on the design of ultra-fast electro-mechanical actuators

On the Design of Ultra-Fast Electro-Mechanical

Actuators

ARA BISSAL

Licentiate Thesis

Stockholm, Sweden 2013

TRITA-EE 2013:015ISSN 1653-5146ISBN 978-91-7501-713-6

Electromagnetic EngineeringSchool of Electrical Engineering, KTH

SE-100 44 StockholmSWEDEN

Akademisk avhandling som med tillstnd av Kungl Tekniska hgskolan framlggestill offentlig granskning fr avlggande av teknologie licentiatexamen onsdagen den8 maj 2013 klockan 10.00 i F3, Kungl Tekniska hgskolan, Lindstedtsvgen 26,Stockholm.

Ara Bissal, May 2013

Tryck: Universitetsservice US AB

iii

Abstract

The continuously increasing demand for connecting electric grids withremote renewable energy sources such as wind power and photovoltaic cellshas rekindled interest in high voltage direct current (HVDC) multi-terminalnetworks. Although HVDC networks have numerous benefits, their adoptionrelies entirely on the availability of HVDC circuit breakers which, comparedto traditional alternating current circuit breakers, have to operate in a timeframe of milliseconds.

This thesis deals with the design of ultra-fast electro-mechanical actua-tors based on the so-called Thomson coil (TC) actuator. The simulation ofa (TC) actuator constitutes a multi-physical problem where electromagnetic,thermal, and mechanical aspects must be considered. Moreover, it is complexsince all those variables are co-dependent and have to be solved for simulta-neously. As a result, a multi-physics simulation model that can predict thebehavior and performance of such actuators with a high degree of accuracywas developed.

Furthermore, other actuator concepts were also investigated and modeledin light of searching for a drive with a superior efficiency. The theory behindthe force generation principles of two different types of ultra-fast electrome-chanical actuators, the TC and the double sided coil (DSC), were comparedby the use of static, frequency, and comprehensive transient multi-physicsfinite element simulation models.

Although, simulation models serve as a powerful tool for modeling anddesigning such state of the art actuators, without validation, they are weakand prone to errors since they rely on approximations and simplifications thatmight not always hold. Therefore, a prototype was built in the laboratoryand the model was validated experimentally.

Finally, it is important to note that the drives in this thesis are intendedto actuate metallic contacts. As such, their behavior and performance uponmechanical loading was studied. Furthermore, some scaling techniques wereapplied to boost their performance and efficiency.

Keywords: Electro-mechanical drive, Circuit breakers, HVDC transmission,Eddy currents, Finite element, Electromagnetic, Thermal, Mechanical, Coils,Armature, Image motion analysis.

Acknowledgements

Firstly, I would like to express my gratitude to Prof. Gran Engdahl for his guid-ance, innovative ideas, and numerous comments.

A lot of this thesis work was made possible due to the collaborative and fruitfulworking atmosphere at ABB AB Corporate research. Therefore, I would like tothank Dr. Mikael Dahlgren and Magnus Backman for employing me and givingme the opportunity to work with Dr. Thomas Eriksson and Dr. Ener Salinas.Their advice and guidance was very beneficial and they have helped me quite muchespecially when it came to the building of some of the prototypes.

I would also like to thank my friend Jesper Magnusson, with whom I alwaysend up discussing interesting ideas.

Furthermore, I would like to thank Dr. Henrick Breder, and Dr. Lars Liljestrandat ABB for answering a lot of my questions.

Additionally, I would like to express my gratitude to Patricia for her sweetnessand kind support and especially my friends, Samer Shisha, Andreas Krings, ShuangZhao, and Antonios Antonopoulos whom I have visited their offices numerous timesfor help and guidance.

I would also like to give my special thanks to my sister Jessy for her nice jokesand kind heart.

As for my mother, there are simply no words to thank her enough for all thethings I have put her through and for that reason I dedicate this thesis in her name.Thank you very much. I would have never made it so far without you. I hope Imake you as proud as I am for having such a great mum like you.

Ara Bissal

Stockholm, May 2013

v

Contents

Contents vii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Ultra fast actuators 5

2.1 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Generation of the fast impulse . . . . . . . . . . . . . . . . . . . . . . 72.3 Description of the TC and DSC actuators . . . . . . . . . . . . . . . 8

3 Modeling 11

3.1 Static model (DC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Stationary model (AC) . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Transient model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.2 Simulation results for three test cases . . . . . . . . . . . . . 27

4 Experimental verification 43

4.1 The experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 Loadability and scalability aspects 49

5.1 Loadability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Scalability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2.1 Scaling technique A . . . . . . . . . . . . . . . . . . . . . . . 535.2.2 Scaling technique B . . . . . . . . . . . . . . . . . . . . . . . 555.2.3 Scaling technique C . . . . . . . . . . . . . . . . . . . . . . . 57

vii

viii CONTENTS

6 Conclusion 59

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Bibliography 61

List of Figures 66

Chapter 1

Introduction

1.1 Background

After the adoption of the Kyoto Protocol in 1997, the industrialized countries werebound to reduce greenhouse gases. As a result, a lot of incentives for investing ingreen power emerged. Moreover, the development of more efficient wind turbinesand solar panels have made these renewable technologies more attractive. Unfor-tunately, very often, many of these renewable energy based generation plants arelocated in remote areas. One main issue lies in integrating offshore wind power[16, 24, 25] and solar thermal generation built in desert terrains to the electric gridwith minimum transmission losses.

The continuously increasing demand for connecting the grids with those re-mote renewable energy sources has rekindled interest in high voltage direct current(HVDC) multi-terminal networks. One of the major sources of large-scale renewableenergy sources in Europe, is offshore wind power. Recently, ABB won a 1 billiondollar contract to connect large wind farms to the German grid. This project willavoid more than 3 million tons of carbon dioxide emissions and upon its completionin 2015, it will deliver clean renewable electric power via an HVDC link to morethan 1.5 million households [1].

Why HVDC?

Although consumers receive electric power in the form of alternating voltage (AC),it is a must to resort to HVDC for long cable links since it is one of the viablesolutions at hand with the existing technology. Cables can be seen as distributedcapacitors that constantly need charging under ac voltage. At some critical length,this charge current will be equal to the maximum transmission capacity of the cablehindering power transmission.

The advantages of HVDC are not limited only to long cables. Some of the otheradvantages compared to AC systems are the following [42]

1

2 CHAPTER 1. INTRODUCTION

Lower losses

Asynchronous interconnections

Lower environmental impact

Lower investment costs

Added controllability

Limitations of the HVDC network

Although HVDC networks have numerous benefits, their adoption relies entirelyon the availability of HVDC circuit breakers [10, 14]. HVDC circuit breakers havemuch more stringent requirements than conventional AC circuit breakers renderingthem a key technology for the new emerging multi-terminal HVDC network. Dueto the absence of a natural current zero crossing as in AC systems and due to thelow inductive nature of the network, these circuit breakers must be able to interruptfault currents very quickly before the current increases in magnitude. As a result,it is critical to have ultra-fast opening times in direct current (DC) circuit breakerscompared to AC breakers.

Currently, three types of (DC) circuit breakers exist: mechanical, power elec-tronic, and hybrid breakers all suitable only for low and medium voltage applica-tions. The state of the art in 2009 for mechanical breakers is an operation time of60 ms and that of a power electronic breaker is 1 s [18]. As for the worlds firststate of the art hybrid HVDC breaker released by ABB in 2012, it has an operationtime of 5 ms [11].

Limitation of DC breakers

DC breakers face a challenge when a short circuit occurs due to the low impedancein an HVDC network [11]. Large currents complicate the design of the breakersbecause these are harder to interrupt. Moreover, all other equipments have to berated to withstand enormous fault currents [15]. Equipments rated for large faultcurrents become bulky and expensive and in some cases, an extra cooling systemmust be designed to dissipate the excess heat. These cooling systems require furthermonitoring and maintenance.

Mechanical breakers are cheap and have low on state losses but are relativelyslow in operation time. On the other hand, although solid state breakers have afast operation time that is in the order of micro seconds, they are expensive andsuffer from high on state losses. Nowadays, if state of the art mechanical breakersare used in an HVDC system, the grid owners usually compensate for the extraoperational time by inserting an extra inductance in the system to limit the rate ofrise of fault currents so that they do not have to overrate all other equipments toexcessively large fault currents. This however is not an optimum solution since itintroduces losses and voltage fluctuations. The main aim of this PhD thesis work

1.2. PURPOSE OF THE THESIS 3

is to develop promising designs of ultra-fast actuators that can be used to actuatecontact systems to reduce the opening time of appropriate current switches from therange of hundreds of milliseconds down to the order of hundreds of microseconds.

