Comparative Study and Electromagnetic Analysis of a Moving Magnet Linear Motor
Rajesh V R, Biju T Kuzhiveli
8-P1-39
Centre for Advanced Studies in Cryogenics (CASC)
Dept. of Mechanical Engg., National Institute of Technology Calicut
Kerala, India – 673 601.
Stirling coolers typically have a dual piston linear compressor and an
expander, which connects to the cold space. But when the temperature
requirement is too low, single stage cooler may not be sufficient. In
such cases, a two stage cooler has an upper hand over the
conventional single stage counter part. The reciprocating motion of the
pistons of the linear compressor gives the adequate pressure pulses to
drive the working gas and thereby the expander. The cooling capacity
in the displacer’s expansion space is generated by the motion of the
displacer and the pressure wave. Therefore, the dynamic
characteristics of the linear compressor’s pistons and displacer have a
strong effect on the thermodynamic performance of the refrigerator.
This paper explores the possibility of employing a radially energized
moving magnet motor for a compact cooler running on reversed Stirling
cycle. The design and analysis are performed to meet the constraints
such as compact size, limited availability of permanent magnet and
minimum overall weight.
The permanent magnets are used instead of dc windings to provide a
constant magnetic flux field. The inner iron provides the flux return
path. When current is applied to the circumferentially wound coil, it
interacts with the radial magnetic field of the permanent magnet
assembly as per the Lorentz Force Principle to create an axial force
(i.e., mutually perpendicular to the vectors of the current flow and the
magnetic field) between the coil and magnet assemblies.
The physical dimension of PM and air gap give the exact value of flux
density.The magnetic field in the air gap is the superposed fields of the
PM and the exciting coil. A PM is characterized by its demagnetisation
curve or second quadrant property. In the case of Nd-Fe-B PM, it is
almost linear, and can be expressed as a linear function,
B
HBr
 Br
Hc
The axial symmetry of the motor helps in modelling: the 2-D model in
cylindrical co-ordinates would serve the purpose. Finite element
method helps realize both the analysis and optimal design of the
magnetic field distribution and the accurate calculation of the
parameters of the electromagnetic force. The performance of the
designed model is evaluated using the results obtained.
Coil
Inner
Yoke
Bobbin
Axis of
Symmetry
Cross-section of Motor with
Single Magnet ring
Fig. 1
Constraints for design
1. Available Permanent Magnet and its dimensions (supply is
limited to strategic applications)
2. Outer diameter limit
3. Stroke length
4. Overall mass of the system
Various configurations are modeled by varying the position of the
permanent magnet with respect to the yoke teeth and the coil
winding.
ICEC26-ICMC2016, March 7-11,2016, Manekshaw Centre, New Delhi, India
Poster template by ResearchPosters.co.za
30mm PM
60
40
20
0
-10
-8
-6
-4
-2
0
x(mm)
2
4
6
8
10
Force vs. Air Gap
160
140
120
100
80
60
40
20
0
0.25
0.5
0.75
1
1.25
air gap (mm)
1.5
1.75
2
2.25
Force (N)
40
30
20
10
0
Results & Discussion
Analysis of Magnetic Field Distribution and Flux Density
The performance of the motor is influenced by the air-gap flux density,
magnet volume and the current density of the coil. Also the material of
permanent magnet and yokes play an important role in the flux density.
The magnetic flux distribution for various geometries of the motor at the
balanced position (PM is at “0 stroke” position) is shown in the Figure 2
2.5
3
3.5
4
PM thickness (mm)
4.5
5
5.5
• The magnet thickness chiefly affects the Z-direction force
• Generally the force can be gradually increased with the increase of
the magnet thickness
• But the increase in magnet thickness increases the overall weight
of the system
• Also the increase of the magnet mass leads to the gradual
decrease of the dynamic response and further cripples the
performance of the cryocooler
Conclusion
• The work highlights the necessity of electromagnetic analysis in
the design of a linear motor for the use in a cryocooler
• The effect of various geometric and electromagnetic parameters
on the performance can be clearly understood from the analysis
• The FEA ends up with the sufficient results for the selection of
components in the design of a linear motor
Working
Moving magnet configuration is chosen as it meets the necessary
requirements such as less space utilization, less magnet volume
and high reliability. Also, as the moving magnet does not contact
any of the motor's stationary elements, so there is none of the
frictional wear associated with.
40mm PM
80
50
Features

