The University of Southampton

# FPProvisional000004 ELEC3 - USMC 3211 Electromechanical tranduscers

## Module Overview

To introduce the students to fundamental concepts of low frequency electromagnetics with application in mechatronic systems. To give students an appreciation of the importance of computational electromagnetics in the context of engineering and in electromechanical actuators.To introduce the students to fundamental numerical techniques for solving field problems.To equip the students with basic knpwledge of CAD skills applicable to electromagnetic devices. To introduce the students to the concept of principles of electromechanical energy conversion based on Hamilton’s principle.

### Aims & Objectives

#### Aim

Having successfully completed this module, you will be able to:

• To introduce the students to fundamental concepts of low frequency electromagnetics with application in mechatronic systems

#### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• To understand the Basic concepts of electromagnetic theory; To use Vector algebra in the electromagnetic field context; To understand Properties of static and time-varying electromagnetic fields as well as Physical meaning of Maxwell's equations A5. Mathematical description of fundamental laws of electromagnetism A6. Electric and magnetic properties of matter A7. Electromechanical energy conversion as based on Hamilton’s principle A8. Fundamentals of modelling and simulation techniques applied to electromagnetics A9. Dual energy bounds techniques A10. Principles of finite difference and finite element formulations A11. Advantages and limitations of various field modelling techniques

#### Subject Specific Intellectual

Having successfully completed this module, you will be able to:

• Demonstrate electromagnetic theory applied to simple practical situations; Explain the meaning and consequences of field theory; Apply Maxwell's equations to problems involving simple configurations ; Interpret electromagnetic solutions; Explain the operation of electromagnetic devices especially actuators; Apply mathematical methods and vector algebra to practical problems; Be familiar with running commercial electromagnetic design environment software; Set up, solve and interrogate solutions to problems using FE software

#### Transferable and Generic

Having successfully completed this module, you will be able to:

• Use electromagnetic CAD packages; Write technical reports; Work in a small team to conduct an experiment

#### Subject Specific Practical

Having successfully completed this module, you will be able to:

• Design, anlayze and test electromagnetic devices used as actuators in mechatronic systems

### Syllabus

Approximate methods of field solution (2 lectures)

o          Geometrical properties of fields; method of ‘tubes and slices’.

•           Flow of steady current (2 lectures)

o          Potential gradient; current density; divergence; nabla operator; Laplace's equation.

•           Electrostatics (3 lectures)

o          The electric field vector; scalar electric potential; Gauss's theorem and divergence; conservative fields; Laplace and Poisson equations; electric dipole, line charge, surface charge; solution of Laplace's equation by separation of variables; polarisation; dielectrics, electric boundary conditions.

•           Magnetostatics (4 lectures)

o          Non-conservative fields, Ampere's law and curl; magnetic vector potential; magnetization and magnetic boundary conditions; magnetic screening with examples.

•           Electromagnetic induction (2 lectures)

o          Faraday's law; induced and conservative components of the electric field, emf and potential difference.

•           Maxwell's equations (2 lectures)

o          Displacement current; Maxwell's and constituent equations; the Lorentz guage;

wave equation.

•           Time-varying fields in conductors (3 lectures)

o          Diffusion and Helmholtz equations; skin depth; eddy currents in slabs, plates and cylindrical conductors; deep bar effect.

•           Computational aspects of approximate methods of field solution (1 lecture)

o          The method of tubes and slices.

•           Review of field equations (1 lecture)

o          Classification of fields: Laplace's, Poisson's, Helmholtz, diffusion, wave equations; Vector and scalar formulations.

•

•           Finite element method (5 lectures)

o          Variational formulation, first-order triangular elements, discretisation and matrix assembly; the art of sparse matrices; alternative approximate formulations (including Galerkin).

•           Principles of electromechanical energy conversion (11 lectures)

o          Generalised variables for electromechanical systems; Hamilton’s principle and Lagrangian state function; conservative and non-conservative systems; examples.

o          Comparison between field and equivalent circuit calculations.

Analysis of elctromechanical systems

### Learning & Teaching

#### Learning & teaching methods

Lectures, tutorials, labs and self study (coursework).

### Assessment

#### Assessment methods

MethodHoursPercentage contribution
Magnetostatic screening; Eddy currents screening; Electromagnetic actuator characterization.-15%
Electromagnetic actuator analysis.-20%
Exam2 hours65%

Referral Method: By examination