# Investigation of Segmented Halbach Array Design for Passive Magnetorheological Brake System
## 1 Introduction  
Permanent magnets (PMs) have significant advantages over ordinary electromagnets since they work as a static source and do not require continuous energy inputs. The creation of the neodymium-iron-boron (Nd-Fe-B) magnet, a permanently magnetized hard magnetic material capable of producing relatively greater field strengths, has broadened the use of PMs in engineering applications [1, 2]. The magnetic array is formed using tiny NdFeB magnets, which increases the magnitude of the necessary magnetic flux. [PERSON] developed this concept of Halbach magnetization in 1980 to focus particle accelerator beams; later, the proposed configuration was utilized to improve the magnetic flux concentration, which is an effective solution in low-torque-density devices [3, 4]. Permanent magnets generate a magnetic field without requiring constant external power, making them dependable and energy-efficient. The distribution of magnetic fields can be determined by the method employed for mounting permanent magnets in various orientations. The Halbach array is a hypothetical arrangement of permanent magnets that enhances the flux gradient, and its direction describes the increase in attractive andtangential magnetic forces among various magnet structures, resulting in larger field strengths [5,6]. Linear Halbach structures of varying sizes of NdFeB permanent magnets of the same dimension produce a stronger magnetic field and achieve homogeneous magnetic field intensity with an increment of approximately three times [7,8]. [PERSON] et al. proposed an analytical formulation for the magnetic field strength generated by PM Halbach arrays for validation in complex configurations, such as cylindrical structures, and the research exhibited an excellent agreement with magneto-static finite element modeling (FEM) simulations [9]. [PERSON] et al. focused on the use of Halbach arrays in axial flux permanent-magnet machines, highlighting their potential for increasing efficiency in rotating systems. The individual permanent-magnet dimensions, including length, width, and height, have a considerable impact on the strength, directionality, and concentration of the magnetic field created by the Halbach array. However, there remains a gap in translating these designs to cylindrical Halbach arrays used in other applications [10]. [PERSON] et al. investigated the transmission performance of a cylindrical Halbach array, but their focus was mainly on the idealized performance without a detailed examination and practical limitations. A research gap exists in understanding how to optimize cylindrical Halbach arrays for diverse practical systems [11]. The connection between flux density and magnet width relative to pole pitch is crucial for optimizing array performance. Changing the permanent-magnet geometry in an array can have a substantial impact on its performance. [PERSON] et al. optimized linear arrays, yet their adaptation to cylindrical geometries for specific applications, like electric motors and sensors, remains underexplored. There is an opportunity to tailor Halbach arrays for cylindrical geometries, ensuring that they meet specific application demands such as high efficiency, low weight, or compactness [12]. Additionally, [PERSON] et al. emphasized the need to understand magnetic field interactions in complex geometries, particularly in the presence of conductive or ferromagnetic materials, and highlighted the gaps in the research on cylindrical Halbach arrays, which is useful in future engineering applications where space is limited [13]. Recent research on segmented Halbach arrays in electromagnetic applications has led to significant advancements. Analytical and numerical approaches are widely employed in the study of Halbach arrays to understand and optimize their magnetic field distributions. Analytical methods, such as magnetostatic field analysis, provide closed-form solutions for idealized configurations.