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Electro-magnetism - Lecture notes Electro-magnetism

Module taught by Prof. Layi Alatise
Module

Electromechanical System Design (ES2C6)

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Academic year: 2019/2020
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ES2C6: Basic electro-magnetism and electro-mechanical machines

Lecture 1:

Electricity  Clean / widely available and continuous supply  Easy, efficient : ≅4hp out of every 13A socket  Easy integration → easy control BUT.. many things are purely electrical?  EM m/c are cheap an convenient : - Closing the loop improves control, allowing you to use coarser / simpler devices more carefully to get a precision effect

Ways to go - Physicists can over-complicate it with too much field theory - Engineers simplify electro-magnetism - We’re going to ‘work the problem’. So : - Quick design study : how does a tiny electromagnet control a 40T truck?

Powering a 40T truck  You’re at an interview and you’re being tested on your systems-think...

Q - Explain how electricity controls engine power, by controlling fuel flow. Fuel ‘tap’ opens and shuts, so how much is simply a function of how long you open it.

You are told that - Throttle pedal has a pot. that gives 0 – 24V. - Injector timing can vary from 0-5 ms - You need a 10 A signal to ‘fire’ the injector - 5 ms injection → max engine power - Injector’s electro-magnet switches a pressure source → injection

Energy amplification - Input : Control of a low energy electrical signal (via throttle pedal, 24 V, several mA)  ECU – Engine Control Unit, throttle ‘demand’ converted to ‘drive’ signal for the engine’s injectors ( A amp pulses)← why current?  Very small electromagnet used to set amount of fuel injected with each pulse, so power

  • Controls switching of a high energy density pressure source that can actuate quickly  40T truck controlled by a valve that moves 30μm  Electrical actuators enact control

E/m actuators are incredibly useful. - We can use small signals switched by electronics to control huge systems - Electro-magnetic actuators often form an integral part of control systems - Control systems are built to integrate directly with these actuators providing a direct, accurate, robust way to get things moving. - So how do we make an electro-magnetic actuator? (A type of electro-magnetic machine)

3 basic elements of any electrical machine 1. Something to create the magnetism on demand

  1. Something to channel the magnetic field

  2. Something to be usefully acted upon by the field

Magnetic fields and magnet structureMagnet structure - Magnets are dipoles – north (seeking) pole & - south (seeking) pole

B =

Φ

A

(Wb m-2), or tesla (T)

Loops  What if there is more than one conducting wire?  Current in opposite directions –reduces field

 Current in same direction – augments field

Adding loops magnifies effect →

aka Turns  Schweigger showed the effect of extra turns in his galvanometer  Uses a magnet and a winding - also called a coil , or a solenoid.  Each turn develops a given flux, this is re-enforced by the next turn  More turns → more regular field inside the coil – outside it’s less regular & far weaker  Total flux available = flux linkage : product of the flux in each turn

and the number of turns, λ = N Φ (Wb)

Solenoids  Adapt the Corkscrew rule:  Imagine the fingers of the right-hand wrapped in the direction of current flow...  Your thumb points along North.  By controlling current in a coil, we have our first requirement - a controllable, source of magnetism – which we can make powerful with loops  But how do we channel this?

Some materials are easier to magnetize  Permeability, μ , is a measure of how well a material builds a field under the influence of a magnetizing source.  A coil of so many turns, N , carrying current, I , and having length, L , develops a magnetic field intensity, H (in At/m ) of H = NI / ℓ amp-turns / metre  The useful magnetic field, B , from which is : B = μH weber/m 2

 So the larger the value of μ , the greater the useful field.  Material permeability ( μm ) often given in terms of the permeability of free space ( μ 0 ), and the material's relative permeability to this ( μr ) , or: μm= μrμ 0 henry / metre

Material Matters – CORES  Air (and any other non-magnetic material) has a permeability, μ 0 , of 4π x 10 -7 Hm-  Ferromagnetic materials are especially good at developing a magnetic field –high μ values  Neighboring dipoles arrange into domains  No magnetizing field : - Randomly orientated →minimal energy  Under a field : - the nearly-aligned domains align, ‘add-in’ field - they expand at the expense of unaligned domains - After field is removed, some effect remains *  Material cores are used to channel the field, direct the flux to the point of use

Cores and Effect*  Permeable cores channel flux – creating an iron circuitA strong field is used to create a high flux densityRelative to the surrounding air, the permeability of the core is many times more, so the flux stays in the core - The field is effectively channeled - Flux much more likely to follow cores than jump outside – keeps to the easiest path - Allows us to concentrate field in area of interestChanneling the field allows concentrated action at a given point.

