Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Abstract This paper details the design considerations of a peranent agnet (PM), three phase, high speed, synchronous achine for fault tolerant operation. A ultidisciplinary approach to the optial design of the achine is adopted targeted at iniising the additional losses resulting fro faulty operating conditions and accounting for the reedial control strategy ipleented. The design of a closed slot, slots, pole achine is presented. The achine is prototyped and tested to validate the analytical-coputational perforances predicted in the design and analysis stage under healthy and faulty conditions. Index Ters Peranent Magnet Machine Design, Fault Tolerant, High Speed, Theral Modelling. A A High Speed Peranent Magnet Machine for Fault-Tolerant Drivetrains I. INTRODUCTION dopting fault tolerant electrical achines can potentially reduce the overall syste weight for safety critical drive applications by introducing redundancy of less reliable coponents rather than having redundancy at the drive syste level [-]. The issues with achine and control design to achieve this are widely reported, however ost of ties in a disjoint fashion. The choice of the control technique adopted, especially in a failure case will result in different stator and rotor losses as well as output torque ripple. In this work, a krp, kw, slots, poles, phase surface PM achine is designed following a fault tolerant design approach. The novel aspect of the work is the consideration of fault tolerance fro an early design stage. Having an optiised design for balanced operation does not necessarily translate in the best design for faulty conditions. If operation is to be aintained with an incurred open or short circuit fault it is likely that such operating conditions would deterine the size of the achine []. The choice of slot-pole cobination, winding distribution and achine geoetry should be selected with prie consideration of faulty operation in order to attain iniu ass. The reedial control strategy adopted will also have a considerable influence on the achine losses and their distribution. Maintaining the pre-fault, positive sequence, synchronous rotating field whilst iniising any additional air gap fields is desirable in order not to excite any additional eddy current losses in the rotor conducting coponents and then to iniise torque pulsations. However, this often results in higher winding copper loss. This loss distribution is thus highly dependent on the control strategy adopted and consequently has to be accounted for at the design stage of the achine. This paper first presents an effective and coputationally efficient, analytically based eddy current estiation technique and then copares the resulting losses for various winding configurations during both healthy and faulty operation. The design process of the fault tolerant achine is then presented. Optiising the achine geoetry for iniu weight requires a careful consideration of sleeve thickness and teperature distribution [], []; slot opening geoetry optiization is carried out to iniise rotor losses. The echanical analysis adopted is described. The reedial control strategy adopted after an open circuit fault consists in ultiplying the agnitude of the currents in the reaining healthy phases by. and shifting their phases by [deg] away fro the faulty phase current phasor []. This ethod keeps the sae agnitude and direction (positive or negative) of the whole haronic rotating field spectru except for tripplen haronics []. Fig.. Eddy Current Density distribution in the rotor of a slots poles achine at rated load and krp In fact, if tripplen haronics occur in the single phase MMF, they do not cancel out when one phase is lost and generally create both positive and negative sequence fields, resulting in additional rotor losses. The reedial strategy following a short circuit fault consists of ensuring a terinal short circuit through the converter and then adopting the control strategy described above. Having the achine designed with unity p.u. inductance ensures a short circuit fault current liited to rated value and inial braking torque within the operating speed range. A prototype of the designed achine is built and a fully instruented test rig is used to perfor basic tests focused on validating the ain perforances in healthy and faulty operating conditions of the closed slot achine. II. EDDY CURRENT LOSS ESTIMATION Eddy current losses in the agnets and in any conducting
Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS retaining sleeve are particularly critical in high speed achines. As can be seen in Fig., the losses in the sleeve are doinant. A stainless steel retaining sleeve is used for this siulation. In this section, a siple eddy current odelling ethod able to predict the eddy currents in both the conducting sleeve and the agnets is presented. The accuracy of this approach will be evaluated by coparison with FE results before using if for a trade-off analysis of different winding configurations. A. Eddy Current Modelling The proposed ethod is based on an analytical agnetostatic tie stepping odel [], []. It being so, the reaction field of the induced eddy currents is not taken into account. This is however a valid and realistic assuption considering that these currents are ostly resistance liited at relatively low excitation frequencies []. The eddy currents created by the arature winding field are derived fro the vector potential A z (t) in the agnet region. The eddy current density at any point in the agnet segent cross section is given by: J Eddy Az ( t) C( t) t Thus, at any point of the agnet, the wavefor of the eddy current density is obtained fro the wavefor of the vector potential by perforing a nuerical tie derivation. In (), is the resistivity of the agnet and C(t) is a tie dependent function which has to be chosen to ipose a zero net current through the cross section of the considered agnet segent [-]. This akes the odel able to account for circuferential agnet segentation by considering each agnet segent of a pole separately and assuing it as electrically