1.2 Purpose of the thesis

This thesis is focuses on using the Thomson coil (TC) based principle to simu-late and develop ultra-fast actuators. The simulation of a TC actuator constitutesa multi-physical problem where electromagnetic, thermal, and mechanical aspectsmust be considered. Moreover, it is complex since all involved variables are co-dependent and have to be solved for simultaneously. As a result, one of the maingoals of this thesis is to develop a multi-disciplinary simulation model that can pre-dict the behavior and performance of such actuators with a high degree of accuracy.Another goal is to build a prototype to validate the model experimentally.

A further objective is to design and build a flexible test bench, primarily tostudy the parameters influencing the generation of those high impulse forces andsecondly, to identify and study critical materials and key components influencingthe force transmission.

Finally, based on the acquired knowledge, different configurations are to bepresented with suggestions of possible improvements.

1.3 Outline of the thesis

Chapter 1: This chapter introduces TC based actuators and issues that aretreated in this thesis.

Chapter 2: This chapter provides a background of what has been done and thestate of the art of TC based actuators. It also presents a brief introduction to thetopic and a description of the actuators used in this thesis.

Chapter 3: In this chapter, a multi-physics FEM model is derived and presented.The use of such a complicated model is justified by providing test cases that treatsuch actuators with and without involving thermal and mechanical aspects.

Chapter 4: In this chapter, to add credibility, the developed multi-physics sim-ulation model is experimentally validated.

Chapter 5: This chapter highlights the influence of the mechanical loading ofthe actuator performance. Scaling techniques are presented to improve performanceand efficiency.

Chapter 6: This chapter concludes the thesis, the results are summarized, andfuture work is suggested.

4 CHAPTER 1. INTRODUCTION

1.4 Contributions

The work of the author has resulted in the following contributions to the state ofthe art:

A comprehensive description of the physics involved when generating ultra-fast mechanical impulses by TC like actuators.

A description of the nature of the involved nonlinear transients.

A development and experimental verification of a multi-physics finite elementsimulation model of TC actuators.

A description of the behavior of such actuators when loaded mechanically.

Scaling techniques to improve actuator efficiency and performance.

1.5 Publications

The work presented in this thesis has resulted in the international conference paperslisted below:

A. Bissal, J. Magnusson, and G. Engdahl, "Comparison of Two Ultra-Fast Ac-tuator Concepts," Magnetics, IEEE Transactions on, vol.48, no.11, pp.3315-3318, November 2012.

A. Bissal, J. Magnusson, E. Salinas, G. Engdahl, A. Eriksson, "On the Designof Ultra-Fast Electromechanical Actuators: A Comprehensive Multi-PhysicalSimulation Model," Electromagnetic Field Problems and Applications (ICEF),2012 Sixth International Conference on, pp.1-4, June 2012.

A. Bissal, J. Magnusson, G. Engdahl, E. Salinas, "Loadability and scaling as-pects of Thomson based ultra-fast actuators," in 13th Internation Conferenceon New Actuators, Bremen, Germany, June 2012.

Chapter 2

Ultra fast actuators

This section presents the state of the art, explains the principle of generating anultra fast impulsive force, and provides insight into the geometry and operatingmechanisms of the TC and the double sided coil (DSC) actuator concepts.

2.1 State of the art

Traditionally, switching devices such as circuit breakers and disconnecters are com-posed of springs and gears. Recently, some of them have been replaced by perma-nent magnet based actuators due to their advantages of being maintenance free andhighly reliable with applications in vacuum and gas circuit breakers [37, 38, 7, 8].They exist in many forms such as the helix coil launcher, the reconnection gun, thecoil gun etc... Recently, ultra-fast actuators are being studied more and more dueto their diverse applications in robotics, automotive, steel punching, and switch-ing devices. New research is performed on repulsive actuators based on Thomsondrives.

2.1.1 Applications

Due to the modern needs of power networks, there is a greater need for high-performance current limiting or interrupting devices. To achieve these ultra-fastswitching requirements, Thomson drives are being used to develop new circuitbreakers. For example, in [26], a Thomson drive is used in a hybrid DC circuitbreaker consisting of a mechanical switch, two power IGCTs connected in paral-lel, diodes, and a metal-oxide varistor for dissipating the energy. In [40], a detaileddescription of a high speed single phase Mitsubishi circuit breaker is given. A Thom-son drive incorporating a closing coil, an opening coil, and a repulsion plate is used.Moreover, the vacuum interrupter, the moving contacts, and the bellows are shown.This circuit breaker has an opening time of 1 ms and a breaking time of around20 ms. Yet another example is shown in [41], where a high voltage circuit breaker

5

6 CHAPTER 2. ULTRA FAST ACTUATORS

is described based on an electromagnetic repulsion drive and a permanent magnetspring. This drive incorporates two fixed coils and a movable coil in between. Thecurrent pulse is fed to the top and movable coils for an opening operation and tothe bottom and movable coils for a closing operation. Additionally, in [9], a DChybrid current limiting breaker is shown. This breaker consists of a Thomson driveand a fast switch. The contact in this circuit breaker opens in 200 s and can attaina speed of 10 m s1. Furthermore, in [39], a conducting aluminum ring is used tobridge two current carrying contacts. To operate this repulsion drive, a currentpulse is injected in the driving coil causing a repulsive force. The armature reachesspeeds of 20 m s1 and contact separation is achieved in as short as 100 s. A drivewith a slightly larger opening time is shown in [17], where a high speed switch thatis capable of opening within 1 ms was developed and integrated into a hybrid drive.Moreover, in [36], a repulsion drive is used to investigate the interruption capabilityof a DC current by injecting a high frequency counter current. Other works donewith these drives are shown in [34, 5, 4], where the electromagnetic drive mecha-nism of a fast acting circuit breaker is examined, a high speed repulsion actuator isanalyzed and compared with a a permanent magnet actuator, and the effect of twoconsecutive discharges through a Thomson drive are shown respectively. Lastly, in[22], a TC is implemented in an arc eliminator.

Thomson drives have not been limited to linear actuation. Rotational uses ofThomson drives have also been implement as for example in [12], where a rotationalrepulsion drive is shown that has an extremely short breaking time (within a few100 s). Although this drive mechanism can achieve velocities up to 50 m s1, itsuffers from an efficiency of less than 5 %.

Thomson drives also play an important role in superconductive fault currentlimiters. Superconductors may be damaged due to excessive heating resulting fromlarge currents. Therefore, it is vital to use a high speed drive. In [13], a study ofa superconductive fault current limiter using a vacuum interrupter driven by anelectromagnetic repulsion force is shown.

2.1.2 Modeling

Modeling of TCs is crucial to be able to design such complex drives for the newemerging switching devices. Traditionally, simple circuit based schemes are usuallypreferred to minimize computational effort. In [35] an equation based modelingof a Thomson drive is implemented. While, in [21], an adaptive equivalent circuitmodeling method is shown. Furthermore, an analytical model based on the tableaumethod is shown in [40] and a reduced modeling of an eddy current-driven elec-tromechanical drive is explained in [20]. Finally, a general method for modelingfast-acting solenoid actuators has been done in [33] using an interpolation functionand electric equivalent networks to account for the eddy currents.

Subsequently, researchers have focused on optimization studies to improve theefficiency of the TC using equivalent circuit methods as in [23].

Although multi-physical simulations are important and are increasing in popu-

2.2. GENERATION OF THE FAST IMPULSE 7

larity, not much effort has been done to merge all necessary physics in one simulationmodel that describes the behavior of a TC as done for other applications. One ex-ample of such a coupling can be seen in [19] for similar types of actuators wherethe field computations are coupled with circuits to model an electromagnetic de-vice. Moreover, in [31] for example, a dynamic simulation using the finite elementmethod (FEM) for an electric screw driver was performed to calculate the inducedtorque. Additionally in [6], a coupled magneto-mechanical model is used to investi-gate the dynamics of electromagnetic valves. In [28], motion is incorporated in a 3Deddy current transient problem to model electromagnetic devices containing mov-ing conducting parts. Furthermore in [32], magneto-thermal-mechanical coupledsimulation problems for low frequency electrical engineering devices ranging fromsmall actuators to large synchronous generators are discussed. Finally in [29], analgorithm is presented that is comprised of a dynamical field-circuit coupled simula-tion to design linear electromagnetic actuators aimed at automated control systems.Therefore, one of the objectives of this thesis is to present a unified multi-physicalvalidated model that accurately predicts the behavior of TC based actuators.

2.2 Generation of the fast impulse

Several techniques are used to generate forces where some of them are based onmechanical springs, magnets, electromagnets, hydraulics, and pneumatics. As dis-cussed in the introduction, in the case of low inductive systems, ultra-fast actuationis required. Therefore, TC based actuators capable of generating the required highimpulsive forces are considered.

Mechanical springs are traditionally used as means of energy storage. Thesprings are maintained in a compressed state and released when needed. Thisprinciple is simple and effective but lacks ultra-fast speeds. Similarly, magnets canbe used to generate attractive or repulsive forces. However, this force generationmechanism also falls short of generating large impulsive forces. One way to achievethese required forces within fractions of milliseconds can be realized by inspectingBiot and Savarts law applied on two current carrying wires in proximity of eachother.

