Golovanov, Dmitry and Galea, Michael and Gerada, C. (2016) High specific torque motor for propulsion system of aircraft. In: ESARS Itec 2016, 2-4 Nov 2016, Toulouse, France.

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High Specific Torque Motor for Propulsion Systemof Aircraft.

Dmitry Golovanov, Michael Galea, Chris Gerada

PEMC Research GroupThe University of NottinghamNottingham, United Kingdom

Abstract This paper proposes an analytical model thatconsiders the torque characteristics for high specific torquesynchronous machine with outer rotor and a Halbachpermanent magnet array. The distribution of the magnetic fieldin the air gap is obtained with a linear assumption by solvingNeumanns problem. The analytical model presented in thepaper allows preliminary estimation and fast optimization of themachines geometry and can be used to develop a first cutdesign of the machine.

The application of the analytical model proposed isdemonstrated via the adaptation and modification of a tractionmachine designed for electrical taxiing to a machine forpropulsion of electric aircraft.

Index Terms Analytical solution, Halbach array,permanent magnets.

The concept of the more electric aircraft (MEA) pushesresearchers to search for innovative topologies of electricalmachines suitable for aircraft propulsion. At first glance,synchronous machines with permanent magnets (PMs) lookthe most attractive, in terms of meeting such demands ofspecific torque characteristics and efficiency [1, 2], in theshort term future. One of the most promising topologies waspresented in [3, 4, 5]. The so called green taxiing motor (GT)was developed for taxiing a medium range aircraft on theground. The main advantage of this motor is an ability toreach highest specific torque in terms of torque-to-mass andtorque-to-volume ratios. The studied GT motor conceptinvolves application of outer rotor with Halbach PM arrayand using 3-phase double-star winding configuration [1]. Thedesign of GT was optimized for low rotation speed 120-180 rpm, high torque 7 kNm, high specific torque 64 Nm/kg and short-term operation in intermittent mode 2000 s.

The main requirements for propulsion motors are hightorque-density or power-density characteristics and highefficiency (>97%) at the speed of rotation, typically around2500 rpm. The GT characteristics seem acceptable to satisfythe mentioned above requirements. Thereby, while the GTmotor was originally designed for traction purposes, howeverthe topology can be a good starting point for furtherinvestigation for optimal motor design of propulsion.

An analytical model can be a useful tool at the first stageof research. It allows doing a quick estimation of machinescharacteristics for a wide range of parameters: pole pairs,machine dimension, current load, size of PM, etc. At thesame time the preliminary machine design optimization alsocan be performed by using the analytical model. This can

result in a narrowed range for parameters for more accurateand time consuming optimization by applying finite elementanalysis (FEA).

This paper contains an analytical solution for thementioned GT motor topology and shows results of theestimation of its specific power and specific torquecharacteristics as well as its efficiency. All this is shown,once the analytical model has been applied to convert theoptimal design for traction to a design more suitable forpropulsion.

I. SOLUTION OF MAGNETOSTATIC PROBLEM FORSYNCHRONOUS MOTOR WITH HALBACH PM ARRAY

The Halbach array is a well known structure of PMswhich allows the increasing of flux density [4] of machines,mainly by improving the harmonic quality of the main air-gap flux. The Halbach magnetic cylinder gives the effect ofconcentration of magnetic flux for either outward or inwardcylinder and can be used in synchronous machines with PM[7, 8]. The topology of this kind of synchronous machinewith inner concentration of magnetic field is shown in Fig. 1.The Halbach cylinder is placed in between two ferromagneticdomains with infinite permeability. The inner ferromagneticdomain represents stator with winding described bydiscontinuous current sheet on the surface .

Fig. 1 Outer rotor machine with Halbach PM array

In order to obtain an analytical solution of the magneticfield distribution for this kind of topology the followingassumptions were taken:

chiandoneFont monospazio978-1-5090-0813-1/16/$31.00 2016 IEEE

- Stator domain and rotor yoke are described asferromagnetic cylinders with infinite permeability but without taking in account slotting effect -Fig. 1;

- The Halbach PM array consists of 4 magnets perpole pitch with 45 in between vectors ofmagnetization of neighboring magnets;

- The magnets have uniform magnetization = with relative magnetic permeability =

1 - Fig. 1.- The current in stators winding is described as

discontinuous current sheets on the surface of stator;- Stator slots are not considered and replaced with

smooth ferromagnetic surface- The magnetic fields are plane-parallel and 3D

effects are not considered;

The analytical solution of the magnetic field for thismachine consists of sum of fields produced across theHalbach cylinder taking into account the influence of theferromagnetic domains and field of the discontinuous currentsheet.

