Design of a
Moving-Coil Driver
Year 2
Electrical design project module
©2004 J D Edwards
DESIGN OF A MOVING-COIL DRIVER
This document is based on a guide prepared for a Year 2 electrical design project module in the
Department of Engineering and Design at the University of Sussex. The module runs for ten weeks,
and absorbs 25% of student time.
The aim of the project is to compare several different designs for a moving-coil driver of the kind used
in loudspeakers and vibration generators. A simplified design theory has been developed for the
project, based on a simple model for heat transfer from the moving coil. Three different kinds of
magnet structure are considered:
• Ceramic ferrite ring magnet: a low-cost option, with the disadvantage of a high external
magnetic field
• Neodymium iron boron centre-pole magnet: a high performance option, with a low external
magnetic field
• Shielded ceramic: a modification of the simple low-cost design, with the addition of shield
components to reduce the external magnetic field
In each case, two different kinds of design are to be considered: high performance and low cost. The
high-performance design aims to make the device non-linearity as small as possible, subject to a cost
constraint. The low-cost design aims to minimise the cost, regardless of the penalty in non-linearity.
Initial designs can be produced quite easily from a table of pre-defined magnets. These serve as the
starting points for a design study that uses MagNet linked to an Excel spreadsheet. This combination
forms a most effective design tool for systematically exploring design changes.
For the project, students were given individual device specifications that had been pre-tested to ensure
they would result in sensible designs. It is an effective way of eliminating plagiarism and collusion in
work of this kind.
The outline spreadsheet described in the document is available from Infolytica Corporation.
Design of a Moving-Coil Driver Copyright © 2004 J D Edwards
CONTENTS
1
1.1
2
INTRODUCTION .................................... 1
The design topic ...............................................1
DESIGN CONCEPTS .............................. 2
2.1
Driver properties .............................................2
2.2
Coil properties .................................................2
3
INITIAL DESIGN PROCEDURE ................. 4
3.1
Introduction .....................................................4
3.2
Design with a spreadsheet ...............................4
3.3
NdFeB magnet design......................................9
3.4
Material quantities and costs..........................9
4
ANALYSIS WITH MAGNET.................... 13
6.1
Introduction ................................................... 13
6.2
Using MagNet ................................................ 13
6.3
Using the spreadsheet.................................... 13
7
MODIFYING THE DESIGNS ................... 16
7.1
Introduction ................................................... 16
7.2
Current non-linearity.................................... 16
7.3
Position non-linearity.................................... 16
7.4
Saturation ...................................................... 17
7.5
Ceramic magnet............................................. 17
7.6
NdFeB magnet ............................................... 18
INITIAL DESIGNS ................................ 10
4.1
Design specification ....................................... 10
4.2
Design procedure ........................................... 10
5
6
FINAL DESIGNS.................................. 11
5.1
Introduction ................................................... 11
5.2
Non-linearity .................................................. 11
5.3
External magnetic field ................................. 12
8
MAGNETIC SHIELDING ........................ 19
8.1
Introduction ................................................... 19
8.2
Modifying the workbook .............................. 19
8.3
Designing the shielded magnet ..................... 22
8.4
Design refinement.......................................... 22
9
MAGNET DATA................................... 23
9.1
Ceramic magnet data .................................... 23
9.2
NdFeB magnet data....................................... 24
List of Symbols
Ac cross-sectional area of wire in the coil
Ag cross-sectional area of the airgap
Am cross-sectional area of the magnet
B airgap flux density
C material unit cost
Cc ceramic unit cost
Cn NdFeB unit cost
Cs steel unit cost
d axial depth of a cylinder
da active axial depth of the coil
dbp depth of the magnet bottom plate
dc total axial depth of the coil
dcm minimum total axial depth of the coil
dcn nominal total axial depth of the coil
dcp practical total axial depth of the coil
dm maximum axial movement of the coil
do overall diameter of the wire
dmm depth of the permanent magnet
dpm minimum depth of the magnet centre pole
dpo axial position offset of the coil
dpp total depth of the magnet centre pole
dsbp depth of the shield bottom plate
dsp depth of the steel centre pole
dtp depth of the magnet top plate
dw diameter of the wire conductor
dwp practical diameter of the wire conductor
e voltage induced in the coil
f force on the coil
G transducer constant or coefficient
Gav average value of the transducer constant
Gc calculated value of the transducer constant
Gmax maximum value of the transducer constant
Gmin minimum value of the transducer constant
Gs specified value of the transducer constant
i coil current
I RMS coil current
Im maximum coil current
kc cooling coefficient
ki wire insulation factor
l length of wire in the active part of the coil
lc total length of wire in the coil
lct radial thickness of the coil
lg radial length of the airgap
lm radial mechanical clearance of the coil
lmc main cylinder wall thickness
lsc shield cylinder wall thickness
lsg shield cylinder radial gap
M mass of a cylinder
N number of turns per layer in the coil
Na number of turns in the active part of the coil
Ne effective number of turns in the coil
Na number of turns in the active part of the coil
Nl number of layers in the coil
Np practical number of turns per layer in the coil
P power dissipated in the coil
Q non-linearity
Qav average value of the non-linearity
Qi current non-linearity
Qy position non-linearity
r radius of a cylinder
ri inner radius of a cylinder
ro outer radius of a cylinder
rbp radius of the magnet bottom plate
rcm mean radius of the coil
rmmi inner radius of the main magnet
rmmo outer radius of the main magnet
rsmi inner radius of the shield magnet
rsmo outer radius of the shield magnet
rsbp radius of the shield bottom plate
R reluctance of the magnetic circuit
Rg reluctance of the airgap
Rm reluctance of the magnet
Rp reluctance of the saturated centre pole
R resistance of the coil
Rc calculated value of the resistance of the coil
Rs specified value of the resistance of the coil
S area of the curved surfaces of the coil
Ta temperature of the ambient air
Tc temperature of the coil
Tcm maximum temperature of the coil
u velocity of the coil
V volume of a cylinder
y axial displacement of the coil from its rest position
ΔG deviation of G from the average value
ΔT temperature rise above ambient
ΔTm maximum temperature rise above ambient
α temperature coefficient of resistance
μ mass density
μc ceramic mass density
μn NdFeB mass density
μs steel mass density
φ magnet airgap flux
φcm maximum flux from the coil
φm magnet airgap flux from table
φs required magnet airgap flux
ρ resistivity at the coil temperature Tc
ρm resistivity at the maximum coil temperature Tcm
ρ0 resistivity at 20ºC
Section 1 – Introduction
1
INTRODUCTION
1.1
The design topic
moving coil
1
centre pole
top plate
cylinder
The primary objective of the project is to explore
different designs for a moving-coil driver of the kind
used in vibration generators and loudspeakers, as
described below. Secondary objectives are to
develop skills in using a spreadsheet for engineering
design, using a professional electromagnetics
software package, and linking the two packages to
form a powerful design tool.
Figure 1 shows a half section of the magnet and
coil for a typical moving-coil driver. This diagram
shows only the parts that affect the electromagnetic
action of the device; mechanical details such as the
supports for the coil are omitted. A ring of
permanent-magnet material is the source of the
magnetic field. The steel top plate, bottom plate and
centre pole act as flux guides, which concentrate the
magnetic flux in the narrow gap where the coil
moves.
centre pole
moving coil
top plate
permanent
magnet
bottom plate
Figure 1: Moving-coil driver: ceramic magnet.
This form of magnet uses a low-cost ceramic
ferrite material with a low remanence – typically
Br = 0.4 T – so the magnet ring has a large crosssectional area. Although inexpensive and simple to
manufacture, this form of magnet has the serious
disadvantage of a significant external magnetic field,
so it requires magnetic shielding if it is to be placed
close to a video monitor or TV set. Highperformance magnetic materials such as neodymium
iron boron (NdFeB) have a much higher remanence –
typically 1.2 T – so a different kind of magnet design
is possible, as shown in figure 2.
permanent
magnet
bottom plate
Figure 2: Moving-coil driver: NdFeB magnet.
In this form of magnet, the permanent-magnet
material is effectively a continuation of the centre
pole. The steel top plate, cylinder, and bottom plate
complete the magnetic circuit. These parts form a
shield around the permanent-magnet material, so the
external field is greatly reduced, but the permanentmagnet material is much more expensive than
ceramic ferrite.
Three different kinds of design for a moving-coil
driver are to be investigated, based on these two
magnet configurations:
• Unshielded ceramic magnet
• NdFeB magnet
• Shielded ceramic magnet
In each case, two variants of the design will be
considered: (a) low cost, (b) high performance.
Initial designs of the unshielded ceramic magnet and
the NdFeB magnet will make use of tabulated
magnet data. Final designs for these magnets, and the
design of the shielded magnet, require an
electromagnetics software package to determine the
magnetic field and the force on the coil.
2
Design of a Moving-Coil Driver
2
DESIGN CONCEPTS
2.1
Driver properties
where dc is the total axial depth of the coil.
Calculation of the coil resistance (see below)
requires the wire conductor diameter dw. Let the
overall diameter of the wire be:
d o = ki d w
Transducer constant
Part of the coil moves in the magnet gap where the
average magnetic flux density is B. This is the active
part of the coil. If the total length of wire in the
active part is l, and the coil carries a current i, there
will be a force f exerted on the coil, given by:
(1)
f = Bli = Gi
where G = Bl. If the coil moves with velocity u, there
will be an EMF e induced in the coil, given by:
e = Blu = Gu
(2)
These are the classical equations of the moving-coil
transducer. The coefficient G is known as the force
constant or the transducer constant.
Active depth and magnet flux
The depth of the active part of the coil will be
greater than the depth of the top plate in figure 1 or
figure 2, because the field is not confined to this
region. Beyond a distance equal to the length of the
airgap, the fringing field decays very rapidly, so an
active depth da may be defined by:
d a = d tp + 2l g
(3)
where dtp is the depth of the top plate or outer pole,
and lg is the radial length of the airgap. See figure 3
(page 3) for key dimensions of the coil and magnet.
The average flux density B is defined as follows.