A long conductive straight wire, carrying a current I1 generates a magnetic fieldat a distance r from the wire given by:

B1 =0I1

2r(2.1)

If in the presence of another conductive straight and parallel wire with a length Land carrying a current denoted by I2, a force will act on wire 2 that is given by:

F = L0I1I2

2r(2.2)

This force can be tuned by varying the magnitude of the currents and thelength of the wires. Repelling or attractive forces can be generated depending

8 CHAPTER 2. ULTRA FAST ACTUATORS

(a) TC

(b) DSC

Figure 2.1: Sketches of the drives

on current directions in both wires. From (2.1), it is evident that in order togenerate substantial forces, currents in the order of tens of kilo Amperes are needed.Such high amplitude impulsive currents can be generated by discharging a seriesand parallel combination of capacitors. If the conductor cross section is not largeenough, excessive temperatures can arise and destroy the coil. In this thesis, theultra fast force impulse generation capabilities of a TC and a DSC based on theabove principle are analyzed.

2.3 Description of the TC and DSC actuators

The Thomson coil (TC), originally discovered by Elihu Thomson [3], consists of acoil with a conducting ring on top. By applying a varying AC voltage source, thefield of the coil induces currents in the ring and generates a repulsive force. Thomsonproved this concept by levitating objects. This section presents a modificationof the original TC to be suited for ultra-fast actuators and compares it with itscounterpart, the DSC.

The TC used in this thesis consists of a spiral shaped flat multi-turn coil withan electrically conducting object in its proximity, while the DSC consists of twomirrored spiral coils that are connected in series. The main difference between thetwo configurations is the currents in the propagating armature. In the TC, the timederivative of the axial magnetic flux density results in azimuthal eddy currents inthe armature. However, in the DSC the same current that flows in the primarycoil also flows in the secondary coil but in opposite direction. In principle, theproduct of this azimuthal current with the radial magnetic flux density producesthe required axial forces to repel the armature. Additionally, undesired compressiveradial forces are also generated from the axial component of the flux density. These

2.3. DESCRIPTION OF THE TC AND DSC ACTUATORS 9

forces are considerably lower than the axial forces and are manageable mechanically.It is important to define both actuators as identical as possible to be able to

compare them. The base coils in this study are identical and equipped with con-ductors of rectangular cross section with a width of 2 mm and height of 4 mm. Thecross section is dimensioned to satisfy the electro-magnetic, thermal, and mechani-cal constraints. The coil is made of copper and consists of 10 turns that are isolatedwith a 0.1 mm layer of enamel. However, these inter-turn gaps are neglected in thesimulations. The inner and outer diameters are 50 mm and 90 mm respectively. Forthe DSC, the actuating armature consists of yet another series connected identicalcoil while for the TC, the armature consists of a copper ring with the same dimen-sions as that of the coil. The armature axis and the main axis of the coil coincide.The coil to coil electrical connection can be made by using brushes but they even-tually may wear out. Therefore, they have to be maintained more often. Anotherfeasible solution is to use flexible leads of copper wire. These also in the long runwill break due to fatigue. Figure 2.1 shows the geometry of both configurations.

Chapter 3

Modeling

In this section, the theory behind the force generation principles of the two differ-ent types of ultra-fast electromechanical actuators are modeled starting with simplemodels and gradually building up into a comprehensive multi-physics finite elementsimulation model.

3.1 Static model (DC)

The aim of carrying out a static model is to perform a preliminary study of thebehavior of both actuator concepts under DC excitation and analyze the flux andcurrent distributions of both actuators. In this study, an energizing circuit is cou-pled to the terminals of both coils in the FEM models. This circuit is comprises a500 V DC voltage source in series with a 5 m resistor representing the cable leads.The equations used for the DC simulation in the FEM model are:

1

( A) = Je (3.1)

Je =eVcoil

2r(3.2)

where, is the magnetic permeability, A is the magnetic vector potential, Je standsfor the external current density, e is the electrical conductivity, Vcoil is the voltageacross the coil that is coupled to a SPICE circuit [27], and r is the radial position.

Exciting the TC with a DC voltage results in a homogeneous current distributionin the coil without inducing any currents in the armature as shown in Figure 3.1.This current leads to the creation of a constant magnetic flux density envelopingthe coil as can be seen in Figure 3.2. It has a maximum value exceeding 20 Tand is mostly concentrated adjacent to the innermost turn of the coil. This fieldpenetrates the armature totally and is not influenced by any electrically conductivebodies in its proximity.

Applying the same principle to a DSC results in a completely different magneticflux density distribution. Although the currents in both coils are homogenous as

11

12 CHAPTER 3. MODELING

r [mm]

z[m

m]

15 20 25 30 35 40 45 50 550

1

2

3

4

5

6109

-10

-5

0

5

10

15

Figure 3.1: A homogenous current density in [A m2] only in the coil of a TCsubjected to a DC voltage excitation.

r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

5

10

15

20

-10

-5

0

5

10

15

Figure 3.2: Magnetic flux density in [T] of a TC subjected to a DC voltage excita-tion. The field penetrates the armature and is highest close to the innermost coilturn.

3.2. STATIONARY MODEL (AC) 13

r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

2

4

6

8

10

12

14

16

18

-10

-5

0

5

10

15

Figure 3.3: Magnetic flux density in [T] for a DSC subjected to a DC voltageexcitation mostly confined in the air gap between the primary and secondary coilturns.

shown in Figure 3.4, the magnetic flux density is mostly confined in the air gapseparating both coils and peaks at 18 T (see Figure 3.3). It is lower than that of aTC since in this case, the main current drawn from the power supply is smaller dueto the added resistivity coming from the secondary coil. A smaller current results ina smaller field but leads to the generation of the desired repulsive electromagneticforces.

In principle, to generate an axially directed electromagnetic force, the armatureshould have an azimuthal current and be subjected to a radial field. Although aDSC generates smaller magnetic fields compared to a TC, it has currents circulatingin its secondary coil. Therefore, unlike a TC, a DSC is capable of generating arepulsive force when excited with a DC voltage source.

3.2 Stationary model (AC)

The aim of carrying out a stationary simulation model is to study the behaviorof both actuator concepts under AC conditions and analyze their flux and currentdistributions when influenced by skin and proximity effects. In this study theactuator consists of a lumped impedance added in series with a 500 V AC voltagesource to represent the cable leads under AC excitation. The impedance consistsof a 5 m resistor and a 1.5 H inductor. This circuit is coupled to an FEM modelas explained before. The equations used are as follows:


r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

-4

-3

-2

-1

0

1

2

3

4109

-10

-5

0

5

10

15

Figure 3.4: Homogenous current densities in [A m2] in the primary and secondarycoil of a DSC subjected to a DC voltage excitation.

(je 2)A +1

( A) = Je (3.3)

where, is the angular frequency, and is the electric permittivity.Contrary to the behavior of a TC with DC excitation, when its subjected to

an AC source, currents are induced in the armature as shown in Figure 3.5. Unlikebefore, the magnetic field is now confined in the air gap and peaks at slightly over16 T as shown in Figure 3.6.

At low frequencies, the resistance of a TC and that of a DSC behave differently.Increasing frequency does not maximize the generated force (see Figure 3.7) of aTC due to a rapid increase of resistance in the system. Initially, for the TC, a steepresistance increase can be noticed since more and more currents start flowing inthe armature with increasing frequencies. The magnitude of the induced currentsdepends on both the frequency and number of coil turns. Therefore, similarly to theoperating behavior of a transformer, the resistance of the armature is now addedto the system. This effect can be clearly seen in Figure 3.8 for frequencies up to100 Hz where the TCs resistance changes from 4.6 m to 6.25 m whereas that ofthe DSCs resistance remains constant at a value of 9.2 m. It is also important tonote that at DC, the DSCs resistance is twice as large as that of the TC clearlyexpressing the influence of the induced currents in the secondary coil.

Another factor influencing the generated force at low frequencies is the induc-tance. The inductance of the TC decreases drastically from 8.7 H down to 5.6 H


r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

-3

-2

-1

0

1

2

3

4

5109

-10

-5

0

5

10

15

Figure 3.5: Current densities in [A m2] in the primary coil and the armature of aTC at peak force when subjected to an AC voltage excitation with a frequency of120 Hz.

r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

2

4

6

8

10

12

14

16

-10

-5

0

5

10

15

Figure 3.6: Magnetic flux density in [T] of a TC confined in the air gap whensubjected to an AC voltage excitation with a frequency of 120 Hz.


Frequency [Hz]

Forc

e[k

N]

TC

DSC

0 100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

Figure 3.7: Existence of an optimal frequency for a TC. The force of a DSC decayswith an increase in frequency.

when the frequency is increased from 0 to 100 Hz. This is due to the fact that theinduced currents cancel out the change of magnetic field generated from the pri-mary coil decreasing inductance. As for the DSC operating in the same frequencyrange, its inductance remains constant at 3.8 H since equal currents of oppositemagnitudes circulate in both coils at all frequencies (see Figure 3.9).

