A3DMagneticForce Manipulator DC Prototype

A 3D Magnetic Force

Manipulator DC Prototype

Leandra VicciMicroelectronic Systems LaboratoryDepartment of Computer Science

University of North Carolina at Chapel Hill17 October 2001

(Rev 2) 4 September 2003

Summary

A potentially useful instrument for the biological sciences wouldbe a 3 dimensional force microscope (3DFM) for measurement of 3 di-mensional viscous and elastic fields at sub micrometer scale in-vitro andin-vivo. Substantial development has been conducted on various as-pects of this problem, but a general instrument having this capabilitydoes not yet exist. All approaches I know of utilize a microscopic beadas a mechanical probe, the position of which can be sensed, and theforce on which can be controlled. One force technique is “optical tweez-ers.” This technique requires high optical field intensities which interactstrongly with many materials and may produce undesired side effectson in-vivo experiments. Alternatively, magnetic techniques use a mag-netic bead driven by low frequency magnetic fields which only interactweakly with most biological materials. Related prior work includes highgradient techniques [Haber00], a close proximity single pole rheometer[Bausch98,99], and a two dimensional manipulator [Amblard96]. To myknowledge, our work is the first attempt to implement a full three dimen-sional magnetic manipulator. A low frequency (DC) prototype magneticcircuit and drive electronics have been designed and built to explore thecapabilities of the magnetic technique for a 3DFM. This report com-prises a brief description of the DC prototype, and a complete set of itsdesign documents. This is a report of work in progress, and does notpresent any results of experiments performed on the prototype.

TR01-031(Rev2) UNC Chapel Hill, Department of Computer Science page 1

Leandra Vicci A 3D Magnetic Force Manipulator DC Prototype 17 October 2001

1 Conceptual design

The magnetic manipulator is intended to be a subsystem to work in concert with othercomponents of a 3DFM. The target was to produce three dimensional nanonewton forceson sub micrometer magnetic beads with a bandwidth of the order of 104 [Hz].

A conceptual design phase preceded the design of the first prototype. The conceptualphase began at a very high level of abstraction, leaving many important implementationissues to be determined. This section describes the conceptual design at this abstractionlevel.

1.1 Spatial coexistence

Whatever magnetic structure is devised, it must provide adequate space to accommo-date other subsystems requiring access to the sample under test (SUT).

This includes a sample holder attached to a 3-axis mechanical actuator. Particularattention is paid to the region very local to the SUT in which a liquid sample cell havingoptical quality cover glasses must be fit. The mounting of the sample cell to actuators andthe actuators themselves can occur a small distance away from the SUT where there is lessspatial congestion.

It also includes an optical tracking subsystem, the current embodiment of which usesreentrant high numerical aperture (NA) optics which require an unobstructed space com-prising two reentrant cones corresponding to the NA of the system. Therefore, under theassumption that the magnetic field geometry is to be formed by using high permeabilitymagnetic cores which are optically opaque, it is desirable that the number of field produc-ing poles be small, and the angular separation between the poles be large. Ostensibly, theminimum number of poles needed to provide forces in three dimensions is four.

1.2 Ideal magnetic circuit

The conceptual design starts with idealized assumptions: a linear, low hysteresis mag-netic core material of very high permeability. In this idealization, a magnetic structure canbe envisioned with poles converging from a magnetically interconnecting shell to sharp-ened tips near the SUT, each pole being magnetically driven by a current carrying coil.This situation is reasonably well modeled by a monopole at the location of each tip withstrength proportional to the flux induced in its pole by the various coils in the system.The sum of the aggregate monopole strengths in this model must be zero because the coilscan only generate dipole magnetization.

1.3 The force equation

The force on a permeable soft magnetic bead is caused by the interaction between anincident magnetic field B and the magnetic dipole moment m induced in the bead by B(see Appendix A). Subject to saturation properties of the bead material,

m =πd3

2µ0

(µr − 1µr + 2

)B, [SI units]



where µ0 is the permeability of free space, µr is the relative permeability of the bead, and dis the diameter of the bead. This agrees with the approximate result m = (4πa3/3µ0)χBpublished by [Amblard96] in the limit of small χ = µr − 1, where a is the radius of thebead. The force exerted on m by B is,

F =πd3

2µ0

(µr − 1µr + 2

)∇B2.

The magnitude B of the field generated by a magnetic monopole is of the form Bp/r2

where Bp is the pole strength and r is the distance from the monopole. The correspondinggradient ∇B of the field is 2Bp/r3, directed towards the monopole. Thus the force on abead is towards the monopole, varying as B2

p/r5. Clearly, the distance of the monopolesfrom the bead are of primary concern in the optimizing the magnitude of the force.

1.4 A tetrahedral geometry

The conceptual design, shown withoutthe outer magnetic return path shell

A physical approximation of the monopolemodel uses tapered, high permeability pole cores,radially disposed about the bead location, drivenby current carrying coils, with their outer endsconnected by a high permeability shell to providea magnetic flux return path for each core throughthe other cores. Ideally then, the ith of n physicalpoles approximates n monopoles, the ith havingstrength Bi and the others having strengths Bj

such that∑n

j =i Bj = −Bi.Since the cores are optically opaque and oc-

cupy space, they compete with the system opticsfor solid angle and with the SUT mechanicals forvolume. It is therefore desirable to minimize thenumber of poles used. Since a monopole forceis central, i.e., directed toward the monopole, ittakes at least four monopoles to create forces in three dimensions. A symmetric designas shown here comprises four poles converging from the vertices of a virtual equilateraltetrahedron (ET) towards its center. This geometry is fortuitous in that there are threeorthogonal lines passing through the center, each having the maximum possible angularseparation from the closest poles. This conveniently provides an optical axis normal to aplane for the slide holding the SUT.