We suppose that an idealised field of constant
magnitude B, confined to the active depth da,
replaces the actual field. The value of B is chosen so
that equation 1 gives the true value for the total force
on the coil.
If the active part of the coil has Na turns and a
mean radius rcm, the length of conductor is:
l = 2π rcm N a
(4)
If the coil is made from Nl layers of round wire with
an overall diameter do (including the insulation
thickness), then the number of active turns in each
layer is da / do. The total number of active turns is
therefore:
Nd
(5)
Na = l a
do
Similarly, the total number of turns in the coil is:
Nd
(6)
Nc = l c
do
(7)
where ki is an insulation factor. Equation 5 becomes:
Nd
Nd
(8)
Na = l a = l a
do
ki d w
The transducer constant is then given by:
2π rcm N l d a B N l φ
G = Bl = 2π rcm N a B =
=
ki d w
ki d w
(9)
where φ is the airgap flux, given by:
φ = AB = 2π rcm d a B
(10)
where A is the area of a cylindrical surface of radius
rcm and depth da. If the flux φ is taken to be the total
flux that would be obtained with a very long coil,
then equation 10 gives the equivalent uniform flux
density over the depth da that would have the same
effect.
2.2
Coil properties
Coil resistance
If lc is the total length of the wire in the coil, and Ac
is its cross-sectional area, the resistance of the coil is
given by:
R=
ρ lc
Ac
=ρ
2π rcm N c
2
πd w /4
=
8 ρ rcm N l d c
2
dod w
=
8 ρ rcm N l d c
ki d 3w
(11)
where ρ is the resistivity. The value of the resistivity
depends on the coil temperature, as follows:
ρ = ρ 0 {1 + α (Tc − 20)}
(12)
where ρ0 is the resistivity at 20ºC, Tc is the coil
temperature, and α is the temperature coefficient of
resistance.
Coil heating
Current flowing in the coil will result in power
dissipation in the form of heat, with a consequent
rise in the coil temperature. The cooling conditions
are very complex, so an exact calculation of the
temperature rise is difficult. For the purposes of this
design project, it will be assumed that the
temperature rise ΔT above ambient is given by
ΔT = k c P / S
(13)
where P is the power dissipated in the coil, S is the
area of the two curved surfaces, and kc is a cooling
Section 2 – Design Concepts
coefficient with a typical value of 0.04 Km2/W. The
temperature rise is thus:
ΔT =
kc I 2 R
4π rcm d c
(14)
where I is the RMS current in the coil. Substituting
for the coil resistance R from equation 11 gives
ΔT =
2 ρ k c I 2 N l ρ k c I m2 N l
=
π k i d w3
π k i d w3
(15)
(16)
where Ta is the ambient air temperature.
Magnet airgap
lct = N l d o = N l k i d w
(20)
The magnet airgap length lg must accommodate this
thickness plus a mechanical clearance lm on each side
to ensure that the coil does not touch the magnet.
The minimum length of the airgap is therefore:
l gm = lct + 2lm = N l k i d w + 2lm
Coil movement
If the coil movement is very small, the minimum
depth of the coil is simply the active depth da. In
practice the coil is required to move an axial distance
of ±dm from its rest position. If this movement is not
to take the coil out of the active region of the
magnet, the minimum depth of the coil must be
increased to:
d cm = d a + 2d m = d tp + 2l g + 2d m
(17)
So far, it has been assumed that the rest position
of the coil is symmetrical with respect to the top
plate of the magnet, as shown in figures 1 and 2.
However, with some designs of magnet, this gives a
force/displacement characteristic that is not
symmetrical: see section 5.2. The performance can
be improved if the rest position of the coil is offset
by a distance dpo from this symmetrical position. The
minimum coil depth is then given by:
d cm = d a + 2d m + d po = dtp + 2l g + 2d m + d po
d cm + dtp
2
+ d m + d po
(19)
(21)
In practice, the coil is usually wound on a rigid
cylindrical former, so the thickness of the former
must be included. The gap between the coil and the
centre pole will then be larger than the gap between
the coil and the top plate. This lack of symmetry
makes very little difference to the design, so it will
be ignored in this project. The value of lm given in
the design specification (section 4.1) should be
understood to mean the air space plus half the
thickness of the coil former.
lct
rcm
lg
dc
dtp
rbp
dbp
dpp
dmm
(18)
The offset dpo is positive if the coil is displaced
downwards from its symmetrical position, so that
more of the coil projects below the top plate.
The magnet centre pole must be deep enough to
accommodate the coil when it moves. The required
condition can be found as follows. If there is no
offset, the coil in its rest position has equal amounts
projecting above and below the top plate. Given that
dtp is the depth of the top plate, the centre of the coil
is a distance dtp / 2 below the top of the pole. The
bottom of the coil is therefore a distance
dc / 2 + dtp / 2 below the top of the pole. To allow for
coil movement and a position offset, the minimum
depth of the pole is therefore:
d pm =
In practice, the total depth of the centre pole dpp must
be greater than this, since the coil must not make
contact with the bottom plate of the magnet. For a
ceramic magnet, this depth is just the steel pole
depth, but for a NdFeB magnet, it is the sum of the
steel pole depth dsp and the magnet depth dmm (see
figure 3).
The radial thickness of the coil is given by
where Im = √2I is the maximum coil current, and ρ is
the resistivity at the coil temperature Tc. The
temperature rise ΔT is defined as:
ΔT = Tc − Ta
3
(a)
lct
rcm
lg
lmc
dsp
dc
dtp
rbp
dbp
dmm
(b)
Figure 3: Moving-coil driver main dimensions:
(a) ceramic magnet, (b) NdFeB magnet.
4
Design of a Moving-Coil Driver
3
INITIAL DESIGN PROCEDURE
3.1
Introduction
The specification of a moving-coil driver will
usually include the required values of the following
quantities:
•
The transducer constant Gs
•
The coil resistance Rs
•
The maximum coil current Im
• The coil axial movement ±dm
The notation Gs and Rs indicates the specified values
of G and R, which must be distinguished from the
calculated values Gc and Rc for a particular design. In
addition, other quantities such as the maximum coil
temperature Tcm will be specified. For the designer,
the problem is to determine the dimensions of the
coil and magnet that will satisfy this specification.
As with most engineering design problems, there
are many possible solutions that will satisfy this
specification. Choosing the “best” solution will
involve other factors such as the quantities of
materials used in the magnet, and measures of
performance such as linearity and the external
magnetic field.
Any design must satisfy the equations for the
coil developed in section 2, and the design will also
involve the magnet through the relationship of the
airgap flux φ to the magnet dimensions. The final
design will require electromagnetic simulation
software to explore the effects of changing the
magnet dimensions. However, a useful initial design
can be based on tabulated results for a few
representative magnet configurations. Section 3.2
describes a systematic way of doing this.
Magnet tables
The tables in section 9 give values of the airgap flux
for the following ranges of variables:
• Airgap length values of 3 mm, 4 mm and 6 mm.
• Pole depth values of 20 mm and 30 mm for the
smaller airgaps, and 25 and 35 mm for an airgap
of 6 mm.
• Mean coil radius values that give a useful range
of magnet flux values.
The other magnet dimensions have been chosen to
give a reasonably good magnet design. For
simplicity, the top plate thickness is held constant at
6 mm. These magnet dimensions will accommodate
a wide range of coil designs, so they are suitable for
the initial driver design.
The NdFeB designs use more permanent-magnet
material than is common in commercial designs, so
the resulting magnet costs are much higher than for
equivalent ceramic designs. However, these designs
give much improved device performance, as will be
seen in section 6. One of the aims of the project is to
explore the trade-off between performance and cost.
3.2
Design with a spreadsheet
An Excel spreadsheet will be used for the initial
design, so that the effects of changes can be explored
systematically. The sections below explain the
design sequence and the procedure for developing
the spreadsheet. When this spreadsheet is working
correctly with the example data, it can be used for
the initial designs as specified in section 4.
An outline of a spreadsheet is supplied in the
Excel workbook file Driver Design Outline.xls.
This has the descriptive text entered and certain cells
named, but it will need to be completed as described
below.
Opening the workbook
This workbook uses macros. When you open the file,
the following dialog may be displayed:
Click Enable Macros to continue. However, you may
see a different dialog telling you that macros have
been disabled:
In this case, click OK to continue. From the Tools
menu, select Options / Security / Macro Security,
and change the level to Medium. Close the workbook
and re-open it.
Workbook versions
During the project, you will need to save several
different versions of the Excel workbook file. It is
helpful to have a logical sequence of names and
version numbers, so that it is easy to keep track of
the work. The instructions in this document give
preferred file names for the different stages of the
project. However, you are free to use different
names, provided there is a logical sequence.
Begin by saving a copy of the outline workbook,
with the following file name:
Driver Design Example 1a.xls
Section 3 – Initial Design Procedure
As you develop the spreadsheet, it is a good idea to
save successive stages with different suffix letters
such as:
Driver Design Example 1b.xls
Do this frequently, to minimise loss of work in the
event of mistakes or computer failure.
Spreadsheet layout
The design spreadsheet is in the Design sheet of the
workbook. Ignore the Analysis sheet at this stage – it
is required later for the final design.
The spreadsheet is set out with data in clearly
marked areas, separate from the calculations. Data
values that may be changed for the designs are
shown in red. Calculated values that need to be
inspected as part of the design process are grouped
together and shown in blue.
It is essential not to alter any of the cell
locations for the coil data and magnet data on the
spreadsheet. The workbook includes a link to the
MagNet electromagnetic simulation software that
takes data values from these cells. This link will fail
if the locations are changed. Also, the names of the
worksheets (Design and Analysis) must not be
changed.
Enter your name in cell C1 of the Design Sheet. This
helps to identify the file when you submit it for
comment or assessment.
Magnet Data
Cells B23 – D38 contain data for the magnets for
each design. For the initial design, values will be
taken from the tables in section 9. Subsequently,
these values will be modified when the driver is
modelled with MagNet. Example data values for two
magnets have already been entered in the outline
spreadsheet. These values are required for
developing the rest of the spreadsheet. Once the
development is complete, it will be necessary to
enter different data values for the initial designs.