At higher frequencies, the resistance and the inductance of both the DSC and theTC behave similarly and change drastically due to the combined influences of skinand proximity effects acting on both systems. Resistance increases with frequencydue to decreasing skin depths as shown in Figure 3.10. The current density is nolonger homogenous and is mostly concentrated on the facing surfaces of the coil andthe armature. This increase in resistance leads to a smaller current and a smallermagnetic flux density peak. By comparing Figure 3.6 and Figure 3.11, it can beseen that the magnetic flux density peak of a TC drops from 16 T down to 7 Tand is confined more in the air gap at higher frequencies. Due to decreasing skindepths, opposing current densities get closer to each other and hence, the TC andthe DSC inductances decrease with frequency.


Frequency [Hz]

Res

ista

nce

[m

]

DSC

TC

DSC

0 100 200 300 400 500 600 700 800 900 10004

5

6

7

8

9

10

11

12

13

Figure 3.8: Increase in resistance of a TC and a DSC with an increase in frequency.

Skin effect arises due to oppositely oriented eddy currents induced in the pres-ence of a time varying alternating current. Currents tend to circulate more in theouter shell of a conductor [30]. Skin effect cannot be disregarded and has to beaccounted for in most electric power devices since it can contribute significantlyto resistive losses and heating. At 120 Hz, the skin effect is not an issue for theTC or the DSC since the skin depth of copper at this operating frequency is 6 mmwhich is larger than the coil conductor depth. The skin depth can be calculatedas follows:

1fe

(3.4)

The proximity effect on the other hand refers to the constraint of current distribu-tions to smaller regions due to the influence of other currents in nearby conductors.The analytical treatment of the skin depth is rather complicated and will not beelaborated further in this thesis.

Another important aspect to study is the degree of influence of the coil to coilseparation distance on resistance, inductance, and peak force. Increasing the airgap increases inductance due to reduced coupling (see Figure 3.13). The opposing


Frequency [Hz]

Induct

ance

[H

]

TC

DSC

0 100 200 300 400 500 600 700 800 900 10003

4

5

6

7

8

9

Figure 3.9: Decrease in inductance of a TC and a DSC with an increase in frequency.

currents are now further apart and do not cancel out to the same extent as forsmall separation distances. Resistance on the other hand decreases with increasedseparation due to the decreased influence of proximity effect (see Figure 3.14).This change in resistance and inductance affects the peak force. Figure 3.12 showsthe maximum generated force with respect to frequency at different separationdistances. The force decreases and peaks at lower frequencies with increased sep-aration distances. The decreases in force is due to lower magnetic flux densitiesand lower induced armature currents as the separation distance is increased. Theresonance frequency of the system is inversely proportional to the square root ofthe inductance. Since inductance increases with increasing separation distances,the force will peak at lower frequencies as the coil to coil distance is increased.

In conclusion, the obtained results show that a time varying magnetic flux den-sity is needed to induce currents in the armature of a TC and generate a repul-sive force at the expense of increased resistance. However, there exists a criticalfrequency at which the generated force of a TC is maximized as can be seen inFigure 3.7. Increasing frequency further results in increased losses attributed withskin and proximity effects. As for the DSC, the generated force is maximized atDC since the required currents for generating a repulsive force do not depend on a


r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

-3

-2

-1

0

1

2

3109

-10

-5

0

5

10

15

Figure 3.10: Current densities in [A m2] of a TC subjected to an AC voltageexcitation with a frequency of 1000 Hz influenced by skin and proximity effects.

r [mm]

z[m

m]

15 20 25 30 35 40 45 50 55

1

2

3

4

5

6

7

-10

-5

0

5

10

15

Figure 3.11: Magnetic flux density in [T] of a TC confined mostly in the air gapwhen subjected to an AC voltage excitation with a frequency of 1000 Hz.

time varying magnetic flux density. Therefore, exciting a stationary DSC with anAC voltage source results in unnecessary losses.


Frequency [Hz]

Forc

e[k

N]

1.3 mm

2 mm

3 mm

4 mm

5 mm

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400

Figure 3.12: Overall decrease in generated force with larger coil to armature airgaps.

Stationary simulations are insufficient to predict the behavior of these actuatorssince in reality, the position of the armature is changing dynamically. Therefore,the analysis provided above serves as a good understanding of the influence of someof the involved parameters and motivates the need for a time dependent simulationmodel that incorporates all influencing variables.

3.3 Transient model

The influence of the armature position was elaborated in the previous section witha frequency based simulation model. Although it served as a good example fordemonstrating the effect of one of the dynamic variables, there are many more thathave to been taken into account for. In reality a capacitor bank capable of sup-plying high currents is used as the energizing source. Therefore, a time dependentsimulation model is developed to capture the transients upon its discharge in theTC and DSC coils.

The systems under study are composed of an electrical source that is connected

3.3. TRANSIENT MODEL 21

Frequency [Hz]

Induct

ance

[H

]

mm

1.3 mm

2 mm

3 mm

4 mm

5 mm

0 100 200 300 400 500 600 700 800 900 10003

4

5

6

7

8

9

Figure 3.13: Inductance increase of a TC with larger coil to armature air gaps.

either to a TC or a DSC. The electrical source is modeled as a SPICE circuit, whilethe TC and DSC are modeled as FEM models. Subsequently, the FEM and circuitmodels are coupled together and simulated for both actuator concepts as shown inFigure 3.16 and Figure 3.15.

The electrical source consists of an electrolytic capacitor bank charged up to500 V, a diode, a thyristor, and the connecting cables to the coil. The diodes mainpurpose is to prevent a negative voltage build up across the capacitor bank. Afterthe capacitor bank is fully charged, the thyristor is triggered causing it to dischargea current through the coil configurations shown in Figure 3.15 and Figure 3.16.The resistance of the capacitor bank is assumed to be frequency independent andhence is represented by the use of a constant resistance denoted Rc. The thyristorand connecting cables are modeled as two lumped static stray parameters denotedby Rstray and Lstray. RTC and LTC represent the resistance and the inductanceof the TC respectively while for the DSC, RCp, LCp, RCs, and LCs represent theimpedances of its primary and secondary coils respectively. These parameters arevariable and calculated dynamically with the FEM model.

The TC consists of a spirally wound coil with a conductive object, a so called


Frequency [Hz]

Res

ista

nce

[m

]

1.3 mm

2 mm

3 mm

4 mm

5 mm

0 100 200 300 400 500 600 700 800 900 10004

5

6

7

8

9

10

11

Figure 3.14: Resistance decrease of a TC with larger coil to armature air gaps.

Vc

Rstray

RCp

Lstray

LCp

Rc

RCs

LCs

Figure 3.15: SPICE circuit for a DSC

armature near one of its flat sides. Following the discharge of the capacitor bank,high current densities are created in the coil cross section increasing its temperatureand resistance. Concurrently, in a matter of a millisecond, flux densities in the


Vc

Rstray

RTC

Lstray

LTC

Arm

atu

re

Rc

Figure 3.16: SPICE circuit for a TC

order of 5 T can build up in the coil and the conducting plane in proximity ofthe coil. The conductive armature then is subjected to a magnetic kick. Thederivative of the axial component of the flux density induces eddy currents in thearmature. As a result, the azimuthal eddy currents and the radial component of theflux density create an impulsive force that repels the armature. However, the forcedistribution is not homogeneous enough to cause a smooth vertically oriented lineardisplacement. Therefore, stresses are induced straining the material and causingdeformations which in turn affect the system behavior. These deformations arerelatively large so the nonlinear effect of the change in geometry needs to be takeninto account. For that, the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor are used.

A moving mesh based on the Arbitrary Lagrangian-Euler method (ALE) is usedsince the induced forces are highly dependent on the proximity of the armature.The mesh is progressively stretched until a specified mesh quality factor is violated.Subsequently, it is re-meshed and this cycle is repeated.

3.3.1 Methodology

The movable armatures consisting of a copper ring for a TC and a secondary coil fora DSC are denoted by TCs and DSCs respectively. The induced current densitiesof such mobile armatures with a relative velocity v generated by the Lorentz forceis given by:

JiTCs = JiDSCs = e(E + v B) (3.5)

, where JiTCs and JiDSCs are the current densities induced in TCs and DSCs re-spectively, e is the electrical conductivity of the material, E is the electric fieldand v represents the velocity of the moving armature. As for the stationary basecoils of the TC and the DSC given by TCp and DSCp respectively, their induced


current densities reduce to:

JiTCp = JiDSCp = eE (3.6)

For a DSC, the current densities in both coils are composed of the sum of theinduced and the externally applied currents since the innermost and outermost turnof DSCp and DSCs respectively are connected to the terminals of a capacitor bank.Although DSCp and DSCs have different induced current formulations, they shouldhave identical currents since they are series connected, and moreover, they shouldhave identical current densities since according to the center of masses referenceframe, both are moving relative to each other.