The First Electromagnets - actuators  1820 – Arago places iron bar inside a current carrying coil and notes the bar is magnetized  1825 – Sturgeon wraps a few turns around a horseshoe shaped bar, and uses this to lift small masses  Soon after Joseph Henry much improves Sturgeon’s design, and ultimately produces electromagnets capable of lifting 750 kg  Soon used in telegraphy... Early Machines – Henry’s Telegraph

𝐀=𝐀𝐀𝐀/𝐀 𝐀

  • Super-fine! Some galvanometers are capable of reading pA.

Applications – Main Types  Linear actuators / electromagnets

 Rotary motors / generators

Electromagnets  Current, magnetism, and movement are linked  Coils can develop strong fields  Ferromagnetic materials channel flux - Such materials include : Fe, Co, Ni.  Iron-circuits can be configured to develop force to produce movement  Movement enables change

Lecture 2: EM Machines Lecture intent :to generate student understanding of how to model electro- magnetic machines.  Show how the three elements of an electrical machine are applied to make ‘things’ work.  Start simple : how does a doorbell work?

How’s it work?  Push-switch is normally open (NO)  Push-Switch made: current flows in circuit  Current through coil turns develops a field  Field attracts the armature: 2 effects - Ball end of armature hits bell - Armature switch (NC) breaks electrical circuit - →→→

Doorbell fnc.  →  Circuit not made: current stops  Field decays, armature released and returns to original position by spring action (not shown), closing armature switch  Current flows, armature moves again  Repeats until NO push-switch released  How can we model this magnetic effect?

Circuit analogies  You’re all familiar with electrical, or copper, circuits...  Think of magnetic circuits, or iron-circuits in the same way

In an electrical circuit : V = IR, Ohm’s relationship Relates voltage (or electro-motive force (not a real force)), V, ( volts ) ; current, I , (amps) and resistance, R, ( ohms ). e

In an iron-circuit : ℱ= 𝐀 ℛ, Hopkinson’s Law Relates Magneto-motive force (not a real force), ℱ (ampere-turns); flux, 𝐀 (weber, Wb); and reluctance, ℛ ( amps/weber, AWb-1).

ℱ= 𝐀 ℛ, Hopkinson’s Law – How does this help?  Because ℱ=𝐀𝐀=𝐀 ℓ (as you probably guessed from the units! (AT)) - the product of the number of turns and the current - this is readily obtainable, helping you design the circuit  The MMF can be considered as a value for the potential for a device to produce flux in an iron-circuit...  Cf. an electric circuit : voltage source provides the electrical potential to generate current.

Flux : 𝐀 ℱ============================== ℓ  Flux is akin to magnetic current  The reluctance (or magnetic resistance) defines how much flux a given potential develops – cf. resistance  We only consider the dominant loads – just like in electrical circuits

Relucance : ℛ ℱ = 𝐀𝐀 = 𝐀 ℓ = 𝐀ℛ  Reluctance is a function of the geometry and material of the flux pathway.  XSA (cross-sectional area) matters as the narrower this is the more we confine the flux  In iron-circuits, the reluctance often changes : components move, changing the flux path or changing an air-gap.

  • F = 300 At =¿ ,

thus I =

F

N

=

300 At

300 t

= 1 A

Or via reluctance ...  Reluctance may be expressed as a function of the flux path length, the cross- sectional area through which this flows, and the substance permeability :

R =

l

μmA (in amp / weber )

 Remembering that B = μH, then

  • μm =

B

H

=1 T

1500 At

=833 × 10 − 6 H / m

 So in this case the reluctance is:

R = l

μmA

= 0 m

833 × 1 0− 6 H

m

× 400 m m 2

=600 000 A

Wb

∨ per H

 Check this works... -

F = φR = 500 μWb × 600 000

A

Wb

= 300 At

  • F = 300 At =¿ implies 1A required through 300 turns.
  • Same as before. (Phew! The laws of Physics remain intact, for now... )

Lenz’s law – multiple coils

What if we added another coil? How might we predict the current direction?