isolated fro others. Actually, C(t) is the spatial average of (da z /dt) over the agnet cross section []. Each agnet segent is subdivided into several eleents as shown in Fig. and the wavefor of the eddy current losses in this agnet is calculated by (), P EddyperSegent NbrEleents k axial k Eddy, k ( t) () l sec t J () where l axial is the axial length of the achine and sect k the surface of the k-th eleent. An identical ethod is used to calculate the eddy current in the non-agnetic conducting sleeve foring only one coponent and also subdivided into several eleents (Fig. ). Fig.. Subdivision of the sleeve and one agnet segent B. Validation Finite Eleent (FE) calculation results are used to validate the accuracy of the proposed eddy current odelling approach. Figures and copare the eddy current density wavefors at one point of the sleeve and one point of a agnet segent respectively. Fig. shows a good agreeent between both ethods. The slight discrepancies are due to the eddy current reaction effect which is not taken into account in the analytical ethod. In Fig., the agnitude of the eddy current density in the agnet obtained fro FE ethod is lower, again, due to the fact that the FE analysis takes into account the eddy current reaction in the sleeve and the resulting shielding effect on the agnets. The overall agreeent is however acceptable. Current Density in one point of the sleeve [A/^].E+.E+.E+.E+ -.E+.. -.E+ -.E+ -.E+ Analytical Transient FE Fig.. Coparison of analytical and FE results of Eddy Current Density in one point of the sleeve of a slots poles achine. Current Density in one point of a agnet segent [A/^].E+.E+.E+.E+.E+.E+.E+ -.E+.. -.E+ Analytical Transient FE Fig.. Coparison of analytical and FE results of Eddy Current Density in one point of a agnet segent of a slots poles achine. III. INFLUENCE OF WINDING CONFIGURATION The proposed odelling ethod above was then used to copare the eddy current losses for various possible winding configurations of the circuferentially segented, surface ount, pole PM achine equipped with its stainless steel retaining can. Rotor eddy current losses, torque and torque ripple are the ain aspects investigated for selecting the winding. Analysis was ade for both healthy and faulty operating conditions. Four typical winding configurations are considered: - slots, overlap winding with / short pitch (Fig. ): conventionally used to iniize the th and th MMF haronics; - slots, overlap winding with fractional. slots per pole per phase (spp) (Fig.): often used in order to
Torque [N] Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS obtain a very sooth back EMF with iniu slotting effects and thus avoiding skew; - slots, overlap winding with / shorted pitch (Fig.): often used to reove the rd haronic of the MMF; - slots, double layer concentrated (or non-overlap) winding (Fig.): ease of anufacture, fault tolerant, short end winding and better slot fill factor. The stator configurations above adopt the sae rotor presented in Fig.. Circuferential agnet segentation is used as a conventional way to reduce agnet eddy current losses. Both healthy and faulty behaviour of the achines are copared. The calculated torque wavefors and sleeve losses are reported in Figure for each winding configuration. As expected, results show that overlap windings always exhibit lower eddy current losses copared to the non-overlap winding in the rotor conducting coponents. This is due to the lower haronic content of overlap windings MMF. Aong the overlap windings considered, the fractional. spp shows the highest sleeve losses (Fig. ) due to its slightly ore haronic rich MMF. It can be observed that both the / short pitch winding and the. spp, fractional slot topology display significant torque ripple and eddy current loss in faulty operation when copared to the noral healthy operation (Fig. and ). On the other hand, the torque wavefors and the rotor eddy current losses in faulty operating ode reain the sae as to those in healthy ode for both the overlap / shorted pitch winding and the non-overlap one (Fig. and ). The underlying reason is the fact that tripplen haronics are inexistent in the single phase MMF for a coil span of degrees []. Thus, the whole haronic arature reaction airgap field in faulty operation is identical to that of the healthy case. This also explains the fact that the torque wavefors and the rotor eddy current losses are identical in both healthy and reedial operating odes for the two latter winding configurations as shown in Fig. and Fig.. This is of a key iportance since the resulting extra losses in a fault tolerant operating ode are liited only to the additional winding losses which are less probleatic in ters of theral anageent. For the two other configurations, tripplen haronics are present in the single phase MMF. Hence, when one phase is lost, tripplen haronic fields rotating in both directions appear and are responsible of the significant increase in the sleeve losses when in faulty operation ode. In addition, these haronic rotating fields also result in large nd and th haronic torque ripple content when interacting with the fundaental rotor field. These are clearly shown in Fig..a and Fig -a. Torque [N].. Sleeve Losses [W].. Fig.. Distributed Winding with slots and / shorted pitch: Torque, Eddy Current Losses in Sleeve. Torque [N].. Sleeve Losses [W].. Fig.. Distributed winding with slots and. slots per pole per phase: Torque, Eddy Current Losses in Sleeve. Torque [N].. Sleeve Losses [W].. Fig.. Distributed Winding with slots and / shorted pitch: Torque, Eddy Current Losses in Sleeve. Fault Tolerant Mode.. Sleeve Losses [W] Fault Tolerant Mode.. Fig.. Non overlap slots poles winding: Torque; Eddy Current Losses in Sleeve. Fig.. Field lines distribution when only a phase is supplied For this work the slots poles non overlap winding is adopted, ainly driven by the fault tolerant aspects of this configuration in ters of agnetic and physical isolation between phases (Fig. ) as well as for its identical behaviour in both healthy and fault tolerant operation as far as torque quality and rotor losses are concerned.