JDSC = JDSCp = JDSCs = Je + Ji (3.7)

, where JDSCp is the current density in DSCp, JDSCs is the current density in DSCs,Je is the externally applied current density, and Ji represents the induced currentdensities in each coil respectively.

Contrary to the DSC, the currents of a TC circulating in the coil and armatureare different. The only currents circulating in the armature of a TC are due to theinduced eddy currents since no external currents are applied. The TC currents areexpressed by:

JTCp = Je + JiTCp (3.8)

JTCs = JiTCs (3.9)

Based on Maxwells equations and by expressing the magnetic flux density interms of the magnetic vector potential one has:

H = J (3.10)

E = B

t(3.11)

B = A (3.12)

where, H is the magnetic field intensity, J is the current density, B is the magneticflux density, and A is the magnetic vector potential. The magnetic equations forboth TCp and DSCp are given by:

eA

t+

1

( A) = Je (3.13)

As for the mobile armatures, the magnetic equations of TCs and DSCs are respec-tively given by,

eA

t+

1

( A) ev ( A) = 0 (3.14)

eA

t+

1

( A) ev ( A) = Je (3.15)


The DSC has the intrinsic property of a very low initial inductance due to theoppositely chosen current directions and the good coupling between the primaryand secondary coils. The mutual inductance will reduce the contribution of theself inductance of both coils resulting in a low inductive system in the order ofsome micro Henrys. This low resistive and low inductive system leads to highinrush currents causing a very steep current rise that is hard to estimate unlessmodeled with FEM. However, as the coils separate, the current tends to diffuseinto the coil for three reasons. First, the current derivative decreases as the currentpulse approaches its peak, secondly, the inductance of the system starts to increaselimiting the current build up, and thirdly, the conductivity of the material, mainlyin locations with high current densities, decreases due to temperature rise. Thisdecrease in conductivity affects the current distribution as the current will deviateto take a less resistive path. A similar effect is also seen in a TC although it has alarger initial inductance.

Due to the dynamics of the current density and large current density gradients,it is important to model the temperature distributions and their effect on systemperformance. The temperature equation for the stationary coils can be written as:

CpT

t= (kT ) + Q (3.16)

, where is the density of the material, Cp is the heat capacity, T is the temperature,k is the thermal conductivity, and Q is the heat source density and is consideredto be originating from the power loss density. It is given by:

Q =J2

e(3.17)

To simulate the temperature in the armatures, the thermal equations of thestationary coils need to be slightly modified to account for the movements. Avelocity term needs to be added since the system of equations are solved in astationary reference frame. Therefore, the thermal equations for TCs and DSCsare given by:

Cp(T

t+ v T ) = (kT ) + Q (3.18)

Sufficiently large temperature changes are often associated with conductivitychanges. It is important to calculate the change in conductivity as a function oftemperature to reduce losses and design the conductor accordingly. Hence thechange in conductivity is modeled by:

e = e0[1 + (T T0)]1 (3.19)

During the capacitor bank discharge, the high current densities result in a con-centration of the magnetic flux in between the stationary and moving objects re-sulting in a Lorentz force denoted by F as shown in (3.20).

F = J B (3.20)


One way to calculate the velocity of the moving armature is to integrate the forcedensity in accordance with Newtons law as shown in (3.21) under the assumptionthat the armature is infinitely stiff, in other words, it is not prone to bending. Thesum of the of the masses of the armature and that of the load to be actuated thenare lumped together and given by m.

F rdrddz = mdv

dt(3.21)

This technique reduces computational effort since the mechanical stresses are notcalculated. However, if a thorough simulation needs to be done to design a morecomplex armature, then the following equation is used where the stresses and strainsof materials are computed:

2u

t2 m = fem (3.22)

, where u is the displacement vector, and m is the mechanical stress tensor.In this case, the following assumptions are made:

Thermal expansions of materials are neglected since the coefficient of linearthermal expansion for metals is in the order of 1 105 C1.

The system is considered to be adiabatic since within these extremely shorttime scales, there is no opportunity for significant heat exchange with thesurrounding medium. As a result, the normal component of the temperaturegradient on the boundaries is set to zero.

The temperature rise is assumed to be only in the coil and armatures. It isnot modeled in the cable leads. Therefore, the temperature conduction fromthe coils to the cable leads are neglected.

The thermal conductivity and heat capacity are assumed to be invariant dueto an operating temperature range of 20 C to 200 C.

Materials are assumed to be isotropic.

The spiral coil is model as concentric rings and assumed to be rigid andincompressible. Therefore the displacement vector on the boundary of thecoil is set to zero.

Heat conduction between the coil turns is disregarded due to the concentricrings assumption.

Mechanical damping, hardening, and plasticity are neglected since the actua-tor should not operate in this region. Otherwise, it will decrease in efficiencyas the bending of the armature increases and eventually break downs com-pletely.

Air turbulence and friction are disregarded.


3.3.2 Simulation results for three test cases

This section presents results of a chosen set of test cases to primarily explain theelectromagnetic, mechanical, and thermal features of such an actuator, and sec-ondly, to justify the importance of multi-physics simulations and the importance ofusing the appropriate differential equations when needed.

The first two cases denoted by TC and DSC are used to show the electromagneticfeatures and serve as a base comparison between a TC and a DSC. The energizingsource consists of a 10 mF capacitor bank charged up to 500 V. The second two casesdenoted by "with SM", and "without SM", are used to demonstrate the bending ofthe armature of a TC and compare both outcomes using either equation (3.22)or (3.21) respectively. A copper disc is used as the actuating armature and itis centrally loaded with a mass of 1 kg. Furthermore, its thickness is reduced to2 mm and the capacitance is increased to 33 mF to ease bending and study theconsequential implications. The final set of test cases denoted by "with T", and"without T" are used to demonstrate the outcome of the simulations of a TC withand without using equations (3.18), (3.16), (3.17), and (3.19). The capacitance isdecreased to 500 F to get a faster current pulse. Accordingly, the charging voltageis increased to 10 kV to compensate for the decrease of electric energy by decreasingcapacitance. To demonstrate a distinct difference, the coil conductor cross sectionis also reduced to a width of 0.5 mm and a depth of 2 mm.

Electromagnetic features

Figure 3.17 shows the current density distribution after 20 s where the effect ofinrush currents and proximity effect are witnessed. The current distributes in theconductor in a way that counteracts the generation of the magnetic field due tothe injected current. Similarly as was shown in the frequency simulations, due toproximity and skin effects, the current densities are highest and mostly concentratedat the top of the coil conductor and the bottom layer of the conductive armaturefor a TC and at the top and bottom of the primary and secondary coils respectivelyfor a DSC. The currents concentrate in vicinity of each other to reduce the totalinductance resulting in a large amplitude of radial magnetic flux density confinedin the air gap (see Figure 3.18). Similarly, the current also concentrates betweenconsecutive conductor turns rendering the middle and bottom of the primary coilconductor almost entirely unused.

The current and magnetic flux density distributions evolve with time and aremostly dependent on the time derivative of the current pulse and armature proxim-ity. As the armature advances by some millimeters, the mutual inductance decreasesthereby increasing the total inductance of the system and limiting the rate of riseof the current pulse. Furthermore, the proximity effect is less dominant and thecurrent density tends to diffuse more into the material due to a lower current deriva-tive as shown in Figure 3.19. Similarly, although the magnetic flux density is stillmostly confined in the air gap, it penetrates deeper into the conductive armature


r [mm]

z[m

m]

20 25 30 35 40 45 50

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2109

-5

0

5

10

15

Figure 3.17: Current densities concentrated on the top and bottom of the primaryand secondary coils respectively of a DSC shown in [A m2] 20 s after the dischargeof a capacitor bank.

r [mm]

z[m

m]

20 25 30 35 40 45 50

0.2

0.4

0.6

0.8

1

1.2

1.4

-5

0

5

10

15

Figure 3.18: The magnetic flux density in [T] after 20 s barely penetrates thearmature and is mostly confined in the air gap.


r [mm]

z[m

m]

20 25 30 35 40 45 50-2

-1.5

-1

-0.5

0

0.5

1

1.5109

-5

0

5

10

15

Figure 3.19: Upon the discharge of the capacitor bank in a DSC, the current pulsepeaks at 200 s. The current density shown in [A m2], tends to homogenize.

r [mm]

z[m

m]

20 25 30 35 40 45 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

-5

0

5

10

15

Figure 3.20: At 200 s, the magnetic flux density shown in [T] penetrates deeperinto the material due to a zero flux time derivative.

as shown in Figure 3.20.


Time [ms]

Curr

ent

[kA

]

DSCTC

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

Figure 3.21: The peak current of a primary coil of a TC is larger than that of aDSC.

The current pulses of both actuators are shown in Figure 3.21. The DSC peaksat 9.5 kA and the TC peaks at 11.5 kA. Although the current flowing in the primarycoil of a TC is larger than that of a DSC, the induced currents in its armature arelower than that of a DSC. This is because the current flowing in the armature of aDSC is the same as that flowing in its primary coil, and as for a TC, the armaturecurrents are induced based on the time derivative of the current pulse and armatureproximity.