Other magnet dimensions are calculated from the
magnet data by formulae in cells G31 to I42.
5
Constants and Specification
Enter data in column B of the Design sheet as
follows:
A
B
4
5
Specification
Transducer constant Gs (N/A)
6
Coil resistance Rs (ohms)
5.00
7
Maximum current Im (A)
2.00
8
Axial movement dm (mm)
6.00
8.00
9
Max. coil temperature Tc (ºC)
120
10
Ambient temperature Ta (ºC)
30.0
11
Cooling coefficient kc (Km /W)
12
Coil insulation factor ki
1.10
13
Coil mechanical clearance lm (mm)
1.00
2
0.0400
The first four values are examples only, and are
different from the individual specifications issued to
students for this project.
Enter data in column G of the Design sheet as follows:
F
1
2
G
Constants
Copper cold resistivity ρ0 (nΩ.m)
17.2
3
4
Temperature coefficient α
5
Ceramic mass density μc (kg/m )
4900
6
NdFeB mass density μn (kg/m )
7390
7
Steel unit cost Cs (£/kg)
2.00
8
Ceramic unit cost Cc (£/kg)
1.00
9
NdFeB unit cost Cn (£/kg)
50.0
0.00390
7600
Steel mass density μs (kg/m3)
3
3
Cell names
Cells B5 – B13 and G2 – G9 contain values that will
be the same for all designs. These cells have been
given names, so that they can be referenced by name
in the formulae for the design calculations. Cells
G12 and G13 also have names, but all other cells in
the spreadsheet are referenced by their column letter
and row number. With this form of reference,
formulae created in column G for the ceramic design
can be copied to column H for the NdFeB design.
When a formula is copied, any column references
will be changed automatically to refer to cells in the
next column, but cell names will continue to refer to
the original cells.
Inspect the cell names by selecting the cells in turn
and viewing the name in the text box to the left of
the Formula Bar above the spreadsheet grid. If the
cell does not have a name, its column/row reference
will be shown instead.
6
Design of a Moving-Coil Driver
Calculated values
Enter formulae in cells G12 and G13 to calculate the
maximum coil temperature rise (equation 16) and the
resistivity of copper at the maximum coil
temperature (equation 12) as follows:
G12
G13
=Tcm-Ta
=Rho0*(1+Alpha*(Tcm-20))
d wm
13
G
Max. temperature rise ΔTm (K)
90.0
Copper hot resistivity ρm (nΩ.m)
23.9
Coil Data
The Coil Data section is used for entering data
values as the design progresses. Initially, a value
must be specified for the number of layers – see (a)
below – and for the coil position offset.
Enter the value 4 in cell B16 and 3.0 in cell B20:
A
B
Ceramic
Coil Data
17
Practical wire diameter dwp (mm)
18
Nominal coil depth dc (mm)
19
Coil mean radius rcm (mm)
20
Coil position offset dpo (mm)
Number of layers Nl
4
•
Rho, Kc, Im, Ki, and DTm are the names of cells
containing the values of ρm, kc, Im, ki and ΔTm
respectively.
•
Pi is a constant that has been defined in the
spreadsheet to have the value of π.
•
B16 is the cell containing the value of the
number of layers Nl.
The result should be:
F
Most of the design equations in section 2 involve the
number of layers Nl. A value must be assumed for Nl
at the outset. Other quantities that depend on Nl may
be calculated, to see whether this assumption leads to
a feasible design. If not, the value of Nl can be
changed and the process repeated.
For this design project Nl can be 2, 4 or 6, so a
sensible starting point is to try Nl = 4.
(b) Wire diameter and magnet flux
15
16
Coil Calculation
Minimum wire diameter dwm (mm)
G
Ceramic
0.366
The value for the minimum wire diameter must
be rounded up to the nearest 0.01 mm for a practical
design: call this value dwp.
A larger diameter may be used if required by
other design considerations – see (e) below.
Enter the value of the practical wire diameter
(0.37 mm) in cell B17.
Once the wire diameter has been chosen, the
required magnet airgap flux φs can be determined
from equation 9:
Consider equation 15:
ρ k c I m2 N l
π k i d w3
All of the numerical values displayed on the
spreadsheet are in convenient SI multiples, such as
μWb for flux values and mm for lengths. This makes
the spreadsheet easy to use, but some formulae must
include the corresponding factors to convert these
values to SI units. In the formula for wire diameter
above, the resistivity is in nΩm, which must be
multiplied by 10–9 to get the SI value in Ωm. When
the cube root is taken, the resulting factor of 10–3 is
cancelled by the factor of 103 for converting the
result from m to mm, so no conversion factors
appear in the final version of the formula. It could
have been entered as:
=1e3*(1e-9*Rho*Kc*Im^2*B16/(Pi*Ki*DTm))^(1/3)
3.0
(a) Starting point for the design
ΔT =
(22)
=(Rho*Kc*Im^2*B16/(Pi*Ki*DTm))^(1/3)
F
Calculated values
15
16
1/ 3
⎞
⎟
⎟
⎠
To calculate this value, enter a formula in cell G16
as follows:
These formulae should give the following results:
11
12
⎛ ρ k I2N
=⎜ m c m l
⎜ π k ΔT
i
m
⎝
[15]
For a given coil current Im, the temperature rise
depends on the number of layers Nl and the wire
diameter dw. It does not depend on the depth or the
radius of the coil. Therefore, once the number of
layers has been chosen, the wire diameter can be
calculated. If the maximum allowable value ΔTm is
chosen for the temperature rise, re-arranging
equation 15 gives the minimum wire diameter:
G=
N lφ
ki d w
[9]
If Gs is the specified value of the transducer constant,
rearranging this equation gives:
φs =
k i d wp G s
Nl
(23)
Section 3 – Initial Design Procedure
Enter a formula in cell G19 to calculate the value of
φs from equation 23, using cell names for ki and Gs,
and column/row references for dwp and Nl. Unit
conversions are required. The result should be
814 μWb.
Before a magnet can be selected from the tables,
however, the airgap length must be calculated.
(c) Airgap length and coil depth
Equations 20 and 21 can be used to determine the
minimum airgap length for the magnet:
lct = N l k i d wp
[20]
l gm = l ct + 2l m
[21]
dimensions are calculated by the formulae already
entered in cells G31 to G34.
Enter the coil mean radius (14 mm) in cell B19.
(e) Coil resistance
Once the coil mean radius rcm has been found,
equation 11 with ρ = ρ0 gives the coil resistance at
20ºC in terms of the coil depth:
8ρ r N d
Rs = 0 cm3 l c
[11]
ki d wp
This equation determines the coil depth dcr that will
give the specified coil resistance Rs. Re-arranging
equation 11 gives:
where lm is the specified mechanical clearance.
dcr =
Enter formulae in cells G23 and G20 to calculate the
value of lct and lgm from these equations. The results
should be 1.63 mm and 3.63 mm respectively.
From the magnet tables, a practical value of
airgap length lg larger than lgm must be selected. The
nearest available airgap length is 4 mm, which has
already been entered in cell B24.
Now that the airgap length is known, equation 3
gives the active coil depth da, and equation 18 gives
the minimum coil depth dcm:
d a = d tp + 2l g
[3]
d cm = d a + 2d m + d po
[18]
where dm is the specified axial movement of the coil
and dpo is the coil position offset (cell B20).
Enter formulae in cells G22 and G17 to calculate the
value of da and dcm from these equations. The results
should be 14.0 mm and 29.0 mm respectively.
(d) Coil mean radius
To determine the coil mean radius rcm, a magnet must
be selected from the tables that will give a value of
airgap flux φm close to the required value φs found in
(b) above. It is now possible to find two ceramic
magnets from the table that will give a flux density
close to the required value. One has a pole depth of
20 mm, and the other has a pole depth of 30 mm.
Since the required depth is unknown at this stage, a
value of 30 mm is selected. The required minimum
pole depth will be found later, and a different magnet
can be chosen if necessary.
From the tables of ceramic magnet data, a
magnet designed for a mean coil radius of 14 mm
will be suitable. This gives an airgap flux value of
782 μWb, which is within 4% of the required value
of 814 μWb. The data for this magnet has already
been entered in cells B23 to B31. Other magnet
7
ki d 3wp Rs
8 ρ0 rcm Nl
(24)
Enter a formula in cell G18 to calculate the value of
dcr from equation 24. Unit conversions are required.
The result should be 36.2 mm.
The minimum coil depth dcm has already been
found from equation 18 – see (c) above. If dcr > dcm,
as it is for the example data, then setting dc = dcr will
meet both the coil resistance specification and the
coil movement specification. A possible design has
been achieved, provided that the pole depth
requirement is also satisfied – see (f) below. The
tolerance of ±10% in the coil resistance can be
exploited to make dc < dcr, which is beneficial
because it requires less pole depth. A suitable choice
is 34 mm.
Enter a value of 34 mm in cell B18.
This is the nominal coil depth dcn, which must be
modified by practical considerations.
(f) Practical coil depth and pole depth
There must be a whole number of turns in each layer
of the coil. A practical coil depth dcp that will
achieve this can be calculated as follows.
• Calculate the exact number of turns per layer as:
N=
•
•
dc
k i d wp
(25)
Round this value to the nearest integer Np. See
below for the Excel function to do this.
Calculate the practical coil depth from:
d cp = N p k i d wp
(26)
8
Design of a Moving-Coil Driver
•
Calculate the minimum practical pole depth by
substituting the value of dcp in equation 19:
d pm =
d cp + dtp
2
+ d m + d po
(27)
Example results
The coil data values for the example specification
should be as follows:
A
where dtp is the depth of the top plate and dm is the
coil axial movement. In the spreadsheet, to round a
number to the nearest integer, use the Excel function
ROUND:
ROUND(number, num_digits)
number – the value to be rounded
num_digits – the number of digits. Setting this to
zero will round the value to the nearest integer.
Enter formulae in cells G24, G25, G26 and G21 to
calculate the values of N, Np, dcp and dpm from these
equations. The results should be 83.5, 84, 34.2 mm
and 29.1 mm respectively.