Rotor Eddy Losses [W] Average Torque [N] Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS IV. FAULT TOLERANT DESIGN For a fixed stator outer diaeter, the split ratio and the stator tooth width are key design paraeters since they have direct influence on the copper vs. iron loss balance and thus on the electrical and agnetic loading. Therefore, they significantly affect the torque production as well as the arature reaction field, and consequently the losses in the rotor conducting coponents and the resulting teperatures. The influences of the split ratio and the relative tooth width (in % of the tooth pitch) on the average torque and the total rotor eddy current losses are shown in Fig. and Fig. for fixed winding copper losses of W. According to these figures, both paraeters couldn t be chosen to axiise the torque and iniize the rotor eddy losses at once. Hence, the split ratio and the tooth width have been chosen as a trade-off between the torque and the rotor eddy current losses. The slot opening is sized in order to achieve sufficient phase inductance to liit the short circuit current as well as to iniize rotor eddy current losses due to slotting effect which are critical at high speed [], []. Fig. shows the notable reduction of the rotor eddy current losses while reducing the slot opening or even closing it. Closing the slot increases the slot leakage flux and consequently leads to a relatively sall reduction of the output torque therefore the choice of such a design is fairly justified by the reduced aount of eddy current losses. Fig.. No Load Flux density and Flux Lines distribution of the optiized slots poles design. Finally, a split ratio of. and a relative tooth width of % of the tooth pitch have been selected as an initial coproise between the two opposing goals. Fig. shows the resulting optiized design geoetry and the flux density shaded distribution (upper half figure) and the contour flux lines distribution (lower half figure) at no load. One can note the high saturation level in the tooth tips which is a key issue in closed slot design in order to prevent agnetic short circuit at the junction of two adjacent tooth tips. Average Torque [N].... Split Ratio Rotor Eddy Losses [W].... Split Ratio Fig.. Influence of the split ratio: on the average torque; on the rotor eddy current losses. Average Torque [N] Relative Tooth Span [%] Rotor Eddy Losses [W] Relative Tooth Span [%] Fig.. Influence of the tooth width: on the average torque; on the rotor eddy current losses.... Relative Slot Opening... Relative Slot Opening Fig.. Influence of the slot opening: on the rotor total eddy current losses; on the average torque. V. MECHANICAL ANALYSIS AND PROTOTYPE MANUFACTURING Mechanical analysis includes rotor dynaics as well as stress analysis was perfored to ensure echanical integrity of the achine. Stress analysis is required in particular to choose the aterial of the agnet-retaining sleeve and deterining its thickness which is a critical aspect of design. The priary stresses in the sleeve are due to the inertial hoop stress of the sleeve itself together with the additional hoop stress due to the agnet [], []. Another iportant stress coponent is theral stress (i.e. stress due to different expansion rates of agnet and sleeve), which however can be reduced by having a suitable echanical fit between the agnet and the sleeve. Theral analysis is carried out using a luped paraeter network as in [] and following the ethodology described in [-]. While hoop stresses can be evaluated accurately using cylinder theory, in order to capture stress concentrations in the rotor, echanical FEA is used as shown in Fig.. The thickness of the sleeve is an iportant optiization paraeter [], [] which is chosen based on achieving a desired factor of safety at a defined over-speed condition while at the sae tie keeping the eddy-current losses induced in the sleeve to low values.
Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Fig.. Mechanical FEA of rotor structure. The designed slots poles achine has been prototyped. The aterials adopted are NdFeB agnets with an H C = - ka/ and a μ r =.. The agnets were axially and radially segented to reduce eddy current losses. A non-agnetic stainless steel having a conductivity of σ= ks/ was adopted as the retraining sleeve and lainated non oriented silicon steel (B SAT =. T) was used for the rotor and stator core. Fig.. Photos of the wound closed-slot stator and rotor assebly Fig..a. shows photos of the wound stator assebly housed in a fluid-cooled housing. The rotor is shown in Fig..b. It can be noted that the stainless steel sleeve is axially segented for further reduction of the eddy current losses. VI. PERFORMANCE RESULTS In this section, the perforances of the designed achine in ters of torque capability and quality as well as fault tolerance are highlighted. A. Torque Capability and Quality FE approach is used to evaluate the perforances of the designed achine. The odel is created in a CAD environent and siulated using FE software (MagNet). In Fig. the esh used to solve the odel is presented. The esh is refined in the air gap for reason of solution accuracy as the torque coputation is perfored in this region. Fig.. Siulation esh of the slots poles design. Fig.. Half Load and Full Load Flux density and Flux Lines distribution of the slots poles design. The half-load and full-load shaded flux density solution are presented in Fig..a and b. Fig. shows the cogging torque and no load back EMF of the closed slot design against the ones of a conventional open slot design. The reoval of the slot cogging torque is obvious when a closed slot design is used. In addition, closing the slots significantly soothes the back EMF. Fig. shows the torque wavefors of the proposed design copared to an open slot one. Closing the slot in order to obtain sufficiently high inductance (Fig. ) will naturally result in a decrease of the average torque due to the increased slot leakage as can be observed fro Fig...
Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS However, in addition to the reduced rotor losses entioned in an earlier section, it also benefits fro significantly reduced torque ripple. Cogging Torque [N].. -. - -. Mechanical Angle [deg] Closed Slot Open Slot Back EMF [V] -.. - - - Closed Slot Open Slot Fig.. Classical vs. Closed Slot Design: No load EMF; Cogging Torque. Torque [N] Open Slot Closed Slot Mechanical Angle [deg] Fig. Torque wavefors of the closed slot and the classical open slot designs The achine presented was initially considered as a nonsalient type and all the preceding results are based on the assuption that load current is orthogonal to the peranent agnet flux linkage, i.e. q-axis current. Considering the fact of the highly non-linear flux density distribution introduced by the closed slots a non-unifor effective air-gap can be assued. Fig.. Torque against load angle (β d,q) The effective anisotropy was investigated to axiise the torque produced per apere. The torque produced by the achine can be expressed according to (). T e = p PM iq (Ld Lq ) id iq () where p is the nuber of pair poles, L d and L q the d and q axis inductances respectively, PM the no load flux linkage, i d the d-axis current and i q the q-axis current. The inductance values are expected to be highly loaddependent due to the nature of the slot geoetry. Fig. shows the torque vs. load angle characteristic for different loading levels. β d,q is the angle of advance. Fig.. L d and L q as a function of the load current Fig.. Torque Ripple with respect current aplitude I It can be seen that there is a significant coponent of saliency torque to be exploited out of this achine especially at high load. Fig. illustrates the variation of d- and q- axis inductance as a function of d and q axis current. Figure shows the axiu torque per ap produced for different current levels as a function of tie. B. Fault Tolerance The fault tolerance capability of the design to open circuit fault has been deonstrated in previous sections. For the case of short circuit faults, the short circuit current should stay below a reasonable level in order to prevent overheating. One coon way to achieve this is to design the achine to have high self-inductance.