Currents in the presence of a magnetic field result in electromagnetic forces.The product of the azimuthal current density with the radial magnetic flux densityproduces the forces required to repel the armature. Similarly, the coil conductorswill also be subjected to an undesirable radially directed compressive force. How-ever, these forces are considerably lower than the axial forces and are manageablemechanically. Although the primary coil current of a TC is larger, its generatedforce impulse peaks at 33 kN and that of a DSC peaks at 36 kN as shown in Fig-ure 3.22. This shows that a DSC has a superior efficiency than that of a TC sinceit attains a larger steady state velocity with the same input energy as shown inFigure 3.23.

Large current densities also lead to a temperature rise. Unlike a DSC, a TC hasimbalanced current densities in its primary coil and armature. Since the currentsin the primary coil of a TC are larger than those of a DSC, a higher temperaturerise is witnessed as shown in Figure 3.24. On the other hand, the temperaturerise of the armature of a TC is significantly lower than that of a DSC as seen inFigure 3.25. As a result, not only does a DSC have lower requirements than a TCin terms of powering source component ratings, it is also superior in performance


Time [ms]

Forc

e[k

N]

DSCTC

0 0.5 1 1.5-10

0

10

20

30

40

Figure 3.22: The DSC generates a larger peak force than a TC.

Time [ms]

Vel

oci

ty[m

/s]

DSCTC

0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

70

Figure 3.23: The steady state velocity of a DSC is larger than that of a TC.

and has a higher efficiency.

Mechanical features

In these set of test cases, the electromagnetic forces generated by discharging a4125 J capacitor bank are enough to bend a centrally loaded armature and to studyits influence on the actuator while it is being repelled away.

After discharging the capacitor bank, large inhomogeneous axially oriented force


Time [ms]

Coil

tem

per

atu

re[

C]

DSCTC

0 0.5 1 1.5 2 2.5 320

22

24

26

28

Figure 3.24: The temperature rise in the primary coil of a TC exceeds that of aDSC.

Time [ms]

Arm

atu

rete

mp

eratu

re[

C]

DSCTC

0 0.5 1 1.5 2 2.5 320

21

22

23

24

25

Figure 3.25: The temperature rise in the armature of a TC is lower than that of aDSC due the lower primary coil to armature coupling.

densities are generated in only a portion of the armature that is situated directlyon top of the primary coil. The central part of the disc, where it is axially loadedwith 1 kg, experiences a maximum stress of 211 MN m2 after 100 s as shown inFigure 3.26. These extreme accelerations result in high stresses that deform thearmature even further before repelling it away. Figure 3.27 shows a severe bendingof the armature with respect to its central axis as it is moving away. The maximum


Figure 3.26: Von Mises stress of a TC armature in [N m2] after 100 s.

Figure 3.27: Von Mises stress in [N m2] after 320 s severely deforming the TCarmature as it moves away.

stress that it is subjected to is in the order of 15 GN m2 clearly demonstrating thatthis armature will deform plastically. The used model however does not take intoconsideration plastic deformation since in reality, the system should be designedto operate with stress levels that are significantly lower than the yield stresses andattain several thousands of operations during the course of its lifetime. To simulatethe actuator, a moving mesh based on the Arbitrary Lagrangian-Euler method(ALE) is used. The mesh is progressively stretched until a 10 % mesh expansionor compression factor is violated. Subsequently, it is re-meshed and this cycle isrepeated. For this specific example, 222 re-meshings have been done to simulatethe actuator for 3 ms.

When the armature is subjected to such extreme deformations, the electromag-netic system is affected. As the armature bends away, proximity effect decreasesand inductance increases considerably. Moreover, smaller currents are induced in


Time [ms]

Curr

ent

[kA

]

TC with SM

TC without SM

0 0.5 1 1.5 2 2.5 30

5

10

15

20

Figure 3.28: The current pulse in the primary coil of a TC is distorted due to therapid increase of inductance associated with the extreme bending of the armature.

the conductive armature since the effective air gap is increased thereby decreasingits efficiency. This bending effect can be clearly seen in the current pulse of theprimary coil shown in Figure 3.28. The current pulse with SM begins to deviatecompared to a simulation without SM at 100 s. The slope of the current pulsedecreases and then suddenly starts to increase once more at 320 s after bendingpeak as shown in Figure 3.29. Once the strain energy becomes larger than the in-duced forces, the armatures bending decreases as it heads backwards towards thecoil behaving just like a spring until once again, at 500 s, the induced forces exceedthe elastic forces bending it once more time away from the coil. During this timeperiod, the current pulse experiences a steeper slope after 320 s since the armaturetends to shrink the air gap as it relaxes. This phenomenon causes another peakcurrent at 500 s that is even larger than the peak current of a TC without SM.Finally, after 1 ms, the electromagnetic forces are almost zero allowing the armatureto bend negatively and attain a negative peak of around 5 mm. Afterwards, itstarts oscillating since mechanical damping is not modelled.

As explained before, the force generated by a TC is proportional to its inducedcurrents that in turn are directly proportional to the time derivative of the primarycurrent pulse. This coupling effect can be clearly seen in Figure 3.30. The forcepeaks at 30 kN just after 100 s since the slope of the current pulse decreases here-inafter. However, as soon as as the slope of the current pulse increases once moreat 320 s, the force increases in magnitude and peaks at 500 s exactly where thesecond current peak occurs.

Due to the bending, the generated force magnitude is smaller than when com-pared with an infinitely stiff armature. Consequently, the steady state velocity of


Time [ms]

Arm

atu

reb

endin

g[m

m]

0 0.5 1 1.5 2 2.5 3-5

0

5

10

Figure 3.29: The bending of the armature taken as the difference in displacementbetween the center of the armature and a point located at its outer diameter.

Time [ms]

Forc

e[k

N]

TC with SM

TC without SM

0 0.5 1 1.5 2 2.5 3-20

0

20

40

60

80

Figure 3.30: Clear deterioration of the generated force due to the influence of thebending of the armature.

the armature is reduced by 5 m s1 severely impacting its performance and efficiency(see Figure 3.31).

As for the temperature rise of the primary coil of a TC, it is larger when thearmature deforms due to the second attained current peak (see Figure 3.32). On theother hand, the armature of a deformable armature results in a lower temperaturerise since the induced currents due to bending are lower when compared with an


Time [ms]

Vel

oci

ty[m

/s]

TC without

TC with SM

TC without SM

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

Figure 3.31: The average velocity of a TC is significantly lower if finite deformationssuch as bending are taken into consideration.

Time [ms]

Coil

tem

per

atu

re[

C]

TC with SM

TC without SM

0 0.5 1 1.5 2 2.5 320

25

30

35

40

45

50

Figure 3.32: The primary coil temperature of a TC is larger when deformations aretaken into consideration.

infinity stiff system as can be seen in Figure 3.33.In conclusion, it is important to design against bending to maximize the num-

ber of operations, increase efficiency, and decrease the primary coil current peak.Bending can lead to destructive stresses deforming the armature plastically if notaccounted for. One way of reducing stresses is to embed a conductive armature ina stiff material or simply increase its thickness enough such that it can withstand


Time [ms]

Arm

atu

rete

mp

eratu

re[

C]

TC with SM

TC without SM

0 0.5 1 1.5 2 2.5 320

21

22

23

24

25

26

27

Figure 3.33: The currents induced in the armature decrease with increase in bendingresulting in lower temperatures when compared with an infinitely stiff TC.

the generated forces. Another way to decrease mechanical stresses is to generatea force impulse with a smaller peak and prevail it for a longer time period. Thishowever serves as a good topic for another study.

Thermal features

The final set of test cases denoted by "with T" and "without T" simulate the TCactuator with and without temperature dependence. The capacitance is decreasedto 500 F to get a fast electrical force impulse, but the charging voltage on the otherhand is increased to 10 kV to compensate for the corresponding decrease in energyand to demonstrate the effect of temperature increase on conductivity and overallperformance. Moreover, a uniform load of 5 kg is used to get a higher current peakby limiting the increase of inductance caused by the repulsion of the armature.

Due to the proximity effect, large current densities appear in the top and bottomof the primary coil and armature of a TC respectively as explained before. Theselarge current densities heat up the material at the facing surfaces and decrease theirconductivity. Hot spots arise significantly deteriorating the conductivity of regionswith high current density concentrations as shown in Figure 3.34. Temperaturedifferences up to 220 C appear causing nonlinear coil conductivity distributionswith differences as large as 50 % as can be seen in Figure 3.35. This change inconductivity affects the current distribution and forces it to peak at greater depthsin the coil conductors with undisturbed conductivities.