Parametric studies showed this geometry to be close to optimal for given pole strengthB0, and separation r0. Consider k poles of strength B0/k equally spaced around a circleof radius a, coaxial with r0 at location rp. The tetrahedron is represented by n = 3,a = 0.94r0, rp = −0.33r0. The force was found to be independent of k for k > 1, andwithin 11% of the maximum, which occurs at rp = −0.6 (see Appendix B).



2 Physical implementation

The conceptual design was done at a very high level of abstraction. This luxuryis forfeited in the process of implementing a buildable design. Consequently, a numberof trade offs and compromises must be made. The primary goal was to maximize theamount of force attainable without interference to the 0.7 NA optics used by the existingexperimental setup.

2.1 Spatial considerations

NA = 0.7WD = 6.0 mm

6.0mm.

44.455

8.5mm.

12.6mm.

4.1mm.

7.8mm.

6.7mm.

15.1mm.

16.1mm.

The system lenses

It was decided not to intrude into the solid angle ofthe optical path, which comprises two reentrant cones, eachwith included angle of about 89 . It was also decided notto cut into the lens bodies to accommodate the magneticpoles. The lenses were Mitutoyo M Plan ApochromaticAPO100 with a working distance of 6 [mm]. The lens bod-ies fill an angle of 110 which is very close to the 109.5

included angle between vertices of an ET.The finite thickness of the magnet poles themselves

precludes even approximating the pole angles of the ab-stract design unless the lens body or the poles are modifiedwith relief cuts. It made more sense to modify pole anglesfrom 35.3 to 22.5 inclination from horizontal, while stillplacing the pole tips at the vertices of an ET. A pole tiptaper angle of 9.5 leaves 7.75 angular clearance from thelens body, but placement of the pole tips on an ET large enough to accommodate the SUTcell uses up nearly all of the linear pole to lens body clearance. (See Appendix C, sheet 1.)

Due to the 1/r5 force dependence, the size of the SUT cell is a very strong determiner ofthe achievable bead force. It was desired that the cells comprise readily available materials,that they provide a reasonably well sealed liquid SUT environment, and that they haveadequate optical properties. These factors led to the choice of a sandwich comprising twomicroscope cover slips separated by Scotch #136 tape (3mil transparent double-backed)with a hole punched to contain the SUT. The thickness of the cell is approximately 440[µm].

The pole tips are of course not sharp points, but may be regarded as spherical. Forvery high permeability, the virtual monopole location is approximately at the center ofthe sphere. Thus for a horizontal cell, the vertical separation between upper and lowermonopoles must be at least the sum of the sphere radii (each specified as ≤ 50 [µm]) andthe cell thickness. Allowing 160 [µm] clearance for handling and insertion of the cell, thevertical separation of each tip from the center of the cell is 300 [µm], or 350 [µm] verticallyfrom each monopole to the center. The total distance of each monopole from the cell centeris 350/ cos(109.5/2) = 606 [µm]. This is the closest we can reasonably expect to get themonopoles with this SUT cell and design approach.



2.2 Core materials

Second only to compactness, the B2 force dependence motivated us to maximize thefield strength. Even with very high permeability µr, leakage flux between poles everywhereexcept at the tips is wasted flux, and cannot be avoided. Since B is proportional to themagnetomotive force (MMF), or Ampere turns linking the magnetic path, this can becompensated at the expense of coil size and current. Of course there are thermal limitationsdue to resistive losses in the coils.

For high µr the B field is also strongly dependent on the geometry of the air gapnear the pole tips. The bigger the separation, the weaker the field. In fact, any air gapin the main flux path will strongly affect the B field because µcore

r µairr = 1. For

example, if µcorer = 1000, introducing a 100 [µm] gap in a toroidal core 3 [cm] in diameter

will approximately halve any induced B field. This has serious implications for the coredesign, where uniformity of performance of the four poles is important. It is thereforeimportant that the design avoid spurious air gaps; or if they cannot be avoided, that theybe controlled for uniformity.

While high µcorer is important, even more important is high core saturation Bcore

sat .This is because we are trying to funnel as much flux as possible through the tapered poleto exit at the tip. For a given total flux Φm, the flux density B varies inversely with thecore area. For high flux, it will exceed Bcore

sat at some place in the taper where the areagets too small. The flux density at the tip is limited by Bcore

sat . Excess flux escapes fromthe sides of the taper in the saturated parts of the tip. Increasing the MMF merely movesthe saturation point back up the taper.

The highest saturation materials available are vanadium permendur and hiperco, bothof which are not only expensive, but extremely difficult to fabricate. A good compromiseis ASTM A 848 Magnet Iron which saturates at about 1.6 [T].

Complicating things even further, these desirable core materials are electrically con-ductive metals which means, according to Faraday’s law ∇× E + ∂B/∂t = 0, changes inB induce voltage gradients and consequently cause eddy currents in the core. The morerapid the change, the greater the current. This limits the bandwidth over which the coreis operational. For the design in question, the bandwidth is in the low tens of Hertz, es-sentially DC. Accordingly, and to forestall false expectations, this design is called, a “DCPrototype.”

Conventional methods of reducing eddy currents are by laminating thin sheets of thematerial to make up the core, or to mix a powder of the material with a non-conductivebinder and cast the core. Lamination offers possibilities which can be explored, but powdersrarely approach either the permeability or saturation properties of the base material.

