Characterisation of Soft Magnetic Materials Under Rotational Magnetisation

Stanislaw Zurek

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351397070
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

The book presents practical aspects related to the measurement of rotational power loss in soft magnetic materials. The book furthermore focuses on practical aspects of performing such measurements, the associated difficulties as well as solutions to the most common problems. Numerous practical aspects, hands-on experience, and most commonly encountered pitfalls are heavily discussed in the book. The text begins with introduction to magnetism, then follows with definitions of measurement methods of rotational power loss from physical viewpoint. Two chapters describe and detail the various sensors which can be employed for such measurements as well as all the aspects of designing, making, and using a magnetising apparatus. A synthesis of the likely optimal design of a magnetising apparatus is also given, preceded with the full reasoning based on all the research carried out to date. Characterisation of Soft Magnetic Materials Under Rotational Magnetisation serves as an excellent starting point for any student having to perform magnetic measurements under rotational magnetisation, but also under 1D, 2D or 3D excitation. Because the methods, sensors, and apparatus are extensively discussed it will also be a great reference for more senior researchers and experts in the field. There is a whole chapter devoted to analysis of measurement uncertainty. This subject is rarely published for magnetic measurements, which makes it more difficult for all researchers to understand the concepts and methodology used in uncertainty estimation. This chapter not only introduces the whole subject, but also provides multiple step-by-step examples which can be easily followed, from very simple cases to much more complex ones. All equations are presented with full SI units which greatly helps in practical application of the presented methodology. Each chapter is written in such a way that it can be studied on its own, so that the reader can focus only on the specific aspects, as required.

1

Introduction

1.1Brief Introduction to Magnetism

A magnetic field is produced whenever there are electric charges in motion, which represent the electric current, I, measured in amperes* (A). A magnetic field can also be produced by other magnetic sources (permanent magnets, magnetic dipoles, etc.), but these are primarily also always generated by the macroscopic motion of electric charges or fundamental subatomic properties such as spin magnetic moment and orbital magnetic moment.

For a visual representation, the magnetic field is often depicted by magnetic field lines (Figure 1.1). The lines encircle the conductor with current, and the magnetic field strength, H, is always generated in a direction (and plane) perpendicular to the current causing it.

Figure 1.1 An electric current I in a wire generates a magnetic field measurable as magnetic field strength H: (a) general view, (b) cross-sectional view.

The strength of the magnetic field at a given point in space depends on the magnetic path length, l, measured in metres (m), through which the field travels.

Looking at the example shown in Figure 1.1, we can see that the magnetic field lines follow a path, whose length for a given radius, r, is

l=2⋅π⋅r(m)	(1.1)

Therefore, the path l increases proportionally with the distance r. At any point in space, a magnetic field can be described quantitatively by a value† of magnetic field strength, H. Because the field strength is produced by the current I (A) over a path l (m), the resulting unit is ampere per metre (A/m).

From the Maxwell equations (describing the laws of electromagnetism), the magnetic field strength can be derived for the configuration shown in Figure 1.1, and for an infinitely long conductor, the magnetic field strength at a given point is

H=Il=I2⋅π⋅r(A/m)	(1.2)

Hence, the value of H is directly proportional to the current generating it but inversely proportional to the distance, or more precisely to the magnetic path length. This means that the field is strongest near the source (in this case, current-carrying conductor) and reduces with the distance from it.

If instead of a single wire, there are N closely positioned parallel wires carrying the same current I (e.g. as in a multi-stranded wire), this is equivalent to a single wire with the equivalent total cross-sectional area and a combined current N ⋅ I; therefore,

H=N⋅Il(A/m)	(1.3)

which can be rearranged taking a form of simplified Ampere’s law (one of the Maxwell equations) in a scalar notation for a uniform medium:

N⋅I=H⋅l(A)	(1.4)

where N ⋅ I represents the so-called magnetomotive force, or MMF, with the unit of ampere (A), commonly referred to as ampere–turn product (N is unitless). The magnetomotive force represents a source generating magnetic field and the magnetic field strength H can be a measure of the so-called applied magnetic field.

When the current is ‘wrapped’ in a coil, the field inside such a loop is intensified due to the contributions from all the sides (Figure 1.2a).

Figure 1.2 Magnetic field around a loop of current (a) and a computer simulation of the cross section showing the increased density of magnetic field lines inside the current loop (b).

It can be calculated that, at the centre of such single-turn flat loop with radius r, the magnetic field strength is equal to

H=I2⋅r(A/m)	(1.5)

The current loops can be placed one after another in a series, creating a long coil or a solenoid (Figure 1.3). The magnetic field lines are concentrated inside the solenoid where the resulting magnetic field is the most uniform.

Figure 1.3 An example of a coil: solenoid (a) and a computer simulation of the cross section showing...