Tailoring of Pole Shapes of Multipolar Injection Molded Magnets

Transcription

• Overview Injection Molded Magnets
• Origins of Fields around Permanent Magnets
• Basic Configurations
• Realization for Injection Molded Magnets
• Remarks about Design
Tailoring of Pole Shapes of Multipolar Injection Molded Magnets, Magnetics 2016, Jacksonville, FL
Thomas Schliesch, Head of Research and Development, Email: [email protected]
1
Manufacturing: Magnetic Compounds
Compounds:
- Magnetic powder
(0.1µm-200µm)
(40-70% vol.)
- Polymer
- Additives
Polymers:
- Thermoplastic resins
- Thermoplastic elastomers
- Elastomers
- Duroplastic resins
Manufacturing methods:
- Classical injection molding
- Injection molding of duroplastic
resins and elastomers
Magnetic materials:
- Ferrites
- NdFeB
- SmCo
- SmFeN
- Alnico
2
Manufacturing: Injection Molding
Classical injection molding
High grade of automatization
Overmolding, multi-component systems
Testing and packing at injection molding machine
3
Injection Molding: Field Orientation Inside Mold
Magnetic Compound
50-70 Vol % magnet powder
+ thermoplastic resin + additives
Melting
cylinder temperature 250°C- 350°C
Injection and Magnetization
mold temperature 70°C-140°C
80 kA/m <~ H´ <~ 1000 kA/m
Cooling and Ejection
Remark: Majority of magnetic materials
are still Ferrites. Ferrites usually get their
final magnetization in the mold by the
orienting field and do not need a pulse
magnetizing process in most cases.
Standard multipolar assembly for pole orientation with permanent
magnets and tool for injection molding
4
Magnetization by Pulse Discharge Process
Circumferential
magnetization
Magnetizing coil for axial-lateral magnetization
5
Derivation of Permanent Magnetic Fields from Maxwell Equations
Maxwell equation, divergence free B-field
 
B  0
(1)

  
 : ( , , )
x y z
Constitutive relation for magnetic material

 
B  μ 0 (H  M)
Nabla operator
2
2
2
 : 2  2  2
x
y
z
(2)
Laplace operator
(1) and (2) lead to:
 
 
  H    M
(3)
On the other hand in a permanent magnet neither macroscopic currents nor time varying
electric polarizations play a role. Using Amperes law then reveals:

   D
H  j 
0
t
(4)
=>

H  Φ
(5)
(Curl free vectors can be expressed as gradients of scalar potentials.) Eq. (3) and (5) lead to:
=>
 
ΔΦ    M
(6)
Poisson Equation
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Origins of Permanent Magnetic Fields
By solving Poisson eq. (6) together with (5) we get a general formula for the fields of permanent
magnets (derivation can be seen in many textbooks):
 '
' 
 