Another possibility is a class of materials called “Metglas.” These materials are metalsformed as an amorphous rather than a crystalline solid by a process of hyperfast chillingof the metal from the molten state. Magnetic alloys such as mumetal are commerciallyproduced as metglas with very good properties. Whether or not high saturation metglasmaterials can be obtained I do not know.

While not properly an issue for the DC prototype, this problem will have to be ad-dressed if this design is to be developed for higher bandwidths.



2.3 Coil considerations

Looking at the concept picture on page 3, it is evident that the coils are awkward.Not only must they be tapered in the front, but how they will fit within the magneticshell (which is conveniently not shown) is problematical. Add to this the need for lots ofampere turns in a limited conductor cross section, and the fact that winding coils withsteeply conical end profiles is exceedingly difficult, it becomes apparent that this geometryleaves a lot to be desired.

Conceptual design

Shell

Bead

As built design

Bead

This problem was addressed by moving the coils elsewhere.Considering a magnetic circuit model of the magnetic paths,each pole can be modeled as a MMF (depicted as overlappingcircles in the figure) induced by the current in its coil, in serieswith a reluctance (depicted by the resistor symbol, or zigzagline) partially due to the pole core itself, but mostly incurredat the air gap between the pole tip and the location of thebead. The topology of the conceptual design consists of twonodes (depicted as s) representing the magnetic shell and thebead respectively, connected by four arcs representing the fourpoles.

This topology can be extended by replacing the shell nodeby four back end nodes, each representing the back end of apole, and by moving the MMFs from the pole arcs to the arcsconnecting the back end nodes. In this topology, each pole isdriven by two MMFs in parallel. The reluctances shown inseries with each MMF those of the cores connecting the back end nodes and are smallrelative to the pole reluctances. Thus to a first approximation the effective MMF drivinga pole is the average of the MMFs connected to its back end node. To the extent that theMMFs differ, they cause flux to circulate in the ring connecting the back end nodes.

This topology allows considerable flexibility in choice of the geometry used to imple-ment it. As shown in Sheet 1 of the drawings in Appendix C, the coils were chosen tobe easily wound on cylindrical bobbins with copious cross sectional area to allow for largeAmpere turns.

2.4 A potential but probably not serious degeneracy

So called parasitic imperfections incurred by using real components which are only im-perfectly represented by simple circuit models are often the cause of engineering headaches.They rarely work to one’s advantage. However in this case, they probably do. In particular,they probably remove a mathematical degeneracy.

That is, we chose four poles as the minimum number to provide forces in full threedimensions. But the idea that the pole strengths sum to zero is a constraint that nullifiesone degree of freedom. You can appreciate this if you try to find a set of drive currentsthat will pull the bead in a direction exactly half way between two poles, or to a directionopposite one of the poles.

The circuit models of the previous section enforce the concept of zero net flux from thefour pole tips; or in other words, the sum of the strengths of the approximated monopoles



is zero. In fact, there are significant parasitic reluctances not shown due to leakage fluxbetween various parts of the cores connecting the back end nodes and parts of the polecores themselves. These parasitics mitigate the effects of the bothersome constraint. Itremains to be seen how effective this reprieve will be.

References

[Amblard96] Francois Amblard, B.Y. Pargellis, A. Pargellis, S. Leibler, “A magnetic ma-nipulator for studying local rheology and micromechanical properties of bi-ological systems,” Review of Scientific Instruments, v.67 no.3, March 1996,pp818-827.

[Bausch98] Andreas R. Bausch, F. Ziemann, A. A. Boulbitch, K. Jacobson, E. Sackmann,“Local Measurements of Viscoelastic Parameters of Adherent Cell Surfacesby Magnetic Bead Rheometry,” Biophysical Journal, v.75, October 1998,pp2038-2049.

[Bausch99] Andreas R. Bausch, W. Moller, E. Sackmann, “Measurement of Local Vis-coelasticity and Forces in Living Cells by Magnetic Tweezers,” BiophysicalJournal, v.76, January 1999, pp573-579.

[Haber00] Charbel Haber, D. Wirtz, “Magnetic Tweezers for DNA micromanipulation,”Review of Scientific Instruments, v.71 no.12, December 2000, pp4561-4570.

[Jackson62] J. D. Jackson, “Classical Electrodynamics,” John Wiley & Sons, New York,1962.



Appendix A: Force on a soft magnetic bead in a magnetic field

NOTE: the original derivation was erroneous and is here corrected

According to [Jackson62], the magnetization induced in a permeable sphere by anapplied external field B is

M =34π

(µ − 1µ + 2

)B, (J :5.115)†

in Gaussian units. From Jackson’s Appendix on Units and Dimensions, we convert to SIunits according to M → M

√µ0/4π, B → B

√4π/µ0, and µ → µ/µ0, obtaining

M =3µ0

(µr − 1µr + 2

)B, (A.1)

where µr = µ/µ0 is the relative permeability inside the sphere.To obtain the magnetic dipole moment m of the sphere, we integrate M over its

volume. Since the magnetization M inside the sphere is uniform, the integral is simplythe volume of the sphere times M, or

m =πd3

2µ0

(µr − 1µr + 2

)B. (A.2)

Again from Jackson, the force on a magnetic moment m in a magnetic field B is,

F = ∇× (B × m) = (m · ∇)B = ∇(m · B) (J :5.69)

Substituting eq(A.2) into eq(J: 5.69):

F =πd3

2µ0

(µr − 1µr + 2

)∇(B2). (A.3)

†Equation numbers prefixed by “J:” are from [Jackson62].