A. The solution for isolated Halbach cylinder

Halbach cylinder consist of a sequence of PMs,magnetized in different directions Fig. 2a. The consideredcylinder has four periodically repeated PM elements (markedfrom 1 to 4 in Fig. 2a). The total field of cylinder was foundas a sum of fields of these PM elements. Laplace and Poissonequations with appropriate boundary conditions showed inFig. 2b were solved for each PM element in each domain(external domain: , internal domain 0 andPM region ( [9, 10].

a) Halbach cylinder

b) boundary conditions for isolated elements of Halbach cylinder

Fig. 2 Schematic representation of magnetostatic problem for isolatedHalbach cylinder

The result of the solution is presented for the internalregion only. For the internal region 0 we have (1-4):

=

()() ) ( (1)

=

() +

+

) ( (2)

=

()) (

(3)

=

()

) ( (4)

Here 0

angle of PMs elements, 0

direction of magnetization of elements 2 and 4 Fig. 2b.

B. The influence of the ferromagnetic region

The Fourier series (5) with coefficients and describesthe influence of ferromagnetic domain.

= +

sin( ( < > (5)

Coefficients and (8, 9) were received from theboundary conditions (6, 7).

+

+

+

+

,

= 0 (6)

+

+

+

+

,

= 0 (7)

=

1

1 01+

2

()1

sin( (

1 1 , (8)

=

()

()

()

(9)

here () and () are defined as (10, 11).

() =

()

+

+

+ ) (

+ ) ( ) ( +

(10)

() =

()

+

+

) (

+ ) (

) ( (11)

C. Solution for ferromagnetic yoke

The expressions (12, 13) give the description ofdistribution of magnetic field within external ( < >) and internal ( < > ) ferromagnetic yokes.

_ = +

) ( < > (12)

_ = +

) ( < > (13)

Taking into account boundary conditions (14 - 17)coefficients , , , can be defined as (18 - 21)respectively.

at = : _ = 0 (14)

at = : _ = + + + + (15)

at = : _ = + + + + (16)

at = : _ = 0 (17)

= (,)(,)(,)(,)(,)

()

(18)

=

(19)

= Fe3(1,1+( 2+(,1) 3+(,1) 4+(,1) (,1)

()

(20)

=

(21)

II. SOLUTION OF MAGNETOSTATIC PROBLEM FORDOUBLE STAR DISCONTINUOUS CURRENT SHEET

A double-star 3-phase winding was implemented in theGT motor to reduce the torque pulsations and simplify thecoils design. The double star concept involves the use of twosets of 3-phase windings with 30 shift in between of sets,powered by two separate converters and with a common star-point [5]. With the implementation of such a double starsystem, improvements in the torque ripple can be achieved.Due to the suystem having a common star point (for both 3-phase systems) no extra losses are incurred.

For the analytical model, the three phase stator windingscan be described as discontinuous current sheets on thesurfaces of ferromagnetic region Fig. 3. The field of thecurrent sheet is described as a superposition of the fields ofcurrents - ,_ ,_ ,_ and - ,_ ,_ ,_respectively, which represents the double star winding -Fig. 3.

Fig. 3 Schematic representation of magnetostatic problem fordiscontinuous current sheet

The current _ can be represented as a Fourier series(22), (23) for a positive and negative current direction in thecoil. The angular position of current sheet elements can befound in Fig. 3.

_ =

+ ) ( (22)

_ =

+

+

+ ) ( (23)

here peak value of current load, power angle, coil angle, tooth angle, number of coils per phase, Fig. 3.

The magnetic field in between and is described byLaplace equation (24) with boundary conditions (25, 26).

_ = 0 (24)

at = :_

= _ (25)

at = :_

= 0 (26)

The expression (27) can be obtained after solving (24 -26). The same analytical approach as for current _ had

been applied for other current and results are shown below (28 38). The total field produced by current sheet Fig. 3 is asum of separately solutions (27 38).