Note that the ROUND function must be used in a
formula in cell G25. Do not enter the numerical
value 84, since this will give wrong results with
other data.
Coil Data
17
Practical wire diameter dwp (mm)
18
Nominal coil depth dc (mm)
34.0
19
Coil mean radius rcm (mm)
14.0
20
Coil position offset dpo (mm)
F
15
16
17
18
19
20
21
22
(g) Calculated results
Gc =
N lφm
k i d wp
(28)
It is also necessary to calculate the coil resistance R
using equation 11 with ρ = ρ0:
Rc =
8 ρ 0 rcm N l d cp
k i d 3wp
(29)
Enter formulae in cells G27 and G28 to calculate the
value of Gc and Rc from these equations. Unit
conversions are required. The results should be
7.69 N/A and 4.73 Ω respectively.
These values are within ±10% of the specified
values of 8 N/A and 5 Ω. If either quantity had been
outside the permitted range, the design would have
had to be changed.
Number of layers Nl
4
0.370
3.0
The corresponding calculated results are:
The depth of the centre pole for the ceramic
design, or the total depth of the steel centre pole and
the magnet for the NdFeB design, must exceed the
minimum value dpm. For the example ceramic design,
the selected pole depth of 30 mm exceeds the
minimum of 29.1 mm. In this case, it is not possible
to use a magnet with a pole depth of 20 mm.
From the final values of the coil dimensions, it is
necessary to calculate the transducer constant G
using equation 9 with the actual magnet flux φm:
B
Ceramic
15
16
Coil Calculation
Minimum wire diameter dw (mm)
Minimum coil depth dcm (mm)
Coil depth dcr for given Rs (mm)
Required airgap flux φs (μWb)
Minimum airgap length lgm (mm)
Minimum pole depth dpm (mm)
G
Ceramic
0.366
29.0
36.2
814
Active coil depth da (mm)
3.63
29.1
14.0
23
Coil radial thickness lct (mm)
1.63
24
Number of turns per layer N
83.5
25
Practical no. of turns per layer Np
26
Practical coil depth dcp (mm)
34.2
27
Calculated trans. const. Gc (N/A)
7.69
28
Calculated coil resistance Rc (Ω)
4.73
84
Note that cells G16 – G28 contain formulae, which
display the values shown above.
Do not proceed to the next section until the
spreadsheet is giving correct results for the
ceramic magnet.
Section 3 – Initial Design Procedure
3.3
NdFeB magnet design
Open the workbook Driver Design Example 1x,
where x is the last suffix letter used in section 3.2.
Save the file with the following file name:
Driver Design Example 2a.xls
The spreadsheet can be extended as follows for the
NdFeB magnet design.
Copy the contents of cells G16–G28 to H16–H28.
This will give several #DIV/0! errors, because coil
data values are missing from column C.
Enter values for the Coil Data in column C, using a
procedure similar to that for the ceramic magnet:
•
Start by setting the number of layers to 4 and
the coil position offset to 0 for this design.
•
Use a value of 18 mm for the coil mean
radius.
•
The nominal coil depth dc can be set to the
minimum value of 26 mm.
Results for Gc and Rc should be 7.71 N/A and 4.63 Ω
respectively.
3.4
9
Material quantities and costs
An important aspect of a design is the quantity of
material used. All of the components of the magnets
are solid or hollow cylinders, so the following
equations can be used. The mass of a solid cylinder
is given by
M = μV = μπ r 2 d
(30)
where μ is the mass density, V is the volume, r is the
radius and d is the depth. It follows that the mass of a
hollow cylinder is
M = μV = μπ ( ro2 − ri2 )d
(31)
where ri and ro are the inner and outer radii. The cost
of the material is then given by CM, where C is the
unit cost in £/kg.
Enter formulae in the relevant cells in the range G45
to H58 to calculate the mass and cost values.
For the component dimensions, use cell
references from the Magnet Data area (B23 to C32)
and the Magnet Dimensions area (G31 to H42).
For the density and unit cost values, use cell
names from the Constants area (G2 to G9). Use the
constant Pi for the value of π. The results should be
as shown below.
Note that all of these cells contain formulae that
produce the numerical results shown. The formula
for a total just needs to refer to the values that have
already been calculated in other cells; for example,
the formula for the total mass of steel in G51 is
=G45+G46+G47. The total mass of PM (permanent
magnet) material will be equal to the mass of the
main magnet for these two designs, but for the
shielded design it will include the mass of the shield
magnet. Ignore the shielded design at this stage.
F
Magnet Calculation
Mass of centre pole (kg)
Mass of top plate (kg)
Mass of bottom plate (kg)
Mass of cylinder (kg)
Mass of shield cylinder (kg)
Mass of shield bottom plate (kg)
Total mass of steel (kg)
Mass of main magnet (kg)
Mass of shield magnet (kg)
Total mass of PM material (kg)
Total mass of magnet (kg)
Cost of steel (£)
Cost of PM material (£)
Total cost of material (£)
G
H
Ceramic NdFeB
0.103
0.037
0.216
0.099
0.253
0.156
0.142
0.572
0.603
0.433
0.143
0.603
1.175
1.14
0.60
1.75
0.143
0.576
0.87
7.13
8.00
When the spreadsheet is working correctly, ensure
that you save the final version of the file.
10
Design of a Moving-Coil Driver
4
INITIAL DESIGNS
2
4.1
Design specification
Enter the practical wire diameter in cell B17, by
rounding up the minimum wire diameter
(cell G16) to the nearest 0.01 mm.
3
Scan the magnet data tables in section 9 for a
magnet with (a) an airgap length greater than the
minimum, (b) a flux close to the required value
(cell G19), with a pole depth of 30 mm.
4
Enter the coil mean radius in cell B19. Leave the
coil position offset set to 3.0 mm in cell B20.
5
Compare the two calculated values of coil depth
(cells G17 and G18). If dcr > dcm, you can use dcr
for the nominal coil depth. However, if dcr < dcm,
the following procedure is required.
Two initial designs are required for a moving-coil
driver. The first design is to use a ceramic magnet,
and the second design is to use a NdFeB magnet.
Both designs are to meet the following specification.
Transducer constant:
** N/A ±10%.
Coil resistance at 20ºC:
** Ω ±10%.
Maximum current:
** A.
Coil axial movement:
±** mm.
Maximum coil temperature: 120ºC.
Ambient temperature:
30ºC.
Cooling coefficient:
0.04 Km2/W.
Coil insulation factor:
1.1.
Coil mechanical clearance: 1.0 mm.
Number of layers:
2, 4 or 6.
** Individual specification for the first four items.
The resistivity of copper at 20ºC is 17.2 nΩm, and
the temperature coefficient of resistance is 0.0039.
Properties of the magnet materials are as follows:
Material
Steel
Ceramic ferrite
NdFeB
Mass density
7600 kg/m3
4900 kg/m3
7390 kg/m3
Unit cost
2.0 £/kg
1.0 £/kg
50 £/kg
The unit cost figures are for the material alone, and
do not include the cost of manufacture.
For each design, a suitable magnet is to be
selected from the tables in section 9.
4.2
Open the completed version of the project workbook
containing the example data. This should be named
Driver Design Example 2x, where x is the suffix
letter of the last saved version. Before starting the
design work, save the workbook with the following
file name:
Driver Design Initial 1a.xls
Enter your individual specification in cells B5 – B8
of the Design sheet. Start with the ceramic design,
following the procedure described in section 3. In
summary, the steps are as follows.
1
Start with a value of 4 for the number of layers.
Check whether it is possible to meet the coil
resistance specification by setting the
nominal coil depth to the minimum dcm.
•
If the resulting value of R is outside the 10%
tolerance, increase the practical wire
diameter dwp by 0.01 mm, since this will
increase the value of dcr. The spreadsheet
will re-calculate the flux φ.
•
If the new value of φ requires it, select a
different magnet from the data tables, and
enter the new value of coil mean radius rcm.
•
Compare the new values of coil depth.
•
Repeat this process as required.
•
Alternatively, choose a different value for Nl
and repeat the design process.
6
Check whether the magnet pole depth could be
reduced to 20 mm. If so, select a different
magnet from the tables.
7
When you have a design that meets the
specification, enter all the magnet data in cells
B23 – B31.
8
Save the workbook.
Design procedure
Ceramic magnet
•
NdFeB magnet
Open the project workbook containing the initial
ceramic design. This should be named
Driver Design Initial 1x, where x is the suffix letter
of the last saved version. Save the workbook with the
following file name:
Driver Design Initial 2a.xls
Follow a similar design procedure with this magnet,
but with the coil position offset set to 0. Note that the
total pole depth is the sum of the depths of the steel
pole and the central magnet, so the data tables for
NdFeB have entries for total pole depths of 20 mm
and 30 mm (or 25 mm and 35 mm with an airgap of
6 mm).
Section 5 – Final Designs
5
FINAL DESIGNS
5.1
Introduction
Final designs are required for the drivers, where the
ceramic and NdFeB magnets have been redesigned
using the MagNet electromagnetic simulation
software. In addition, designs for a third driver are
required, using a ceramic magnet with shielding to
reduce the external magnetic field. All of these
designs must meet the performance specification.
Section 5.2 discusses non-linearity, which is a
feature of most moving-coil devices. The NdFeB
magnet of the initial design has better linearity than
the ceramic magnet, but it is much more costly. One
of the aims of the project is to investigate the tradeoff between performance and cost, by considering
alternative designs as follows:
Ceramic magnet
(a) Low cost, based on the initial design.
(b) Non-linearity improved as much as possible.
NdFeB magnet
(a) Good linearity, based on the initial design.
(b) Cost reduced as much as possible.
Shielded ceramic magnet
Low external magnetic field together with:
(a) Low values of weight, size and cost.
(b) Low values of non-linearity.
Workbook versions
The Excel workbook for the project has columns for
all three magnet configurations: ceramic, NdFeB and
shielded. For each configuration there are two
variants: low cost, and high performance (low values
of non-linearity). An effective way of organising the
workbooks is to use one sequence of files for the
low-cost designs, and another for the highperformance designs. This principle will be followed
for the recommended file names in sections
6, 7 and 8.