Appendix B: Parametric simulations of monopole configurations

r

z

xy

Q

-Q/5

z0

zc

bead

-Q/5

-Q/5

-Q/5-Q/5

Example geometry, n=5

A parametric study of the monopole model was conductedwith Matlab code. The model consists of a magnetic bead lo-cated at the origin, a “driven” monopole of strength Q on thez-axis at z = z0, and n “return” monopoles of strength −Q/narranged equally spaced around a circle of radius r coaxial withz and located at z = zc. For n = 3, r = 0.9428, zc = −z0/3,this model represents an equilateral tetrahedral pole geometry.

Using the function Fcoax(), it was first determined thatfor 2 ≤ n ≤ 20, the force was independent of n, demonstratingno advantage in force from a larger number of poles.

−1 −0.5 0 0.5 1 1.5 2 2.5 30.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

zc normalized to z0

For

ce n

orm

aliz

ed to

Fm

ax

Equilateral case

z0

The function parametric() was thenconstructed to investigate the forcebehavior of non equilateral tetrahe-dra of the kind modeled. A plotof normalized force as a function ofposition zc shows that the equilat-eral tetrahedron produces 89.8% ofthe maximum force, which occursfor a slightly elongated tetrahedronfrom equilateral.

Matlab codes are included next.Fcoax() is the function that calcu-lates a single instance of the beadforce. Parametric() makes a plot ofbead force while varying zc.

function F = Fcoax(Q, n, z0, r, zc, chi, a)% Fcoax(Q, n, z0, r, zc, chi, a) -- Calculate the force on a bead of% radius a and susceptibility chi at the origin exerted by n poles% positioned coaxially about the z axis at z = zc, each with strength% -Q/n, and one pole on the z axis at z = z0 with strength Q.

R = coax(z0, r, zc, n);for i = 1:n

q(i) = -Q/n;endq(n+1) = Q;F = Fbead(q, R, chi, a);



function parametric(n)% parametric(n) -- Calculate the force at the origin as zc is varied.% Let the dominant pole be located at z0 = 1, and zc be the location% of the center of a circle coaxial with z. Report the position zm% of the maximum force Fm, and the percentage force 100*Ft/Fm at% zt = -1/3 which represents an equilateral tetrahedron (circle radius% of 0.9428). Generates a normalized plot of F(z) where "x" marks% position of the main pole, and "o" marks the tetrahedral case.

n = 2*fix(n/2)+1; % ensure n is odds = 1;D = 2;z = linspace(s-D,s+D,n);for i = 1:n

F(i,:) = Fcoax(1, 3, s, 0.942809041582, z(i),1000,1.0e-7);if abs(z(i)-s) < D/(n-1)

zs = i;endif abs(z(i)+s/3) < D/(n-1)

zc = i;endif i == 1

Fmax = F(i,1);else

if F(i,1) > FmaxFmax = F(i,1);imax = i;

endend

endplot(z, F(:,1)/Fmax, ’k’,...

z(zc), F(zc,1)/Fmax, ’ko’,...z(zs), F(zs,1)/Fmax, ’kx’);

xlabel(’zc normalized to z0’);ylabel(’Force normalized to Fmax’);text(z(zc)+0.1, F(zc,1)/Fmax, ’Equilateral case’);text(z(zs)+0.1, F(zs,1)/Fmax, ’z0’);zmax = z(imax)percent = F(zc,1)/Fmax



function p = coax(z0, r, zc, n)% coax(z0, r, zc, n) -- generate n points on a circle of radius r coaxial% with z, located z = zc from the origin, and one point at [z0,0,0].

dphi = 2*pi/n;for i = 1:n

phi = i*dphi;p(i,:) = [zc, r*sin(phi), r*cos(phi)];

endp(n+1,:) = [z0, 0, 0];function F = Fbead(q, R, chi, a)% Fbead(q, R, chi, a) -- Force on a spherical bead of susceptibility chi% and radius a, located at the origin, exerted by magnetic poles of% strengths q located at locations R.

B = sum(Bfield(q, R),1);dB = sum(GradB(q, R),1);F = (4*pi*a3/3)*chi*dot(B, dB)*B/norm(B);

function B = Bfield(q, R)% Bfield(q, R) -- N magnetic induction vectors B at the origin induced% by N magnetic poles of strength q at locations R. [SI units]% q is a 1:N list of pole strengths, R is an N:3 matrix of N vectors R.

if length(q) = length(R(:,1))error(’Number of poles q inconsistent with number of locations R.’);

endfor i = 1:length(R(:,1))

B(i,:) = q(i)*R(i,:)/(4*pi*norm(R(i,:))3);end



function Gb = Gradb(q, R)% gradB(q, R) -- Gradient of scalar B-field strength b at the origin,% contributed by a pole of scalar strength q at vector location R.% [SI units]

% Notation:% Let Du v be the total derivative of u wrt v, and du v be the partial% derivative. Let w represent a scalar, W represent a vector, and W^% represent a unit vector.%% The scalar Db r is the magnitude of the gradient vector DB r which% points along the unit vector R. Thus the directional derivatives% of b along the coordinate axes can be written,% x*db x = x*Db r*dr x, and similarly for y, and z.% Thus, grad*b = Db r*grad*r = Db r*R/r.% q is a 1:N list of pole strengths, R is an N:3 matrix of N vectors R.

if length(q) = length(R(:,1))error(’Number of poles q inconsistent with number of locations R.’);

endfor i = 1:length(q)

r = norm(R(i,:));gradr = -R(i,:)/r; % Negative because direction is towards the origin.dbdr = -q(i)/(2*pi*r3);Gb(i,:) = dbdr*gradr;

end



Appendix C: Specification of the Magnets

This appendix contains the shop drawings specifying the materials and constructionof the DC prototype magnet assembly.

