A Summary of Twenty Years Experience with Linear Motors and Alternators
Robert Redlich
Sunpower, Inc.
Athens, Ohio, U.S.A.
Copyright © Sunpower, Inc. 1996
Sunpower, Inc., Athens, Ohio, U.S.A., has been developing linear motion Stirling machines and linear compressors for over twenty years, and during this time has carried out extensive analysis, development and experimentation concerning linear motors and alternators. Moving coil, moving iron, and various moving magnet configurations were tried. All but one were eventually abandoned, usually because of effects which were either unknown or regarded as unimportant at the outset, but proved disqualifying in practice. Following is a summaryof Sunpower's experience with and assessment of the common types of linear motor-alternators.
Moving Coil
A typical application and analysis is given in Ref. 1. Moving coil motor-alternators (Figure 1) are easy to understand and analyze, and were in fact the first type used at Sunpower, with the then relatively new Samarium Cobalt magnets as a source of field. They were soon abandoned in favor of other types because, as analysis shows and experience confirms, the magnet volume required to generate the field of a moving coil machine is many times greater than that of a moving magnet machine of the same power and efficiency. Since magnets are by far the most expensive constituent of either type, moving coil machines are only suitable for price insensitive applications.
Fig. 1. An example of a moving coil alternator. Figure 1 from Ref. 1.
Another troublesome but not insurmountable difficulty with moving coil motor-alternators is their need for sliding or flexing contacts to the coil.
One clear advantage of the moving coil type is absence of radial forces,open circuit axial forces, and torques on the moving coil. Such effects are very important in linear machines. Radial forces due to misalignment are presentin some other types and can overwhelm gas bearings or even oil bearings and lead to lossy operation or failure.
Moving Iron
Several types were tried in an effort to eliminate costly magnets. Fieldwas generated by a winding and the moving iron functioned by channelling flux through or around an armature winding. These efforts were discontinued because of an unforeseen and disabling effect. It was found that the moving iron was rotationally unstable in its air gap. If tilted, it tended to tilt further and close the gap, acting like a negative torsion spring with such a high spring constant that it defeated all attempts at stabilization by better initial alignment and greater mechanical rigidity.
Moving Magnet
These come in several configurations, distinguished from each other by presence or absence of moving iron, number of magnets per armature coil, whether the moving magnet leaves the air gap partly or entirely during any part of the motion cycle, and orientation of the plane of the iron laminations.
Radial laminations
Fig. 2. An example of a moving magnet alternator with radial laminations.
Adapted from Figure 1, Ref. 3.
An early example of this type is described in Ref. 2 (Figure 2). A nominally 25 kW version of such a machine, using one armature coil and four magnets of alternating polarity, was built (not by Sunpower) and found to fall far short of predicted efficiency. The cause of excessive loss was isolated and corrected (Ref. 3), but the required correction itself is a substantial constraint onthe use of such machines. It was found that, because one of the four magnets was entirely out of the air gap at each extreme of motion, strong, long range alternating fringing fields existed which induced serious eddy current lossin both stationary and moving metallic structure around the machine. The cure was careful selection and placement of all conducting materials in the vicinityof the motor-alternator. The only certain test of whether such measures are successful requires a dynamometer, since analytic methods or finite element analyses are difficult and uncertain because of complicated boundary conditions, non-linear permeability, very low skin depths in critical ferromagnetic material, etc. Losses of this type are akin to eddy current braking and occur whenever the magnets move, regardless of whether there is armature current.
Another configuration in which the endmost magnets emerge from the air gap in which they move axially is disclosed in Ref. 4. It too is vulnerable to eddy current losses in surrounding structure.
Another less serious drawback to the configurations of Refs. 2 and 4 is that they are non-linear in the sense that for an alternator, the induced voltage per unit of magnet velocity is not a constant but depends on magnet location because of complicated fringing that changes during the motion cycle. Non-linearity makes analysis of a complete electromechanical system difficult to carry out and to generalize. For a motor, the force on the magnets per unit of armature current is not constant but depends on magnet position.
Even with no armature current, axial forces are exerted on the magnets of these configuration at all uncentered magnet locations, as a result of interaction of magnets and iron structure. The forces are conservative, that is, absorb no energy over a complete cycle. Their prediction requires fringing field computation, and they are strong enough to significantly alter system dynamics.
The configuration of Ref. 2 has moving iron as well as moving magnets, and is therefore subject to side forces and to torques resulting from misalignment.
Axially Stacked Laminations
Most linear motor-alternators will be symmetric around the axis of reciprocation. The field in axially symmetric machines as described in Refs. 2 and 4 lies in planes passing through the symmetry axis. To minimize eddy currents, the iron structure should be laminated to have low circumferential conductivity, which, for a solid structure, implies tapered radial laminations. Although such laminations were actually used in the experimental machine described in Ref. 3, they are too costly for most applications. The alternative commonly used is stacks of laminations oriented like spokes of a wheel fanning out from a cylindrical air gap. The practical problems of fabricating such a structure and holding it together have been one motivation for other configurations in which the entire iron structure is a single stack of identical laminations, as in rotary machines. One of these, in which the magnets move perpendicular to the plane of the laminations, is described in Ref. 5 (Figure 3), and another whose magnets move parallel to the lamination plane, in Ref. 6 (Figure 4). In both, the magnets emerge from the air gap. Surroundings must therefore be carefully controlled to prevent high eddy current loss in them. Both machines are non-linear, and both will generate axial magnetic forces even with no armature current. The machine of Ref. 5 has strong time varying fringing fields entering the iron perpendicular to the lamination plane, and which therefore are a possible source of significant eddy current loss that couldonly be detected by dynamometer tests. This configuration must have closely controlled angular position of the magnets, which will be made more difficult by a negative torsional spring effect as the magnets approach the iron.