The direction of an induced EMF is always such that the current it produces acts to oppose the change in flux or motion causing the induced EMF.

 A CW field is generated by the first coil  Add a coil – the flux from the first coil links with the second coil turns...  Inducing an EMF across the turns  The more turns, the more linkage.. more EMF across the whole coil  EMF drives a current in the second coil  →→→

 →

 This 2nd coil’s current acts to oppose the change, so tries to reduce the field - Think of this as generating a flux flowing CCW in this case  Applying the Grip rule, we see that the current must flow out of pt X.  EMF out and current out are a fnc of the ratio between coil turns because of the flux linkage (this is how transformers work)

Path of least resistance: point of least reluctance  So how does this help?

  • Because you can both think about the way the iron-circuit works in terms of reluctance, iron circuits, and Lenz’s law; and also calculate physical effects given quite limited information.

What’s the point - of least reluctance  Consider a simple coil and armature:  An armature exposed to a magnetic field will try to move to a point where the least reluctance to flux exists.  Cf. a gravitational field, where an object tends to move downward to the point of lowest potential.

One step at a time... 1. Here’s the solenoid 2. We turn on the current 3. A field develops 4. We insert a soft iron bar 5. The bar is partially, temporarily magnetized 6. A resultant force drags bar in towards the centre of the coil 7. As it moves a counter current is generated in coil (Lenz’s law), reducing net field, and force. 8. The field isn’t homogeneous, it lessens at the ends: the field is strongest in the centre, so the force is strongest there. 9. Eventually bar comes to rest at the point of least reluctance – where the field (and force) is strongest. (Analogous to a ball finding the lowest place between two peaks).

Real Force developed – the Maxwell Pulling Force  So, we understand there is a force directed towards the point of least reluctance, but how big is this force?  Start by thinking of energy stored in the coil, and get to work - This is a function of the coil’s inductance – commonly part of coil spec. - Inductance – that property of a material that defines its ability to store energy in the form of moving charge (current) or a magnetic field. The unit of inductance in the henry (H).

  • Voltage across an inductor given a : V = L

dI

dt

(volts)

  • Thus the power, P , can be found as: VI = P = LI

dI

dt

(watts)

  • And the work done, Wf , determined by integration of power over time such that

Wf =∫ P dt = L ∫ I

dI

dt

dt =

1

2

L I 2 (joules)

Maxwell Pulling Force – REAL forces that accelerate  There are several ways to easily determine the force developed :

  • Material constraints
  • Outer control loop – the injector is only part of the system (it runs o/l)...

Material Constraints  Certainly a challenge  Highly permeable materials such as soft iron might not be robust enough for extended duty. - Called soft iron for a reason  They might need to be used with stronger, less magnetic materials.  This will increase the reluctance in the flux path  What else can electro-magnets do? Turbo / Force balance  Applications like the injector are ‘digital’ in that they require on or off responses...  .. you can also use coils to produce proportional effectsE ., a turbo vane controller.  Because we understand electromagnetism, we can use it to enforce international standards rather than clumps of metal! New kg.

All 50 types of magnet at the LHC are electromagnets - 1232 Main Dipole magnets - bend the path of the particles - Each 15 m long, 35T, 8 tesla superconducting electromagnets - 11 850 A  Big enough for you?

  • I hope so! Next size up is planetary magnetics.

Remember  Current, magnetism, and movement are linked  Coils develop strong fields, which can be channeled to produce movement  Iron-circuits are analogous to electrical circuits - Ohm’s Relationship cf. Hopkinson’s Law  We can easily deduce the current and turns needed to generate the magnetic potential needed

 We can use F =¿= H l = φR readily

Next time we’ll talk about how to harness the concepts of electro-magnetism to produce effective rotary actuators.