To the best of my knowledge, the included drawing revisions are the current as-builtprototype configuration. Please note the drawings are in units of [cm] – the choice seemedwell motivated at the time, but after working with the instrument makers in the PhysicsMachine Shop, I think I’d do it in inches next time.


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icci

DA

TE

16 M

arch

200

1

MS

LS

HE

ET

4 O

F 8

SC

ALE

2: 1

DW

G N

OM

agne

t 1.2

.1

RE

V1.

2

SIZ

E A

Mag

neti

c cr

oss

piec

es -

- 4

ea.

Mat

eria

l is

AST

M A

848

Typ

e 1

Low

Car

bon

Mag

netic

Iro

nD

imen

sion

s in

cm

.T

oler

ance

s, e

xcep

t whe

re n

oted

oth

erw

ise

-- f

or d

imen

sion

s sh

own

to 2

pla

ces:

+/-

0.0

1cm

, f

or d

imen

sion

s sh

own

to 3

pla

ces:

+/-

0.0

04cm

. a

ngul

ar: +

/- 0

.1 d

egre

es, b

ut

vari

atio

n be

twee

n pi

eces

to b

e le

ss th

an 0

.01

degr

ees

.

Prot

ect f

rom

oxi

datio

n du

ring

fab

rica

tion,

fin

ish

with

blu

eing

pro

cess

(fe

rrou

s ox

ide)

unt

il vi

sibl

y bl

ack,

then

ligh

tly o

il.

Not

e 1:

Hol

e dr

illin

g an

d th

read

ing

oper

atio

ns to

be

prec

isel

y al

igne

d.

3.75

1.50

Ø 1

.5 +

/-0.

1

0.50

1.00

1.50

Ø #

3 dr

ill h

ole

tapp

ed to

1/4

-28

for

full

leng

th (

see

Not

e 1)

#26

drill

hol

e

0.75

0

3.00

03.

000

3.75

Ref

eren

ce s

urfa

ce,

fine

mac

hine

d te

xtur

e

Ref

eren

surf

ac

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe M

agne

tic P

oles

and

Jam

nut

s

DR

AW

N B

YLe

andr

a V

icci

DA

TE

20 F

ebru

ary

2001

MS

LS

HE

ET

5 O

F 8

SC

ALE

2: 1

DW

G N

OM

agne

t 1.2

.2

RE

V1

SIZ

E A

0.25

0in.

5.00

0

1.50

03.

000

Pol

es -

- 4

ea.

Jam

nut

s --

12e

a

Dim

ensi

ons

in c

m.

Tol

eran

ces:

+/-

0.0

04cm

.

Pole

mat

eria

l is

AST

M A

848

Typ

e 1

Low

Car

bon

Mag

netic

Iro

n,Po

le th

read

ed 1

/4-2

8 N

F fo

r 3c

m.

Pole

uni

form

ly ta

pere

d fo

r 1.

5cm

to a

poi

nt n

ot e

xcee

ding

0.0

05cm

dia

met

er.

Prot

ect p

ole

from

oxi

datio

n du

ring

fab

rica

tion,

fin

ish

with

blu

eing

pro

cess

(fe

rrou

s ox

ide)

unt

il vi

sibl

y bl

ack,

then

ligh

tly o

il.

Jam

nut

is 1

/4-2

8 N

F.M

ater

ial i

s br

ass

or n

on-m

agne

tic s

tain

less

ste

el.

Ø 3

.50

Ø#3

6 dr

ill h

ole

tapp

ed 6

-32

NC

3.00

0

3.00

0

7.50

7.50

3.00

0

3.00

0

3.75

3.75

0.64

0.64

0.50

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe M

ount

ing

plat

es

DR

AW

N B

YLe

andr

a V

icci

DA

TE

16 M

arch

200

1

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LS

HE

ET

6 O

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SC

ALE

1: 1

DW

G N

OM

agne

t 1.3

RE

V1.

2

SIZ

E A

Ø 3

.50

Ø#2

7 dr

ill h

ole

3.00

0

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7.50

3.00

0

3.75

3.00

03.

000

3.75

0.64

0.64

0.50

0.79

0.79

0.79

#50

drill

,ta

p 2-

56

Top

Pla

te -

- 1e

a

Dim

ensi

ons

in c

m.

Tol

eran

ces,

for

dim

ensi

ons

show

n to

2 p

lace

s: +

/- 0

.01c

m,

for

dim

ensi

ons

show

n to

3 p

lace

s: +

/- 0

.004

cm.

Mat

eria

l: 1/

8 in

ch 2

024

Alu

min

um o

r eq

uiva

lent

Ter

min

al b

lock

s (n

ot s

how

n):

Bea

u In

terc

onne

ct, 4

pol

e,ty

pe C

1504

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, sto

ck n

o. 8

9F59

90; 2

ea.

Bot

tom

Pla

te -

- 1e

a

Dim

ensi

ons

in c

m.

Tol

eran

ces,

for

dim

ensi

ons

show

n to

2 p

lace

s: +

/- 0

.01c

m,

for

dim

ensi

ons

show

n to

3 p

lace

s: +

/- 0

.004

cm.