=_

( + 1)

+ ( 1)

+ ) ( (27)

_ =

( + 1)

+ ( 1)

+

+

+ ) ( (28)

=_

( + 1)

+ ( 1)

+ () (29)

_ =

( + 1)

+ ( 1)

+

+ ) ( (30)

_ =

( + 1)

+ ( 1)

+ ) ( (31)

_ =

( + 1)

+ ( 1)

+

+ ) ( (32)

_ =

( + 1)

+ ( 1)

+

+ ) ( (33)

_ =

( + 1)

+ ( 1)

+ ) ( (34)

_ =

( + 1)

+ ( 1)

+

+ ) ( (35)

_ =

( + 1)

+ ( 1)

+ ) ( (36)

_ =

( + 1)

+ ( 1)

+ ) ( (37)

_ =

( + 1)

+ ( 1)

+

+ ) ( (38)

Where:

= 2 , =

, =

,

= 0, =

, =

. These

coefficients are given for the starting time = 0, where we

have = , = =

and = =

,

= 0.

= 1,3.. odd harmonics, 0

, power angle,

pole-pairs from current sheet, peak phase current, number of turns per one coil of phase, coefficient wasdefined from boundary conditions (25 26) and expressed as(39)

=

(39)

III. COMPARISON ANALYTICAL AND FEA RESULTS ANDTORQUE CHARACTERISTICS

The analytical and FEA computations had beenperformed with GT motor parameters listed in Table 1. Theanalytical model was compared with FEA solution atdifferent conditions:

- linear assumption of steel permeability and withouttaking into account slotting effect;

- linear assumption with slotting effect;

- nonlinear assumption with slotting effect.

TABLE I PARAMETERS OF THE OUTER ROTOR MACHINE WITH HALBACHARRAY

Parameter Symbol Value Unit

Magnetization of PMs 775

Relative permeability of PMs 1 -

Number of pole pairs 21 -Internal radius of stator 142 External radius of stator 203.5 Internal radius of outer ring 225 External radius of outer ring 235 Internal radius of PMscylinder

205

External radius of PMscylinder

225

Angle of PMs element

(3.75)

Phase peak current 225 A

Coil turns 33 -

The common distribution of the magnetic flux lineswithin active part of GT motor at no-load conditions foranalytical computation; for FEA without slots; and for FEAwith slots, is shown in Fig. 4a; Fig. 4b; Fig. 4c, respectively.As can be seen from the Fig 4 the slots cause significantredistribution of magnetic field in active part of machine incomparison with nonslots case.

a) Analytical b) FEA without slots c) FEA with slots

Fig. 4 The distribution of magnetic flux lines within active part of GT motor for nonload condition

The comparison of magnetic flux density distribution inthe air gap of machine obtained from analytical and FEAsolutions are given in Fig. 5a, b. The results are shown forradial component of flux density at lineal assumption ofstator material permeability without considering slots Fig. 5a and with slotting effect Fig. 5b. Very goodagreement can be observed in case of slots absence Fig. 5a.When taking into account the stators open slots, a significantdifference between analytical and FEA results occur. This isshown in Fig 5b.

a) linear assumption, without slotting effect

b) linear assumption, FEA solution with slotting effect

Fig. 5 Radial component of flux density in the air gap for nonloadcondition

The torque performance of the GT motor was estimatedanalytically by using Maxwell stress tensor (40) andcompared with FEA results at different conditions Fig. 6.

= _

_ _ ,

_ _ , (40)

The analytical solution gives good agreament with FEAin case of considering smooth stator surface (no slots) atlinear assumption. The difference can be seen in case ofconsidering open slots in FEA model. At peak phase current225 A the difference in torque caused by opened slots is13.5%. So, the open slots have significant influence on fielddistribution and thus on torque.

It should be also mentioned that GT motor is a highlysaturated machine due to the high current load. Taking intoaccount the nonlinear properties of stator material(Vacoflux 50, 0.35 mm laminations) the difference betweenanalytical result and FEA reaches 33% - Fig. 6.

Fig. 6 Torque characteristic ) = 775

, = ,21 =

, =

=,2/ 21)

The nominal RMS current density of GT motor atreference speed 120 180 rpm is 26 A/mm2 that allowsreaching 64 Nm/kg (for the inactive materials only) ofspecific torque at short term operation. While such a currentdensity, might seem quite high at first glance, however in thereal application, this is mitigated by implementing a highlyefficient, thermal management technique [6].

The specific torque and specific power as well as the totallosses and efficiency of the original GT motor were estimatedat 2500 rpm, in order to verify its potential in terms of aconversion for propulsion activities. The results wereobtained from FEA and are given in Fig 7, 8. The total lossesnonlinearly rise mainly due to Ohmic and eddy current lossesand reach 55 kW at 26 A/mm2 - Fig 7. Eddy current lossescan be reduced by applying less thickness stator laminationswhich originally were 0.35 mm. The specific torque whichhas nonlinear correlation with current density rises from9 Nm/kg at 3 A/mm2 to 64 Nm/kg at 26 A/mm2 of currentdensity.

