EENG20005 Coursework Script

Overview

Submission

•   Summative submission: A technical report in Week 23 accompanied by a package of all simulation models and codes.

Laboratory sessions

Report elements

A.   Description of approach/methodology

B.   Mathematical working

C.   Simulation waveform.

D.   Diagrams - phasor diagram, circuit diagram

E.   Results in data points presented in a table or a visualised graph (e.g. curve)

F.   Analysis and discussion of results

Part 3. Ferromagnetic Actuator

Summary

Numerical and analytical modelling and simulation of a linear ferromagnetic actuator.

Learning outcomes

1.   Learning how to use FEA techniques (such as FEMM) to model a linear ferromagnetic actuator and simulate its electromagnetic characteristics.

2.   Learning how to build analytical models for the linear ferromagnetic actuator.

3.   Learning how to calculate the inductance of the actuator by using both the FEA technique and the analytical method.

4.   Learning how to calculate the electromagnetic force by using the energy method.

Tools

FEMM and MATLAB 2024a.

Learning materials

1.   An incomplete FEA model draft in the EMLab file named “ Draft_construct_actuator ”. (students need to build a FEA model based on it.)

2.   FEMM Programming Manual – a guide to MATLAB Codes for FEMM.

3.   A guidebook for MATLAB - “ Matlab_primer ”.

4.   Lab Scripts (Part A and Part B) as asupplementary guidebook.

Case 3A FEA modelling of the ferromagnetic actuator.

Build a Finite Element Analysis (FEA) model of a linear ferromagnetic actuator. The schematic view is shown as below. The specifications can be found in the EMLab file: named “coil1p”, “coil2p”, “coil3p”, “coil4p”, “corep”, and “ moverp”. Lab Script. “ Part A” can be used as a detailed guidebook to assist your FEA modelling based on FEMM software. In order to support your learning of the FEA modelling technique, two tutorial sessions will be provided:

(1) Tutorial 1 – Introduction of FEA modelling technique based on FEMM software.

(2) Tutorial 2 – How to use MATLAB code to assist FEMM modelling (including how to use the Programming Manual to search for suitable MATLAB codes for FEMM modelling).

Fig. 1: Schematic of concentrated and distributed e-machine windings with round and rectangular conductors.

Fig.2: A draft FEMM model - “ Draft_construct_actuator ” will be provided as shown above.

Task 3.1

Open the incomplete FEA model (FEMM model) “ Draft_construct_actuator ”, go through the MATLAB codes for the FEMM draft model which is currently incomplete. You will need to build the rest of the FEA model (FEMM model) and complete the model before proceeding with the rest of the tasks.

The learning materials and resources provided, including “ Programming Manual Book” and   “ Lab Scripts - Part A and Part B”, will assist you in completing the build of the model. The lab scripts provided also give instruction on building the sections of model that have already been provided. It is recommended that you read the lab script. to understand how FEMM modelling works.

Task 3.2

In your technical report, show the completed FEMM model, its mesh result plot, number of elements after the mesh, and describe & discuss these results briefly.

Case 3B Analytical modelling of the ferromagnetic actuator.

Build an analytical model of the same ferromagnetic actuator based on its Magnetic Equivalent circuit. Below are some suggested tasks to help complete the task 3.2.

Task 3.3

Draw the circuit diagram of the magnetic equivalent circuit of the ferromagnetic actuator. Calculate the magnetic reluctance (R) of each component and the total magnetic reluctance of the actuator (∑R).

Task 3.4

Work out the analytical equation of the inductance of the ferromagnetic actuator. Note: The airgap will change when the “mover” iron core moves linearly (forwards or backwards). Discuss how the inductance changes when the airgap changes. If there is any assumption in your analytical equation of inductance, please describe and justify it or explain how the assumption(s) impact the accuracy of the inductance equation.

Task 3.5

Write a MATLAB code to present the analytical equation of the inductance of the ferromagnetic actuator in Task 3.4. These codes can be used to calculate the inductance quickly through code rather than hand-written calculation, especially when the airgap changes (i.e.,the airgap has a set of different values when the “mover” iron core moves).

Case 3C Calculating the inductance of the ferromagnetic actuator.

Calculate the inductance of the ferromagnetic actuator by using both FEA technique (Case 3A) and analytical methods (Case 3B).

Task 3.6

Calculate the inductance values of the ferromagnetic actuator when the airgap increases from 0.1mm to 5.0 mm with a step of 0.1mm, using the analytical modelling method in Case 3B.

In your technical report, show the plot of inductance with the airgap on the x-axis and the inductance on the y-axis. Discuss the inductance results and the plot.

Task 3.7

FEA techniques (FEMM model) can help simulate and calculate many useful results. Among these results, flux linkage (Ψ) and winding current (I) are useful for calculating the inductance of the actuator.

In your technical report, please write down the equation showing the relation of the inductance of the actuator with the flux linkage (Ψ) and winding current (I).

Task 3.8

Calculate the inductance values of the ferromagnetic actuator when the airgap increases from 0.1mm to 5.0 mm with a step of 0.1mm, using the FEA (FEMM) modelling method in Case 3A. Show a plot of the same (airgap on the x-axis, inductance on the y-axis). To make a good comparison with analytical calculation results, it is recommended that the inductance values of the ferromagnetic actuator are calculated when the airgap increases from 0.1mm to 5.0 mm with the same step of 0.1mm.

Task 3.9

Are there are any assumptions or limitations in your analytical method and FEA numerical method? Explain how the assumption(s) impact the accuracy of the inductance results.

Case 3D Calculate the electromagnetic force of the ferromagnetic actuator.

Calculate the electromagnetic force based on energy methods. Use both methods: FEA technique based on FEMM and Analytical Methods based on MATLAB codes.

Task 3.10

Explain the energy balance law and how the energy methods are used to calculate the electromagnetic force of the linear ferromagnetic actuator. Show the equations to aid your explanations.

Task 3.11

Plot the Ψ − I curves of the ferromagnetic actuator. By using the Ψ − I curves, calculate the energy, such as electrical energy and magnetic energy. Both FEA methods and analytical methods should be used in this task. You can provide a comparison of the results obtained through both methods.

Task 3.12 (Advanced Task)

Calculate the electromagnetic force based on energy methods as descripted in task 3.10 and the Ψ − I curve in task 3.11. Plot the force-airgap curve to show how the force changes with  the airgap. Discuss the results. Note that both FEA methods and analytical methods should be used in this task.