INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 16 (2006) S290–S296 doi:10.1088/0960-1317/16/9/S17

Design optimization of an 8 W, microscale,axial-flux, permanent-magnet generatorDavid P Arnold1,3, Florian Herrault1, Iulica Zana1,4,Preston Galle1, Jin-Woo Park1,5, Sauparna Das2,6,Jeffrey H Lang2 and Mark G Allen1

1 School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta,GA 30332, USA2 Department of Electrical Engineering and Computer Science,Massachusetts Institute of Technology, Cambridge, MA, 01239, USA

E-mail: mark.allen@ece.gatech.edu

Received 20 January 2006, in final form 10 March 2006Published 11 August 2006Online at stacks.iop.org/JMM/16/S290

AbstractThis paper presents the design optimization and characterization of amicroscale, permanent-magnet (PM) generator, capable of supplying 8 W ofdc power to a resistive load at a rotational speed of 305 000 rpm. Thegenerator is a three-phase, axial-flux, PM machine, consisting of a statorwith Cu surface windings and a multi-pole SmCo PM rotor. Optimization ofthe machine geometries has enabled a 30% improvement in power density(for the same rotational speed) over a previously reported machine.Furthermore, these design improvements, in combination with higherrotational speeds, have enabled a >7× improvement in total output powerand a net power density of 59 W cm−3.

1. Introduction

Permanent-magnet (PM) generators can be used for convertingrotational mechanical energy into electrical energy for a widevariety of applications. Compared to other types of magneticmachines, PM machines have several benefits for miniaturizedor microscale applications. First, the magnetic interactionsgoverning the machine operation scale independently with size(assuming an increased current density capacity as length scaleis reduced) [1]. Second, the high costs typically associatedwith PM materials are of less concern when consideringdevices of small size. Lastly, axial-flux PM machineshave planar geometries, which merge well with conventionalMEMS microfabrication.

In PM devices, rare-earth magnets (e.g. SmCo, NdFeB)are typically employed because they possess high energyproducts for maximum electromechanical energy conversion.For many applications, NdFeB, with its slightly higher energy

3 Present address: Department of Electrical and Computer Engineering,University of Florida, Gainesville, FL, 32611, USA.4 Present address: Center for Materials for Information Technology,University of Alabama, Tuscaloosa, AL, 35487, USA.5 Present address: CardioMEMS, Atlanta, GA, 30308, USA.6 Present address: Linear Technology, North Chelmsford, MA, 01863, USA.

product, is the material of choice. However, when consideringintegration of a PM generator in a high-temperature (∼300 ◦C)microengine power generator [2], SmCo is preferred for itshigher Curie temperature and low remanence loss at elevatedtemperatures [3].

One major challenge for microscale PM machines isthe fabrication and integration of the required machinecomponents. There are no well-developed processes for themicromachining of PM materials with magnetic properties thatapproach those of bulk, rare-earth materials. Thus, in manycases, a hybrid approach is used. Precise microfabricationis employed for the coils and stator, while bulk-machining isused for the PM and rotor. Another challenge for these typesof devices is that they rely on some input mechanical power,such as a fluid flow or heat engine [2]. Thus, the source ofpower must be considered in the design and application of thegenerator.

Several microscale PM generator devices have beenpreviously reported, all using different constructionapproaches. A self-contained flow-driven device has produced1.1 mW at 30 krpm for a 7.5 mm diameter SU-8 rotor, whichcontained individual NdFeB magnets [4]. Another group hasreported 14.6 mW of output power at 58 krpm using an 8 mmdiameter NdFeB rotor [5], but in the corresponding conference

0960-1317/06/090290+07$30.00 © 2006 IOP Publishing Ltd Printed in the UK S290

Design optimization of an 8 W, microscale, axial-flux, permanent-magnet generator

Figure 1. Axial-flux permanent-magnet machine perspective viewand radial cross-section.

presentation, presented 5 W at 380 krpm for the same device.The authors of this paper have previously reported a PMgenerator that demonstrated 2.6 W of mechanical-to-electricalpower conversion and delivery of 1.1 W of dc power to aresistive load at a rotor speed of 120 krpm using a 9.5 mmdiameter annular SmCo rotor [6, 7].

