MATHEMATICAL MODEL OF PIEZOELECTRIC OSCILLATING SYSTEM WITH ELECTRODES OF VARIABLE NONLINEAR AND CONSTANT LINEAR AIR GAP

2017 ◽  
Vol 76 (18) ◽  
pp. 1639-1648 ◽  
Author(s):  
S. Khutornenko ◽  
O. Osadchuk ◽  
I. Osadchuk ◽  
D. Vasilchuk ◽  
D. Semenets ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Air Gap

A Mathematical Model for Air-gap Formation at the Metal—Mould Interface in the Computer Simulation of the Solidification of Al—12%Si in a Sand Mould

Cast Metals ◽  
1994 ◽  
Vol 6 (4) ◽  
pp. 231-236 ◽  
Author(s):  
H. R. Shahverdi ◽  
F. Farhadi ◽  
A. Karimitaheri ◽  
P. Davami ◽  
K. Asgari
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Air Gap ◽  
Gap Formation ◽  
Sand Mould

A novel mathematical model of bearingless switched reluctance motor considering air-gap edge effect

2017 ◽  
Vol 36 (1) ◽  
pp. 108-128 ◽  
Author(s):  
Ling Chen ◽  
Honghua Wang ◽  
Chao Tan
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Flux Density ◽  
Edge Effect ◽  
Air Gap ◽  
Magnetic Saturation ◽  
Content Type ◽  
Switched Reluctance ◽  
Coupling Relationship ◽  
Rotor Poles

Purpose This paper aims to propose a novel mathematical model of bearingless switched reluctance motor (BSRM). This model differs from conventional mathematical models in the calculation of torque and suspension forces. Conventional mathematical models neglect the coupling relationship between the α- and β-axes or ignore the magnetic saturation of the Si-Fe material. This study considers these issues simultaneously. Additionally, considering the air-gap edge effect, the fringing coefficient is used to establish a high-precision mathematical model. Design/methodology/approach An innovative mathematical model of BSRM based on the Maxwell stress method was established by selecting an appropriate integration path. The fringing coefficient of the air-gap was computed based on the finite element analysis results at the aligned position of the stator and rotor poles. Using the least squares fitting method, the piecewise fitted magnetization curve of the Si-Fe material was utilized to calculate flux density. Findings The appropriate integration path of the Maxwell stress method was selected, which considered the coupling relationship of the suspension forces in the α- and β-axes and was closer to the actual situation. The fringing coefficient of the air-gap improved the calculation accuracy of air-gap flux density. The magnetomotive force was consumed by the magnetic resistance of the stator and rotor poles considering the magnetic saturation. Originality/value A novel mathematical model of BSRM is proposed. Different from conventional mathematical models, the proposed model can effectively solve the coupling relationship of the suspension forces in the α- and β-axes. Additionally, this model is consistent with the actual situation of motor as it includes a reasonable calculation of the air-gap flux density, considering the air-gap edge effect and magnetic saturation.

scholarly journals Combination Traction and Lateral Stabilisation System for Magnetic Levitation Transport

2017 ◽  
Vol 3 (4) ◽  
pp. 107-126
Author(s):  
Andrey V Solomin
Keyword(s):  
Mathematical Model ◽  
Magnetic Flux ◽  
Induction Motor ◽  
Transverse Magnetic ◽  
Air Gap ◽  
Human Society ◽  
Magnetomotive Force ◽  
Linear Induction ◽  
Linear Induction Motor ◽  
Secondary Element

The problems of improvement of modern types of transport and creation of new ones are important and topical for the human society development. One of the most promising and environmentally-friendly modes of transport is the high-speed maglev transport, moving at speeds of approximately 500 km/h. Objective. Justification of linear induction motor, development and research of various constructions of this type of motors. Methods. Description of linear induction motor with longitudinal and transverse magnetic flux for combined traction and lateral stabilisation system of maglev transport, having increased lateral stabilisation forces. The mathematical modelling of magnetomotive force (MF) in the air gap of traction linear motor of this type has been conducted. To analyse the MF the assumption has been made about even distribution of magnetic induction in the air gap in transverse direction and its sinusoidal longitudinal direction, making it possible to develop new mathematical model of MF distribution in the air gap of linear induction motor with longitudinal and transverse magnetic flux Results. The developed mathematical model for calculation of MF on traction linear machine will enable increasing accuracy of traction and lateral stabilisation combined system forces for maglev transport. The same relates to mutual location of inductor to the secondary element. All this proves the successful ten-year commercial operation experience of magnetically suspended train carrying passengers from an airport to Shanghai, P.R. China. The values of traction and lateral stabilisation forces of linear induction motor with longitudinal and transverse magnetic flux is greatly influenced by the character of current distribution in the secondary element. The character itself is influenced by MF distribution in the air gap.

