# Simulation and Optimization of the Currency in a Matlab Model. Visualization of the Currency and the Voltage in Dependency of the Anchors Force

Excerpt

## List of Contents

Project worker

Supervisor at Pforzheim University of applied sciences

Executive Summary

List of Contents

Glossary

Formula Table

Formula Symbols with Latin Characters

Formula Symbols with Greek Characters

Indexes

1 Introduction

3 Initial situation

4 State of the Art
4.1 Magnetic force FM
4.2 Duty cycle
4.3 Inner resistance of the coil
4.4 Derivation of MSDS - Mass-Spring-Damper-System
4.4.1 The spring stiffness
4.4.2 The damper stiffness
4.4.3 The anchors mass
4.5 Airgap

5 From FEMM into a Simulink model
5.1 FEMM
5.2 Creating the Matlab Simulink model
5.2.1 Electric part of the Simulink model
5.2.2 Mechanical part of the Simulink model

6 Use of the system

7 Conclusion

8 Table of Figures

9 References

11 Appendix
11.1 FEMM Files
11.1.1 F(delta, I)
11.1.2 F(delta, L)
11.2 Coil Calculations

HOCHSCHULE PFORZHEIM

Simulation of the currency and voltage in a MATLAB Simulink model

This paper is based on a MATLAB Simulink model showing an anchor movement in a direct current magnet. The result is to get a visualization of the currency I in [A] and the voltage U in [V] in dependency of the anchors force.

## Project worker

Robert J. G. Wenndorff

## Executive Summary

In the “Konstruktionsseminar Summer term 2014” the idea is to optimize a given ar­tificial heart by the last semester. The target is to reduce the weight and to raise the force of the heart engine. Some constructive ideas took place, for example the material has been changed from machining steel to an iron-cobalt material to have a higher flux density. For the engine, a solenoid is used to give a linear movement of the anchor to push blood into each heart chamber. In the high-pressure side, the coil will be set un­der currency to produce magnetic force via 0rsted's law.

The system will be seen as a mass-spring-damper-system and will be analyzed in Matlab Simulink. With FEMM, a tool to simulate finite elements method for mag­netism, the forces and inductivities, the airgap and the currency of the solenoid can be taken and implemented into Matlab Simulink. The target is to control the input of the designed system with a change of the voltage level, so that the currency can be in­creased and decreased and the movement of the anchor can be controlled over the whole airgap.

Due having an idly system, the voltage has to be regulated into an extremely short period that the time for the anchor can be set for half a second. This period of time is necessary to have a heart rate of about 60 beats per minutes. During the other half second, a spring pushed the anchor back into the initial condition and the cycle can start again. Having a shorter period of time means that the blood as a fluid doesn't move permanently and a result could be the bursting of veins in the body where the resistance is low. Or for example a turbulent flow can be produced which block veins in thin regions, so there will be a blood jam and parts of the body cannot receive ox­ygens.

After putting all incoming facts into the Matlab Simulink model, the simulation shows that the time for the anchor to move in the airgap is too short with about 0,1s that all those negative facts may come true.

Having a system like this, the control of the voltage can be made manually but the idly of the dependent currency makes it hard to control the movement:

- The force to push the blood cannot be reached
- The time for the anchor to move is too short
- The spring cannot push the anchor back due the idly of the currency

## Glossary

bpm: bpm is a short form of “beats per minute”. This is the heart beat of a human adult without any kind of sportive efforts.

bps: bps is a short form of “beats per second”. It is bpm divided by 60 to get the beats per second. 1 bpm = 60 bps.

DC: DC is the short form for “duty cycle”. Duty cycle is the particular time when the voltage on.

FEMM: FEMM is the acronym for Finite Element Method Magnetics. It is a numeric FE program to solve stationary static magnetic field problems in a two-dimensional way.

HP-side: HP-side stands for the high-pressure side. This is the active chamber of the artificial heart. It connects the heart with the body blood loop.

LP-side: LP-side stands for the low-pressure side. This is the passive chamber of the artificial heart. It connects the heart with the lung blood loop.

MSDS: MSDS is a short form for mass-spring-damper system, which gives us the equa­tion of motion.