These preliminary investigations have demonstrated thepotential of such devices for various energy conversionapplications. However, a dedicated effort to optimize andmaximize the performance (power output, efficiency, etc) ofthese devices has not yet been undertaken. In this paper,design considerations and tradeoffs are presented and analyzedin order to maximize the output power of a microscale,axial-flux PM generator. A significantly redesigned, second-generation generator is presented that is fabricated similarlyto the machine in [6, 7], but possesses an improved windingscheme and optimized machine geometries. This redesigneddevice is experimentally characterized and its performanceimprovements are quantified.

2. Machine design

The generator is a three-phase, multi-pole, axial-flux,synchronous machine comprising a rotor with an annular PMand soft magnetic back iron and a stator with Cu surfacewindings on a magnetically soft substrate, which also servesas a magnetic back iron. In operation, time-varying magneticfields from the spinning rotor induce voltages in the statorwindings. When connected to a load, current flows throughthe windings, and electrical power is supplied from the device.

The stator uses interleaved, electroplated Cu windings thatare dielectrically isolated from a 1 mm thick NiFeMo (MolyPermalloy) substrate by a 5 µm polyimide layer, as depictedin figure 1. The rotor consists of an 8-pole, 500 µm thick,annular SmCo PM and a 500 µm thick FeCoV (Hiperco 50)back iron. For this design, both the rotor magnet and backiron have an inner diameter of 5 mm and an outer diameter of10 mm.

(a) (b)

Figure 2. Stator winding patterns for (a) original, 8-pole,2-turn/pole machine [7] and (b) optimized, 8-pole, 3-turn/polemachine.

2.1. Design improvements

In PM machine design, many of the scaling laws are evidentfrom the first-order governing equations [7]. For example,power increases as air gap is reduced, rotor surface areais increased, speed is increased, etc. However, some of theintricacies of the physical construction of the device arenot captured by these engineering equations, particularly inrelation to the windings. Furthermore, these equations do notmodel well three-dimensional effects, such as radial leakageflux, end-turn effects, etc. Thus, some additional analysis isneeded.

In this particular machine, many of the design parameters(dimensions, materials, etc) are fixed based on futurecompatibility and integration with a microturbine engine [8].Thus, in the design of this second-generation device, the goalwas to maintain similar overall dimensions, but to focus on twofundamental issues: (1) improving the winding pattern and (2)determining the optimum values for the number of poles (p)and number of winding turns/pole (n).

There are several design improvements in the second-generation stator aimed at reducing the winding resistances bymaking more effective use of the available winding volume inthe gap between the rotor magnet and stator substrate. First,the radial conductor segments occupy the full thickness ofboth metal layers, as depicted in figures 1 and 2. The radialconductors are thicker, 200 µm rather than ∼100 µm, andtherefore have lower resistance. Second, the inter-conductorspacing was reduced from 130 µm to 50 µm, further increasingthe Cu cross-sectional area for lower resistance. Third, theradial conductors were shortened by 500 µm relative to therotor magnet radial span, permitting optimal flux linkage ofradial leakage flux while minimizing the total coil length.

The new design also features a more effective windingpattern with an improved end-turn connection scheme.Figure 3 shows the winding diagrams for the original [7]and optimized devices. The number of ‘crossovers’ and thusvias was reduced (from 96 to 3) by using variable-pitch coilsand permitting each end-turn segment to occupy only onelayer (either top or bottom). Also, each end-turn’s segment

S291

D P Arnold et al

(a)

(b)

A

A

B

B

C

C

Figure 3. A comparison of the winding diagrams for the (a) original 2-turn/pole machine [7] and (b) optimized 3-turn/pole machine. Solidlines represent layer 1, and dashed lines, layer 2. Phase A is darkened for reference.

width, length and shape were optimized for minimum overallresistance.