Fig. 7 Specific torque and Losses characteristics (at 2500 rpm)

The specific power and efficiency characteristics of theGT motor at 2500 rpm are shown in Fig. 8. The efficiency ofthe motor is higher than 97% in the wide range of currentload. For the nominal value of motor current density26 A/mm2 it is ~96.8% wherein specific power riches~15.8 kW/kg. It also should be mentioned that the power ofthe GT machine at 2500 rpm and nominal current density26 A/mm2 is 1.7 MW. As it was mentioned above, theefficiency of GT still can be increased by redisign andoptimization of its topology for high frequency and highrotation speed.

Fig. 8 Specific power and efficiency characteristics (at 2500 rpm)

It should be mentioned that the GT works in intermittentmode with a maximum duration of 2500 seconds, whichleads to periodic thermal heating. The original design of theGT included the use of forced air cooling, aided by otherthermal management techniques as illustrated in [6]. The airflow passes through cooling radiator that is placed on theinner stator surface above in Fig. 1. The estimation ofthermal state of GT was presented in [3-5]. When upgradingthe original technology to propulsion, then the normalsteady state operation, indicates that a liquid cooling systemwould be more promising and feasible.

IV. CONCLUSION

The description of the analytical model based on asolution of Laplace and Poisson equations for synchronousmachine with a Halbach array are given in this paper. Themodels allow performing the calculation of magnetic fielddistribution within active parts of machine as well asestimation of torque characteristic. They give goodagreement in case of non-slotting geometry of the stator. Themodels can be extremely useful at the first stage of researchfor the described topology as well as for the design andoptimization of the machines magnetic circuit when a linearassumption for different number of pole pairs, PMdimension, stator dimension, direction and amplitude of PMmagnetization and current load is taken.

The simulation of the GT traction motor topology for thepurpose of electric aircraft propulsion was also demonstrated.The simulated GT motor (applied with propulsion operationcharacteristics) can provide a high specific power (up to 15.8kW/kg) and specific torque (up to 64 Nm/kg) characteristicsat keeping efficiency higher than 97%. Thereby, all thisconfirms that the GT topology can be considered for furtherinvestigation from the standpoint of applying it as a motor forpropulsion of electric aircraft.

V. REFERENCES

[1] M. Galea, L. Papini, H. Zhang, C. Gerada, and T. Hamiti,"Demagnetization Analysis for Halbach Array Configurations inElectrical Machines," Magnetics, IEEE Transactions on, vol. 51, pp. 1-9, 2015.

[2] Bulent Sarlioglu, Casey T. Morris "More Electric Aircraft: Review,Challenges, and Opportunities for Commercial Transport Aircraft"IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION, VOL.1, NO. 1, JUNE 2015

[3] M. Galea, Z. Xu, C. Tighe, T. Hamiti, C. Gerada, and S. Pickering,"Development of an aircraft wheel actuator for green taxiing," inElectrical Machines (ICEM), 2014 International Conference on, 2014,pp. 2492-2498.

[4] T. Raminosoa, T. Hamiti, M. Galea, and C. Gerada, "Feasibility andelectromagnetic design of direct drive wheel actuator for greentaxiing," in Energy Conversion Congress and Exposition (ECCE), 2011IEEE, 2011, pp. 2798-2804.

[5] M. Galea, "High Performance, Direct Drive Machines for AerospaceApplications," PhD, Faculty of Engineering, University of Nottingham,UK, 2013.

[6] M. Galea, C. Gerada, T. Raminosoa, and P. Wheeler, "A ThermalImprovement Technique for the Phase Windings of ElectricalMachines," Industry Applications, IEEE Transactions on, vol. 48, pp.79-87, 2012.

[7] Z. Q. Zhu and D. Howe, "Halbach permanent magnet machines andapplications: a review," Electric Power Applications, IEE Proceedings -, vol. 148, pp. 299-308, 2001.

[8] Yang Shen, Zi-Qiang Zhu, "General analytical model for calculatingelectromagnetic performance of permanent magnet brushless machineshaving segmented Halbach array"

[9] D. Golovanov, "Synchronous high temperature superconductor motorswith permanent magnets", PhD. Thesis, Moscow aviation institute,2010.

[10] L. Kovalev, Y. Kavun, D. Golovanov. "The limiting characteristics ofsynchronous machines with permanent magnets and high-temperaturesuperconductors" // Electricity 2008. 12