Electro‐Quasistatic Analysis of an Electrostatic Induction Micromotor Using the Cell Method

Abstract

An electro-quasistatic analysis of an induction micromotor has been realized by using the Cell Method. We employed the direct Finite Formulation (FF) of the electromagnetic laws, hence, avoiding a further discretization. The Cell Method (CM) is used for solving the field equations at the entire domain (2D space) of the micromotor. We have reformulated the field laws in a direct FF and analyzed physical quantities to make explicit the relationship between magnitudes and laws. We applied a primal-dual barycentric discretization of the 2D space. The electric potential has been calculated on each node of the primal mesh using CM. For verification purpose, an analytical electric potential equation is introduced as reference. In frequency domain, results demonstrate the error in calculating potential quantity is neglected (<3‰). In time domain, the potential value in transient state tends to the steady state value.

New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

“…Then, in this section, we calculated, through , the heat conduction in the tube of Figure 6. The matrix was proposed as an alternative to the matrices used in [18][19]. These results will be compared with those obtained with the new matrix in the Section 3.2.…”

“…On the one hand, a 2D FEMM calculation of 11,042 nodes was carried out, and on the other hand, five calculations were made with CM for an increasing number of nodes, ranging from 108 to 13,136 Then, in this section, we calculated, through [M λ ], the heat conduction in the tube of Figure 6. The matrix [M λ ] was proposed as an alternative to the matrices used in [18,19]. These results will be compared with those obtained with the new matrix [M τ ] in the Section 3.2.…”

“…In the present work, we propose the finite formulation (FF) [10][11][12][13][14][15], as well as the Cell Method (CM), [16][17] as an associated numerical method to analyze the numerical models proposed. In this methodology, we work with the global magnitudes associated with space-oriented elements such as volumes, surfaces, lines, and points of the discretized space, as well as to temporal elements, instead of the field magnitudes associated with independent variables with spatial and temporal coordinates [16][17][18][19][20]. In addition, the equations of constitutive type (equations of the medium) are clearly differentiated from the topological type (equations of balance) [10].…”

Thermal Analysis of a Magnetic Brake Using Infrared Techniques and 3D Cell Method with a New Convective Constitutive Matrix

“…In the present work we propose the Finite Formulation—FF [7], and the CM [8,9] as an associated numerical method to analyse this type of devices. In this methodology we work with global magnitudes associated to space oriented elements such as volumes, surfaces, lines and points of the discretized space, as well as to temporal elements, instead of field magnitudes associated to independent variables –spatial and temporal coordinates [10].…”

New Constitutive Matrix in the 3D Cell Method to Obtain a Lorentz Electric Field in a Magnetic Brake

“…In most of the works consulted in the bibliography, approximate analytical equations or numerical methods such as the FEM are used. In the present work, we propose the finite formulation (FF) [ 3 ], and the cell method (CM) as its associated numerical method [ 4 , 5 ], to analyze this type of device.…”