Practical considerations
For ease of manufacture, all of the designs must use
simple shapes such as cylinders and flat plates. Other
shapes are unsuitable. For example, the thickness of
the bottom plate could be tapered so that the
magnitude of the flux density was uniform. This
would reduce the volume of the plate, and apparently
save material. In practice the tapered plate would
have to be made from a flat plate by machining it on
a lathe. This would increase the cost of manufacture,
and the material removed would be wasted.
11
Similarly, a hollow centre pole is not a useful design
change.
5.2
Non-linearity
The force on the moving coil is given by equation 1:
[1]
f = Bli = Gi
In section 2, G was termed the transducer constant.
In practice, however, G is not constant. Its value
depends on the coil current i and the axial
displacement y of the coil from its rest position. The
quantity G should therefore be called the transducer
coefficient, rather than the transducer constant.
Consider the effect of the coil current. So far, it
has been assumed that the flux density B in equation
1 is the value created by the permanent magnet.
However, current flowing in the coil will create an
additional component of flux in the magnet gap, with
a value proportional to the current. Since the force
depends on the product of the current and the flux
density, there will be an additional component of
force, with a magnitude that varies as the square of
the current, and a direction that remains constant – it
does not reverse when the current reverses.
The main flux in the airgap is the constant
quantity produced by the permanent magnet; for a
given position of the coil, this will give a force
proportional to the current. Since the additional
component of force varies as the square of the
current, the total force on the moving coil will not be
a linear function of the coil current. Moreover, since
the additional component adds to the main force for
one direction of current, and subtracts for the other
direction, the characteristic is not symmetrical.
However, the effect is usually small, so we can
continue to use equation 1 if we specify that the
value of G is no longer a constant, but varies with the
coil current. This variation in the value of G is a
measure of the non-linearity of the characteristic.
Coil displacement also affects the value of G. If
the total coil depth dc is not much greater than the
active depth da, it will take only a small displacement
to move part of the coil out of the magnet gap. When
this happens, the effective value of da will be
reduced and the value of G will fall. A further source
of non-linearity is a lack of symmetry in the
magnetic field above and below the top plate of the
magnet.
In most applications both types of non-linearity
are undesirable, so a designer may need to minimise
the non-linearity. This is particularly important for
hi-fi loudspeakers, where non-linearity will result in
distortion of the sound output.
Numerical measures of non-linearity can be
defined as follows in terms of the transducer
12
Design of a Moving-Coil Driver
coefficient G. If the maximum and minimum values
of G are Gmax and Gmin, then the average value is
G
+ Gmin
(32)
Gav = max
2
The maximum deviation from the average is
ΔG = Gmax − Gav = Gav − Gmin
=
Gmax − G min
2
(33)
The non-linearity Q is defined as the maximum
deviation divided by the average:
Gmax − Gmin
G − Gmin
ΔG
2
=
= max
Q=
Gav Gmax + Gmin Gmax + Gmin
2
(34)
The current non-linearity Qi is the value given
by equation 34 when Gmax and Gmin are the values of
G determined with the coil in its normal rest
position, with currents of +Im and –Im, where Im is
the maximum rated current.
The position non-linearity Qy is the value given
by equation 34 when Gmax and Gmin are the maximum
and minimum values of G in the working position
range, with the current equal to its rated value and
acting in a direction to give the highest value of G.
The average non-linearity Qav is the average of
Qi and Qy. It is a useful general measure of
performance when comparing different designs.
The transducer constant is the value of G when
the current is small and the coil is in its rest position.
In practice it may be found by taking the average of
the values calculated for small positive and negative
currents, and it will be very close to the value of Gav
given by equation 32 for currents of +Im and –Im.
Determining the values of G
The values of G can be determined as follows, using
the electromagnetic simulation package MagNet. A
model of the device is created, and the y-component
of the force on the coil is determined. This force is
equal to Gi, where i is the coil current. For the
current non-linearity, it is sufficient to find the
values of G for (a) i = +Im, (b) i = –Im. The transducer
constant is the mean of these values. For the position
non-linearity, the current direction that gives the
largest value of G is used. Values of G are then
found for several displacement steps in each
direction, and the lowest and highest values are
selected.
5.3
External magnetic field
All driver magnets will produce some external
magnetic field. Since one of the project objectives is
to reduce the external field by screening, a numerical
measure of the field is required so that designs can
be compared. For this project, a measure of the
external field is defined as follows. It is the
maximum value of the flux density magnitude over
the surface of a sphere of radius 200 mm, when there
is no current in the coil. The centre of the sphere is at
the centre of the top face of the centre pole. The
required flux density value is determined from the
field solution generated by the MagNet package, by
sampling the field at regularly spaced angles and
taking the maximum.
Section 6 – Analysis with MagNet
6
6.1
13
ANALYSIS WITH MAGNET
6.2
Introduction
The MagNet package is described in the document
An Introduction to MagNet for Static 2D Modeling.
MagNet is a professional electromagnetic simulation
software package that is widely used as an industrial
design tool. For this project, it will be used as a
“virtual laboratory” to try out the effects of design
changes on the performance of the moving-coil
driver. With MagNet, a model of the device is built
and then solved to determine the magnetic field. Flux
plots and colour maps of the flux density can be
displayed to guide the designer, and the force on the
moving coil can be calculated.
The Excel workbook for this project can interact
with the MagNet software, as described in section
6.3. This enables the model to be created
automatically from the magnet and coil data, with the
resulting force values imported into the workbook.
Before using the workbook in this way, however, it
is necessary to gain experience of using MagNet
interactively, as described in section 6.2.
The Excel link exploits a powerful feature of
MagNet known as scripting. Scripts are text files
containing commands that control MagNet. These
commands can reproduce actions that the user would
have taken when running the package interactively.
Through the Microsoft Automation interface, other
packages such as Excel can control MagNet with
scripts. The workbook contains procedures, written
in Visual Basic for Applications, that use scripting
commands to interact with MagNet.
For the ceramic and NdFeB drivers, the Visual
Basic procedures are fully functional, and can be
used to develop the final designs. However, for the
shielded driver the procedures are incomplete, so one
of the tasks is to complete them, using the working
procedures as examples.
Using MagNet
1
Read at least the first part of chapter 1, so that
you understand the principles of representing a
3D object by a 2D model.
2
Log on to one of the computers in the laboratory
where MagNet is installed.
3
Double-click the MagNet icon.
•
Wait for the program to load,
which may take up to 40 seconds.
4
Work through the whole of the tutorial in
chapter 2, even though the device is quite
different from a moving-coil driver, because it
introduces essential features of the package.
5
Read the introduction to chapter 4.
6
Work through the case study on the moving-coil
transducer in chapter 4. This is very similar to
the driver with a ceramic magnet in this project.
6.3
Using the spreadsheet
The case study on the moving-coil transducer should
have shown two things: the power of MagNet to
produce useful results, and the need for a faster
method of constructing the model if many different
designs are to be analysed. The project workbook
meets this need.
Analysis
The Analysis sheet of the workbook handles the link
between Excel and MagNet. Buttons on this sheet
activate the main Visual Basic procedures for
starting and closing MagNet, and for building and
solving models. Results for forces and magnetic flux
density values are displayed in the lower part of the
sheet; calculated driver performance values are
displayed in the upper part. Calculations are carried
out in a Visual Basic procedure and the results
displayed on the sheet, so there are no formulae in
any cells on the Analysis sheet. See section 8.2 for
information about the Visual Basic procedures. The
driver performance is calculated from the force
values returned by MagNet, using the methods
described in section 5.2.
The transducer constant Gav is used to update the
value for the magnet flux φm on the Design sheet as
follows. Equation 9 gives a relationship between G
and the flux:
G = Bl = 2π rcm N a B =
2π rcm N l d a B N lφ
=
ki d w
ki d w
[9]
14
Design of a Moving-Coil Driver
Analysing the ceramic model
Re-arranging this equation gives:
φm =
k i d w Gav
Nl
(35)
1
Consequently, the calculation of the transducer
constant on the Design sheet gives the same result as
Gav, since the formula is derived from equation 9.
Starting
2
In the Solution Data for the Ceramic model,
enter the following values:
•
Number of current increments 1
•
Number of position increments 5
Click Solve Ceramic.
•
Click the MagNet icon on the task bar to
display the Solver Progress dialog.
1
Log on to one of the computers in the laboratory
(ENGG III F7) where MagNet is installed.
3
2
Open the version of the project workbook
containing the example data.
When the solutions are complete, click the
MagNet icon to display the MagNet window.
4
In the MagNet window, display the flux plot and
the shaded plot of |B| smoothed.
5
Use the Field Probe to investigate the values of
flux density in the centre pole and the bottom
plate.
•
3
This should be named
Driver Design Example 2x, where x is the
suffix letter of the last saved version.
Save the file with the following file name:
•
Driver Design Example 3a
4
In the Design sheet, change the value of the coil
position offset (cell B20) from 3.0 to 0.
5
Select the Analysis sheet, and inspect its
contents.
•
6
6
Take care not to alter the names of the
materials in cells B11, B12 and B13.
Click the Start MagNet button.
•
Wait for the normal mouse pointer to return.
Confirm that the values are above 1.8 T in
some parts of these components.
Display the B/H curve for the steel as follows:
•
In the Project bar, click the Material tab.
•
If necessary, expand the Model Materials tree.
•
Right-click CR10: Cold rolled 1010 steel,
and select Properties.
•
In the Properties dialog, click the Magnetic
Permeability tab.
•
Re-size the Properties dialog to display the
curve more clearly.
7
Click the MagNet Visibility button.
8
In the dialog box, click Yes to make MagNet
visible.
This should display the MagNet main window
and the MagNet icon on the task bar.
7
•
Driver performance
If the MagNet main window is not displayed,
click the MagNet icon on the task bar.
Building the ceramic model.
1
Click the Excel icon on the task bar.
2
In the Excel window, click Build Ceramic.
3
When the normal pointer returns, click the
MagNet icon on the task bar.
This should display the MagNet main window,
with the model visible in the View window.