Mat

eria

l: 1/

8 in

ch 2

024

Alu

min

um o

r eq

uiva

lent

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe Z

Alig

nmen

t Jig

DR

AW

N B

YLe

andr

a V

icci

DA

TE

7 M

arch

200

1

MS

LS

HE

ET

7 O

F 8

SC

ALE

2: 1

DW

G N

OM

agne

t 1.4

RE

V1.

2

SIZ

E A

0.75

1.00

00

6.00

3.70

2.95

Ø#3

6 dr

ill h

ole

tapp

ed 6

-32

NC

to 1

cm

dep

th

Z A

lignm

ent

Jig

--

1ea

Dim

ensi

ons

in c

m.

Tol

eran

ces,

for

dim

ensi

ons

show

n to

1 p

lace

: nom

inal

for

dim

ensi

ons

show

n to

2 p

lace

s: +

/- 0

.01c

m,

for

dim

ensi

ons

show

n to

4 p

lace

s: a

s ac

cura

te a

s yo

u ca

n m

ake

it.

Mat

eria

l: 3/

4 in

ch 2

024

Alu

min

um o

r eq

uiva

lent

0.75

7.5

1.9

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe Z

Alig

nmen

t Jig

usa

ge d

etai

l

DR

AW

N B

YLe

andr

a V

icci

DA

TE

7 M

arch

200

1

MS

LS

HE

ET

8 O

F 8

SC

ALE

2: 1

DW

G N

OM

agne

t 1.4

.1

RE

V1.

1

SIZ

E A

Z A

lignm

ent

Jig

usag

e

Mou

nt m

agne

tic c

ross

pie

ce a

nd c

ore

asse

mbl

y w

ith ja

m n

uts,

torq

ue m

ount

ing

scre

ws

to s

pec,

adju

st c

ore

for

Z ti

p cl

eara

nce

clea

ranc

esh

own,

usi

ng m

icro

scop

e an

d re

ticle

,lo

ck c

ore

adju

stm

ent w

ith ja

m n

ut.

0.75

1.00

00

6.00

3.70

2.95

Ø#3

6 dr

ill h

ole

tapp

ed 6

-32

NC

to 1

cm

dep

th

0.75

7.5


Appendix D: Specification of the Drive Electronics

This appendix contains the shop drawings specifying the parts and construction of theDC prototype magnet drive electronics. The drawings do not show the as-built ventilationholes in the top and bottom of the enclosure and rubber feet to provide bottom clearance.These were added to provide better cooling for the power supplies contained in the box.

If I were to design this again, I would forego the grounded-load circuit topology of thetransconductance amplifiers. As built, even with significant debug effort, small oscillationsin the MHz range still occur under certain operating conditions. While these do notapparently cause distortion of the transconductance gain at low frequencies, it is still nota desirable situation. My best guess is that floating the load (coil) and grounding thecurrent sense resistor would provide a topology free of this problem. The cabling to thecoils would support this topology without modification.


TIT

LE

3DF

MD

ES

CR

IPT

ION D

C p

roto

type

coi

l driv

er e

lect

roni

cs

DR

AW

N B

YLe

andr

a V

icci

DA

TE

9 M

ay 2

001

MS

LS

HE

ET

1 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.0

RE

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E A

Tra

nsco

nduc

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ifie

r

Tra

nsco

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ifie

r

Tra

nsco

nduc

tanc

eA

mpl

ifie

r

Tra

nsco

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tanc

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mpl

ifie

r

out

com

in-

in+

out

com

in-

in+

out

com

in-

in+

out

com

in-

in+

Pow

erSu

pply

+15

+15

+15

+15 -15

-15

-15

-15

+15

-15

com

shie

lded

cabl

e

9 co

nduc

tor

#22

AW

Gca

ble

mag

net

asse

mbl

y

coil

1

coil

2

coil

3

coil

4 fram

e

gnd

neut

line

pow

er s

witc

h

120

VA

Cpo

wer

DB

-9co

nnec

tors

2 6 3 7 4 8 5 9 1

DB

-15

conn

ecto

rs

2 9 4 11 6 13 8 15 13 75

sign

al c

om

sign

al 1

sign

al 2

sign

al 3

sign

al 4

+15

V p

wr

-15V

pw

r

pwr

com

WH

BN

WH

RD

WH

OR

WH

YL

WH

WH

GN

BK

RD

BU OR

VL

YL

BK

GN

WH

BN

BK

/WH

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe tr

ansc

ondu

ctan

ce a

mpl

ifier

DR

AW

N B

YLe

andr

a V

icci

DA

TE

13 J

une

2001

MS

LS

HE

ET

2 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.1

.0

RE

V1

SIZ

E A

LM

675T

20K

10K

20K

10K

1[Ω

] 10

[W]

3900.1

µF

0.1

mF

0.1

µF

+15

-15

Mag

net

Coi

l

1

5

4

3

2

Coi

l dri

ver

tran

scon

duct

ance

am

plif

ier,

gai

n =

0.5

[A/V

].

(

4ea)

Slew

rat

e lim

it ap

prox

120

0 [A

/s]

for

a 10

[m

H]

coil.

All

resi

stor

s 1%

, met

al f

ilm; e

xcep

t for

a 1

[Ω

] 1

0 [W

] w

ire

wou

nd,

Dal

e R

H-1

0 1[

Ω]

1%, N

ewar

k P/

N 0

1F95

97.

All

capa

cito

rs a

re X

7R c

eram

ic, 5

0 [V

] or

equ

ival

ent.

