## 5 Conclusions  
In this study, the application of circular magnet arrays was investigated in terms of energy harvesting performance. Characteristics of the Halbach array with a certain space between the cubic magnets were studied. A theoretical model of an electromagnetic energy harvester in cylindrical coordinates was established based on the coordinates of the cubic magnet nodes. The finite element method was used to calculate the magnetic flux density and induced voltage of the two magnet arrays. The arrangement of the magnets in the Halbach array and the space between the 16 magnets were found to affect the magnetic flux density distribution. In the Halbach array used in this paper, 16 cubic magnets instead of arc magnets were arranged in a special way. The large space between the cubic magnets resulted in the REMEH with the Halbach array having poor energy harvesting performance when the gap was smaller than a threshold value. Through simulation and experimental verification, the induced voltage in the coil under the two kinds of magnet array was found to continuously decrease as the gap between the magnets and the coil increased. The two-directional array has better performance when the gap is less than the threshold gap and the Halbach array has better performance when the gap is greater than the threshold gap. The Halbach array has the characteristic of an enhanced magnetic flux density, which may help with energy harvesting on some special occasions or in a confined space. In summary, the magnet array should be remanufactured so that there is no space between the magnets when the Halbach array is applied in a REMEH. It can be seen from the simulation results that as the gap diameter increases, the maximum magnetic flux density and the area of the Halbach array's poles become larger than those of the  
Figure 22: Comparison of the RMS value of the voltage in the REMEH between the Halbach array and the two-directional array under different gaps when the rotation speed was 10 r/s in the experiment. two-directional array. The gap between the magnets and the coils and the space between the magnets have obvious effects on the electromagnetic energy conversion. S.G. ([PERSON]): Conceptualization, Writing--Original Draft; S.G. ([PERSON]): Methodology, Supervision; L.J. : Investigation, Formal Analysis; X.D. : Data Curation, Software; Q.W. : Editing, Visualization; J.S. : Supervision, Visualization. All authors have read and agreed to the published version of the manuscript. * (18) [PERSON]; [PERSON] Cylindrical halbach magnet array for electromagnetic vibration energy harvesters. In Proceedings of the 2015 28 th IEEE International Conference on Micro Electro Mechanical Systems (MEMS), Estoril, Portugal, 18-22 January 2015; pp. 1051-1054. * (19) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Design and Optimization of an Electromagnetic Vibration Energy Harvester Using Dual Halbach Arrays. _IEEE Trans. Magn._**2015**, _51_, 8204204. [CrossRef]
* (20) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A Low-Frequency Resonant Electromagnetic Vibration Energy Harvester Employing the Halbach Arrays for Intelligent Wireless Sensor Networks. _IEEE Trans. Magn._**2015**, _51_, 8600604. [CrossRef]
* (21) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Multi-directional electromagnetic vibration energy harvester using circular Halbach array. _AIP Adv._**2017**, \(7\), 056672. [CrossRef]
* (22) [PERSON]; [PERSON]; [PERSON]; [PERSON] Vibration energy harvesting using the Halbach array. _Smart Mater. Struct._**2012**, _21_, 075020. [CrossRef]
* (23) [PERSON]; [PERSON]; [PERSON]; [PERSON] Increasing output power of electromagnetic vibration energy harvesters using improved Halbach arrays. _Sens. Actuat A Phys._**2013**, _203_, 11-19. [CrossRef]
* (24) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Electromagnetic energy harvester based on a finger trigger rotational gear module and an array of disc Halbach magnets. _Appl. Energy_**2019**, _250_, 776-785.