Additionally, because the output power scales with thesquare of the rotational speed, emphasis was placed onincreasing the rotor speed. For this design, the limitingfactor for speed was determined both experimentally andtheoretically to be the mechanical integrity of the brittle SmComaterial in the rotor [9]. At high speeds, centrifugal forces canreadily exceed the ultimate strength of the material, resultingin brittle fracture and catastrophic failure of the rotor assembly.This problem was addressed by reinforcing the rotor assemblywith a Ti housing, which also serves as a mounting adaptor forconnection to the experimental test stand.

2.2. Machine optimization

The design goal is to maximize the flux linkage betweenthe rotor and stator for maximum induced voltage whileminimizing the stator winding resistance for maximum outputpower. For a generator of a fixed volume operating at aconstant rotational speed, first-order analysis indicates thatoutput power scales independently of the number of poles (p)and number of winding turns/pole (n). Increasing either p or nincreases the voltage linearly while simultaneously increasingthe winding resistance quadratically (winding length increaseslinearly, and cross-sectional area decreases linearly).

In a typical macroscale machine design, the values of p andn can be used to adjust the relative voltage and current levels,with little impact on output power or efficiency. However, formicroscale machines, these values can dramatically impactthe machine performance. For example, a machine with alow p and/or n may not provide sufficient voltage levels forcompatibility with the power electronics, whereas a machinewith a high p and/or n requires finer physical features and mayexceed the geometrical size limitations of photolithography,magnetic patterning, etc. Also, as p is increased, the lateralleakage flux between adjacent rotor poles becomes significant;in other words, less magnetic flux is coupled from the rotor tothe stator.

Therefore, a parametric optimization was performedto find the optimum values for p and n along with

Table 1. Optimization parameters.

Parameter Description Value Units

Fixed parametersmo Magnet outer radius 5.0 mmmi Magnet inner radius 2.5 mmro Stator radial conductor 4.75 mm

outer radiusri Stator radial conductor 2.75 mm

inner radiustbi Back iron thickness 500 µmtmag Magnet thickness 500 µmtcond Radial conductor thickness 200 µmtend End-turn thickness 80 µmtsub Substrate thickness 1000 µmg Air gap 100 µmwmin Minimum feature width 50 µmRpe Power electronics 50 m�

equivalent resistance

Variable parametersp Number of poles 2–12 –n Number of turns/pole 1–6 –ho Outer end-turn extension 0–1.6 mmhi Inner end-turn extension 0–1.6 mm

the corresponding optimal winding pattern geometries formaximum output power. Both p and n were varied whileenforcing certain microfabrication constraints for the rotor andstator. The geometric parameters are listed in table 1. Theradial dimensions of the magnet were fixed, as were all axialparameters (e.g. air gap, thicknesses, etc), while the radialdimensions of the stator windings were varied. A four-stepprocedure was used for the optimization as follows:

(1) For each combination of p and n, the inner and outer end-turn extensions, hi and ho, were varied to find the windingpattern that yielded the lowest electrical resistance.The relative resistance contribution of each windingsegment (radial conductors, inner end-turns, and outerend-turns) and the total resistance were calculated usinggeometrical relations and an assumed resistivity of ρCu =1.7 µ� cm.

S292

Design optimization of an 8 W, microscale, axial-flux, permanent-magnet generator

yz

x

y

z x

-2

-22

2

2

0 00

0

2

4

4

6

60

2

4

6

Figure 4. Finite-element model results showing the z-directed B-field 100 µm above the stator surface for the case of p = 8.

(a) (b) (c)

rms

Figure 5. Predicted (a) single-phase winding resistance, (b) single-phase open-circuit voltage, and (c) three-phase matched-load outputpower at 300 krpm, indicating maximum performance for an 8-pole, 3-turn/pole configuration.

