# Investigation of Segmented Halbach Array Design for Passive Magnetorheological Brake System
## 5 Validation of Halbach Configuration in Magnetorheological Brake  
Figure 10 illustrates a stator featuring stationary and adjustable segments of NdFeB permanent magnets that can be arranged in a cylindrical pattern. These segments are embedded in the stator, with the magnets evenly spaced. The purpose of this segmented configuration is to enhance the magnetic flux interaction between the stator and the rotor. The radial arrangement of the magnets allows for a uniform distribution of the magnetic field  
Figure 8: Flux distribution through magnets in adjustable segments towards magnets in the stationary segment at different positions. (**a**) Down (\(-5\) mm). (**b**) Center (0 mm). (**c**) Up (5 mm).  
Figure 9: Magnetic flux density across various positions of smaller magnets (5 mm of length) from reference point to surface.  
across the stator, optimizing the performance of the brake. '\(R\)' represents the radial distance to a specific magnet, indicating the symmetry of the system. This design is commonly seen in high-performance axial-flux machines.  
The performance characteristics of the proposed design segmented Halbach structure are compared against the conventional permanent magnets in the cylindrical structure of a brake with the same PM size, dimension, and overall volume of the brake. The braking torque was also evaluated from the simulation results of the PM brake.  
In this brake configuration, the Halbach array plays a key role in enhancing the magnetic field strength within the working fluid. The array's segmentation allows for precise control over the adjustment of the magnetic field, which is essential for regulating the braking torque. Figure 11 illustrates three distinct positions of the adjustable segment magnets: down, center, and up. At the \(-5\) mm position (down), the adjustable magnets are positioned far deeper from the MRF surface, potentially reducing the flux flow significantly. The center position represents a neutral or intermediate setting, where the flux flow is optimal for achieving the desired braking torque. In contrast, the up position, where the adjustable magnets are closer to the MRF layer, strengthens the magnetic field, leading to an increase in braking torque.  
Figure 11: Flux distribution in a magnetorheological brake when the adjustable segment magnets vary their positions. (**a**) Down (\(-5\) mm). (**b**) Center (\(0\) mm). (**c**) Up (\(5\) mm).  
Figure 10: The stator of an MRB with a segmented Halbach structure of NdFeB permanent magnets.  
Figure 12 shows the braking torque among the conventional permanent-magnet Halbach structure and proposed segmented Halbach structure in a brake configuration across different radial ranges of magnets placed away from the center of the axis with values from 27 mm to 31 mm. As the radial dimension increases, the center of the permanent magnets that act as poles increases, resulting in varying gap widths between the magnets. After a certain limit of increased radial dimension, the enhancement of flux flow becomes limited since the shear force exerted by the MRF will become constant. The data show that the proposed Halbach structure in a brake consistently achieves the highest values, indicating a stronger braking force or enhanced magnetic field effect on the magnetorheological fluid, resulting in greater performance compared to the conventional permanent-magnet brake configuration. Additionally, the data reveal that as the radial distance increases, the torque output of the brake increases up to a certain point, peaking around 29-29.5 mm, after which they begin to gradually decrease. This trend might indicate an optimal operating range of around 29-29.5 mm for the disc-type MRB system.