Difference between revisions of "Lecture 1. - Assignment"

Revision as of 15:23, 3 April 2021

Contents

• 1 Purpose of the Assignment
• 2 Knowledge needed to solve the problem
• 3 The Problem
  • 3.1 Inductance Calculation
  • 3.2 Force Calculation
• 4 Evaluation of Results
  • 4.1 Knowledge needed to solve the problem
• 5 References

Purpose of the Assignment

The student will learn the main steps of the finite element method, such as creating the model (creating or importing geometry), specifying material parameters, boundary conditions, and excitation through simulation of the electromagnetic part of the fuel injector.

Knowledge needed to solve the problem

• The steps of the finite element method;
• Theoretical knowledge of the static magnetic field (for defining materials, for excitation);
• Knowledge of the basics of FEMM and Agros2D.

The Problem

The cross-section view of the solenoid valve.

The problem (if we neglect the transient state occurring at the switch on) can be considered as an axisymmetric static magnetic problem. The effect of the movement of the iron core (valve opening/closing) is also examined accordingly, i.e. each position is an individual simulation.

The height of the cylindrical core is 14mm and the radii is 3.6mm. Dimensions of the coil: height is 20mm, inner radii is 4mm and outer radii is 10mm.

The materials:

• Core/Vasmag: Steel with nonlinear B-H curve (Steel1008);
• Coil/Tekercs: Copper ([math]\mu_r = 1.0[/math]) and the number of turns is 2000. The current is 0.2 A;
• Region: Air ([math]\mu_r = 1.0[/math]).

The task is to determine the inductance of the solenoid valve and the force acting on the iron core. As a first step, it is recommended to validate the simulation with the values given in the table when the iron core is in the middle of the solenoid. Then it is worth examining the two quantities as a function of the position of the iron core.

Inductance Calculation

The most widely used method for determining inductance in finite element analysis is based on magnetic energy. From the magnetic energy, the inductance [math]L[/math] can be determined by the following formula:

[math]L=\frac{2\cdot W_{\text{m}}}{I^2}[/math]

where [math]W_{\text{m}}[/math] the magnetic energy of the whole problem and [math]I[/math] is the current (in this case 0.2A).

Force Calculation

The force acting on the iron core can also be determined by surface and line integration. In the case of surface integration, the core should be selected. However, in both cases, Maxwell's stress tensor (FEMM - Force via Weighted Stress Tensor / Agros2D - Maxwell force - y) used for integration.

Evaluation of Results

Coil inductance and plunger force in the function of plunger position.

Here you can plot the field quantities (magnetic flux density, magnetic vector potential, etc.) and checked the value of the inductance of the coil and the acting force on the iron core. The following values were obtained for these quantities, the arrangement according to the cross-sectional view being 0 mm position.

The results of the simulation for validation.

Software	Maxwell 2D	Maxwell 3D	FEMM	Agros2D
Inductance [[math]\text{mH}[/math]]	51.911	51.812	51.821	51.89
Force [[math]\mu\text{N}[/math]]	88.603	63.29	74.53	57.45

In addition, it is possible to parameterize the geometry or most of the simulation parameters (position, size, current, number, ...) via script (FEMM - LUA script, Agro2D - Python). The result of a parameterized simulation is shown in the figure where the parameter is the position of the iron core. As a result, the modification of the parameter and the evaluation of results are automatic.

Knowledge needed to solve the problem

The problem solution with

• [FEMM]
• [Agros2D]

References

1. ↑ https://upload.wikimedia.org/wikipedia/commons/2/29/Injector3.gif