The temperature difference initially is highest at the coil to armature interfacesand decreases progressively in magnitude with time as it diffuses into the mate-rial. Although temperature variations decrease, the coil temperature continues to


r [mm]

z[m

m]

23 24 25 26 27 28 29 30 31 32

40

60

80

100

120

140

160

180

200

220

-1

0

1

2

3

4

5

6

7

8

Figure 3.34: Large temperature differences up to 220 C, 40 s after the dischargeof the capacitor bank.

increase until it attains 870 C (see Figure 3.36). Unlike the coil temperature, thetemperature of the armature increases only up to 90 C primarily because the cur-rent densities in the armature are much smaller than those in the primary coil andsecondly, since the armature cross section is larger than that of the coil conductors(see Figure 3.37).

In this case, the armature thickness was chosen intentionally to be larger thanthat of the coil to demonstrate the importance of dimensioning current carryingconductors to limit temperature increase. Electronics and processors are usuallymounted with heat sinks. Air flows between the ducts of the heat sink and coolsdown the equipment by convection. However, in these short time scales, convectionis not a solution since high temperatures can arise in some microseconds. Instead,these temperatures can be avoided by using a larger heat reservoir. This can beachieved by increasing the cross-section of the current carrying conductors. How-ever, the geometrical configuration of the wire cross-section has a great influenceon the induced forces. In essence, the aim is to have as high current densities aspossible adjacent to the armature without sacrificing number of turns. This can


r [mm]

z[m

m]

23 24 25 26 27 28 29 30 31 320.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

-1

0

1

2

3

4

5

6

7

8

Figure 3.35: Large electrical conductivity variations plotted in per unit 40 s afterthe discharge of the capacitor bank.

be solved by using rectangular shaped copper conductors where the width of theconductor can be adjusted to dimension the force impulse and underlying numberof turns, while its depth can be increased depending on the required temperaturelimitation. Increasing the depth of the wire ensures a heat flow from the top to thebottom of the conductor. In this way, high concentrations of current densities dueto the proximity effect will not serve as a bottle neck for the system.

Another significant advantage with limiting the temperature rise is to increasethe frequency of operation. If successive operations are required, then the tempera-ture increase per operation has to be small enough such that the total temperaturerise after all operations is small enough to avoid destroying the epoxy or any othermaterials in the proximity of the conductors.

This temperature dependence increases resistance and leads to a smaller currentpulse in the primary coil as shown in Figure 3.38. Hence, a lower current pulsegenerates a substantially smaller force impulse as can be seen in Figure 3.39. Asa result, the performance of the system deteriorates significantly where the steadystate velocity drops from 10 m s1 down to 6 m s1 as shown in Figure 3.40.


Time [ms]

Coil

tem

per

atu

re[

C]

TC with T

TC without T

0 0.1 0.2 0.3 0.4 0.50

200

400

600

800

Figure 3.36: Temperature up to 850 C are attained in only 250 s.

Time [ms]

Arm

atu

rete

mp

eratu

re[

C]

TC with T

TC without T

0 0.1 0.2 0.3 0.4 0.5

20

40

60

80

100

Figure 3.37: The temperature of the armature increases up to 90 C when temper-ature is taken into consideration.

In conclusion, a temperature increase deteriorates performance. If possible, hightemperatures should be avoided all together since they can reduce the lifetime ofactuators, and increase their cost and complexity especially if a cooling system ischosen to be incorporated.

In this section, the effect of thermal and mechanical calculations were shown.Although it is of course better to avoid adding complexity when not needed, butif simplifications are introduced based on unrealistic assumptions, then the sim-


Time [ms]

Curr

ent

[kA

]

TC with T

TC without T

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

35

Figure 3.38: Larger peak current for a TC with no temperature computations.

Time [ms]

Forc

e[k

N]

TC with T

TC without T

0 0.1 0.2 0.3 0.4 0.50

100

200

300

400

500

Figure 3.39: Generated force of a TC decreases when temperature is taken intoconsideration.

ulations are not trustworthy at all. For example, if no deformations or bendingare involved (as in the case of a ring type armature loaded homogeneously), thensimulating such an actuator with (3.22) will only add complexity and increase com-putational effort without any beneficial gain. On the other hand, in case of a discshaped thin armature that is centrally loaded, then deformations have to be takeninto consideration as was described earlier. Additionally, temperature calculationscan also be avoided if a slow electromagnetic force impulse is used and the conduc-


Time [ms]

Vel

oci

ty[m

/s]

TC with T

TC without T

0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

Figure 3.40: Performance of a TC suffers due to high temperature rises.

tors are dimensioned to withstand the temperature rise. In conclusion, a simulationmodel should aim for a minimum complexity that is sufficient enough to simulatethe behavior of an ultra-fast actuator within the required tolerances.

Chapter 4

Experimental verification

Although, simulation models serve as a powerful tool for modeling and designing thedescribed ultra-fast actuators, without validation, they are weak and prone to errorssince they rely on approximations and simplifications that might not always hold.Therefore, this chapter aims at adding credibility to the multi-physics simulationmodels by experimental validation.

There are several involved parameters that are easily accessible in the simulationcontext. However experimentally, it is relatively hard to get controllability on allof them since some of them are not even observable. For example, it is difficultto access different parts of the actuator such as the coil. The coil is embedded inepoxy and is initially in direct contact with the armature. Thus, it is hard to attacha temperature sensor to the coil and measure its temperature. An infra red cameracannot be used either since the actual hot spots are not visible. Thus low chargingvoltages are used and discharged in a relatively large conductor with a cross sectionof (24 mm2) to isolate the thermal effects. In these set of experiments, the effect ofbending and mechanical deformations are isolated as well by using a thick enoughring type armature subjected to low stresses and without any mechanical loading.Since the efficiency and performance of these actuators are of utmost importance,only the velocity of the armature will be validated.

4.1 The experimental setup

The coil consists of 10 turns and is embedded in a bakelite housing with a fillingof epoxy to hold it in place. The bakelite is screwed to a steel plate and the wholestructure is clamped down by 4 steel bars to a massive, rigid steel table to avoidvibrations as shown in Figure 4.1. A Pearson probe is used to measure the currentpulse with a sampling rate of 2 MS/s. The voltage of the capacitor bank is alsomeasured and used to trigger a high speed camera. To verify the accuracy of thesimulation tool, the conductivity of the armature and the charging level of thecapacitor bank are varied. One of the used armatures is made of oxygen-free high

43

44 CHAPTER 4. EXPERIMENTAL VERIFICATION

Figure 4.1: Experimental test setup showing the capacitor bank, the TC, the pear-son coil, and the positioning of the high speed camera and its trigging signal comingfrom the oscilloscope.

Figure 4.2: Illustration of the experimental test setup.

conductivity copper (OFHC) UNS C10200, and the other is made of Aluminum6082 T651. The test is repeated three times at charging voltages of 50 V and 100 Vfor each of the armatures. Moreover, they are tagged with markers and filmed witha high speed camera at 25000 fps as shown in Figure 4.2. Subsequently, the imagesequences are calibrated and tracked to determine the position and velocity of thearmatures for each shot.

4.2. VALIDATION 45

Time [ms]

Curr

ent

[kA

]

Exp 1Exp 2Exp 3

Simulation

0 0.5 1 1.50

1

2

3

4

Figure 4.3: Primary coil current validation of a TC with an Aluminum armatureon top due to a discharge of a capacitor bank charged up to 100 V.

4.2 Validation

To verify the model, the simulated current pulse and armature velocity are com-pared with the measured ones. The simulated current coincides with the measuredone with a good degree of accuracy as shown in Figure 4.3 and Figure 4.4. Inaddition, Figure 4.5 and Figure 4.6 show the experimental measurements for botharmature velocities compared with the simulation results. The maximum deviationbetween different measurements is 3 % while the difference between the simulationand experimental results at 50 V and 100 V is at most 6 % and 8 %, respectively.It can also be noted that although copper has a superior conductivity, this gain inconductivity is not enough to compensate for its high density. Therefore, the alu-minum armatures have a superior speed when compared to copper at both chargingvoltages. Some of the factors that lead to the discrepancy are as follows:

According to MatWeb, the electrical resistivity of the used armature materi-als ranges from 1.69 m to 1.73 m for the copper armature and between3.13 m to 4.17 m for the aluminum armature [2].

The mean displacement from simulations are compared with the displace-ments of the outer edge of the armature discs.

The armature may be prone to tilting due to unpredicted air flows that candisturb the movement or due to any initial misalignments in the centering ofthe armature. This cannot be compensated for since the presented model isaxis-symmetric.

46 CHAPTER 4. EXPERIMENTAL VERIFICATION

Time [ms]

Curr

ent

[kA

]

Exp 1Exp 2Exp 3

Simulation

0 0.5 1 1.50

1

2

3

4

5

Figure 4.4: Primary coil current validation of a TC with a Copper armature on topdue to a discharge of a capacitor bank charged up to 100 V.