Self Inductance [H] Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS This goal was attained with the closed slot design of the slots poles achine. Fig. shows the phase inductance profiles of both the open and closed slot designs highlighting the increased self-inductance for the closed slot design. Experiental results in the following section will deonstrate the effectiveness of the design in dealing with short-circuit faults. Closed Slot Open Slot Mechanical Angle [deg] Fig.. Inductance profiles of the closed slot and the classical open slot designs VII. EXPERIMENTAL RESULTS The prototype is tested on an instruented test rig shown in Fig.. A vector-controlled dual-three phase level inverter [] is used to supply the achine. The achine coils were separately brought out to enable the experientation of different winding connections. A phase winding configuration is considered for the experiental results that are presented in this docuent. Rotor position is obtained fro a resolver transducer. The d-q axis control schee consists in conventional nested current loop and speed loop. The control syste is ipleented on a control board consisting of a DSP board featuring a TMSC DSK processor and Actel ProAsic FPGA. Fig.. Experiental Test-rig The PWM switching signals, directly controlling the IGBT inverter, are transitted to the gate drivers by eans high perforance fibre optic links. The loading achine set-up on the rig consists in a vector-controlled induction achine with rated power of kw and axiu speed of krp. The coupling between the two achines is ade by eans a torque transducer. Water-cooling syste is used under operative condition and the teperatures in the slots are onitored by eans of therocouples. The ain achine paraeters are reported in Tab. I. The no load test is perfored to validate the no load FE siulation. The easured wavefors at the terinal of the phases are copared with the one obtained fro FE analysis and results are reported in Fig..a. The fundaental of the wavefor atches perfectly although a sall asyetry can be observed across the peak of the experiental wavefor. A good atch between the wavefors can be observed as well as the haronic content featured that is shown in Fig..b. TABLE I MACHINE PARAMETERS Paraeter Value Pole pair nuber (p) kw Rating kw Turn/phase PM Flux (φ PM). Wb Maxiu Speed (ω ) krp Rated Current (I) A Phase resistance (R). Ω d-axis Inductance (L d). H (@ A) q-axis Inductance (L q). H (@ A) GEOMETRICAL PARAMETERS Outer Stator Bore Inner Stator Bore Air-gap thickness Retrain Sleeve thickness Magnets thickness. Fig.. Back-EMF: Coparison FE and experiental wavefors and haronic content The load perforances of the achine are experientally evaluated. Basic tests are carried out to achieve a validation of the torque capabilities of the achine. The torque constant paraeter (K T ) is easured perforing a test where only q-
Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS axis current is supplied to the achine: results are copared with the FE as shown in Fig. Fig.. Torque vs. I q: Coparison FE and experiental results The differences between easured and estiated (FE) torque can be attributed to additional iron losses due to the anufacturing process and uncertainty in the echanical losses. Due to the achine anisotropy, the torque produced as a function of the load angle β d,q is validated and the average easured torque is copared with the FE results in Fig.. Fig. Torque against load angle (β d,q): experiental results A. Balanced Short Circuit Test To verify the fault tolerant capabilities of the achine and validate the faulty condition odel, a balanced three phase short circuit is perfored at the phase terinal of the achine. The short circuit current and the breaking torque can be estiated by solving the voltage equation transfored in the Park reference frae []. The solutions are reported in () for the current and in () for the braking torque. I ssc = ( L q (R PM ) + L + ( R d L q ) PM ) () = - (R + L ) q R PM (R + Ld Lq ) Tbreak p () The previous relations are function of the echanical speed and thus can be copared with the easureents obtained fro a balanced -phase short circuit test perfored on the achine. FE siulations were ade under the sae conditions and the coparison of the resulting braking torque is shown in Fig.. Fig.. Breaking torque: Coparison FE, experiental and analytical results The effect of the teperature on the winding resistance is taken into account as teperature readings were taken during the test. The values of the inductances are instead considered constant due to the high short-circuit current. The peak of the breaking torque occurs when the speed reaches the value calculated as (). For the achine in question this works out to be @ rp Experiental results showed a peak @ rp, FE @ rp. = () L L * R d q The short circuit current is liited by the ratio of the no load PM flux with respect the d-axis inductance. The peak value of the short circuit current with respect the echanical speed is reported in Fig. ; in Fig a coparison between the easured short circuit currents and the one coputed by eans FE is shown. Fig.. Short Circuit current: Coparison experiental and analytical results *
