanent magnet into a certain shape. Take the block magnet in the following figure as an example. If you measure the magnetization curve in the open circuit state along the x, y, and z directions of the magnet, you can find that the magnetization along the x direction requires only a lower magnetic field. (H1) can be magnetized to technical saturation, while measured along the y and z directions, respectively, higher magnetic fields are required to magnetize it to technical saturation, a phenomenon known as shape anisotropy of permanent magnets. The direction that requires a smaller magnetic field to magnetize it to technical saturation is called the easy magnetization direction; the direction that requires the largest magnetic field to magnetize it to technical saturation is called the hard magnetization direction.

Anisotropy of Permanent Magnet Shape and Demagnetization Field

Demagnetizing field Hd

Why do permanent magnets of a certain shape (non-spherical) appear shape anisotropy? This is related to the demagnetization field of the permanent magnet.

We know that block or cylindrical permanent magnets always have N poles and S poles, and the existence of magnetic poles will generate magnetic fields around them and inside the magnet. The magnetic field generated by the poles of a permanent magnet is always from N pole to S pole, both around and inside the magnet. The demagnetization field inside the permanent magnet is represented by Hd, its direction is from N pole to S pole, and the direction of permanent magnet magnetic moment Mm or magnetization direction is from S pole to N pole. The Hd inside the permanent magnet is opposite to the direction of the magnetization M, which plays the role of demagnetization, so it is called the demagnetization field.

How is the demagnetizing field of a permanent magnet generated? We can regard a permanent magnet as composed of two magnets, A and B. The A magnet is just in the magnetic field generated by the B magnet, and the B magnet is also in the magnetic field generated by the A magnet. These magnetic fields are just from N pole to S pole, so it is opposite to the magnetization direction of the magnet, so it is called demagnetization field.

The demagnetizing field strength of a permanent magnet is related to the shape and size of the permanent magnet. For example, for a ring-shaped permanent magnet, the demagnetization field strength varies with the size of the gap of the ring-shaped permanent magnet (that is, the length of the permanent magnet). When magnetizing along the ring axis of the ring-shaped permanent magnet, no demagnetization field is generated; when the ring-shaped permanent magnet is cut in half, the demagnetization field of the half ring is Hd; the shorter the ring-shaped permanent magnet is cut , the absolute value of its demagnetizing field Hd also increases gradually. The order of the absolute value of the demagnetizing field increases gradually is Hd (e) > Hd (d) > Hd (c) > Hd (b) > Hd (a)→0.

It can be inferred from this that when the coercive force Hcj of the permanent magnet is not large enough, if the permanent magnet is made thin and magnetized along the thin direction, it may not be charged because the demagnetizing field is too large.

Anisotropy of Permanent Magnet Ring Shape Demagnetization Field Demagnetization Factor

Demagnetization factor N

The above example shows that the demagnetization field of the permanent magnet is related to the shape and size ratio of the magnet. Experiments and theoretical calculations can prove that the demagnetization field of permanent magnets Hd=-NM, where M is the magnetization intensity of permanent magnets, N is the demagnetization factor, and the negative sign in the formula means that Hd is in the opposite direction to M.

For an infinitely long round rod-shaped permanent magnet, the demagnetization factor N1 along the length direction and the demagnetization factor Nd in the diameter direction can be expressed as the following formula, where k is the size factor, k=l/d, and d is the rod-shaped magnet. diameter and l is the length.

The demagnetization factor (N1+Nd+Nd=1) of any permanent magnet in three mutually perpendicular directions is equal to 1.0. It can be seen that k=l/d=0, which is equivalent to a very thin plate, and its demagnetization factor N1→1.0; for a round rod-shaped permanent magnet magnetized along the axial direction, the change of its demagnetization factor along the length l is shown in the figure below. When the length l is equivalent to 200 times the diameter, the demagnetization factor can be ignored, and the demagnetization field can be considered.