All

"gro

und"

con

nect

ions

are

to a

com

mon

poi

nt c

lose

to th

e op

am

ppa

ckag

e, a

nd c

onne

cted

clo

sely

to th

e he

at s

ink.

Nat

iona

l Sem

icon

duct

or L

M67

5T p

ower

op

amp

(TO

-220

cas

e) to

be

insu

late

d fr

om h

eat s

ink

by a

ppro

pria

te in

sula

ting

was

her

and

fast

ener

.

in-

in+

out

com

(Hea

t Sin

k)

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe c

oil d

river

ele

ctro

nics

pow

er h

arne

ss

DR

AW

N B

YLe

andr

a V

icci

DA

TE

13 J

une

2001

MS

LS

HE

ET

3 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.1

.1

RE

V1

SIZ

E A

Pow

erSw

itch

GN

YL

BN

BN

YL

BN

GN

GN

AC

filte

ran

dco

nnec

tor

GN

D

NE

UT

LIN

E

MA

P110

-101

2Po

wer

Sup

plyJ1 J2

51 3 4 71 3

MA

P110

-101

2Po

wer

Sup

plyJ1 J2

51 3 4 71 3

WH

BK

WH

BU

WH

WH

RD

BK

Dri

ve c

ircu

its

-15V

+15

V

CO

M

Pow

er s

uppl

ies:

Pow

er O

ne M

AP

110-

1012

.

(2e

a)A

djus

t V1

to 1

5 [V

]. E

ach

supp

ly r

ated

at 1

5[V

]/8[

A].

AC

pow

er h

arne

ss m

atin

g w

ith J

1 us

es M

olex

09-

50-3

051-

P sh

ell

(New

ark

#44F

4483

) w

ith M

olex

08-

52-0

072-

C p

ins

(New

ark

#93F

9690

)

DC

pow

er h

arne

ss m

atin

g w

ith J

2 us

es M

olex

09-

50-3

131-

P sh

ell

(New

ark

#94F

9664

) w

ith M

olex

08-

52-0

072-

C p

ins

(New

ark

#93F

9690

)

TIT

LE

3DF

MD

ES

CR

IPT

ION D

C p

roto

type

driv

e el

ectr

onic

s bo

x

DR

AW

N B

YLe

andr

a V

icci

DA

TE

30 M

arch

200

1

MS

LS

HE

ET

4 O

F 1

3S

CA

LE1:

2

DW

G N

OD

river

1.2

RE

V0

SIZ

E A

7.00

4.00

5.00

8.00

6.00

Dri

ve e

lect

roni

cs b

ox.

(1

ea)

Tw

o pi

eces

to b

e fo

lded

and

TIG

wel

ded

to m

ake

up th

e bo

x.

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

box

piec

e pa

ttern

DR

AW

N B

YLe

andr

a V

icci

DA

TE

30 M

arch

200

1

MS

LS

HE

ET

5 O

F 1

3S

CA

LE1:

2

DW

G N

OD

river

1.2

.1

RE

V0

SIZ

E A

4.93

87.

938

5.87

6

0.75

03.

500

2.00

04.

000

0.68

81.

938

0.43

8

Pat

tern

for

dri

ve e

lect

roni

cs b

ox.

(2e

a).

Mat

eria

l: 0.

064"

606

1-0

Alu

min

um s

heet

.

Patte

rn is

siz

ed f

or f

abri

catio

n w

ith a

ben

d ra

dius

of

1.5

x m

ater

ial t

hick

ness

= 0

.096

".T

he c

alcu

late

d be

nd a

llow

ance

BA

= 0

.196

" an

d th

e ca

lcul

ated

set

back

SB

= 0

.160

".(E

ach

leg

is s

hort

ened

by

(SB

- B

A/2

) =

0.0

62"

for

each

fol

d to

whi

ch it

is a

djac

ent)

0.25

0

12.8

76

Ø 0

.187

5

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

fron

t pan

el a

ssem

bly

DR

AW

N B

YLe

andr

a V

icci

DA

TE

3 A

pril

2001

MS

LS

HE

ET

6 O

F 1

3S

CA

LE1:

2

DW

G N

OD

river

1.3

RE

V0

SIZ

E A

Pow

erS

witc

h

DB-15

DB-9

Pow

erC

onne

ctor

Hea

t sin

k

Fro

nt p

anel

5.0

8.0

4.0

5.0

0.12

51.

2

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics,

rear

vie

w o

f fro

nt p

anel

ass

embl

yD

RA

WN

BY

Lean

dra

Vic

ci

DA

TE

4 A

pril

2001

MS

LS

HE

ET

7 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.3

.0

RE

V0

SIZ

E A

Rea

r vi

ew o

f fro

nt p

anel

ass

embl

y w

ith h

eat s

ink

outli

nesh

own

as a

hid

den

line.

The

circ

uit b

oard

with

its

mou

ntin

g br

acke

ts is

sho

wn

alon

g w

ith th

e cu

rren

t sen

sere

sist

ors

and

pow

er O

p A

mps

.

LM 6

75T

LM 6

75T

LM 6

75T

LM 6

75T

RH

-10

RH

-10

RH

-10

RH

-10

PowerConnector

PowerSwitch

DB15

DB-9

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

heat

sin

k, r

ear

view

DR

AW

N B

YLe

andr

a V

icci

DA

TE

5 A

pril

2001

MS

LS

HE

ET

8 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.3

.1

RE

V0

SIZ

E A

Hea

t si

nk

(1

ea)

cut f

rom

Wak

efie

ld #

4678

alu

min

umex

trus

ion

with

Fsa

= 2

.3 [

o C/W

/3in

]. C

ut e

nds

to b

e m

illfin

ishe

d to

sm

ooth

, per

pend

icul

ar s

urfa

ces.

