Linear PM DC Motors3

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Introduction to Magnetic

actuators

Prepared byDr. Osama S. Ebrahim

Faculty of Engineering, Ain shams university

Egypt

This lecture note covers

-PM DC Motors/Actuators

- DC Solenoid


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Magnetic actuators are energy conversion devices that use magnetic fields to

produce motion over limited range [1].

Block diagram of magnetic actuator.

Applications:

-Electro-hydraulic valves in airplanes, tractors, robots, automobiles, and other mobile or stationary

equipment

-Fuel injectors in engines of automobiles, trucks, and locomotives

-Biomedical prosthesis devices for artificial hearts, limbs, ears, and other organs-Head positioners for computer hard disk drives (HDD)

-Loudspeakers

-Contactors, circuit breakers, and relays to control electric motors and other

Equipments.

-Switchgear and relays for electric power transmission and distribution systems.


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Types:

Swing VCA

Motion in an arc

Linear VCA

Motion in a straight line

Linear PM DC Motors/Actuators


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Advantages of Linear PM DC actuators

-Very Simple Construction

-No commutator-Directly coupled to the loads allowing fast acceleration/decelration rate

Application Example

Hard disk drive (HDD)An example of a motion control system that uses both a magnetic actuator and a magnetic

sensor is the computer hard disk drive (HDD) head assembly shown below.

The head assembly is a magnetic sensor that senses (reads) not only the computer datarecorded on the hard disk but also the position (track) on the disk. To position the head at

various radii on the disk, a magnetic actuator called a voice coil actuator is used.


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Elements of Hard disk drive


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Four-head hard disk drive from IBM


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Construction of VCA for HDD

The magnetic assembly (or housing)consists of:

- PM (red) - made out of strong

permanent magnet material such as

neodymium. The PM creates normal

magnetic flux in the air gap.-Steel plates (blue)- made out of un-

laminated iron coated nickel and used to

complete the magnetic circuitas well as

to minimize flux leakage from the

structure.

The VCA for HDD consist of two separate

parts: Magnetic assembly and flat coil.

-The Coil is made of insulated copper or

aluminum wire and has n turns (n=Z/2).


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Basic Principles

)()(

BvLEBiLF

KiZBLiF

- By reversing the direction of the current (i), the direction of the force (F) will be

changed.

-If the current is constant, the force will be constant over the stroke length which is

good.

For Z conductors

KvZBLvE


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Where

v= coil velocity (m/s)

H=magnetic field intensity (A.turns/m).

B= magnetic field density (Tesla) =magnetic flux (Wb)

Z= total number of conductors.

E= motor back emf (V) F= force (N.m)


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Analysis of Magnetic circuit containing PM

Magnetic circuit with PM

0. dH

ggmm HH

gm

gog HB

Applying amperes law

We get

Assuming

ggmm ABAB

then

Also, we have

(1)

(b)

(c)

N

S

(a)


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Fig. 5 Operating point of a magnetic

circuit containing PM (1) Iron core is

neglected. (2) Iron core is included

From (a)-(c), we obtain

mm

CHB

Where, the constant C is

gmmgo AAC /)(

(d)

Solving (d) with the PM

demagnetization curve,

Bm = Fn(Hm)

The steady state operating point

can be determined as in Fig. 5


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Equivalent mmf Method

The PM can be replaced with an equivalent current sheet on two sufaces. Inside

The current sheet, the PM has permeability equal to the slop of the demagnetization

Curve which nearly equal o

The equivalent mmf has ampere. turns in the direction of magnetization

mcHNI

/mmf

The magnetic flux can be computed from


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Inductance

The inductance of a coil is defined as

INL /

2

)( NININL

The magnetic energy stored is

2

5.0

)(5.0

)(5.0

LI

ANI

A

ABHWmag

The relation between inductance and reluctance is


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Current buildup in a coil

When voltage VB is suddenly applied to the coil of VCA which has a resistance R and

inductance L, certain amount of magnetic energy will be stored in the coil(W=0.5 L i2). Since the stored energy can not change instantaneously, a delay will be

experienced in building up the current i.

The time constant is

Since the VCA force is function of coil current, this delay will deteriorates the

transient performance.