4
Maximise the MagNet window.
5
Inspect the model of the device. It should
resemble the model created in the case study.
6
Minimise the MagNet window.
Observe the shape of the curve, which is
approaching saturation at 1.8 T.
•
Close the Properties dialog.
Minimise the MagNet window. In the Excel Analysis
sheet, inspect the computed performance figures for
the ceramic magnet. These have been calculated
from the MagNet results listed in the lower part of
the spreadsheet.
Modifying the example design
The MagNet results show a marked asymmetry in the
variation of force with coil position, which partly
accounts for the position non-linearity value of about
5.1%. Notice that the maximum force is obtained
with a coil position between –4.8 mm and –3.6 mm.
If a position offset of about 4 mm is introduced,
the maximum force should be developed in the rest
position. However, this would require a minimum
pole depth of 30.1 mm; since the actual pole depth is
only 30 mm, the coil would hit the bottom plate of
the magnet when it moved below the rest position.
Section 6 – Analysis with MagNet
15
To allow some mechanical clearance, the pole depth
should be increased to about 32 mm. This will give a
corresponding increase in the depth of the permanent
magnet material. Proceed as follows.
NeFeB magnet
1
Select the Design sheet.
1
2
In the Coil Data, change the coil position offset
to 4.0 mm.
In the Solution Data for the NdFeB design, set
the Number of Position Increments to 5.
2
3
In the Magnet Data, change the total centre pole
depth in cell B25 to 32 mm.
Click Build NdFeB, and wait for the normal
mouse pointer to return.
3
Click Solve NdFeB.
4
Select the Analysis sheet.
4
5
Copy the Ceramic Driver Performance results to
column H, so that they can be compared with the
new results.
6
Click MagNet Visibility, and click Yes in the
dialog box to make MagNet invisible.
Compare the non-linearity values for the two
designs.
The position non-linearity for NdFeB is
somewhat smaller, because the fringing field is
more symmetrical, and the current non-linearity
is very much smaller.
5
Save the final version of the workbook.
6
Click Close Magnet before closing the
workbook.
7
Click Build Ceramic, and wait for the normal
mouse pointer to return.
8
Click Solve Ceramic.
Results should appear in the lower part of the
spreadsheet as the model is solved successively.
9
When the solution is complete, compare the new
performance figures in column D with the
previous values in column H.
10 Observe that the force/position characteristic is
nearly symmetrical.
11 Change the number of position increments from
5 to 1, and click Solve Ceramic.
•
The solution is much faster, but the position
non-linearity value is virtually unchanged.
Provided the force/position characteristic is
nearly symmetrical, only one position increment
is required for calculating the non-linearity.
It is instructive to compare the performance of the
ceramic magnet with that of the NdFeB magnet.
16
Design of a Moving-Coil Driver
7
MODIFYING THE DESIGNS
7.1
Introduction
Both types of non-linearity are important properties.
Design changes that improve the position nonlinearity may have an adverse effect on the current
non-linearity, and vice versa, so we require a
constraint on the relative magnitudes. For the
purpose of this project, the ratio of one type of nonlinearity to the other should not exceed 3:1.
In principle, it would be possible to improve the
designs by making random changes to the design
parameters and selecting the best results. However, a
better approach is to consider the origin of the nonlinearity and take appropriate counter-measures.
7.2
Current non-linearity
The origin of the current non-linearity is the variable
component of airgap flux that results from the coil
current, which aids or opposes the constant flux from
the permanent magnet. Making the variable
component of flux small in comparison with the
constant component will reduce the non-linearity.
The magnetic circuit concept gives a simple way of
deciding which parameters to change.
If the magnetic circuit has reluctance R, the
maximum flux from the coil is given by:
N I
(36)
φ cm = e m
R
where Ne is the effective number of coil turns linking
the magnetic circuit, and Im is the maximum coil
current. Reducing the coil depth dc will reduce the
value of Ne, and therefore reduce φcm, but this will
increase the position non-linearity. Increasing the
reluctance R will also reduce φcm. If the steel is
unsaturated, the reluctance is given by:
lg
d mm
R = R g + Rm =
+
μ0 Ag μ0 μr Am
(37)
lg
d mm
≈
+
μ0 Ag μ0 Am
where Rg is the reluctance of the airgap, Rm is the
reluctance of the permanent magnet, dmm is the depth
of the permanent magnet, and Ag and Am are the
corresponding cross-sectional areas. The value of μr
for ceramic or neodymium magnets is close to 1.
From equation 37, increasing the depth dmm of
the permanent magnet will increase the reluctance.
This change will also tend to increase the permanentmagnet flux φm. Increasing lg will not help because it
also affects the permanent-magnet flux φm.
With some designs, however, part of the centre
pole may be driven into saturation when the depth of
the permanent magnet is increased. The centre pole
then has significant reluctance, so equation 37 must
be modified:
R = Rg + Rm + R p ≈
lg
μ0 Ag
+
d mm
+ R p (38)
μ0 Am
where Rp is the reluctance of the centre pole. In this
case, saturation may have a beneficial effect on the
performance. Note, however, that the bottom plate
must be deep enough to avoid saturation. Although
saturation of this plate would increase the reluctance,
it would also increase the external magnetic field.
With a ceramic magnet, the area Am represents
the effective area of the top plate, not the permanentmagnet material, so altering the inner and outer radii
of the magnet will not change the value of Am.
7.3
Position non-linearity
As the example in section 6.3 has shown, the first
step towards reducing the position non-linearity is to
introduce an offset in the coil position that will make
the force/position characteristic symmetrical.
The position non-linearity has two sources: the
finite depth of the coil, and the fringing field above
and below the top plate of the magnet.
Increasing the coil depth dc will reduce the
position non-linearity, but it will tend to increase the
current non-linearity. To compensate for the increase
in coil resistance when dc is changed, the wire
diameter can be increased, but this may require an
increase the magnet airgap length.
The airgap length has only a limited effect on the
fringing field, so changing this length will not
usually make much difference to the position nonlinearity.
Section 7 – Modifying the Designs
7.4
Saturation
If the flux density in parts of the steel is too high, the
material will be saturated magnetically. This will
increase the reluctance of the magnetic circuit, and
therefore reduce the airgap flux. Electromagnetic
devices are normally designed to avoid saturation,
but saturation can be beneficial in reducing the
current non-linearity of the moving-coil driver if the
size of the magnet is increased to compensate for the
increased steel reluctance. See section 7.2.
Small regions of high flux density (above 1.8 T)
will probably have little effect. A simple way of
assessing whether saturation is significant is to set an
option in MagNet so that the solver treats each
material as linear, with a constant permeability equal
to the initial slope of the B/H characteristic. This is
equivalent to ignoring saturation in all parts of the
model. Proceed as follows.
1
Start MagNet and build the model as usual.
2
Copy the current solution results to a free part of
the Analysis sheet.
3
Click the Material Type button and select Linear.
4
Solve the model.
5
Compare the new values with the original values.
A large difference in the value of the transducer
constant indicates that saturation is significant.
6
Restore the non-linear solution option by
clicking the Material Type button again.
7.5
17
Ceramic magnet
Design for low cost
Open the workbook Driver Design Initial 2x, where x
is the last suffix letter used in section 4.2. Save the
file with the following file name:
Driver Design Low Cost 1a.xls
After each design change, save the file with a
different suffix: 1b, 1c, etc., so that it is always
possible to go back to a previous design change.
• All trial designs should have the position nonlinearity minimised by adjusting the coil position
offset. If necessary, increase the depth of the
centre pole.
• See whether there it is possible to reduce the
dimensions of any of the components, including
the depth of the centre pole, and still meet the
specification.
• If you change the magnet airgap length, ensure
that it is not less than the minimum value given
in cell G16 of the Design Sheet.
• Build and solve the ceramic model after each
design change.
When exploring design changes, you can speed up
the solution by using the Solution Accuracy button
on the Analysis sheet to change the adaption
tolerance from 0.5% to 1%, but it must be restored to
0.5% or less for the final results.
Note that the top and bottom plates do not
completely cover the magnet. If the plates are
extended to cover the magnet, the airgap flux will
decrease, with a resulting reduction in the G value.
However, the initial design does not necessarily have
the optimum plate size.
Although the non-linearity values are of
secondary importance when considering a low-cost
design, the average non-linearity should not be too
large. You can use the non-linearity to compare
alternative low-cost designs. Do not allow the ratio
of the non-linearity values to exceed 3:1.
With each successive design change, save a new
version of the workbook, and record the results in
your logbook.
Do not spend too long on the low-cost design at
this stage; the initial design is already quite a good
low-cost design.
18
Design of a Moving-Coil Driver
Design for high performance
Design for low cost
Start a new file series for the high performance
designs as follows. Open the workbook Driver
Design Initial 2x, where x is the last suffix letter used
in section 4.2. Save the file with the following file
name:
Driver Design High Perf 1a.xls
Try the strategies discussed in sections 7.2 to 7.4 for
reducing the non-linearity. A different number of
layers for the coil may help. To explore this option,
begin by following the initial design process with a
new magnet selected from the table in section 9.
Ensure that the magnet airgap length is not less than
the minimum value given in cell G16 of the Design
Sheet.
To compare different designs, use the average
non-linearity value as a figure of merit. Do not allow
the ratio of the non-linearity values to exceed 3:1.
In principle, it is possible to keep reducing the
non-linearity by increasing the magnet size. To set a
limit to this process, do not allow the cost to be
more than 2 times the cost of the initial design.
Start a new low-cost file series as follows. Open the
workbook Driver Design Low Cost 1x, where x is the
last suffix letter used for the low-cost ceramic
design. Save the file with the following file name:
7.6
NdFeB magnet
Design for high performance
Start a new high-performance file series as follows.
Open the workbook Driver Design High Perf 1x,
where x is the last suffix letter used for the highperformance ceramic design. Save the file with the
following file name:
Driver Design High Perf 2a.xls
Save new versions of the file as the work progresses.
The initial design should have a low current nonlinearity, but further work may be needed to improve
the position non-linearity. Begin by adjusting the coil
position offset, if necessary increasing the depth of
the centre pole.