8 ho

les

drill

ed a

ndta

pped

for

2-56

NC

3 ho

les

drill

ed a

ndta

pped

for

6-32

NC

2 ho

les

drill

ed a

ndta

pped

for

4-40

NC

4 ho

les

drill

ed a

ndta

pped

for

4-40

NC

2.00

03.

750

0.25

0

1.50

0

2.50

0

3.50

0

0.50

0 1.00

0

3.00

0

2.18

53.

185

1.18

50.

185

1.81

02.

810

3.81

0

0.81

0

4.00

0

1.20

0

0.20

0

5.00

0

2.10

3

2.49

4

3.65

1

0.49

7

4.87

54.21

6

3 ho

les

drill

ed a

ndta

pped

for

6-32

NC

2.00

0

3.75

0

0.25

0

2.52

9

2.91

4

3.72

4

4.10

9

0.78

10.

931

1.08

1

1.55

6

1.70

6

1.85

6

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

fron

t pan

el (

rear

vie

w)

DR

AW

N B

YLe

andr

a V

icci

DA

TE

18 A

pril

2001

MS

LS

HE

ET

9 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.3

.2

RE

V1

SIZ

E A

8 ho

les

arou

ndpe

riphe

ry, #

27 d

rill

0.75

0

2.50

0

2.00

02.

6253.

000

5.50

06.00

07.

000

7.75

08.

000

4.25

0

5.0

Cut

hol

e w

ith1/

2" e

nd m

ill

0.85

0

0.25

0

4.75

0

4.15

0

Cut

hol

e w

ith1/

4" e

nd m

ill

Cut

hol

e w

ith3/

8" e

nd m

ill

1.08

31.

718

0.90

5

1.89

50.

745

0.91

81.

883

2.05

5

1.02

3

2.88

6 3.75

1

1.78

8

2.07

8

1.27

00.

775

Fro

nt

Pan

el: (

1 ea

) M

ater

ial:

1/8"

202

4 A

lum

inum

she

et.

Cut

hol

e w

ith1/

8" e

nd m

ill

Cut

hol

e w

ith1/

8" e

nd m

ill

6 ho

les

#27

dril

l

2 ho

les

#27

drill

4 ho

les

tapp

edfo

r 4-

40 N

C

0.25

0

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

circ

uit b

oard

ass

embl

y

DR

AW

N B

YLe

andr

a V

icci

DA

TE

4 A

pril

2001

MS

LS

HE

ET

10 O

F 1

3S

CA

LE2:

1

DW

G N

OD

river

1.3

.3

RE

V0

SIZ

E A

LM 6

75T

LM 6

75T

LM 6

75T

LM 6

75T

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

circ

uit b

oard

and

mou

ntin

g br

acke

t det

ails

DR

AW

N B

YLe

andr

a V

icci

DA

TE

5 A

pril

2001

MS

LS

HE

ET

11 O

F 1

3S

CA

LE2:

1

DW

G N

OD

river

1.3

.4

RE

V0

SIZ

E A

0.12

5

0.12

5

0.25

00.65

00.

750

0.31

3

0.50

0

0.25

0

0.12

5

0.12

5

Bra

cket

s (2

ea)

cut f

rom

1/2

x 3

/4 x

1/8

alum

inum

ang

le.

Cir

cuit

bo

ard

(1e

a) c

ut fr

om v

ecto

rboa

rd s

tock

0.0

60"

glas

s ep

oxy.

4 ho

les

drill

ed 0

.116

" (#

32 d

rill)

cent

ered

on

exis

ting

boar

d ho

les.

All

boar

d di

men

sion

s to

be

refe

renc

ed to

the

hole

sho

wn

in b

lack

.

Ø 0

.116

2 ho

les

tapp

ed 4

-40

NC

1.25

0

0.40

0

0.25

0

2.85

02.00

0

0.85

0

MAP110-1012 Power Supply

MAP110-1012 Power Supply

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

back

pan

el a

ssem

bly

DR

AW

N B

YLe

andr

a V

icci

DA

TE

30 M

arch

200

1

MS

LS

HE

ET

12 O

F 1

3S

CA

LE1:

2

DW

G N

OD

river

1.4

RE

V0

SIZ

E A

5.00

8.00

Map

110-

1012

Pow

er S

uppl

y

0.12

5

TIT

LE

3DF

MD

ES

CR

IPT

ION

DC

pro

toty

pe d

rive

elec

tron

ics

back

pan

el

DR

AW

N B

YLe

andr

a V

icci

DA

TE

18 A

pril

2001

MS

LS

HE

ET

13 O

F 1

3S

CA

LE1:

1

DW

G N

OD

river

1.4

.1

RE

V1

SIZ

E A

0.75

1.18

1.47

0.25

2.82

3.53

3.82

2.18

2.00

2.05

2.35

0.25

4.10

5.65

5.95

3.90

7.75

6.00

8.00

5.0

Bac

k P

anel

: (1

ea)

Mat

eria

l: 1/

8" 2

024

Alu

min

um s

heet

.A

ll ho

les

0.14

95",

#25

dril

l.

4.75

4.25

A3DMagneticForce Manipulator DC Prototype

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Transcript of A3DMagneticForce Manipulator DC Prototype