(2) For each value of p, a three-dimensional (3D), nonlinear,finite-element model (FEM) was used (FEMLAB v3.1)to solve for the static magnetic B-fields in the machine.The rotor was modeled by assuming a square-wavemagnetization with a remanence of Br = ±0.5 T andrelative permeability of µr = 1. (Note that the value of0.5 T was used based on previous modeling experienceof this type of machine [6, 7].) The FeCoV backiron and NiFeMo stator substrate were modeled usingexperimentally measured nonlinear material properties[6]. The FEM employed two magnetic half-poles andenforced periodic boundary conditions. Figure 4 showsan example for p = 8 of the axial directed B-field at amidpoint through the thickness of the stator coils (i.e.100 µm above the stator substrate), indicating a peakmagnetic flux density of approximately ±0.3 T. Thismodel accurately captures most of the physics of thedevice, but does not account for the armature reactionfields from the stator currents nor does it include eddy-current generation. Both of these effects have beenpreviously determined to be small with respect to the fieldsproduced by the PM [6].

(3) Using the optimized winding dimensions and the resultsfrom the FEM, the induced voltage waveforms and rmsvoltages were then computed. This was accomplished

using a MATLAB script to numerically integrate the B-field map to determine the flux through an area definedby the shape of the coil. The integration area was then‘rotated’ in 1◦ step increments to simulate the relativemotion of the rotor. This process was used to determinetime rate of change of flux through the coil, and hencethe induced single-phase open-circuit voltage at a speedof 300 krpm.

(4) The rms value of the open-circuit voltage was then usedas an input to a circuit model using a per-phase seriesequivalent resistance of 50 m� to account for losses inthe power electronics [7]. The three-phase matched-load(maximum power transfer) output power was calculatedfrom the model. Additionally, the short-circuit currentdensity in all segments of the conductors was verified tonot exceed the maximum capacity (<2 × 109 A m−2).

Figure 5 shows the predicted values for single-phaseresistance, single-phase voltage and three-phase matched-loadoutput power as a function of poles, p, and turns/pole, n.While there are valid data only for integer values for p and n,the plots use a continuously shaded interpolation to illustratethe differing response curves. Also, the unplotted regionsindicate geometries that exceed the limitations of thefabrication design rules, i.e. the conductors are too narrow.

S293

D P Arnold et al

(a)

(b)

(c)(d )

µm

Figure 6. (a) Fabricated 3-turn, 8-pole stator. (b) Close-up of innerend-turns. (c) Close-up of outer end-turns and electrical connectionto bond pad. (d) SEM cross-section image of the windings (comparewith figure 1).

A maximum output power of 12.7 W is indicated forthe 8-pole, 3-turn/pole configuration. This corresponds toa single-phase winding resistance of 100 m� and an open-circuit voltage of 1.6 Vrms. While not shown, it is interestingto note the relative breakdown of the winding resistance: 18%in the radial conductors, 36% in the outer end-turns and 46%in the inner end-turns. The end-turns account for over 80%of the total resistance of the winding. This clearly illustratesone major difference between microscale machine design andconventional macroscopic machine design.

3. Machine fabrication

To confirm an improvement in the overall design, 8-pole,3-turn/pole optimized machines were built using previouslyreported methods [7, 10]. As shown in figure 6, the fabricatedstator consists of two electroplated Cu layers, 80 µm and60 µm thick, respectively, with 40 µm of SU-8 as the dielectricinsulation between the layers. The fabricated geometry differsslightly from the modeled geometry (80 µm Cu layers with40 µm insulation) due to process variations. Consequently,the single-phase winding resistance and inductance for theoptimized machine are 160 m� and 0.31 µH, respectively.These values are slightly higher than the projected values of100 m� and 0.138 µH.

4. Experimental results

Using the spinning rotor test stand and experimental methodsdescribed in [7], electrical characterizations were performedto analyze open-circuit voltage, output power and efficiency.

4.1. Open-circuit voltage

The open-circuit voltage Voc is linear with speed and decayswith air gap, as depicted in figure 7. A voltage of 0.8 Vrms

(a)

(b)

Figure 7. Open-circuit voltages (a) versus rotational speed for100 µm air gap and (b) versus air gap at 100 000 rpm for original [7]and optimized machines. Data points represent measurements; linesrepresent analytical model [6].

was achieved at 150 krpm and 100 µm gap. The experimentalvalues are seen to closely match analytical models [6], aswell as the FEM-based predictions used for the machineoptimization.

