# Investigation of Segmented Halbach Array Design for Passive Magnetorheological Brake System
## 4 Simulation and Analysis
### Magnetic Flux Intensity at Different Positions of the Magnets  
The influence of adjustable segment magnets on the flux distribution of a stationary segment magnet is demonstrated as their position changes from below (down) to above (up). The position of smaller track magnets, measured as offsets \(P_{1}\) and \(P_{2}\) (1-5 mm from the larger magnet's axis), is key to aligning and directing the magnetic field in the Halbach array. Fine-tuning these offsets optimizes the magnetic gradient, concentrating field lines in the magnetorheological fluid region for improved performance. Smaller magnets in the adjustable track enhance flux through the MRF, amplifying the magnetorheological effect while minimizing flux leakage. When positioned below the larger magnet, they increase flux intensity at the bottom, though lowering the overall intensity, offering strategic control for application. As the smaller magnets are aligned laterally, they redistribute the flux evenly around the middle of the larger magnet, creating a balanced field. When the smaller magnets move to the top, they concentrate the flux at the upper region, pulling the magnetic intensity upward. The color gradient regions with higher flux density ranging from blue to red indicate varying levels of flux intensity across these structures. From Figure 8, the visual representation of the red regions shows higher flux intensities, while the blue regions indicate lower intensities. This interaction showcases how smaller magnets can dynamically alter and shape the magnetic field of a larger magnet based on their relative position. This trend could indicate that the possible magnetic flux density has increased as the position varies slightly within this range. These data can provide useful insights for fine-tuning spacing in applications requiring precise control over field strength.  
Figure 7: Magnetic flux density across various lengths of adjustable segment magnets and varying gap widths between the magnets.  
The position of the magnets can depend on the specific context, but generally, identifying the magnet's location is relative to a point of reference. When studying the effect of the magnet field, the position is often described as a distance from a specific point or object, measured in straight line segments. This can be useful for evaluating the strength of the magnetic field at various points. In the proposed design of a segmented Halbach array in cylindrical configuration, the magnetic flux density across various positions \(P_{1}\) and \(P_{2}\) of magnets in the adjustable segment from the reference point (half the distance of a larger magnet in an array) to the surface is shown in Figure 9. The optimal distance between magnets in the segmented Halbach array was determined through the results obtained when reducing the gap width between magnets, which increases the magnetic flux density but poses manufacturing challenges, while changing the position highlights how adjustable magnets dynamically shape the flux distribution. From the optimized results, the values of the gap width and length of smaller magnets were used in this simulation. As the position of the adjustable segment magnets moves away from the center towards the down surface (weak side), a positions indicated by \(P_{2}\), which ranges from \(-1\) mm to \(-5\) mm, and from the center to the upside surface (strong side), denoted by \(P_{1}\), ranging from 1 mm to 5 mm, the flux intensity increases.