If the ratio of position non-linearity to current
non-linearity is less than 3:1, this will be a
satisfactory high-performance design. Do not attempt
any further improvement at this stage, but go on to
the low-cost design.
If the ratio of position non-linearity to current
non-linearity is greater than 3:1, you will need to
make design changes that improve the position nonlinearity. As with the ceramic magnet, use the
average non-linearity value to compare different
designs. Do not allow the cost to be more than 1.5
times the cost of the initial design.
Driver Design Low Cost 2a.xls
Save new versions of the file as the work progresses.
To reduce the cost, it is necessary to reduce the
volume of expensive permanent-magnet material.
Try increasing the depth of the steel centre pole,
which will result in a corresponding reduction in the
depth of the permanent magnet. This will reduce the
magnet flux, so the driver may not meet the G
specification. It will be necessary to make other
changes such as increasing the radius of the centre
pole, with a corresponding change to the coil mean
radius. The coil depth may need to be adjusted to
meet the coil resistance specification.
As with the ceramic design, it may be worth
selecting a different number of layers for the coil.
Begin by following the initial design process with a
new magnet selected from the table in section 9.
To compare different designs with similar costs,
use the average non-linearity value as a figure of
merit. Do not allow the ratio of the non-linearity
values to exceed 3:1.
Aim for a cost which is no more than half of the
cost of the high-performance design, although it may
be difficult to achieve this with some driver
specifications.
Section 8 – Magnetic Shielding
8
MAGNETIC SHIELDING
8.2
8.1
Introduction
Workbook file
There is a significant external magnetic field around
a moving-coil driver with a simple ceramic magnet.
The external field can be greatly reduced by an
external steel shield together with a shield magnet,
which counteracts the external field of the main
magnet. Figure 4 shows the cross-section of this type
of shielded magnet, together with the key dimensions
of the shield components, and figure 5 shows the
corresponding magnetic flux plot.
lsc
lsg
dsm
rsmi
dsbp
Figure 4: Moving-coil driver: shielded magnet.
19
Modifying the workbook
Start a new low-cost file series as follows. Open the
workbook Driver Design Low Cost 2x, where x is the
last suffix letter used for the low-cost NdFeB design.
Save the file with the following file name:
Driver Design Low Cost 3a.xls
Save new versions of the file as the work progresses.
Design sheet
The Design sheet of the Excel workbook will need to
be completed for the shielded magnet, in a similar
way to the NdFeB magnet as described in section
3.3.
Initially the main part of the shielded magnet
will be identical to the ceramic magnet. Copy the
magnet data, coil data and coil calculation formulae
for the ceramic magnet to the corresponding columns
for the shielded magnet. If this is done correctly, the
numerical results should be identical. In a similar
way, the ceramic magnet calculations can be copied
to the shielded column.
Enter test data for the shield as follows:
•
Make the dimensions of the shield magnet the
same as those of the main magnet.
•
Use a value of 10 mm for the shield cylinder
radial gap lsg.
O
•
Use a value of 3 mm for the bottom plate depth
and the cylinder wall thickness.
Add formulae to calculate the mass and cost figures
for the shielded magnet. Check the results of these
formulae by hand calculation.
Analysis sheet
Figure 5: Shielded magnet flux plot.
The shield magnet is magnetised in the opposite
direction to the main magnet. Together with the steel
shield, its effect is to cancel the external field of the
main magnet, and to increase the flux crossing the
airgap.
In this example, the shield magnet is identical to
the main magnet. This reduces the manufacturing
cost, but it is unlikely to give the best performance.
In contrast to the unshielded design, the magnets do
not project beyond the top and bottom plates. Note
that the top of the shield cylinder is in line with the
upper surface of the main magnet top plate.
It is necessary to complete the Visual Basic
procedures for analysing the shielded design. The
instructions below give the outline of what is
required. Refer to the document An Introduction to
MagNet for Static 2D Modeling for background
information.
The sequence described below will develop the
new procedures for the shielded design by adapting
the procedures for the ceramic design. Initially, this
should produce exactly the same MagNet model,
with the same results in the spreadsheet. When this
part is working correctly, further changes can be
made to analyse the shielded design.
20
Design of a Moving-Coil Driver
Preliminary
Solving the shielded model
1
Begin by saving a new version of the workbook
file.
1
Select Excel and click Close MagNet.
2
Select Visual Basic.
2
In the Tools menu, click Macro and select Visual
Basic Editor.
3
3
Maximise the Visual Basic window and the code
window for Module 1.
Copy the contents of the SolveCeramic
subroutine to the incomplete SolveShielded
subroutine.
4
4
Scroll through the code, noting the following
points.
Change the test of the Model variable to use a
value of 3 instead of 1.
5
Change the call to SolveModel to put the results
in the correct column by changing CeramicCol to
ShieldCol.
6
Select Excel and test the subroutine as follows:
•
The Option Explicit statement means that all
variables must be declared.
•
Constants are set at the start of the module to
specify the rows and columns used in the
worksheets for data and results.
•
Click Start MagNet.
•
Global variables are declared with Dim
statements at the start of the module.
•
Click Build Shielded
•
Click Solve Shielded.
•
The first 11 subroutines are public
subroutines, linked to buttons in the Analysis
sheet.
•
The model should be solved and results
displayed in column D.
•
Of these subroutines, the first five control
the operation of MagNet.
•
Check that the results are the same as for the
ceramic model.
•
The next four call other subroutines to build
and solve the ceramic and NdFeB models.
•
The subroutines BuildShielded and
SolveShielded are incomplete.
Building the shielded model – 2
The next stage is to get data from the correct column
in the Analysis sheet.
1
Click Close MagNet and select Visual Basic.
2
In the BuildShielded subroutine, change the call to
GetCoilData to get the data from the correct
column by changing CeramicCol to ShieldCol.
Building the shielded model – 1
3
The first stage is to build a duplicate of the ceramic
model.
In the BuildShielded subroutine, change the
statement GetCeramicData to GetShieldedData.
4
Copy the contents of the GetCeramicData
subroutine to the incomplete GetShieldedData
subroutine.
5
Make the following changes to the copy:
5
1
Study the BuildCeramic subroutine, and see how
each component is constructed by calling the
private subroutine BuildComponent.
Copy the contents of the BuildCeramic
subroutine to the incomplete BuildShielded
subroutine.
2
Change the last statement from Model = 1 to
Model = 3.
3
Select Excel and test the subroutine as follows:
•
Start MagNet and make it visible.
•
Click Build Shielded.
•
Select MagNet, and check that the model is
the same as the ceramic model.
•
6
Change all the column references from
CeramicCol to ShieldCol.
Select Excel and test the subroutine as follows:
•
Click Build Shielded and then Solve
Shielded.
•
If the values for the main magnet in column
D of the Design sheet are the same as for the
ceramic magnet in column B, the results in
the Analysis sheet should be the same.
•
Reduce the outer radius of the main magnet
in column D of the Design Sheet to match
the top and bottom plates, and check that the
model is changed when you click Build
Shielded in the Analysis Sheet.
Section 8 – Magnetic Shielding
Building the shielded model – 3
Debugging
The final stage is to get data for the shield
components and add them to the model.
It is likely that there will be errors at some stage,
particularly the last. A Visual Basic error may
produce a dialog box similar to this:
1
Select Excel, click Close MagNet, and select
Visual Basic.
2
At the beginning of the module, add a Dim
statement after the comment line to declare
variables for the data and dimensions of the
shield components.
•
3
See the text in the Analysis sheet for suitable
variable names.
In the GetShieldedData subroutine, add
statements to get the data for the shield
components from the Analysis sheet.
4
In the GetShieldedData subroutine, add
statements to calculate the dimensions of the
shield components.
5
In the BuildShielded subroutine, add new calls to
BuildComponent that will build the new
components.
•
•
6
21
The parameters of BuildComponent are
defined as follows:
BuildComponent(Offset, Inner, Outer,
Depth, Name, Material, Direction)
Offset: the distance of the top of the
component below the x-axis.
Inner: the inner radius of the component.
Outer: the outer radius of the component.
Depth: the axial depth of the component.
Name: the name of the component.
Material: the name of the material of the
component.
Direction: this specifies the magnetisation
direction, with one of the following values: 0
for a non-magnetic material, 1 for the
positive direction, –1 for the negative
direction.
Use the variable name CeramicMat for the
name of the material for the permanent
magnet.
•
The direction of magnetisation of the shield
magnet must be the reverse of the main
magnet, so the last parameter must be 1
instead of –1 for this component.
•
All components must have different names.
Select Excel and test the subroutines.
If this happens, proceed as follows.
1
Click Debug.
This should take you to the line in the Visual
Basic code where the error occurred.
2
Identify the source of the error, and correct it.
3
Press F5 to continue.
If there are no Visual Basic errors, but the model is
not built or solved correctly, the mistakes may be
hard to find. A useful technique is to single-step
through the Visual Basic code:
1
Start MagNet and make it visible.
2
Select the Visual Basic editor, and place the
insertion point anywhere in the subroutine
BuildShielded.
3
Press F8.
This will begin single-step debugging, where the
program code is executed one line at a time.
4
Press F8 repeatedly until you reach a line of code
that you want to examine.
5
Inspect the value of any variable by pausing the
mouse pointer over the variable name.
6
Continue single-stepping and inspecting variable
values as required.
7
Press F5 to continue running the program.
22
Design of a Moving-Coil Driver
8.3
Designing the shielded
magnet
9
Design for low cost
Save the modified Excel workbook with the
following file name:
Driver Design Low Cost 3x.xls
where x is the next suffix letter in sequence after the
workbook modifications. Save new versions of the
file as the work progresses.
The low-cost ceramic design has already been
used for developing the shielded parts of the
workbook. This is a suitable starting point for the
low-cost shielded design.
Experiment with the dimensions of the shield
magnet, and the dimensions of the steel shield, to
achieve the following:
Select the Analysis sheet, then:
•
Start MagNet
•
Build and solve the ceramic design
•
Build and solve the NdFeB design
10 Save the modified workbook.
At the end of this sequence, the workbook named
Driver Design High Perf 3a should contain the
Visual Basic procedures for the shielded design,
together with the data and results for (a) the highperformance ceramic and NdFeB designs, (b) the
low-cost shielded design.