The new, optimized machine exhibits a 26% higher open-circuit voltage as compared to the original machine [7].This increase ideally should be 50% (3 turns/pole ratherthan 2 turns/pole), assuming equal magnetic properties anddimensions. However, the original machine possessed a 9%larger magnet surface area (3.2 mm ID, 9.5 mm OD, comparedto 5 mm ID, 10 mm OD). In addition, the magnets weremanufactured by two different vendors, and may not possessequal magnetic properties. Also, because of the experimentalsetup, there is some variability in setting the magnetic gap.Therefore, a direct comparison of the voltage data is difficult.

4.2. Power

For power measurements, the air gap was fixed at 100 µm.A passive ac/dc converter, comprising a three-phase �/wye-connected (1:6 turns ratio) transformer and a three-phase diodebridge rectifier, was used to provide dc power to a resistive load[7]. The output power was measured as a function of loadresistance at 100 krpm, and the matched-load condition wasexperimentally determined by the point of maximum powertransfer to be 37 �. The load was then fixed, and the powerwas measured as a function of speed. The load resistance wasre-measured at each speed to ensure accuracy as the resistorheated.

S294

Design optimization of an 8 W, microscale, axial-flux, permanent-magnet generator

Figure 8. Matched-load dc output power for original [7] andoptimized machines. Data points represent measurements; linesrepresent analytical model [6].

As shown in figure 8, a maximum dc output power of 8 Wwas achieved at 305 krpm for a matched load. For an activevolume of 136 mm3 (OD = 10 mm, ID = 5 mm, thickness =2.3 mm), this corresponds to a power density of 59 W cm−3.Above 305 krpm, the SmCo permanent magnet sufferedcatastrophic mechanical failure, resulting in destruction ofboth the rotor and stator. The 8 W of measured power islower than 12.7 W predicted by the device optimization model,primarily because of the under-prediction of the stator windingresistance.

As for comparison, the first-generation machine achieveda maximum dc output power of 1.1 W at 120 krpm [7]. Atthe same speed, the second-generation machine demonstrates1.3 W. Accounting for the differences in rotor size, thiscorresponds to a 30% improvement in power density.

4.3. Efficiency

To characterize the machine efficiency, the input mechanicalpower must be measured in addition to the electrical outputpower. The mechanical shaft power is the product of angularspeed and torque. Speed is measured using a shaft encoder,but measurement of shaft torque using conventional methodsis difficult because of the low torques and high rotationalspeeds associated with the micromachine. Because of this,electrical measurements are made at the system output, anddevice models are used to extract the induced voltages andthe torque, as described in [6, 7]. The extracted torque ismultiplied by the measured speed to obtain an estimate ofinput mechanical power.

Two different efficiencies are plotted as a function of speedin figure 9 under maximum power transfer conditions (i.e.matched-load). The generator efficiency, ηg, represents theefficiency of the entire generator system. It is the ratio ofthe dc electrical output power to the mechanical shaft inputpower (neglecting mechanical bearing and windage losses).The electrical efficiency, ηe, is the efficiency of the systemfrom the induced voltage to the load. It takes into accountthe stator conduction losses and power electronics losses, butneglects the magnetic core losses in the stator substrate. Thedifference between the two curves is the magnetic losses in thestator substrate (primarily eddy current losses), which could

Figure 9. Electrical system efficiency, ηe, and generator systemefficiency, ηg, versus speed under matched-load conditions.

be reduced by including magnetic laminations in the stator[11].

As shown in the figure, both efficiencies increase withincreasing speed, primarily because losses (e.g. transformercore, diode drops) in the ac/dc converter become lesssignificant. A net generator efficiency of 28% is achievedat 300 krpm, and the electrical efficiency approaches thetheoretical maximum of 50% for a matched-load condition.