1
Mn
1
 M
H( r )       ' dA '      ' dV '
4π A r  r
4π V r  r
Permanent magnets originate
magnetic fields by:
- Polarization vectors at
pole faces
- Sources or sinks of
polarization inside
magnetic body
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Basic Configurations for Multipolar Cylinders: Homogeneous Poles
Field sources: External pole faces only
(faces inside cancel mutually)
Realizable by:
-assemblies of single magnets only
Radial field at 1 mm radial distance from 8 pole cylinder with inner diameter 20mm, outer diameter 40mm,
axial length 10mm, remanent flux density 400mT.
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Basic Configurations: Radially Magnetized Poles
  1
  M  Mr
r
Field sources: External pole faces as
well as sources of magnetization
div(M)>0
Realizable by:
-assemblies of single magnets
-injection molded magnets
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Basic Configurations: Convergent Magnetization
Field sources: Outer pole faces as
well as sinks of magnetization
along pole center, div(M)<0
Realizable by:
10
Basic Configurations: Divergent Magnetization
Field sources: Outer pole faces as
well as sources of magnetization
along pole center, div(M)>0
Realizable by:
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Basic Configurations: Halbach Magnetization
Field sources: Outer pole faces
as well as div(M)<0
Realizable by:
- assemblies of single magnets
- injection molded anisotropic
magnets
- all sorts of isotropic magnets
M x  M r cos(j(   0 ))
M y  M r sin(j(   0 ))
j  2,3,4,5....  n p  2,4,6,8...
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Basic Configurations for Multipolar Cylinders - Radial Fields
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Orienting and Magnetizing by Alternating Fields Inside Mold
Example: Standard assembly for 8-pole magnet, cavity diameter 40mm. Bars of sintered rare earth magnets of
width 12mm originate magnetic fields inside cavity, radial component of H being shown here.
14
Orienting and Magnetizing by Alternating External Fields
In contradiction to idealized models there
is not a complete saturation due to the
finite strength of external fields at high
distances from their origin
At a first glance magnetization looks
Halbach-like but fields outside the magnet
(1mm distance) show deviations from
ideal sinusoidal shape
Distribution of M can be influenced by: Width and
shape of sintered bar magnets, core material as well
as direction of magnetization of field sources
15
Attempts to Get Fields with Improved Sinusoidal Shape
(e.g. for Sensor Systems)
Decrease of bar width being too large
(7mm)
Medium decrease of bar width
(to 9.8mm) and slight increase of
radial bar distance (increase of bush
thickness). Results are better in
respect to sinusoidal shape, but still are
not perfect
16
Attempts to Get a Radial Field with Improved Trapezoidal Shape
by Changing Inner Diameter and Core Material
Trapezoidal shape can be of advantage
e.g. for motor magnets
Reduced radial thickness and use of
soft magnetic core material increases
rectangularity of radial fields.
(Additional rectangularity could be provided
by increased width of bar magnets around
cavity, not done here.)
17
Measurement of Rotation Angles with Hall Sensors
  atan2(
B tan
)  0
Brad
 b  atan2(
B tan /B t0
)  0
Brad /B r0
Real field angle
Balanced amplitudes
18
Measurement of Rotation Angles with Hall Sensors
19
Impact of Pole Shapes on Angular Error
Field amplitudes balanced
20
Other Configurations: Convergent Magnetization
in Injection Molded Magnets
21
Other Configurations: Divergent Magnetization
in Injection Molded Magnets
22
Design Method for Pole Oriented Magnets
Virgin curve at T
Virgin curve and demagnetization
curves at injection temperature
derived from experimental data
below
H´
FEM analysis injection molding tool
=> H´
Br, µr
M || H´
Experimental data of magnetic compound under varying homogenous fields
T.Schliesch, Calculation of parameter distributions in anisotropic
Model for parameter distribution bonded magnets with ANSYS®-EMAG, 16. CADFEM Users‘ Meeting,
Bad-Neuenahr, Germany, 1998, in German (Method used since 1993)
23
Injection Molded Halbach-Magnet with 4 Poles
FEM-Simulation Compared to Measurements
Diameter 40mm -> Pole Size 31mm !
24
Pulse Magnetization of a 4 Pole Isotropic Rotor Magnet
Trapezoidal Version
Parameters that influence shape
of poles:
- Tangential distance between wire
bundles/thickness of wire bundles
- Number of wires and current
- Radial distance to magnets surface
(bushing)
- Core material (soft magnetic or
non magnetic, laminated or non
laminated)
Eddy current density in pulse coil when core is not laminated
H(t) inside magnet as function at different locations
25
Pulse Magnetization of a 4 Pole Isotropic Rotor Magnet
Sinusoidal Version
Large Bundles of wires, increased distance to magnet, right choice of materials, laminated steel core
26
Comparison of Predicted Trapezoidal and Sinusoidal Field
Diameter of magnet 19mm, radial distance 0.35mm
27
FEM Prediction and Measured Field of Manufactured Trapezoidal
Rotor Magnet
Surface flux density at realized trapezoidal version with large mutual distance of wire bundles
28
Design Method for Pulse Magnetized Magnets
Electric circuit of magnetizer
Calculation of M and µr distribution
in the magnet at field maximum,
M || H in case of isotropic materials
coupled, stepwise solution of
the time transient problem
Mr
Mφ
N.Nakata, N. Takahashi, Numerical Analysis of Transient Magnetic
Field in a Capacitor-Discharge Impulse Magnetizer, IEEE
Transactions on Magnetics, Vol.22, No.5, p.526, 1986
29
Thank you for your attention !
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Tailoring of Pole Shapes of Multipolar Injection Molded Magnets

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