PT1: PT1 is delay element or lag element in the control engineering. This element is a continuous rising element until it reaches its upper limit.

## Formula Symbols with Latin Characters

illustration not visible in this excerpt

## 1 Introduction

The present work is about the design of a linear magnet for an artificial heart in the “Kon­struktionsseminar Summer term 2014” at the University of Applied Science HS Pforzheim. This work is one part of three different topics about the heart in the course “electric ma­chines”. It covers the simulation and optimization of the engine from an artificial heart using a linear magnet or further named solenoid. In the winter term 2013, the last semes­ter, a group of students already designed a virtual prototype of the heart and the magnet. But they could not meet the weight requirements therefore the goal and the focus in the “Konstruktionsseminar Summer term 2014” was to lower the total weight. However, no analyses had been made of the movement of the anchor and pushing the blood into the chamber. To lower the weight and to raise the power of the solenoid by an exchange of the material, the whole system will be more dynamic as before. To get an optimum of a low weight plus having a dynamic system, which can be controlled by changing the voltage and therefore the currency, the system is getting into an idly condition.

## 2 Description of the task

Given is an artificial heart, using a solenoid as kind of an engine for the engineered prod­uct. The magnet should give the patient an opinion for a normal life.

The basic idea is using a solenoid like a common rail injection pump as an actuator in the system. The solenoid is placed centered in the artificial heart moving itself in a horizontal direction. On each side is a chamber with an income and outgoing flow of blood. The mag­net is connected to a membrane on each side, minimizing the chambers space and to get the blood flow. To move the solenoid's anchor, a specific currency and voltage has to be connected via a battery. There is only one side the anchor is moving to, for the other, there is spring which pushes the anchor back in the opposite direction. So, there is a high- and a low-pressure side. The high-pressure side is in the active anchor direction, where the magnet force is pointing to, to have the higher force in just that chamber. This side pushed the blood into the body loop. The spring pushed the anchor back in the low-pressure side, the lung loop.

The voltage is changing from off to on and the currency starts rising. An electric field is available and the anchor is moving due to 0rsteds law.1

This represents a mass-spring-damper system. The moving mass is the anchor, the spring is placed to push the anchor back in the starting condition and the damper is given to minimize the impact of the anchor to each ground side plus the blood damper while with the anchor pushed the membrane into the blood in the chamber and continuing the blood in the body loop.

The MSDS can be built up in a MATLAB Simulink model to simulate the movement of the anchor with a defined currency. Due to the fact this solenoid should be implemented into a human body the temperature is a big problem. Therefore, voltage and currency are imi­tating factors for the solenoid. The purpose is to get the currency for the solenoid to move it from the low to the high-pressure side until the impact with the ground side.

## 3 Initial situation

illustration not visible in this excerpt

Figure 1 – Final situation of the solenoid from the group of winter term 13/142

An optimized geometric design from a previous group is given in Figure 1. Major changes, seen in Figure 2, to the previous groups are the exchange of the anchor to an iron-cobalt material. Additionally, the geometry has been changed to minimize volume and weight. Radiuses are added to fulfill a good and direct current flow.

illustration not visible in this excerpt

Figure 2 - Initial situation at the beginning of the simulation and optimization3

There have no previous tasks like this, to control the currency and voltage in a MATLAB/Simulink model, taken place before.

## 4 State of the Art

In this section, every part of the system will be explained and calculated manually. First, the magnetic force which is mandatory to move the anchor. More information will be in chapter 4.1. Second, the duty cycle: a moving magnet is not a straight line by moving from one to another position. So, this will be explained in chapter 4.2. In chapter 4.3 the inner resistance of the coil and the length of the copper wire are taken place. Next part is an introduction of the MSDS. This also includes the spring and damper stiffness and the an­chor mass. For more info go to chapter 4.4. The last chapter, 4.5, is about the airgap, which is a variable over the whole process of movement.