Page of IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Fig.. Short Circuit current wavefors: Coparison experiental and FE results VIII. CONCLUSION This work proposes a design approach for fault tolerant peranent agnet synchronous achines operating at elevated speeds. Having the achine operating in a faulty ode, results in an unbalance of both the air gap agnetic field and of the achine s theral distribution. A cobined analytical loss prediction odel and a theral odel of the achine have been adopted to ensure the optiu size for operation in such conditions. The fault tolerance capability of the proposed design has been deonstrated and details of the design procedure adopted are presented together with soe perforance results. The achine is prototyped and tested to validate the ain characteristic expected in the design and analysis stage. Results for healthy and faulty operating points are copared and are a good atch. REFERENCES [] Villani, M.; Tursini, M.; Fabri, G.; Castellini, L.;, "High Reliability Peranent Magnet Brushless Motor Drive for Aircraft Application," Industrial Electronics, IEEE Transactions on, vol., no., pp.-, May doi:./tie.. [] Bennett, J.W.; Mecrow, B.C.; Atkinson, D.J.; Maxwell, C.; Benarous, M.;, "Fault-tolerant electric drive for an aircraft nose wheel steering actuator," Electrical Systes in Transportation, IET, vol., no., pp.-, Septeber doi:./iet-est.. [] Villani, M.; Tursini, M.; Fabri, G.; Castellini, L.;, "Multi-phase fault tolerant drives for aircraft applications," Electrical Systes for Aircraft, Railway and Ship Propulsion (ESARS),, vol., no., pp.-, - Oct. doi:./esars.. [] D. Gerada, A. Mebarki, R.P. Mokhadkar, N.L. Brown, C. Gerada, Design Issues of High-Speed Peranent Magnet Machines for High-Teperature Applications, IEEE International Electric Machines and Drives Conference,,- May, pp.. [] C. Gerada, K. Bradley, Integrated PM Machine Design for an Aircraft EMA, IEEE, Vol., No., pp. -, Septeber [] Rainosoa, T.; Gerada, C.; Othan, N.; Lillo, L.D, Rotor losses in faulttolerant peranent agnet synchronous achines IET Electric Power Applications, Volue:, Issue:,, Page(s): - [] Z. Q. Zhu, D. Howe, Instantaneous Magnetic Field Distribution in Brushless Peranent dc Motors, Part II: Arature-Reaction Field, IEEE Trans. on Magn., vol., No., pp., January. [] Z. Q. Zhu, D. Howe, C. C. Chan, Iproved Analytical Model for Predicting the Magnetic Field Distribution in Brushless Peranent-Magnet Machines, IEEE Trans. on Magn., vol., No., pp., January. [] D. Ishak, Z.Q. Zhu, D. Howe, Eddy-current loss in the rotor agnets of peranent-agnet brushless achines having a fractional nuber of slots per pole, IEEE Trans. on Magn., vol., No., pp., Sept.. [] Y Aara, Jiabin Wang, D. Howe, Analytical prediction of eddy-current loss in odular tubular peranent-agnet achines, IEEE Trans. on Ener. Conv., vol., No., pp., Dec.. [] Boglietti, A.; Bojoi, R.I.; Cavagnino, A.; Guglieli, P.; Miotto, A.;, "Analysis and Modeling of Rotor Slot Enclosure Effects in High-Speed Induction Motors," Industry Applications, IEEE Transactions on, vol., no., pp.-, July-Aug. doi:./tia.. [] T.J.E. Miller, Siple Calculation of Retaining Sleeves for PM Brushless Machines in Proc. UKMAG seinar on High Speed Machines, Noveber. [] T. Wang, F. Wang, H. Bai, and J. Xing, Optiization Design of Rotor Structure for High Speed Peranent Magnet Machines in Proc. International Conference on Electrical Machines and Systes, ICEMS ', October, pp.. [] Rainosoa T., Gerada D., Gerada C.: "Fault Tolerant Design of a High Speed Peranent Magnet Machine", PEMD [] D. Staton, and A. Cavagnino, Convection heat transfer and flow calculations suitable for electrical achines theral odels, IEEE Trans. Industrial Electronics, vol., no., pp.-, October. [] Boglietti, A.; Cavagnino, A.; Staton, D.;, "Deterination of Critical Paraeters in Electrical Machine Theral Models," Industry Applications, IEEE Transactions on, vol., no., pp.-, July-aug. doi:./tia.. [] D. Gerada, A. Mebarki, and C. Gerada, Optial Design of a High Speed Concentrated Wound PMSM in Proc. International Conference on Electrical Machines and Systes, ICEMS ', Noveber, pp.- [] De Lillo, L.; Epringha, L.; Wheeler, P.W.; Khwan-on, S.; Gerada, C.; Othan, M.N.; Xiaoyan Huang;, "Multiphase Power Converter Drive for Fault-Tolerant Machine Developent in Aerospace Applications," Industrial Electronics, IEEE Transactions on, vol., no., pp.-, Feb. doi:./tie.. [] Bianchi, N.; Bolognani, S.; Dai Pre, M.;, "Design of a Fault-tolerant IPM Motor for Electric Power Steering," Power Electronics Specialists Conference,. PESC '. IEEE th, vol., no., pp., - June doi:./pesc..