Modify the magnet and coil dimensions, using
the high-performance ceramic design as a guide, and
make corresponding changes to the shield
components. Work on the design to achieve the
following:
•
An external magnetic field comparable with the
value in the NdFeB design.
•
A low value for the average non-linearity, with a
ratio of not more than 3:1 in the two types of
non-linearity.
It may be necessary to alter the coil position offset to
minimise the position non-linearity. The main
magnet dimensions will also need to be changed if
the value of the transducer constant is outside the
permitted range.
•
A total cost that is not more than 3 times the cost
for the low-cost shielded design.
Design for high performance
The workbooks Driver Design Low Cost 3x and
Driver Design High Perf 3y should now contain the
latest designs for all three magnets: ceramic, NdFeB
and shielded. Compare these designs, and see
whether any further design improvement can be
achieved.
•
External magnetic field comparable with the
value in the NdFeB design.
•
Minimum total cost.
It is necessary to merge two workbook files to start a
new high-performance file series. Proceed as
follows.
1
Open the workbook Driver Design Low Cost 3x,
where x is the last suffix letter used above.
2
Save this file with a new name:
Driver Design High Perf 3a
3
Open the workbook Driver Design High Perf 2y,
were y is the last suffix letter used for the high
performance NdFeB design.
4
Select the Design sheet in this workbook.
5
Select all the coil and magnet data cells in this
sheet: the range B16 to C32.
6
Copy the contents to the clipboard by pressing
Ctrl+C.
7
In the Window menu, click
Driver Design High Perf 3a.
8
Select the Design sheet, then:
•
Select cell B16.
•
Press Ctrl+V to insert the copied cells.
8.4
Design refinement
Section 9 – Magnet Data
9
MAGNET DATA
9.1
Ceramic magnet data
23
Airgap flux (μWb)
Airgap length (mm)
Coil mean radius (mm)
Centre pole radius (mm)
Centre pole depth (mm)
Top plate inner radius (mm)
Top plate outer radius (mm)
Top plate depth (mm)
Bottom plate radius (mm)
Bottom plate depth (mm)
Magnet inner radius (mm)
Magnet outer radius (mm)
Magnet depth (mm)
612
3
12.5
11
20
14
41
6
41
6
21
45
14
698
3
14.5
13
20
16
43
6
43
6
23
47
14
776
3
16.5
15
20
18
45
6
45
6
25
49
14
851
3
18.5
17
20
20
47
6
47
6
27
51
14
923
3
20.5
19
20
22
49
6
49
6
29
53
14
1155
3
22.5
21
20
24
51
6
51
6
31
55
14
633
3
11.5
10
30
13
40
6
40
6
20
44
24
826
3
13.5
12
30
15
42
6
42
6
22
46
24
962
3
15.5
14
30
17
44
6
44
6
24
48
24
1071
3
17.5
16
30
19
46
6
46
6
26
50
24
1141
3
19.5
18
30
21
48
6
48
6
28
52
24
1264
3
21.5
20
30
23
50
6
50
8
30
54
24
Airgap flux (μWb)
Airgap length (mm)
Coil mean radius (mm)
Centre pole radius (mm)
Centre pole depth (mm)
Top plate inner radius (mm)
Top plate outer radius (mm)
Top plate depth (mm)
Bottom plate radius (mm)
Bottom plate depth (mm)
Magnet inner radius (mm)
Magnet outer radius (mm)
Magnet depth (mm)
626
4
15
13
20
17
43
6
43
6
23
47
14
696
4
17
15
20
19
45
6
45
6
25
49
14
763
4
19
17
20
21
47
6
47
6
27
51
14
827
4
21
19
20
23
49
6
49
6
29
53
14
892
4
23
21
20
25
51
6
51
6
31
55
14
955
4
25
23
20
27
53
6
53
6
33
57
14
616
4
12
10
30
14
40
6
40
6
20
44
24
782
4
14
12
30
16
42
6
42
6
22
46
24
898
4
16
14
30
18
44
6
44
6
24
48
24
995
4
18
16
30
20
46
6
46
6
26
50
24
1086
4
20
18
30
22
48
6
48
6
28
52
24
1173
4
22
20
30
24
50
6
50
6
30
54
24
Airgap flux (μWb)
Airgap length (mm)
Coil mean radius (mm)
Centre pole radius (mm)
Centre pole depth (mm)
Top plate inner radius (mm)
Top plate outer radius (mm)
Top plate depth (mm)
Bottom plate radius (mm)
Bottom plate depth (mm)
Magnet inner radius (mm)
Magnet outer radius (mm)
Magnet depth (mm)
602
6
14
11
25
17
41
6
41
6
21
45
19
688
6
16
13
25
19
43
6
43
6
23
47
19
764
6
18
15
25
21
45
6
45
6
25
49
19
837
6
20
17
25
23
47
6
47
6
27
51
19
908
6
22
19
25
25
49
6
49
6
29
53
19
976
6
24
21
25
27
51
6
51
6
31
55
19
627
6
13
10
35
16
40
6
40
6
20
44
29
789
6
15
12
35
18
42
6
42
6
22
46
29
907
6
17
14
35
20
44
6
44
6
24
48
29
1008
6
19
16
35
22
46
6
46
6
26
50
29
1102
6
21
18
35
24
48
6
48
6
28
52
29
1186
6
23
20
35
26
50
6
50
8
30
54
29
23
24
9.2
Design of a Moving-Coil Driver
NdFeB magnet data
Airgap flux (μWb)
Airgap length (mm)
Coil mean radius (mm)
Centre pole radius (mm)
Total centre pole depth (mm)
Steel centre pole depth (mm)
Top plate inner radius (mm)
Top plate outer radius (mm)
Top plate depth (mm)
Bottom plate radius (mm)
Bottom plate depth (mm)
Magnet radius (mm)
Magnet depth (mm)
Cylinder inner radius (mm)
Cylinder outer radius (mm)
Cylinder depth (mm)
590
3
15.5
14
20
6
17
31
6
31
6
14
14
27
31
14
670
3
16.5
15
20
6
18
32
6
32
6
15
14
28
32
14
753
3
17.5
16
20
6
19
33
6
33
6
16
14
29
33
14
840
3
18.5
17
20
6
20
34
6
34
6
17
14
30
34
14
930
3
19.5
18
20
6
21
35
6
35
6
18
14
31
35
14
1024
3
20.5
19
20
6
22
36
6
36
6
19
14
32
36
14
648
3
15.5
14
30
6
17
31
6
31
6
14
24
27
31
24
831
3
17.5
16
30
6
19
33
6
33
6
16
24
29
33
24
931
3
18.5
17
30
6
20
34
6
34
6
17
24
30
34
24
1035
3
19.5
18
30
6
21
35
6
35
6
18
24
31
35
24
1145
3
20.5
19
30
6
22
36
6
36
6
19
24
32
36
24
1258
3
21.5
20
30
6
23
37
6
37
6
20
24
33
37
24
Airgap flux (μWb)
Airgap length (mm)
Coil mean radius (mm)
Centre pole radius (mm)
Total centre pole depth (mm)
Steel centre pole depth (mm)
Top plate inner radius (mm)
Top plate outer radius (mm)
Top plate depth (mm)
Bottom plate radius (mm)
Bottom plate depth (mm)
Magnet radius (mm)
Magnet depth (mm)
Cylinder inner radius (mm)
Cylinder outer radius (mm)
Cylinder depth (mm)
571
4
16
14
20
6
20
31
6
31
6
14
14
27
31
14
646
4
17
15
20
6
19
32
6
32
6
15
14
28
32
14
724
4
18
16
20
6
20
33
6
33
6
16
14
29
33
14
805
4
19
17
20
6
21
34
6
34
6
17
14
30
34
14
890
4
20
18
20
6
22
35
6
35
6
18
14
31
35
14
976
4
21
19
20
6
23
36
6
36
6
19
14
32
36
14
635
4
16
14
30
6
18
31
6
31
6
14
24
27
31
24
785
4
18
16
30
6
20
33
6
33
6
16
24
29
33
24
913
4
19
17
30
6
21
34
6
34
6
17
24
30
34
24
1011
4
20
18
30
6
22
35
6
35
6
18
24
31
35
24
1118
4
21
19
30
6
23
36
6
36
6
19
24
32
36
24
1225
4
22
20
30
6
24
37
6
37
8
20
24
33
37
24
Airgap flux (μWb)
Airgap length (mm)
Coil mean radius (mm)
Centre pole radius (mm)
Total centre pole depth (mm)
Steel centre pole depth (mm)
Top plate inner radius (mm)
Top plate outer radius (mm)
Top plate depth (mm)
Bottom plate radius (mm)
Bottom plate depth (mm)
Magnet radius (mm)
Magnet depth (mm)
Cylinder inner radius (mm)
Cylinder outer radius (mm)
Cylinder depth (mm)
603
6
17
14
25
6
20
31
6
31
6
14
19
27
31
19
682
6
18
15
25
6
21
32
6
32
6
15
19
28
32
19
765
6
19
16
25
6
22
33
6
33
6
16
19
29
33
19
852
6
20
17
25
6
23
34
6
34
6
17
19
30
34
19
942
6
21
18
25
6
24
35
6
35
6
18
19
31
35
19
1033
6
22
19
25
6
25
36
6
36
6
19
19
32
36
19
649
6
17
14
35
6
20
31
6
31
6
14
29
27
31
29
741
6
18
15
35
6
21
32
6
32
6
15
29
28
32
29
934
6
20
17
35
6
23
34
6
34
6
17
29
30
34
29
994
6
21
18
35
6
24
35
6
35
6
18
29
31
35
29
1140
6
22
19
35
6
25
36
6
36
6
19
29
32
36
29
1256
6
23
20
35
6
26
37
6
37
6
20
29
33
37
29
J D Edwards
10 March 2006
Edp0506GuideExport_LtrSize.doc
Revision 1