The stator envelopes the outer yoke, the coil and the inner yoke

Mover includes the magnet

Small effective air gap helps achieving high air gap flux density
Design
100
60
Cross-section of Motor with Two
Magnet rings
When ac is provided to the coil winding, the alternating
electromagnetic field that the current produced interacts with the
constant magnetic field produced by the magnet. This produces a
force in the axial direction, that drives the mover (the magnet
assembly) back and forth continuously, together with the
connecting part, which can move the piston.
120
Force vs. Magnet thickness
Classification of Linear Motor
Magnet
140
• When the air gap increases, leakage flux increases rapidly and as
a result of that the force generated decreases
– This is because the reduction in the useful flux
Linear Motor
Outer Yoke
Electromagnetic force generated at different magnet positions
Parametric analysis and optimal design are performed based on
Maxwell Ansoft (V14).
The linear Stirling cryocoolers are directly driven by linear motors and
the latter forms an integral part of the cooler. Therefore, the motor
behavior has a very good impact on the performance of the motor.
A recent trend in linear motor technology is to adopt moving magnet
linear motors (MMLMs) instead of conventional moving coil motor. In a
MMLM, the magnet assembly moves while the winding part is
stationary. This type of motor has high reliability and long life, makes it
suitable for space and remote applications.
In the present design, radially energized permanent magnet rings (NdFe-B) are selected.
Linear motors can be classified according to many factors or features.
Here the different types are identified based on the way in which
magnets and coil winding are arranged relative to one another.
Results & Discussion
F(N)
Compared to moving coil linear motor, moving magnet type offers
numerous advantages such as less magnet volume, good thermal
dissipation characteristics of the coil windings etc. A recent tendency is
to replace the moving coil type motor with moving magnet type motor
for the compressor.
Electromagnetic Analysis
F(N)
Introduction
Stirling cycle cryocoolers are widely employed in applications where
compact size, less weight and long maintenance-free operating life are
critical performance requirements. Deployment of unique linear drive
mechanism in Stirling cryocooler makes them most attractive for space
and military applications because of high reliability over extended
periods.
Extreme End
In Between
Fig. 2
Balanced Position
• The force generated is different for different positions of the magnet.
• This is because of the difference in the superposed field distribution
of magnet and the current carrying coil
• The figure also shows the force generated at different magnet
positions for two different permanent magnets.
• As it can be seen that the 40 mm magnet produces more force, but
the trend of variation is the same (But it can increase the weight of
the system, which is not advantageous from the application point of
view)
• Also, it is observed that the saturation flux in the inner yoke is more
for 40 mm long permanent magnet
• The peak value of electromagnetic force is reached, when the
magnet is on/near the balanced position
• When the magnet moves away from the balanced position, the
interaction of the magnetic fields (of coil and magnet) varies and
hence the force also reduces
• It is also observed that based on the direction of current supply in
the coil, the force variation also changes
• The rare-earth magnets selected are very light in weight with
highest energy product available, and hence this cooler is most
suitable for weight sensitive applications such as in remote
sensing and space science
• With the design curves produced, it is easier to design the linear
motor system and to understand the performance
References
S.A.Nasar (2002), Electric Machines and Power Systems, Tata
McGraw-Hill edition
R. Z. Unger, N. van der Walt (1996), “Linear compressors for nonCFC refrigeration”, Int. Appliance Technical Conference, Purdue
University, Indiana.
Eero Byckling and Kari Perkio (1980), “Dynamic Properties of
Moving Magnet Transducers”, IEEE transactions on magnetics
Berchowitz D.M. (1992), Free-piston Stirling coolers, International
Refrigeration and Air Conditioning Conference, Purdue University,
paper 171, pp 327-336.
Deuk-Yong Koh, Yong-Ju Hong, Seong-Je Park, Hyo-Bong Kim,
Kwan-Soo Lee (2002), A study on the linear compressor
characteristics of the Stirling cryocooler, Cryogenics, vol.42, pp 427432.
SESSION: TUESDAY, March 08, 2016 :: 14:15 – 15:45