Fig. 3. An example of a moving magnet alternator with axially stacked
laminations. Adapted from Figure 6, Ref. 5.
Fig. 4. An example of a moving magnet configuration. Adapted from Ref. 6.
Sunpower Moving Magnet
Fig. 5. Schematic and hardware, Sunpower linear alternator with moving
magnet contained within air gap (see text).
Fig. 6. Sunpower linear alternator in refrigerator compressor (29 prototypes
delivered to sponsors by mid-1995).
Fig. 7. Sunpower liner alternator in Stirling cooler, Model 223A (77
coolers, 27 cryocoolers delivered to sponsors by mid-1995).
Fig. 8. Sunpower linear alternator in 400 watt free-piston Stirling engine /
alternator. The linear alternator has been used in various engine designs, from
150 watts to 10 kW output.
Ref. 7 describes the configuration which Sunpower has used exclusively for about ten years, in sizes ranging from a few watts to 10,000 W (Figure 5). Examples of hardware incorporating this linear alternator are given in Figures 6 - 8. All of the difficulties associated with other moving magnet configurations and with other types of linear motor-alternators are either eliminated or eased to the point where they can be overcome, as indicated by the following summary:
1. Magnets do not leave the air gap. Magnet fringing fields do not change with magnet position and therefore do not induce eddy currents in surrounding stationary metal structures.
2. Axial magnetic forces with no armature current are practically zero when the magnet position is in its operating range.
3. Absence of moving iron reduces torques and side forces to easily manageable levels.
4. The machines are so linear that they can be and have been used as accurate motion transducers (Ref. 8).
5. Simple and reliable design procedures do not require finite element analysis and give results within a few percent of predictions.
6. Radial untapered lamination stacks are used but improved fabrication techniques have largely nullified difficulties associated with this type of construction.
7. Efficiencies of 92 % are typical but can be higher at greater cost. Efficiency has been verified with dynamometer tests. The efficiency remains almost constant from rated power down to about 25% of rated power (Figure 9).
8. A simple equivalent circuit eases analysis and generalization of the complete electromechanical system always associated with a linear motor-alternation application.
Fig. 9. Efficiency of Sunpower linear motor - alternator vs. power out/in.
Other Factors
[Mass/Power] and [(Magnet Volume)/Power] are rough figures of merit of moving magnet linear motor-alternators. They are directly influenced by frequency, efficiency, magnet energy, and saturation flux density of the iron structure. Meaningful comparisons between configurations must therefore specify frequency, efficiency, and materials. Each configuration will be limited in power by such considerations as saturation of iron adjacent to the air gap, specificationof power factor, and finally, demagnetization, which can occur at elevated magnet temperature and high armature current. Because demagnetization is catastrophic, no design is acceptable if demagnetization can occur under any load conditions below a specified temperature. On fundamental grounds, there was reason to believe that, when all the above factors are taken into account, no configuration would have decisively better figures of merit than others. Detailed calculations based on 26 megagauss-oersted magnets and standard M19 non-oriented transformer iron confirmed this. At 60 Hz, typical [Mass/Power] is in the range 4.8 - 7 kg/kW, considerably higher than reported claims as lowas 1 kg/kW.
Conclusions
All the linear motor-alternator designs discussed here will function, and no moving magnet configuration will have a decisive advantage when compared to others on a basis of equal frequency, efficiency, demagnetization temperature, magnet energy, and saturation flux density. The criteria for practical choice are cost and less obvious factors that can cause serious difficulties, e.g., large open circuit axial forces, strong AC fringing fields that can cause high eddy current loss, torques and side forces, and non-linearity leading to difficulty in analysis and in generalizing conclusions from specific simulations of a complete electromechanical system.
References
1. Marquardt, E. and Radebaugh, R. "Design Equations For Linear Compressors with Flexure Springs." Proc. International Cryocooler Conference. Sante Fe,New Mexico, November 17- 19, 1992. Phillips Laboratory, Air Force Material Command. Kirtland Air Force Base, NM 87117-5776.
2. Bhate, S.K. U.S. 4,349,757. 1982.
3. Dhar, M., Rauch, J., Huang, S., and R. Bolton. 1989 "Space Power Demonstrations Engine Linear Alternator Dynamometer Test Results." IEEE 899596, pp. 1103-1107.
4. Benson, G. U.S. 4,454,426. 1984.
5. Corey, J., and Yarr, G. "HOTS to WATTS, the FPSE Linear Alternator System Revisited." IECEC 1992, 27th Intersociety Energy Conversion Engineering Conference Proceedings, 5: 289-303.
6. Shtrikman, S. U.S. 4,346,318. 1982.
7. Redlich, R. U.S. 4,602,174. 1986.
8. Redlich, R. U.S. 5,342,176. 1994.
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