### 4.1 Magnetic force FM

The force of the solenoid, which pushes into the high-pressure side, must be as high as the area AHP times the pressure on the high-pressure side pHP. It also has to push the pre­stressed spring against the working force Fs.4

illustration not visible in this excerpt

Pressure pHP and area AHP are calculated by using values of an adult person. Normally one push into the high-pressure side is about [illustration not visible in this excerpt] The area AHP is the size of the membrane which pushed the blood into the body loop. This value can be calculated by knowing that every minute about 4 liter of blood has to be pumped through the human body without any sportive efforts.5 With a heart beat of about 60 bpm, every beat has to push about

illustration not visible in this excerpt

67 milliliter per second into the human body. This value has to divided by the chambers height to get the area, which is about 4000mm2.6

illustration not visible in this excerpt

The solenoid has to produce a force FM of about 95N constantly.

### 4.2 Duty cycle

Applying the voltage to a higher value, the currency will also increase by time. In this coil, voltage at the start is set from U = 0V to a higher value. In a function diagram, it is a step response.

The duty cycle can be calculated with the control engineering mathematics. The duty cycle of a solenoid is basically a PT1-element giving a step response. The increasing ramp of this unit step response can be calculated with the following equation:7

illustration not visible in this excerpt

The following figure is a symbol figure for such a unit step response:

illustration not visible in this excerpt

Figure 3: symbol figure for a PT1 unit step response8

KPT1 is the currency, the function is heading to. TPT1 is the time constant, describing the increase of the function. The tangent in the red line, of the starting point, hits the final value at 100%. At 95% of the function can be calculated with:

illustration not visible in this excerpt

The voltage for the duty cycle will just applied for some particular seconds. It will be de­creased because of the magnetic force and the air gap which is getting smaller. It will not directly be turned off; the reduction will be stepwise to get a continually movement of the

### 4.3 Inner resistance of the coil

The inner resistance of the coil can be determined with the geometry and the resistivity of the copper wire. For a temperature of 20°C, it can be calculated with the formula:9

illustration not visible in this excerpt

The resistivity of the copper wire is approximately [illustration not visible in this excerpt] The cross-sectional area is determined by the diameter of the wire.

illustration not visible in this excerpt

The length of the copper wire can be calculated by the geometry of the coil. The cant of the coil gives a split of the coil in two areas, a red and a blue one. Furthermore, the number of windings has be defined in every area. Those measurements are taken from the CAD model.

illustration not visible in this excerpt

Figure 4 - Measurements of the coil

illustration not visible in this excerpt

The final length is set with 91371 mm. The calculation of the length is in 11.2 “Coil Calcu­lations”.

From equation (6), the results for the inner resistance is R20 = 5.125 Ω.

As the inner resistance is a temperature-dependent variable, the calculation is by using the max. temperature of the coil in action. According to simulations with an FEM-program, of the thermo-group, the maximal temperature on the coil amounts approximately 50 °C. The dependency of the resistance is described by following equation:

[...]

1 Heidrich (2014): Magnetism; S.23f

2 Riewe et al. (2013): Vollständige Nachbildung des menschlichen Herzens

3 Rommelfanger et al. (2014): Nachbildung des menschlichen Herzens

4 Kallenbach et al. (2012): Elektromagnete; S.295f

5 Bauer and Enneker (2008): Herzklappenchirurgie; S.10

6 Calculation in Rommelfanger et al. (2014): Nachbildung des menschlichen Herzens

7 Boege and Boege (2013): Handbuch Maschinenbau; S.H17

8 Self creation in Matlab Simulink

9 Heidrich, Peter (2014): Magnetism; S.8

Excerpt out of 28 pages

Details

Title
Simulation and Optimization of the Currency in a Matlab Model. Visualization of the Currency and the Voltage in Dependency of the Anchors Force
College
Pforzheim University
Course
Electric Machines
1.3
Author
Year
2014
Pages
28
Catalog Number
V386648
ISBN (eBook)
9783668607408
ISBN (Book)
9783668607415
File size
1290 KB
Language
English
Tags
Electric Machines, HS Pforzheim, Konstruktionsseminar, FEMM, Magnetismus, MATLAB, Simulink, MFDS, MSDS, Solenoid, Magnet
Quote paper
Robert J. G. Wenndorff (Author), 2014, Simulation and Optimization of the Currency in a Matlab Model. Visualization of the Currency and the Voltage in Dependency of the Anchors Force, Munich, GRIN Verlag, https://www.grin.com/document/386648