Spherical brushless direct current motor: modeling, magnetostatic analysis, and control

Abstract

Mechatronic systems, including electric cars, urban aerial vehicles, and walking robots, often demand multi-degree of freedom motions. To meet these requirements, this research focuses on the development of a Spherical Brushless Direct Current motor (SBLDC) suited for robotics and mobility applications that requires both spinning and tilting actions. The SBLDC is designed to generate the 3D torque and further control the spinning and tilting torques separately. The stator is split into three layers. The middle layer creates the spinning torque, while the two outer layers handle the tilting torque. Each layer has a different winding layout, based on the direction of the torque it produces, but they all use the pole-slot combination typical in three-phase BLDC motors. Both spinning and tilting torque are analyzed by the interactions of harmonics from the rotor and stator. Using the Maxwell stress tensor, torque models are formulated based on their dominant harmonics. The rotor dynamics are further derived to offer insights into how the motor torques affect its movement. Given the SBLDC's intricate design and multiple magnetic sources, traditional magnetostatic analysis methods face challenges. The thesis introduces the moment method based distributed multipoles (MMDMP) for efficient computation of magnetic fields and forces. This method models the magnetic materials, including a permanent magnet (PM), an electromagnet (EM), and ferromagnetic material (FM), as distribution of finite local sources. The magnetic field and force from these local sources are computed based on the context of moment method and the distributed multipoles model. Building on the MMDMP, two further methods are presented: the MMDMP network analysis (MNA) designed for electric motors, and a MMDMP based sub-domain method (MSM) to study the iron-core SBLDC's magnetostatics. Drive and control methods are also discussed. Firstly, an open-loop control system is developed to control the rotor tilt angle with continuous spin motion. A six steps commutation is proposed to control the tilting and the spinning torque independently. Additionally, the stability of the control system is analyzed with respect to equilibria, and it will offer the basis of the control system design. Next, a closed-loop system and torque drive method is designed for 3D orientation control. Additionally, state estimator is designed for the full state feedback, based on the 6-axis inertial measurement unit and bipolar Hall-effect sensors. Lastly, the torque drive and the open-loop control are validated experimentally. The experiments are carried out using an air-core SBLDC prototype with standard BLDC drivers. The results show the substantial potential of the SBLDC in mobility where there's a demand for orientation control coupled with rapid spinning. Furthermore, the compatibility of conventional drivers amplifies the commerciality of this motor.