Force developed – the Maxwell Pulling Force

 Wf = force × distance = Fx

∴ F =

Wf

x

= L I

2

2 x

(newtons, N)

 How does this relate to reluctance? From Faraday’s law

V = L

di

dt

= N

dφ

dt

,∴LI = φN, → I =

Nφ

L

(in a continuous system)

MMF, F =¿= φR ,∴N

2 φ

L

= φR , ∨¿

reluctance R = N

2

L

, so F = L I

2

2 x

= N

2 I 2

2 R x

(N)

 Remembering that R =

x

μA

,

F = μA

N 2 I 2

2 x 2

(N)

 In terms of field, B , this becomes

F =

B 2 A

2 μ

(N)

(Try deriving this – use F = H l , ∧ B = μmH )

SEE EXERCICES

Lecture 3: Lecture Intent : To create student understanding of key methods used to control electro-magnetic actuators.

Direct Current Drive Basics  Certain drive circuits that are worth a look  When things are on or off, or slow, it’s easy  But switching rapidly can give problems : why? - Inductance ... - Force is a function of current, which is a function of inductance change - So actuator reaction time a function of inductance  Most switching now controlled digitally - Digital control is convenient: logic -> power stage -> coil - Even digital circuits can’t break the laws of physics!  The time constant, τ , tau, relates L/RTransient response specification for 1st order system as informs on initial r.o.  0-63% Imax = one time constant, τ  Rise Time, Tr = 10 - 90% ≈ 2 τ

Loads  Remember that a motor or actuator load IS NOT purely resistive where current rises at the same rate as voltage ( V=IR )  With an inductive load, the inductance wants to keep the same current ...  So it takes time to turn on an inductive load – becomes a design constraint in fast devices. E.,  Direct electrical control would need a big coil to provide lots of force... - big coils takes a long time to switch

Inductance effects

 Inductance can be used to our advantage in rapid switching.  But remember that inductance (and electromagnetism in general) is a tricky concept in transient systems : - Inductance is a function of geometry – so armature position - Field strength is a function of field intensity and permeability - Permeability is very non-linear, and remanent effects ... - Don’t forget back-emf – the coil wants to store electro-magnetic energy and acts to change any change imposed.  This does though enable a possibility ...

Inductance Sensing  Using inductance to implicitly sense position - potentially useful  Inductance is a function of armature position and so ‘measures’ actuator action

Noise / EM interference, other consequences

 Clearly there’s a lot of switching going on  Sometimes the energy might find a path you didn’t expect  Other components in close proximity might suffer - The case here is extreme – but the idea is the same even for low voltages – switching causes noise - This is a particular problem if you have fast-switched circuits next to precision measurement circuits.

Noise / EM interference : Components

 Most every circuit is susceptible to electrical noise , aka: - electromagnetic interference / Break-through, or - Cross-over / cross-talk  Sometimes simple components can help - caps  You can use filters, sometimes called chokes on big machines, or use twisted pairs to ‘undo’ the aerial - It’s better to kill the noise at source so filtering a big machine stops noise getting on to the mains - More of a problem than it used to be - because control electronics now need less energy to switch, so the noise floor needs to be lower.  Diodes can protect windings from large –ve voltages, but the noise will still be there.

Noise / EM interference : Shielding

 You can protect against noise using a Faraday cage, (aka screening and shielding and connecting shield to a fixed potential.) - But noise will usually find a way through as you can’t shield everything! - Often it is conducted through common power supply connections

Using a mixed approach of shielding and filtering is often best.

Other effects – Magnetic effects – e., hysteresis.

 Finally, a few words on other effects that come into play and can be important.  Hysteresis – already mentioned - the effect where the magnetization intensity required is a function of the existing degree of magnetization.  Note the non-linearity  Note the ‘remanence’ when magnetizing field intensity is removed.  Nothing for free!

  • E., INJECTOR - use a soft iron armature mated to a hard steel valve – drops useful MMF
  • E., RELAY - Use a soft iron armature to make/break low resistance gold-plated contacts

Drive  Drive format is important in working out how to power a device.  Using rapidly switched current from a digitally controlled source can be a very effective way to developing effective control.  There will be assorted secondary effects to consider.  The physical function will dictate the format of the device and the electrical machine will be sub- ordinate to the final function.  Iron-circuit numerical Q’s follow →→→→→→→

SEE EXAMPLE

The power of servo’s - Finally, don’t forget that there may be high-density energy around that you can tap into - E., the injector uses 3000 bar pressure, pressure is analogous to energy density, you can use a small electrical signal to switch a big pressure. - This is just like using mA to switch many A in a relay.