)1()(/t

e

R

Vti B

RL/


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Improving the linearity

It is possible to alleviate the current buildup delay problem by:

a) Increasing the system damping-By use of shorted turn(s) concentric to the coil but fixed to the magnet/pole

structure in case of linear DC actuator

-By use of un-laminated steel plates in case of VCA.

b) Use of high voltage and fast current control .

Also

C) Careful magnetic design is needed to minimize secondary effects such as saturation of

pole steel and leakage flux across the air gap.


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Motion controlVCAs are usually used to control motion of an object using closed loop feedback

control system. As shown below, the feedback system contains both an actuator and

a sensor. The sensor output is compared with the desired command and thedifference (error) is fed into the controller. The controller adjusts the actuator input

in such a way to minimize error. It is found that accurate control requires an accurate

sensor.

Basic feedback control system that may use both a magnetic actuator and a magnetic sensor.


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Define:Vc=cutoff speed (max. speed for soft-end stop) < terminal velocity.

a = acceleration/ deceleration rate

dm= maximum travel (seek) distance.

ds = distance for soft-end stop.

m= carriage mass.

ta = average access time = it is the time needed to make a large number of

travels (or seeks) of every length divided by the number of travels. It is assumed

that for each seek, any starting point or ending point on the length of possible

travel has equal probability.

tm = maximum access time.

Average Motion times of actuators for

random access devicesAn actuator designer would like to have, as a starting point for his design, information such as

the required current, maximum forces, accelerations, etc. Instead, he is often given anaverage access time, carriage mass, distances allowed for deceleration in a soft crash and

other system performance information, from which the parameters of actuator performance

must be derived.


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Provided that the intended control scheme meets certain conditions, an approximate method

exists (ref. 2) for first estimates of performance and as a check for CAD calculations (ref. 3).

This procedure uses trapezoidal speed-time curves and the effects of damping, friction and even

of back EMF are ignored. For the last simplification to be reasonable, the cutoff speed should belimited to less than about 65% or so of the terminal velocity. Acceleration and deceleration are

assumed to be constant and equal (except for direction).

The cutoff speed is set so that when the VCA coil starts at one extreme end of its travel,

accelerating toward the other end, cutoff speed is reached when 1/6 of the total travel is

reached, i.e., ds = dm/6.

If, at that point, current is reversed and deceleration is begun, the coil will stop after traveling a

total of 1/3 of the total stroke (in acceleration plus deceleration). It can be shown that the time

for this seek (motion) is equal to the average access time. The time required to make the longest

seek, from one extreme end to the other, is just twice this time. For this longest seek, it

accelerates over the first 1/6th of the distance, coasts for 2/3 of the distance at the cutoff speedand then decelerates for the final 1/6 distance(as shown below). Any seek which is less than 1/3

of the total distance is made by accelerating, then decelerating, with no coasting period,

because the coil never reaches the cutoff speed. A seek longer than 1/3 of the total distance

coasts for a period dependent on distance.


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vc = (2/3) (dm/ta)

a= (4/3) dm/ta2

tm= 2taGiven m, the force can

be determined from

F=m a

The required current is

I= F/k


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DC Solenoid (or Relay)


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The magnetomotive force (mmf) set up by the coil is:

Assuming uniformity of field and a constant gap length,

Ignore the reluctance of iron core, then we get


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The energy stored in a volume containing magnetic field is

The mechanical energy produced against the magnetic force is

Furthermore, the mechanical work must be equal to the electrical energy

given up:

Thus, the energy stored in the air gap is


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The flux exerts force (or torque) to reduce its length in

the air gap, i.e., minimizing the magnetic reluctance.

Typical

Solenoid force-

distance curve

Note:

The inverse-squared dependence of the

solenoid force with distance is not

adequate for actuators. At the beginning

of the stroke, when the load is to be

accelerated, very little force is available.

On the other hand, at the end of the

stroke, when the load should be

decelerating to a stop, the force increases

dramatically.


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Application Example

Start/stop circuit of DC motor with

field loss relay

Text Book pages (578-581)


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References

[1] J. R. Brauer, Maagnetic actuators and sensors,

IEEE press, 2006

[2] F. R. Hertrich, "Average Motion Times of

Positioners in Random Access Devices", IBM Journal,

March 1965.

[3] G. P. Gogue and J. J. Stupak, Theory and Practiceof Electromagnetic Design of DC Motors and

Actuators, available online

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