# Investigation of Segmented Halbach Array Design for Passive Magnetorheological Brake System
## 2 Permanent-Magnet Halbach Array Design  
### Concept of Halbach Array  
The permanent-magnet orientation is a central design criterion for Halbach array configuration. The ideal Halbach array is crucial for several reasons, particularly in applications where the magnetic field controls efficiency and performance. The arrangement of the magnet poles in the Halbach array helps to strengthen the field on one side of the array while cancelling out the field on the other side, as shown in Figure 1.  
The proper configuration of the Halbach array has a magnetic field that is maximized to its fullest potential, improving the overall efficiency of the system. A Halbach array's magnetic field concentration strongly depends on accurate design and setup. Poorly designed geometries, such as inappropriate diameters or aspect ratios, could affect the array's ability to concentrate the magnetic field effectively. Similarly, utilizing magnets that are either too tiny or too large for the desired design might reduce the field intensity and uniformity. Furthermore, inaccuracies in the spacing, positioning, and alignment of the magnets could negatively impact the consistent distribution of the magnetic field. Optimizing the Halbach configuration, the array exhibits several benefits which significantly increase the magnetic field and can achieve a higher magnetic flux density with fewer magnets or within a smaller volume.  
NdFeB magnets composed of neodymium, iron, and boron are widely used due to their exceptional magnetic properties and high magnetic strength, making them the most powerful type of permanent magnets available today. NdFeB magnets are more beneficial than conventional permanent magnets made from materials like ferrites and alnico, allowing for compact and lightweight designs with superior performance. Despite being more expensive, prone to corrosion, and sensitive to high temperatures, their ability makes them essential for advanced and space-constrained applications where weight and size are critical. The key magnetic properties of NdFeB magnets are depicted in Table 1.  
Figure 1: Halbach array configuration of the north and south poles.  
Permanent magnets are materials that maintain a constant magnetic field without the need for an external power source. Their magnetic properties are characterized by several key factors. Remanence (Br) refers to the strength of the magnetic field that remains in the magnet after it has been fully magnetized. Higher remanence indicates a stronger magnetic field. Coercivity (Hc) measures the resistance of a magnet to becoming demagnetized by external magnetic fields. Magnets with high coercivity retain their magnetism even in challenging conditions. Energy product (BHmax) is the maximum amount of magnetic energy stored in a magnet, which reflects how efficiently a magnet can generate a magnetic field. Permanent magnets typically have high energy, making them effective in compact applications like motors and sensors. Additionally, Curie temperature is the temperature above which a permanent magnet loses its magnetic properties. Permanent magnets also exhibit a hysteresis loop, which shows their behavior during magnetization and demagnetization cycles.