Lecture 4 Lecture Intent : to develop awareness of simple, rotatory e/m devices such as stepper motors as used in precision instruments.

Rotary Motion – one way  So we have a linear motion – how can we make this a rotary motion - 2 easy ways – one much better than the other!

Stepper Motors  Stepper motors can be considered an array of individual actuators, timed in their operation to induce rotary motion.  In this (unusual) example : - 5 actuators attached to a crank - cam operated switching (belted to crank) - Variac controls voltage (so current, so force, so speed) - There are better ways...

Rotary Motion – The best way  Rotary motion can be achieved using attraction, however there is a better way...  Most electrical machines are rotating and these rely on alignment forces.

 Misaligned poles, the system tries to decrease the system reluctance , but this time by : - Reducing the gap AND - Increasing the effective cross-sectional area by trying to align the poles. - We might need to start worrying more about flux leakage – the geometry gets harder  The force of alignment is given as:

fe =

B 2 A

2 μ 0

=

B 2 l lg

2 μ 0

(where lg is the airgap and l the pole width)

N. Not a continuous function...  Moving the poles past alignment would make the force go –ve.  This implies that we need some way to time (or synchronize) the motor.  The way the airgap changes is also non-linear

Stepper Motors – Principle of Operation  SMs work by producing a series of indexed movements  Individual pulses cause a rotation of a given angle  A series of pulses produces a shaft rotation that is the product of the angle / pulse and the number of pulses  At high stepping rates (kHz), the operation is smooth - think about the inertia in the system  Widely used - Disc heads / printers / camera lenses / scanners - Machine tools ( e. via leadscrews to produce translations) - Plus...

Many High-precision Applications:  Small step magnified by gearing ratio → high precision  Lots of applications in vehicles...  Automotive  Cost – cheap ∵ control  Quality  Robust  Aerospace  Precision  Proven technology  Redundancy – detent

Stepper Motors Basics – Two Types:Variable Reluctance , and Hybrid  Same effect in each, so-called ‘ reluctance torque ’ - A suspended iron bar tries to align itself with the local field - Changing the field orientation alters the angle of the bar - The turning effect is known as the reluctance torque - Basically the same effect as in an actuator where the core seeks the position of least reluctance – but in a radial context  Variable reluctance steppers use only coils to produce magnetic fields  Hybrid steppers use coils and permanent magnets on the rotor

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Electro-magnetism - Lecture notes Electro-magnetism

Module: Electromechanical System Design (ES2C6)

28 Documents
Students shared 28 documents in this course

University: The University of Warwick

Was this document helpful?
ES2C6: Basic electro-magnetism and electro-mechanical machines
Lecture 1:
Electricity
Clean / widely available and continuous supply
Easy, efficient : ≅4hp out of every 13A socket
Easy integration → easy control
BUT…how many things are purely electrical?
EM m/c are cheap an convenient :
–Closing the loop improves control, allowing you to use coarser / simpler devices more
carefully to get a precision effect
Ways to go
•Physicists can over-complicate it with too much field theory
•Engineers simplify electro-magnetism - We’re going to ‘work the problem’. So :
•Quick design study : how does a tiny electromagnet control a 40T truck?
Powering a 40T truck
You’re at an interview and you’re being tested on your systems-think...
Q - Explain how electricity controls engine power, by controlling fuel flow.
Fuel ‘tap’ opens and shuts, so how much is simply a function of how long you open it.
You are told that
–Throttle pedal has a pot. that gives 0 – 24V.
–Injector timing can vary from 0-5 ms
–You need a 10 A signal to ‘fire’ the injector
–5 ms injection → max engine power
–Injector’s electro-magnet switches a pressure source → injection
Energy amplification
–Input : Control of a low energy electrical signal (via throttle pedal, 24 V, several mA)
ECU – Engine Control Unit, throttle ‘demand’ converted to ‘drive’ signal for the engine’s injectors (10
A amp pulses)← why current?
Very small electromagnet used to set amount of fuel injected with each pulse, so power
–Controls switching of a high energy density pressure source that can actuate quickly
40T truck controlled by a valve that moves 30µm
Electrical actuators enact control
1

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