A two-dimensional mathematical model estimating the torque of a Halbach Array surface permanent magnet (SPM) motor with a non-overlapping winding layout is developed. The magnetic field domain for the two-dimensional (2-D) motor model is divided into five regions: slots, slot openings, air gap, rotor magnets and rotor back iron. Applying the separation of variable method, an expression of magnetic vector potential distribution can be represented as Fourier series. By considering the interface and boundary conditions connecting the proposed regions, the Fourier series constants are determined. The proposed model offers a computationally efficient approach to analyze SPM motor designs including those having a Halbach Array. Since the tooth-tip and slots parameters are included in the model, the electromagnetic performance of an SPM motor, described using the cogging torque, back-EMF and electromagnetic torque, can be calculated as function of the slots and tooth-tips effects. The proposed analytical predictions are compared with results obtained from finite-element analysis. Finally, a performance comparison between a conventional and Halbach Array SPM motor is performed.

Physics-based models are efficient solutions capable of predicting the dynamic performance of engineering systems. Owing to the rapid data growth in sensor technologies, enormous datasets are readily available creating a unique opportunity to seamlessly fuse analytical physics based models with system data. This integration has produced a physics-based machine learning (PBML) knowledge base that overcomes the costly limitations of deep learning solutions and associated false discoveries of machine learning (ML) methods. Presented in this paper is a University of Houston invented PBML approach to monitor the condition and performance applied to an annular preventer. A PBML model that describes the relationship between annular closing pressure and its cylinder displacement is derived. The model coefficients are adapted via system identification methods using real time collected data. The resulting coefficients are clustered to classify annular health from early age to middle age to aged cycles using the K-means method. Life cycle test of multiple annular preventers is performed using a full-scale testing facility. The results show that annular elastomer degradation can be detected and quantified using the proposed real-time adaptive physics based model solution given sensing information.