Study on the Air Damping of the Movable Armature

2013 ◽  
Vol 562-565 ◽  
pp. 1397-1401
Author(s):  
Ben Dong Liu ◽  
Jia Hui Yang ◽  
Yu De Wu
Keyword(s):  
Mathematical Model ◽  
Mean Free Path ◽  
Air Gap ◽  
Damping Coefficient ◽  
Mems Devices ◽  
Damping Force ◽  
Small Vibration ◽  
Damping Characteristics ◽  
Air Damping ◽  
The Mathematical Model

The distance of air gap is much larger than the mean free path of gas molecules for MEMS devices with small vibration. The nonlinear Reynolds equation can be transformed into linear Reynolds Eq. based on this condition and under certain assumptions. Then the mathematical model of damping of the movable armature is established with the linear Renault equation. The damping characteristics of the movable armature are studied based on the damping force mathematical model. The relation of damping coefficient and the dimensions of movable armature, the dimensions of air gap are analyzed. The research in this paper provides references for the design and analysis of the damping coefficient of the MEMS devices with small vibration.

Generalized optimization procedure for rotational magnetized direction permanent magnet thrust bearing configuration

2018 ◽  
Vol 233 (7) ◽  
pp. 2563-2573 ◽  
Author(s):  
Siddappa Iranna Bekinal ◽  
Mrityunjay Doddamani ◽  
Mohan Vanarotti ◽  
Soumendu Jana
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
Axial Force ◽  
Thrust Bearing ◽  
Computational Cost ◽  
Three Dimensional ◽  
Air Gap ◽  
Geometrical Parameters ◽  
Outer Diameter ◽  
Design Variables

Optimization of rotational magnetized direction permanent magnet thrust bearing configuration is carried out using generalized three-dimensional mathematical model. The bearing features namely axial force and stiffness are maximized using in-house developed mathematical expressions solved using MATLAB. The design variables selected for the optimization are axial offset, number of ring pairs, air gap and inner radius of inner and outer rings. The maximized axial force values of the optimized configuration are validated with the finite element analysis results. To overcome the high computational cost associated with three-dimensional equations, generalized method of optimization is sucessfully demonstrated using plots representing variation of optimal design variables as a function of air gap with respect to bearing’s outer diameter. Simple and useful method of using the generalized plots for the process of optimization is presented by dimension optimization of representative bearing configuration with a particular aspect ratio. The proposed optimization using mathematical model and generalized approach assists designer in selecting optimized geometrical parameters of rotational magnetized direction thrust bearing configurations easily for variety of high-speed applications.

Experimentation and Mathematical Model Reseach on Air Gap Membrane Distillation

2012 ◽  
Vol 581-582 ◽  
pp. 89-93
Author(s):  
Ying Guan ◽  
Hong Jiang Cui
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Flow Rate ◽  
Membrane Distillation ◽  
Air Gap ◽  
Working Fluid ◽  
Fluid Temperature ◽  
Air Gap Membrane Distillation ◽  
Set Up ◽  
The Mathematical Model

Air gap membrane distillation (AGMD) experiments were done to reseach flux of membrane distillation at different working fluid temperature and mass flow rate. The driving power of distillation experiments is solar power. The experimental flux of membrane distillation reached 49kg/m2•h. The mathematical model of AGMD’ heat and mass transfer was set up. The biggest relative error is less than 9% between results of experiment and mathematical model calculation. The mathematical model can be used to forecast the distillation flux and the thermal efficiency.

Optimization of Axially Magnetized Stack Structured Permanent Magnet Thrust Bearing Using Three-Dimensional Mathematical Model

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Siddappa I. Bekinal ◽  
Mrityunjay Doddamani ◽  
Soumendu Jana
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Optimization Method ◽  
Air Gap ◽  
Geometrical Parameters ◽  
Outer Diameter ◽  
Element Analysis ◽  
Cylindrical Volume

This work deals with optimization of axially magnetized stack structured permanent magnet (PM) thrust bearing using generalized three-dimensional (3D) mathematical model having “n” number of ring pairs. The stack structured PM thrust bearing is optimized for the maximum axial force and stiffness in a given cylindrical volume. matlab codes are written to solve the developed equations for optimization of geometrical parameters (axial offset, number of ring pairs, air gap, and inner radius of inner and outer rings). Further, the results of proposed optimization method are validated using finite element analysis (FEA) and further, generalized by establishing the relationship between optimal design variables and air gap pertaining to cylindrical volume constraint of bearing's outer diameter. Effectiveness of the proposed method is demonstrated by optimizing PM thrust bearing in a given cylindrical volume. Mathematical model with optimized geometrical parameters dealt in the present work helps the designer in developing PM thrust bearings effectively and efficiently for variety of applications.

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