Time [ms]

Arm

atu

revel

oci

ties

[m/s]

Sim Al 50 VSim Cu 50 V

0 2 4 6 8 100

0.5

1

1.5

2

2.5

Figure 4.5: Experimental measurements compared with simulations for both ar-matures, copper and aluminum upon the discharge of a capacitor bank charged to50 V. The legend in the figure only shows the simulated velocities for each arma-ture. Every simulation is compared with 3 corresponding experimentally measureddata plots for the same charging voltage and armature material.

Although a higher current pulse is achieved by using copper as a conductivearmature, the generated force impulse is not high enough to compensate for theadded mass. Copper has a higher density than aluminum and in this case, it is

4.2. VALIDATION 47

Time [ms]

Arm

atu

revel

oci

ties

[m/s]

Sim Al 100 VSim Cu 100 V

0 2 4 6 8 100

2

4

6

8

Figure 4.6: Experimental measurements compared with simulations for both ar-matures, copper and aluminum upon the discharge of a capacitor bank charged to100 V. The legend in the figure only shows the simulated velocities for each arma-ture. Every simulation is compared with 3 corresponding experimentally measureddata plots for the same charging voltage and armature material.

more efficient to use aluminum although it has a lower electrical conductivity. Ascan be seen in Figure 4.6, the velocity of an armature made of aluminum due to acapacitor bank charged to 100 V attains 8 m s1 while an armature made of copperattains only 3 m s1.

Chapter 5

Loadability and scalability aspects

The main purpose of using the described actuators is to actuate metallic contacts.Therefore, it is important to study the their behavior and their performance whenloaded mechanically. This section treats the effects of mechanically loading thesedrives and presents some scaling techniques to boost performance and efficiency.

5.1 Loadability

The standard primary coil, described in Figure 5.7 be used again in this section tostudy the influence of loading. To study the effect of loadability and its degree ofinfluence on the system, the armature is progressively loaded with masses startingfrom 1 kg to 4 kg in steps of 1 kg. Excluding the load, the armature itself weighsonly 153 g.

Based on Figure 5.1, it can be seen that the current peak increases with increasedloads. However, it does not increase linearly and at some added load it will saturate.Mechanical loads delay and encumber the repulsion of the armature increasing theinduced forces at smaller air gaps. The smaller the air gap, the less the inductanceof the system, and hence the greater the current peak. As a result, it is veryimportant to dimension the electronics of the drive based on the load to be driven.

Similarly, due to the increase in current, the generated force is increased aswell. However, the force impulses exhibits a greater degree of variation since it isproportional to the square of the current as can be seen in Figure 5.2. The peakforce was increased from 54 kN to 64 kN by increasing the load from 1 kg to 4 kg.This gain in force is achieved since the armature is hindered from moving too farfrom the force induction region due to the added mass. Increased forces lead tohigher stresses and can strain the armature significantly if it is not designed towithstand those generated impulses based on the load to be actuated.

Although the generated force impulse is increased, it is not enough to fullycompensate for the increase of load and maintain the same velocity. The end

49

50 CHAPTER 5. LOADABILITY AND SCALABILITY ASPECTS

Time [ms]

Curr

ent

[kA

]

Load: 1kg

Load: 2kg

Load: 3kg

Load: 4kg

0 0.2 0.4 0.6 0.8 10

5

10

15

Figure 5.1: Increase of peak current of a TC with increased loads.

Time [ms]

Forc

e[k

N]

Load: 1kg

Load: 2kg

Load: 3kg

Load: 4kg

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

Figure 5.2: Increase of peak generated force of a TC with increased loads.

velocity decreases significantly from 15 m/s to only 5 m/s (see Figure 5.3). Thisincrease in mass deteriorates the efficiency and performance of the drive. Althoughthe efficiency in reality drops from 4.8 % down to 2 %, it is not as bad as it wasexpected to be due to the additional gain in force. If the force is assumed to bekept constant, then the efficiency decrease can be scaled to be strictly inverselyproportional to the mass as shown in Figure 5.4. However, due to the increase inforce, the simulated efficiency is actually higher.

The DSC behaves similarly to the TC. The generated force impulse is increased

5.1. LOADABILITY 51

Time [ms]

Vel

oci

ty[m

/s]

Load: 1kg

Load: 2kg

Load: 3kg

Load: 4kg

0 0.5 1 1.5 2 2.5 30

5

10

15

20

Figure 5.3: Armature velocity of a TC drops with increased loads.

Mass [kg]

Effi

cien

cy[%

]

SimulationScaled

1 1.5 2 2.5 3 3.5 4 4.51

2

3

4

5

Figure 5.4: TC efficiency decreases with increased loads but is still higher thanexpected due to increased force generation.

but again is still not enough to compensate for the added load. As a result, the endvelocity drops from 20 m/s to only 7 m/s and the efficiency drops from 8 % downto 4 % as can be seen in Figure 5.5 and Figure 5.6. Without loading, the efficiencyof the DSC is 67 % higher than that of the TC, however with loading, the efficiencyof the DSC doubles.

The change in velocity exhibits a nonlinear characteristic with respect to me-chanical loading. This also holds for the current and force impulses. This is due to


Time [ms]

Vel

oci

ty[m

/s]

Load: 1kg

Load: 2kg

Load: 3kg

Load: 4kg

0 0.5 1 1.5 2 2.5 30

5

10

15

20

Figure 5.5: DSC armature velocity drops with increased loads.

Mass [kg]

Effi

cien

cy[%

]

SimulationScaled

1 1.5 2 2.5 3 3.5 4 4.52

3

4

5

6

7

8

9

Figure 5.6: The efficiency of a DSC decreases with increased loads but is still higherthan expected due to increased force generation.

the nonlinearities in the TC mostly associated with skin and proximity effects aswas described in previous sections. Therefore, it is hard to be able to predict theperformance of such drives without a FEM based simulation model.

To sum up, it is very important to dimension the system according to the loadthat needs to be actuated since both the current peak and the mechanical stressesincrease with added loads. Although the DSC exhibits the same behavior as a TC,it is more efficient and has a superior performance especially when loaded.

5.2. SCALABILITY 53

Figure 5.7: Two dimensional axis-symmetric diagram of the TC.

5.2 Scalability

In the previous section, it was shown that the performance of both drives, the TCand the DSC, were significantly deteriorated due to increased mechanical loads.Therefore, in this section, three different scaling techniques (A, B, C) will be dis-cussed in light of seeking methods to manage the drop in actuator performance. ATC loaded with 3 kg is chosen as reference.

If the scaling technique is applied to the geometry, then the scaling factor (SF) ismultiplied with the width of the coil conductor (cw), the depth of the coil conductor(cd), the width of the armature (aw), and the depth of the armature (ad) keepingthe air gap length (h) constant (see Figure 5.7). Scaling the charging voltage of thecapacitor bank squares the input energy. On the other hand, scaling the geometryinfluences the cross sectional area, the mean diameters of the coil and armature,and the armatures mass. The area is proportional to the square of scaling factor(SF). As for the armatures mass, it increases with the cube of the SF while thedepth and mean diameters are directly proportional to the SF. The added load ismaintained constant throughout this section. The diagram of a TC before and afterintroducing a SF of 2 is shown in Figure 5.8.

5.2.1 Scaling technique A

According to scaling technique A, the geometry of the actuator is scaled up keepingthe charging voltage of the capacitor bank fixed. Increasing the mean diameters ofthe coil and armature increases inductance and decreases resistance. This leads toa slight increase in the current peak as SF is increased as can be seen in Figure 5.9.Increasing the conductor cross sections of both the armature and the coil lead tolower resistive losses. As a result, the maximum coil temperature decreases from38 C down to 22 C with increasing SF from 1 to 2 (see Figure 5.10). Due tothe increase in the current and the increased active area i.e. the cross sectionalarea between the coil and armature with high magnetic pressure, the generated


r [mm]

z[m

m]

0 10 20 30 40 50 60

0

10

20

30

Figure 5.8: The TC before and after introducing a SF of 2.

Scaling Factor

Maxim

um

Curr

ent

[kA

]

ABC

1 1.2 1.4 1.6 1.8 215

20

25

30

35

Figure 5.9: Peak current of a TC actuator versus scaling factor for scaling techniquesA, B, and C

force peak increases as well (see Figure 5.11). However, the force does not continueto increase with increasing SF as shown in Figure 5.11. This is clearly shown inthe velocity curve where the end velocity peaks at 12 m/s and then drops down to11 m/s (refer to Figure 5.12). By simply expanding the area of the current carryingconductors, the efficiency was increased from 6.5 % to 10.5 % as demonstrated inFigure 5.13. This demonstrates that there exists an optimal conductor cross sectionif the input voltage is kept constant.

5.2. SCALABILITY 55

Scaling Factor

Maxim

um

Tem

per

atu

re[

C]

ABC

1 1.2 1.4 1.6 1.8 220

40

60

80

100

Figure 5.10: Temperature rise of a TC actuator versus scaling factor for scalingtechniques A, B, and C

Scaling Factor

Maxim

um

Forc

e[kN

]

ABC

1 1.2 1.4 1.6 1.8 250

100

on the design of ultra-fast electro-mechanical actuators

Documents