At an efficiency of 28%, large amounts of power aredissipated in the machine, resulting in the potential for hightemperatures. In the case of a matched load at 300 krpm,the machine must dissipate ∼20 W of power (∼8 W fromstator conduction losses and ∼12 W by core losses in thestator substrate). Fortunately, machines of this scale possesshigh surface-to-volume ratios, so heat is dissipated muchmore readily than in macroscale machines. For the testresults presented here, the machine stator was clamped toan aluminum mounting plate (which served as a mechanicalsupport and heat sink), and no significant temperature riseswere detected.

5. Conclusions

The PM generator demonstrated 16 W of mechanical-to-electrical power conversion and delivery of 8 W of dc powerto a resistive load at a rotational speed of 305 krpm. Thiscorresponds to a net power density of 59 W cm−3, more thanan order of magnitude higher than macroscale generators. Thissecond-generation machine demonstrates a corresponding30% improvement in power density attributed solely to statorenhancements. The stator improvements, combined with thehigher rotational speeds (305 krpm), have enabled a 7.2×improvement in total output power.

These machine results are for matched-load conditionswhere maximum power transfer occurs. In certain applicationswhere small machine size is critical, power density may be theprimary design goal. In other applications, efficiency may bethe primary design goal. For these cases, higher efficienciescan be obtained by operating the machine with a reduced load,but this sacrifices output power. Maintaining high efficiencyand high output power requires a larger machine. Thus,the intended application and overall system level design andintegration issues become very important for the design of thegenerator.

S295

D P Arnold et al

In summary, if these PM microgenerators can beintegrated with suitably scaled mechanical power sources (e.g.micro heat engines) and small power electronics, extremelycompact, high power-density energy converters may berealizable. The machine reported here shows progress towardthis goal.

Acknowledgments

This work was supported by the United States Army ResearchLaboratory Collaborative Technology Alliance (DAAD19-01-2-0010).

References

[1] Cugat O, Delamare J and Reyne G 2003 Magneticmicro-actuators and systems (MAGMAS) IEEE Trans.Magn. 39 3607–12

[2] Jacobson S A and Epstein A H 2003 An informal survey ofpower MEMS Proc. Int. Symp. Micro-Mechanical Eng.pp 513–20

[3] Campbell P A 1994 Permanent Magnet Materials and theirApplication (New York: Cambridge University Press)

[4] Holmes A S, Hong G and Pullen K R 2005 Axial-fluxpermanent magnet machines for micropower generationJ. Microelectromech. Syst. 14 54–62

[5] Raisigel H, Cugat O, Delamare J, Wiss O and Rostaing H2005 Magnetic planar micro generator Transducers ’05: Proc.13th Int. Conf. Solid-State Sensors, Actuators andMicrosystems pp 757–61

[6] Das S, Arnold D P, Zana I, Park J-W, Allen M G and Lang J H2006 Microfabricated high-speed axial-flux multi-wattpermanent-magnet generators: Part I. ModelingJ. Microelectromech. Syst. (at press)

[7] Arnold D P, Das S, Zana I, Park J-W, Lang J H and Allen M G2006 Microfabricated high-speed axial-flux multi-wattpermanent-magnet generators: Part II. Design, fabrication,and testing J. Microelectromech. Syst. (at press)

[8] Epstein A H 2004 Millimeter-scale, MEMS gas turbineengines ASME J. Eng. Gas Turbines Power126 205–26

[9] Arnold D P, Joung Y-H, Zana I, Park J-W, Das S, Lang J H,Veazie D and Allen M G 2005 High-speed characterization andmechanical modeling of microscale, axial-flux,permanent-magnet generators Transducers ’05: Proc. 13thInt. Conf. Solid-State Sensors, Actuators and Microsystemspp 701–4

[10] Zana I, Herrault F, Arnold D P and Allen M G 2005 Magneticpatterning of permanent-magnet rotors for microscalemotor/generators, Proc. 5th Int. Workshop MicroNanotechnology For Power Generation and EnergyConversion Applications (PowerMEMS 2005) (Tokyo,Japan) pp 116–9

[11] Lammeraner J and Stafl M 1966 Eddy Current (London:Iliffe) chapters 1–2

S296